# To convert this to a readable file, filter through "tr '\015' '\012'"
file a/blur/cart.uu
for photograph of moving cart, for testing deblurring algorithms
lang uuencoded, compressed 1200 by 1200 array of 8-bit gray pixels
by David Lee
ref J Royal Statistical Society
size 1.4 MB
lib a/blur
for image deblurring
editor David Lee
lib a/wavelet
for wavelet construction and transforms
file a/catalog.html
for hypertext catalog of approximation algorithms
by Eric Grosse
# sadly, this has fallen out of date
size 318 kB
file a/dloess
for smoothing of multivariate scattered data
by Cleveland, Grosse, and Shyu
ref Statistics and Computation 1:1
prec double
lang Fortran77 and C
gams K5, L8h
alg moving least squares quadratic, k-d trees, blending functions
see go/lowess
, (for the older, univariate code)
file a/loess-notes.tgz
for internal documentation on the dloess program
by Grosse
lang pine
file a/cloess.ps
for user manual for a/dloess
by Cleveland, Grosse, and Shyu
size 701 kB
file a/cloess.pdf
for PDF reformatting of a/cloess.ps
file a/loess
for Fortran-only, limited version of a/dloess
file a/stl
for decompose time series into trend + seasonal + remainder
by Cleveland and Cleveland
lang Fortran77
gams K5, L10a
file a/cdfcor.f
for rational approximation to finite set of data
by E. H. Kaufman, Jr. and G. D. Taylor
alg differential correction algorithm to compute a
, best uniform generalized rational approximation p/q to a function
, defined on a finite set of grid points, with the options of including
, a weight function and linear equality and inequality constraints on
, the coefficients.
gams k2
file a/difcor
for rational approximation to finite set of data
by E. H. KAUFMAN, JR. AND G. D. TAYLOR
lang Fortran77
alg differential correction
file a/sdifcor
for rational approximation to finite set of data
by E. H. KAUFMAN, JR. AND G. D. TAYLOR
lang Fortran77
alg differential correction
gams k2
file a/sdifcor.doc
for rational approximation to finite set of data
by E. H. KAUFMAN, JR. AND G. D. TAYLOR
lang Fortran77
alg differential correction
file a/gaim
for fitting generalized additive models,
by T. Hastie and R. Tibshirani
ref Stat. Sci 1,297 and JASA June 1987.
lang Fortran77
gams l8h
file a/fun.f
for test functions for approximation algorithms
gams k6d
file a/masa.f
for approximation for scattered data in many variables
by J. H. Friedman and E. H. Grosse and W. Stuetzle",
ref SIAM J. Sci Stat Comp 4,291-301
, a dusty old deck from Stanford, 1980
gams k1b1a
file a/dbspvt.f
for derivatives of B-splines with respect to knots
by Eric Grosse, derived from de Boor's pppack/bsplvb
ref Grosse and Hobby, Improved Rounding for Spline Coefficients...
prec double
gams e3d, k6d
file a/coca.shar
for COmplex linear Chebyshev Approximation
by Bernd Fischer and Jan Modersitzki
ref Fischer and Modersitzki, An Algorithm for Complex Linear Approximation..
lang matlab
gams k2
file a/beatson
for bivariate monotone interpolation by Beatson and Ziegler Mar 85
lang fortran
gams e2a
file a/perlman
for normal, chi-square, and F distributions
alg translations of TOMS algorithms into C
by Gary Perlman.
gams l5a1c, l5a1f, l5a1n
age superseded
see toms/322
file a/tension
for splines under tension
lang C
by J. R. Van Zandt
alg A. K. Cline.
gams e1a
file a/datred.uu
title P19253
for knot removal from B-spline curve
by Knut Moerken and Tom Lyche
ref IMA J. of Num. Anal. 8 (1988) 185-208. CAGD 4 (1987) 217-230.
lang Fortran uuencoded compressed shar
gams e3d, k2, k6b, k6d
size 274 kB
file a/minsurf1.f
for minimal surfaces
alg Sobolev gradients
by R. J. Renka and J. W. Neuberger
ref SIAM J. Sci. Comp., to appear
file a/minsurf2.f
for minimal surfaces
alg Sobolev gradients
by R. J. Renka and J. W. Neuberger
ref SIAM J. Sci. Comp., to appear
file a/changes
file a/wavelets94
for tables for Wavelets on the Interval and Fast Wavelet Transforms
by Albert Cohen, Ingrid Daubechies and Pierre Vial
ref Applied and Computational Harmonic Analysis, 1993
file a/FreeFormSplines.tgz
for surfaces of high smoothness from control nets of arbitrary topology
by Univ. Karlsruhe/Inst. Op. and Dialog Systems/Geom. Design Group
contact H. Prautzsch
lang C++
see http://i33www.ira.uka.de
ref Freeform splines, CAGD, 14(3): 201-206, 1997
size 489 kB
file a/FFS-manual.ps.gz
for user manual for a/FreeFormSplines.tgz
file a/pcp2nurb.tar.gz
for submesh of a planar cut polyhedron (pcp) into a nurbs patch
keywords spline
by Jorg Peters
ref ACM TOMS
lib a/ml
for machine learning
file a/mvp.tgz
for manipulating multivariate polynomials
alg interpolates by least polynomial method of de Boor and Ron
by Thomas.Grandine@PSS.Boeing.com
lang C
file a/bspllib.tgz
for pppack with IMSL interface, plus B-spline interpolation in 2d and 3d
by Wolfgang Schadow or schadow@physik.uni-bonn.de
lang Fortran77, Fortran90
lib a/sf
for miscellaneous special functions
seealso amos elefunt fdlibm fn slatec specfun vfnlib
file a/esl.tgz
for estimation and smoothing by UDU**T and square root information filter SRIF for Kalman filtering
by Keith and Gerald Bierman
lang Fortran
ref "Factorization Methods for Discrete Sequential Estimation", Academic Press 1977. Republished by Dover
file a/ml/ltree.tgz
for oblique decision trees
by Joao Gama
alg constructive induction
file a/sf/bessfin.f90
for modified Bessel function In(x) of first kind, integer order, real
by Brian Geelen
lang Fortran90
seealso toms/597
file a/wavelet/waili.tgz
for wavelets with integer lifting
by Uytterhoeven and VanWulpen, Computer Science, K.U.Leuven, Belgium
lang C++
file a/wavelet/waili.pdf
for manual for a/wavelet/waili.tgz
file access/webget.c
for getting a file from netlib's web server when all else fails
by Eric Grosse
file access/webget.exe
for Win32 executable of access/webget.c
file access/unshar.c
for unpacking shell archives from netlib
by Eric Grosse
file access/unshar.exe
for precompiled version of unshar.c
lang DOS executable
file access/stree
for C source for Unix programs that collapse (restore) file trees
, into (from) a single file -- ASCII if the file trees are ASCII,
, with times, links, and execute permissions preserved.
by Eric Grosse and David Gay
# (ehg 1995: shar or tar are now preferred, but we keep this
, for historical reasons, in case backup files need unarchiving.)
file access/depend.shar
for extracting dependencies in large source directories
by Eric Grosse
===== How to use netlib =====
This file is the reply you'll get to:
mail netlib@netlib.org
send index
Here are examples of the various kinds of requests.
* get the full index for a library
send index from eispack
* get a particular routine and all it depends on
send dgeco from linpack
* get just the one routine, not subsidiaries
send only dgeco from linpack
* get dependency tree, but excluding a subtree
send dgeco but not dgefa from linpack
* just tell how large a reply would be, don't actually send the file
send list of dgeco from linpack
* get a list of sizes and times of all files in a library
send directory for benchmark
* search for somebody in the SIAM membership list:
who is gene golub
* keyword search for netlib software
find cubic spline
* ask to be notified of new and changed files in a library
mail netlib@research.att.com
subscribe eispack
(For now, send to netlib.att.com; lists will be distributed later.)
* set the chunk size used for reply
mailsize 100k
* (optional) end of request
quit
The Internet address "netlib@netlib.org" refers to a gateway
machine, at Oak Ridge National Laboratory in Oak Ridge, Tennessee.
This address should be understood on all the major networks.
For access from Europe, try the duplicate collection in Oslo:
Internet: netlib@netlib.no
EARN/BITNET: netlib%netlib.no@norunix.bitnet
For the Pacific, try netlib@nchc.gov.tw in Taiwan.
The former netlib/matlab directory is now maintained at
matlib@mathworks.com.
A collection of statistical software is available from
statlib@temper.stat.cmu.edu.
The TeX User Group distributes TeX-related software from
tuglib@math.utah.edu .
The symbolic algebra system REDUCE is supported by
reduce-netlib@rand.org.
An excellent guide to the mysteries of networks and address syntax is:
Donnalyn Frey and Rick Adams (1989) "!%@:: A Directory of Electronic
Mail Addressing and Networks", O'Reilly & Associates, Inc, 632 Petaluma
Ave, Sebastopol CA 95472. Background about netlib is in Jack J.
Dongarra and Eric Grosse, Distribution of Mathematical Software Via
Electronic Mail, Comm. ACM (1987) 30,403-407 and in a quarterly column
published in the SIAM News and SIGNUM Newsletter.
Bugs reports, comments, and annual lists of recipients will be
forwarded to the code authors when possible. Many of these codes are
designed for use by professional numerical analysts who are capable of
checking for themselves whether an algorithm is suitable for their
needs. One routine can be superb and the next awful. So be careful!
-------quick summary of contents---------
a - approximation algorithms
aicm - selected material from Advances in Computational Mathematics
alliant - set of programs collected from Alliant users
amos - special functions by D. Amos. = toms/644
apollo - set of programs collected from Apollo users
arpack - solution of large-scale eigenvalue problems
benchmark - various benchmark programs and a summary of timings
bib - bibliographies
bihar - Bjorstad's biharmonic solver
blas - machine constants, vector and matrix * vector BLAS
bmp - Brent's multiple precision package
c - another "misc" library, for software written in C
ccm - SPMD Collective Communication Module
chammp - solution of shallow water equations in spherical geometry
cheney-kincaid - programs from the 1985 text
clapack - C version of LAPACK (See description for lapack)
confdb - conference database
conformal - conformal mapping
contin - continuation, limit points
c++ - code in the C++ language
dierckx - Spline fitting on various geometries.
domino - communication and scheduling of multiple tasks; Univ. Maryland
eispack - matrix eigenvalues and vectors
elefunt - Cody and Waite's tests for elementary functions
errata - corrections to numerical books
f2c - Fortran to C converter
fishpack - separable elliptic PDEs; Swarztrauber and Sweet
floppy - fortan code syntax and flow control checker
fitpack - Cline's splines under tension
fftpack - Swarztrauber's Fourier transforms
fmm - software from the book by Forsythe, Malcolm, and Moler
fn - Fullerton's special functions
fortran - single-double precision converter, static debugger
fp - floating point arithmetic
gcv - Generalized Cross Validation
gmat - multi-processing Time Line and State Graph tools, Mark Seager
go - "golden oldies" gaussq, zeroin, lowess, ...
graphics - auto color, ray-tracing benchmark
harwell - MA28 sparse linear system
hence - Heterogeneous Network Computing Environment
hompack - nonlinear equations by homotopy method
ieeecss - IEEE / Control Systems Society
ijsa - International Journal of Supercomputer Applications
intercom - Interprocessor Collective Communications (InterCom) Library
itpack - iterative linear system solution by Young and Kincaid
jakef - automatic differentiation of Fortran subroutines
jgraph - tool to create Postscript graphs (located in misc library)
kincaid-cheney - programs from the 1990 text
lapack - solving the most common problems in numerical linear algebra
lapack3e - update to LAPACK v3.0 enhanced with features of Fortran 90
lanczos - Cullum and Willoughby's Lanczos programs
lanz - Large Sparse Symmetric Generalized Eigenproblem, Jones and Patrick
laso - Scott's Lanczos program for eigenvalues of sparse matrices
linalg - various linear algebra stuff collected over time
linpack - gaussian elimination, QR, SVD by Dongarra, Bunch, Moler, Stewart
lp - linear programming
lyapack - Ricatti and Lyapunov equations, optimal control
machines - short descriptions of various computers
microscope - Alfeld and Harris' system for discontinuity checking
minpack - nonlinear equations and least squares by More, Garbow, Hillstrom
misc - everything else
mpi - message passing interface (draft specifications)
na-digest - archive of mailings to NA distribution list
napack - numerical algebra programs
netlib - items pertaining to the netlib system itself
news - Grosse's Netlib News column for na-net, SIAM News, SIGNUM Newsletter
numeralgo - algorithms from the new journal "Numerical Algorithms"
ode - ordinary differential equations
odepack - ordinary differential equations from Hindmarsh
odrpack - orthogonal distance regression, Boggs Byrd Donaldson Schnabel
opt - optimization
p4 - portable programs for parallel processors
paragraph - display of algorithms on message-passing multiprocessor
paranoia - Kahan's floating point test
parmacs - parallel programmming macros
pascal - another "misc" library, for software written in Pascal
parkbench - (formerly pbwg) parallel benchmark working group
pchip - hermite cubics Fritsch+Carlson
pdes/madpack - a multigrid package, by Craig Douglas
picl - portable instrumented communication library for multiprocessors
pltmg - Bank's multigrid code; too large for ordinary mail
polyhedra - Hume's database of geometric solids
popi - Digital Darkroom image manipulation software (Holzmann)
port - the public subset of PORT library
posix - draft standards
pppack - subroutines from de Boor's Practical Guide to Splines
pvm - parallel virtual machine
pvm3 - parallel virtual machine version 3
quadpack - univariate quadrature by Piessens, de Donker, Kahaner
research - miscellanea from AT&T Bell Labs, Computing Science Research Center
rib - REPOSITORY IN A BOX (RIB) is a software package for creating WWW metadata repositories
scalapack - software for MIMD distributed memory computers for some of the lapack routines
sched - environment for portable parallel algorithms in a Fortran setting.
scidac - SciDAC application codes (password protected)
sciport - portable version of Cray SCILIB, by McBride and Lamson
sequent - software from the Sequent Users Group
slap - Seager + Greenbaum, iterative methods for symmetric and unsymmetric
slatec - comprehensive mathematical and statistical software package
sparse - Kundert + Sangiovanni-Vincentelli, C sparse linear algebra
sparse-blas - BLAS by indirection
sparspak - George + Liu, sparse linear algebra core
specfun - transportable special functions
spin - simulation and validation of communication protocols, G. Holzmann
srwn - Software Repository Working Notes
stringsearch - string matching
toeplitz - linear systems in Toeplitz or circulant form by Garbow
toms - Collected Algorithms of the ACM
typesetting - typesetting macros and preprocessors
uncon/data - optimization test problems
vanhuffel - total least squares, partial SVD by Van Hufell
vfftpk - vectorized FFT; variant of fftpack
voronoi - Voronoi diagrams and Delaunay triangulations
xnetlib - X windows interface to netlib
y12m - sparse linear system (Aarhus)
file aicm/smmp
for sparse matrix multiply, transpose, format conversion
by Bank and Douglas
ref Advances in Computational Mathematics, 1 (1993)
lang Fortran, PostScript
file aicm/sl11f.f
for eigenvalue problems for Hamiltonian systems
by Marco Marletta
ref Advances in Computational Mathematics, 2 (1994) 155-184
file aicm/sl11f.tex
for documentation on sl11f.f
file aicm/sl12f.f
for eigenvalue problems for Hamiltonian systems
by Marco Marletta
ref Advances in Computational Mathematics, 2 (1994) 155-184
file aicm/sl12f.tex
for documentation on sl12f.f
file alliant/benchmark
for Contains Alliant specific standard benchmarks.
by David Krowitz 11/17/86 mit-erl!mit-kermit!krowitz@eddie.mit.edu
file alliant/v2d
for V2d is a demo program originally written by Jim Rees to
, show how an Apollo network could get transparent file access
, to any BSD 4.2 system running TCP/IP.
file alliant/users
for List of people on the info-alliant@anl-mcs.arpa mailing list.
file alliant/sendrec
for package which converts Apollo binary data file (REC file types)
, to Alliant binary format data files which can be read with an
, unformatted Fortran READ statement on the Alliant and vice-versa
, (ie. it will convert Alliant format files for reading on an Apollo).
file alliant/shar
for does the same function as your BUNDLE shell script, but is more
, extensive. It adds in some error checking and can handle packing
, entire directories into an archive file for mailing out over the
, network. This file was created by the command 'shar shar.dir'.
file alliant/mm
for Simple matrix-matrix multiply that runs fast on the Alliant.
by Jack Dongarra and Dan Sorensen, 1/26/87.
file alliant/lu
for LU decomposition with partial pivoting designed to run fast on the Alliant.
by Dan Sorensen, 2/18/87.
file alliant/compress
for a utility which can save a considerable amount of disk space.
by David Krowitz, MIT 2/11/87
file alliant/vtu
for This program reads the VAX/VMS DCL command procedure and converts the
, DCL commands to the equivalent C Shell Script commands that run under
, the ALLIANT CONCENTRIX operating system which is a Berkeley Unix 4.2
, system.
by Glen D. West, May 23, 1987
file alliant/libcray.tgz
for This gzipped tar file contains the source code (and test
, routines) for the Cray Compatibility Library (libCRAY.a).
, libCRAY.a is a set of routines for Concentrix V3.0 that give
, the same multiprocessing capability for fortran and C programs
, on the Alliant FX/8 as the Cray Research multiprocessing
, library (eg, tskstart, lockon and evpost) on the Cray X-MP.
by Mark Seager, Oct 8, 1987
file alliant/makemake
for A utility to generate automatically the makefile needed to build
, the executable image of a fortran application program to be run on
, an ALLIANT computer.
by Dick Hessel, Oct 16, 1987
lib alliant/quad
for A subset of the quadpack routines optimized for the alliant. To get the
, index use "send index from alliant/quad". The complete non-Alliant
, versions are available via "send index from quadpack"
by Dick Hessel, Oct 16, 1987
lib alliant/ode
for A subset of the odepack routines optimized for the alliant. To get the
, index use "send index from alliant/ode". The complete non-Alliant
, versions are available via "send index from odepack"
by Dick Hessel, Oct 16, 1987
file alliant/screen
for is a virtual terminal manager for people with regular terminals (folks
, too poor to buy Sun's for every programmer). It lets you have multiple
, independant sessions, each on it's own full size screen. It's very
, useful, seemingly bug free, and we use it here quite a lot.
by Patrick Wolfe Nov 1987
file alliant/vgrindefs
for additions for Alliant fortran
, Appending this to your /usr/lib/vgrindefs file allows you to
, use "vgrind -lf" on your *.f files. Nothing fancy.
by bob@uhmanoa.ics.hawaii.edu Wed Apr 20 18:06:01 1988
file alliant/vmstapes
for Here is a program for reading VMS backup tapes on BSD4.2 systems
, which I got from the comp.sources archive on uunet.uu.net. For
, some reason people keep sending us data on VMS backup tapes as
, a "standard" distribution method!
by David Krowitz krowitz@richter.mit.edu (18.83.0.109)
# Index for alliant/ode/demo
file alliant/ode/demo/ex2lsode.f
file alliant/ode/demo/exlsoda.f
file alliant/ode/demo/exlsodar.f
file alliant/ode/demo/exlsode.f
file alliant/ode/demo/exlsodes.f
file alliant/ode/demo/exlsodi.f
file alliant/ode/demo/exlsoibt.f
file alliant/ode/demo/make.lsoda
file alliant/ode/demo/make.lsodar
file alliant/ode/demo/make.lsode
file alliant/ode/demo/make.lsode2
file alliant/ode/demo/make.lsodes
file alliant/ode/demo/make.lsodi
file alliant/ode/demo/make.lsoibt
file alliant/ode/demo/test.lsoibt
file alliant/ode/doc
for documentation provided with ODEPACK
lib alliant/ode/demo
for test programs of the ODEPACK solvers
lib alliant/ode/prog
for the subroutines of the package and those which have been tuned
(files fn-1.f).
file alliant/ode/prog/adjlr.f
file alliant/ode/prog/aigbt.f
file alliant/ode/prog/ainvg.f
file alliant/ode/prog/bnorm.f
file alliant/ode/prog/cdrv.f
file alliant/ode/prog/cfode.f
file alliant/ode/prog/cntnzu.f
file alliant/ode/prog/decbt-1.f
file alliant/ode/prog/decbt.f
file alliant/ode/prog/ewset.f
file alliant/ode/prog/fnorm.f
file alliant/ode/prog/intdy.f
file alliant/ode/prog/iprep.f
file alliant/ode/prog/jgroup.f
file alliant/ode/prog/lsoda.f
file alliant/ode/prog/lsodar.f
file alliant/ode/prog/lsode.f
file alliant/ode/prog/lsodes.f
file alliant/ode/prog/lsodi.f
file alliant/ode/prog/lsoibt.f
file alliant/ode/prog/md.f
file alliant/ode/prog/mdi.f
file alliant/ode/prog/mdm.f
file alliant/ode/prog/mdp.f
file alliant/ode/prog/mdu.f
file alliant/ode/prog/nnfc.f
file alliant/ode/prog/nnsc.f
file alliant/ode/prog/nntc.f
file alliant/ode/prog/nroc.f
file alliant/ode/prog/nsfc.f
file alliant/ode/prog/odrv.f
file alliant/ode/prog/pjibt.f
file alliant/ode/prog/prep.f
file alliant/ode/prog/prepj.f
file alliant/ode/prog/prepji.f
file alliant/ode/prog/prja.f
file alliant/ode/prog/prjs.f
file alliant/ode/prog/rchek.f
file alliant/ode/prog/roots.f
file alliant/ode/prog/slsbt.f
file alliant/ode/prog/slss.f
file alliant/ode/prog/solbt-1.f
file alliant/ode/prog/solbt.f
file alliant/ode/prog/solsy.f
file alliant/ode/prog/sro.f
file alliant/ode/prog/stoda-1.f
file alliant/ode/prog/stoda.f
file alliant/ode/prog/stode-1.f
file alliant/ode/prog/stode-1.s
file alliant/ode/prog/stode.f
file alliant/ode/prog/stodi-1.f
file alliant/ode/prog/stodi.f
file alliant/ode/prog/vmnorm.f
file alliant/ode/prog/vnorx.f
file alliant/ode/prog/xerrwx.f
# Index for alliant/quad
file alliant/quad/makefile.1
for Makefile.1 is the makefile for the program testp.f which tests the
, subroutines dqk15, dqk21, dqk31, dqk41, dqk51, dqk61 with the CNCALL
, directive inserted to allow concurrent calls to the external function
, to be integrated. I used four different functions provided by the
, subroutines testf1 testf2 testf3 test4 which must be compiled with
, the recursive option. The functions to be integrated and the
, corresponding intervals of integration are as follow:
, -1: sin(x) on [0, 314.14159];
, -2: exp(x) on [0, 1];
, -3: sqrt (abs (x-.2345)) on [0, 1];
, -4: 1+x**2+1/(1+100*x**2) on [-1, 2].
file alliant/quad/makefile.2
for Makefile.2 makes the executable for the adaptive quadrature. The test
, program is called dquad.f and uses one the external functions as
, before.
file alliant/quad/dqag.f
file alliant/quad/dqage.f
file alliant/quad/dqk15.f
file alliant/quad/dqk21.f
file alliant/quad/dqk31.f
file alliant/quad/dqk41.f
file alliant/quad/dqk51.f
file alliant/quad/dqk61.f
file alliant/quad/dqpsrt.f
file alliant/quad/dquad.f
file alliant/quad/fdump.f
file alliant/quad/j4save.f
file alliant/quad/s88fmt.f
file alliant/quad/testf1.f
file alliant/quad/testf2.f
file alliant/quad/testf3.f
file alliant/quad/testf4.f
file alliant/quad/testp.f
file alliant/quad/xerabt.f
file alliant/quad/xerctl.f
file alliant/quad/xerprt.f
file alliant/quad/xerror.f
file alliant/quad/xerrwv.f
file alliant/quad/xersav.f
file alliant/quad/xgetua.f
file amos/readme
for overview of amos
file amos/cairy.f
gams C10d
file amos/cbesh.f
gams C10a4
file amos/cbesi.f
gams C10b4
file amos/cbesj.f
gams C10a4
file amos/cbesk.f
gams C10b4
file amos/cbesy.f
gams C10a4
file amos/cbiry.f
gams C10d
file amos/dgamln.f
gams C7a
file amos/gamln.f
gams C7a
file amos/zairy.f
gams C10d
file amos/zbesh.f
gams C10a4
file amos/zbesi.f
gams C10b4
file amos/zbesj.f
gams C10a4
file amos/zbesk.f
gams C10b4
file amos/zbesy.f
gams C10a4
file amos/zbiry.f
gams C10d
file ampl/changes
for Changes to AMPL since 1 Nov. 1992, plus recent bug fixes.
file ampl/fixlog
for Log of bug fixes and changes since 1 Nov. 1992.
lib ampl/looping
for Description and examples of new flow-of-control constructs.
lib ampl/models
for sample models from older papers.
file ampl/readme
lib ampl/solvers
for solver interface code.
lib ampl/student
for directories of student binaries for several platforms.
lib ampl/tables
for information on tables and constructing table handlers
file ampl/looping/NEW_CMDS
file ampl/looping/README
file ampl/looping/changes
file ampl/looping/cut.mod
file ampl/looping/cut.run
file ampl/looping/cutA.dat
file ampl/looping/cutB.dat
file ampl/looping/cutC.dat
file ampl/looping/cutD.dat
file ampl/looping/cutE.dat
file ampl/looping/cutF.dat
file ampl/looping/multi1.dat
file ampl/looping/multi1.mod
file ampl/looping/multi1.run
file ampl/looping/multi2.dat
file ampl/looping/multi2.mod
file ampl/looping/multi2.run
file ampl/looping/multi3.dat
file ampl/looping/multi3.mod
file ampl/looping/multi3.run
file ampl/looping/new_cmds
file ampl/looping/readme
file ampl/looping/sens.dat
file ampl/looping/sens.mod
file ampl/looping/sens.run
file ampl/looping/stoch.dat
file ampl/looping/stoch.mod
file ampl/looping/stoch.run
file ampl/looping/trnloc1.dat
file ampl/looping/trnloc1d.mod
file ampl/looping/trnloc1d.run
file ampl/looping/trnloc1p.mod
file ampl/looping/trnloc1p.run
file ampl/looping/trnloc2.dat
file ampl/looping/trnloc2a.mod
file ampl/looping/trnloc2a.run
file ampl/looping/trnloc2b.mod
file ampl/looping/trnloc2b.run
file ampl/looping/trnloc2c.mod
file ampl/looping/trnloc2c.run
file ampl/models/compl/README
file ampl/models/compl/bertsek.dat
file ampl/models/compl/bertsek.mod
file ampl/models/compl/bertsek.run
file ampl/models/compl/changes
file ampl/models/compl/choi.dat
file ampl/models/compl/choi.mod
file ampl/models/compl/compchk
for AMPL script for checking complementarity conditions
file ampl/models/compl/ehl_def.mod
file ampl/models/compl/ehl_kost.mod
file ampl/models/compl/josephy.dat
file ampl/models/compl/josephy.mod
file ampl/models/compl/josephy.run
file ampl/models/compl/kojshin.mod
file ampl/models/compl/kojshin.run
file ampl/models/compl/munson1.mod
file ampl/models/compl/nash.dat
file ampl/models/compl/nash.mod
file ampl/models/compl/nash.run
file ampl/models/compl/obstacle.mod
file ampl/models/compl/obstacle.run
file ampl/models/compl/pies.dat
file ampl/models/compl/pies.mod
file ampl/models/compl/pies.run
file ampl/models/compl/runall
for AMPL script for running most of these examples: the ones
, reported in "Expressing Complementarity Problems in an
, Algebraic Modeling Language and Communicating Them to Solvers"
# ===== index for ampl/models =====
lib ampl/models/compl
for sample complementarity problems
file ampl/models/dist.mod
for DIST model from CSTR
file ampl/models/dist.n
for network (nodes and arcs) version of DIST
file ampl/models/dist03.dat
file ampl/models/dist08.dat
file ampl/models/dist13.dat
file ampl/models/egypt1.dat
file ampl/models/egypt1.mod
for ordered-pair version of CSTR's EGYPT model
file ampl/models/egypt2.dat
file ampl/models/egypt2.mod
for EGYPT model from CSTR
file ampl/models/m2a
lang awk
for converting MPS to AMPL data for mps.mod or mps1.mod
file ampl/models/m2ai
lang awk
for converting MPS with integer 'MARKER' lines to AMPL data for mpsi.mod
file ampl/models/mod8.dat
for Figure 1-4 in CSTR
file ampl/models/mod8.mod
for Figure 1-3 in CSTR
file ampl/models/oil.dat
file ampl/models/mps.mod
for model for use with m2a and MPS data: short, but may change row order
file ampl/models/mps1.mod
for model for use with m2a and MPS data: preserves row order
file ampl/models/mpsi.mod
for model for use with m2ai and MPS data with integer 'MARKER' lines
lib ampl/models/nlmodels
for nonlinear models assembled by Elena Bobrovnikova
file ampl/models/oil.mod
file ampl/models/optimal.val
for optimal values for some of the models
file ampl/models/p2gon.mod
for Nonlinear model--maximize area of unit-diameter N-gon, Prieto version 2
file ampl/models/pgon.mod
for Prieto version 1 of p2gon.mod
file ampl/models/prod.mod
for PROD model from CSTR
file ampl/models/prod03.dat
file ampl/models/prod08.dat
file ampl/models/prod13.dat
file ampl/models/score.mod
for Appendix B in "Expressing Special Structure..." (TM 11274-910530-06)
file ampl/models/score1.dat
file ampl/models/struc.mod
for Appendix C in "Expressing Special Structure..." (TM 11274-910530-06)
file ampl/models/struc1.dat
file ampl/models/struc6.dat
file ampl/models/struc8.dat
file ampl/models/train.n
for node-and-arc version of TRAIN -- use with train1.dat
file ampl/models/train1.dat
file ampl/models/train1.mod
file ampl/models/train2.dat
file ampl/models/train2.mod
file ampl/models/changes
# ===== index for ampl/models/nlmodels =====
file ampl/models/nlmodels/README
file ampl/models/nlmodels/blend.mod
file ampl/models/nlmodels/branin.mod
file ampl/models/nlmodels/camel1.mod
file ampl/models/nlmodels/changes
file ampl/models/nlmodels/chemeq.mod
file ampl/models/nlmodels/chi.mod
file ampl/models/nlmodels/gold.mod
file ampl/models/nlmodels/gridneta.mod
file ampl/models/nlmodels/griewank.mod
file ampl/models/nlmodels/hs105.mod
file ampl/models/nlmodels/hs106.mod
file ampl/models/nlmodels/hs109.mod
file ampl/models/nlmodels/hs111.mod
file ampl/models/nlmodels/hs112.mod
file ampl/models/nlmodels/hs114.mod
file ampl/models/nlmodels/hs116.mod
file ampl/models/nlmodels/hs15.mod
file ampl/models/nlmodels/hs23.mod
file ampl/models/nlmodels/hs35.mod
file ampl/models/nlmodels/hs44.mod
file ampl/models/nlmodels/hs5.mod
file ampl/models/nlmodels/hs54.mod
file ampl/models/nlmodels/hs6.mod
file ampl/models/nlmodels/hs62.mod
file ampl/models/nlmodels/hs64.mod
file ampl/models/nlmodels/hs8.mod
file ampl/models/nlmodels/hs87.mod
file ampl/models/nlmodels/kowalik.mod
file ampl/models/nlmodels/levy3.mod
file ampl/models/nlmodels/ljcluster.mod
file ampl/models/nlmodels/minos.out
for solutions computed by MINOS 5.5 for *.mod
file ampl/models/nlmodels/osborne1.mod
file ampl/models/nlmodels/powell.mod
file ampl/models/nlmodels/price.mod
file ampl/models/nlmodels/rosenbr.mod
file ampl/models/nlmodels/s324.mod
file ampl/models/nlmodels/s383.mod
file ampl/models/nlmodels/schwefel.mod
file ampl/models/nlmodels/shekel.mod
file ampl/models/nlmodels/steenbre.mod
file ampl/models/nlmodels/tre.mod
file ampl/models/nlmodels/weapon.mod
file ampl/solvers/bpmpd/README
file ampl/solvers/bpmpd/changes
file ampl/solvers/bpmpd/main.c
file ampl/solvers/bpmpd/makefile
file ampl/solvers/bpmpd/xsum0.out
file ampl/solvers/cplex/README.1st
file ampl/solvers/cplex/README.cplex
file ampl/solvers/cplex/ampl110.pdf
for "ILOG AMPL CPLEX System Version 11.0 User's Guide"
, courtesy of ILOG/CPLEX.
file ampl/solvers/cplex/changes
file ampl/solvers/cplex/configure
file ampl/solvers/cplex/configurehere
file ampl/solvers/cplex/cplex.c
file ampl/solvers/cplex/cplex4.c
file ampl/solvers/cplex/cplex60.c
file ampl/solvers/cplex/cplex66.c
file ampl/solvers/cplex/makefile.u
file ampl/solvers/cplex/makefile.vc
file ampl/solvers/cplex/version4.c
file ampl/solvers/cplex/version60.c
file ampl/solvers/cplex/version66.c
file ampl/solvers/cplex/xsum0.out
file ampl/solvers/donlp2/README
file ampl/solvers/donlp2/changes
file ampl/solvers/donlp2/donlp.c
file ampl/solvers/donlp2/makefile.u
for Unix makefile
file ampl/solvers/donlp2/makefile.vc
file ampl/solvers/donlp2/xsum0.out
file ampl/solvers/donlp2/setup1.f
# ====== index for ampl/solvers/examples ======
#### *.amp, *.nl, *.out, *.row, *.col *.sol are sample input and
#### output files: see README
file ampl/solvers/examples/README
file ampl/solvers/examples/README.gjh
for "solver" gjh for computing gradients, Jacobians,
and Lagrangian Hessians
file ampl/solvers/examples/amplfun4.c
for MATLAB 4.x .mex file (dense Jacobian, Hessian)
file ampl/solvers/examples/amplfunc.c
for MATLAB 5.x .mex file (dense Jacobian, Hessian)
file ampl/solvers/examples/ch3.amp
file ampl/solvers/examples/ch3.nl
file ampl/solvers/examples/ch3mng.out
file ampl/solvers/examples/ch3mng.sol
file ampl/solvers/examples/ch3mnh.out
file ampl/solvers/examples/ch3mnh.sol
file ampl/solvers/examples/ch3nl2.out
file ampl/solvers/examples/ch3nl2.sol
file ampl/solvers/examples/ch3nl21.out
file ampl/solvers/examples/ch3qtest.out
file ampl/solvers/examples/ch3tn.out
file ampl/solvers/examples/ch3tn.sol
file ampl/solvers/examples/changes
file ampl/solvers/examples/diet.amp
file ampl/solvers/examples/diet.col
file ampl/solvers/examples/diet.nl
file ampl/solvers/examples/diet.row
file ampl/solvers/examples/diet.sol
file ampl/solvers/examples/dietd.nl
file ampl/solvers/examples/dietd.sol
file ampl/solvers/examples/dietl1.out
file ampl/solvers/examples/dietl2.out
file ampl/solvers/examples/dietl3.out
file ampl/solvers/examples/dietu.sol
file ampl/solvers/examples/dminos
lang Bourne shell script
file ampl/solvers/examples/dualconv.c
file ampl/solvers/examples/enewt.m
file ampl/solvers/examples/evalchk.c
for source for "solver" evalchk that sets suffix .numerr on
constraints and objectives to nonzero values if the
entity cannot be evaluated at the given starting point.
file ampl/solvers/examples/evalf.m
file ampl/solvers/examples/evalg.m
file ampl/solvers/examples/evalw.m
file ampl/solvers/examples/fmng1.f
file ampl/solvers/examples/fnl21.f
file ampl/solvers/examples/gjh.c
file ampl/solvers/examples/hist.c
for providing command-line history to interactive programs
(such as ampl); uses the GNU history and readline libs.
file ampl/solvers/examples/hkeywds.c
file ampl/solvers/examples/hs100.amp
file ampl/solvers/examples/hs100.nl
file ampl/solvers/examples/hs100.so0
file ampl/solvers/examples/init.m
file ampl/solvers/examples/keywds.c
file ampl/solvers/examples/lin1.c
file ampl/solvers/examples/lin1diet.out
file ampl/solvers/examples/lin2.c
file ampl/solvers/examples/lin2diet.out
file ampl/solvers/examples/lin3.c
file ampl/solvers/examples/lin3diet.out
file ampl/solvers/examples/linrc.c
file ampl/solvers/examples/linrcdie.out
file ampl/solvers/examples/makefile
file ampl/solvers/examples/makefile.sy
for Symantec C++
file ampl/solvers/examples/makefile.vc
for Microsoft Visual C++
file ampl/solvers/examples/makefile.wat
for WATCOM C/C++
file ampl/solvers/examples/mng.c
file ampl/solvers/examples/mng1.c
file ampl/solvers/examples/mnh.c
file ampl/solvers/examples/nl2.c
file ampl/solvers/examples/nl21.c
file ampl/solvers/examples/qtest.c
file ampl/solvers/examples/rvmsg.c
file ampl/solvers/examples/rvmsg.h
file ampl/solvers/examples/savesol.m
file ampl/solvers/examples/spamfunc.c
for MATLAB 5.x .mex file (sparse Jacobian, Hessian)
file ampl/solvers/examples/tnmain.c
file ampl/solvers/examples/v8.c
file ampl/solvers/examples/v8ch3.out
file ampl/solvers/examples/ve08.c
file ampl/solvers/examples/ve08ch3.out
file ampl/solvers/examples/xsum0.out
for checksums
file ampl/solvers/fsqp/README
file ampl/solvers/fsqp/changes
file ampl/solvers/fsqp/fsqp.c
file ampl/solvers/fsqp/makefile
file ampl/solvers/fsqp/version.c
file ampl/solvers/fsqp/xsum0.out
file ampl/solvers/funclink/README
file ampl/solvers/funclink/amplfunc.def
for use with makefile.vc
file ampl/solvers/funclink/amplfunc.lnk
for use with makefile.wat
file ampl/solvers/funclink/funcadd.c
file ampl/solvers/funclink/funcadd0.c
file ampl/solvers/funclink/funcaddk.c
file ampl/solvers/funclink/funcout.exp
for use with makefile.rs6k
file ampl/solvers/funclink/htest.out
for sample output from htest.x
file ampl/solvers/funclink/htest.x
file ampl/solvers/funclink/libmain.c
for use with makefile.wat
file ampl/solvers/funclink/makefile.alpha
file ampl/solvers/funclink/makefile.cygwin
for Cygwin and MinGW
file ampl/solvers/funclink/makefile.freebsd
file ampl/solvers/funclink/makefile.hp
file ampl/solvers/funclink/makefile.i386solaris
file ampl/solvers/funclink/makefile.krsolaris
file ampl/solvers/funclink/makefile.lcc
file ampl/solvers/funclink/makefile.linux
file ampl/solvers/funclink/makefile.macosx
file ampl/solvers/funclink/makefile.rs6k
file ampl/solvers/funclink/makefile.sgi
file ampl/solvers/funclink/makefile.solaris
file ampl/solvers/funclink/makefile.sunos
file ampl/solvers/funclink/makefile.vc
file ampl/solvers/funclink/makefile.wat
file ampl/solvers/funclink/makefile.xsum
file ampl/solvers/funclink/outargex.c
for illustration of OUT and INOUT args (AMPL only)
file ampl/solvers/funclink/outargex.run
for script using function "outargex" of outargex.c
file ampl/solvers/funclink/silly.2
for sample stderr from silly.x
file ampl/solvers/funclink/silly.out
for sampl stdout from silly.x
file ampl/solvers/funclink/silly.x
for example
file ampl/solvers/funclink/xsum0.out
for checksums
file ampl/solvers/gurobi/README.1st
file ampl/solvers/gurobi/README.gurobi
file ampl/solvers/gurobi/changes
file ampl/solvers/gurobi/gurobi.c
file ampl/solvers/gurobi/makefile.u
file ampl/solvers/gurobi/makefile.vc
file ampl/solvers/gurobi/xsum0.out
# ====== index for ampl/solvers ======
# NOTE: The E-mail request "send all from ampl/solvers"
# retrieves all the source files in this directory,
# but not the "lib" subdirectories.
file ampl/solvers/README
file ampl/solvers/README.f77
file ampl/solvers/README.SGI
file ampl/solvers/README.suf
for temporary documentation about suffixes
file ampl/solvers/amplsolv.lbc
for use with makefile.lc, makefile.vc and makefile.wat
file ampl/solvers/amplsolv.sy
for use with makefile.sy
file ampl/solvers/arith.ibm
file ampl/solvers/arith.h0
file ampl/solvers/arithchk.c
file ampl/solvers/asl.h
file ampl/solvers/asl_pfg.h
file ampl/solvers/asl_pfgh.h
file ampl/solvers/asldate.c
file ampl/solvers/atof.c
file ampl/solvers/auxinfo.c
file ampl/solvers/avltree.c
file ampl/solvers/avltree.h
file ampl/solvers/b_search.c
file ampl/solvers/basename.c
file ampl/solvers/bscanf.c
file ampl/solvers/changes
file ampl/solvers/com2eval.c
file ampl/solvers/comeval.c
file ampl/solvers/comptry.bat
file ampl/solvers/con1ival.c
file ampl/solvers/con2ival.c
file ampl/solvers/con2val.c
file ampl/solvers/conadj.c
file ampl/solvers/configure
file ampl/solvers/configurehere
file ampl/solvers/conpval.c
file ampl/solvers/conscale.c
file ampl/solvers/conval.c
file ampl/solvers/derprop.c
file ampl/solvers/details.c0
file ampl/solvers/dtoa.c
file ampl/solvers/dtoa1.c
file ampl/solvers/duthes.c
file ampl/solvers/dvalue.hd
file ampl/solvers/dynlink.c
file ampl/solvers/errchk.h
file ampl/solvers/f_read.c
file ampl/solvers/fg_read.c
file ampl/solvers/fg_write.c
file ampl/solvers/fgh_read.c
file ampl/solvers/float.h0
file ampl/solvers/fpecatch.c
file ampl/solvers/fpinit.c
file ampl/solvers/fpinitmt.c
file ampl/solvers/fpsetprec.s
file ampl/solvers/fpsetprec64.s
file ampl/solvers/fullhes.c
file ampl/solvers/func_add.c
file ampl/solvers/funcadd.c
file ampl/solvers/funcadd.h
file ampl/solvers/funcadd0.c
file ampl/solvers/funcadd1.c
file ampl/solvers/funcaddk.c
file ampl/solvers/funcaddr.c
file ampl/solvers/g_fmt.c
file ampl/solvers/genrowno.c
file ampl/solvers/getenv.c
file ampl/solvers/getstub.c
file ampl/solvers/getstub.h
file ampl/solvers/htcl.c
file ampl/solvers/indic_cons.c
file ampl/solvers/jac0dim.c
file ampl/solvers/jac2dim.c
file ampl/solvers/jac2dim.h
file ampl/solvers/jacdim.c
file ampl/solvers/jacinc.c
file ampl/solvers/jacinc1.c
file ampl/solvers/jacpdim.h
file ampl/solvers/libnamsave.c
file ampl/solvers/mach.c
file ampl/solvers/mainexit.c
file ampl/solvers/makefile.lc
file ampl/solvers/makefile.u
file ampl/solvers/makefile.sy
file ampl/solvers/makefile.vc
file ampl/solvers/makefile.wat
file ampl/solvers/mip_pri.c
file ampl/solvers/misc.c
file ampl/solvers/mpec_adj.c
file ampl/solvers/mpec_adj0.c
file ampl/solvers/mypow.c
file ampl/solvers/names.c
file ampl/solvers/nl_obj.c
file ampl/solvers/nlp.h
file ampl/solvers/nlp2.h
file ampl/solvers/nqpcheck.c
file ampl/solvers/obj2val.c
file ampl/solvers/obj_adj.c
file ampl/solvers/obj_adj.h
file ampl/solvers/obj_adj0.c
file ampl/solvers/obj_prec.c
file ampl/solvers/objconst.c
file ampl/solvers/objval.c
file ampl/solvers/objval_.c
file ampl/solvers/op_type.c
file ampl/solvers/op_type.hd
file ampl/solvers/op_typeb.hd
file ampl/solvers/opcode.hd
file ampl/solvers/opnos.hd
file ampl/solvers/pfg_read.c
file ampl/solvers/pfghread.c
file ampl/solvers/printf.c
file ampl/solvers/pshvprod.c
file ampl/solvers/psinfo.h
file ampl/solvers/punknown.c
file ampl/solvers/qp_read.c
file ampl/solvers/qpcheck.c
file ampl/solvers/qsortv.c
file ampl/solvers/r_op.hd
file ampl/solvers/r_opn.hd
file ampl/solvers/r_opn0.hd
file ampl/solvers/r_qp.hd
file ampl/solvers/readsol.c
file ampl/solvers/repwhere.c
file ampl/solvers/rnd_prod.s
file ampl/solvers/rops.c
file ampl/solvers/rops2.c
file ampl/solvers/sigcatch.c
file ampl/solvers/sjac0dim.c
file ampl/solvers/sos_add.c
file ampl/solvers/sphes.c
file ampl/solvers/sprintf.c
file ampl/solvers/sscanf.c
file ampl/solvers/stderr.c
file ampl/solvers/stdio1.h0
file ampl/solvers/strerror.c
file ampl/solvers/studchk0.c
file ampl/solvers/suf_sos.c
file ampl/solvers/value.c
file ampl/solvers/writesol.c
file ampl/solvers/wrtsol_.c
file ampl/solvers/ws_desc.c
file ampl/solvers/wsu_desc.c
file ampl/solvers/x2check.c
file ampl/solvers/xectim.c
file ampl/solvers/xp1known.c
file ampl/solvers/xp2known.c
file ampl/solvers/xsum0.out
for checksums
lib ampl/solvers/bpmpd
for interface to BPMPD (an interior-point LP solver)
lib ampl/solvers/cplex
for interface to CPLEX (a linear, mixed-integer, and QP solver)
lib ampl/solvers/donlp2
for interface to DONLP2 (a nonlinear solver)
lib ampl/solvers/examples
for examples to accompany "Hooking Your Solver to AMPL"
, Postscript for which is
, ftp://netlib.bell-labs.com/REFS/hooking.ps.gz
lib ampl/solvers/fsqp
for interface to CFSQP (a nonlinear solver)
lib ampl/solvers/funclink
for system-dependent details of shared libraries for imported functions
lib ampl/solvers/gurobi
for interace to Gurobi (a linear and mixed integer solver)
lib ampl/solvers/lancelot
for interface to LANCELOT (a nonlinear solver)
lib ampl/solvers/lbfgsb
for interface to L-BFGS-B (a solver for problems with simple-bound constraints)
lib ampl/solvers/loqo
for interface to LOQO (a linear and nonlinear interior-point solver)
lib ampl/solvers/lpsolve
for interface to lp_solve (a linear and mixed-integer solver: simplex)
lib ampl/solvers/minos
for interface to MINOS 5.4 and 5.5 (a linear and nonlinear solver)
lib ampl/solvers/nlc
for program "nlc" that converts AMPL .nl files to C or Fortran 77
lib ampl/solvers/npopt
for interface to NPOPT (a nonlinear solver: SQP, dense linear algebra)
lib ampl/solvers/npsol
for interface to NPSOL (a nonlinear solver: SQP, dense linear algebra)
lib ampl/solvers/osl
for interface to OSL (a linear and mixed-integer solver)
, based on IBM's Optimization Subroutine Library
lib ampl/solvers/path
for interface to PATH (a solver of "square" complementarity problems)
lib ampl/solvers/snopt
for interface to SNOPT (a nonlinear solver: SQP, sparse linear algebra)
lib ampl/solvers/xpress
for interface to XPRESS-MP (a solver of linear, mixed-integer, linear
, and quadratic programming problems by Dash Optimization)
file ampl/solvers/lancelot/README
file ampl/solvers/lancelot/changes
file ampl/solvers/lancelot/lancelot.c
file ampl/solvers/lancelot/makefile.u
file ampl/solvers/lancelot/xsum0.out
file ampl/solvers/lbfgsb/README
file ampl/solvers/lbfgsb/changes
file ampl/solvers/lbfgsb/index
file ampl/solvers/lbfgsb/lbfgsb.c
file ampl/solvers/lbfgsb/makefile.u
file ampl/solvers/lbfgsb/makefile.vc
file ampl/solvers/lbfgsb/xsum0.out
file ampl/solvers/loqo/README.1st
file ampl/solvers/loqo/README.loqo
file ampl/solvers/loqo/aloqo.c
file ampl/solvers/loqo/changes
file ampl/solvers/loqo/makefile.u
file ampl/solvers/loqo/makefile.vc
file ampl/solvers/loqo/xsum0.out
file ampl/solvers/lpsolve/README
file ampl/solvers/lpsolve/changes
file ampl/solvers/lpsolve/lpsolve4.c
for driver for LP_SOLVE 4.0.1
file ampl/solvers/lpsolve/lpsolve5.c
for driver for LP_SOLVE 5.5.2
file ampl/solvers/lpsolve/makefile.u
for Unix makefile using lpsolve5.c
file ampl/solvers/lpsolve/makefile.vc
for Microsoft VC++ makefile using lpsolve5.c
file ampl/solvers/lpsolve/makefile4.u
for Unix makefile using lpsolve4.c
file ampl/solvers/lpsolve/makefile4.u
for Unix makefile using lpsolve4.c
file ampl/solvers/lpsolve/xsum0.out
file ampl/solvers/lpsolve/lp_solve_4.0.tar.gz
for lp_solve source used in building ampl/student/*/lpsolve* using lpsolve4.c
file ampl/solvers/minos/README.1st
file ampl/solvers/minos/README.minos
file ampl/solvers/minos/configure
file ampl/solvers/minos/configurehere
file ampl/solvers/minos/m551.c
file ampl/solvers/minos/makefile.u
file ampl/solvers/minos/makefile.vc
file ampl/solvers/minos/xsum0.out
for checksums
file ampl/solvers/minos/changes
file ampl/solvers/nlc/README
file ampl/solvers/nlc/c_op.hd
file ampl/solvers/nlc/cops.c
file ampl/solvers/nlc/makefile.u
file ampl/solvers/nlc/makefile.vc
file ampl/solvers/nlc/nlc.c
file ampl/solvers/nlc/nlc.h
file ampl/solvers/nlc/nlcmisc.c
file ampl/solvers/nlc/r_ops1.hd
file ampl/solvers/nlc/xsum0.out
file ampl/solvers/nlc/changes
#### sample input and output files: see README ####
file ampl/solvers/nlc/ch3.amp
file ampl/solvers/nlc/ch3.nl
file ampl/solvers/nlc/ch3.c
file ampl/solvers/nlc/ch3.kc
file ampl/solvers/nlc/ch3.f
file ampl/solvers/nlc/mngnlc.c
file ampl/solvers/nlc/nl2nlc.c
file ampl/solvers/nlc/ch3mng.out
file ampl/solvers/nlc/ch3nl2.out
file ampl/solvers/npopt/README
file ampl/solvers/npopt/changes
file ampl/solvers/npopt/makefile
file ampl/solvers/npopt/xsum0.out
file ampl/solvers/npopt/npopt.c
file ampl/solvers/npopt/version.c
file ampl/solvers/npsol/README
file ampl/solvers/npsol/changes
file ampl/solvers/npsol/makefile.u
for Unix systems
file ampl/solvers/npsol/makefile.vc
for Microsoft VC++
file ampl/solvers/npsol/xsum0.out
file ampl/solvers/npsol/npsol.c
file ampl/solvers/npsol/version.c
lib ampl/solvers/npsol/src
for src/makefile.vc and src/npsol.lbc
file ampl/solvers/npsol/src/makefile.vc
for Microsoft VC++
file ampl/solvers/npsol/src/npsol.lbc
for helping make npsol.lib
file ampl/solvers/osl/README.1st
file ampl/solvers/osl/README.osl
file ampl/solvers/osl/changes
file ampl/solvers/osl/makefile.u
for Unix makefile
file ampl/solvers/osl/makefile.vc
for MS VC++ makefile
file ampl/solvers/osl/makefile.wat
for WATCOM makefile
file ampl/solvers/osl/osl.c
file ampl/solvers/osl/osl.h
lib ampl/solvers/osl/osl1.2
for AMPL/OSL 1.2 driver
file ampl/solvers/osl/xsum0.out
for checksums
file ampl/solvers/osl/osl1.2/changes
file ampl/solvers/path/README
file ampl/solvers/path/changes
file ampl/solvers/path/makefile.u
file ampl/solvers/path/makefile.vc
file ampl/solvers/path/path.c
for PATH 4.6
file ampl/solvers/path/path44.c
for PATH 4.4
file ampl/solvers/path/xsum0.out
for checksums
file ampl/solvers/snopt/README
file ampl/solvers/snopt/changes
file ampl/solvers/snopt/configure
file ampl/solvers/snopt/configurehere
file ampl/solvers/snopt/makefile.u
file ampl/solvers/snopt/makefile.vc
file ampl/solvers/snopt/snopt.c
file ampl/solvers/snopt/snopt_.c
file ampl/solvers/snopt/xsum0.out
lib ampl/solvers/snopt/src
for makefiles for snopt lib
file ampl/solvers/snopt/src/makefile.fu
file ampl/solvers/snopt/src/makefile.u
file ampl/solvers/snopt/src/makefile.vc
file ampl/solvers/snopt/src/snopt.lbc
file ampl/solvers/xpress/README.1st
file ampl/solvers/xpress/README.xpress
file ampl/solvers/xpress/changes
file ampl/solvers/xpress/makefile.u
file ampl/solvers/xpress/makefile.vc
file ampl/solvers/xpress/xpress.c
file ampl/solvers/xpress/xpress.linux
file ampl/solvers/xpress/xpress.macosx
file ampl/solvers/xpress/xsum0.out
# The programs in this directory are "student" versions that
# restrict problem sizes (to 300 variables and 300 general
# constraints) and are intended for noncommercial use.
# For serious commercial use, you should (eventually) license
# commercial versions, even if your applications never exceed
# the limits of the student versions.
# DEC Alpha Unix (OSF/1 V4.0) binaries
file ampl/student/alpha/README
file ampl/student/alpha/ampl.gz
for DEC Alpha (OSF/1 V2.0) student AMPL processor
file ampl/student/alpha/cplex.tgz
for gzipped tar file with student CPLEX 8.0 solver and LICENSE
file ampl/student/alpha/minos.gz
for DEC Alpha (OSF/1 V2.0) student MINOS solver
file ampl/student/alpha/lpsolve.gz
for LP/MIP solver based on lp_solve 3.2; see ampl/solvers/lpsolve/README
file ampl/student/alpha/snopt.gz
for DEC Alpha (OSF/1 V2.0) student SNOPT solver
# The programs in this directory are "student" versions that
# restrict problem sizes (to 300 variables and 300 general
# constraints) and are intended for noncommercial use.
# For serious commercial use, you should (eventually) license
# commercial versions, even if your applications never exceed
# the limits of the student versions.
# Linux (2.0.34) DEC Alpha binaries (which work with Red Hat
# Linux 5.x amd 6.x but not 4.x, due to a change in the format
# of executable files)
file ampl/student/alphalinux/README
file ampl/student/alphalinux/ampl.gz
for student AMPL processor
file ampl/student/alphalinux/minos.gz
for student MINOS solver
file ampl/student/alphalinux/lpsolve.gz
for LP/MIP solver based on lp_solve 3.2; see ampl/solvers/lpsolve/README
file ampl/student/alphalinux/snopt.gz
for student SNOPT solver
# The programs in this directory are "student" versions that
# restrict problem sizes (to 300 variables and 300 general
# constraints) and are intended for noncommercial use.
# For serious commercial use, you should (eventually) license
# commercial versions, even if your applications never exceed
# the limits of the student versions.
# FreeBSD (release 3.2 on Intel CPUs) binaries
file ampl/student/freebsd/README
file ampl/student/freebsd/ampl.gz
for student AMPL processor
file ampl/student/freebsd/minos.gz
for student MINOS solver
file ampl/student/freebsd/lpsolve.gz
for LP/MIP solver based on lp_solve 3.2; see ampl/solvers/lpsolve/README
file ampl/student/freebsd/snopt.gz
for student SNOPT solver
# The programs in this directory are "student" versions that
# restrict problem sizes (to 300 variables and 300 general
# constraints) and are intended for noncommercial use.
# For serious commercial use, you should (eventually) license
# commercial versions, even if your applications never exceed
# the limits of the student versions.
# HP 9000/778 and compatible binaries (created under HP-UX B.10.20 A)
file ampl/student/hp/README
file ampl/student/hp/ampl.gz
for student AMPL processor
file ampl/student/hp/minos.gz
for student MINOS solver
file ampl/student/hp/lpsolve.gz
for LP/MIP solver based on lp_solve 3.2; see ampl/solvers/lpsolve/README
file ampl/student/hp/snopt.gz
for student SNOPT solver
# The AMPL processors and solvers in the subdirectories below
# (which, following netlib conventions, are labeled "lib") are
# "student" versions that restrict problem sizes (to 300 variables
# and 300 general constraints) and are intended for noncommercial
# use. For serious commercial use, you should (eventually)
# license commercial versions, even if your applications never
# exceed the limits of the student versions.
file changes
lib ampl/student/alpha
for DEC Alpha (OSF/1 V2.0) student binaries
lib ampl/student/alphalinux
for DEC Alpha Linux student binaries
lib ampl/student/freebsd
for FreeBSD (Intel) student binaries
lib ampl/student/hp
for HP 9000/715 and compatible student binaries
lib ampl/student/macosx
for Macintosh OS X binaries
lib ampl/student/linux
for Linux (ELF) student binaries
lib ampl/student/msdos
for MS-DOS student binaries
lib ampl/student/mswin
for MS Windows student binaries
lib ampl/student/powerpc
for IBM PowerPC (AIX 4.3) student binaries
lib ampl/student/rs6k
for IBM Risk System 6000 student binaries
lib ampl/student/sgi
for SGI student binaries
lib ampl/student/solaris
for Solaris Sparc student binaries
lib ampl/student/solaris_i86pc
for Solaris Intel student binaries
# The programs in this directory are "student" versions that
# restrict problem sizes (to 300 variables and 300 general
# constraints) and are intended for noncommercial use.
# For serious commercial use, you should (eventually) license
# commercial versions, even if your applications never exceed
# the limits of the student versions.
# Intel Linux (ELF, glibc) binaries
file ampl/student/linux/README
file ampl/student/linux/ampl.gz
for student ampl processor
file ampl/student/linux/cplex.tgz
for gzipped tar file with student CPLEX 11.0.1 solver and LICENSE
file ampl/student/linux/gjh.gz
for "solver" that computes the objective gradient (g), the constraint
, Jacobian (J), and the Hessian of the Lagrangian (H) at the
, current point (primal and dual variable values). The solver
, message shows commands to read these as params and delete
, the temporary file that conveys them. When multiple objectives
, are present, the first is used unless the objectives have suffix
, objweight ==> g is the gradient of the weighted sum of objectives.
, Source = /netlib/ampl/solvers/examples/gjh.c.
file ampl/student/linux/gurobi.tgz
for student GUROBI solver for LP/MIP problems
file ampl/student/linux/lpsolve.gz
for LP/MIP solver based on lp_solve 4.0; see ampl/solvers/lpsolve/README
file ampl/student/linux/minos.gz
for student MINOS solver
file ampl/student/linux/snopt.gz
for student SNOPT solver
lib ampl/student/macosx/x86_32
for Intel 32-bit MacOSX student solvers.
# The programs in this directory are "student" versions that
# restrict problem sizes (to 300 variables and 300 general
# constraints) and are intended for noncommercial use.
# For serious commercial use, you should (eventually) license
# commercial versions, even if your applications never exceed
# the limits of the student versions. For simplicity, these
# are 32-bit Power PC binaries, which generally also run on
# Intel Macs (albeit more slowly than native Intel binaries).
# Should feedback suggest it warranted, Intel student binaries
# could be made available.
file ampl/student/macosx/x86_32/README
file ampl/student/macosx/x86_32/ampl.gz
for student ampl processor
file ampl/student/macosx/x86_32/cplex.tgz
for gzipped tar file with student CPLEX 11.0.1 solver and LICENSE
file ampl/student/macosx/x86_32/gjh.gz
for "solver" that computes the objective gradient (g), the constraint
, Jacobian (J), and the Hessian of the Lagrangian (H) at the
, current point (primal and dual variable values). The solver
, message shows commands to read these as params and delete
, the temporary file that conveys them. When multiple objectives
, are present, the first is used unless the objectives have suffix
, objweight ==> g is the gradient of the weighted sum of objectives.
, Source = /netlib/ampl/solvers/examples/gjh.c.
file ampl/student/macosx/x86_32/gurobi.tgz
for student GUROBI solver for LP/MIP problems
file ampl/student/macosx/x86_32/lpsolve.gz
for LP/MIP solver based on lp_solve 4.0; see ampl/solvers/lpsolve/README
file ampl/student/macosx/x86_32/minos.gz
for student MINOS solver
file ampl/student/macosx/x86_32/snopt.gz
for student SNOPT solver
file ampl/student/msdos/readme
file ampl/student/msdos/ampl.exe.gz
for Updated version, compiled by Symantec, of the AMPL.EXE that
, accompanied the AMPL book prior to 1997, with bug fixes and
, new flow-of-control constructs.
size 391 kB
file ampl/student/msdos/lpsolve.exe.gz
for LP/MIP solver based on lp_solve 3.0; see ampl/solvers/lpsolve/README
size 88 kB
file ampl/student/msdos/minos.exe.gz
for Updated version, compiled by Symantec, of the MINOS.EXE that
, accompanied the AMPL book prior to 1997.
size 194 kB
file ampl/student/msdos/watampl.exe.gz
for Updated version, compiled by WATCOM, of the AMPL.EXE that
, accompanied the AMPL book, with bug fixes and new flow-of-control
, constructs. Requires DOS4GW.EXE.
size 452 kB
file ampl/student/msdos/dos4gw.exe.gz
for Helper program (DOS4GW.EXE) required by WATAMPL.EXE.
size 144 kB
file ampl/student/msdos/wemu387.386.gz
for Needed by WATAMPL.EXE underon machines with no math coprocessor
, when running MS Windows. See readme.
file ampl/student/msdos/pminfo.exe.gz
for Diagnosing computing environment for WATAMPL.EXE (not normally needed)
file ampl/student/msdos/rminfo.exe.gz
for Diagnosing computing environment for WATAMPL.EXE (not normally needed)
# The programs in this directory are "student" versions that
# restrict problem sizes (to 300 variables and 300 general
# constraints) and are intended for noncommercial use.
# For serious commercial use, you should (eventually) license
# commercial versions, even if your applications never exceed
# the limits of the student versions.
file ampl/student/mswin/readme
file ampl/student/mswin/ampl.exe.gz
for Win32 "console" version of the AMPL processor;
, runs under MS Windows 95, 98, or NT.
size 389 kB
file ampl/student/mswin/ampltabl.dll.gz
for standard ODBC table handler;
, see http://www.ampl.com/ampl/NEW/tables.html
file ampl/student/mswin/cplex.zip
for student CPLEX 11.0.1 solver (Win32 console version), cplex110.dll
, (must be in the same directory as cplex.exe), LICENSE.txt
file ampl/student/mswin/exhelp32.exe.gz
for helping ampl.exe (and wampl.exe) run DOS solvers.
file ampl/student/mswin/minos.exe.gz
for student MINOS solver (Win32 console version)
file ampl/student/mswin/gjh.exe.gz
for "solver" that computes the objective gradient (g), the constraint
, Jacobian (J), and the Hessian of the Lagrangian (H) at the
, current point (primal and dual variable values). The solver
, message shows commands to read these as params and delete
, the temporary file that conveys them. When multiple objectives
, are present, the first is used unless the objectives have suffix
, objweight ==> g is the gradient of the weighted sum of objectives.
, Source = /netlib/ampl/solvers/examples/gjh.c.
file ampl/student/mswin/gurobi.zip
for student GUROBI solver for LP/MIP problems
file ampl/student/mswin/lpsolve.exe.gz
for LP/MIP solver based on lp_solve 4.0; see ampl/solvers/lpsolve/README
file ampl/student/mswin/readme.sw
for information about using scrolling windows provided by sw.exe
file ampl/student/mswin/sw.exe.gz
for scrolling windows with accessible text for simple console programs
file ampl/student/mswin/swsrc.zip
for source for sw.exe
file ampl/student/mswin/wampl.exe.gz
for Updated version of the WAMPL.EXE (Windows AMPL) that came
, with the original AMPL Plus (starting in 1997). Only useful in
, connection with other files that accompanied the AMPL book.
, Superceded by ampl.exe and AMPL Plus 1.6.
size 414 kB
file ampl/student/mswin/snopt.exe.gz
for student SNOPT solver (Win32 console version)
# The programs in this directory are "student" versions that
# restrict problem sizes (to 300 variables and 300 general
# constraints) and are intended for noncommercial use.
# For serious commercial use, you should (eventually) license
# commercial versions, even if your applications never exceed
# the limits of the student versions.
# IBM PowerPC (AIX 4.3) binaries
file ampl/student/powerpc/README
file ampl/student/powerpc/ampl.gz
for student ampl processor
file ampl/student/sgi/cplex.tgz
for gzipped tar file with student CPLEX 8.0 solver and LICENSE
file ampl/student/powerpc/minos.gz
for student MINOS solver
file ampl/student/powerpc/gjh.gz
for "solver" that computes the objective gradient (g), the constraint
, Jacobian (J), and the Hessian of the Lagrangian (H) at the
, current point (primal and dual variable values). The solver
, message shows commands to read these as params and delete
, the temporary file that conveys them. When multiple objectives
, are present, the first is used unless the objectives have suffix
, objweight ==> g is the gradient of the weighted sum of objectives.
, Source = /netlib/ampl/solvers/examples/gjh.c.
file ampl/student/powerpc/lpsolve.gz
for LP/MIP solver based on lp_solve 3.2; see ampl/solvers/lpsolve/README
file ampl/student/powerpc/snopt.gz
for student SNOPT solver
# The programs in this directory are "student" versions that
# restrict problem sizes (to 300 variables and 300 general
# constraints) and are intended for noncommercial use.
# For serious commercial use, you should (eventually) license
# commercial versions, even if your applications never exceed
# the limits of the student versions.
# IBM Risk System 6000 (AIX 3.2) binaries
# Imported functions do not work with AIX 3.2
# (but do under AIX 4.3: see ../powerpc).
file ampl/student/rs6k/README
file ampl/student/rs6k/ampl.gz
for student ampl processor
file ampl/student/rs6k/minos.gz
for student MINOS solver
file ampl/student/rs6k/gjh.gz
for "solver" that computes the objective gradient (g), the constraint
, Jacobian (J), and the Hessian of the Lagrangian (H) at the
, current point (primal and dual variable values). The solver
, message shows commands to read these as params and delete
, the temporary file that conveys them. When multiple objectives
, are present, the first is used unless the objectives have suffix
, objweight ==> g is the gradient of the weighted sum of objectives.
, Source = /netlib/ampl/solvers/examples/gjh.c.
file ampl/student/rs6k/lpsolve.gz
for LP/MIP solver based on lp_solve 3.2; see ampl/solvers/lpsolve/README
file ampl/student/rs6k/snopt.gz
for student SNOPT solver
# The programs in this directory are "student" versions that
# restrict problem sizes (to 300 variables and 300 general
# constraints) and are intended for noncommercial use.
# For serious commercial use, you should (eventually) license
# commercial versions, even if your applications never exceed
# the limits of the student versions.
# SGI IRIX binaries (should run under IRIX 5.x and 6.x)
file ampl/student/sgi/README
file ampl/student/sgi/ampl.gz
for student ampl processor
file ampl/student/sgi/cplex.tgz
for gzipped tar file with student CPLEX 8.0 solver and LICENSE
file ampl/student/sgi/minos.gz
for student MINOS solver
file ampl/student/sgi/gjh.gz
for "solver" that computes the objective gradient (g), the constraint
, Jacobian (J), and the Hessian of the Lagrangian (H) at the
, current point (primal and dual variable values). The solver
, message shows commands to read these as params and delete
, the temporary file that conveys them. When multiple objectives
, are present, the first is used unless the objectives have suffix
, objweight ==> g is the gradient of the weighted sum of objectives.
, Source = /netlib/ampl/solvers/examples/gjh.c.
file ampl/student/sgi/lpsolve.gz
for LP/MIP solver based on lp_solve 3.2; see ampl/solvers/lpsolve/README
file ampl/student/sgi/snopt.gz
for student SNOPT solver
# The programs in this directory are "student" versions that
# restrict problem sizes (to 300 variables and 300 general
# constraints) and are intended for noncommercial use.
# For serious commercial use, you should (eventually) license
# commercial versions, even if your applications never exceed
# the limits of the student versions.
# Solaris (5.8) SPARC binaries (runable under Solaris 5.8)
file ampl/student/solaris/README
file ampl/student/solaris/ampl.gz
for student ampl processor
file ampl/student/solaris/cplex.tgz
for gzipped tar file with student CPLEX 11.0.1 solver and LICENSE
file ampl/student/solaris/minos.gz
for student MINOS solver
file ampl/student/solaris/gjh.gz
for "solver" that computes the objective gradient (g), the constraint
, Jacobian (J), and the Hessian of the Lagrangian (H) at the
, current point (primal and dual variable values). The solver
, message shows commands to read these as params and delete
, the temporary file that conveys them. When multiple objectives
, are present, the first is used unless the objectives have suffix
, objweight ==> g is the gradient of the weighted sum of objectives.
, Source = /netlib/ampl/solvers/examples/gjh.c.
file ampl/student/solaris/lpsolve.gz
for LP/MIP solver based on lp_solve 3.2; see ampl/solvers/lpsolve/README
file ampl/student/solaris/snopt.gz
for student SNOPT solver
# The programs in this directory are "student" versions that
# restrict problem sizes (to 300 variables and 300 general
# constraints) and are intended for noncommercial use.
# For serious commercial use, you should (eventually) license
# commercial versions, even if your applications never exceed
# the limits of the student versions.
# Solaris 5.8 on Intel processors (i86pc)
file ampl/student/solaris_i86pc/README
file ampl/student/solaris_i86pc/ampl.gz
for student ampl processor
file ampl/student/solaris_i86pc/minos.gz
for student MINOS solver
file ampl/student/solaris_i86pc/lpsolve.gz
for LP/MIP solver based on lp_solve 3.2; see ampl/solvers/lpsolve/README
file ampl/student/solaris_i86pc/snopt.gz
for student SNOPT solver
file ampl/tables/README
file ampl/tables/TABLES.RME
file ampl/tables/amplodbc.c
file ampl/tables/ampltabl.def
file ampl/tables/ampltabl.dll.gz
for "standard" ODBC table handler for Microsoft Windows (W9x, NT)
, available only by ftp or http (as ampltabl.dll.gz)
file ampl/tables/calories.tab
file ampl/tables/changes
file ampl/tables/diet.mod
file ampl/tables/diet2a.dat
file ampl/tables/diettab.x
file ampl/tables/diettabw.x
file ampl/tables/dietwrit.x
file ampl/tables/foods.tab
file ampl/tables/fullbit.c
file ampl/tables/makefile.linux32
file ampl/tables/makefile.linux64
file ampl/tables/makefile.macosx32
file ampl/tables/makefile.macosx64
file ampl/tables/makefile.vc
file ampl/tables/nutrients.tab
file ampl/tables/simpbit.c
file ampl/tables/tableproxy.c
file ampl/tables/tableproxyver.h
file ampl/tables/xsum0.out
file anl-reports/tm41
file anl-reports/tm88
file anl-reports/tm97
file anl-reports/tm99
file anl-reports/tm109
file anl-reports/argonne50
# Index for apollo
file apollo/hpplot
for program which converts Apollo GMR graphics output files into ascii text
, files of HPGL (Hewlitt Packard Graphics Language) commands which can
, then be sent to any HP graphics device (the HP7550 plotter in
, particular).
file apollo/7550a
for pen plotter which runs on the Apollo.
, Complete instructions on compiling and installing the print-server are
, included.
file apollo/qsend
for program allows a user at one Apollo
, workstation to send messages to other users, other nodes, all
, users, all nodes, their own node (from a background job), and
, to themselves (if they are logged in on more than one machine).
file apollo/toshiba
for print-server for a Toshiba 1351 dot matrix
, printer running on an Apollo workstation with an RS232 interface.
file apollo/image
for Apple Imagewriter dot matrixprinter running on an Apollo
, workstation with an RS232 interface.
file apollo/rand
for random number generators for the Apollos
file apollo/v2d
for V2d is a demo program originally written by Jim Rees to
, show how an Apollo network could get transparent file access
, to any BSD 4.2 system running TCP/IP.
file apollo/ftp
for A set of small programs which will startup
, the TCP/IP FTP, RIP, and TELNET servers on the Apollos after
, a suitable delay to allow the TCP/IP server to get initialized.
file apollo/sendrec
for package which converts Apollo binary data file (REC file types)
, to Alliant binary format data files which can be read with an
, unformatted Fortran READ statement on the Alliant and vice-versa
, (ie. it will convert Alliant format files for reading on an Apollo).
file apollo/ckmail
for checks if new network mail has arrived for you on the Apollo network
, and will (optionally) pop up a window to notify you about the new mail.
file apollo/shar
for does the same function as your BUNDLE shell script, but is more
, extensive. It adds in some error checking and can handle packing
, entire directories into an archive file for mailing out over the
, network (e.g. this file was created by the command
, 'shar shar.dir >foobar').
file apollo/batch
for allows you to start a background job running on any machine in
, the network and then log out without killing the job.
file apollo/compress
for a utility which can save a considerable amount of disk space.
by From: David Krowitz, MIT 2/11/87
file apollo/v2
for Apollo to BSD 4.2 (Alliant FX/1)
, transparent file access software. This version works correctly on
, Apollo workstations running the new SR9.5 release of AEGIS. The
, version I gave you previously works under SR9.2 -- the new version
, will not run on SR9.2. Please add this to your software library.
by David Krowitz 2/28/87
file apollo/gone
for When the user wants to leave the node unattended, the gone routine borrows
, the display, puts a message on the screen, and waits for the user to type
, a password. The user can specify the password and the message
, font with a configuration file in the user's ~user_data directory.
by David Krowitz, MIT 3/21/87
file apollo/hp7570
for new HP 7570 print server
by David Krowitz, MIT 5/16/87
file apollo/hp7475
for new HP 7475 print server
by David Krowitz, MIT 5/16/87
file apollo/hp7550
for revised HP 7550 print server
by David Krowitz, MIT 5/16/87
file apollo/nec-p9xl
for Apollo print server for NEC P9XL Pinwriter
by David Krowitz, MIT 7/30/87
file apollo/remote
for is a short file daemon program which periodically
, checks a directory and executes a shell command for each of the
, files it finds there before deleting them.
file apollo/kermit
for kermit program for the apollo
file atlas/archives/aix/atlas3.4.1_AIX_POWER3_2.tgz
for Dual IBM Power3
size 2830578
file atlas/archives/aix/atlas3.4.1_AIX_POWER4.tgz
for IBM Power4, using xlf/gcc
size 2046490
lib atlas/archives/aix
for AIX prebuilts
lib atlas/archives/hp-ux
for HP-UX prebuilts
lib atlas/archives/irix
for IRIX prebuilts
lib atlas/archives/linux
for Linux prebuilts
lib atlas/archives/osf1
for OSF1 prebuilts
lib atlas/archives/sunos
for SunOS prebuilts
lib atlas/archives/windows
for Windows prebuilts
lib atlas/archives/osx
for OS X prebuilts
# Archive of prebuilt ATLAS libraries for IRIX
#
# These files are library archives created by installing ATLAS on various
# architectures. They are provided as a convenience only. If you have
# compiler / OS / performance / version problems, you should download the
# code and compile it yourself.
#
# The tarfile name is encoded in this manner:
# atlas_vp-_.tgz
#
# The tarfiles create a subdirectory corresponding to the
# _ string, and place five files there:
# libatlas.a : the ATLAS library, containing complete BLAS with
# their Fortran 77 and C interfaces;
# liblapack.a : Recursive implementation of some LAPACK routines,
# with their Fortran 77 and C interfaces;
# cblas.h : The C header file you need to include in your
# program if you call the C BLAS interface.
# Make._: The ATLAS make include used to generate
# these libraries:
# SUMMARY.LOG : The log file summarizing the details of this ATLAS
# install.
file atlas/archives/irix/atlas_v3p2_IRIX_SGIIP28.tgz
for SGI R10000, IP28 (1MB L2)
size 2843762
file atlas/archives/irix/atlas_v3p2_IRIX_SGIIP30.tgz
for SGI R12000, IP30 (2MB L2)
size 3135767
file atlas/archives/linux/atlas3.4.1_Linux_IA64Itan_2.tgz
file atlas/archives/linux/atlas3.4.1_Linux_PIIISSE1.tgz
file atlas/archives/osf1/atlas3.2.0_OSF1_21164.tgz
for DEC ev56, 2MB L3
size 1387863
file atlas/archives/osf1/atlas3.4.1_OSF1_21264GOTO.tgz
for Compaq ev6, 4MB L2
size 1986634
file atlas/archives/osx/atlas3.4.1_OSX_PPCG4AltiVec_2.tgz
for Apple G4 running OS X
size 1807167
file atlas/archives/sunos/atlas3.5.0beta_SunOS_SunUS2_2.tgz
for Sun Ultra2, model 2200
size 1184111
file atlas/archives/sunos/atlas3.2.0_SunOS_SunUS5.tgz
for Sun Ultra5/10
size 1206427
file atlas/archives/windows/atlas330_WinNT_P4SSE2.zip
file atlas/archives/windows/atlas321_WinNT_PIIISSE1.zip
file atlas/archives/windows/atlas321_WinNT_PII.zip
file atlas/archives/windows/atlas321_WinNT_PPRO.zip
file atlas/archives/windows/atlas3.0.2_WinNT_ATHLON.tgz
file atlas/archives/windows/atlas3.0.3_WinNT_ATHLON256L2.tgz
file atlas/developer/atlas3.5.13.tgz
file atlas/developer/atlas3.5.10.tgz
file atlas/developer/atlas3.5.9.tgz
file atlas/developer/atlas3.5.6.tgz
file atlas/developer/atlas3.5.4.tgz
file atlas/developer/atlas3.5.1.tgz
file atlas/developer/atlas3.5.0.tgz
file atlas/developer/atlas3.3.13.tgz
file atlas/developer/atlas3.3.12.tgz
file atlas/developer/atlas3.3.9.tgz
file atlas/developer/atlas3.3.8.tgz
file atlas/developer/atlas3.3.7.tgz
file atlas/developer/atlas3.3.6.tgz
file atlas/developer/atlas3.3.5.tgz
file atlas/developer/atlas3.3.4.tgz
file atlas/developer/atlas3.3.3.tgz
file atlas/developer/atlas3.3.2.tgz
file atlas/developer/atlas3.3.1.tgz
file atlas/developer/atlas3.3.0.tgz
file atlas/cblasqref.ps.gz
file atlas/lapackqref.ps.gz
file benchmark/bipopt/intro.bmrk
for Troff(-mm)/Eqn/Pic file; general description, references;
file benchmark/bipopt/cmmode.bmrk
for common-mode circuit; Troff/Eqn and PostScript at end!
file benchmark/bipopt/casc.bmrk
for Schmitt trigger cascade
file benchmark/bipopt/dcnine.bmrk
for circuit from Chua
file benchmark/bipopt/hybr.bmrk
for all-NPN voltage reference from Banwell
file benchmark/bipopt/oa741.bmrk
for input stage of 741 op-amp
file benchmark/bipopt/vref.bmrk
for Brokaw voltage reference
file benchmark/comm.tgz
file utk/people/JackDongarra/faq-linpack.html
file benchmark/laserprinter.ps
file benchmark/linpackc.new
file benchmark/mp-computers.ps
file benchmark/top500.ps
file benchmark/sparsebench/readme
file benchmark/sparsebench/install.ps
file benchmark/sparsebench/install.pdf
file benchmark/sparsebench/benchmark.tgz
file benchmark/sparsebench/bench.ps
file benchmark/sparsebench/bench.pdf
file bib/thesaurus.html
for vocabulary for attribute/value pairs used in netlib index files
by Eric Grosse
file bib/ericjack.html
for another key file associated with indices...who to blame!
file bib/mirrors.html
for official netlib mirror sites
file bib/moremirrors.html
for informal netlib mirror sites
file bib/compression.html
for background and how-to advice on .Z and .gz files in netlib
file bib/gams
for classification of numerical software
by Boisvert and others
file bib/gams.html
for GAMS problem taxonomy
file bib/reports
for listing of ftp sites for technical reports
editor Eric Grosse ehg@research.bell-labs.com
file bib/journals
for listing of electronic journals in scientific computing
editor Eric Grosse ehg@research.bell-labs.com
file bib/gvl.bib
for Golub and Van Loan, "Matrix Computations", 2nd Edn.
size 203 kB
by Charles Van Loan, Chris Paige and Clement Pellerin
file bib/stewart-bib
for matrix bibliography
by Pete Stewart
size 772 kB
see (includes almost all the material in bib/gvl.bib and more)
file bib/stewart-prog
for extracting sub-bibliographies from stewart-bib
by Pete Stewart
lang C
file bib/ovr.bib
for Parallel and Vector Numerical Algorithms
by Ortega, Voigt and Romine
size 443 kB
# Probably best to coarse search by email, as in
# mail netlib@research.bell-labs.com
# send golub from linalg.
file bib/ovr-strings
for journal abbreviations used in "find ... from linalg"
by Ortega, Voigt and Romine
file bib/acm.bib
for Collected Algorithms of the ACM
lang BibTeX
by Rice, Hanson, Hopkins, Morse
file bib/ipmbib.bbl
by Eberhard Kranich
for "Interior Point Methods for Mathematical Programming: A Bibliography".
, Formerly called intbib.bbl; citation keys now begin with "ipm:".
, Send comments to aw81kr@nos1.pb.bib.de (Eberhard Kranich).
size 680 kB
file bib/ipmbib.tex
by Eberhard Kranich
see ipmbib.bbl
file bib/ipmbib.bib
for ipmbib.bbl
by Eberhard Kranich
lang (big) BibTeX
size 820 kB
file bib/all_brec.readme
for Automatic Differentiation -- notes on bibliography
by George Corliss
file bib/all_brec.tex
for typesetting all_brec.bib
by George Corliss
file bib/all_brec.bib
for Automatic Differentiation database
by George Corliss
size 279 kB
file bib/origami.fmt
for bibliography on paper folding
by Friends of the Origami Center of America
file bib/origami.db
for awk'able version of origami.fmt
file bib/keywords
for searching netlib by keyword
by Eric Grosse
size 1.7 MB
file bib/libraries
for cryptic listing of netlib directories
file bib/combline.c
for converts paragraphs into lines, for convenient grep searching
, undo by "tr '\015' '\012'
by Eric Grosse
file bib/cite.tex
for sample file to use with gvl.bib
file bib/siam
for author, titles from SIAM journals
editor bdilisi@siam.org
file bib/changes
file bib/evdv
for reference from the book Concurrent Scientific Computing,
by Eric F. Van de Velde, Number 16 in Texts in Applied Mathematics,
, Springer-Verlag 1994.
file bibnet/authors/b/bartolini-c.bib
file bibnet/authors/b/beebe-nelson-h-f.bib
file bibnet/authors/b/bell-brad.bib
file bibnet/authors/b/berger-marsha-j.bib
file bibnet/authors/b/bethe-hans.bib
file bibnet/authors/b/bohr-niels.bib
file bibnet/authors/b/born-max.bib
file bibnet/authors/b/brandt-achi.bib
file bibnet/authors/b/brun-luc.bib
file bibnet/authors/b/bryant-chris.bib
file bibnet/authors/c/cody-william-j.bib
file bibnet/authors/c/coughran-william-m.bib
file bibnet/authors/c/cowsar-lawrence-c.bib
file bibnet/authors/c/crandall-richard-e.bib
file bibnet/authors/d/dehnert-juliane.bib
file bibnet/authors/d/dirac-p-a-m.bib
file bibnet/authors/d/dongarra-jack-j.bib
file bibnet/authors/d/duff-iain-s.bib
file bibnet/authors/e/einstein.bib
file bibnet/authors/f/fastmultipole.bib
file bibnet/authors/f/fazio-riccardo.bib
file bibnet/authors/f/fermi-enrico.bib
file bibnet/authors/f/feynman-richard-p.bib
file bibnet/authors/f/fleishman-shachar.bib
file bibnet/authors/f/flusser-jan.bib
file bibnet/authors/f/foresti-stefano.bib
file bibnet/authors/f/forsgren-anders.bib
file bibnet/authors/f/forsythe-george-elmer.bib
file bibnet/authors/f/fractal-image-comp.bib
file bibnet/authors/g/gamow-george.bib
file bibnet/authors/g/gay-david-m.bib
file bibnet/authors/g/gebhardt-friedrich.bib
file bibnet/authors/g/golub-gene-h.bib
file bibnet/authors/g/gould-nicholas-ian.bib
file bibnet/authors/g/grosse-eric.bib
file bibnet/authors/g/grundy-jim.bib
file bibnet/authors/h/hanyga-andrzej.bib
file bibnet/authors/h/harwood-aaron.bib
file bibnet/authors/h/heinzmann-jochen.bib
file bibnet/authors/h/heisenberg-werner.bib
file bibnet/authors/h/hemker-pieter-w.bib
file bibnet/authors/h/higham-nicholas-john.bib
file bibnet/authors/h/homeier-herbert-h-h.bib
file bibnet/authors/h/hopkins-tim.bib
file bibnet/authors/i/ingber-lester.bib
file bibnet/authors/i/ipsen-ilse-c-f.bib
lib bibnet/authors/a
lib bibnet/authors/b
lib bibnet/authors/c
lib bibnet/authors/d
lib bibnet/authors/e
lib bibnet/authors/f
lib bibnet/authors/g
lib bibnet/authors/h
lib bibnet/authors/i
lib bibnet/authors/j
lib bibnet/authors/k
lib bibnet/authors/l
lib bibnet/authors/m
lib bibnet/authors/n
lib bibnet/authors/o
lib bibnet/authors/p
lib bibnet/authors/q
lib bibnet/authors/r
lib bibnet/authors/s
lib bibnet/authors/t
lib bibnet/authors/u
lib bibnet/authors/v
lib bibnet/authors/w
lib bibnet/authors/x
lib bibnet/authors/y
lib bibnet/authors/z
file bibnet/authors/j/jagadeesan-radha.bib
file bibnet/authors/j/jain-raj.bib
file bibnet/authors/j/jurisica-igor.bib
file bibnet/authors/k/kahan-william-m.bib
file bibnet/authors/k/kearfott-r-baker.bib
file bibnet/authors/k/kincaid-david-r.bib
file bibnet/authors/k/knyazev-andrew.bib
file bibnet/authors/l/lanczos-cornelius.bib
file bibnet/authors/l/leaver-edward-w.bib
file bibnet/authors/l/louchet-jean.bib
file bibnet/authors/l/lowdin-per-olov.bib
file bibnet/authors/m/mandelbrot-benoit.bib
file bibnet/authors/m/marsaglia-george.bib
file bibnet/authors/m/metropolis-nicholas.bib
file bibnet/authors/m/moler-cleve-b.bib
file bibnet/authors/m/moore-ramon-e.bib
file bibnet/authors/m/more-jorge.bib
file bibnet/authors/m/muskens-reinhard-a.bib
file bibnet/authors/n/nebel-bernhard.bib
file bibnet/authors/n/neta-beny.bib
file bibnet/authors/n/nissan-ephraim.bib
file bibnet/authors/n/nitsche-ulrich.bib
file bibnet/authors/o/oppenheimer-j-robert.bib
file bibnet/authors/p/paloschi-jorge-r.bib
file bibnet/authors/p/parlett-beresford-n.bib
file bibnet/authors/p/pauli-wolfgang.bib
file bibnet/authors/p/peters-jorg.bib
file bibnet/authors/p/pourzandi-makan.bib
file bibnet/authors/p/pozarlik-roman.bib
file bibnet/authors/r/rice-john-r.bib
file bibnet/authors/r/ruede-ulrich.bib
file bibnet/authors/r/ruhe-axel.bib
file bibnet/authors/s/saad-yousef.bib
file bibnet/authors/s/saffiotti-alessandro.bib
file bibnet/authors/s/schneider-georg-j.bib
file bibnet/authors/s/schroedinger-erwin.bib
file bibnet/authors/s/shannon-claude-elwood.bib
file bibnet/authors/s/shen-jie.bib
file bibnet/authors/s/slater-john-clarke.bib
file bibnet/authors/s/slissenko-anatol.bib
file bibnet/authors/s/smith-barry-francis.bib
file bibnet/authors/s/spinellis-diomidis.bib
file bibnet/authors/s/steels-luc.bib
file bibnet/authors/s/stenger-frank.bib
file bibnet/authors/s/strehl-alexander.bib
file bibnet/authors/s/strehl-karsten.bib
file bibnet/authors/s/surmann-hartmut.bib
file bibnet/authors/s/szilard-leo.bib
file bibnet/authors/t/teller-edward.bib
file bibnet/authors/t/trefethen-lloyd-n.bib
file bibnet/authors/t/tukey-john-w.bib
file bibnet/authors/t/turing-alan-mathison.bib
file bibnet/authors/u/ulam-stanislaw-m.bib
file bibnet/authors/v/vandervorst-henk-a.bib
file bibnet/authors/v/vandroogenbroeck-marc.bib
file bibnet/authors/v/veldhuizen-todd-l.bib
file bibnet/authors/v/verner-jim-hamilton.bib
file bibnet/authors/v/von-neumann-john.bib
file bibnet/authors/w/wagner-jean-marc.bib
file bibnet/authors/w/wermelinger-michel.bib
file bibnet/authors/w/wickerhauser-m-victor.bib
file bibnet/authors/w/wigner-eugene.bib
file bibnet/authors/w/wilkinson-james-hardy.bib
file bibnet/authors/w/wolkowicz-henry.bib
file bibnet/authors/x/xue-jingling.bib
file bibnet/authors/y/young-david-m.bib
file bibnet/authors/z/zeugmann-thomas-u.bib
lib bibnet/authors
for bibliographies of individuals, in subdirectories
, keyed by the first letter of the last name
file bibnet/BaKoMa-CM.Fonts
for BaKoMa fonts copyright notice
file bibnet/faq.html
for frequently asked questions about bibnet
lib bibnet/journals
for bibliographies of selected journals
file bibnet/readme
for description of the BibNet project, with guidelines for contributors
file bibnet/readme.old
for expanded description of the BibNet project, with guidelines for contributors
lib bibnet/subjects
for bibliographies by subject
lib bibnet/tools
for software and macros to assist with bibliographies
file bibnet/journals/applnummath.bib
for Applied Numerical Mathematics: Transactions of IMACS BibTeX file
file bibnet/journals/applnummath.dvi
for TeX DVI file from applnummath.bib
file bibnet/journals/applnummath.html
for HTML form of applnummath.bib
file bibnet/journals/applnummath.ltx
for LaTeX wrapper for typesetting applnummath.bib
file bibnet/journals/applnummath.pdf.gz
for gzip-compressed Adobe Acrobat PDF file from applnummath.ps
file bibnet/journals/applnummath.ps.gz
for gzip-compressed PostScript file from applnummath.dvi
file bibnet/journals/applnummath.sok
for spelling exception dictionary for applnummath.bib
file bibnet/journals/applnummath.twx
for title word index for applnummath.bib
file bibnet/journals/elefunt.bib
for elementary function computation bibliography
file bibnet/journals/elefunt.dvi
for TeX DVI file from elefunt.bib
file bibnet/journals/elefunt.html
for HTML form of elefunt.bib
file bibnet/journals/elefunt.ltx
for LaTeX wrapper for typesetting elefunt.bib
file bibnet/journals/elefunt.pdf.gz
for gzip-compressed Adobe Acrobat PDF file from elefunt.ps
file bibnet/journals/elefunt.ps.gz
for gzip-compressed PostScript file from elefunt.dvi LaTeX wrapper
file bibnet/journals/elefunt.sok
for spelling exception dictionary for elefunt.bib
file bibnet/journals/elefunt.twx
for title word index for elefunt.bib
file bibnet/journals/linala1960.bib
for BibTeX file for the journal Linear Algebra and its Applications (1968--1969)
file bibnet/journals/linala1960.dvi
for TeX DVI file from linala1960.bib
file bibnet/journals/linala1960.html
for HTML form of linala1960.bib
file bibnet/journals/linala1960.ltx
for LaTeX wrapper for typesetting linala1960.bib
file bibnet/journals/linala1960.pdf.gz
for gzip-compressed Adobe Acrobat PDF file from linala1960.ps
file bibnet/journals/linala1960.ps.gz
for gzip-compressed PostScript file from linala1960.dvi
file bibnet/journals/linala1960.sok
for spelling exception dictionary for linala1960.bib
file bibnet/journals/linala1960.twx
for title word index for linala1960.bib
file bibnet/journals/linala1970.bib
for BibTeX file for the journal Linear Algebra and its Applications (1970--1979)
file bibnet/journals/linala1970.dvi
for TeX DVI file from linala1970.bib
file bibnet/journals/linala1970.html
for HTML form of linala1970.bib
file bibnet/journals/linala1970.ltx
for LaTeX wrapper for typesetting linala1970.bib
file bibnet/journals/linala1970.pdf.gz
for gzip-compressed Adobe Acrobat PDF file from linala1970.ps
file bibnet/journals/linala1970.ps.gz
for gzip-compressed PostScript file from linala1970.dvi
file bibnet/journals/linala1970.sok
for spelling exception dictionary for linala1970.bib
file bibnet/journals/linala1970.twx
for title word index for linala1970.bib
file bibnet/journals/linala1980.bib
for BibTeX file for the journal Linear Algebra and its Applications
(1980--1989)
file bibnet/journals/linala1980.dvi
for TeX DVI file from linala1980.bib
file bibnet/journals/linala1980.html
for HTML form of linala1980.bib
file bibnet/journals/linala1980.ltx
for LaTeX wrapper for typesetting linala1980.bib
file bibnet/journals/linala1980.pdf.gz
for gzip-compressed Adobe Acrobat PDF file from linala1980.ps
file bibnet/journals/linala1980.ps.gz
for gzip-compressed PostScript file from linala1980.dvi
file bibnet/journals/linala1980.sok
for spelling exception dictionary for linala1980.bib
file bibnet/journals/linala1980.twx
for title word index for linala1980.bib
file bibnet/journals/linala1990.bib
for BibTeX file for the journal Linear Algebra and its Applications (1990--1999)
file bibnet/journals/linala1990.dvi
for TeX DVI file from linala1990.bib
file bibnet/journals/linala1990.html
for HTML form of linala1990.bib
file bibnet/journals/linala1990.ltx
for LaTeX wrapper for typesetting linala1990.bib
file bibnet/journals/linala1990.pdf.gz
for gzip-compressed Adobe Acrobat PDF file from linala1990.ps
file bibnet/journals/linala1990.ps.gz
for gzip-compressed PostScript file from linala1990.dvi
file bibnet/journals/linala1990.sok
for spelling exception dictionary for linala1990.bib
file bibnet/journals/linala1990.twx
for title word index for linala1990.bib
file bibnet/journals/mathcomp.bib
for publications in the journal Mathematics of Computation, and its predecessors
file bibnet/journals/mathcomp.dvi
for TeX DVI file from mathcomp.bib
file bibnet/journals/mathcomp.html
for HTML form of mathcomp.bib
file bibnet/journals/mathcomp.ltx
for LaTeX wrapper for typesetting mathcomp.bib
file bibnet/journals/mathcomp.pdf.gz
for gzip-compressed Adobe Acrobat PDF file from mathcomp.ps
file bibnet/journals/mathcomp.ps.gz
for gzip-compressed PostScript file from mathcomp.dvi
file bibnet/journals/mathcomp.sok
for spelling exception dictionary for mathcomp.bib
file bibnet/journals/mathcomp.twx
for title word index for mathcomp.bib
file bibnet/journals/numlinaa.bib
for BibTeX file for the Journal of Numerical Linear Algebra with Applications and the journal Numerical Linear Algebra with Applications
file bibnet/journals/numlinaa.dvi
for TeX DVI file from numlinaa.bib
file bibnet/journals/numlinaa.html
for HTML form of numlinaa.bib
file bibnet/journals/numlinaa.ltx
for LaTeX wrapper for typesetting numlinaa.bib
file bibnet/journals/numlinaa.pdf.gz
for gzip-compressed Adobe Acrobat PDF file from numlinaa.ps
file bibnet/journals/numlinaa.ps.gz
for gzip-compressed PostScript file from numlinaa.dvi
file bibnet/journals/numlinaa.sok
for spelling exception dictionary for numlinaa.bib
file bibnet/journals/numlinaa.twx
for title word index for numlinaa.bib
file bibnet/journals/nummath.bib
for BibTeX file for the journal Numerische Mathematik
file bibnet/journals/nummath.dvi
for TeX DVI file from nummath.bib
file bibnet/journals/nummath.html
for HTML form of nummath.bib
file bibnet/journals/nummath.ltx
for LaTeX wrapper for typesetting nummath.bib
file bibnet/journals/nummath.pdf.gz
for gzip-compressed Adobe Acrobat PDF file from nummath.ps
file bibnet/journals/nummath.ps.gz
for gzip-compressed PostScript file from nummath.dvi
file bibnet/journals/nummath.sok
for spelling exception dictionary for nummath.bib
file bibnet/journals/nummath.twx
for title word index for nummath.bib
file bibnet/journals/siamjcomput.bib
for SIAM Journal on Computing BibTeX file
file bibnet/journals/siamjcomput.dvi
for TeX DVI file from siamjcomput.bib
file bibnet/journals/siamjcomput.html
for HTML form of siamjcomput.bib
file bibnet/journals/siamjcomput.ltx
for LaTeX wrapper for typesetting siamjcomput.bib
file bibnet/journals/siamjcomput.pdf.gz
for gzip-compressed Adobe Acrobat PDF file from siamjcomput.ps
file bibnet/journals/siamjcomput.ps.gz
for gzip-compressed PostScript file from siamjcomput.dvi
file bibnet/journals/siamjcomput.sok
for spelling exception dictionary for siamjcomput.bib
file bibnet/journals/siamjcomput.twx
for title word index for siamjcomput.bib
file bibnet/journals/siamjmatanaappl.bib
for SIAM Journal on Matrix Analysis and Applications BibTeX file
file bibnet/journals/siamjmatanaappl.dvi
for TeX DVI file from siamjmatanaappl.bib
file bibnet/journals/siamjmatanaappl.html
for HTML form of siamjmatanaappl.bib
file bibnet/journals/siamjmatanaappl.ltx
for LaTeX wrapper for typesetting siamjmatanaappl.bib
file bibnet/journals/siamjmatanaappl.pdf.gz
for gzip-compressed Adobe Acrobat PDF file from siamjmatanaappl.ps
file bibnet/journals/siamjmatanaappl.ps.gz
for gzip-compressed PostScript file from siamjmatanaappl.dvi
file bibnet/journals/siamjmatanaappl.sok
for spelling exception dictionary for siamjmatanaappl.bib
file bibnet/journals/siamjmatanaappl.twx
for title word index for siamjmatanaappl.bib
file bibnet/journals/siamjnumeranal.bib
for SIAM Journal on Computing BibTeX file
file bibnet/journals/siamjnumeranal.dvi
for TeX DVI file from siamjnumeranal.bib
file bibnet/journals/siamjnumeranal.html
for HTML form of siamjnumeranal.bib
file bibnet/journals/siamjnumeranal.ltx
for LaTeX wrapper for typesetting siamjnumeranal.bib
file bibnet/journals/siamjnumeranal.pdf.gz
for gzip-compressed Adobe Acrobat PDF file from siamjnumeranal.ps
file bibnet/journals/siamjnumeranal.ps.gz
for gzip-compressed PostScript file from siamjnumeranal.dvi
file bibnet/journals/siamjnumeranal.sok
for spelling exception dictionary for siamjnumeranal.bib
file bibnet/journals/siamjnumeranal.twx
for title word index for siamjnumeranal.bib
file bibnet/journals/siamreview.bib
for SIAM Review BibTeX file
file bibnet/journals/siamreview.dvi
for TeX DVI file from siamreview.bib
file bibnet/journals/siamreview.html
for HTML form of siamreview.bib
file bibnet/journals/siamreview.ltx
for LaTeX wrapper for typesetting siamreview.bib
file bibnet/journals/siamreview.pdf.gz
for gzip-compressed Adobe Acrobat PDF file from siamreview.ps
file bibnet/journals/siamreview.ps.gz
for gzip-compressed PostScript file from siamreview.dvi
file bibnet/journals/siamreview.sok
for spelling exception dictionary for siamreview.bib
file bibnet/journals/siamreview.twx
for title word index for siamreview.bib
file bibnet/subjects/all_brec.bib
for automatic differentiation
size 271 kB
file bibnet/subjects/all_brec.html
file bibnet/subjects/all_brec.readme
file bibnet/subjects/all_brec.tex
file bibnet/subjects/as.bib
for Applied Statistics
file bibnet/subjects/as.html
file bibnet/subjects/as.ltx
file bibnet/subjects/cacm1950.bib
for Communications of the ACM (1958--1959)
file bibnet/subjects/cacm1950.html
file bibnet/subjects/cacm1950.ltx
file bibnet/subjects/cacm1950.sok
file bibnet/subjects/cacm1960.bib
for Communications of the ACM (1960--1969)
file bibnet/subjects/cacm1960.html
file bibnet/subjects/cacm1960.ltx
file bibnet/subjects/cacm1960.sok
file bibnet/subjects/cacm1970.bib
for Communications of the ACM (1970--1979)
file bibnet/subjects/cacm1970.html
file bibnet/subjects/cacm1970.ltx
file bibnet/subjects/cacm1970.sok
file bibnet/subjects/cacm1980.bib
for Communications of the ACM (1980--1989)
file bibnet/subjects/cacm1980.html
file bibnet/subjects/cacm1980.ltx
file bibnet/subjects/cacm1980.sok
file bibnet/subjects/cacm1990.bib
for Communications of the ACM (1990--1999)
file bibnet/subjects/cacm1990.html
file bibnet/subjects/cacm1990.ltx
file bibnet/subjects/cacm1990.sok
file bibnet/subjects/case-based.bib
for case-based reasoning, from project FABEL of GMD
file bibnet/subjects/case-based.html
file bibnet/subjects/domain-decomp.bib
for domain decomposition
file bibnet/subjects/domain-decomp.html
file bibnet/subjects/domain-decomp.ltx
file bibnet/subjects/domain-decomp.sed
file bibnet/subjects/fractal-image-comp.bib
for fractal image compression
file bibnet/subjects/fractal-image-comp.html
file bibnet/subjects/fractal-image-comp.ltx
file bibnet/subjects/gvl.bib
for Golub and Van Loan, Matrix Computations
size 253 kB
file bibnet/subjects/gvl.html
file bibnet/subjects/gvl.ltx
file bibnet/subjects/maple-extract.bib
for Maple symbolic algebra system
file bibnet/subjects/maple-extract.html
file bibnet/subjects/maple-extract.ltx
file bibnet/subjects/matched-field-proc.bib
for matched field processing
file bibnet/subjects/matched-field-proc.html
file bibnet/subjects/matched-field-proc.ltx
file bibnet/subjects/multilevel-prog.bib
for bilevel and multilevel programming and Stackelberg problems
file bibnet/subjects/multilevel-prog.html
file bibnet/subjects/multilevel-prog.ltx
file bibnet/subjects/ovr.bib
for Parallel and Vector Numerical Algorithms
by Ortega, Voigt, and Romine
size 579 kB
file bibnet/subjects/ovr.bib-001
file bibnet/subjects/ovr.bib-002
file bibnet/subjects/ovr.bib-003
file bibnet/subjects/ovr.bib-004
file bibnet/subjects/ovr.bib-005
file bibnet/subjects/ovr.bib-006
file bibnet/subjects/toms.bib
for ACM Transactions on Mathematical Software
, (TOMS), completely covering all issues from
, March 1975 -- June 1994. All papers,
, including editorials, policy statements,
, remarks, and corrigenda are included.
size 434 kB
file bibnet/subjects/toms.html
file bibnet/subjects/toms.ltx
file bibnet/subjects/toms.sok
file bibnet/tools/emacs/btxaccnt.el
file bibnet/tools/emacs/clsc.el
file bibnet/tools/emacs/filehdr-1.30.tar.gz
file bibnet/tools/examples/bibmods.sty
for LaTeX style file with modifications to
, improve spacing
file bibnet/tools/examples/bibnames.sty
for TeX and LaTeX style file with standard
, definitions of TeX-related proper names
, (needs texnames.sty; see below)
file bibnet/tools/examples/bibtex-doc.bib
for sample BibTeX bibliography
file bibnet/tools/examples/bibtex-doc.ltx
for LaTeX wrapper for printing the bibnet-doc.bib
, bibliography
file bibnet/tools/examples/bibtex-doc.sok
for spelling exceptions in bibtex-doc.bib
file bibnet/tools/examples/bibtex-doc.twx
for cross-reference of title words in bibtex-doc.bib
file bibnet/tools/examples/fmtwords.awk
for awk program to format the output of keywords.awk
file bibnet/tools/examples/is-abbrv.bst
for modified BibTeX alpha style to show ISBN
, and ISSN numbers, and support @Periodical
file bibnet/tools/examples/is-alpha.bst
for modified BibTeX alpha style to show ISBN
, and ISSN numbers, and support @Periodical
file bibnet/tools/examples/is-plain.bst
for modified BibTeX plain style to show ISBN
, and ISSN numbers, and support @Periodical
file bibnet/tools/examples/is-unsrt.bst
for modified BibTeX unsrt style to show ISBN
, and ISSN numbers, and support @Periodical
file bibnet/tools/examples/keywords.awk
for awk program to extract words from entry titles
file bibnet/tools/examples/makefile
for UNIX makefile to format the bibliographies
file bibnet/tools/examples/path.sty
for AmSTeX, LaTeX, TeX style file for
, typesetting path names
file bibnet/tools/examples/showtags.sty
for LaTeX style file to produce a bibliography
, with highlighted tags (handy for making
, printed reference bibliographies)
file bibnet/tools/examples/template.bib
for sample empty BibTeX templates, plus one real
, example of each entry type
file bibnet/tools/examples/template.ltx
for LaTeX wrapper for printing the template.bib
, bibliography
file bibnet/tools/examples/template.sok
for spelling exceptions in template.bib
file bibnet/tools/examples/template.twx
for cross-reference of title words in template.bib
file bibnet/tools/examples/texnames.sty
for standard macro names for TeXware
lib bibnet/tools/emacs
for GNU Emacs bibliography support
lib bibnet/tools/examples
for sample styles, templates, and bibliography
lib bibnet/tools/software
for software for bibliography file checking,
, conversion, maintenance, and prettyprinting
lib bibnet/tools/strings
for BibTeX string abbreviations for
, institutions, journals, and publishers
file bibnet/tools/software/biblabel-0.01.tar.gz
file bibnet/tools/software/bibtex-to-html.awk
file bibnet/tools/software/journal-toc.awk
file bibnet/tools/strings/institut.bib
for institute string abbreviations
file bibnet/tools/strings/journal.bib
for journal string abbreviations
file bibnet/tools/strings/mrabbrev.bib
for Math Reviews journal abbreviations
file bibnet/tools/strings/publish.bib
for publisher and publisher address string abbreviations
file bihar/dbihar.f
for biharmonic PDE solver in rectangular geometry
prec double
gams I2b1c
file bihar/dbiplr.f
for biharmonic PDE solver in polar coordinates
prec double
gams I2b1c
file bihar/dbmult.f
for biharmonic multiply in rectangular geometry
prec double
gams I2b4
file bihar/dbplrm.f
for biharmonic multiply in polar coordinates
prec double
gams I2b4
file bihar/dlmult.f
for Laplace multiply in rectangular geometry
prec double
gams I2b4
file bihar/dlplrm.f
for Laplace multiply in polar coordinates
prec double
gams I2b4
file bihar/sbihar.f
for biharmonic PDE solver in rectangular geometry
prec single
gams I2b1c
file bihar/sbiplr.f
for biharmonic PDE solver in polar coordinates
prec single
gams I2b1c
file bihar/sbmult.f
for biharmonic multiply in rectangular geometry
prec single
gams I2b4
file bihar/sbplrm.f
for biharmonic multiply in polar coordinates
prec single
gams I2b4
file bihar/slmult.f
for Laplace multiply in rectangular geometry
prec single
gams I2b4
file bihar/slplrm.f
for Laplace multiply in polar coordinates
prec single
gams I2b4
file bihar/fft.doc
for documentation of FFT routines used in the bihar routines
prec double
see fftpack
file bihar/drffti.f
for initialize drfftf and drfftb
prec double
see fftpack
file bihar/drfftf.f
for forward transform of a real periodic sequence
prec double
see fftpack
file bihar/drfftb.f
for backward transform of a real coefficient array
prec double
see fftpack
file bihar/defftf.f
for a simplified real periodic forward transform
prec double
see fftpack
file bihar/defftb.f
for a simplified real periodic backward transform
prec double
see fftpack
file bihar/dsinti.f
for initialize dsint
prec double
see fftpack
file bihar/dsint.f
for sine transform of a real odd sequence
prec double
see fftpack
file bihar/dcosti.f
for initialize dcost
prec double
see fftpack
file bihar/dcost.f
for cosine transform of a real even sequence
prec double
see fftpack
file bihar/dsinqi.f
for initialize dsinqf and dsinqb
prec double
see fftpack
file bihar/dsinqf.f
for forward sine transform with odd wave numbers
prec double
see fftpack
file bihar/dsinqb.f
for unnormalized inverse of dsinqf
prec double
see fftpack
file bihar/dcosqi.f
for initialize dcosqf and dcosqb
prec double
see fftpack
file bihar/dcosqf.f
for forward cosine transform with odd wave numbers
prec double
see fftpack
file bihar/dcosqb.f
for unnormalized inverse of dcosqf
prec double
see fftpack
file bihar/dcffti.f
for initialize dcfftf and dcfftb
prec double
see fftpack
file bihar/dcfftf.f
for forward transform of a complex periodic sequence
prec double
see fftpack
file bihar/dcfftb.f
for unnormalized inverse of dcfftf
prec double
see fftpack
file bihar/changes
file bihar/dbipl.f
file bihar/dbisld.f
file bihar/dbislf.f
file bihar/dcftb1.f
file bihar/dcftf1.f
file bihar/dcfti1.f
file bihar/dcmult.f
file bihar/dconju.f
file bihar/dcsqb1.f
file bihar/dcsqf1.f
file bihar/defft1.f
file bihar/deffti.f
file bihar/dftrnx.f
file bihar/dftrny.f
file bihar/dpssb.f
file bihar/dhzeri.f
file bihar/dhzero.f
file bihar/dmatge.f
file bihar/dpentf.f
file bihar/dpmult.f
file bihar/dpplrm.f
file bihar/dpreco.f
file bihar/dpssb2.f
file bihar/dpssb3.f
file bihar/dpssb4.f
file bihar/dpssb5.f
file bihar/dpssf.f
file bihar/dpssf2.f
file bihar/dpssf3.f
file bihar/dpssf4.f
file bihar/dpssf5.f
file bihar/dradb2.f
file bihar/dradb3.f
file bihar/dradb4.f
file bihar/dradb5.f
file bihar/dradbg.f
file bihar/dradf2.f
file bihar/dradf3.f
file bihar/dradf4.f
file bihar/dradf5.f
file bihar/dradfg.f
file bihar/drftb1.f
file bihar/drftf1.f
file bihar/drfti1.f
file bihar/dstart.f
file bihar/dtrigi.f
file bihar/dupdat.f
file bihar/pois.f
file bihar/sbipl.f
file bihar/sbisld.f
file bihar/sbislf.f
file bihar/scfftb.f
file bihar/scfftf.f
file bihar/scffti.f
file bihar/scftb1.f
file bihar/scftf1.f
file bihar/scfti1.f
file bihar/scmult.f
file bihar/sconju.f
file bihar/scosqb.f
file bihar/scosqf.f
file bihar/scosqi.f
file bihar/scost.f
file bihar/scosti.f
file bihar/scsqb1.f
file bihar/scsqf1.f
file bihar/sefft1.f
file bihar/sefftb.f
file bihar/sefftf.f
file bihar/seffti.f
file bihar/sftrnx.f
file bihar/sftrny.f
file bihar/shzeri.f
file bihar/shzero.f
file bihar/smatge.f
file bihar/spentf.f
file bihar/spmult.f
file bihar/spplrm.f
file bihar/spreco.f
file bihar/spssb.f
file bihar/spssb2.f
file bihar/spssb3.f
file bihar/spssb4.f
file bihar/spssb5.f
file bihar/spssf.f
file bihar/spssf2.f
file bihar/spssf3.f
file bihar/spssf4.f
file bihar/spssf5.f
file bihar/sradb2.f
file bihar/sradb3.f
file bihar/sradb4.f
file bihar/sradb5.f
file bihar/sradbg.f
file bihar/sradf2.f
file bihar/sradf3.f
file bihar/sradf4.f
file bihar/sradf5.f
file bihar/sradfg.f
file bihar/srfftb.f
file bihar/srfftf.f
file bihar/srffti.f
file bihar/srftb1.f
file bihar/srftf1.f
file bihar/srfti1.f
file bihar/ssinqb.f
file bihar/ssinqf.f
file bihar/ssinqi.f
file bihar/ssint.f
file bihar/ssinti.f
file bihar/sstart.f
file bihar/strigi.f
file bihar/supdat.f
file blacs/archives/readme
file blacs/archives/blacs_MPI-AIX46K-0.tgz
file blacs/archives/blacs_MPI-HPPA-0.tgz
file blacs/archives/blacs_MPI-LINUX-0.tgz
file blacs/archives/blacs_MPI-SGI64-0.tgz
file blacs/archives/blacs_MPI-SUN4-0.tgz
file blacs/archives/blacs_MPI-SUN4SOL2-0.tgz
file blacs/archives/blacs_PVM-RS6K-0.tgz
file blacs/archives/blacs_PVM-ALPHA-0.tgz
file blacs/archives/blacs_PVM-HPPA-0.tgz
file blacs/archives/blacs_PVM-SUN4-0.tgz
file blacs/archives/blacs_PVM-SUN4SOL2-0.tgz
file blacs/archives/blacs_PVM-LINUX-0.tgz
file blacs/archives/blacs_MPI-T3E-0.tgz
file blacs/archives/blacs_MPI-SP2-0.tgz
file blacs/archives/blacs_MPL-SP2-0.tgz
file blacs/archives/blacs_NX-PGON-0.tgz
file blacs/archives/blacs_MPI-PGON-0.tgz
file blacs/archives/blacs_MPI-PCA-0.tgz
file blacs/archives/blacs_MPI-O2K-64-0.tgz
file blacs/archives/blacs_MPI-O2K-N32-0.tgz
file blacs/mpiblacs_issues.ps
file blacs/mpi_prop.ps
file blas/archives/readme
file blas/archives/blas_alpha.tgz
file blas/archives/blas_hppa.tgz
file blas/archives/blas_irix64-64.tgz
file blas/archives/blas_irix64-n32.tgz
file blas/archives/blas_linux.tgz
file blas/archives/blas_rs6k.tgz
file blas/archives/blas_solaris.tgz
####################################################################
file blas/gemm_based/ssgemmbased.tgz
for The Superscalar GEMM-based Level 3 BLAS library is a further
, development of the GEMM-based Level 3 BLAS targeted towards
, superscalar processors.
prec double
size 61 kB
file blas/gemm_based/dbench.tgz
for performance evaluation of Level 3 BLAS kernel programs
prec double
size 314 kB
file blas/gemm_based/dgbl3b.tgz
for Level 3 BLAS tuned for single processors with caches
prec double
size 207 kB
file blas/gemm_based/sbench.tgz
for performance evaluation of Level 3 BLAS kernel programs
prec single
size 314 kB
file blas/gemm_based/sgbl3b.tgz
for Level 3 BLAS tuned for single processors with caches
prec single
size 207 kB
file blas/gemm_based/zbench.tgz
for performance evaluation of Level 3 BLAS kernel programs
prec doublecomplex
size 418 kB
file blas/gemm_based/zgbl3b.tgz
for Level 3 BLAS tuned for singlecomplex processors with caches
prec doublecomplex
size 260 kB
file blas/gemm_based/cbench.tgz
for performance evaluation of Level 3 BLAS kernel programs
prec singlecomplex
size 418 kB
file blas/gemm_based/cgbl3b.tgz
for Level 3 BLAS tuned for singlecomplex processors with caches
prec singlecomplex
size 260 kB
#####################################################################
# BLAS Index (Levels 1, 2, and 3) #
# #
# NOTE: All BLAS routines are listed in the order in which #
# they appear on the BLAS Quick Reference Guide. #
# #
# Organization of this index: #
# Documentation and Test Suites #
# Miscellaneous and Auxiliary Routines #
# Level 1 BLAS routines #
# Level 2 BLAS routines #
# Level 3 BLAS routines #
# Extended precision Level 2 BLAS routines #
#####################################################################
file blas/faq.html
for List of frequently asked questions about blas
file blas/blas.tgz
for Fortran77 reference implementation of the LEVEL 1, 2, and 3
, BLAS routines in all precisions
, (If only a specific precision or level is desired, please
, see the appropriate section of this index for details.)
prec single, double, complex, doublecomplex
lang fortran
LAST UPDATE: Tuesday Apr 19th 2011
file blas/blast-forum/cblas.tgz
for C interface to the BLAS
prec single, double, complex, doublecomplex
lang C
LAST UPDATE: Thursday Jan 20th 2011
ref ACML AMD Core Math Library
ref Intel Math Kernel Library
, The AMD Core Math Library (ACML) and the Intel Math Kernel Library
, (Intel MKL) includes BLAS, LAPACK, and ScaLAPACK, which are designed
, to be used by a wide range of software developers to obtain excellent
, performance from their applications running on AMD and Intel platforms.
file blas/blast-forum/cinterface.ps
file blas/blast-forum/cinterface.pdf
for Documentation for the C interface to the BLAS
lib blas/gemm_based
for Level 3 BLAS tuned for single processors with caches
by Kagstrom B., Ling P., and Van Loan C.
title High Performance GEMM-Based Level-3 BLAS
ref High Performance Computing II, 1991, North-Holland
lang Fortran
lib atlas
for Automatically Tuned Linear Algebra Software (ATLAS)
by R. C. Whaley and J. J. Dongarra
lang C
lib blas/blast-forum
for BLAS Technical Forum Standard
, Document, Reference Implementations, and Minutes from
, the BLAST Technical Forum meetings
#
# DOCUMENTATION AND TEST SUITES
#
file blas/blasqr.ps
for quick reference guide for the BLAS.
lang postscript
file blas/blas3-paper.ps
for details on the Level 3 BLAS
lang PostScript
file blas/blas2-paper.ps
for details on the Level 2 BLAS
lang PostScript
file blas/blas2test.f
for original test driver for the real level two blas
file blas/sblat1
for Level 1 BLAS Test Suite
prec single
lang fortran
file blas/dblat1
for Level 1 BLAS Test Suite
prec double
lang fortran
file blas/cblat1
for Level 1 BLAS Test Suite
prec complex
lang fortran
file blas/zblat1
for Level 1 BLAS Test Suite
prec doublecomplex
lang fortran
file blas/sblat2
for Level 2 BLAS Test Suite
prec single
lang fortran
file blas/dblat2
for Level 2 BLAS Test Suite
prec double
lang fortran
file blas/cblat2
for Level 2 BLAS Test Suite
prec complex
lang fortran
file blas/zblat2
for Level 2 BLAS Test Suite
prec doublecomplex
lang fortran
file blas/sblat2d
for Data file required by the Level 2 BLAS Test Suite
file blas/dblat2d
for Data file required by the Level 2 BLAS Test Suite
file blas/cblat2d
for Data file required by the Level 2 BLAS Test Suite
file blas/zblat2d
for Data file required by the Level 2 BLAS Test Suite
file blas/sblat3
for Level 3 BLAS Test Suite
prec single
lang fortran
file blas/dblat3
for Level 3 BLAS Test Suite
prec double
lang fortran
file blas/cblat3
for Level 3 BLAS Test Suite
prec complex
lang fortran
file blas/zblat3
for Level 3 BLAS Test Suite
prec doublecomplex
lang fortran
file blas/sblat3d
for Data file required by the Level 3 BLAS Test Suite
file blas/dblat3d
for Data file required by the Level 3 BLAS Test Suite
file blas/cblat3d
for Data file required by the Level 3 BLAS Test Suite
file blas/zblat3d
for Data file required by the Level 3 BLAS Test Suite
#
# MISCELLANEOUS AND AUXILIARY ROUTINES
#
file blas/i1mach.f
gams r1
for integer machine constants (like Fortran units for standard input)
file blas/r1mach.f
gams r1
for real machine constants (like "machine epsilon" and "biggest number")
file blas/d1mach.f
gams r1
for double precision machine constants
file blas/old1mach
gams r1
for machine constants for obsolete computers
file blas/machar.f
gams r1
prec single, double
, precisions can be extracted from the supplied source
, code with simple editing changes. NOTE: at least one
, version MUST be extracted before the source will compile.
for MACHAR is an evolving subroutine for dynamically determining thirteen
, fundamental parameters associated with floating-point arithmetic. The
, original version was published in Cody and Waite, Software Manual for
, the Elementary Functions, Prentice-Hall, 1980. The present version has
, been modified to operate correctly with IEEE floating-point arithmetic.
, It will malfunction on many CRAY and most CYBER systems, however. See
by W. J. Cody
ref "MACHAR: dynamically determine machine parameters," TOMS 14, Dec 1988
file blas/machar.c
gams r1
for C source for machar and a driver. Float and double
, versions are selected with compiler directives.
file blas/smach.f
for computes machine parameters of floating point
, arithmetic for use in testing only.
prec single
file blas/dmach.f
for computes machine parameters of floating point
, arithmetic for use in testing only.
prec double
file blas/cmach.f
for computes machine parameters of floating point
, arithmetic for use in testing only.
prec complex
file blas/zmach.f
for computes machine parameters of floating point
, arithmetic for use in testing only.
prec doublecomplex
file blas/slamch.f
for LAPACK routine to determine machine parameters
prec single
file blas/dlamch.f
for LAPACK routine to determine machine parameters
prec double
file blas/dgelu.f
file blas/dgelub.f
for LU factorization of an m-by-n matrix A
prec double
file blas/dmr
prec double
for DGEMM for IBM RS/6000 by Dongarra, Mayes, and Radicatti
gams D1b6
lang Fortran
file blas/scabs1.f
for computes absolute value of a complex number
, (Auxiliary Routine for a few Level 1 BLAS routines)
prec complex
file blas/dcabs1.f
for computes absolute value of a doublecomplex number
, (Auxiliary Routine for a few Level 1 BLAS routines)
prec doublecomplex
file blas/lsame.f
for Test if the characters are equal.
, (Auxiliary Routine in Level 2 and 3 BLAS routines)
file blas/xerbla.f
for error handler for the Level 2 and 3 BLAS routines.
, (Auxiliary Routine)
#
# LEVEL 1 BLAS ROUTINES
#
file blas/blas1.tgz
for Level 1 BLAS routines in all precisions
prec single, double, complex, doublecomplex
gams D1a
file blas/sblas1.f
for all the Level 1 BLAS for this type
prec single
gams D1a
file blas/dblas1.f
for all the Level 1 BLAS for this type
prec double
gams D1a
file blas/cblas1.f
for all the Level 1 BLAS for this type
prec complex
gams D1a
file blas/zblas1.f
for all the Level 1 BLAS for this type
prec doublecomplex
gams D1a
file blas/srotg.f
for setup Givens rotation
prec single
gams D1b10
file blas/drotg.f
for setup Givens rotation
prec double
gams D1b10
file blas/crotg.f
for setup Givens rotation
prec complex
gams D1b10
file blas/zrotg.f
for setup Givens rotation
prec doublecomplex
gams D1b10
file blas/srotmg.f
for setup modified Givens rotation
prec single
file blas/drotmg.f
for setup modified Givens rotation
prec double
file blas/srot.f
for apply Givens rotation
prec single
gams D1a8, D1b10
file blas/drot.f
for apply Givens rotation
prec double
gams D1a8, D1b10
file blas/csrot.f
for apply Givens rotation
prec complex
gams D1a8, D1b10
file blas/zdrot.f
for apply Givens rotation
prec doublecomplex
gams D1a8, D1b10
file blas/srotm.f
for apply modified Givens rotation
prec single
file blas/drotm.f
for apply modified Givens rotation
prec double
file blas/sswap.f
for swap x and y
prec single
gams D1a5
file blas/dswap.f
for swap x and y
prec double
gams D1a5
file blas/cswap.f
for swap x and y
prec complex
gams D1a5
file blas/zswap.f
for swap x and y
prec doublecomplex
gams D1a5
file blas/sscal.f
for x = a*x
prec single
gams D1a6
file blas/dscal.f
for x = a*x
prec double
gams D1a6
file blas/cscal.f
for x = a*x
prec complex
gams D1a6
file blas/zscal.f
for x = a*x
prec doublecomplex
gams D1a6
file blas/csscal.f
for x = a*x
prec complex
gams D1a6
file blas/zdscal.f
for x = a*x
prec doublecomplex
gams D1a6
file blas/scopy.f
for copy x into y
prec single
gams D1a5
file blas/dcopy.f
for copy x into y
prec double
gams D1a5
file blas/ccopy.f
for copy x into y
prec complex
gams D1a5
file blas/zcopy.f
for copy x into y
prec doublecomplex
gams D1a5
file blas/saxpy.f
for y = a*x + y
prec single
gams D1a7
file blas/daxpy.f
for y = a*x + y
prec double
gams D1a7
file blas/caxpy.f
for y = a*x + y
prec complex
gams D1a7
file blas/zaxpy.f
for y = a*x + y
prec doublecomplex
gams D1a7
file blas/sdot.f
for dot product
prec single
gams D1a4
file blas/ddot.f
for dot product
prec double
gams D1a4
file blas/sdsdot.f
for dot product with extended precision accumulation
file blas/dsdot.f
for dot product with extended precision accumulation and result
file blas/cdotu.f
for dot product
prec complex
gams D1a4
file blas/zdotu.f
for dot product
prec doublecomplex
gams D1a4
file blas/cdotc.f
for dot product, conjugating the first vector
prec complex
gams D1a4
file blas/zdotc.f
for dot product, conjugating the first vector
prec doublecomplex
gams D1a4
file blas/snrm2.f
for Euclidean norm
prec single
gams D1a3b
file blas/dnrm2.f
for Euclidean norm
prec double
gams D1a3b
file blas/scnrm2.f
for Euclidean norm
prec complex
gams D1a3b
file blas/dznrm2.f
for Euclidean norm
prec doublecomplex
gams D1a3b
file blas/sasum.f
for sum of absolute values
prec single
gams D1a3a
file blas/dasum.f
for sum of absolute values
prec double
gams D1a3a
file blas/scasum.f
for sum of absolute values
prec complex
gams D1a3a
file blas/dzasum.f
for sum of absolute values
prec doublecomplex
gams D1a3a
file blas/isamax.f
for index of max abs value
prec single
gams D1a2,D1a3c,N5a
file blas/idamax.f
for index of max abs value
prec double
gams D1a2,D1a3c,N5a
file blas/icamax.f
for index of max abs value
prec complex
gams D1a2,D1a3c,N5a
file blas/izamax.f
for index of max abs value
prec doublecomplex
gams D1a2,D1a3c,N5a
#
# LEVEL 2 BLAS ROUTINES
#
file blas/blas2.tgz
for Level 2 BLAS routines in all precisions
prec single, double, complex, doublecomplex
gams D1a
file blas/sblas2.f
for all the Level 2 BLAS for this type
prec single
gams D1a
file blas/dblas2.f
for all the Level 2 BLAS for this type
prec double
gams D1a
file blas/cblas2.f
for all the Level 2 BLAS for this type
prec complex
gams D1a
file blas/zblas2.f
for all the Level 2 BLAS for this type
prec doublecomplex
gams D1a
file blas/sblas2time.f
for timing the Level 2 BLAS
prec single
file blas/dblas2time.f
for timing the Level 2 BLAS
prec double
file blas/cblas2time.f
for timing the Level 2 BLAS
prec complex
file blas/zblas2time.f
for timing the Level 2 BLAS
prec doublecomplex
file blas/sgemv.f
for matrix vector multiply
prec single
gams D1b4
file blas/dgemv.f
for matrix vector multiply
prec double
gams D1b4
for matrix vector multiply
prec complex
gams D1b4
file blas/cgemv.f
file blas/zgemv.f
for matrix vector multiply
prec doublecomplex
gams D1b4
file blas/sgbmv.f
for banded matrix vector multiply
prec single
gams D1b4
file blas/dgbmv.f
for banded matrix vector multiply
prec double
gams D1b4
file blas/cgbmv.f
for banded matrix vector multiply
prec complex
gams D1b4
file blas/zgbmv.f
for banded matrix vector multiply
prec doublecomplex
gams D1b4
file blas/chemv.f
for hermitian matrix vector multiply
prec complex
gams D1b6
file blas/zhemv.f
for hermitian matrix vector multiply
prec doublecomplex
gams D1b6
file blas/chbmv.f
for hermitian banded matrix vector multiply
prec complex
gams D1b4
file blas/zhbmv.f
for hermitian banded matrix vector multiply
prec doublecomplex
gams D1b4
file blas/chpmv.f
for hermitian packed matrix vector multiply
prec complex
gams D1b4
file blas/zhpmv.f
for hermitian packed matrix vector multiply
prec doublecomplex
gams D1b4
file blas/ssymv.f
for symmetric matrix vector multiply
prec single
gams D1b4
file blas/dsymv.f
for symmetric matrix vector multiply
prec double
gams D1b4
file blas/ssbmv.f
for symmetric banded matrix vector multiply
prec single
gams D1b4
file blas/dsbmv.f
for symmetric banded matrix vector multiply
prec double
gams D1b4
file blas/sspmv.f
for symmetric packed matrix vector multiply
prec single
gams D1b4
file blas/dspmv.f
for symmetric packed matrix vector multiply
prec double
gams D1b4
file blas/strmv.f
for triangular matrix vector multiply
prec single
gams D1b4
file blas/dtrmv.f
for triangular matrix vector multiply
prec double
gams D1b4
file blas/ctrmv.f
for triangular matrix vector multiply
prec complex
gams D1b4
file blas/ztrmv.f
for triangular matrix vector multiply
prec doublecomplex
gams D1b4
file blas/stbmv.f
for triangular banded matrix vector multiply
prec single
gams D1b4
file blas/dtbmv.f
for triangular banded matrix vector multiply
prec double
gams D1b4
file blas/ctbmv.f
for triangular banded matrix vector multiply
prec complex
gams D1b4
file blas/ztbmv.f
for triangular banded matrix vector multiply
prec doublecomplex
gams D1b4
file blas/stpmv.f
for triangular packed matrix vector multiply
prec single
gams D1b4
file blas/dtpmv.f
for triangular packed matrix vector multiply
prec double
gams D1b4
file blas/ctpmv.f
for triangular packed matrix vector multiply
prec complex
gams D1b4
file blas/ztpmv.f
for triangular packed matrix vector multiply
prec doublecomplex
gams D1b4
file blas/strsv.f
for solving triangular matrix problems
prec single
gams D2a3,D2c3
file blas/dtrsv.f
for solving triangular matrix problems
prec double
gams D2a3,D2c3
file blas/ctrsv.f
for solving triangular matrix problems
prec complex
gams D2a3,D2c3
file blas/ztrsv.f
for solving triangular matrix problems
prec doublecomplex
gams D2a3,D2c3
file blas/stbsv.f
for solving triangular banded matrix problems
prec single
gams D2a3,D2a2,D2c2,D2c3
file blas/dtbsv.f
for solving triangular banded matrix problems
prec double
gams D2a3,D2a2,D2c2,D2c3
file blas/ctbsv.f
for solving triangular banded matrix problems
prec complex
gams D2a3,D2a2,D2c2,D2c3
file blas/ztbsv.f
for solving triangular banded matrix problems
prec doublecomplex
gams D2a3,D2a2,D2c2,D2c3
file blas/stpsv.f
for solving triangular packed matrix problems
prec single
gams D2a3,D2c3
file blas/dtpsv.f
for solving triangular packed matrix problems
prec double
gams D2a3,D2c3
file blas/ctpsv.f
for solving triangular packed matrix problems
prec complex
gams D2a3,D2c3
file blas/ztpsv.f
for solving triangular packed matrix problems
prec doublecomplex
gams D2a3,D2c3
file blas/sger.f
for performs the rank 1 operation A := alpha*x*y' + A,
prec single
gams D1b5
file blas/dger.f
for performs the rank 1 operation A := alpha*x*y' + A,
prec double
gams D1b5
file blas/cgeru.f
for performs the rank 1 operation A := alpha*x*y' + A
prec complex
gams D1a5
file blas/zgeru.f
for performs the rank 1 operation A := alpha*x*y' + A
prec doublecomplex
gams D1a5
file blas/cgerc.f
for performs the rank 1 operation A := alpha*x*conjg( y' ) + A
prec complex
gams D1a5
file blas/zgerc.f
for performs the rank 1 operation A := alpha*x*conjg( y' ) + A
prec doublecomplex
gams D1a5
file blas/cher.f
for hermitian rank 1 operation A := alpha*x*conjg(x') + A
prec complex
gams D1b5
file blas/zher.f
for hermitian rank 1 operation A := alpha*x*conjg(x') + A
prec doublecomplex
gams D1b5
file blas/chpr.f
for hermitian packed rank 1 operation A := alpha*x*conjg( x' ) + A
prec complex
gams D1b5
file blas/zhpr.f
for hermitian packed rank 1 operation A := alpha*x*conjg( x' ) + A
prec doublecomplex
gams D1b5
file blas/cher2.f
for hermitian rank 2 operation
, A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A
prec complex
gams D1b5
file blas/zher2.f
for hermitian rank 2 operation
, A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A
prec doublecomplex
gams D1b5
file blas/chpr2.f
for hermitian packed rank 2 operation
, A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A
prec complex
gams D1b5
file blas/zhpr2.f
for hermitian packed rank 2 operation
, A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A
prec doublecomplex
gams D1b5
file blas/ssyr.f
for performs the symmetric rank 1 operation A := alpha*x*x' + A
prec single
gams D1b5
file blas/dsyr.f
for performs the symmetric rank 1 operation A := alpha*x*x' + A
prec double
gams D1b5
file blas/sspr.f
for symmetric packed rank 1 operation A := alpha*x*x' + A
prec single
gams D1b5
file blas/dspr.f
for symmetric packed rank 1 operation A := alpha*x*x' + A
prec double
gams D1b5
file blas/ssyr2.f
for performs the symmetric rank 2 operation
, A := alpha*x*y' + alpha*y*x' + A
prec single
gams D1b5
file blas/dsyr2.f
for performs the symmetric rank 2 operation
, A := alpha*x*y' + alpha*y*x' + A
prec double
gams D1b5
file blas/sspr2.f
for performs the symmetric packed rank 2 operation
, A := alpha*x*y' + alpha*y*x' + A
prec single
gams D1b5
file blas/dspr2.f
for performs the symmetric packed rank 2 operation
, A := alpha*x*y' + alpha*y*x' + A
prec double
gams D1b5
#
# LEVEL 3 BLAS ROUTINES
#
file blas/blas3.tgz
for Level 3 BLAS routines in all precisions
prec single, double, complex, doublecomplex
gams D1b
file blas/sblas3.f
for all the Level 3 BLAS of this type
prec single
gams D1b
file blas/dblas3.f
for all the Level 3 BLAS of this type
prec double
gams D1b
file blas/cblas3.f
for all the Level 3 BLAS of this type
prec complex
gams D1b
file blas/zblas3.f
for all the Level 3 BLAS of this type
prec doublecomplex
gams D1b
file blas/sblas3time.f
for timing the Level 3 BLAS
prec single
file blas/dblas3time.f
for timing the Level 3 BLAS
prec double
file blas/cblas3time.f
for timing the Level 3 BLAS
prec complex
file blas/zblas3time.f
for timing the Level 3 BLAS
prec doublecomplex
file blas/sgemm.f
for matrix matrix multiply
prec single
gams D1b6
file blas/dgemm.f
for matrix matrix multiply
prec double
gams D1b6
file blas/cgemm.f
for matrix matrix multiply
prec complex
gams D1b6
file blas/zgemm.f
for matrix matrix multiply
prec doublecomplex
gams D1b6
file blas/ssymm.f
for symmetric matrix matrix multiply
prec single
gams D1b6
file blas/dsymm.f
for symmetric matrix matrix multiply
prec double
gams D1b6
file blas/csymm.f
for symmetric matrix matrix multiply
prec complex
gams D1b6
file blas/zsymm.f
for symmetric matrix matrix multiply
prec doublecomplex
gams D1b6
file blas/chemm.f
for hermitian matrix matrix multiply
prec complex
gams D1b6
file blas/zhemm.f
for hermitian matrix matrix multiply
prec doublecomplex
gams D1b6
file blas/ssyrk.f
for symmetric rank-k update to a matrix
prec single
gams D1b5
file blas/dsyrk.f
for symmetric rank-k update to a matrix
prec double
gams D1b5
file blas/csyrk.f
for symmetric rank-k update to a matrix
prec complex
gams D1b5
file blas/zsyrk.f
for symmetric rank-k update to a matrix
prec doublecomplex
gams D1b5
file blas/cherk.f
for hermitian rank-k update to a matrix
prec complex
gams D1b5
file blas/zherk.f
for hermitian rank-k update to a matrix
prec doublecomplex
gams D1b5
file blas/ssyr2k.f
for symmetric rank-2k update to a matrix
prec single
gams D1b5
file blas/dsyr2k.f
for symmetric rank-2k update to a matrix
prec double
gams D1b5
file blas/csyr2k.f
for symmetric rank-2k update to a matrix
prec complex
gams D1b5
file blas/zsyr2k.f
for symmetric rank-2k update to a matrix
prec doublecomplex
gams D1b5
file blas/cher2k.f
for hermitian rank-2k update to a matrix
prec complex
gams D1b5
file blas/zher2k.f
for hermitian rank-2k update to a matrix
prec doublecomplex
gams D1b5
file blas/strmm.f
for triangular matrix matrix multiply
prec single
gams D1b6
file blas/dtrmm.f
for triangular matrix matrix multiply
prec double
gams D1b6
file blas/ctrmm.f
for triangular matrix matrix multiply
prec complex
gams D1b6
file blas/ztrmm.f
for triangular matrix matrix multiply
prec doublecomplex
gams D1b6
file blas/strsm.f
for solving triangular matrix with multiple right hand sides
prec single
gams D2a3,D2c3
file blas/dtrsm.f
for solving triangular matrix with multiple right hand sides
prec double
gams D2a3,D2c3
file blas/ctrsm.f
for solving triangular matrix with multiple right hand sides
prec complex
gams D2a3,D2c3
file blas/ztrsm.f
for solving triangular matrix with multiple right hand sides
prec doublecomplex
gams D2a3,D2c3
#
# EXTENDED PRECISION LEVEL 2 BLAS
#
file blas/ecblas2.f
for all the Level 2 BLAS for this type, with extended
, precision accumulation
prec complex
gams D1a
file blas/ecgbmv.f
file blas/ecgemv.f
for performs one of the matrix-vector operations:
, y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y,
, or y := alpha*conjg( A' )*x + beta*y
file blas/ecgerc.f
for performs the rank 1 operation A := alpha*x*conjg( y' ) + A
file blas/ecgeru.f
for performs the rank 1 operation A := alpha*x*y' + A
file blas/echemv.f
file blas/echbmv.f
file blas/echpmv.f
for performs the matrix-vector operation y := alpha*A*x + beta*y
file blas/echer.f
for performs the hermitian rank 1 operation A := alpha*x*conjg( x' ) + A
file blas/echer2.f
for hermitian rank 2 operation
, A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A
file blas/echpr.f
for hermitian rank 1 operation A := alpha*x*conjg( x' ) + A
file blas/echpr2.f
for hermitian rank 2 operation
, A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A
file blas/ectrmv.f
file blas/ectbmv.f
file blas/ectpmv.f
for performs one of the matrix-vector operations
, x := A*x, or x := A'*x, or x := conjg( A' )*x
file blas/ectrsv.f
file blas/ectbsv.f
file blas/ectpsv.f
for solves one of the systems of equations
, A*x = b, or A'*x = b, or conjg( A' )*x = b
file blas/esblas2.f
for all the Level 2 BLAS for this type, with extended
, precision accumulation
prec single
gams D1a
file blas/esgbmv.f
file blas/esgemv.f
for performs one of the matrix-vector operations
, y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y
file blas/esger.f
for performs the rank 1 operation A := alpha*x*y' + A
, where alpha is a scalar, x is an m element vector, y is an n element
, vector and A is an m by n matrix.
file blas/essymv.f
file blas/essbmv.f
file blas/esspmv.f
for performs the matrix-vector operation y := alpha*A*x + beta*y
file blas/essyr.f
file blas/esspr.f
for performs the symmetric rank 1 operation A := alpha*x*x' + A
, where alpha is a real scalar, x is an n element vector and A is an
, n by n symmetric matrix.
file blas/essyr2.f
file blas/esspr2.f
for performs the symmetric rank 2 operation
, A := alpha*x*y' + alpha*y*x' + A, where alpha is a scalar, x and
, y are n element vectors and A is an n by n symmetric matrix.
file blas/estrmv.f
file blas/estbmv.f
file blas/estpmv.f
for performs one of the matrix-vector operations x := A*x, or x := A'*x
, where x is n element vector and A is an n by n unit, or non-unit,
, upper or lower triangular matrix.
file blas/estrsv.f
file blas/estbsv.f
file blas/estpsv.f
for solves one of the systems of equations A*x = b, or A'*x = b,
, where b and x are n element vectors and A is an n by n unit, or
, non-unit, upper or lower triangular matrix.
file blast/blast-comm
file blast/blast-core
file blast/blast-funct
file blast/blast-lite
file blast/blast-parallel
file blast/blast-sparse
file blast/blast-lb
file blast/blast-nearterm
file bmp/descr.deck
for description of sorts of a multi-precision arithmetic in Fortran
file bmp/istkgt.f
for stack allocation routines for the multi-precision arithmetic package
file bmp/mcsupport.f
for multi-precision complex arithmetic in a meta-Fortran
file bmp/mcsupport.aug
for multi-precision complex artihmetic using bmp routines
file bmp/mp.f
for multi-precision arithmetic in Fortran
size 237 kB
file bmp/msupport.f
for multi-precision mathematical functions using bmp routines
file bmp/msupport2.f
for multi-precision arithmetic auxillary routines in a meta-Fortran
file bmp/msupport2.aug
for auxillary routines for (mp)
file bmp/seterr.f
for error handling routines
file bmp/test1.f
for a test code for the multi-precision arithmetic package
file bmp/test2.f
for a test code for the multi-precision arithmetic package
file bmp/guide
for user's guide
file c++/answerbook/2.1
file c++/answerbook/2.10
file c++/answerbook/2.11
file c++/answerbook/2.12
file c++/answerbook/2.13
file c++/answerbook/2.14
file c++/answerbook/2.2
file c++/answerbook/2.3
file c++/answerbook/2.4
file c++/answerbook/2.5
file c++/answerbook/2.6
file c++/answerbook/2.7
file c++/answerbook/2.8
file c++/answerbook/2.9
file c++/answerbook/3.1
file c++/answerbook/3.10
file c++/answerbook/3.11
file c++/answerbook/3.12
file c++/answerbook/3.13
file c++/answerbook/3.14
file c++/answerbook/3.15
file c++/answerbook/3.16
file c++/answerbook/3.17
file c++/answerbook/3.2
file c++/answerbook/3.3
file c++/answerbook/3.4
file c++/answerbook/3.5
file c++/answerbook/3.6
file c++/answerbook/3.7
file c++/answerbook/3.8
file c++/answerbook/3.9
file c++/answerbook/4.1
file c++/answerbook/4.10
file c++/answerbook/4.11
file c++/answerbook/4.12
file c++/answerbook/4.13
file c++/answerbook/4.14
file c++/answerbook/4.15
file c++/answerbook/4.16
file c++/answerbook/4.17
file c++/answerbook/4.2
file c++/answerbook/4.3
file c++/answerbook/4.4
file c++/answerbook/4.5
file c++/answerbook/4.6
file c++/answerbook/4.7
file c++/answerbook/4.8
file c++/answerbook/4.9
file c++/answerbook/5.1
file c++/answerbook/5.10
file c++/answerbook/5.11
file c++/answerbook/5.12
file c++/answerbook/5.2
file c++/answerbook/5.3
file c++/answerbook/5.4
file c++/answerbook/5.5
file c++/answerbook/5.6
file c++/answerbook/5.7
file c++/answerbook/5.8
file c++/answerbook/5.9
file c++/answerbook/6.1
file c++/answerbook/6.10
size 735 kB
file c++/answerbook/6.11
size 593 kB
file c++/answerbook/6.12
file c++/answerbook/6.13
file c++/answerbook/6.14
file c++/answerbook/6.15
file c++/answerbook/6.16
file c++/answerbook/6.17
file c++/answerbook/6.18
file c++/answerbook/6.2
file c++/answerbook/6.3
file c++/answerbook/6.4
file c++/answerbook/6.5
file c++/answerbook/6.6
file c++/answerbook/6.7
file c++/answerbook/6.8
file c++/answerbook/6.9
file c++/answerbook/7.1
file c++/answerbook/7.10
file c++/answerbook/7.2
file c++/answerbook/7.3
file c++/answerbook/7.4
file c++/answerbook/7.5
file c++/answerbook/7.6
file c++/answerbook/7.7
file c++/answerbook/7.8
file c++/answerbook/7.9
file c++/answerbook/8.1
file c++/answerbook/8.10
file c++/answerbook/8.11
file c++/answerbook/8.12
file c++/answerbook/8.13
file c++/answerbook/8.2
file c++/answerbook/8.3
file c++/answerbook/8.4
file c++/answerbook/8.5
file c++/answerbook/8.6
file c++/answerbook/8.7
file c++/answerbook/8.8
file c++/answerbook/8.9
file c++/answerbook/appendixb
file c++/answerbook/shape
file c++/answerbook/tools
file c++/answerbook/changes
file c++/answerbook/readme
file c++/idioms/10-1.c
file c++/idioms/10-2.c
file c++/idioms/11-2.c
file c++/idioms/2-2a.c
file c++/idioms/2-2b.c
file c++/idioms/2-4.c
file c++/idioms/2-5.c
file c++/idioms/2-8.c
file c++/idioms/2angle.h
file c++/idioms/2const.c
file c++/idioms/2funcp.c
file c++/idioms/2pi1.c
file c++/idioms/2pi2.c
file c++/idioms/2smf.c
file c++/idioms/2table.c
file c++/idioms/3-1.c
file c++/idioms/3-10.c
file c++/idioms/3-10.h
file c++/idioms/3-11.h
file c++/idioms/3-12.c
file c++/idioms/3-13.c
file c++/idioms/3-14.h
file c++/idioms/3-15.c
file c++/idioms/3-16.c
file c++/idioms/3-18.c
file c++/idioms/3-19.c
file c++/idioms/3-2.c
file c++/idioms/3-3.c
file c++/idioms/3-4.c
file c++/idioms/3-6.h
file c++/idioms/3-7.c
file c++/idioms/3-8.c
file c++/idioms/3-9.c
file c++/idioms/3ctdstk.c
file c++/idioms/4-1.c
file c++/idioms/4-2.c
file c++/idioms/4-3.c
file c++/idioms/4-4.c
file c++/idioms/4-5.c
file c++/idioms/5-10.c
file c++/idioms/5-11.c
file c++/idioms/5-12.c
file c++/idioms/5-13.c
file c++/idioms/5-14.c
file c++/idioms/5-15.c
file c++/idioms/5-16.c
file c++/idioms/5-17.c
file c++/idioms/5-18.c
file c++/idioms/5-19.c
file c++/idioms/5-2.c
file c++/idioms/5-20.c
file c++/idioms/5-21.c
file c++/idioms/5-22.c
file c++/idioms/5-23.c
file c++/idioms/5-5.c
file c++/idioms/5-7.c
file c++/idioms/5-8.c
file c++/idioms/5-9.c
file c++/idioms/5nmarow.c
file c++/idioms/5nmatom.c
file c++/idioms/5num.c
file c++/idioms/6-4.c
file c++/idioms/7-1.c
file c++/idioms/7-2.c
file c++/idioms/7-3.c
file c++/idioms/7-4.c
file c++/idioms/7-5.c
file c++/idioms/8-1.c
file c++/idioms/8-2.h
file c++/idioms/8-3a.c
file c++/idioms/8-3b.c
file c++/idioms/8-5.c
file c++/idioms/9-10.c
file c++/idioms/9-11.c
file c++/idioms/9-13.c
file c++/idioms/9-2.c
file c++/idioms/9-3.h
file c++/idioms/9-4.h
file c++/idioms/9-5.h
file c++/idioms/9-6.h
file c++/idioms/9-7.h
file c++/idioms/9-8.h
file c++/idioms/appa.c
file c++/idioms/ecoord.h
file c++/idioms/ek.c
file c++/idioms/ek.h
file c++/idioms/eload.c
file c++/idioms/emain.c
file c++/idioms/emptr.h
file c++/idioms/erect.c
file c++/idioms/erect.h
file c++/idioms/eshape.c
file c++/idioms/eshape.h
file c++/idioms/eshaprp.c
file c++/idioms/eshaprp.h
file c++/idioms/etop.c
file c++/idioms/etringl.c
file c++/idioms/etringl.h
file c++/idioms/ev2tri.c
file c++/idioms/ev2tri.h
file c++/idioms/ev3tri.h
file c++/idioms/ev3tria.c
file c++/idioms/ev3trib.c
file c++/idioms/ev3tric.c
file c++/idioms/ev3trim.c
file c++/idioms/fbubble.c
file c++/idioms/fvideo.c
file c++/idioms/fvideo2.c
file c++/idioms/readme
file c++/links.html
for pointers to related resources
lib c++/answerbook
for code from Hansen's C++ Answers book
by Tony L. Hansen
ref "The C++ Answer Book", Addison-Wesley, 1990, ISBN 0-302-11497-6
lib c++/idioms
for code from Coplien's, "Advanced C++ Programming Styles and Idioms"
by James O. Coplien
ref "Advanced C++ Programming Styles and Idioms", Addison-Wesley, 1992, ISBN 0-201-54855-0
file c++/fft.tgz
for Radix-2 Fast Fourier Transform, real or complex; sin/cos transform
by Oleg Kiselyov
see c++/linalg.tgz
file c++/linalg.tgz
for basic linear algebra classes and applications (SVD,
# interpolation, multivariate optimization)
by Oleg Kiselyov
prec single/double
# singular value decomposition (SVD), regularized solution of
, simultaneous linear equations (with possibly rectangular matrices)
, and (pseudo)matrix inverse.
, also includes Aitken-Lagrange
, interpolation over the table of uniform or arbitrary mesh, and a
, Hook-Jeevse local multidimensional minimizer
, Matrix views, various Matrix
, streams, and LazyMatrices. Lazy construction allows one to write
, matrix expressions in a natural way while imposing no hidden
, temporaries, no deep copying, and no reference counting.
file c++/serv_cc.shar
for a couple of functions that ought to be in the standard
, C++ environment;
, - Updated G++ class File that allows now for the file name to
, include pipes, say,
, File in_file("zcat aaa.Z |","r");
, - Resource facility, or managing global "private" parameters
, that specify various program "options". It helps keep
, reasonable number of arguments in function calls.
by Oleg Kiselyov
file c++/shar.shar
for Builder for the .shar archive.
by Oleg Keselyov 22 Feb 1996
# see also /netlib/access/unshar.c
lib c++/mxyzptlk
for C++ implementation of differential algebra
by Leo Michelotti
file c++/lparx-1.0.tar.Z
for LPARX provides efficient run-time support for dynamic, non-uniform
, scientific calculations running on MIMD distributed memory
, architectures. It extends HPF's data decomposition model to provide
, support for dynamic, block irregular data structures. LPARX
, represents data decompositions as first-class objects and expresses
, data dependencies in a manner which is logically independent of data
, decomposition and problem dimension. LPARX applications are portable
, across a diversity of MIMD machines.
by Scott Baden and Scott Kohn
size 1.8 MB
file c++/mxyzptlk/cxxlibr.src
file c++/mxyzptlk/header.src
file c++/mxyzptlk/index
file c++/mxyzptlk/makefile
file c++/mxyzptlk/matrix.src
file c++/mxyzptlk/mxyzptlk.src
size 279 kB
file c++/mxyzptlk/read.me
for copyright notice
file c++/mxyzptlk/read.me.too
for mxyzptlk revision history
file c++/mxyzptlk/rebuild
file c++/mxyzptlk/tests.src
file c++/mxyzptlk/util.src
size 263 kB
lib c/meschach
by David E. Stewart des@thrain.anu.edu.au
for numerical linear algebra, dense and sparse, with permutations,
, error handling, input/output,
, dynamic allocation, de-allocation, re-sizing and copying of objects,
, dense complex matrices and vectors as well as real matrices
, and vectors,
, input and output routines for these objects, and MATLAB
, save/load format,
, error/exception handling,
, basic numerical linear algebra -- linear combinations, inner
, products, matrix-vector and matrix-matrix products,
, including transposed and adjoint forms,
, vector min, max, sorting, componentwise products, quotients,
, dense matrix factorise and solve -- LU, Cholesky, LDL^T, QR,
, QR with column pivoting, symmetric indefinite (BKP),
, dense matrix factorisation update routines -- LDL^T, QR
, (real matrix updates only),
, eigenvector/eigenvalue routines -- symmetric, real Schur
, decomposition, SVD, extract eigenvector,
, sparse matrix "utility" routines,
, sparse matrix factorise and solve -- Cholesky, LU and BKP
, (Bunch-Kaufman-Parlett symmetric indefinite factorisation),
, sparse incomplete factorisations -- Cholesky and LU,
, iterative techniques -- pre-conditioned conjugate gradients,
, CGNE, LSQR, CGS, GMRES, MGCR, Lanczos, Arnoldi,
, allowance for "procedurally defined" matrices in the iterative
, techniques,
, various "torture" routines for checking aspects of Meschach,
, memory tracking for locating memory leaks
lang C
prec double
# true master copy: ftp thrain.anu.edu.au:pub/meschach/
file c/dcg.shar
for Preconditioned Conjugate Gradient
by Mark Seager, LLNL.
file c/sge.shar
for LINPACK functions SGECO/SGEFA/SGESL
, (dense matrix conditon number estimate, factorization and solution
, routines) and some of the BLAS in C. There is a driver which shows
, how to set up column oriented matrices in C for these routines.
by Mark K. Seager (seager@lll-crg.llnl.gov) 4/8/88.
gams d2a1
file c/frac
for finds rational approximation to floating point value
by Robert Craig, AT&T Bell Labs - Naperville
ref Jerome Spanier and Keith B. Oldham, "An Atlas of Functions," Springer-Verlag, 1987, pp. 665-7.
gams a2, a6c
file c/brent.shar
for Brent's univariate minimizer and zero finder.
by Oleg Keselyov May 23, 1991
ref G.Forsythe, M.Malcolm, C.Moler, Computer methods for mathematical computations.
# Contains the source code for the program fminbr.c and
# zeroin.c, test drivers for both, and verifivation protocols.
see serv.shar
gams f1b, g1a2
file c/serv.shar
for numerical programming in C
# These files are needed to compile the programs in packages
# brent.shar *vector.shar shar.shar task_env.shar
# Verification programs and data are included as well.
by Oleg Keselyov May 23, 1991
gams l6a14, n1, r1
file c/vector.shar
for Low and Intermediate Level functions to manage vectors in C.
# In fact, the vector declaration as a special structure and
# a wide set of procedures to handle it define a class (in
# the sence of C++ or SMALLTALK). It is still a common C,
# however.
# Features: high reliability and fool-proof checking, the
# user can operate on single elements of the vector in the
# customary C manner, or he may wish to handle the vector as
# a whole (as an atomary object) with high-effective functions
# (that can clear the vector, assign vectors or obtain their
# scalar product, find the vector norm(s), etc.).
by Oleg Keselyov May 23, 1991
gams d1a
file c/hl_vector.shar
for high level vector operations. Involves the
, Aitken-Lagrange interpolation over the table of uniform or
, arbitrary mesh, Hook-Jeevse local multidimensional minimizer.
by Oleg Keselyov May 23, 1991
gams e2a, g1b2
file c/task_env.shar
for Resource facility, or managing global "private" parameters
, that specify various program "options". It help keep
, reasonable number of arguments in function calls.
by Oleg Keselyov May 23, 1991
gams z
file c/numcomp-free-c
for index of free source code for numerical computation written in C or C++
by Ajay Shah
gams z
file c/sgefa.shar
# see also ode/cvode.tar.Z
file c/bcc.tar.gz
for bounds checking patches for gcc
by Richard W.M. Jones
alg tracks heap, stack, and static objects and checks all references
size 692 kB
ref ftp://dse.doc.ic.ac.uk/pub/misc/bcc/bounds-checking-*-*.tgz
# requires source for gcc
file c/meschach/meschach0.shar
for housekeeping routines + utility stuff
size 429 kB
file c/meschach/meschach1.shar
for basic dense linear algebra
file c/meschach/meschach2.shar
for dense factorisations
file c/meschach/meschach3.shar
for sparse matrix operations
file c/meschach/meschach4.shar
for complex matrix operations
file c/meschach/oldmeschach.shar
file c/meschach/rcs_logs
file c/meschach/readme
file ccm/tars/api.tar
file ccm/tars/mpi_src.tar
file ccm/tars/shmem_src.tar
file ccm/tars/test.tar
file ccm/tars/time.tar
file ccm/pages/api/ccm_allreduce_x1.f90
file ccm/pages/api/ccm_allreduce_x2.f90
file ccm/pages/api/ccm_alltoall_x1.f90
file ccm/pages/api/ccm_alltoallv_x1.f90
file ccm/pages/api/ccm_alltoallv_x2.f90
file ccm/pages/api/ccm_barrier_x1.f90
file ccm/pages/api/ccm_bcast_x1.f90
file ccm/pages/api/ccm_bcast_x2.f90
file ccm/pages/api/ccm_checkin_x1.f90
file ccm/pages/api/ccm_close_x1.f90
file ccm/pages/api/ccm_gather_x1.f90
file ccm/pages/api/ccm_gather_x2.f90
file ccm/pages/api/ccm_gatherv_x1.f90
file ccm/pages/api/ccm_gatherv_x2.f90
file ccm/pages/api/ccm_info_x1.f90
file ccm/pages/api/ccm_info_x2.f90
file ccm/pages/api/ccm_init_x1.f90
file ccm/pages/api/ccm_init_x2.f90
file ccm/pages/api/ccm_reduce_x1.f90
file ccm/pages/api/ccm_reduce_x2.f90
file ccm/pages/api/ccm_scatter_x1.f90
file ccm/pages/api/talk
file ccm/pages/api/ccm_scatter_x2.f90
file ccm/pages/api/ccm_scatterv_x1.f90
file ccm/pages/api/ccm_scatterv_x2.f90
file ccm/pages/api/ccm_testing_x1.f90
file ccm/pages/api/ccm_time_x1.f90
file ccm/pages/api/ccm_unique_x1.f90
file ccm/pages/api/ccm_warning_x1.f90
file ccm/pages/api/makefile
file ccm/pages/api/api.tar
file ccm/pages/api/mpi_src.tar
file ccm/pages/api/shmem_src.tar
file ccm/pages/api/test.tar
file ccm/pages/api/time.tar
file cephes/cephes.doc
for documentation of cephes package as plain text
file cephes/qlibdoc.html
for documentation of cephes extended precision special functions
file cephes/singldoc.html
for documentation of cephes single precision special functions
file cephes/ldoubdoc.html
for documentation of cephes 80-bit precision special functions
file cephes/doubldoc.html
for documentation of cephes double precision special functions
file cephes/128bdoc.html
for documentation of cephes 128-bit precision special functions
file cephes/128bit.tgz
for arithmetic and math functions for 128-bit reals
size 252kB
file cephes/bessel.tgz
for Bessel and hypergeometric functions
# needs cprob/gamma.c and eval.tgz or cmath.tgz
file cephes/c9x-complex.tgz
for support of complex type as in the C9X standard
size 455kB
file cephes/cmath.tgz
for double precision elementary functions
# also contains mod2pi.c to test range reduction of trig functions
# and mtst.c to check consistency of math functions
# Some of the functions defined here are also defined in Standard C
# or in the widely distribued 4.3BSD math collection:
# acos StandardC
# acosh 4.3BSD
# asin StandardC
# asinh 4.3BSD
# atan StandardC
# atan2 StandardC
# atanh 4.3BSD
# cbrt 4.3BSD
# ceil StandardC
# chbevl cephes
# cos StandardC
# cosh StandardC
# cot cephes
# drand cephes
# exp StandardC
# exp10 cephes
# fabs StandardC
# floor StandardC
# frexp StandardC
# ldexp StandardC
# log StandardC
# log10 StandardC
# mtherr cephes
# p1evl cephes
# polevl cephes
# pow StandardC
# powi cephes
# radian cephes
# ranwh cephes
# round cephes
# sin StandardC
# sincos cephes
# sinh StandardC
# sqrt StandardC
# tan StandardC
# tanh StandardC
# Be aware that the tabulated error behavior for
# other functions in cephes depends on the quality of these
# elementary functions, which is not specified by Standard C.
file cephes/cprob.tgz
for probability integrals and their inverses
# needs eval.tgz or cmath.tgz
file cephes/ellf.tgz
for elliptic integrals and elliptic filter calculator
# needs eval.tgz or cmath.tgz
file cephes/eval.tgz
for mconf.h, mtherr.c, polevl.c, chbevl.c used by other cephes functions
# This is a subset of cmath.tgz.
file cephes/ieee.tgz
for floating point arithmetic in standard precisions
# needs eval.tgz or cmath.tgz
file cephes/ldouble.tgz
for IEEE 80-bit extended real elementary functions
# needs eval.tgz or cmath.tgz
size 225 kB
file cephes/linalg.tgz
for C translations of eigens, lmdif
# needs eval.tgz or cmath.tgz
file cephes/ode.tgz
file cephes/misc.tgz
for fresnel integrals, polylogarithms, Planck radiation formula...
for Adams-Bashforth-Moulton and Runge-Kutta, solar system integration
# needs eval.tgz or cmath.tgz
file cephes/polyn.tgz
for arithmetic on rationals and polynomials
# needs eval.tgz or cmath.tgz
file cephes/qfloat.tgz
for 144- or 336-bit precision floating point arithmetic and functions
# needs eval.tgz or cmath.tgz
file cephes/remes.tgz
for minimax rational approximation
# needs eval.tgz or cmath.tgz
file cephes/readme
file cephes/single.tgz
for 32-bit floating point versions of cephes functions
# chammp
# ======
#
# This directory contains items relating to the numerical solution
# of the shallow water equations in spherical geometry.
# The shallow water equations are used as a kernel for both
# oceanic and atomospheric general circulation models and
# are of interest in evaluating numerical methods for weather
# forecasting and climate modeling. The DOE Computer Hardware,
# Advanced Mathematics and Model Physics (CHAMMP) program
# is interested in the development of new mathematical methods
# for these problems. To promote this developmet, a set of
# test cases has been proposed and example software and reference
# solutions are provided.
file chammp/shallow.tex
for LaTeX document containing benchmarks and results pertaining to
, shallow water equation solution methods.
, To retrieve from netlib type: "send shallow.tex from chammp"
age Last updated: 10/1/93
file chammp/shallow.bib
for LaTeX bibliography file of articles and reports dealing with
, the test cases.
, To retrieve from netlib type: "send shallow.bib from chammp"
age Last updated: 10/1/93
file chammp/stswm.tgz
for NCAR spectral transform shallow water model and documentation.
, This code computes reference solutions for all test cases in
, [Reference solutions generated by this code are available by
, anonymous ftp from ftp.ucar.edu (IP address 128.117.64.4)
, in directory chammp/shallow.]
by Authors J.J. Hack and R. Jakob
, Williamson et. al., JCP Vol 102, p. 211-224 (1992).
age Last updated: 10/1/93
file chammp/pstswm.tgz
for Parallel version of stswm for message passing parallel computers.
, Contains a variety of parallel algorithms implementing the
, spectral transform method. Code useful for comparison of
, parallel algorithms: transpose vs. transform, overlapped vs.
, nonoverlapped communication, etc. Uses PICL for portability.
by P.H. Worley and I.T. Foster
age Last updated: 10/1/93
file cheney-kincaid/pi.f
ref text 4
for Simple code to illustrate programming in double precision
file cheney-kincaid/exp.f
ref text 11-12
for First programming experiment
file cheney-kincaid/xsinx.f
ref text 63-65
for Example of programming f(x) = x - sin(x) carefully (F)
file cheney-kincaid/bisect1.f
ref text 77-78
for First version of Bisection method (BISECT,F,G)
file cheney-kincaid/bisect2.f
ref text 77-78
for Second version of Bisection method (BISECT,F,G)
file cheney-kincaid/newton.f
ref text 85-86
for Sample Newton method program
file cheney-kincaid/coef.f
ref text 117-118
for Newton interpolation polynomial for sin(x) at equidistant points (COEF,EVAL)
file cheney-kincaid/deriv.f
ref text 141-142
for Derivative by center differences and Richardson extrapolation (DERIV,F)
file cheney-kincaid/ulsum.f
ref text 155-156
for Upper and lower sums programming experiment for an integral
file cheney-kincaid/trap.f
ref text 161
for Trapezoid rule programming experiment for an integral
file cheney-kincaid/rombrg.f
ref text 173-174
for Romberg arrays for three separate functions (ROMBRG,F,G,P)
file cheney-kincaid/simp.f
ref text 187-190
for Adaptive scheme for Simpson's rule (SIMP,ASMP,PUSH,POP,FCN)
file cheney-kincaid/ngauss.f
ref text 208-209
for Naive Gaussian elimination to solve linear systems (NGAUSS)
file cheney-kincaid/gauss.f
ref text 220-223
for Gaussian elimination with scaled partial pivoting (GAUSS,SOLVE,TSTGAUS)
file cheney-kincaid/triqnt.f
ref text 233-236
for Solves tridiagonal & pentadiagonal linear systems (TRI,PENTA)
file cheney-kincaid/spl1.f
ref text 261
for Interpolates table using a first-degree spline function (SPL1)
file cheney-kincaid/spl3.f
ref text 277-278
for Natural cubic spline function for sin(x) at equidistant points (SPL3,ZSPL3)
file cheney-kincaid/aspl2.f
ref text 297-298
for Interpolates table using a quadratic B-spline function (ASPL2,BSPL2)
file cheney-kincaid/sch.f
ref text 300
for Interpolates table using Schoenberg's process (SCH,ESCH,F)
file cheney-kincaid/euler.f
ref text 306-307
for Euler's method for solving an ordinary differential equation
file cheney-kincaid/taylor.f
ref text 307-308
for Taylor series method (order 4) for solving an ordinary differential equation
file cheney-kincaid/rk4.f
ref text 315-316
for Runge-Kutta method of order 4 for solving an initial value problem (RK4,F)
file cheney-kincaid/rk45.f
ref text 326
for Runge-Kutta-Fehlberg method for solving an initial value problem (RK45,F)
file cheney-kincaid/rk45ad.f
ref text 326-328
for Adaptive scheme based on Runge-Kutta-Fehlberg method (RK45AD,RK45,F)
file cheney-kincaid/random.f
ref text 337
for Example to compute, store, and print random numbers (RANDOM)
file cheney-kincaid/testra.f
ref text 338
for Coarse check on the random-number generator (RANDOM)
file cheney-kincaid/mctst1.f
ref text 347
for Volume of a complicated region in three-space by Monte Carlo (RANDOM)
file cheney-kincaid/mctst2.f
ref text 345-346
for Numerical value of integral over a disk in xy-space by Monte Carlo (RANDOM)
file cheney-kincaid/cone.f
ref text 348
for Ice cream cone example (RANDOM)
file cheney-kincaid/sim1.f
ref text 351-352
for Loaded die problem simulation (RANDOM)
file cheney-kincaid/brthdy.f
ref text 352-354
for Birthday problem simulation (PROB,BRTHDY,RANDOM)
file cheney-kincaid/sim2.f
ref text 354-355
for Buffon's needle problem simulation (RANDOM)
file cheney-kincaid/sim3.f
ref text 355-356
for Two dice problem simulation (RANDOM)
file cheney-kincaid/sim4.f
ref text 356-358
for Neutron shielding problem simulation (RANDOM)
file cheney-kincaid/taysys.f
ref text 393
for Taylor series method (order 4) for system of ordinary differential equations
file cheney-kincaid/rk4sys.f
ref text 394-396
for Runge-Kutta method of order 4 for a system of ode's (RK4SYS,XPSYS)
file cheney-kincaid/amrk.f
ref text 406-408
for Adams-Moulton method for systems of ode's (AMRK,RKSYS,AMSYS,XPSYS)
file cheney-kincaid/amrkad.f
ref text 408-409
for Adaptive scheme for Adams-Moulton method for systems of ode's
, (AMRKAD,XPSYS,AMSYS,AMRK,RKSYS)
file cheney-kincaid/bvp1.f
ref text 418-420
for Boundary value problem solved by discretization technique (TRI)
file cheney-kincaid/bvp2.f
ref text 421-423
for Boundary value problem solved by shooting method (RK4SYS,XPSYS)
file cheney-kincaid/pde1.f
ref text 433
for Parabolic partial differential equation problem
file cheney-kincaid/pde2.f
ref text 434
for Parabolic pde problem solved by Crank-Nicolson method (TRI)
file cheney-kincaid/string.f
ref text 441-442
for Hyperbolic pde problem solved by discretization (F,TRUE)
file cheney-kincaid/seidel.f
ref text 449-451
for Elliptic pde solved by discretization and Gauss-Seidel method
, (SEIDEL,F,G,BNDY,USTART,TRUE)
file cheney-kincaid/info-code.tex
for TeX file with general code information
file cheney-kincaid/info-code.tty
for text file with general code information
file cheney-kincaid/changes
file cheney-kincaid/makefile
file clapack/cblas/caxpy.c
file clapack/cblas/ccopy.c
file clapack/cblas/cdotc.c
file clapack/cblas/cdotu.c
file clapack/cblas/cgbmv.c
file clapack/cblas/cgemm.c
file clapack/cblas/cgemv.c
file clapack/cblas/cgerc.c
file clapack/cblas/cgeru.c
file clapack/cblas/chbmv.c
file clapack/cblas/chemm.c
file clapack/cblas/chemv.c
file clapack/cblas/cher.c
file clapack/cblas/cher2.c
file clapack/cblas/cher2k.c
file clapack/cblas/cherk.c
file clapack/cblas/chpmv.c
file clapack/cblas/chpr.c
file clapack/cblas/chpr2.c
file clapack/cblas/crotg.c
file clapack/cblas/cscal.c
file clapack/cblas/csscal.c
file clapack/cblas/cswap.c
file clapack/cblas/csymm.c
file clapack/cblas/csyr2k.c
file clapack/cblas/csyrk.c
file clapack/cblas/ctbmv.c
file clapack/cblas/ctbsv.c
file clapack/cblas/ctpmv.c
file clapack/cblas/ctpsv.c
file clapack/cblas/ctrmm.c
file clapack/cblas/ctrmv.c
file clapack/cblas/ctrsm.c
file clapack/cblas/ctrsv.c
file clapack/cblas/dasum.c
file clapack/cblas/daxpy.c
file clapack/cblas/dcabs1.c
file clapack/cblas/dcopy.c
file clapack/cblas/ddot.c
file clapack/cblas/dgbmv.c
file clapack/cblas/dgemm.c
file clapack/cblas/dgemv.c
file clapack/cblas/dger.c
file clapack/cblas/dnrm2.c
file clapack/cblas/drot.c
file clapack/cblas/drotg.c
file clapack/cblas/dsbmv.c
file clapack/cblas/dscal.c
file clapack/cblas/dspmv.c
file clapack/cblas/dspr.c
file clapack/cblas/dspr2.c
file clapack/cblas/dswap.c
file clapack/cblas/dsymm.c
file clapack/cblas/dsymv.c
file clapack/cblas/dsyr.c
file clapack/cblas/dsyr2.c
file clapack/cblas/dsyr2k.c
file clapack/cblas/dsyrk.c
file clapack/cblas/dtbmv.c
file clapack/cblas/dtbsv.c
file clapack/cblas/dtpmv.c
file clapack/cblas/dtpsv.c
file clapack/cblas/dtrmm.c
file clapack/cblas/dtrmv.c
file clapack/cblas/dtrsm.c
file clapack/cblas/dtrsv.c
file clapack/cblas/dzasum.c
file clapack/cblas/dznrm2.c
file clapack/cblas/icamax.c
file clapack/cblas/idamax.c
file clapack/cblas/index
file clapack/cblas/isamax.c
file clapack/cblas/izamax.c
file clapack/cblas/lsame.c
file clapack/cblas/sasum.c
file clapack/cblas/saxpy.c
file clapack/cblas/scasum.c
file clapack/cblas/scnrm2.c
file clapack/cblas/scopy.c
file clapack/cblas/sdot.c
file clapack/cblas/sgbmv.c
file clapack/cblas/sgemm.c
file clapack/cblas/sgemv.c
file clapack/cblas/sger.c
file clapack/cblas/snrm2.c
file clapack/cblas/srot.c
file clapack/cblas/srotg.c
file clapack/cblas/ssbmv.c
file clapack/cblas/sscal.c
file clapack/cblas/sspmv.c
file clapack/cblas/sspr.c
file clapack/cblas/sspr2.c
file clapack/cblas/sswap.c
file clapack/cblas/ssymm.c
file clapack/cblas/ssymv.c
file clapack/cblas/ssyr.c
file clapack/cblas/ssyr2.c
file clapack/cblas/ssyr2k.c
file clapack/cblas/ssyrk.c
file clapack/cblas/stbmv.c
file clapack/cblas/stbsv.c
file clapack/cblas/stpmv.c
file clapack/cblas/stpsv.c
file clapack/cblas/strmm.c
file clapack/cblas/strmv.c
file clapack/cblas/strsm.c
file clapack/cblas/strsv.c
file clapack/cblas/xerbla.c
file clapack/cblas/zaxpy.c
file clapack/cblas/zcopy.c
file clapack/cblas/zdotc.c
file clapack/cblas/zdotu.c
file clapack/cblas/zdscal.c
file clapack/cblas/zgbmv.c
file clapack/cblas/zgemm.c
file clapack/cblas/zgemv.c
file clapack/cblas/zgerc.c
file clapack/cblas/zgeru.c
file clapack/cblas/zhbmv.c
file clapack/cblas/zhemm.c
file clapack/cblas/zhemv.c
file clapack/cblas/zher.c
file clapack/cblas/zher2.c
file clapack/cblas/zher2k.c
file clapack/cblas/zherk.c
file clapack/cblas/zhpmv.c
file clapack/cblas/zhpr.c
file clapack/cblas/zhpr2.c
file clapack/cblas/zrotg.c
file clapack/cblas/zscal.c
file clapack/cblas/zswap.c
file clapack/cblas/zsymm.c
file clapack/cblas/zsyr2k.c
file clapack/cblas/zsyrk.c
file clapack/cblas/ztbmv.c
file clapack/cblas/ztbsv.c
file clapack/cblas/ztpmv.c
file clapack/cblas/ztpsv.c
file clapack/cblas/ztrmm.c
file clapack/cblas/ztrmv.c
file clapack/cblas/ztrsm.c
file clapack/cblas/ztrsv.c
############################################################################
# PLEASE NOTE: #
# #
# THE CBLAS ARE NOT PROVIDED BY NETLIB WHEN CLAPACK ROUTINES ARE REQUESTED.#
# #
# It is assumed that an optimized version of the BLAS are already #
# present on your machine. If this is not the case, please refer #
# to the clapack/cblas directory. #
############################################################################
file clapack/index
for This index
file clapack/readme
for overview of clapack
file clapack/readme.install
for Details of how to install CLAPACK
, (!!!VERY IMPORTANT!!! PLEASE READ!!!)
file clapack/readme.maintain
for Details of how CLAPACK was created
, (!!!VERY IMPORTANT!!! PLEASE READ!!!)
file clapack/clapack.h
for Include file of C prototypes
file clapack/f2c.h
for Include file of f2c
file clapack/clapack.tgz
for CLAPACK, version 3.2.1 (threadsafe)
, (7221385 bytes).
, Updated: June 25, 2009
by Peng Du, Keith Seymour and Julie Langou (University of Tennessee)
file clapack/CLAPACK-3.1.1-VisualStudio.zip
for CLAPACK, version 3.1.1 for Windows (42574025 bytes)
by Julie Langou
file clapack/LIB_WINDOWS/prebuilt_libraries_windows.html
for: CLAPACK, version 3.1.1 for Windows Prebuilt libraries for Windows 32 bits and 64 bits : Release, Debug, Release without wrap, Debug without wrap
by Julie Langou
file clapack/clapack-3.2.1-CMAKE.tgz
for: CLAPACK, version 3.2.1 CMAKE package.
, for UNIX Make, MAC xcode, Windows (Nmake, Visual Studio all versions) 32 or 64 bits.
, [REQUIRE CMAKE - http://www.cmake.org/ Running doc: http://www.cmake.org/cmake/help/runningcmake.html]
, FEEDBACK WELCOME --> http://icl.cs.utk.edu/lapack-forum
by Julie Langou
#------------------
# Previous releases:
#------------------
file clapack/clapack-3.1.1.1.tgz
for CLAPACK, version 3.1.1.1 (threadsafe version of 3.1.1)
, (5306483 bytes).
, Updated: October 8, 2008
file clapack/LAPACK-revisions3.1.0.info
for 3.1.0 revision info
file clapack/LAPACK-revisions3.1.1.info
for 3.1.1 revision info
file clapack/CLAPACK-revisions3.1.1.1.info
for 3.1.1.1 revision info
by Julie Langou and Peng Du (University of Tennessee)
file clapack/clapack3.tgz
for CLAPACK, version 3.0
, (6157628 bytes).
, Updated: September 20, 2000
by David Bindel (dbindel@cs.berkeley.edu) & Jim Demmel (demmel@cs.berkeley.edu)
file clapack/CLAw32.zip
for CLAPACK for Win32. Refer to the readme.claw32 for details.
, Requires clapack2.tgz (version 2.0)
, (6939277 bytes).
, Contributed by Bob Denny
file clapack/clapack2.tgz
for CLAPACK, version 2.0 (required by CLAw32.zip)
, (6157628 bytes).
, Updated: Sept, 1994
file clapack/CLAPACK3-Windows.zip
for CLAPACK, version 3.0 Windows
, (34159268 bytes)
, Contributed by Bob Denny
#------------------
# Related Projects:
#------------------
# For the Fortran 77 implementation of LAPACK see directory lapack
lib lapack
for LAPACK.
# For the Fortran95 interface to LAPACK see directory lapack95
lib lapack95
for LAPACK95 is the Fortran95 interface to LAPACK.
by Jerzy Wasniewski
# For the Fortran-to-Java LAPACK see directory java/f2j/
lib java/f2j
for JLAPACK
# For a c++ implementation of LAPACK see directory c++/lapack++
lib c++/lapack++
for LAPACK++. LAPACK extensions for high performance linear
, algebra computations. This version includes support for solving linear
, systems using LU, Cholesky, and QR matrix factorizations.
by Roldan Pozo
# For a distributed-memory implementation of LAPACK see directory scalapack
lib scalapack
for ScaLAPACK. A portable implementation of some of the core
, routines in LAPACK across MPI, PVM, Intel Paragon, IBM SP, and SGI O2K.
# *******************
# Questions/comments? Direct email to lapack@cs.utk.edu or post on the LAPACK forum: http://icl.cs.utk.edu/lapack-forum/
# *******************
# -------------------------------------------------------
# Available SIMPLE and DIVIDE AND CONQUER DRIVER routines:
# -------------------------------------------------------
file clapack/complex/cgesv.c
for Solves a general system of linear equations AX=B.
gams d2c1
file clapack/complex/cgbsv.c
for Solves a general banded system of linear equations AX=B.
gams d2c2
file clapack/complex/cgtsv.c
for Solves a general tridiagonal system of linear equations AX=B.
gams d2c2a
file clapack/complex/cposv.c
for Solves a Hermitian positive definite system of linear
, equations AX=B.
gams d2d1b
file clapack/complex/cppsv.c
for Solves a Hermitian positive definite system of linear
, equations AX=B, where A is in packed storage.
gams d2d1b
file clapack/complex/cpbsv.c
for Solves a Hermitian positive definite banded system
, of linear equations AX=B.
gams d2d2
file clapack/complex/cptsv.c
for Solves a Hermitian positive definite tridiagonal system
, of linear equations AX=B.
gams d2d2a
file clapack/complex/csysv.c
for Solves a complex symmetric indefinite system of linear equations AX=B.
gams d2c1
file clapack/complex/chesv.c
for Solves a complex Hermitian indefinite system of linear equations AX=B.
gams d2d1a
file clapack/complex/cspsv.c
for Solves a complex symmetric indefinite system of linear equations AX=B,
, where A is held in packed storage.
gams d2c1
file clapack/complex/chpsv.c
for Solves a complex Hermitian indefinite system of linear equations AX=B,
, where A is held in packed storage.
gams d2d1a
file clapack/complex/cgels.c
for Computes the least squares solution to an over-determined system
, of linear equations, A X=B or A**H X=B, or the minimum norm
, solution of an under-determined system, where A is a general
, rectangular matrix of full rank, using a QR or LQ factorization
, of A.
gams d9a1
file clapack/complex/cgglse.c
for Solves the LSE (Constrained Linear Least Squares Problem) using
, the GRQ (Generalized RQ) factorization
gams d9b1
file clapack/complex/cggglm.c
for Solves the GLM (Generalized Linear Regression Model) using
, the GQR (Generalized QR) factorization
file clapack/complex/cheev.c
for Computes all eigenvalues and, optionally, eigenvectors of a complex
, Hermitian matrix.
gams d4a3
file clapack/complex/cheevd.c
for Computes all eigenvalues and, optionally, eigenvectors of a complex
, Hermitian matrix. If eigenvectors are desired, it uses a divide
, and conquer algorithm.
gams d4a3
file clapack/complex/chpev.c
for Computes all eigenvalues and, optionally, eigenvectors of a complex
, Hermitian matrix in packed storage.
gams d4a3
file clapack/complex/chpevd.c
for Computes all eigenvalues and, optionally, eigenvectors of a complex
, Hermitian matrix in packed storage. If eigenvectors are desired, it
, uses a divide and conquer algorithm.
gams d4a3
file clapack/complex/chbev.c
for Computes all eigenvalues and, optionally, eigenvectors of a complex
, Hermitian band matrix.
gams d4a3, d4a6
file clapack/complex/chbevd.c
for Computes all eigenvalues and, optionally, eigenvectors of a complex
, Hermitian band matrix. If eigenvectors are desired, it uses a divide
, and conquer algorithm.
gams d4a3, d4a6
file clapack/complex/cgees.c
for Computes the eigenvalues and Schur factorization of a general
, matrix, and orders the factorization so that selected eigenvalues
, are at the top left of the Schur form.
gams d4a4
file clapack/complex/cgeev.c
for Computes the eigenvalues and left and right eigenvectors of
, a general matrix.
gams d4a4
file clapack/complex/cgesvd.c
for Computes the singular value decomposition (SVD) of a general
, rectangular matrix.
gams d6
file clapack/complex/chegv.c
for Computes all eigenvalues and the eigenvectors of a generalized
, Hermitian-definite generalized eigenproblem,
, Ax= lambda Bx, ABx= lambda x, or BAx= lambda x.
gams d4b3
file clapack/complex/chpgv.c
for Computes all eigenvalues and eigenvectors of a generalized
, Hermitian-definite generalized eigenproblem, Ax= lambda
, Bx, ABx= lambda x, or BAx= lambda x, where A and B are in packed
, storage.
gams d4b3
file clapack/complex/chbgv.c
for Computes all the eigenvalues, and optionally, the eigenvectors
, of a complex generalized Hermitian-definite banded eigenproblem, of
, the form A*x=(lambda)*B*x. A and B are assumed to be Hermitian
, and banded, and B is also positive definite.
file clapack/complex/cgegs.c
for Computes the generalized eigenvalues, Schur form, and left and/or
, right Schur vectors for a pair of nonsymmetric matrices
file clapack/complex/cgegv.c
for Computes the generalized eigenvalues, and left and/or right
, generalized eigenvectors for a pair of nonsymmetric matrices
file clapack/complex/cggsvd.c
for Computes the Generalized Singular Value Decomposition
# ---------------------------------
# Available EXPERT DRIVER routines:
# ---------------------------------
file clapack/complex/cgesvx.c
for Solves a general system of linear equations AX=B, A**T X=B
, or A**H X=B, and provides an estimate of the condition number
, and error bounds on the solution.
gams d2c1
file clapack/complex/cgbsvx.c
for Solves a general banded system of linear equations AX=B,
, A**T X=B or A**H X=B, and provides an estimate of the condition
, number and error bounds on the solution.
gams d2c2
file clapack/complex/cgtsvx.c
for Solves a general tridiagonal system of linear equations AX=B,
, A**T X=B or A**H X=B, and provides an estimate of the condition
, number and error bounds on the solution.
gams d2c2a
file clapack/complex/cposvx.c
for Solves a Hermitian positive definite system of linear
, equations AX=B, and provides an estimate of the condition number
, and error bounds on the solution.
gams d2d1b
file clapack/complex/cppsvx.c
for Solves a Hermitian positive definite system of linear
, equations AX=B, where A is held in packed storage, and provides
, an estimate of the condition number and error bounds on the
, solution.
gams d2d1b
file clapack/complex/cpbsvx.c
for Solves a Hermitian positive definite banded system
, of linear equations AX=B, and provides an estimate of the condition
, number and error bounds on the solution.
gams d2d2
file clapack/complex/cptsvx.c
for Solves a Hermitian positive definite tridiagonal
, system of linear equations AX=B, and provides an estimate of
, the condition number and error bounds on the solution.
gams d2d2a
file clapack/complex/csysvx.c
for Solves a complex symmetric
, indefinite system of linear equations AX=B, and provides an
, estimate of the condition number and error bounds on the solution.
gams d2c1
file clapack/complex/chesvx.c
for Solves a complex Hermitian
, indefinite system of linear equations AX=B, and provides an
, estimate of the condition number and error bounds on the solution.
gams d2d1a
file clapack/complex/cspsvx.c
for Solves a complex symmetric
, indefinite system of linear equations AX=B, where A is held
, in packed storage, and provides an estimate of the condition
, number and error bounds on the solution.
gams d2c1
file clapack/complex/chpsvx.c
for Solves a complex Hermitian
, indefinite system of linear equations AX=B, where A is held
, in packed storage, and provides an estimate of the condition
, number and error bounds on the solution.
gams d2d1a
file clapack/complex/cgelsx.c
for Computes the minimum norm least squares solution to an over-
, or under-determined system of linear equations A X=B, using a
, complete orthogonal factorization of A.
gams d9a1
file clapack/complex/cgelss.c
for Computes the minimum norm least squares solution to an over-
, or under-determined system of linear equations A X=B, using
, the singular value decomposition of A.
gams d9a1
file clapack/complex/cheevx.c
for Computes selected eigenvalues and eigenvectors of a Hermitian matrix.
gams d4a3
file clapack/complex/chpevx.c
for Computes selected eigenvalues and eigenvectors of a
, Hermitian matrix in packed storage.
gams d4a3
file clapack/complex/chbevx.c
for Computes selected eigenvalues and eigenvectors of a
, Hermitian band matrix.
gams d4a3, d4a6
file clapack/complex/cgeesx.c
for Computes the eigenvalues and Schur factorization of a general
, matrix, orders the factorization so that selected eigenvalues
, are at the top left of the Schur form, and computes reciprocal
, condition numbers for the average of the selected eigenvalues,
, and for the associated right invariant subspace.
gams d4a4
file clapack/complex/cgeevx.c
for Computes the eigenvalues and left and right eigenvectors of
, a general matrix, with preliminary balancing of the matrix,
, and computes reciprocal condition numbers for the eigenvalues
, and right eigenvectors.
gams d4a4
# ---------------------------------
# Available COMPUTATIONAL routines:
# ---------------------------------
file clapack/complex/cbdsqr.c
for Computes the singular value decomposition (SVD) of a real bidiagonal
, matrix, using the bidiagonal QR algorithm.
gams d6
file clapack/complex/cgbbrd.c
, Reduces a complex general band matrix to real upper bidiagonal form
, by a unitary transformation.
file clapack/complex/cgbcon.c
for Estimates the reciprocal of the condition number of a general
, band matrix, in either the 1-norm or the infinity-norm, using
, the LU factorization computed by CGBTRF.
gams d2c2
file clapack/complex/cgbequ.c
for Computes row and column scalings to equilibrate a general band
, matrix and reduce its condition number.
gams d2c2
file clapack/complex/cgbrfs.c
for Improves the computed solution to a general banded system of
, linear equations AX=B, A**T X=B or A**H X=B, and provides forward
, and backward error bounds for the solution.
gams d2c2
file clapack/complex/cgbtrf.c
for Computes an LU factorization of a general band matrix, using
, partial pivoting with row interchanges.
gams d2c2
file clapack/complex/cgbtrs.c
for Solves a general banded system of linear equations AX=B,
, A**T X=B or A**H X=B, using the LU factorization computed
, by CGBTRF.
gams d2c2
file clapack/complex/cgebak.c
for Transforms eigenvectors of a balanced matrix to those of the
, original matrix supplied to CGEBAL.
gams d4c4
file clapack/complex/cgebal.c
for Balances a general matrix in order to improve the accuracy
, of computed eigenvalues.
gams d4c1a
file clapack/complex/cgebrd.c
for Reduces a general rectangular matrix to real bidiagonal form
, by an orthogonal/unitary transformation.
gams d6
file clapack/complex/cgecon.c
for Estimates the reciprocal of the condition number of a general
, matrix, in either the 1-norm or the infinity-norm, using the
, LU factorization computed by CGETRF.
gams d2c1
file clapack/complex/cgeequ.c
for Computes row and column scalings to equilibrate a general
, rectangular matrix and reduce its condition number.
gams d2c1
file clapack/complex/cgehrd.c
for Reduces a general matrix to upper Hessenberg form by an
, unitary similarity transformation.
gams d4c1b2
file clapack/complex/cgelqf.c
for Computes an LQ factorization of a general rectangular matrix.
gams d5
file clapack/complex/cgeqlf.c
for Computes a QL factorization of a general rectangular matrix.
gams d5
file clapack/complex/cgeqpf.c
for Computes a QR factorization with column pivoting of a general
, rectangular matrix.
gams d5
file clapack/complex/cgeqrf.c
for Computes a QR factorization of a general rectangular matrix.
gams d5
file clapack/complex/cgerfs.c
for Improves the computed solution to a general system of linear
, equations AX=B, A**T X=B or A**H X=B, and provides forward and
, backward error bounds for the solution.
gams d2c1
file clapack/complex/cgerqf.c
for Computes an RQ factorization of a general rectangular matrix.
gams d5
file clapack/complex/cgetrf.c
for Computes an LU factorization of a general matrix, using partial
, pivoting with row interchanges.
gams d2c1
file clapack/complex/cggbak.c
for Forms the right or left eigenvectors of the generalized eigenvalue
, problem by backward transformation on the computed eigenvectors of
, the balanced pair of matrices output by CGGBAL.
file clapack/complex/cggbal.c
For Balances a pair of general complex matrices for the generalized
, eigenvalue problem A x = lambda B x.
file clapack/complex/cgghrd.c
for Reduces a pair of complex matrices to generalized upper
, Hessenberg form using unitary similarity transformations.
file clapack/complex/cggqrf.c
for Computes a generalized QR factorization of a pair of matrices.
file clapack/complex/cggrqf.c
for Computes a generalized RQ factorization of a pair of matrices.
file clapack/complex/cggsvp.c
for Computes unitary matrices as a preprocessing step
, for computing the generalized singular value decomposition
file clapack/complex/cgtcon.c
for Estimates the reciprocal of the condition number of a general
, tridiagonal matrix, in either the 1-norm or the infinity-norm,
, using the LU factorization computed by CGTTRF.
gams d2c2a
file clapack/complex/cgtrfs.c
for Improves the computed solution to a general tridiagonal system
, of linear equations AX=B, A**T X=B or A**H X=B, and provides
, forward and backward error bounds for the solution.
gams d2c2a
file clapack/complex/cgttrf.c
for Computes an LU factorization of a general tridiagonal matrix,
, using partial pivoting with row interchanges.
gams d2c2a
file clapack/complex/cgttrs.c
for Solves a general tridiagonal system of linear equations AX=B,
, A**T X=B or A**H X=B, using the LU factorization computed by
, CGTTRF.
gams d2c2a
file clapack/complex/chgeqz.c
for Implements a single-/double-shift version of the QZ method for
, finding the generalized eigenvalues of the equation
, det(A - w(i) B) = 0
file clapack/complex/chsein.c
for Computes specified right and/or left eigenvectors of an upper
, Hessenberg matrix by inverse iteration.
gams d4c3
file clapack/complex/chseqr.c
for Computes the eigenvalues and Schur factorization of an upper
, Hessenberg matrix, using the multishift QR algorithm.
gams d4c2b
file clapack/complex/cupgtr.c
for Generates the unitary transformation matrix from
, a reduction to tridiagonal form determined by CHPTRD.
gams d4c1b1
file clapack/complex/cupmtr.c
for Multiplies a general matrix by the unitary
, transformation matrix from a reduction to tridiagonal form
, determined by CHPTRD.
gams d4c4
file clapack/complex/cungbr.c
for Generates the unitary transformation matrices from
, a reduction to bidiagonal form determined by CGEBRD.
gams d6
file clapack/complex/cunghr.c
for Generates the unitary transformation matrix from
, a reduction to Hessenberg form determined by CGEHRD.
gams d4c1b2
file clapack/complex/cunglq.c
for Generates all or part of the unitary matrix Q from
, an LQ factorization determined by CGELQF.
gams d5
file clapack/complex/cungql.c
for Generates all or part of the unitary matrix Q from
, a QL factorization determined by CGEQLF.
gams d5
file clapack/complex/cungqr.c
for Generates all or part of the unitary matrix Q from
, a QR factorization determined by CGEQRF.
gams d5
file clapack/complex/cungrq.c
for Generates all or part of the unitary matrix Q from
, an RQ factorization determined by CGERQF.
gams d5
file clapack/complex/cungtr.c
for Generates the unitary transformation matrix from
, a reduction to tridiagonal form determined by CHETRD.
gams d4c1b1
file clapack/complex/cunmbr.c
for Multiplies a general matrix by one of the unitary
, transformation matrices from a reduction to bidiagonal form
, determined by CGEBRD.
gams d6
file clapack/complex/cunmhr.c
for Multiplies a general matrix by the unitary transformation
, matrix from a reduction to Hessenberg form determined by CGEHRD.
gams d4c4
file clapack/complex/cunmlq.c
for Multiplies a general matrix by the unitary matrix
, from an LQ factorization determined by CGELQF.
gams d5
file clapack/complex/cunmql.c
for Multiplies a general matrix by the unitary matrix
, from a QL factorization determined by CGEQLF.
gams d5
file clapack/complex/cunmqr.c
for Multiplies a general matrix by the unitary matrix
, from a QR factorization determined by CGEQRF.
gams d5
file clapack/complex/cunmrq.c
for Multiplies a general matrix by the unitary matrix
, from an RQ factorization determined by CGERQF.
gams d5
file clapack/complex/cunmtr.c
for Multiplies a general matrix by the unitary
, transformation matrix from a reduction to tridiagonal form
, determined by CHETRD.
gams d4c4
file clapack/complex/cpbcon.c
for Estimates the reciprocal of the condition number of a
, Hermitian positive definite band matrix, using the
, Cholesky factorization computed by CPBTRF.
gams d2d2
file clapack/complex/cpbequ.c
for Computes row and column scalings to equilibrate a Hermitian
, positive definite band matrix and reduce its condition number.
gams d2d2
file clapack/complex/cpbrfs.c
for Improves the computed solution to a Hermitian positive
, definite banded system of linear equations AX=B, and provides
, forward and backward error bounds for the solution.
gams d2d2
file clapack/complex/cpbstf.c
for Computes a split Cholesky factorization of a complex Hermitian
, positive definite band matrix.
file clapack/complex/cpbtrf.c
for Computes the Cholesky factorization of a Hermitian
, positive definite band matrix.
gams d2d2
file clapack/complex/cpbtrs.c
for Solves a Hermitian positive definite banded system
, of linear equations AX=B, using the Cholesky factorization
, computed by CPBTRF.
gams d2d2
file clapack/complex/cpocon.c
for Estimates the reciprocal of the condition number of a
, Hermitian positive definite matrix, using the
, Cholesky factorization computed by CPOTRF.
gams d2d1b
file clapack/complex/cpoequ.c
for Computes row and column scalings to equilibrate a Hermitian
, positive definite matrix and reduce its condition number.
gams d2d1b
file clapack/complex/cporfs.c
for Improves the computed solution to a Hermitian positive
, definite system of linear equations AX=B, and provides forward
, and backward error bounds for the solution.
gams d2d1b
file clapack/complex/cpotrf.c
for Computes the Cholesky factorization of a Hermitian
, positive definite matrix.
gams d2d1b
file clapack/complex/cpotri.c
for Computes the inverse of a Hermitian positive definite
, matrix, using the Cholesky factorization computed by CPOTRF.
gams d2d1b
file clapack/complex/cpotrs.c
for Solves a Hermitian positive definite system of linear
, equations AX=B, using the Cholesky factorization computed by
, CPOTRF.
gams d2d1b
file clapack/complex/cppcon.c
for Estimates the reciprocal of the condition number of a
, Hermitian positive definite matrix in packed storage,
, using the Cholesky factorization computed by CPPTRF.
gams d2d1b
file clapack/complex/cppequ.c
for Computes row and column scalings to equilibrate a Hermitian
, positive definite matrix in packed storage and reduce its condition
, number.
gams d2d1b
file clapack/complex/cpprfs.c
for Improves the computed solution to a Hermitian positive
, definite system of linear equations AX=B, where A is held in
, packed storage, and provides forward and backward error bounds
, for the solution.
gams d2d1b
file clapack/complex/cpptrf.c
for Computes the Cholesky factorization of a Hermitian
, positive definite matrix in packed storage.
gams d2d1b
file clapack/complex/cpptri.c
for Computes the inverse of a Hermitian positive definite
, matrix in packed storage, using the Cholesky factorization computed
, by CPPTRF.
gams d2d1b
file clapack/complex/cpptrs.c
for Solves a Hermitian positive definite system of linear
, equations AX=B, where A is held in packed storage, using the
, Cholesky factorization computed by CPPTRF.
gams d2d1b
file clapack/complex/cptcon.c
for Computes the reciprocal of the condition number of a
, Hermitian positive definite tridiagonal matrix,
, using the LDL**H factorization computed by CPTTRF.
gams d2d2a
file clapack/complex/cpteqr.c
for Computes all eigenvalues and eigenvectors of a complex symmetric
, positive definite tridiagonal matrix, by computing the SVD of
, its bidiagonal Cholesky factor.
gams d4c2a
file clapack/complex/cptrfs.c
for Improves the computed solution to a Hermitian positive
, definite tridiagonal system of linear equations AX=B, and provides
, forward and backward error bounds for the solution.
gams d2d2a
file clapack/complex/cpttrf.c
for Computes the LDL**H factorization of a Hermitian
, positive definite tridiagonal matrix.
gams d2d2a
file clapack/complex/cpttrs.c
for Solves a Hermitian positive definite tridiagonal
, system of linear equations, using the LDL**H factorization
, computed by CPTTRF.
gams d2d2a
file clapack/complex/chbgst.c
for Reduces a complex Hermitian-definite banded generalized eigenproblem
, A x = lambda B x to standard form, where B has been factorized by
, CPBSTF (Crawford's algorithm).
file clapack/complex/chbtrd.c
for Reduces a Hermitian band matrix to real symmetric
, tridiagonal form by a unitary similarity transformation.
gams d4c1b1
file clapack/complex/cspcon.c
for Estimates the reciprocal of the condition number of a
, complex symmetric indefinite
, matrix in packed storage, using the factorization computed
, by CSPTRF.
gams d2c1
file clapack/complex/chpcon.c
for Estimates the reciprocal of the condition number of a
, complex Hermitian indefinite
, matrix in packed storage, using the factorization computed
, by CHPTRF.
gams d2d1a
file clapack/complex/chpgst.c
for Reduces a Hermitian-definite generalized eigenproblem
, Ax= lambda Bx, ABx= lambda x, or BAx= lambda x, to standard
, form, where A and B are held in packed storage, and B has been
, factorized by CPPTRF.
gams d4c1c
file clapack/complex/csprfs.c
for Improves the computed solution to a complex
, symmetric indefinite system of linear equations
, AX=B, where A is held in packed storage, and provides forward
, and backward error bounds for the solution.
gams d2c1
file clapack/complex/chprfs.c
for Improves the computed solution to a complex
, Hermitian indefinite system of linear equations
, AX=B, where A is held in packed storage, and provides forward
, and backward error bounds for the solution.
gams d2d1a
file clapack/complex/chptrd.c
for Reduces a Hermitian matrix in packed storage to real
, symmetric tridiagonal form by a unitary similarity
, transformation.
gams d4c1b1
file clapack/complex/csptrf.c
for Computes the factorization of a complex
, symmetric-indefinite matrix in packed storage,
, using the diagonal pivoting method.
gams d2c1
file clapack/complex/chptrf.c
for Computes the factorization of a complex
, Hermitian-indefinite matrix in packed storage,
, using the diagonal pivoting method.
gams d2d1a
file clapack/complex/csptri.c
for Computes the inverse of a complex symmetric
, indefinite matrix in packed storage, using the factorization
, computed by CSPTRF.
gams d2c1
file clapack/complex/chptri.c
for Computes the inverse of a complex
, Hermitian indefinite matrix in packed storage, using the factorization
, computed by CHPTRF.
gams d2d1a
file clapack/complex/csptrs.c
for Solves a complex symmetric
, indefinite system of linear equations AX=B, where A is held
, in packed storage, using the factorization computed
, by CSPTRF.
gams d2c1
file clapack/complex/chptrs.c
for Solves a complex Hermitian
, indefinite system of linear equations AX=B, where A is held
, in packed storage, using the factorization computed
, by CHPTRF.
gams d2d1a
file clapack/complex/cstedc.c
for Computes all eigenvalues and, optionally, eigenvectors of a
, symmetric tridiagonal matrix using the divide and conquer algorithm.
file clapack/complex/cstein.c
for Computes selected eigenvectors of a real symmetric tridiagonal
, matrix by inverse iteration.
gams d4c3
file clapack/complex/csteqr.c
for Computes all eigenvalues and eigenvectors of a real symmetric
, tridiagonal matrix, using the implicit QL or QR algorithm.
gams d4a1, d4a5, d4c2a
file clapack/complex/csycon.c
for Estimates the reciprocal of the condition number of a
, complex symmetric indefinite matrix,
, using the factorization computed by CSYTRF.
gams d2c1
file clapack/complex/checon.c
for Estimates the reciprocal of the condition number of a
, complex Hermitian indefinite matrix,
, using the factorization computed by CHETRF.
gams d2d1a
file clapack/complex/chegst.c
for Reduces a Hermitian-definite generalized eigenproblem
, Ax= lambda Bx, ABx= lambda x, or BAx= lambda x, to standard
, form, where B has been factorized by CPOTRF.
gams d4c1c
file clapack/complex/csyrfs.c
for Improves the computed solution to a complex
, symmetric indefinite system of linear equations
, AX=B, and provides forward and backward error bounds for the
, solution.
gams d2c1
file clapack/complex/cherfs.c
for Improves the computed solution to a complex
, Hermitian indefinite system of linear equations
, AX=B, and provides forward and backward error bounds for the
, solution.
gams d2d1a
file clapack/complex/chetrd.c
for Reduces a Hermitian matrix to real symmetric tridiagonal
, form by an orthogonal/unitary similarity transformation.
gams d4c1b1
file clapack/complex/csytrf.c
for Computes the factorization of a complex symmetric-indefinite matrix,
, using the diagonal pivoting method.
gams d2c1
file clapack/complex/chetrf.c
for Computes the factorization of a complex Hermitian-indefinite matrix,
, using the diagonal pivoting method.
gams d2d1a
file clapack/complex/csytri.c
for Computes the inverse of a complex symmetric indefinite matrix,
, using the factorization computed by CSYTRF.
gams d2c1
file clapack/complex/chetri.c
for Computes the inverse of a complex Hermitian indefinite matrix,
, using the factorization computed by CHETRF.
gams d2d1a
file clapack/complex/csytrs.c
for Solves a complex symmetric indefinite system of linear equations AX=B,
, using the factorization computed by CSPTRF.
gams d2c1
file clapack/complex/chetrs.c
for Solves a complex Hermitian indefinite system of linear equations AX=B,
, using the factorization computed by CHPTRF.
gams d2d1a
file clapack/complex/ctbcon.c
for Estimates the reciprocal of the condition number of a triangular
, band matrix, in either the 1-norm or the infinity-norm.
gams d2c2, d2c3
file clapack/complex/ctbrfs.c
for Provides forward and backward error bounds for the solution
, of a triangular banded system of linear equations AX=B,
, A**T X=B or A**H X=B.
gams d2c2, d2c3
file clapack/complex/ctbtrs.c
for Solves a triangular banded system of linear equations AX=B,
, A**T X=B or A**H X=B.
gams d2c2, d2c3
file clapack/complex/ctgevc.c
for Computes some or all of the right and/or left generalized eigenvectors
, of a pair of complex upper triangular matrices.
gams d4b4
file clapack/complex/ctgsja.c
for Computes the generalized singular value decomposition of two complex
, upper triangular (or trapezoidal) matrices as output by CGGSVP.
gams d6
file clapack/complex/ctpcon.c
for Estimates the reciprocal of the condition number of a triangular
, matrix in packed storage, in either the 1-norm or the infinity-norm.
gams d2c3
file clapack/complex/ctprfs.c
for Provides forward and backward error bounds for the solution
, of a triangular system of linear equations AX=B, A**T X=B or
, A**H X=B, where A is held in packed storage.
gams d2c3
file clapack/complex/ctptri.c
for Computes the inverse of a triangular matrix in packed storage.
gams d2c3
file clapack/complex/ctptrs.c
for Solves a triangular system of linear equations AX=B,
, A**T X=B or A**H X=B, where A is held in packed storage.
gams d2c3
file clapack/complex/ctrcon.c
for Estimates the reciprocal of the condition number of a triangular
, matrix, in either the 1-norm or the infinity-norm.
gams d2c3
file clapack/complex/ctrevc.c
for Computes left and right eigenvectors of an complex upper triangular
, matrix.
gams d4c3
file clapack/complex/ctrexc.c
for Reorders the Schur factorization of a matrix by a unitary
, similarity transformation.
gams d4c
file clapack/complex/ctrrfs.c
for Provides forward and backward error bounds for the solution
, of a triangular system of linear equations A X=B, A**T X=B or
, A**H X=B.
gams d2c3
file clapack/complex/ctrsen.c
for Reorders the Schur factorization of a matrix in order to find
, an orthonormal basis of a right invariant subspace corresponding
, to selected eigenvalues, and returns reciprocal condition numbers
, (sensitivities) of the average of the cluster of eigenvalues
, and of the invariant subspace.
gams d4c
file clapack/complex/ctrsna.c
for Estimates the reciprocal condition numbers (sensitivities)
, of selected eigenvalues and eigenvectors of a complex upper
, triangular matrix.
gams d4c
file clapack/complex/ctrsyl.c
for Solves the Sylvester matrix equation A X +/- X B=C where A
, and B are complex upper triangular, and may be transposed.
gams d8
file clapack/complex/ctrtri.c
for Computes the inverse of a triangular matrix.
gams d2c3
file clapack/complex/ctrtrs.c
for Solves a triangular system of linear equations AX=B,
, A**T X=B or A**H X=B.
gams d2c3
file clapack/complex/ctzrqf.c
for Computes an RQ factorization of an upper trapezoidal matrix.
gams d5
# -------------------------------------------------------
# Available SIMPLE and DIVIDE AND CONQUER DRIVER routines:
# -------------------------------------------------------
file clapack/complex16/zgesv.c
for Solves a general system of linear equations AX=B.
gams d2c1
file clapack/complex16/zgbsv.c
for Solves a general banded system of linear equations AX=B.
gams d2c2
file clapack/complex16/zgtsv.c
for Solves a general tridiagonal system of linear equations AX=B.
gams d2c2a
file clapack/complex16/zposv.c
for Solves a Hermitian positive definite system of linear
, equations AX=B.
gams d2d1b
file clapack/complex16/zppsv.c
for Solves a Hermitian positive definite system of linear
, equations AX=B, where A is in packed storage.
gams d2d1b
file clapack/complex16/zpbsv.c
for Solves a Hermitian positive definite banded system
, of linear equations AX=B.
gams d2d2
file clapack/complex16/zptsv.c
for Solves a Hermitian positive definite tridiagonal system
, of linear equations AX=B.
gams d2d2a
file clapack/complex16/zsysv.c
for Solves a complex symmetric indefinite system of linear equations AX=B.
gams d2c1
file clapack/complex16/zhesv.c
for Solves a complex Hermitian indefinite system of linear equations AX=B.
gams d2d1a
file clapack/complex16/zspsv.c
for Solves a complex symmetric indefinite system of linear equations AX=B,
, where A is held in packed storage.
gams d2c1
file clapack/complex16/zhpsv.c
for Solves a complex Hermitian indefinite system of linear equations AX=B,
, where A is held in packed storage.
gams d2d1a
file clapack/complex16/zgels.c
for Computes the least squares solution to an over-determined system
, of linear equations, A X=B or A**H X=B, or the minimum norm
, solution of an under-determined system, where A is a general
, rectangular matrix of full rank, using a QR or LQ factorization
, of A.
gams d9a1
file clapack/complex16/zgglse.c
for Solves the LSE (Constrained Linear Least Squares Problem) using
, the GRQ (Generalized RQ) factorization
gams d9b1
file clapack/complex16/zggglm.c
for Solves the GLM (Generalized Linear Regression Model) using
, the GQR (Generalized QR) factorization
file clapack/complex16/zheev.c
for Computes all eigenvalues and, optionally, eigenvectors of a complex
, Hermitian matrix.
gams d4a3
file clapack/complex16/zheevd.c
for Computes all eigenvalues and, optionally, eigenvectors of a complex
, Hermitian matrix. If eigenvectors are desired, it uses a divide
, and conquer algorithm.
gams d4a3
file clapack/complex16/zhpev.c
for Computes all eigenvalues and, optionally, eigenvectors of a complex
, Hermitian matrix in packed storage.
gams d4a3
file clapack/complex16/zhpevd.c
for Computes all eigenvalues and, optionally, eigenvectors of a complex
, Hermitian matrix in packed storage. If eigenvectors are desired, it
, uses a divide and conquer algorithm.
gams d4a3
file clapack/complex16/zhbev.c
for Computes all eigenvalues and, optionally, eigenvectors of a complex
, Hermitian band matrix.
gams d4a3, d4a6
file clapack/complex16/zhbevd.c
for Computes all eigenvalues and, optionally, eigenvectors of a complex
, Hermitian band matrix. If eigenvectors are desired, it uses a divide
, and conquer algorithm.
gams d4a3, d4a6
file clapack/complex16/zgees.c
for Computes the eigenvalues and Schur factorization of a general
, matrix, and orders the factorization so that selected eigenvalues
, are at the top left of the Schur form.
gams d4a4
file clapack/complex16/zgeev.c
for Computes the eigenvalues and left and right eigenvectors of
, a general matrix.
gams d4a4
file clapack/complex16/zgesvd.c
for Computes the singular value decomposition (SVD) of a general
, rectangular matrix.
gams d6
file clapack/complex16/zhegv.c
for Computes all eigenvalues and the eigenvectors of a generalized
, Hermitian-definite generalized eigenproblem,
, Ax= lambda Bx, ABx= lambda x, or BAx= lambda x.
gams d4b3
file clapack/complex16/zhpgv.c
for Computes all eigenvalues and eigenvectors of a generalized
, Hermitian-definite generalized eigenproblem, Ax= lambda
, Bx, ABx= lambda x, or BAx= lambda x, where A and B are in packed
, storage.
gams d4b3
file clapack/complex16/zhbgv.c
for Computes all the eigenvalues, and optionally, the eigenvectors
, of a complex generalized Hermitian-definite banded eigenproblem, of
, the form A*x=(lambda)*B*x. A and B are assumed to be Hermitian
, and banded, and B is also positive definite.
file clapack/complex16/zgegs.c
for Computes the generalized eigenvalues, Schur form, and left and/or
, right Schur vectors for a pair of nonsymmetric matrices
file clapack/complex16/zgegv.c
for Computes the generalized eigenvalues, and left and/or right
, generalized eigenvectors for a pair of nonsymmetric matrices
file clapack/complex16/zggsvd.c
for Computes the Generalized Singular Value Decomposition
# ---------------------------------
# Available EXPERT DRIVER routines:
# ---------------------------------
file clapack/complex16/zgesvx.c
for Solves a general system of linear equations AX=B, A**T X=B
, or A**H X=B, and provides an estimate of the condition number
, and error bounds on the solution.
gams d2c1
file clapack/complex16/zgbsvx.c
for Solves a general banded system of linear equations AX=B,
, A**T X=B or A**H X=B, and provides an estimate of the condition
, number and error bounds on the solution.
gams d2c2
file clapack/complex16/zgtsvx.c
for Solves a general tridiagonal system of linear equations AX=B,
, A**T X=B or A**H X=B, and provides an estimate of the condition
, number and error bounds on the solution.
gams d2c2a
file clapack/complex16/zposvx.c
for Solves a Hermitian positive definite system of linear
, equations AX=B, and provides an estimate of the condition number
, and error bounds on the solution.
gams d2d1b
file clapack/complex16/zppsvx.c
for Solves a Hermitian positive definite system of linear
, equations AX=B, where A is held in packed storage, and provides
, an estimate of the condition number and error bounds on the
, solution.
gams d2d1b
file clapack/complex16/zpbsvx.c
for Solves a Hermitian positive definite banded system
, of linear equations AX=B, and provides an estimate of the condition
, number and error bounds on the solution.
gams d2d2
file clapack/complex16/zptsvx.c
for Solves a Hermitian positive definite tridiagonal
, system of linear equations AX=B, and provides an estimate of
, the condition number and error bounds on the solution.
gams d2d2a
file clapack/complex16/zsysvx.c
for Solves a complex symmetric
, indefinite system of linear equations AX=B, and provides an
, estimate of the condition number and error bounds on the solution.
gams d2c1
file clapack/complex16/zhesvx.c
for Solves a complex Hermitian
, indefinite system of linear equations AX=B, and provides an
, estimate of the condition number and error bounds on the solution.
gams d2d1a
file clapack/complex16/zspsvx.c
for Solves a complex symmetric
, indefinite system of linear equations AX=B, where A is held
, in packed storage, and provides an estimate of the condition
, number and error bounds on the solution.
gams d2c1
file clapack/complex16/zhpsvx.c
for Solves a complex Hermitian
, indefinite system of linear equations AX=B, where A is held
, in packed storage, and provides an estimate of the condition
, number and error bounds on the solution.
gams d2d1a
file clapack/complex16/zgelsx.c
for Computes the minimum norm least squares solution to an over-
, or under-determined system of linear equations A X=B, using a
, complete orthogonal factorization of A.
gams d9a1
file clapack/complex16/zgelss.c
for Computes the minimum norm least squares solution to an over-
, or under-determined system of linear equations A X=B, using
, the singular value decomposition of A.
gams d9a1
file clapack/complex16/zheevx.c
for Computes selected eigenvalues and eigenvectors of a Hermitian matrix.
gams d4a3
file clapack/complex16/zhpevx.c
for Computes selected eigenvalues and eigenvectors of a
, Hermitian matrix in packed storage.
gams d4a3
file clapack/complex16/zhbevx.c
for Computes selected eigenvalues and eigenvectors of a
, Hermitian band matrix.
gams d4a3, d4a6
file clapack/complex16/zgeesx.c
for Computes the eigenvalues and Schur factorization of a general
, matrix, orders the factorization so that selected eigenvalues
, are at the top left of the Schur form, and computes reciprocal
, condition numbers for the average of the selected eigenvalues,
, and for the associated right invariant subspace.
gams d4a4
file clapack/complex16/zgeevx.c
for Computes the eigenvalues and left and right eigenvectors of
, a general matrix, with preliminary balancing of the matrix,
, and computes reciprocal condition numbers for the eigenvalues
, and right eigenvectors.
gams d4a4
# ---------------------------------
# Available COMPUTATIONAL routines:
# ---------------------------------
file clapack/complex16/zbdsqr.c
for Computes the singular value decomposition (SVD) of a real bidiagonal
, matrix, using the bidiagonal QR algorithm.
gams d6
file clapack/complex16/zgbbrd.c
, Reduces a complex general band matrix to real upper bidiagonal form
, by a unitary transformation.
file clapack/complex16/zgbcon.c
for Estimates the reciprocal of the condition number of a general
, band matrix, in either the 1-norm or the infinity-norm, using
, the LU factorization computed by CGBTRF.
gams d2c2
file clapack/complex16/zgbequ.c
for Computes row and column scalings to equilibrate a general band
, matrix and reduce its condition number.
gams d2c2
file clapack/complex16/zgbrfs.c
for Improves the computed solution to a general banded system of
, linear equations AX=B, A**T X=B or A**H X=B, and provides forward
, and backward error bounds for the solution.
gams d2c2
file clapack/complex16/zgbtrf.c
for Computes an LU factorization of a general band matrix, using
, partial pivoting with row interchanges.
gams d2c2
file clapack/complex16/zgbtrs.c
for Solves a general banded system of linear equations AX=B,
, A**T X=B or A**H X=B, using the LU factorization computed
, by CGBTRF.
gams d2c2
file clapack/complex16/zgebak.c
for Transforms eigenvectors of a balanced matrix to those of the
, original matrix supplied to CGEBAL.
gams d4c4
file clapack/complex16/zgebal.c
for Balances a general matrix in order to improve the accuracy
, of computed eigenvalues.
gams d4c1a
file clapack/complex16/zgebrd.c
for Reduces a general rectangular matrix to real bidiagonal form
, by an unitary transformation.
gams d6
file clapack/complex16/zgecon.c
for Estimates the reciprocal of the condition number of a general
, matrix, in either the 1-norm or the infinity-norm, using the
, LU factorization computed by CGETRF.
gams d2c1
file clapack/complex16/zgeequ.c
for Computes row and column scalings to equilibrate a general
, rectangular matrix and reduce its condition number.
gams d2c1
file clapack/complex16/zgehrd.c
for Reduces a general matrix to upper Hessenberg form by an
, unitary similarity transformation.
gams d4c1b2
file clapack/complex16/zgelqf.c
for Computes an LQ factorization of a general rectangular matrix.
gams d5
file clapack/complex16/zgeqlf.c
for Computes a QL factorization of a general rectangular matrix.
gams d5
file clapack/complex16/zgeqpf.c
for Computes a QR factorization with column pivoting of a general
, rectangular matrix.
gams d5
file clapack/complex16/zgeqrf.c
for Computes a QR factorization of a general rectangular matrix.
gams d5
file clapack/complex16/zgerfs.c
for Improves the computed solution to a general system of linear
, equations AX=B, A**T X=B or A**H X=B, and provides forward and
, backward error bounds for the solution.
gams d2c1
file clapack/complex16/zgerqf.c
for Computes an RQ factorization of a general rectangular matrix.
gams d5
file clapack/complex16/zgetrf.c
for Computes an LU factorization of a general matrix, using partial
, pivoting with row interchanges.
gams d2c1
file clapack/complex16/zggbak.c
for Forms the right or left eigenvectors of the generalized eigenvalue
, problem by backward transformation on the computed eigenvectors of
, the balanced pair of matrices output by CGGBAL.
file clapack/complex16/zggbal.c
For Balances a pair of general complex matrices for the generalized
, eigenvalue problem A x = lambda B x.
file clapack/complex16/zgghrd.c
for Reduces a pair of complex matrices to generalized upper
, Hessenberg form using unitary similarity transformations.
file clapack/complex16/zggqrf.c
for Computes a generalized QR factorization of a pair of matrices.
file clapack/complex16/zggrqf.c
for Computes a generalized RQ factorization of a pair of matrices.
file clapack/complex16/zggsvp.c
for Computes unitary matrices as a preprocessing step
, for computing the generalized singular value decomposition
file clapack/complex16/zgtcon.c
for Estimates the reciprocal of the condition number of a general
, tridiagonal matrix, in either the 1-norm or the infinity-norm,
, using the LU factorization computed by CGTTRF.
gams d2c2a
file clapack/complex16/zgtrfs.c
for Improves the computed solution to a general tridiagonal system
, of linear equations AX=B, A**T X=B or A**H X=B, and provides
, forward and backward error bounds for the solution.
gams d2c2a
file clapack/complex16/zgttrf.c
for Computes an LU factorization of a general tridiagonal matrix,
, using partial pivoting with row interchanges.
gams d2c2a
file clapack/complex16/zgttrs.c
for Solves a general tridiagonal system of linear equations AX=B,
, A**T X=B or A**H X=B, using the LU factorization computed by
, CGTTRF.
gams d2c2a
file clapack/complex16/zhgeqz.c
for Implements a single-/double-shift version of the QZ method for
, finding the generalized eigenvalues of the equation
, det(A - w(i) B) = 0
file clapack/complex16/zhsein.c
for Computes specified right and/or left eigenvectors of an upper
, Hessenberg matrix by inverse iteration.
gams d4c3
file clapack/complex16/zhseqr.c
for Computes the eigenvalues and Schur factorization of an upper
, Hessenberg matrix, using the multishift QR algorithm.
gams d4c2b
file clapack/complex16/zupgtr.c
for Generates the unitary transformation matrix from
, a reduction to tridiagonal form determined by CHPTRD.
gams d4c1b1
file clapack/complex16/zupmtr.c
for Multiplies a general matrix by the unitary
, transformation matrix from a reduction to tridiagonal form
, determined by CHPTRD.
gams d4c4
file clapack/complex16/zungbr.c
for Generates the unitary transformation matrices from
, a reduction to bidiagonal form determined by CGEBRD.
gams d6
file clapack/complex16/zunghr.c
for Generates the unitary transformation matrix from
, a reduction to Hessenberg form determined by CGEHRD.
gams d4c1b2
file clapack/complex16/zunglq.c
for Generates all or part of the unitary matrix Q from
, an LQ factorization determined by CGELQF.
gams d5
file clapack/complex16/zungql.c
for Generates all or part of the unitary matrix Q from
, a QL factorization determined by CGEQLF.
gams d5
file clapack/complex16/zungqr.c
for Generates all or part of the unitary matrix Q from
, a QR factorization determined by CGEQRF.
gams d5
file clapack/complex16/zungrq.c
for Generates all or part of the unitary matrix Q from
, an RQ factorization determined by CGERQF.
gams d5
file clapack/complex16/zungtr.c
for Generates the unitary transformation matrix from
, a reduction to tridiagonal form determined by CHETRD.
gams d4c1b1
file clapack/complex16/zunmbr.c
for Multiplies a general matrix by one of the unitary
, transformation matrices from a reduction to bidiagonal form
, determined by CGEBRD.
gams d6
file clapack/complex16/zunmhr.c
for Multiplies a general matrix by the unitary transformation
, matrix from a reduction to Hessenberg form determined by CGEHRD.
gams d4c4
file clapack/complex16/zunmlq.c
for Multiplies a general matrix by the unitary matrix
, from an LQ factorization determined by CGELQF.
gams d5
file clapack/complex16/zunmql.c
for Multiplies a general matrix by the unitary matrix
, from a QL factorization determined by CGEQLF.
gams d5
file clapack/complex16/zunmqr.c
for Multiplies a general matrix by the unitary matrix
, from a QR factorization determined by CGEQRF.
gams d5
file clapack/complex16/zunmrq.c
for Multiplies a general matrix by the unitary matrix
, from an RQ factorization determined by CGERQF.
gams d5
file clapack/complex16/zunmtr.c
for Multiplies a general matrix by the unitary
, transformation matrix from a reduction to tridiagonal form
, determined by CHETRD.
gams d4c4
file clapack/complex16/zpbcon.c
for Estimates the reciprocal of the condition number of a
, Hermitian positive definite band matrix, using the
, Cholesky factorization computed by CPBTRF.
gams d2d2
file clapack/complex16/zpbequ.c
for Computes row and column scalings to equilibrate a Hermitian
, positive definite band matrix and reduce its condition number.
gams d2d2
file clapack/complex16/zpbrfs.c
for Improves the computed solution to a Hermitian positive
, definite banded system of linear equations AX=B, and provides
, forward and backward error bounds for the solution.
gams d2d2
file clapack/complex16/zpbstf.c
for Computes a split Cholesky factorization of a complex Hermitian
, positive definite band matrix.
file clapack/complex16/zpbtrf.c
for Computes the Cholesky factorization of a Hermitian
, positive definite band matrix.
gams d2d2
file clapack/complex16/zpbtrs.c
for Solves a Hermitian positive definite banded system
, of linear equations AX=B, using the Cholesky factorization
, computed by CPBTRF.
gams d2d2
file clapack/complex16/zpocon.c
for Estimates the reciprocal of the condition number of a
, Hermitian positive definite matrix, using the
, Cholesky factorization computed by CPOTRF.
gams d2d1b
file clapack/complex16/zpoequ.c
for Computes row and column scalings to equilibrate a Hermitian
, positive definite matrix and reduce its condition number.
gams d2d1b
file clapack/complex16/zporfs.c
for Improves the computed solution to a Hermitian positive
, definite system of linear equations AX=B, and provides forward
, and backward error bounds for the solution.
gams d2d1b
file clapack/complex16/zpotrf.c
for Computes the Cholesky factorization of a Hermitian
, positive definite matrix.
gams d2d1b
file clapack/complex16/zpotri.c
for Computes the inverse of a Hermitian positive definite
, matrix, using the Cholesky factorization computed by CPOTRF.
gams d2d1b
file clapack/complex16/zpotrs.c
for Solves a Hermitian positive definite system of linear
, equations AX=B, using the Cholesky factorization computed by
, CPOTRF.
gams d2d1b
file clapack/complex16/zppcon.c
for Estimates the reciprocal of the condition number of a
, Hermitian positive definite matrix in packed storage,
, using the Cholesky factorization computed by CPPTRF.
gams d2d1b
file clapack/complex16/zppequ.c
for Computes row and column scalings to equilibrate a Hermitian
, positive definite matrix in packed storage and reduce its condition
, number.
gams d2d1b
file clapack/complex16/zpprfs.c
for Improves the computed solution to a Hermitian positive
, definite system of linear equations AX=B, where A is held in
, packed storage, and provides forward and backward error bounds
, for the solution.
gams d2d1b
file clapack/complex16/zpptrf.c
for Computes the Cholesky factorization of a Hermitian
, positive definite matrix in packed storage.
gams d2d1b
file clapack/complex16/zpptri.c
for Computes the inverse of a Hermitian positive definite
, matrix in packed storage, using the Cholesky factorization computed
, by CPPTRF.
gams d2d1b
file clapack/complex16/zpptrs.c
for Solves a Hermitian positive definite system of linear
, equations AX=B, where A is held in packed storage, using the
, Cholesky factorization computed by CPPTRF.
gams d2d1b
file clapack/complex16/zptcon.c
for Computes the reciprocal of the condition number of a
, Hermitian positive definite tridiagonal matrix,
, using the LDL**H factorization computed by CPTTRF.
gams d2d2a
file clapack/complex16/zpteqr.c
for Computes all eigenvalues and eigenvectors of a complex symmetric
, positive definite tridiagonal matrix, by computing the SVD of
, its bidiagonal Cholesky factor.
gams d4c2a
file clapack/complex16/zptrfs.c
for Improves the computed solution to a Hermitian positive
, definite tridiagonal system of linear equations AX=B, and provides
, forward and backward error bounds for the solution.
gams d2d2a
file clapack/complex16/zpttrf.c
for Computes the LDL**H factorization of a Hermitian
, positive definite tridiagonal matrix.
gams d2d2a
file clapack/complex16/zpttrs.c
for Solves a Hermitian positive definite tridiagonal
, system of linear equations, using the LDL**H factorization
, computed by CPTTRF.
gams d2d2a
file clapack/complex16/zhbgst.c
for Reduces a complex Hermitian-definite banded generalized eigenproblem
, A x = lambda B x to standard form, where B has been factorized by
, CPBSTF (Crawford's algorithm).
file clapack/complex16/zhbtrd.c
for Reduces a Hermitian band matrix to real symmetric
, tridiagonal form by a unitary similarity transformation.
gams d4c1b1
file clapack/complex16/zspcon.c
for Estimates the reciprocal of the condition number of a
, complex symmetric indefinite
, matrix in packed storage, using the factorization computed
, by CSPTRF.
gams d2c1
file clapack/complex16/zhpcon.c
for Estimates the reciprocal of the condition number of a
, complex Hermitian indefinite
, matrix in packed storage, using the factorization computed
, by CHPTRF.
gams d2d1a
file clapack/complex16/zhpgst.c
for Reduces a Hermitian-definite generalized eigenproblem
, Ax= lambda Bx, ABx= lambda x, or BAx= lambda x, to standard
, form, where A and B are held in packed storage, and B has been
, factorized by CPPTRF.
gams d4c1c
file clapack/complex16/zsprfs.c
for Improves the computed solution to a complex
, symmetric indefinite system of linear equations
, AX=B, where A is held in packed storage, and provides forward
, and backward error bounds for the solution.
gams d2c1
file clapack/complex16/zhprfs.c
for Improves the computed solution to a complex
, Hermitian indefinite system of linear equations
, AX=B, where A is held in packed storage, and provides forward
, and backward error bounds for the solution.
gams d2d1a
file clapack/complex16/zhptrd.c
for Reduces a Hermitian matrix in packed storage to real
, symmetric tridiagonal form by a unitary similarity
, transformation.
gams d4c1b1
file clapack/complex16/zsptrf.c
for Computes the factorization of a complex
, symmetric-indefinite matrix in packed storage,
, using the diagonal pivoting method.
gams d2c1
file clapack/complex16/zhptrf.c
for Computes the factorization of a complex
, Hermitian-indefinite matrix in packed storage,
, using the diagonal pivoting method.
gams d2d1a
file clapack/complex16/zsptri.c
for Computes the inverse of a complex symmetric
, indefinite matrix in packed storage, using the factorization
, computed by CSPTRF.
gams d2c1
file clapack/complex16/zhptri.c
for Computes the inverse of a complex
, Hermitian indefinite matrix in packed storage, using the factorization
, computed by CHPTRF.
gams d2d1a
file clapack/complex16/zsptrs.c
for Solves a complex symmetric
, indefinite system of linear equations AX=B, where A is held
, in packed storage, using the factorization computed
, by CSPTRF.
gams d2c1
file clapack/complex16/zhptrs.c
for Solves a complex Hermitian
, indefinite system of linear equations AX=B, where A is held
, in packed storage, using the factorization computed
, by CHPTRF.
gams d2d1a
file clapack/complex16/zstedc.c
for Computes all eigenvalues and, optionally, eigenvectors of a
, symmetric tridiagonal matrix using the divide and conquer algorithm.
file clapack/complex16/zstein.c
for Computes selected eigenvectors of a real symmetric tridiagonal
, matrix by inverse iteration.
gams d4c3
file clapack/complex16/zsteqr.c
for Computes all eigenvalues and eigenvectors of a real symmetric
, tridiagonal matrix, using the implicit QL or QR algorithm.
gams d4a1, d4a5, d4c2a
file clapack/complex16/zsycon.c
for Estimates the reciprocal of the condition number of a
, complex symmetric indefinite matrix,
, using the factorization computed by CSYTRF.
gams d2c1
file clapack/complex16/zhecon.c
for Estimates the reciprocal of the condition number of a
, complex Hermitian indefinite matrix,
, using the factorization computed by CHETRF.
gams d2d1a
file clapack/complex16/zhegst.c
for Reduces a Hermitian-definite generalized eigenproblem
, Ax= lambda Bx, ABx= lambda x, or BAx= lambda x, to standard
, form, where B has been factorized by CPOTRF.
gams d4c1c
file clapack/complex16/zsyrfs.c
for Improves the computed solution to a complex
, symmetric indefinite system of linear equations
, AX=B, and provides forward and backward error bounds for the
, solution.
gams d2c1
file clapack/complex16/zherfs.c
for Improves the computed solution to a complex
, Hermitian indefinite system of linear equations
, AX=B, and provides forward and backward error bounds for the
, solution.
gams d2d1a
file clapack/complex16/zhetrd.c
for Reduces a Hermitian matrix to real symmetric tridiagonal
, form by an unitary similarity transformation.
gams d4c1b1
file clapack/complex16/zsytrf.c
for Computes the factorization of a complex symmetric-indefinite matrix,
, using the diagonal pivoting method.
gams d2c1
file clapack/complex16/zhetrf.c
for Computes the factorization of a complex Hermitian-indefinite matrix,
, using the diagonal pivoting method.
gams d2d1a
file clapack/complex16/zsytri.c
for Computes the inverse of a complex symmetric indefinite matrix,
, using the factorization computed by CSYTRF.
gams d2c1
file clapack/complex16/zhetri.c
for Computes the inverse of a complex Hermitian indefinite matrix,
, using the factorization computed by CHETRF.
gams d2d1a
file clapack/complex16/zsytrs.c
for Solves a complex symmetric indefinite system of linear equations AX=B,
, using the factorization computed by CSPTRF.
gams d2c1
file clapack/complex16/zhetrs.c
for Solves a complex Hermitian indefinite system of linear equations AX=B,
, using the factorization computed by CHPTRF.
gams d2d1a
file clapack/complex16/ztbcon.c
for Estimates the reciprocal of the condition number of a triangular
, band matrix, in either the 1-norm or the infinity-norm.
gams d2c2, d2c3
file clapack/complex16/ztbrfs.c
for Provides forward and backward error bounds for the solution
, of a triangular banded system of linear equations AX=B,
, A**T X=B or A**H X=B.
gams d2c2, d2c3
file clapack/complex16/ztbtrs.c
for Solves a triangular banded system of linear equations AX=B,
, A**T X=B or A**H X=B.
gams d2c2, d2c3
file clapack/complex16/ztgevc.c
for Computes some or all of the right and/or left generalized eigenvectors
, of a pair of complex upper triangular matrices.
gams d4b4
file clapack/complex16/ztgsja.c
for Computes the generalized singular value decomposition of two complex
, upper triangular (or trapezoidal) matrices as output by CGGSVP.
gams d6
file clapack/complex16/ztpcon.c
for Estimates the reciprocal of the condition number of a triangular
, matrix in packed storage, in either the 1-norm or the infinity-norm.
gams d2c3
file clapack/complex16/ztprfs.c
for Provides forward and backward error bounds for the solution
, of a triangular system of linear equations AX=B, A**T X=B or
, A**H X=B, where A is held in packed storage.
gams d2c3
file clapack/complex16/ztptri.c
for Computes the inverse of a triangular matrix in packed storage.
gams d2c3
file clapack/complex16/ztptrs.c
for Solves a triangular system of linear equations AX=B,
, A**T X=B or A**H X=B, where A is held in packed storage.
gams d2c3
file clapack/complex16/ztrcon.c
for Estimates the reciprocal of the condition number of a triangular
, matrix, in either the 1-norm or the infinity-norm.
gams d2c3
file clapack/complex16/ztrevc.c
for Computes left and right eigenvectors of an complex upper triangular
, matrix.
gams d4c3
file clapack/complex16/ztrexc.c
for Reorders the Schur factorization of a matrix by a unitary
, similarity transformation.
gams d4c
file clapack/complex16/ztrrfs.c
for Provides forward and backward error bounds for the solution
, of a triangular system of linear equations A X=B, A**T X=B or
, A**H X=B.
gams d2c3
file clapack/complex16/ztrsen.c
for Reorders the Schur factorization of a matrix in order to find
, an orthonormal basis of a right invariant subspace corresponding
, to selected eigenvalues, and returns reciprocal condition numbers
, (sensitivities) of the average of the cluster of eigenvalues
, and of the invariant subspace.
gams d4c
file clapack/complex16/ztrsna.c
for Estimates the reciprocal condition numbers (sensitivities)
, of selected eigenvalues and eigenvectors of a complex upper
, triangular matrix.
gams d4c
file clapack/complex16/ztrsyl.c
for Solves the Sylvester matrix equation A X +/- X B=C where A
, and B are complex upper triangular, and may be transposed.
gams d8
file clapack/complex16/ztrtri.c
for Computes the inverse of a triangular matrix.
gams d2c3
file clapack/complex16/ztrtrs.c
for Solves a triangular system of linear equations AX=B,
, A**T X=B or A**H X=B.
gams d2c3
file clapack/complex16/ztzrqf.c
for Computes an RQ factorization of an upper trapezoidal matrix.
gams d5
# --------------------------------------------------------
# Available SIMPLE and DIVIDE AND CONQUER DRIVER routines:
# --------------------------------------------------------
file clapack/double/dgesv.c
for Solves a general system of linear equations AX=B.
gams d2a1
file clapack/double/dgbsv.c
for Solves a general banded system of linear equations AX=B.
gams d2a2
file clapack/double/dgtsv.c
for Solves a general tridiagonal system of linear equations AX=B.
gams d2a2a
file clapack/double/dposv.c
for Solves a symmetric positive definite system of linear
, equations AX=B.
gams d2b1b
file clapack/double/dppsv.c
for Solves a symmetric positive definite system of linear
, equations AX=B, where A is held in packed storage.
gams d2b1b
file clapack/double/dpbsv.c
for Solves a symmetric positive definite banded system
, of linear equations AX=B.
gams d2b2
file clapack/double/dptsv.c
for Solves a symmetric positive definite tridiagonal system
, of linear equations AX=B.
gams d2b2a
file clapack/double/dsysv.c
for Solves a real symmetric indefinite system of linear equations AX=B.
gams d2b1a
file clapack/double/dspsv.c
for Solves a real symmetric indefinite system of linear equations AX=B,
, where A is held in packed storage.
gams d2b1a
file clapack/double/dgels.c
for Computes the least squares solution to an over-determined system
, of linear equations, A X=B or A**H X=B, or the minimum norm
, solution of an under-determined system, where A is a general
, rectangular matrix of full rank, using a QR or LQ factorization
, of A.
gams d9a1
file clapack/double/dgglse.c
for Solves the LSE (Constrained Linear Least Squares Problem) using
, the GRQ (Generalized RQ) factorization
gams d9b1
file clapack/double/dggglm.c
for Solves the GLM (Generalized Linear Regression Model) using
, the GQR (Generalized QR) factorization
file clapack/double/dsyev.c
for Computes all eigenvalues, and optionally, eigenvectors of a real
, symmetric matrix.
gams d4a1
file clapack/double/dsyevd.c
for Computes all eigenvalues, and optionally, eigenvectors of a real
, symmetric matrix. If eigenvectors are desired, it uses a divide
, and conquer algorithm.
gams d4a1
file clapack/double/dspev.c
for Computes all eigenvalues, and optionally, eigenvectors of a real
, symmetric matrix in packed storage.
gams d4a1
file clapack/double/dspevd.c
for Computes all eigenvalues, and optionally, eigenvectors of a real
, symmetric matrix in packed storage. If eigenvectors are desired,
, it uses a divide and conquer algorithm.
gams d4a1
file clapack/double/dsbev.c
for Computes all eigenvalues, and optionally, eigenvectors of a real
, symmetric band matrix.
gams d4a1, d4a6
file clapack/double/dsbevd.c
for Computes all eigenvalues, and optionally, eigenvectors of a real
, symmetric band matrix. If eigenvectors are desired, it uses a
, divide and conquer algorithm.
gams d4a1, d4a6
file clapack/double/dstev.c
for Computes all eigenvalues, and optionally, eigenvectors of a real
, symmetric tridiagonal matrix.
gams d4a1, d4a5
file clapack/double/dstevd.c
for Computes all eigenvalues, and optionally, eigenvectors of a real
, symmetric tridiagonal matrix. If eigenvectors are desired, it uses
, a divide and conquer algorithm.
gams d4a1, d4a5
file clapack/double/dgees.c
for Computes the eigenvalues and Schur factorization of a general
, matrix, and orders the factorization so that selected eigenvalues
, are at the top left of the Schur form.
gams d4a2
file clapack/double/dgeev.c
for Computes the eigenvalues and left and right eigenvectors of
, a general matrix.
gams d4a2
file clapack/double/dgesvd.c
for Computes the singular value decomposition (SVD) of a general
, rectangular matrix.
gams d6
file clapack/double/dsygv.c
for Computes all eigenvalues and the eigenvectors of a generalized
, symmetric-definite generalized eigenproblem,
, Ax= lambda Bx, ABx= lambda x, or BAx= lambda x.
gams d4b1
file clapack/double/dspgv.c
for Computes all eigenvalues and eigenvectors of a generalized
, symmetric-definite generalized eigenproblem, Ax= lambda
, Bx, ABx= lambda x, or BAx= lambda x, where A and B are in packed
, storage.
gams d4b1
file clapack/double/dsbgv.c
for Computes all the eigenvalues, and optionally, the eigenvectors
, of a real generalized symmetric-definite banded eigenproblem, of
, the form A*x=(lambda)*B*x. A and B are assumed to be symmetric
, and banded, and B is also positive definite.
file clapack/double/dgegs.c
for Computes the generalized eigenvalues, Schur form, and left and/or
, right Schur vectors for a pair of nonsymmetric matrices
file clapack/double/dgegv.c
for Computes the generalized eigenvalues, and left and/or right
, generalized eigenvectors for a pair of nonsymmetric matrices
file clapack/double/dggsvd.c
for Computes the Generalized Singular Value Decomposition
# ---------------------------------
# Available EXPERT DRIVER routines:
# ---------------------------------
file clapack/double/dgesvx.c
for Solves a general system of linear equations AX=B, A**T X=B
, or A**H X=B, and provides an estimate of the condition number
, and error bounds on the solution.
gams d2a1
file clapack/double/dgbsvx.c
for Solves a general banded system of linear equations AX=B,
, A**T X=B or A**H X=B, and provides an estimate of the condition
, number and error bounds on the solution.
gams d2a2
file clapack/double/dgtsvx.c
for Solves a general tridiagonal system of linear equations AX=B,
, A**T X=B or A**H X=B, and provides an estimate of the condition
, number and error bounds on the solution.
gams d2a2a
file clapack/double/dposvx.c
for Solves a symmetric positive definite system of linear
, equations AX=B, and provides an estimate of the condition number
, and error bounds on the solution.
gams d2b1b
file clapack/double/dppsvx.c
for Solves a symmetric positive definite system of linear
, equations AX=B, where A is held in packed storage, and provides
, an estimate of the condition number and error bounds on the
, solution.
gams d2b1b
file clapack/double/dpbsvx.c
for Solves a symmetric positive definite banded system
, of linear equations AX=B, and provides an estimate of the condition
, number and error bounds on the solution.
gams d2b2
file clapack/double/dptsvx.c
for Solves a symmetric positive definite tridiagonal
, system of linear equations AX=B, and provides an estimate of
, the condition number and error bounds on the solution.
gams d2b2a
file clapack/double/dsysvx.c
for Solves a real symmetric
, indefinite system of linear equations AX=B, and provides an
, estimate of the condition number and error bounds on the solution.
gams d2b1a
file clapack/double/dspsvx.c
for Solves a real symmetric
, indefinite system of linear equations AX=B, where A is held
, in packed storage, and provides an estimate of the condition
, number and error bounds on the solution.
gams d2b1a
file clapack/double/dgelsx.c
for Computes the minimum norm least squares solution to an over-
, or under-determined system of linear equations A X=B, using a
, complete orthogonal factorization of A.
gams d9a1
file clapack/double/dgelss.c
for Computes the minimum norm least squares solution to an over-
, or under-determined system of linear equations A X=B, using
, the singular value decomposition of A.
gams d9a1
file clapack/double/dsyevx.c
for Computes selected eigenvalues and eigenvectors of a symmetric matrix.
gams d4a1
file clapack/double/dspevx.c
for Computes selected eigenvalues and eigenvectors of a
, symmetric matrix in packed storage.
gams d4a1
file clapack/double/dsbevx.c
for Computes selected eigenvalues and eigenvectors of a
, symmetric band matrix.
gams d4a1, d4a6
file clapack/double/dstevx.c
for Computes selected eigenvalues and eigenvectors of a real
, symmetric tridiagonal matrix.
gams d4a1, d4a5
file clapack/double/dgeesx.c
for Computes the eigenvalues and Schur factorization of a general
, matrix, orders the factorization so that selected eigenvalues
, are at the top left of the Schur form, and computes reciprocal
, condition numbers for the average of the selected eigenvalues,
, and for the associated right invariant subspace.
gams d4a2
file clapack/double/dgeevx.c
for Computes the eigenvalues and left and right eigenvectors of
, a general matrix, with preliminary balancing of the matrix,
, and computes reciprocal condition numbers for the eigenvalues
, and right eigenvectors.
gams d4a2
# ---------------------------------
# Available COMPUTATIONAL routines:
# ---------------------------------
file clapack/double/dbdsqr.c
for Computes the singular value decomposition (SVD) of a real bidiagonal
, matrix, using the bidiagonal QR algorithm.
gams d6
file clapack/double/ddisna.c
for Computes the reciprocal condition numbers for the eigenvectors of a
, real symmetric or complex Hermitian matrix or for the left or right
, singular vectors of a general matrix.
file clapack/double/dgbbrd.c
, Reduces a general band matrix to real upper bidiagonal form
, by an orthogonal transformation.
file clapack/double/dgbcon.c
for Estimates the reciprocal of the condition number of a general
, band matrix, in either the 1-norm or the infinity-norm, using
, the LU factorization computed by DGBTRF.
gams d2a2
file clapack/double/dgbequ.c
for Computes row and column scalings to equilibrate a general band
, matrix and reduce its condition number.
gams d2a2
file clapack/double/dgbrfs.c
for Improves the computed solution to a general banded system of
, linear equations AX=B, A**T X=B or A**H X=B, and provides forward
, and backward error bounds for the solution.
gams d2a2
file clapack/double/dgbtrf.c
for Computes an LU factorization of a general band matrix, using
, partial pivoting with row interchanges.
gams d2a2
file clapack/double/dgbtrs.c
for Solves a general banded system of linear equations AX=B,
, A**T X=B or A**H X=B, using the LU factorization computed
, by DGBTRF.
gams d2a2
file clapack/double/dgebak.c
for Transforms eigenvectors of a balanced matrix to those of the
, original matrix supplied to DGEBAL.
gams d4c4
file clapack/double/dgebal.c
for Balances a general matrix in order to improve the accuracy
, of computed eigenvalues.
gams d4c1a
file clapack/double/dgebrd.c
for Reduces a general rectangular matrix to real bidiagonal form
, by an orthogonal transformation.
gams d6
file clapack/double/dgecon.c
for Estimates the reciprocal of the condition number of a general
, matrix, in either the 1-norm or the infinity-norm, using the
, LU factorization computed by DGETRF.
gams d2a1
file clapack/double/dgeequ.c
for Computes row and column scalings to equilibrate a general
, rectangular matrix and reduce its condition number.
gams d2a1
file clapack/double/dgehrd.c
for Reduces a general matrix to upper Hessenberg form by an
, orthogonal similarity transformation.
gams d4c1b2
file clapack/double/dgelqf.c
for Computes an LQ factorization of a general rectangular matrix.
gams d5
file clapack/double/dgeqlf.c
for Computes a QL factorization of a general rectangular matrix.
gams d5
file clapack/double/dgeqpf.c
for Computes a QR factorization with column pivoting of a general
, rectangular matrix.
gams d5
file clapack/double/dgeqrf.c
for Computes a QR factorization of a general rectangular matrix.
gams d5
file clapack/double/dgerfs.c
for Improves the computed solution to a general system of linear
, equations AX=B, A**T X=B or A**H X=B, and provides forward and
, backward error bounds for the solution.
gams d2a1
file clapack/double/dgerqf.c
for Computes an RQ factorization of a general rectangular matrix.
gams d5
file clapack/double/dgetrf.c
for Computes an LU factorization of a general matrix, using partial
, pivoting with row interchanges.
gams d2a1
file clapack/double/dgetri.c
for Computes the inverse of a general matrix, using the LU factorization
, computed by DGETRF.
gams d2a1
file clapack/double/dgetrs.c
for Solves a general system of linear equations AX=B, A**T X=B
, or A**H X=B, using the LU factorization computed by DGETRF.
gams d2a1
file clapack/double/dggbak.c
For Forms the right or left eigenvectors of the generalized eigenvalue
, problem by backward transformation on the computed eigenvectors of
, the balanced pair of matrices output by DGGBAL.
file clapack/double/dggbal.c
For Balances a pair of general real matrices for the generalized
, eigenvalue problem A x = lambda B x.
file clapack/double/dgghrd.c
for Reduces a pair of real matrices to generalized upper
, Hessenberg form using orthogonal transformations
file clapack/double/dggqrf.c
for Computes a generalized QR factorization of a pair of matrices.
file clapack/double/dggrqf.c
for Computes a generalized RQ factorization of a pair of matrices.
file clapack/double/dggsvp.c
for Computes orthogonal matrices as a preprocessing step
, for computing the generalized singular value decomposition
file clapack/double/dgtcon.c
for Estimates the reciprocal of the condition number of a general
, tridiagonal matrix, in either the 1-norm or the infinity-norm,
, using the LU factorization computed by DGTTRF.
gams d2a2a
file clapack/double/dgtrfs.c
for Improves the computed solution to a general tridiagonal system
, of linear equations AX=B, A**T X=B or A**H X=B, and provides
, forward and backward error bounds for the solution.
gams d2a2a
file clapack/double/dgttrf.c
for Computes an LU factorization of a general tridiagonal matrix,
, using partial pivoting with row interchanges.
gams d2a2a
file clapack/double/dgttrs.c
for Solves a general tridiagonal system of linear equations AX=B,
, A**T X=B or A**H X=B, using the LU factorization computed by
, DGTTRF.
gams d2a2a
file clapack/double/dhgeqz.c
for Implements a single-/double-shift version of the QZ method for
, finding the generalized eigenvalues of the equation
, det(A - w(i) B) = 0
file clapack/double/dhsein.c
for Computes specified right and/or left eigenvectors of an upper
, Hessenberg matrix by inverse iteration.
gams d4c3
file clapack/double/dhseqr.c
for Computes the eigenvalues and Schur factorization of an upper
, Hessenberg matrix, using the multishift QR algorithm.
gams d4c2b
file clapack/double/dopgtr.c
for Generates the orthogonal transformation matrix from
, a reduction to tridiagonal form determined by SSPTRD.
gams d4c1b1
file clapack/double/dopmtr.c
for Multiplies a general matrix by the orthogonal
, transformation matrix from a reduction to tridiagonal form
, determined by DSPTRD.
gams d4c4
file clapack/double/dorgbr.c
for Generates the orthogonal transformation matrices from
, a reduction to bidiagonal form determined by DGEBRD.
gams d6
file clapack/double/dorghr.c
for Generates the orthogonal transformation matrix from
, a reduction to Hessenberg form determined by DGEHRD.
gams d4c1b2
file clapack/double/dorglq.c
for Generates all or part of the orthogonal matrix Q from
, an LQ factorization determined by DGELQF.
gams d5
file clapack/double/dorgql.c
for Generates all or part of the orthogonal matrix Q from
, a QL factorization determined by DGEQLF.
gams d5
file clapack/double/dorgqr.c
for Generates all or part of the orthogonal matrix Q from
, a QR factorization determined by DGEQRF.
gams d5
file clapack/double/dorgrq.c
for Generates all or part of the orthogonal matrix Q from
, an RQ factorization determined by DGERQF.
gams d5
file clapack/double/dorgtr.c
for Generates the orthogonal transformation matrix from
, a reduction to tridiagonal form determined by DSYTRD.
gams d4c1b1
file clapack/double/dormbr.c
for Multiplies a general matrix by one of the orthogonal
, transformation matrices from a reduction to bidiagonal form
, determined by DGEBRD.
gams d6
file clapack/double/dormhr.c
for Multiplies a general matrix by the orthogonal transformation
, matrix from a reduction to Hessenberg form determined by DGEHRD.
gams d4c4
file clapack/double/dormlq.c
for Multiplies a general matrix by the orthogonal matrix
, from an LQ factorization determined by DGELQF.
gams d5
file clapack/double/dormql.c
for Multiplies a general matrix by the orthogonal matrix
, from a QL factorization determined by DGEQLF.
gams d5
file clapack/double/dormqr.c
for Multiplies a general matrix by the orthogonal matrix
, from a QR factorization determined by DGEQRF.
gams d5
file clapack/double/dormrq.c
for Multiplies a general matrix by the orthogonal matrix
, from an RQ factorization determined by DGERQF.
gams d5
file clapack/double/dormtr.c
for Multiplies a general matrix by the orthogonal
, transformation matrix from a reduction to tridiagonal form
, determined by DSYTRD.
gams d4c4
file clapack/double/dpbcon.c
for Estimates the reciprocal of the condition number of a
, symmetric positive definite band matrix, using the
, Cholesky factorization computed by DPBTRF.
gams d2b2
file clapack/double/dpbequ.c
for Computes row and column scalings to equilibrate a symmetric
, positive definite band matrix and reduce its condition number.
gams d2b2
file clapack/double/dpbrfs.c
for Improves the computed solution to a symmetric positive
, definite banded system of linear equations AX=B, and provides
, forward and backward error bounds for the solution.
gams d2b2
file clapack/double/dpbstf.c
for Computes a split Cholesky factorization of a real symmetric positive
, definite band matrix.
file clapack/double/dpbtrf.c
for Computes the Cholesky factorization of a symmetric
, positive definite band matrix.
gams d2b2
file clapack/double/dpbtrs.c
for Solves a symmetric positive definite banded system
, of linear equations AX=B, using the Cholesky factorization
, computed by DPBTRF.
gams d2b2
file clapack/double/dpocon.c
for Estimates the reciprocal of the condition number of a
, symmetric positive definite matrix, using the
, Cholesky factorization computed by DPOTRF.
gams d2b1b
file clapack/double/dpoequ.c
for Computes row and column scalings to equilibrate a symmetric
, positive definite matrix and reduce its condition number.
gams d2b1b
file clapack/double/dporfs.c
for Improves the computed solution to a symmetric positive
, definite system of linear equations AX=B, and provides forward
, and backward error bounds for the solution.
gams d2b1b
file clapack/double/dpotrf.c
for Computes the Cholesky factorization of a symmetric
, positive definite matrix.
gams d2b1b
file clapack/double/dpotri.c
for Computes the inverse of a symmetric positive definite
, matrix, using the Cholesky factorization computed by DPOTRF.
gams d2b1b
file clapack/double/dpotrs.c
for Solves a symmetric positive definite system of linear
, equations AX=B, using the Cholesky factorization computed by
, DPOTRF.
gams d2b1b
file clapack/double/dppcon.c
for Estimates the reciprocal of the condition number of a
, symmetric positive definite matrix in packed storage,
, using the Cholesky factorization computed by DPPTRF.
gams d2b1b
file clapack/double/dppequ.c
for Computes row and column scalings to equilibrate a symmetric
, positive definite matrix in packed storage and reduce its condition
, number.
gams d2b1b
file clapack/double/dpprfs.c
for Improves the computed solution to a symmetric positive
, definite system of linear equations AX=B, where A is held in
, packed storage, and provides forward and backward error bounds
, for the solution.
gams d2b1b
file clapack/double/dpptrf.c
for Computes the Cholesky factorization of a symmetric
, positive definite matrix in packed storage.
gams d2b1b
file clapack/double/dpptri.c
for Computes the inverse of a symmetric positive definite
, matrix in packed storage, using the Cholesky factorization computed
, by DPPTRF.
gams d2b1b
file clapack/double/dpptrs.c
for Solves a symmetric positive definite system of linear
, equations AX=B, where A is held in packed storage, using the
, Cholesky factorization computed by DPPTRF.
gams d2b1b
file clapack/double/dptcon.c
for Computes the reciprocal of the condition number of a
, symmetric positive definite tridiagonal matrix,
, using the LDL**H factorization computed by DPTTRF.
gams d2b2a
file clapack/double/dpteqr.c
for Computes all eigenvalues and eigenvectors of a real symmetric
, positive definite tridiagonal matrix, by computing the SVD of
, its bidiagonal Cholesky factor.
gams d4c2a
file clapack/double/dptrfs.c
for Improves the computed solution to a symmetric positive
, definite tridiagonal system of linear equations AX=B, and provides
, forward and backward error bounds for the solution.
gams d2b2a
file clapack/double/dpttrf.c
for Computes the LDL**H factorization of a symmetric
, positive definite tridiagonal matrix.
gams d2b2a
file clapack/double/dpttrs.c
for Solves a symmetric positive definite tridiagonal
, system of linear equations, using the LDL**H factorization
, computed by DPTTRF.
gams d2b2a
file clapack/double/dsbgst.c
for Reduces a real symmetric-definite banded generalized eigenproblem
, A x = lambda B x to standard form, where B has been factorized by
, DPBSTF (Crawford's algorithm).
file clapack/double/dsbtrd.c
for Reduces a symmetric band matrix to real symmetric
, tridiagonal form by an orthogonal similarity transformation.
gams d4c1b1
file clapack/double/dspcon.c
for Estimates the reciprocal of the condition number of a
, real symmetric indefinite
, matrix in packed storage, using the factorization computed
, by DSPTRF.
gams d2b1a
file clapack/double/dspgst.c
for Reduces a symmetric-definite generalized eigenproblem
, Ax= lambda Bx, ABx= lambda x, or BAx= lambda x, to standard
, form, where A and B are held in packed storage, and B has been
, factorized by DPPTRF.
gams d4c1c
file clapack/double/dsprfs.c
for Improves the computed solution to a real
, symmetric indefinite system of linear equations
, AX=B, where A is held in packed storage, and provides forward
, and backward error bounds for the solution.
gams d2b1a
file clapack/double/dsptrd.c
for Reduces a symmetric matrix in packed storage to real
, symmetric tridiagonal form by an orthogonal similarity
, transformation.
gams d4c1b1
file clapack/double/dsptrf.c
for Computes the factorization of a real
, symmetric-indefinite matrix in packed storage,
, using the diagonal pivoting method.
gams d2b1a
file clapack/double/dsptri.c
for Computes the inverse of a real symmetric
, indefinite matrix in packed storage, using the factorization
, computed by DSPTRF.
gams d2b1a
file clapack/double/dsptrs.c
for Solves a real symmetric
, indefinite system of linear equations AX=B, where A is held
, in packed storage, using the factorization computed
, by DSPTRF.
gams d2b1a
file clapack/double/dstebz.c
for Computes selected eigenvalues of a real symmetric tridiagonal
, matrix by bisection.
gams d4c2a
file clapack/double/dstedc.c
for Computes all eigenvalues and, optionally, eigenvectors of a
, symmetric tridiagonal matrix using the divide and conquer algorithm.
file clapack/double/dstein.c
for Computes selected eigenvectors of a real symmetric tridiagonal
, matrix by inverse iteration.
gams d4c3
file clapack/double/dsteqr.c
for Computes all eigenvalues and eigenvectors of a real symmetric
, tridiagonal matrix, using the implicit QL or QR algorithm.
gams d4a1, d4a5, d4c2a
file clapack/double/dsterf.c
for Computes all eigenvalues of a real symmetric tridiagonal matrix,
, using a root-free variant of the QL or QR algorithm.
gams d4c2a
file clapack/double/dsycon.c
for Estimates the reciprocal of the condition number of a
, real symmetric indefinite matrix,
, using the factorization computed by DSYTRF.
gams d2b1a
file clapack/double/dsygst.c
for Reduces a symmetric-definite generalized eigenproblem
, Ax= lambda Bx, ABx= lambda x, or BAx= lambda x, to standard
, form, where B has been factorized by DPOTRF.
gams d4c1c
file clapack/double/dsyrfs.c
for Improves the computed solution to a real
, symmetric indefinite system of linear equations
, AX=B, and provides forward and backward error bounds for the
, solution.
gams d2b1a
file clapack/double/dsytrd.c
for Reduces a symmetric matrix to real symmetric tridiagonal
, form by an orthogonal similarity transformation.
gams d4c1b1
file clapack/double/dsytrf.c
for Computes the factorization of a real symmetric-indefinite matrix,
, using the diagonal pivoting method.
gams d2b1a
file clapack/double/dsytri.c
for Computes the inverse of a real symmetric indefinite matrix,
, using the factorization computed by DSYTRF.
gams d2b1a
file clapack/double/dsytrs.c
for Solves a real symmetric indefinite system of linear equations AX=B,
, using the factorization computed by DSPTRF.
gams d2b1a
file clapack/double/dtbcon.c
for Estimates the reciprocal of the condition number of a triangular
, band matrix, in either the 1-norm or the infinity-norm.
gams d2a2, d2a3
file clapack/double/dtbrfs.c
for Provides forward and backward error bounds for the solution
, of a triangular banded system of linear equations AX=B,
, A**T X=B or A**H X=B.
gams d2a2, d2a3
file clapack/double/dtbtrs.c
for Solves a triangular banded system of linear equations AX=B,
, A**T X=B or A**H X=B.
gams d2a2, d2a3
file clapack/double/dtgevc.c
for Computes some or all of the right and/or left generalized eigenvectors
, of a pair of upper triangular matrices.
gams d4b2
file clapack/double/dtgsja.c
for Computes the generalized singular value decomposition of two real
, upper triangular (or trapezoidal) matrices as output by DGGSVP.
gams d6
file clapack/double/dtpcon.c
for Estimates the reciprocal of the condition number of a triangular
, matrix in packed storage, in either the 1-norm or the infinity-norm.
gams d2a3
file clapack/double/dtprfs.c
for Provides forward and backward error bounds for the solution
, of a triangular system of linear equations AX=B, A**T X=B or
, A**H X=B, where A is held in packed storage.
gams d2a3
file clapack/double/dtptri.c
for Computes the inverse of a triangular matrix in packed storage.
gams d2a3
file clapack/double/dtptrs.c
for Solves a triangular system of linear equations AX=B,
, A**T X=B or A**H X=B, where A is held in packed storage.
gams d2a3
file clapack/double/dtrcon.c
for Estimates the reciprocal of the condition number of a triangular
, matrix, in either the 1-norm or the infinity-norm.
gams d2a3
file clapack/double/dtrevc.c
for Computes some or all of the right and/or left eigenvectors of
, an upper quasi-triangular matrix.
gams d4c3
file clapack/double/dtrexc.c
for Reorders the Schur factorization of a matrix by an orthogonal
, similarity transformation.
gams d4c
file clapack/double/dtrrfs.c
for Provides forward and backward error bounds for the solution
, of a triangular system of linear equations A X=B, A**T X=B or
, A**H X=B.
gams d2a3
file clapack/double/dtrsen.c
for Reorders the Schur factorization of a matrix in order to find
, an orthonormal basis of a right invariant subspace corresponding
, to selected eigenvalues, and returns reciprocal condition numbers
, (sensitivities) of the average of the cluster of eigenvalues
, and of the invariant subspace.
gams d4c
file clapack/double/dtrsna.c
for Estimates the reciprocal condition numbers (sensitivities)
, of selected eigenvalues and eigenvectors of an upper
, quasi-triangular matrix.
gams d4c
file clapack/double/dtrsyl.c
for Solves the Sylvester matrix equation A X +/- X B=C where A
, and B are upper quasi-triangular, and may be transposed.
gams d8
file clapack/double/dtrtri.c
for Computes the inverse of a triangular matrix.
gams d2a3
file clapack/double/dtrtrs.c
for Solves a triangular system of linear equations AX=B,
, A**T X=B or A**H X=B.
gams d2a3
file clapack/double/dtzrqf.c
for Computes an RQ factorization of an upper trapezoidal matrix.
gams d5
# --------------------------------------------------------
# Available SIMPLE and DIVIDE AND CONQUER DRIVER routines:
# --------------------------------------------------------
file clapack/single/sgesv.c
for Solves a general system of linear equations AX=B.
gams d2a1
file clapack/single/sgbsv.c
for Solves a general banded system of linear equations AX=B.
gams d2a2
file clapack/single/sgtsv.c
for Solves a general tridiagonal system of linear equations AX=B.
gams d2a2a
file clapack/single/sposv.c
for Solves a symmetric positive definite system of linear
, equations AX=B.
gams d2b1b
file clapack/single/sppsv.c
for Solves a symmetric positive definite system of linear
, equations AX=B, where A is held in packed storage.
gams d2b1b
file clapack/single/spbsv.c
for Solves a symmetric positive definite banded system
, of linear equations AX=B.
gams d2b2
file clapack/single/sptsv.c
for Solves a symmetric positive definite tridiagonal system
, of linear equations AX=B.
gams d2b2a
file clapack/single/ssysv.c
for Solves a real symmetric indefinite system of linear equations AX=B.
gams d2b1a
file clapack/single/sspsv.c
for Solves a real symmetric indefinite system of linear equations AX=B,
, where A is held in packed storage.
gams d2b1a
file clapack/single/sgels.c
for Computes the least squares solution to an over-determined system
, of linear equations, A X=B or A**H X=B, or the minimum norm
, solution of an under-determined system, where A is a general
, rectangular matrix of full rank, using a QR or LQ factorization
, of A.
gams d9a1
file clapack/single/sgglse.c
for Solves the LSE (Constrained Linear Least Squares Problem) using
, the GRQ (Generalized RQ) factorization
gams d9b1
file clapack/single/sggglm.c
for Solves the GLM (Generalized Linear Regression Model) using
, the GQR (Generalized QR) factorization
file clapack/single/ssyev.c
for Computes all eigenvalues, and optionally, eigenvectors of a real
, symmetric matrix.
gams d4a1
file clapack/single/ssyevd.c
for Computes all eigenvalues, and optionally, eigenvectors of a real
, symmetric matrix. If eigenvectors are desired, it uses a divide
, and conquer algorithm.
gams d4a1
file clapack/single/sspev.c
for Computes all eigenvalues, and optionally, eigenvectors of a real
, symmetric matrix in packed storage.
gams d4a1
file clapack/single/sspevd.c
for Computes all eigenvalues, and optionally, eigenvectors of a real
, symmetric matrix in packed storage. If eigenvectors are desired,
, it uses a divide and conquer algorithm.
gams d4a1
file clapack/single/ssbev.c
for Computes all eigenvalues, and optionally, eigenvectors of a real
, symmetric band matrix.
gams d4a1, d4a6
file clapack/single/ssbevd.c
for Computes all eigenvalues, and optionally, eigenvectors of a real
, symmetric band matrix. If eigenvectors are desired, it uses a
, divide and conquer algorithm.
gams d4a1, d4a6
file clapack/single/sstev.c
for Computes all eigenvalues, and optionally, eigenvectors of a real
, symmetric tridiagonal matrix.
gams d4a1, d4a5
file clapack/single/sstevd.c
for Computes all eigenvalues, and optionally, eigenvectors of a real
, symmetric tridiagonal matrix. If eigenvectors are desired, it uses
, a divide and conquer algorithm.
gams d4a1, d4a5
file clapack/single/sgees.c
for Computes the eigenvalues and Schur factorization of a general
, matrix, and orders the factorization so that selected eigenvalues
, are at the top left of the Schur form.
gams d4a2
file clapack/single/sgeev.c
for Computes the eigenvalues and left and right eigenvectors of
, a general matrix.
gams d4a2
file clapack/single/sgesvd.c
for Computes the singular value decomposition (SVD) of a general
, rectangular matrix.
gams d6
file clapack/single/ssygv.c
for Computes all eigenvalues and the eigenvectors of a generalized
, symmetric-definite generalized eigenproblem,
, Ax= lambda Bx, ABx= lambda x, or BAx= lambda x.
gams d4b1
file clapack/single/sspgv.c
for Computes all eigenvalues and eigenvectors of a generalized
, symmetric-definite generalized eigenproblem, Ax= lambda
, Bx, ABx= lambda x, or BAx= lambda x, where A and B are in packed
, storage.
gams d4b1
file clapack/single/ssbgv.c
for Computes all the eigenvalues, and optionally, the eigenvectors
, of a real generalized symmetric-definite banded eigenproblem, of
, the form A*x=(lambda)*B*x. A and B are assumed to be symmetric
, and banded, and B is also positive definite.
file clapack/single/sgegs.c
for Computes the generalized eigenvalues, Schur form, and left and/or
, right Schur vectors for a pair of nonsymmetric matrices
file clapack/single/sgegv.c
for Computes the generalized eigenvalues, and left and/or right
, generalized eigenvectors for a pair of nonsymmetric matrices
file clapack/single/sggsvd.c
for Computes the Generalized Singular Value Decomposition
# ---------------------------------
# Available EXPERT DRIVER routines:
# ---------------------------------
file clapack/single/sgesvx.c
for Solves a general system of linear equations AX=B, A**T X=B
, or A**H X=B, and provides an estimate of the condition number
, and error bounds on the solution.
gams d2a1
file clapack/single/sgbsvx.c
for Solves a general banded system of linear equations AX=B,
, A**T X=B or A**H X=B, and provides an estimate of the condition
, number and error bounds on the solution.
gams d2a2
file clapack/single/sgtsvx.c
for Solves a general tridiagonal system of linear equations AX=B,
, A**T X=B or A**H X=B, and provides an estimate of the condition
, number and error bounds on the solution.
gams d2a2a
file clapack/single/sposvx.c
for Solves a symmetric positive definite system of linear
, equations AX=B, and provides an estimate of the condition number
, and error bounds on the solution.
gams d2b1b
file clapack/single/sppsvx.c
for Solves a symmetric positive definite system of linear
, equations AX=B, where A is held in packed storage, and provides
, an estimate of the condition number and error bounds on the
, solution.
gams d2b1b
file clapack/single/spbsvx.c
for Solves a symmetric positive definite banded system
, of linear equations AX=B, and provides an estimate of the condition
, number and error bounds on the solution.
gams d2b2
file clapack/single/sptsvx.c
for Solves a symmetric positive definite tridiagonal
, system of linear equations AX=B, and provides an estimate of
, the condition number and error bounds on the solution.
gams d2b2a
file clapack/single/ssysvx.c
for Solves a real symmetric
, indefinite system of linear equations AX=B, and provides an
, estimate of the condition number and error bounds on the solution.
gams d2b1a
file clapack/single/sspsvx.c
for Solves a real symmetric
, indefinite system of linear equations AX=B, where A is held
, in packed storage, and provides an estimate of the condition
, number and error bounds on the solution.
gams d2b1a
file clapack/single/sgelsx.c
for Computes the minimum norm least squares solution to an over-
, or under-determined system of linear equations A X=B, using a
, complete orthogonal factorization of A.
gams d9a1
file clapack/single/sgelss.c
for Computes the minimum norm least squares solution to an over-
, or under-determined system of linear equations A X=B, using
, the singular value decomposition of A.
gams d9a1
file clapack/single/ssyevx.c
for Computes selected eigenvalues and eigenvectors of a symmetric matrix.
gams d4a1
file clapack/single/sspevx.c
for Computes selected eigenvalues and eigenvectors of a
, symmetric matrix in packed storage.
gams d4a1
file clapack/single/ssbevx.c
for Computes selected eigenvalues and eigenvectors of a
, symmetric band matrix.
gams d4a1, d4a6
file clapack/single/sstevx.c
for Computes selected eigenvalues and eigenvectors of a real
, symmetric tridiagonal matrix.
gams d4a1, d4a5
file clapack/single/sgeesx.c
for Computes the eigenvalues and Schur factorization of a general
, matrix, orders the factorization so that selected eigenvalues
, are at the top left of the Schur form, and computes reciprocal
, condition numbers for the average of the selected eigenvalues,
, and for the associated right invariant subspace.
gams d4a2
file clapack/single/sgeevx.c
for Computes the eigenvalues and left and right eigenvectors of
, a general matrix, with preliminary balancing of the matrix,
, and computes reciprocal condition numbers for the eigenvalues
, and right eigenvectors.
gams d4a2
# ---------------------------------
# Available COMPUTATIONAL routines:
# ---------------------------------
file clapack/single/sbdsqr.c
for Computes the singular value decomposition (SVD) of a real bidiagonal
, matrix, using the bidiagonal QR algorithm.
gams d6
file clapack/single/sdisna.c
for Computes the reciprocal condition numbers for the eigenvectors of a
, real symmetric or complex Hermitian matrix or for the left or right
, singular vectors of a general matrix.
file clapack/single/sgbbrd.c
, Reduces a general band matrix to real upper bidiagonal form
, by an orthogonal transformation.
file clapack/single/sgbcon.c
for Estimates the reciprocal of the condition number of a general
, band matrix, in either the 1-norm or the infinity-norm, using
, the LU factorization computed by SGBTRF.
gams d2a2
file clapack/single/sgbequ.c
for Computes row and column scalings to equilibrate a general band
, matrix and reduce its condition number.
gams d2a2
file clapack/single/sgbrfs.c
for Improves the computed solution to a general banded system of
, linear equations AX=B, A**T X=B or A**H X=B, and provides forward
, and backward error bounds for the solution.
gams d2a2
file clapack/single/sgbtrf.c
for Computes an LU factorization of a general band matrix, using
, partial pivoting with row interchanges.
gams d2a2
file clapack/single/sgbtrs.c
for Solves a general banded system of linear equations AX=B,
, A**T X=B or A**H X=B, using the LU factorization computed
, by SGBTRF.
gams d2a2
file clapack/single/sgebak.c
for Transforms eigenvectors of a balanced matrix to those of the
, original matrix supplied to SGEBAL.
gams d4c4
file clapack/single/sgebal.c
for Balances a general matrix in order to improve the accuracy
, of computed eigenvalues.
gams d4c1a
file clapack/single/sgebrd.c
for Reduces a general rectangular matrix to real bidiagonal form
, by an orthogonal transformation.
gams d6
file clapack/single/sgecon.c
for Estimates the reciprocal of the condition number of a general
, matrix, in either the 1-norm or the infinity-norm, using the
, LU factorization computed by SGETRF.
gams d2a1
file clapack/single/sgeequ.c
for Computes row and column scalings to equilibrate a general
, rectangular matrix and reduce its condition number.
gams d2a1
file clapack/single/sgehrd.c
for Reduces a general matrix to upper Hessenberg form by an
, orthogonal similarity transformation.
gams d4c1b2
file clapack/single/sgelqf.c
for Computes an LQ factorization of a general rectangular matrix.
gams d5
file clapack/single/sgeqlf.c
for Computes a QL factorization of a general rectangular matrix.
gams d5
file clapack/single/sgeqpf.c
for Computes a QR factorization with column pivoting of a general
, rectangular matrix.
gams d5
file clapack/single/sgeqrf.c
for Computes a QR factorization of a general rectangular matrix.
gams d5
file clapack/single/sgerfs.c
for Improves the computed solution to a general system of linear
, equations AX=B, A**T X=B or A**H X=B, and provides forward and
, backward error bounds for the solution.
gams d2a1
file clapack/single/sgerqf.c
for Computes an RQ factorization of a general rectangular matrix.
gams d5
file clapack/single/sgetrf.c
for Computes an LU factorization of a general matrix, using partial
, pivoting with row interchanges.
gams d2a1
file clapack/single/sgetri.c
for Computes the inverse of a general matrix, using the LU factorization
, computed by SGETRF.
gams d2a1
file clapack/single/sgetrs.c
for Solves a general system of linear equations AX=B, A**T X=B
, or A**H X=B, using the LU factorization computed by SGETRF.
gams d2a1
file clapack/single/sggbak.c
For Forms the right or left eigenvectors of the generalized eigenvalue
, problem by backward transformation on the computed eigenvectors of
, the balanced pair of matrices output by SGGBAL.
file clapack/single/sggbal.c
For Balances a pair of general real matrices for the generalized
, eigenvalue problem A x = lambda B x.
file clapack/single/sgghrd.c
for Reduces a pair of real matrices to generalized upper
, Hessenberg form using orthogonal transformations
file clapack/single/sggqrf.c
for Computes a generalized QR factorization of a pair of matrices.
file clapack/single/sggrqf.c
for Computes a generalized RQ factorization of a pair of matrices.
file clapack/single/sggsvp.c
for Computes orthogonal matrices as a preprocessing step
, for computing the generalized singular value decomposition
file clapack/single/sgtcon.c
for Estimates the reciprocal of the condition number of a general
, tridiagonal matrix, in either the 1-norm or the infinity-norm,
, using the LU factorization computed by SGTTRF.
gams d2a2a
file clapack/single/sgtrfs.c
for Improves the computed solution to a general tridiagonal system
, of linear equations AX=B, A**T X=B or A**H X=B, and provides
, forward and backward error bounds for the solution.
gams d2a2a
file clapack/single/sgttrf.c
for Computes an LU factorization of a general tridiagonal matrix,
, using partial pivoting with row interchanges.
gams d2a2a
file clapack/single/sgttrs.c
for Solves a general tridiagonal system of linear equations AX=B,
, A**T X=B or A**H X=B, using the LU factorization computed by
, SGTTRF.
gams d2a2a
file clapack/single/shgeqz.c
for Implements a single-/double-shift version of the QZ method for
, finding the generalized eigenvalues of the equation
, det(A - w(i) B) = 0
file clapack/single/shsein.c
for Computes specified right and/or left eigenvectors of an upper
, Hessenberg matrix by inverse iteration.
gams d4c3
file clapack/single/shseqr.c
for Computes the eigenvalues and Schur factorization of an upper
, Hessenberg matrix, using the multishift QR algorithm.
gams d4c2b
file clapack/single/sopgtr.c
for Generates the orthogonal transformation matrix from
, a reduction to tridiagonal form determined by SSPTRD.
gams d4c1b1
file clapack/single/sopmtr.c
for Multiplies a general matrix by the orthogonal
, transformation matrix from a reduction to tridiagonal form
, determined by SSPTRD.
gams d4c4
file clapack/single/sorgbr.c
for Generates the orthogonal transformation matrices from
, a reduction to bidiagonal form determined by SGEBRD.
gams d6
file clapack/single/sorghr.c
for Generates the orthogonal transformation matrix from
, a reduction to Hessenberg form determined by SGEHRD.
gams d4c1b2
file clapack/single/sorglq.c
for Generates all or part of the orthogonal matrix Q from
, an LQ factorization determined by SGELQF.
gams d5
file clapack/single/sorgql.c
for Generates all or part of the orthogonal matrix Q from
, a QL factorization determined by SGEQLF.
gams d5
file clapack/single/sorgqr.c
for Generates all or part of the orthogonal matrix Q from
, a QR factorization determined by SGEQRF.
gams d5
file clapack/single/sorgrq.c
for Generates all or part of the orthogonal matrix Q from
, an RQ factorization determined by SGERQF.
gams d5
file clapack/single/sorgtr.c
for Generates the orthogonal transformation matrix from
, a reduction to tridiagonal form determined by SSYTRD.
gams d4c1b1
file clapack/single/sormbr.c
for Multiplies a general matrix by one of the orthogonal
, transformation matrices from a reduction to bidiagonal form
, determined by SGEBRD.
gams d6
file clapack/single/sormhr.c
for Multiplies a general matrix by the orthogonal transformation
, matrix from a reduction to Hessenberg form determined by SGEHRD.
gams d4c4
file clapack/single/sormlq.c
for Multiplies a general matrix by the orthogonal matrix
, from an LQ factorization determined by SGELQF.
gams d5
file clapack/single/sormql.c
for Multiplies a general matrix by the orthogonal matrix
, from a QL factorization determined by SGEQLF.
gams d5
file clapack/single/sormqr.c
for Multiplies a general matrix by the orthogonal matrix
, from a QR factorization determined by SGEQRF.
gams d5
file clapack/single/sormrq.c
for Multiplies a general matrix by the orthogonal matrix
, from an RQ factorization determined by SGERQF.
gams d5
file clapack/single/sormtr.c
for Multiplies a general matrix by the orthogonal
, transformation matrix from a reduction to tridiagonal form
, determined by SSYTRD.
gams d4c4
file clapack/single/spbcon.c
for Estimates the reciprocal of the condition number of a
, symmetric positive definite band matrix, using the
, Cholesky factorization computed by SPBTRF.
gams d2b2
file clapack/single/spbequ.c
for Computes row and column scalings to equilibrate a symmetric
, positive definite band matrix and reduce its condition number.
gams d2b2
file clapack/single/spbrfs.c
for Improves the computed solution to a symmetric positive
, definite banded system of linear equations AX=B, and provides
, forward and backward error bounds for the solution.
gams d2b2
file clapack/single/spbstf.c
for Computes a split Cholesky factorization of a real symmetric positive
, definite band matrix.
file clapack/single/spbtrf.c
for Computes the Cholesky factorization of a symmetric
, positive definite band matrix.
gams d2b2
file clapack/single/spbtrs.c
for Solves a symmetric positive definite banded system
, of linear equations AX=B, using the Cholesky factorization
, computed by SPBTRF.
gams d2b2
file clapack/single/spocon.c
for Estimates the reciprocal of the condition number of a
, symmetric positive definite matrix, using the
, Cholesky factorization computed by SPOTRF.
gams d2b1b
file clapack/single/spoequ.c
for Computes row and column scalings to equilibrate a symmetric
, positive definite matrix and reduce its condition number.
gams d2b1b
file clapack/single/sporfs.c
for Improves the computed solution to a symmetric positive
, definite system of linear equations AX=B, and provides forward
, and backward error bounds for the solution.
gams d2b1b
file clapack/single/spotrf.c
for Computes the Cholesky factorization of a symmetric
, positive definite matrix.
gams d2b1b
file clapack/single/spotri.c
for Computes the inverse of a symmetric positive definite
, matrix, using the Cholesky factorization computed by SPOTRF.
gams d2b1b
file clapack/single/spotrs.c
for Solves a symmetric positive definite system of linear
, equations AX=B, using the Cholesky factorization computed by
, SPOTRF.
gams d2b1b
file clapack/single/sppcon.c
for Estimates the reciprocal of the condition number of a
, symmetric positive definite matrix in packed storage,
, using the Cholesky factorization computed by SPPTRF.
gams d2b1b
file clapack/single/sppequ.c
for Computes row and column scalings to equilibrate a symmetric
, positive definite matrix in packed storage and reduce its condition
, number.
gams d2b1b
file clapack/single/spprfs.c
for Improves the computed solution to a symmetric positive
, definite system of linear equations AX=B, where A is held in
, packed storage, and provides forward and backward error bounds
, for the solution.
gams d2b1b
file clapack/single/spptrf.c
for Computes the Cholesky factorization of a symmetric
, positive definite matrix in packed storage.
gams d2b1b
file clapack/single/spptri.c
for Computes the inverse of a symmetric positive definite
, matrix in packed storage, using the Cholesky factorization computed
, by SPPTRF.
gams d2b1b
file clapack/single/spptrs.c
for Solves a symmetric positive definite system of linear
, equations AX=B, where A is held in packed storage, using the
, Cholesky factorization computed by SPPTRF.
gams d2b1b
file clapack/single/sptcon.c
for Computes the reciprocal of the condition number of a
, symmetric positive definite tridiagonal matrix,
, using the LDL**H factorization computed by SPTTRF.
gams d2b2a
file clapack/single/spteqr.c
for Computes all eigenvalues and eigenvectors of a real symmetric
, positive definite tridiagonal matrix, by computing the SVD of
, its bidiagonal Cholesky factor.
gams d4c2a
file clapack/single/sptrfs.c
for Improves the computed solution to a symmetric positive
, definite tridiagonal system of linear equations AX=B, and provides
, forward and backward error bounds for the solution.
gams d2b2a
file clapack/single/spttrf.c
for Computes the LDL**H factorization of a symmetric
, positive definite tridiagonal matrix.
gams d2b2a
file clapack/single/spttrs.c
for Solves a symmetric positive definite tridiagonal
, system of linear equations, using the LDL**H factorization
, computed by SPTTRF.
gams d2b2a
file clapack/single/ssbgst.c
for Reduces a real symmetric-definite banded generalized eigenproblem
, A x = lambda B x to standard form, where B has been factorized by
, SPBSTF (Crawford's algorithm).
file clapack/single/ssbtrd.c
for Reduces a symmetric band matrix to real symmetric
, tridiagonal form by an orthogonal similarity transformation.
gams d4c1b1
file clapack/single/sspcon.c
for Estimates the reciprocal of the condition number of a
, real symmetric indefinite
, matrix in packed storage, using the factorization computed
, by SSPTRF.
gams d2b1a
file clapack/single/sspgst.c
for Reduces a symmetric-definite generalized eigenproblem
, Ax= lambda Bx, ABx= lambda x, or BAx= lambda x, to standard
, form, where A and B are held in packed storage, and B has been
, factorized by SPPTRF.
gams d4c1c
file clapack/single/ssprfs.c
for Improves the computed solution to a real
, symmetric indefinite system of linear equations
, AX=B, where A is held in packed storage, and provides forward
, and backward error bounds for the solution.
gams d2b1a
file clapack/single/ssptrd.c
for Reduces a symmetric matrix in packed storage to real
, symmetric tridiagonal form by an orthogonal similarity
, transformation.
gams d4c1b1
file clapack/single/ssptrf.c
for Computes the factorization of a real
, symmetric-indefinite matrix in packed storage,
, using the diagonal pivoting method.
gams d2b1a
file clapack/single/ssptri.c
for Computes the inverse of a real symmetric
, indefinite matrix in packed storage, using the factorization
, computed by SSPTRF.
gams d2b1a
file clapack/single/ssptrs.c
for Solves a real symmetric
, indefinite system of linear equations AX=B, where A is held
, in packed storage, using the factorization computed
, by SSPTRF.
gams d2b1a
file clapack/single/sstebz.c
for Computes selected eigenvalues of a real symmetric tridiagonal
, matrix by bisection.
gams d4c2a
file clapack/single/sstedc.c
for Computes all eigenvalues and, optionally, eigenvectors of a
, symmetric tridiagonal matrix using the divide and conquer algorithm.
file clapack/single/sstein.c
for Computes selected eigenvectors of a real symmetric tridiagonal
, matrix by inverse iteration.
gams d4c3
file clapack/single/ssteqr.c
for Computes all eigenvalues and eigenvectors of a real symmetric
, tridiagonal matrix, using the implicit QL or QR algorithm.
gams d4a1, d4a5, d4c2a
file clapack/single/ssterf.c
for Computes all eigenvalues of a real symmetric tridiagonal matrix,
, using a root-free variant of the QL or QR algorithm.
gams d4c2a
file clapack/single/ssycon.c
for Estimates the reciprocal of the condition number of a
, real symmetric indefinite matrix,
, using the factorization computed by SSYTRF.
gams d2b1a
file clapack/single/ssygst.c
for Reduces a symmetric-definite generalized eigenproblem
, Ax= lambda Bx, ABx= lambda x, or BAx= lambda x, to standard
, form, where B has been factorized by SPOTRF.
gams d4c1c
file clapack/single/ssyrfs.c
for Improves the computed solution to a real
, symmetric indefinite system of linear equations
, AX=B, and provides forward and backward error bounds for the
, solution.
gams d2b1a
file clapack/single/ssytrd.c
for Reduces a symmetric matrix to real symmetric tridiagonal
, form by an orthogonal similarity transformation.
gams d4c1b1
file clapack/single/ssytrf.c
for Computes the factorization of a real symmetric-indefinite matrix,
, using the diagonal pivoting method.
gams d2b1a
file clapack/single/ssytri.c
for Computes the inverse of a real symmetric indefinite matrix,
, using the factorization computed by SSYTRF.
gams d2b1a
file clapack/single/ssytrs.c
for Solves a real symmetric indefinite system of linear equations AX=B,
, using the factorization computed by SSPTRF.
gams d2b1a
file clapack/single/stbcon.c
for Estimates the reciprocal of the condition number of a triangular
, band matrix, in either the 1-norm or the infinity-norm.
gams d2a2, d2a3
file clapack/single/stbrfs.c
for Provides forward and backward error bounds for the solution
, of a triangular banded system of linear equations AX=B,
, A**T X=B or A**H X=B.
gams d2a2, d2a3
file clapack/single/stbtrs.c
for Solves a triangular banded system of linear equations AX=B,
, A**T X=B or A**H X=B.
gams d2a2, d2a3
file clapack/single/stgevc.c
for Computes some or all of the right and/or left generalized eigenvectors
, of a pair of upper triangular matrices.
gams d4b2
file clapack/single/stgsja.c
for Computes the generalized singular value decomposition of two real
, upper triangular (or trapezoidal) matrices as output by SGGSVP.
gams d6
file clapack/single/stpcon.c
for Estimates the reciprocal of the condition number of a triangular
, matrix in packed storage, in either the 1-norm or the infinity-norm.
gams d2a3
file clapack/single/stprfs.c
for Provides forward and backward error bounds for the solution
, of a triangular system of linear equations AX=B, A**T X=B or
, A**H X=B, where A is held in packed storage.
gams d2a3
file clapack/single/stptri.c
for Computes the inverse of a triangular matrix in packed storage.
gams d2a3
file clapack/single/stptrs.c
for Solves a triangular system of linear equations AX=B,
, A**T X=B or A**H X=B, where A is held in packed storage.
gams d2a3
file clapack/single/strcon.c
for Estimates the reciprocal of the condition number of a triangular
, matrix, in either the 1-norm or the infinity-norm.
gams d2a3
file clapack/single/strevc.c
for Computes some or all of the right and/or left eigenvectors of
, an upper quasi-triangular matrix.
gams d4c3
file clapack/single/strexc.c
for Reorders the Schur factorization of a matrix by an orthogonal
, similarity transformation.
gams d4c
file clapack/single/strrfs.c
for Provides forward and backward error bounds for the solution
, of a triangular system of linear equations A X=B, A**T X=B or
, A**H X=B.
gams d2a3
file clapack/single/strsen.c
for Reorders the Schur factorization of a matrix in order to find
, an orthonormal basis of a right invariant subspace corresponding
, to selected eigenvalues, and returns reciprocal condition numbers
, (sensitivities) of the average of the cluster of eigenvalues
, and of the invariant subspace.
gams d4c
file clapack/single/strsna.c
for Estimates the reciprocal condition numbers (sensitivities)
, of selected eigenvalues and eigenvectors of an upper
, quasi-triangular matrix.
gams d4c
file clapack/single/strsyl.c
for Solves the Sylvester matrix equation A X +/- X B=C where A
, and B are upper quasi-triangular, and may be transposed.
gams d8
file clapack/single/strtri.c
for Computes the inverse of a triangular matrix.
gams d2a3
file clapack/single/strtrs.c
for Solves a triangular system of linear equations AX=B,
, A**T X=B or A**H X=B.
gams d2a3
file clapack/single/stzrqf.c
for Computes an RQ factorization of an upper trapezoidal matrix.
gams d5
#######################################
# Index for clapack/testing/eig #
#######################################
file clapack/testing/eig/index
for This index
file clapack/testing/eig/xerbla.c
for Special version of this routine used in testing
file clapack/testing/eig/ilaenv.c
for Special version of this routine for testing and timing purposes
file clapack/testing/eig/xlaenv.c
for Resets ILAENV values for testing purposes
# ==========================================
# Available Eigenproblem Testing Routines
# ==========================================
file clapack/testing/eig/schkee.c
for Test program driver for eigenproblem testing
prec single
file clapack/testing/eig/dchkee.c
for Test program driver for eigenproblem testing
prec double
file clapack/testing/eig/cchkee.c
for Test program driver for eigenproblem testing
prec complex
file clapack/testing/eig/zchkee.c
for Test program driver for eigenproblem testing
prec doublecomplex
# ===
file clapack/testing/eig/schkbb.c
for Checks the banded SVD routine SGBBRD
prec single
file clapack/testing/eig/dchkbb.c
for Checks the banded SVD routine DGBBRD
prec double
file clapack/testing/eig/cchkbb.c
for Checks the banded SVD routine CGBBRD
prec complex
file clapack/testing/eig/zchkbb.c
for Checks the banded SVD routine ZGBBRD
prec doublecomplex
file clapack/testing/eig/schkbd.c
for Checks the SVD routines (SGEBRD, SORGBR, SBDSQR)
prec single
file clapack/testing/eig/dchkbd.c
for Checks the SVD routines (DGEBRD, DORGBR, DBDSQR)
prec double
file clapack/testing/eig/cchkbd.c
for Checks the SVD routines (CGEBRD, CUNGBR, CBDSQR)
prec complex, doublecomplex
file clapack/testing/eig/zchkbd.c
for Checks the SVD routines (ZGEBRD, ZUNGBR, ZBDSQR)
prec doublecomplex
file clapack/testing/eig/sdrvbd.c
for Checks the SVD driver SGESVD
prec single
file clapack/testing/eig/ddrvbd.c
for Checks the SVD driver DGESVD
prec double
file clapack/testing/eig/cdrvbd.c
for Checks the SVD driver CGESVD
prec complex
file clapack/testing/eig/zdrvbd.c
for Checks the SVD driver ZGESVD
prec doublecomplex
file clapack/testing/eig/serrbd.c
for Tests the error exits for SGEBRD,SORGBR,SORMBR,SBDSQR
prec single
file clapack/testing/eig/derrbd.c
for Tests the error exits for DGEBRD,DORGBR,DORMBR,DBDSQR
prec double
file clapack/testing/eig/cerrbd.c
for Tests the error exits for CGEBRD,CUNGBR,CUNMBR,CBDSQR
prec complex
file clapack/testing/eig/zerrbd.c
for Tests the error exits for ZGEBRD,ZUNGBR,ZUNMBR,ZBDSQR
prec doublecomplex
# ===
file clapack/testing/eig/schkbk.c
for Tests SGEBAK
prec single
file clapack/testing/eig/dchkbk.c
for Tests DGEBAK
prec double
file clapack/testing/eig/cchkbk.c
for Tests CGEBAK
prec complex
file clapack/testing/eig/zchkbk.c
for Tests ZGEBAK
prec doublecomplex
# ===
file clapack/testing/eig/schkbl.c
for Tests SGEBAL
prec single
file clapack/testing/eig/dchkbl.c
for Tests DGEBAL
prec double
file clapack/testing/eig/cchkbl.c
for Tests CGEBAL
prec complex
file clapack/testing/eig/zchkbl.c
for Tests ZGEBAL
prec doublecomplex
# ===
file clapack/testing/eig/schkec.c
for Tests the eigen- condition estimation routines
, STRSYL, STREXC, STRSNA, STRSEN
prec single
file clapack/testing/eig/dchkec.c
for Tests the eigen- condition estimation routines
, DTRSYL, DTREXC, DTRSNA, DTRSEN
prec double
file clapack/testing/eig/cchkec.c
for Tests the eigen- condition estimation routines
, CTRSYL, CTREXC, CTRSNA, CTRSEN
prec complex
file clapack/testing/eig/zchkec.c
for Tests the eigen- condition estimation routines
, ZTRSYL, ZTREXC, ZTRSNA, ZTRSEN
prec doublecomplex
file clapack/testing/eig/serrec.c
for Tests the error exits for the eigen- condition estimation
, routines (STRSYL, STREXC, STRSNA, STRSEN)
prec single
file clapack/testing/eig/derrec.c
for Tests the error exits for the eigen- condition estimation
, routines (DTRSYL, DTREXC, DTRSNA, DTRSEN)
prec double
file clapack/testing/eig/cerrec.c
for Tests the error exits for the eigen- condition estimation
, routines (CTRSYL, CTREXC, CTRSNA, CTRSEN)
prec complex
file clapack/testing/eig/zerrec.c
for Tests the error exits for the eigen- condition estimation
, routines (ZTRSYL, ZTREXC, ZTRSNA, ZTRSEN)
prec doublecomplex
# ===
file clapack/testing/eig/schkgg.c
for Tests SGGHRD, SHGEQZ, and STGEVC
prec single
file clapack/testing/eig/dchkgg.c
for Tests DGGHRD, DHGEQZ, and DTGEVC
prec double
file clapack/testing/eig/cchkgg.c
for Tests CGGHRD, CHGEQZ, and CTGEVC
prec complex
file clapack/testing/eig/zchkgg.c
for Tests ZGGHRD, ZHGEQZ, and ZTGEVC
prec doublecomplex
file clapack/testing/eig/sdrvgg.c
for Tests SGEGS and SGEGV
prec single
file clapack/testing/eig/ddrvgg.c
for Tests DGEGS and DGEGV
prec double
file clapack/testing/eig/cdrvgg.c
for Tests CGEGS and CGEGV
prec complex
file clapack/testing/eig/zdrvgg.c
for Tests ZGEGS and ZGEGV
prec doublecomplex
file clapack/testing/eig/serrgg.c
for Tests the error exits for SGGHRD, SHGEQZ, and STGEVC
prec single
file clapack/testing/eig/derrgg.c
for Tests the error exits for DGGHRD, DHGEQZ, and DTGEVC
prec double
file clapack/testing/eig/cerrgg.c
for Tests the error exits for CGGHRD, CHGEQZ, and CTGEVC
prec complex
file clapack/testing/eig/zerrgg.c
for Tests the error exits for ZGGHRD, ZHGEQZ, and ZTGEVC
prec doublecomplex
# ===
file clapack/testing/eig/schkbk.c
for Testing SGGBAK
prec single
file clapack/testing/eig/dchkbk.c
for Testing DGGBAK
prec double
file clapack/testing/eig/cchkbk.c
for Testing CGGBAK
prec complex
file clapack/testing/eig/zchkbk.c
for Testing ZGGBAK
prec doublecomplex
# ===
file clapack/testing/eig/schkbl.c
for Testing SGGBAL
prec single
file clapack/testing/eig/dchkbl.c
for Testing DGGBAL
prec double
file clapack/testing/eig/cchkbl.c
for Testing CGGBAL
prec complex
file clapack/testing/eig/zchkbl.c
for Testing ZGGBAL
prec doublecomplex
# ===
file clapack/testing/eig/schkhs.c
for Checks the nonsymmetric eigenvalue problem routines
, (SGEHRD, SORGHR, SORMHR, SHSEQR, STREVC, and SHSEIN)
prec single
file clapack/testing/eig/dchkhs.c
for Checks the nonsymmetric eigenvalue problem routines
, (DGEHRD, DORGHR, DORMHR, DHSEQR, DTREVC, and DHSEIN)
prec double
file clapack/testing/eig/cchkhs.c
for Checks the nonsymmetric eigenvalue problem routines
, (CGEHRD, CUNGHR, CUNMHR, CHSEQR, CTREVC, and CHSEIN)
prec complex
file clapack/testing/eig/zchkhs.c
for Checks the nonsymmetric eigenvalue problem routines
, (ZGEHRD, ZUNGHR, ZUNMHR, ZHSEQR, ZTREVC, and ZHSEIN)
prec doublecomplex
file clapack/testing/eig/serrhs.c
for Tests the error exits for SGEHRD, SORGHR, SORMHR, SHSEQR,
, SHSEIN, and STREVC
prec single
file clapack/testing/eig/derrhs.c
for Tests the error exits for DGEHRD, DORGHR, DORMHR, DHSEQR,
, DHSEIN, and DTREVC
prec double
file clapack/testing/eig/cerrhs.c
for Tests the error exits for CGEHRD, CUNGHR, CUNMHR, CHSEQR,
, CHSEIN, and CTREVC
prec complex
file clapack/testing/eig/zerrhs.c
for Tests the error exits for ZGEHRD, ZUNGHR, ZUNMHR, ZHSEQR,
, ZHSEIN, and ZTREVC
prec doublecomplex
file clapack/testing/eig/sdrves.c
for Checks the nonsymmetric eigenvalue (Schur form) problem
, driver SGEES
prec single
file clapack/testing/eig/ddrves.c
for Checks the nonsymmetric eigenvalue (Schur form) problem
, driver DGEES
prec double
file clapack/testing/eig/cdrves.c
for Checks the nonsymmetric eigenvalue (Schur form) problem
, driver CGEES
prec complex
file clapack/testing/eig/zdrves.c
for Checks the nonsymmetric eigenvalue (Schur form) problem
, driver ZGEES
prec doublecomplex
file clapack/testing/eig/sdrvsx.c
for Checks the nonsymmetric eigenvalue (Schur form) problem
, expert driver SGEESX
prec single
file clapack/testing/eig/ddrvsx.c
for Checks the nonsymmetric eigenvalue (Schur form) problem
, expert driver DGEESX
prec double
file clapack/testing/eig/cdrvsx.c
for Checks the nonsymmetric eigenvalue (Schur form) problem
, expert driver CGEESX
prec complex
file clapack/testing/eig/zdrvsx.c
for Checks the nonsymmetric eigenvalue (Schur form) problem
, expert driver ZGEESX
prec doublecomplex
file clapack/testing/eig/sdrvev.c
for Checks the nonsymmetric eigenvalue problem driver SGEEV
prec single
file clapack/testing/eig/ddrvev.c
for Checks the nonsymmetric eigenvalue problem driver DGEEV
prec double
file clapack/testing/eig/cdrvev.c
for Checks the nonsymmetric eigenvalue problem driver CGEEV
prec complex
file clapack/testing/eig/zdrvev.c
for Checks the nonsymmetric eigenvalue problem driver ZGEEV
prec doublecomplex
file clapack/testing/eig/sdrvvx.c
for Checks the nonsymmetric eigenvalue problem expert driver SGEEVX
prec single
file clapack/testing/eig/ddrvvx.c
for Checks the nonsymmetric eigenvalue problem expert driver DGEEVX
prec double
file clapack/testing/eig/cdrvvx.c
for Checks the nonsymmetric eigenvalue problem expert driver CGEEVX
prec complex
file clapack/testing/eig/zdrvvx.c
for Checks the nonsymmetric eigenvalue problem expert driver ZGEEVX
prec doublecomplex
file clapack/testing/eig/serred.c
for Tests the error exits for the eigenvalue driver routines
, (SGEEV,SGEES,SGEEVX,SGEESX,SGESVD)
prec single
file clapack/testing/eig/derred.c
for Tests the error exits for the eigenvalue driver routines
, (DGEEV,DGEES,DGEEVX,DGEESX,DGESVD)
prec double
file clapack/testing/eig/cerred.c
for Tests the error exits for the eigenvalue driver routines
, (CGEEV,CGEES,CGEEVX,CGEESX,CGESVD)
prec complex
file clapack/testing/eig/zerred.c
for Tests the error exits for the eigenvalue driver routines
, (ZGEEV,ZGEES,ZGEEVX,ZGEESX,ZGESVD)
prec doublecomplex
# ===
file clapack/testing/eig/schksb.c
for Tests SSBTRD (the reduction of a symmetric band matrix to
, tridiagonal form, used with the symmetric eigenvalue problem
prec single
file clapack/testing/eig/dchksb.c
for Tests DSBTRD (the reduction of a symmetric band matrix to
, tridiagonal form, used with the symmetric eigenvalue problem
prec double
file clapack/testing/eig/cchkhb.c
for Tests CHBTRD (the reduction of a Hermitian band matrix to
, tridiagonal form), used with the Hermitian eigenvalue problem
prec complex
file clapack/testing/eig/zchkhb.c
for Tests ZHBTRD (the reduction of a Hermitian band matrix to
, tridiagonal form), used with the Hermitian eigenvalue problem
prec doublecomplex
# ===
file clapack/testing/eig/schkst.c
for Checks the symmetric eigenvalue problem routines (SSYTRD,
, SSPTRD,SORGTR,SOPGTR,SSTEQR,SSTERF,SPTEQR,SSTEBZ,SSTEIN)
prec single
file clapack/testing/eig/dchkst.c
for Checks the symmetric eigenvalue problem routines (DSYTRD,
, DSPTRD,DORGTR,DOPGTR,DSTEQR,DSTERF,DPTEQR,DSTEBZ,DSTEIN)
prec double
file clapack/testing/eig/cchkst.c
for Checks the (complex) hermitian eigenvalue problem routines
, (CHETRD,CHPTRD,CUNGTR,CUPGTR,SSTERF,CPTEQR,SSTEBZ,CSTEIN)
prec complex
file clapack/testing/eig/zchkst.c
for Checks the (complex) hermitian eigenvalue problem routines
, (ZHETRD,ZHPTRD,ZUNGTR,ZUPGTR,DSTERF,ZPTEQR,DSTEBZ,ZSTEIN)
prec doublecomplex
file clapack/testing/eig/sdrvst.c
for Checks the symmetric eigenvalue problem drivers
, (SSTEV,SSTEVX,SSYEV,SSYEVX,SSPEV,SSPEVX,SSBEV,SSBEVX)
prec single
file clapack/testing/eig/ddrvst.c
for Checks the symmetric eigenvalue problem drivers
, (DSTEV,DSTEVX,DSYEV,DSYEVX,DSPEV,DSPEVX,DSBEV,DSBEVX)
prec double
file clapack/testing/eig/cdrvst.c
for Checks the Hermitian eigenvalue problem drivers
, (CHEEV,CHEEVX,CHPEV,CHPEVX,CHBEV,CHBEVX)
prec complex
file clapack/testing/eig/zdrvst.c
for Checks the Hermitian eigenvalue problem drivers
, (ZHEEV,ZHEEVX,ZHPEV,ZHPEVX,ZHBEV,ZHBEVX)
prec doublecomplex
file clapack/testing/eig/serrst.c
for Tests the error exits for SSYTRD,SORGTR,SORMTR,SSPTRD,
, SOPGTR,SOPMTR,SSTEQR,SSTERF,SSTEBZ,SSTEIN,SPTEQR,SSBTRD
prec single
file clapack/testing/eig/derrst.c
for Tests the error exits for DSYTRD,DORGTR,DORMTR,DSPTRD,
, DOPGTR,DOPMTR,DSTEQR,DSTERF,DSTEBZ,DSTEIN,DPTEQR,DSBTRD
prec double
file clapack/testing/eig/cerrst.c
for Tests the error exits for CHETRD, CUNGTR, CUNMTR, CHPTRD,
, CUPGTR, CUPMTR, CSTEQR, CSTEIN, CPTEQR, and CHBTRD
prec complex
file clapack/testing/eig/zerrst.c
for Tests the error exits for ZHETRD, ZUNGTR, ZUNMTR, ZHPTRD,
, ZUPGTR, ZUPMTR, ZSTEQR, ZSTEIN, ZPTEQR, and ZHBTRD
prec doublecomplex
file clapack/testing/eig/sdrvsg.c
for Checks the symmetric generalized eigenvalue problem routines
, (SSYGST, SSYTRD, SORGTR, SSTEQR, SSTERF)
prec single
file clapack/testing/eig/ddrvsg.c
for Checks the symmetric generalized eigenvalue problem routines
, (DSYGST, DSYTRD, DORGTR, DSTEQR, DSTERF)
prec double
file clapack/testing/eig/cdrvsg.c
for Checks the complex hermitian generalized eigenvalue problem
, routines (CHEGST, CHETRD, CUNGTR, CSTEQR, SSTERF, CSTEIN)
prec complex, doublecomplex
file clapack/testing/eig/zdrvsg.c
for Checks the complex hermitian generalized eigenvalue problem
, routines (ZHEGST, ZHETRD, ZUNGTR, ZSTEQR, SSTERF, ZSTEIN)
prec doublecomplex
# ===
file clapack/testing/eig/sckglm.c
for Tests SGGGLM
prec single
file clapack/testing/eig/dckglm.c
for Tests DGGGLM
prec double
file clapack/testing/eig/cckglm.c
for Tests CGGGLM
prec complex
file clapack/testing/eig/zckglm.c
for Tests ZGGGLM
prec doublecomplex
# ===
file clapack/testing/eig/sckgqr.c
for Tests SGGQRF and SGGRQF
prec single
file clapack/testing/eig/dckgqr.c
for Tests DGGQRF and DGGRQF
prec double
file clapack/testing/eig/cckgqr.c
for Tests CGGQRF and CGGRQF
prec complex
file clapack/testing/eig/zckgqr.c
for Tests ZGGQRF and ZGGRQF
prec doublecomplex
# ===
file clapack/testing/eig/sckgsv.c
for Tests SGGSVD
prec single
file clapack/testing/eig/dckgsv.c
for Tests DGGSVD
prec double
file clapack/testing/eig/cckgsv.c
for Tests CGGSVD
prec complex
file clapack/testing/eig/zckgsv.c
for Tests ZGGSVD
prec doublecomplex
# ===
file clapack/testing/eig/scklse.c
for Tests SGGLSE
prec single
file clapack/testing/eig/dcklse.c
for Tests DGGLSE
prec double
file clapack/testing/eig/ccklse.c
for Tests CGGLSE
prec complex
file clapack/testing/eig/zcklse.c
for Tests ZGGLSE
prec doublecomplex
#######################################
# Index for clapack/testing #
#######################################
lib clapack/testing/eig
for Subdirectory of Eigenproblem Testing
lib clapack/testing/lin
for Subdirectory of Linear Equation Testing
lib clapack/testing/matgen
for Subdirectory of Matrix Generation Routines (used in testing
, and timing directories)
file clapack/testing/index
for This index
# =======================================
# Input Files for Linear Equation Testing
# =======================================
file clapack/testing/stest.in
for Data file for linear equations/linear least squares test programs
prec single
file clapack/testing/dtest.in
for Data file for linear equations/linear least squares test programs
prec double
file clapack/testing/ctest.in
for Data file for linear equations/linear least squares test programs
prec complex
file clapack/testing/ztest.in
for Data file for linear equations/linear least squares test programs
prec doublecomplex
# =======================================
# Input Files for Eigenproblem Testing
# =======================================
file clapack/testing/nep.in
for Data file for testing the (s,d,c,z) Nonsymmetric
, Eigenproblem computational routines
prec single, double, complex, doublecomplex
file clapack/testing/sep.in
for Data file for testing the (s,d,c,z) Symmetric
, Eigenproblem computational and simple/expert driver routines
prec single, double, complex, doublecomplex
file clapack/testing/svd.in
for Data file for testing the (s,d,c,z) Singular Value
, Decomposition computational and simple/expert driver routines
prec single, double, complex, doublecomplex
file clapack/testing/sec.in
for Data file for testing real Eigen Condition Routines
prec single
file clapack/testing/dec.in
for Data file for testing real Eigen Condition Routines
prec double
file clapack/testing/cec.in
for Data file for testing complex Eigen Condition Routines
prec complex
file clapack/testing/zec.in
for Data file for testing complex Eigen Condition Routines
prec doublecomplex
file clapack/testing/sed.in
for Data file for testing real Nonsymmetric Eigenvalue Driver
prec single
file clapack/testing/ded.in
for Data file for testing real Nonsymmetric Eigenvalue Driver
prec double
file clapack/testing/ced.in
for Data file for testing complex Nonsymmetric Eigenvalue Driver
prec complex
file clapack/testing/zed.in
for Data file for testing complex Nonsymmetric Eigenvalue Driver
prec doublecomplex
file clapack/testing/sgg.in
for Data file for testing the real Nonsymmetric Generalized
, Eigenvalue Problem routines
prec single
file clapack/testing/dgg.in
for Data file for testing the real Nonsymmetric Generalized
, Eigenvalue Problem routines
prec double
file clapack/testing/cgg.in
for Data file for testing the complex Nonsymmetric Generalized
, Eigenvalue Problem routines
prec complex
file clapack/testing/zgg.in
for Data file for testing the complex Nonsymmetric Generalized
, Eigenvalue Problem routines
prec doublecomplex
file clapack/testing/ssb.in
for Data file for testing real Symmetric Banded
, Eigenvalue Problem routines
prec single
file clapack/testing/dsb.in
for Data file for testing real Symmetric Banded
, Eigenvalue Problem routines
prec double
file clapack/testing/csb.in
for Data file for testing complex Symmetric Banded
, Eigenvalue Problem routines
prec complex
file clapack/testing/zsb.in
for Data file for testing complex Symmetric Banded
, Eigenvalue Problem routines
prec doublecomplex
file clapack/testing/ssg.in
for Data file for testing real Symmetric Generalized
, Eigenvalue Problem routines
prec single
file clapack/testing/dsg.in
for Data file for testing real Symmetric Generalized
, Eigenvalue Problem routines
prec double
file clapack/testing/csg.in
for Data file for testing complex Symmetric Generalized
, Eigenvalue Problem routines
prec complex
file clapack/testing/zsg.in
for Data file for testing complex Symmetric Generalized
, Eigenvalue Problem routines
prec doublecomplex
file clapack/testing/sbal.in
for Data file for testing SGEBAL
prec single
file clapack/testing/dbal.in
for Data file for testing DGEBAL
prec double
file clapack/testing/cbal.in
for Data file for testing CGEBAL
prec complex
file clapack/testing/zbal.in
for Data file for testing ZGEBAL
prec doublecomplex
file clapack/testing/sbak.in
for Data file for testing SGEBAK
prec single
file clapack/testing/dbak.in
for Data file for testing DGEBAK
prec double
file clapack/testing/cbak.in
for Data file for testing CGEBAK
prec complex
file clapack/testing/zbak.in
for Data file for testing ZGEBAK
prec doublecomplex
file clapack/testing/sgbal.in
for Data file for testing SGGBAL
prec single
file clapack/testing/dgbal.in
for Data file for testing DGGBAL
prec double
file clapack/testing/cgbal.in
for Data file for testing CGGBAL
prec complex
file clapack/testing/zgbal.in
for Data file for testing ZGGBAL
prec doublecomplex
file clapack/testing/sgbak.in
for Data file for testing SGGBAK
prec single
file clapack/testing/dgbak.in
for Data file for testing DGGBAK
prec double
file clapack/testing/cgbak.in
for Data file for testing CGGBAK
prec complex
file clapack/testing/zgbak.in
for Data file for testing ZGGBAK
prec doublecomplex
file clapack/testing/sbb.in
for Data file for testing banded SVD routines
prec single
file clapack/testing/dbb.in
for Data file for testing banded SVD routines
prec double
file clapack/testing/cbb.in
for Data file for testing banded SVD routines
prec complex
file clapack/testing/zbb.in
for Data file for testing banded SVD routines
prec complex16
file clapack/testing/glm.in
for Data file for testing the (s, d, c, z) GLM routines
prec single, double, complex, doublecomplex
file clapack/testing/gqr.in
for Data file for testing the (s, d, c, z) GQR and GRQ routines
prec single, double, complex, doublecomplex
file clapack/testing/gsv.in
for Data file for testing the (s, d, c, z) GSVD routines
prec single, double, complex, doublecomplex
file clapack/testing/lse.in
for Data file for testing the (s, d, c, z) LSE routines
prec single, double, complex, doublecomplex
#######################################
# Index for clapack/testing/lin #
#######################################
file clapack/testing/lin/index
for This index
file clapack/testing/lin/xerbla.c
for Special version of this routine used in testing
file clapack/testing/lin/ilaenv.c
for Special version used in conjunction with XLAENV
file clapack/testing/lin/xlaenv.c
for Resets ILAENV values for testing purposes
# ==========================================
# Available Linear Equation Testing Routines
# ==========================================
file clapack/testing/lin/schkaa.c
for Test program driver for linear equation testing
prec single
file clapack/testing/lin/dchkaa.c
for Test program driver for linear equation testing
prec double
file clapack/testing/lin/cchkaa.c
for Test program driver for linear equation testing
prec complex
file clapack/testing/lin/zchkaa.c
for Test program driver for linear equation testing
prec doublecomplex
# ===
file clapack/testing/lin/schkeq.c
for Tests equilibration routines (SGEEQU, SGBEQU, SPOEQU,
, SPPEQU and SPBEQU)
prec single
file clapack/testing/lin/dchkeq.c
for Tests equilibration routines (DGEEQU, DGBEQU, DPOEQU,
# DPPEQU and DPBEQU)
prec double
file clapack/testing/lin/cchkeq.c
for Tests equilibration routines (CGEEQU, CGBEQU)
prec complex
file clapack/testing/lin/zchkeq.c
for Tests equilibration routines (ZGEEQU, ZGBEQU)
prec doublecomplex
# ===
file clapack/testing/lin/schkgb.c
for Tests SGBTRF, SGBTRS, SGBRFS, and SGBCON
prec single
file clapack/testing/lin/dchkgb.c
for Tests DGBTRF, DGBTRS, DGBRFS, and DGBCON
prec double
file clapack/testing/lin/cchkgb.c
for Tests CGBTRF, CGBTRS, CGBRFS, and CGBCON
prec complex
file clapack/testing/lin/zchkgb.c
for Tests ZGBTRF, ZGBTRS, ZGBRFS, and ZGBCON
prec doublecomplex
file clapack/testing/lin/sdrvgb.c
for Tests the driver routines SGBSV and SGBSVX
prec single
file clapack/testing/lin/ddrvgb.c
for Tests the driver routines DGBSV and DGBSVX
prec double
file clapack/testing/lin/cdrvgb.c
for Tests the driver routines CGBSV and CGBSVX
prec complex
file clapack/testing/lin/zdrvgb.c
for Tests the driver routines ZGBSV and ZGBSVX
prec doublecomplex
file clapack/testing/lin/schkge.c
for Tests SGETRF, SGETRI, SGETRS, SGERFS, and SGECON
prec single
file clapack/testing/lin/dchkge.c
for Tests DGETRF, DGETRI, DGETRS, DGERFS, and DGECON
prec double
file clapack/testing/lin/cchkge.c
for Tests CGETRF, CGETRI, CGETRS, CGERFS, and CGECON
prec complex
file clapack/testing/lin/zchkge.c
for Tests ZGETRF, ZGETRI, ZGETRS, ZGERFS, and ZGECON
prec doublecomplex
file clapack/testing/lin/sdrvge.c
for Tests the driver routines SGESV and SGESVX
prec single
file clapack/testing/lin/ddrvge.c
for Tests the driver routines DGESV and DGESVX
prec double
file clapack/testing/lin/cdrvge.c
for Tests the driver routines CGESV and CGESVX
prec complex
file clapack/testing/lin/zdrvge.c
for Tests the driver routines ZGESV and ZGESVX
prec doublecomplex
file clapack/testing/lin/serrge.c
for Tests the error exits for the SGE- and SGB- routines
prec single
file clapack/testing/lin/derrge.c
for Tests the error exits for the DGE- and DGB- routines
prec double
file clapack/testing/lin/cerrge.c
for Tests the error exits for the CGE- and CGB- routines
prec complex
file clapack/testing/lin/zerrge.c
for Tests the error exits for the ZGE- and ZGB- routines
prec doublecomplex
# ===
file clapack/testing/lin/schkgt.c
for Tests SGTTRF, SGTTRS, SGTRFS, and SGTCON
prec single
file clapack/testing/lin/dchkgt.c
for Tests DGTTRF, DGTTRS, DGTRFS, and DGTCON
prec double
file clapack/testing/lin/cchkgt.c
for Tests CGTTRF, CGTTRS, CGTRFS, and CGTCON
prec complex
file clapack/testing/lin/zchkgt.c
for Tests ZGTTRF, ZGTTRS, ZGTRFS, and ZGTCON
prec doublecomplex
file clapack/testing/lin/sdrvgt.c
for Tests SGTSV and SGTSVX
prec single
file clapack/testing/lin/ddrvgt.c
for Tests DGTSV and DGTSVX
prec double
file clapack/testing/lin/cdrvgt.c
for Tests CGTSV and CGTSVX
prec complex
file clapack/testing/lin/zdrvgt.c
for Tests ZGTSV and ZGTSVX
prec doublecomplex
file clapack/testing/lin/serrgt.c
for Tests the error exits for the tridiagonal routines (SGT- and SPT-)
prec single
file clapack/testing/lin/derrgt.c
for Tests the error exits for the tridiagonal routines (DGT- and DPT-)
prec double
file clapack/testing/lin/cerrgt.c
for Tests the error exits for the tridiagonal routines (CGT- and CPT-)
prec complex
file clapack/testing/lin/zerrgt.c
for Tests the error exits for the tridiagonal routines (ZGT- and ZPT-)
prec doublecomplex
# ===
file clapack/testing/lin/schklq.c
for Tests SGELQF, SORGLQ and SORMLQ
prec single
file clapack/testing/lin/dchklq.c
for Tests DGELQF, DORGLQ and DORMLQ
prec double
file clapack/testing/lin/cchklq.c
for Tests CGELQF, CUNGLQ and CUNMLQ
prec complex
file clapack/testing/lin/zchklq.c
for Tests ZGELQF, ZUNGLQ and ZUNMLQ
prec doublecomplex
file clapack/testing/lin/serrlq.c
for Tests the error exits for the LQ routines
prec single
file clapack/testing/lin/derrlq.c
for Tests the error exits for the LQ routines
prec double
file clapack/testing/lin/cerrlq.c
for Tests the error exits for the LQ routines
prec complex
file clapack/testing/lin/zerrlq.c
for Tests the error exits for the LQ routines
prec doublecomplex
# ===
file clapack/testing/lin/schkpb.c
for Tests SPBTRF, SPBTRS, SPBRFS, and SPBCON
prec single
file clapack/testing/lin/dchkpb.c
for Tests DPBTRF, DPBTRS, DPBRFS, and DPBCON
prec double
file clapack/testing/lin/cchkpb.c
for Tests CPBTRF, CPBTRS, CPBRFS, and CPBCON
prec complex
file clapack/testing/lin/zchkpb.c
for Tests ZPBTRF, ZPBTRS, ZPBRFS, and ZPBCON
prec doublecomplex
file clapack/testing/lin/sdrvpb.c
for Tests the driver routines SPBSV and SPBSVX
prec single
file clapack/testing/lin/ddrvpb.c
for Tests the driver routines DPBSV and DPBSVX
prec double
file clapack/testing/lin/cdrvpb.c
for Tests the driver routines CPBSV and CPBSVX
prec complex
file clapack/testing/lin/zdrvpb.c
for Tests the driver routines ZPBSV and ZPBSVX
prec doublecomplex
file clapack/testing/lin/schkpo.c
for Tests SPOTRF, SPOTRI, SPOTRS, SPORFS, and SPOCON
prec single
file clapack/testing/lin/dchkpo.c
for Tests DPOTRF, DPOTRI, DPOTRS, DPORFS, and DPOCON
prec double
file clapack/testing/lin/cchkpo.c
for Tests CPOTRF, CPOTRI, CPOTRS, CPORFS, and CPOCON
prec complex
file clapack/testing/lin/zchkpo.c
for Tests ZPOTRF, ZPOTRI, ZPOTRS, ZPORFS, and ZPOCON
prec doublecomplex
file clapack/testing/lin/sdrvpo.c
for Tests the driver routines SPOSV and SPOSVX
prec single
file clapack/testing/lin/ddrvpo.c
for Tests the driver routines DPOSV and DPOSVX
prec double
file clapack/testing/lin/cdrvpo.c
for Tests the driver routines CPOSV and CPOSVX
prec complex
file clapack/testing/lin/zdrvpo.c
for Tests the driver routines ZPOSV and ZPOSVX
prec doublecomplex
file clapack/testing/lin/schkpp.c
for Tests SPPTRF, SPPTRI, SPPTRS, SPPRFS, and SPPCON
prec single
file clapack/testing/lin/dchkpp.c
for Tests DPPTRF, DPPTRI, DPPTRS, DPPRFS, and DPPCON
prec double
file clapack/testing/lin/cchkpp.c
for Tests CPPTRF, CPPTRI, CPPTRS, CPPRFS, and CPPCON
prec complex
file clapack/testing/lin/zchkpp.c
for Tests ZPPTRF, ZPPTRI, ZPPTRS, ZPPRFS, and ZPPCON
prec doublecomplex
file clapack/testing/lin/sdrvpp.c
for Tests the driver routines SPPSV and SPPSVX
prec single
file clapack/testing/lin/ddrvpp.c
for Tests the driver routines DPPSV and DPPSVX
prec double
file clapack/testing/lin/cdrvpp.c
for Tests the driver routines CPPSV and CPPSVX
prec complex
file clapack/testing/lin/zdrvpp.c
for Tests the driver routines ZPPSV and ZPPSVX
prec doublecomplex
file clapack/testing/lin/serrpo.c
for Tests the error exits for the (SPB-, SPO-, SPP-) routines
prec single
file clapack/testing/lin/derrpo.c
for Tests the error exits for the (DPB-, DPO-, DPP-) routines
prec double
file clapack/testing/lin/cerrpo.c
for Tests the error exits for the (CPB-, CPO-, CPP-) routines
prec complex
file clapack/testing/lin/zerrpo.c
for Tests the error exits for the (ZPB-, ZPO-, ZPP-) routines
prec doublecomplex
# ===
file clapack/testing/lin/schkpt.c
for Tests SPTTRF, SPTTRS, SPTRFS, and SPTCON
prec single
file clapack/testing/lin/dchkpt.c
for Tests DPTTRF, DPTTRS, DPTRFS, and DPTCON
prec double
file clapack/testing/lin/cchkpt.c
for Tests CPTTRF, CPTTRS, CPTRFS, and CPTCON
prec complex
file clapack/testing/lin/zchkpt.c
for Tests ZPTTRF, ZPTTRS, ZPTRFS, and ZPTCON
prec doublecomplex
file clapack/testing/lin/sdrvpt.c
for Tests SPTSV and SPTSVX
prec single
file clapack/testing/lin/ddrvpt.c
for Tests DPTSV and DPTSVX
prec double
file clapack/testing/lin/cdrvpt.c
for Tests CPTSV and CPTSVX
prec complex
file clapack/testing/lin/zdrvpt.c
for Tests ZPTSV and ZPTSVX
prec doublecomplex
# ===
file clapack/testing/lin/schkql.c
for Tests SGEQLF, SORGQL and SORMQL
prec single
file clapack/testing/lin/dchkql.c
for Tests DGEQLF, DORGQL and DORMQL
prec double
file clapack/testing/lin/cchkql.c
for Tests CGEQLF, CUNGQL and CUNMQL
prec complex
file clapack/testing/lin/zchkql.c
for Tests ZGEQLF, ZUNGQL and ZUNMQL
prec doublecomplex
file clapack/testing/lin/serrql.c
for Tests the error exits for the QL routines
prec single
file clapack/testing/lin/derrql.c
for Tests the error exits for the QL routines
prec double
file clapack/testing/lin/cerrql.c
for Tests the error exits for the QL routines
prec complex
file clapack/testing/lin/zerrql.c
for Tests the error exits for the QL routines
prec doublecomplex
# ===
file clapack/testing/lin/schkqp.c
for Tests SGEQPF
prec single
file clapack/testing/lin/dchkqp.c
for Tests DGEQPF
prec double
file clapack/testing/lin/cchkqp.c
for Tests CGEQPF
prec complex
file clapack/testing/lin/zchkqp.c
for Tests ZGEQPF
prec doublecomplex
file clapack/testing/lin/serrqp.c
for Tests the error exits for SGEQPF
prec single
file clapack/testing/lin/derrqp.c
for Tests the error exits for DGEQPF
prec double
file clapack/testing/lin/cerrqp.c
for Tests the error exits for CGEQPF
prec complex
file clapack/testing/lin/zerrqp.c
for Tests the error exits for ZGEQPF
prec doublecomplex
# ===
file clapack/testing/lin/schkqr.c
for Tests SGEQRF, SORGQR and SORMQR
prec single
file clapack/testing/lin/dchkqr.c
for Tests DGEQRF, DORGQR and DORMQR
prec double
file clapack/testing/lin/cchkqr.c
for Tests CGEQRF, CUNGQR and CUNMQR
prec complex
file clapack/testing/lin/zchkqr.c
for Tests ZGEQRF, ZUNGQR and ZUNMQR
prec doublecomplex
file clapack/testing/lin/serrqr.c
for Tests the error exits for the QR routines
prec single
file clapack/testing/lin/derrqr.c
for Tests the error exits for the QR routines
prec double
file clapack/testing/lin/cerrqr.c
for Tests the error exits for the QR routines
prec complex
file clapack/testing/lin/zerrqr.c
for Tests the error exits for the QR routines
prec doublecomplex
# ===
file clapack/testing/lin/schkrq.c
for Tests SGERQF, SORGRQ and SORMRQ
prec single
file clapack/testing/lin/dchkrq.c
for Tests DGERQF, DORGRQ and DORMRQ
prec double
file clapack/testing/lin/cchkrq.c
for Tests CGERQF, CUNGRQ and CUNMRQ
prec complex
file clapack/testing/lin/zchkrq.c
for Tests ZGERQF, ZUNGRQ and ZUNMRQ
prec doublecomplex
file clapack/testing/lin/serrrq.c
for Tests the error exits for the RQ routines
prec single
file clapack/testing/lin/derrrq.c
for Tests the error exits for the RQ routines
prec double
file clapack/testing/lin/cerrrq.c
for Tests the error exits for the RQ routines
prec complex
file clapack/testing/lin/zerrrq.c
for Tests the error exits for the RQ routines
prec doublecomplex
# ===
file clapack/testing/lin/schksp.c
for Tests SSPTRF, SSPTRI, SSPTRS, SSPRFS, and SSPCON
prec single
file clapack/testing/lin/dchksp.c
for Tests DSPTRF, DSPTRI, DSPTRS, DSPRFS, and DSPCON
prec double
file clapack/testing/lin/cchksp.c
for Tests CSPTRF, CSPTRI, CSPTRS, CSPRFS, and CSPCON
prec complex
file clapack/testing/lin/zchksp.c
for Tests ZSPTRF, ZSPTRI, ZSPTRS, ZSPRFS, and ZSPCON
prec doublecomplex
file clapack/testing/lin/cchkhp.c
for Tests CHPTRF, CHPTRI, CHPTRS, CHPRFS, and CHPCON
prec complex
file clapack/testing/lin/zchkhp.c
for Tests ZHPTRF, ZHPTRI, ZHPTRS, ZHPRFS, and ZHPCON
prec doublecomplex
file clapack/testing/lin/sdrvsp.c
for Tests the driver routines SSPSV and SSPSVX
prec single
file clapack/testing/lin/ddrvsp.c
for Tests the driver routines DSPSV and DSPSVX
prec double
file clapack/testing/lin/cdrvsp.c
for Tests the driver routines CSPSV and CSPSVX
prec complex
file clapack/testing/lin/zdrvsp.c
for Tests the driver routines ZSPSV and ZSPSVX
prec doublecomplex
file clapack/testing/lin/cdrvhp.c
for Tests the driver routines CHPSV and CHPSVX
prec complex
file clapack/testing/lin/zdrvhp.c
for Tests the driver routines ZHPSV and ZHPSVX
prec doublecomplex
file clapack/testing/lin/schksy.c
for Tests SSYTRF, SSYTRI, SSYTRS, SSYRFS, and SSYCON
prec single
file clapack/testing/lin/dchksy.c
for Tests DSYTRF, DSYTRI, DSYTRS, DSYRFS, and DSYCON
prec double
file clapack/testing/lin/cchksy.c
for Tests CSYTRF, CSYTRI, CSYTRS, CSYRFS, and CSYCON
prec complex
file clapack/testing/lin/zchksy.c
for Tests ZSYTRF, ZSYTRI, ZSYTRS, ZSYRFS, and ZSYCON
prec doublecomplex
file clapack/testing/lin/cchkhe.c
for Tests CHETRF, CHETRI, CHETRS, CHERFS, and CHECON
prec complex
file clapack/testing/lin/zchkhe.c
for Tests ZHETRF, ZHETRI, ZHETRS, ZHERFS, and ZHECON
prec doublecomplex
file clapack/testing/lin/sdrvsy.c
for Tests the driver routines SSYSV and SSYSVX
prec single
file clapack/testing/lin/ddrvsy.c
for Tests the driver routines DSYSV and DSYSVX
prec double
file clapack/testing/lin/cdrvsy.c
for Tests the driver routines SSYSV and SSYSVX
prec complex
file clapack/testing/lin/zdrvsy.c
for Tests the driver routines ZSYSV and ZSYSVX
prec doublecomplex
file clapack/testing/lin/cdrvhe.c
for Tests the driver routines CHESV and CHESVX
prec complex
file clapack/testing/lin/zdrvhe.c
for Tests the driver routines ZHESV and ZHESVX
prec doublecomplex
file clapack/testing/lin/serrsy.c
for Tests the error exits for the (SSP- and SSY-) routines
prec single
file clapack/testing/lin/derrsy.c
for Tests the error exits for the (DSP- and DSY-) routines
prec double
file clapack/testing/lin/cerrsy.c
for Tests the error exits for the (DSP- and DSY-) routines
prec complex
file clapack/testing/lin/zerrsy.c
for Tests the error exits for the (DSP- and DSY-) routines
prec doublecomplex
file clapack/testing/lin/cerrhe.c
for Tests the error exits for the (CHE- and CHP-) routines
prec complex
file clapack/testing/lin/zerrhe.c
for Tests the error exits for the (ZHE- and ZHP-) routines
prec doublecomplex
# ===
file clapack/testing/lin/schktb.c
for Tests STBTRI, STBTRS, STBRFS, and STBCON, and SLATBS
prec single
file clapack/testing/lin/dchktb.c
for Tests DTBTRI, DTBTRS, DTBRFS, and DTBCON, and DLATBS
prec double
file clapack/testing/lin/cchktb.c
for Tests CTBTRI, CTBTRS, CTBRFS, and CTBCON, and CLATBS
prec complex
file clapack/testing/lin/zchktb.c
for Tests ZTBTRI, ZTBTRS, ZTBRFS, and ZTBCON, and ZLATBS
prec doublecomplex
file clapack/testing/lin/schktp.c
for Tests STPTRI, STPTRS, STPRFS, and STPCON, and SLATPS
prec single
file clapack/testing/lin/dchktp.c
for Tests DTPTRI, DTPTRS, DTPRFS, and DTPCON, and DLATPS
prec double
file clapack/testing/lin/cchktp.c
for Tests CTPTRI, CTPTRS, CTPRFS, and CTPCON, and CLATPS
prec complex
file clapack/testing/lin/zchktp.c
for Tests ZTPTRI, ZTPTRS, ZTPRFS, and ZTPCON, and ZLATPS
prec doublecomplex
file clapack/testing/lin/schktr.c
for Tests STRTRI, STRTRS, STRRFS, and STRCON, and SLATRS
prec single
file clapack/testing/lin/dchktr.c
for Tests DTRTRI, DTRTRS, DTRRFS, and DTRCON, and DLATRS
prec double
file clapack/testing/lin/cchktr.c
for Tests CTRTRI, CTRTRS, CTRRFS, and CTRCON, and CLATRS
prec complex
file clapack/testing/lin/zchktr.c
for Tests ZTRTRI, ZTRTRS, ZTRRFS, and ZTRCON, and ZLATRS
prec doublecomplex
file clapack/testing/lin/serrtr.c
for Tests the error exits for the -TR routines
prec single
file clapack/testing/lin/derrtr.c
for Tests the error exits for the -TR routines
prec double
file clapack/testing/lin/cerrtr.c
for Tests the error exits for the -TR routines
prec complex
file clapack/testing/lin/zerrtr.c
for Tests the error exits for the -TR routines
prec doublecomplex
# ===
file clapack/testing/lin/schktz.c
for Tests STZRQF
prec single
file clapack/testing/lin/dchktz.c
for Tests DTZRQF
prec double
file clapack/testing/lin/cchktz.c
for Tests CTZRQF
prec complex
file clapack/testing/lin/zchktz.c
for Tests ZTZRQF
prec doublecomplex
file clapack/testing/lin/serrtz.c
for Tests the error exits for STZRQF
prec single
file clapack/testing/lin/derrtz.c
for Tests the error exits for DTZRQF
prec double
file clapack/testing/lin/cerrtz.c
for Tests the error exits for CTZRQF
prec complex
file clapack/testing/lin/zerrtz.c
for Tests the error exits for ZTZRQF
prec doublecomplex
# ===
file clapack/testing/lin/sdrvls.c
for Tests the least squares driver routines SGELS, SGELSX, and SGELSS
prec single
file clapack/testing/lin/ddrvls.c
for Tests the least squares driver routines DGELS, DGELSX, and DGELSS
prec double
file clapack/testing/lin/cdrvls.c
for Tests the least squares driver routines CGELS, CGELSX, and CGELSS
prec complex
file clapack/testing/lin/zdrvls.c
for Tests the least squares driver routines ZGELS, ZGELSX, and ZGELSS
prec doublecomplex
file clapack/testing/lin/serrls.c
for Tests the error exits for the (SGELS, SGELSS, SGELSX) routines
prec single
file clapack/testing/lin/derrls.c
for Tests the error exits for the (DGELS, DGELSS, DGELSX) routines
prec double
file clapack/testing/lin/cerrls.c
for Tests the error exits for the (CGELS, CGELSS, CGELSX) routines
prec complex
file clapack/testing/lin/zerrls.c
for Tests the error exits for the (ZGELS, ZGELSS, ZGELSX) routines
prec doublecomplex
# ===
file clapack/testing/lin/serrvx.c
for Tests the error exits for the (-SV and -SVX) routines
prec single
file clapack/testing/lin/derrvx.c
for Tests the error exits for the (-SV and -SVX) routines
prec double
file clapack/testing/lin/cerrvx.c
for Tests the error exits for the (-SV and -SVX) routines
prec complex
file clapack/testing/lin/zerrvx.c
for Tests the error exits for the (-SV and -SVX) routines
prec doublecomplex
# ==========================================
# Other Available Testing Routines
# ==========================================
file clapack/testing/lin/sgelqs.c
for Compute a minimum norm solution using the LQ
, factorization computed by SGELQF
prec single
file clapack/testing/lin/dgelqs.c
for Compute a minimum norm solution using the LQ
, factorization computed by DGELQF
prec double
file clapack/testing/lin/cgelqs.c
for Compute a minimum norm solution using the LQ
, factorization computed by CGELQF
prec complex
file clapack/testing/lin/zgelqs.c
for Compute a minimum norm solztion using the LQ
, factorization computed by ZGELQF
prec doublecomplex
file clapack/testing/lin/sgeqls.c
for Solve the least squares problem using the QL
, factorization computed by SGEQLF
prec single
file clapack/testing/lin/dgeqls.c
for Solve the least squares problem using the QL
, factorization computed by DGEQLF
prec double
file clapack/testing/lin/cgeqls.c
for Solve the least squares problem using the QL
, factorization computed by CGEQLF
prec complex
file clapack/testing/lin/zgeqls.c
for Solve the least squares problem using the QL
, factorization computed by ZGEQLF
prec doublecomplex
file clapack/testing/lin/sgeqrs.c
for Solve the least squares problem using the QR
, factorization computed by SGEQRF
prec single
file clapack/testing/lin/dgeqrs.c
for Solve the least squares problem using the QR
, factorization computed by DGEQRF
prec double
file clapack/testing/lin/cgeqrs.c
for Solve the least squares problem using the QR
# factorization computed by CGEQRF
prec complex
file clapack/testing/lin/zgeqrs.c
for Solve the least squares problem using the QR
, factorization computed by ZGEQRF
prec doublecomplex
file clapack/testing/lin/sgerqs.c
for Compute a minimum-norm solution using the RQ
# factorization computed by SGERQF
prec single
file clapack/testing/lin/dgerqs.c
for Compute a minimum-norm solution using the RQ
, factorization computed by DGERQF
prec double
file clapack/testing/lin/cgerqs.c
for Compute a minimum-norm solution using the RQ
# factorization computed by CGERQF
prec complex
file clapack/testing/lin/zgerqs.c
for Compute a minimum-norm solution using the RQ
, factorization computed by ZGERQF
prec doublecomplex
file clapack/testing/matgen/slaran.c
file clapack/testing/matgen/dlaran.c
#########################################
# Index for clapack/timing/eig/eigsrc #
#########################################
file clapack/timing/eig/eigsrc/index
for This index
# ===================================================
# Available Instrumented Eigenproblem LAPACK Routines
# ===================================================
file clapack/timing/eig/eigsrc/sbdsqr.c
for instrumented SBDSQR to count operations
prec single
file clapack/timing/eig/eigsrc/dbdsqr.c
for instrumented DBDSQR to count operations
prec double
file clapack/timing/eig/eigsrc/cbdsqr.c
for instrumented CBDSQR to count operations
prec complex
file clapack/timing/eig/eigsrc/zbdsqr.c
for instrumented ZBDSQR to count operations
prec doublecomplex
file clapack/timing/eig/eigsrc/sgghrd.c
for instrumented SGGHRD to count operations
prec single
file clapack/timing/eig/eigsrc/dgghrd.c
for instrumented DGGHRD to count operations
prec double
file clapack/timing/eig/eigsrc/cgghrd.c
for instrumented CGGHRD to count operations
prec complex
file clapack/timing/eig/eigsrc/zgghrd.c
for instrumented ZGGHRD to count operations
prec doublecomplex
file clapack/timing/eig/eigsrc/shgeqz.c
for instrumented SHGEQZ to count operations
prec single
file clapack/timing/eig/eigsrc/dhgeqz.c
for instrumented DHGEQZ to count operations
prec double
file clapack/timing/eig/eigsrc/chgeqz.c
for instrumented CHGEQZ to count operations
prec complex
file clapack/timing/eig/eigsrc/zhgeqz.c
for instrumented ZHGEQZ to count operations
prec doublecomplex
file clapack/timing/eig/eigsrc/shsein.c
for instrumented SHSEIN to count operations
prec single
file clapack/timing/eig/eigsrc/dhsein.c
for instrumented DHSEIN to count operations
prec double
file clapack/timing/eig/eigsrc/chsein.c
for instrumented CHSEIN to count operations
prec complex
file clapack/timing/eig/eigsrc/zhsein.c
for instrumented ZHSEIN to count operations
prec doublecomplex
file clapack/timing/eig/eigsrc/shseqr.c
for instrumented SHSEQR to count operations
prec single
file clapack/timing/eig/eigsrc/dhseqr.c
for instrumented DHSEQR to count operations
prec double
file clapack/timing/eig/eigsrc/chseqr.c
for instrumented CHSEQR to count operations
prec complex
file clapack/timing/eig/eigsrc/zhseqr.c
for instrumented ZHSEQR to count operations
prec doublecomplex
file clapack/timing/eig/eigsrc/slaebz.c
for instrumented SLAEBZ to count operations
prec single
file clapack/timing/eig/eigsrc/dlaebz.c
for instrumented DLAEBZ to count operations
prec double
file clapack/timing/eig/eigsrc/slaed0.c
for instrumented SLAED0 to count operations
prec single
file clapack/timing/eig/eigsrc/dlaed0.c
for instrumented DLAED0 to count operations
prec double
file clapack/timing/eig/eigsrc/claed0.c
for instrumented CLAED0 to count operations
prec complex
file clapack/timing/eig/eigsrc/zlaed0.c
for instrumented ZLAED0 to count operations
prec doublecomplex
file clapack/timing/eig/eigsrc/slaed1.c
for instrumented SLAED1 to count operations
prec single
file clapack/timing/eig/eigsrc/dlaed1.c
for instrumented DLAED1 to count operations
prec double
file clapack/timing/eig/eigsrc/slaed2.c
for instrumented SLAED2 to count operations
prec single
file clapack/timing/eig/eigsrc/dlaed2.c
for instrumented DLAED2 to count operations
prec double
file clapack/timing/eig/eigsrc/slaed3.c
for instrumented SLAED3 to count operations
prec single
file clapack/timing/eig/eigsrc/dlaed3.c
for instrumented DLAED3 to count operations
prec double
file clapack/timing/eig/eigsrc/slaed4.c
for instrumented SLAED4 to count operations
prec single
file clapack/timing/eig/eigsrc/dlaed4.c
for instrumented DLAED4 to count operations
prec double
file clapack/timing/eig/eigsrc/slaed5.c
for instrumented SLAED5 to count operations
prec single
file clapack/timing/eig/eigsrc/dlaed5.c
for instrumented DLAED5 to count operations
prec double
file clapack/timing/eig/eigsrc/slaed6.c
for instrumented SLAED6 to count operations
prec single
file clapack/timing/eig/eigsrc/dlaed6.c
for instrumented DLAED6 to count operations
prec double
file clapack/timing/eig/eigsrc/slaed7.c
for instrumented SLAED7 to count operations
prec single
file clapack/timing/eig/eigsrc/dlaed7.c
for instrumented DLAED7 to count operations
prec double
file clapack/timing/eig/eigsrc/claed7.c
for instrumented CLAED7 to count operations
prec complex
file clapack/timing/eig/eigsrc/zlaed7.c
for instrumented ZLAED7 to count operations
prec doublecomplex
file clapack/timing/eig/eigsrc/slaed8.c
for instrumented SLAED8 to count operations
prec single
file clapack/timing/eig/eigsrc/dlaed8.c
for instrumented DLAED8 to count operations
prec double
file clapack/timing/eig/eigsrc/claed8.c
for instrumented CLAED8 to count operations
prec complex
file clapack/timing/eig/eigsrc/zlaed8.c
for instrumented ZLAED8 to count operations
prec doublecomplex
file clapack/timing/eig/eigsrc/slaed9.c
for instrumented SLAED9 to count operations
prec single
file clapack/timing/eig/eigsrc/dlaed9.c
for instrumented DLAED9 to count operations
prec double
file clapack/timing/eig/eigsrc/slaeda.c
for instrumented SLAEDA to count operations
prec single
file clapack/timing/eig/eigsrc/dlaeda.c
for instrumented DLAEDA to count operations
prec double
file clapack/timing/eig/eigsrc/slaein.c
for instrumented SLAEIN to count operations
prec single
file clapack/timing/eig/eigsrc/dlaein.c
for instrumented DLAEIN to count operations
prec double
file clapack/timing/eig/eigsrc/claein.c
for instrumented CLAEIN to count operations
prec complex
file clapack/timing/eig/eigsrc/zlaein.c
for instrumented ZLAEIN to count operations
prec doublecomplex
file clapack/timing/eig/eigsrc/slahqr.c
for instrumented SLAHQR to count operations
prec single
file clapack/timing/eig/eigsrc/dlahqr.c
for instrumented DLAHQR to count operations
prec double
file clapack/timing/eig/eigsrc/clahqr.c
for instrumented CLAHQR to count operations
prec complex
file clapack/timing/eig/eigsrc/zlahqr.c
for instrumented ZLAHQR to count operations
prec doublecomplex
file clapack/timing/eig/eigsrc/slasq1.c
for instrumented SLASQ1 to count operations
prec single
file clapack/timing/eig/eigsrc/dlasq1.c
for instrumented DLASQ1 to count operations
prec double
file clapack/timing/eig/eigsrc/slasq2.c
for instrumented SLASQ2 to count operations
prec single
file clapack/timing/eig/eigsrc/dlasq2.c
for instrumented DLASQ2 to count operations
prec double
file clapack/timing/eig/eigsrc/slasq3.c
for instrumented SLASQ3 to count operations
prec single
file clapack/timing/eig/eigsrc/dlasq3.c
for instrumented DLASQ3 to count operations
prec double
file clapack/timing/eig/eigsrc/slasq4.c
for instrumented SLASQ4 to count operations
prec single
file clapack/timing/eig/eigsrc/dlasq4.c
for instrumented DLASQ4 to count operations
prec double
file clapack/timing/eig/eigsrc/spteqr.c
for instrumented SPTEQR to count operations
prec single
file clapack/timing/eig/eigsrc/dpteqr.c
for instrumented DPTEQR to count operations
prec double
file clapack/timing/eig/eigsrc/cpteqr.c
for instrumented CPTEQR to count operations
prec complex
file clapack/timing/eig/eigsrc/zpteqr.c
for instrumented ZPTEQR to count operations
prec doublecomplex
file clapack/timing/eig/eigsrc/sstebz.c
for instrumented SSTEBZ to count operations
prec single
file clapack/timing/eig/eigsrc/dstebz.c
for instrumented DSTEBZ to count operations
prec double
file clapack/timing/eig/eigsrc/sstedc.c
for instrumented SSTEDC to count operations
prec single
file clapack/timing/eig/eigsrc/dstedc.c
for instrumented DSTEDC to count operations
prec double
file clapack/timing/eig/eigsrc/cstedc.c
for instrumented CSTEDC to count operations
prec complex
file clapack/timing/eig/eigsrc/zstedc.c
for instrumented ZSTEDC to count operations
prec doublecomplex
file clapack/timing/eig/eigsrc/sstein.c
for instrumented SSTEIN to count operations
prec single
file clapack/timing/eig/eigsrc/dstein.c
for instrumented DSTEIN to count operations
prec double
file clapack/timing/eig/eigsrc/cstein.c
for instrumented CSTEIN to count operations
prec complex
file clapack/timing/eig/eigsrc/zstein.c
for instrumented ZSTEIN to count operations
prec doublecomplex
file clapack/timing/eig/eigsrc/ssteqr.c
for instrumented SSTEQR to count operations
prec single
file clapack/timing/eig/eigsrc/dsteqr.c
for instrumented DSTEQR to count operations
prec double
file clapack/timing/eig/eigsrc/csteqr.c
for instrumented CSTEQR to count operations
prec complex
file clapack/timing/eig/eigsrc/zsteqr.c
for instrumented ZSTEQR to count operations
prec doublecomplex
file clapack/timing/eig/eigsrc/ssterf.c
for instrumented SSTERF to count operations
prec single
file clapack/timing/eig/eigsrc/dsterf.c
for instrumented DSTERF to count operations
prec double
file clapack/timing/eig/eigsrc/stgevc.c
for instrumented STGEVC to count operations
prec single
file clapack/timing/eig/eigsrc/dtgevc.c
for instrumented DTGEVC to count operations
prec double
file clapack/timing/eig/eigsrc/ctgevc.c
for instrumented CTGEVC to count operations
prec complex
file clapack/timing/eig/eigsrc/ztgevc.c
for instrumented ZTGEVC to count operations
prec doublecomplex
file clapack/timing/eig/eigsrc/strevc.c
for instrumented STREVC to count operations
prec single
file clapack/timing/eig/eigsrc/dtrevc.c
for instrumented DTREVC to count operations
prec double
file clapack/timing/eig/eigsrc/ctrevc.c
for instrumented CTREVC to count operations
prec complex
file clapack/timing/eig/eigsrc/ztrevc.c
for instrumented ZTREVC to count operations
prec doublecomplex
#######################################
# Index for clapack/timing/eig #
#######################################
file clapack/timing/eig/index
for This index
lib clapack/timing/eig/eigsrc
for Subdirectory containing instrumented LAPACK routines
file clapack/timing/eig/ilaenv.c
for Special version to be used in conjunction with XLAENV
file clapack/timing/eig/xlaenv.c
for Resets ILAENV values for timing purposes
# ==========================================
# Available Eigenproblem Timing Routines
# ==========================================
file clapack/timing/eig/stimee.c
for Timing program driver for eigenvalue problem timing
prec single
file clapack/timing/eig/dtimee.c
for Timing program driver for eigenvalue problem timing
prec double
file clapack/timing/eig/ctimee.c
for Timing program driver for eigenvalue problem timing
prec complex
file clapack/timing/eig/ztimee.c
for Timing program driver for eigenvalue problem timing
prec doublecomplex
# ===
file clapack/timing/eig/seispack.c
for Instrumented EISPACK routines used for timing purposes
prec single
file clapack/timing/eig/deispack.c
for Instrumented EISPACK routines used for timing purposes
prec double
file clapack/timing/eig/ceispack.c
for Instrumented EISPACK routines used for timing purposes
prec complex
file clapack/timing/eig/zeispack.c
for Instrumented EISPACK routines used for timing purposes
prec doublecomplex
# ===
file clapack/timing/eig/stim21.c
for Times the nonsymmetric eigenvalue problem LAPACK routines
prec single
file clapack/timing/eig/dtim21.c
for Times the nonsymmetric eigenvalue problem LAPACK routines
prec double
file clapack/timing/eig/ctim21.c
for Times the nonsymmetric eigenvalue problem LAPACK routines
prec complex
file clapack/timing/eig/ztim21.c
for Times the nonsymmetric eigenvalue problem LAPACK routines
prec doublecomplex
# ===
file clapack/timing/eig/stim22.c
for Times the symmetric eigenvalue problem LAPACK routines
prec single
file clapack/timing/eig/dtim22.c
for Times the symmetric eigenvalue problem LAPACK routines
prec double
file clapack/timing/eig/ctim22.c
for Times the symmetric eigenvalue problem LAPACK routines
prec complex
file clapack/timing/eig/ztim22.c
for Times the symmetric eigenvalue problem LAPACK routines
prec doublecomplex
# ===
file clapack/timing/eig/stim26.c
for Times the singular value decomposition LAPACK routines
prec single
file clapack/timing/eig/dtim26.c
for Times the singular value decomposition LAPACK routines
prec double
file clapack/timing/eig/ctim26.c
for Times the singular value decomposition LAPACK routines
prec complex
file clapack/timing/eig/ztim26.c
for Times the singular value decomposition LAPACK routines
prec doublecomplex
# ===
file clapack/timing/eig/stim51.c
for Times the generalized nonsymmetric eigenvalue problem LAPACK
, routines
prec single
file clapack/timing/eig/dtim51.c
for Times the generalized nonsymmetric eigenvalue problem LAPACK
, routines
prec double
file clapack/timing/eig/ctim51.c
for Times the generalized nonsymmetric eigenvalue problem LAPACK
, routines
prec complex
file clapack/timing/eig/ztim51.c
for Times the generalized nonsymmetric eigenvalue problem LAPACK
, routines
prec doublecomplex
#######################################
# Index for clapack/timing #
#######################################
lib clapack/timing/eig
for Subdirectory of Eigenproblem Timing
lib clapack/timing/lin
for Subdirectory of Linear Equation Timing
file clapack/timing/index
for This index
file clapack/timing/large.tgz
for gzipped-tarfile of LARGE timing data files (xBLASA.in, xBLASB.in,
, xBLASC.in, xTIME.in, xBAND.in, xTIME2.in, xGEPTIM.in,
, xNEPTIM.in, xSEPTIM.in, and xSVDTIM.in)
prec single, double, complex, doublecomplex
# ====
# NOTE: SMALL and LARGE refer to the size of the matrices being
# ==== generated. Because of nondifferentiation between upper
# and lowercase letters, the LARGE data set can only be obtained
# via the large.tgz file.
# =======================================
# Input Files for BLAS Timing
# =======================================
file clapack/timing/sblasa.in
for SMALL Data file for timing BLAS (parameters M, N, and K)
, with K small
prec single
file clapack/timing/dblasa.in
for SMALL Data file for timing BLAS (parameters M, N, and K)
, with K small
prec double
file clapack/timing/cblasa.in
for SMALL Data file for timing BLAS (parameters M, N, and K)
, with K small
prec complex
file clapack/timing/zblasa.in
for SMALL Data file for timing BLAS (parameters M, N, and K)
, with K small
prec doublecomplex
file clapack/timing/sblasb.in
for SMALL Data file for timing BLAS (parameters M, N, and K)
, with M small
prec single
file clapack/timing/dblasb.in
for SMALL Data file for timing BLAS (parameters M, N, and K)
, with M small
prec double
file clapack/timing/cblasb.in
for SMALL Data file for timing BLAS (parameters M, N, and K)
, with M small
prec complex
file clapack/timing/zblasb.in
for SMALL Data file for timing BLAS (parameters M, N, and K)
, with M small
prec doublecomplex
file clapack/timing/sblasc.in
for SMALL Data file for timing BLAS (parameters M, N, and K)
, with N small
prec single
file clapack/timing/dblasc.in
for SMALL Data file for timing BLAS (parameters M, N, and K)
, with N small
prec double
file clapack/timing/cblasc.in
for SMALL Data file for timing BLAS (parameters M, N, and K)
, with N small
prec complex
file clapack/timing/zblasc.in
for SMALL Data file for timing BLAS (parameters M, N, and K)
, with N small
prec doublecomplex
# =======================================
# Input Files for Linear Equation Timing
# =======================================
file clapack/timing/stime.in
for SMALL Data file for timing square real linear
, equations/linear least squares routines
prec single
file clapack/timing/dtime.in
for SMALL Data file for timing square real linear
, equations/linear least squares routines
prec double
file clapack/timing/ctime.in
for SMALL Data file for timing square complex linear
, equations/linear least squares routines
prec complex
file clapack/timing/ztime.in
for SMALL Data file for timing square complex linear
, equations/linear least squares routines
prec doublecomplex
file clapack/timing/sband.in
for SMALL Data file for timing banded real linear
, equations/linear least squares routines
prec single, double, complex, doublecomplex
file clapack/timing/dband.in
for SMALL Data file for timing banded real linear
, equations/linear least squares routines
prec double
file clapack/timing/cband.in
for SMALL Data file for timing banded complex linear
, equations/linear least squares routines
prec complex
file clapack/timing/zband.in
for SMALL Data file for timing banded complex linear
, equations/linear least squares routines
prec doublecomplex
file clapack/timing/stime2.in
for SMALL Data file for timing rectangular real linear
, equations/least squares routines
prec single
file clapack/timing/dtime2.in
for SMALL Data file for timing rectangular real linear
, equations/least squares routines
prec double
file clapack/timing/ctime2.in
for SMALL Data file for timing rectangular complex linear
, equations/least squares routines
prec complex
file clapack/timing/ztime2.in
for SMALL Data file for timing rectangular complex linear
, equations/least squares routines
prec doublecomplex
# =======================================
# Input Files for Eigenproblem Timing
# =======================================
file clapack/timing/sgeptim.in
for SMALL Data file for timing the real Generalized
, Nonsymmetric Eigenproblem computational and simple driver routines
prec single
file clapack/timing/dgeptim.in
for SMALL Data file for timing the real Generalized
, Nonsymmetric Eigenproblem computational and simple driver routines
prec double
file clapack/timing/cgeptim.in
for SMALL Data file for timing the complex Generalized
, Nonsymmetric Eigenproblem computational and simple driver routines
prec complex
file clapack/timing/zgeptim.in
for SMALL Data file for timing the complex Generalized
, Nonsymmetric Eigenproblem computational and simple driver routines
prec doublecomplex
file clapack/timing/sneptim.in
for SMALL Data file for timing the real Nonsymmetric
, Eigenproblem computational and simple/expert driver routines
prec single
file clapack/timing/dneptim.in
for SMALL Data file for timing the real Nonsymmetric
, Eigenproblem computational and simple/expert driver routines
prec double
file clapack/timing/cneptim.in
for SMALL Data file for timing the complex Nonsymmetric
, Eigenproblem computational and simple/expert driver routines
prec complex
file clapack/timing/zneptim.in
for SMALL Data file for timing the complex Nonsymmetric
, Eigenproblem computational and simple/expert driver routines
prec doublecomplex
file clapack/timing/sseptim.in
for SMALL Data file for timing the real Symmetric
, Eigenproblem and Generalized Symmetric Eigenproblem
, computational and simple/expert driver routines
prec single
file clapack/timing/dseptim.in
for SMALL Data file for timing the real Symmetric
, Eigenproblem and Generalized Symmetric Eigenproblem
, computational and simple/expert driver routines
prec double
file clapack/timing/cseptim.in
for SMALL Data file for timing the complex Symmetric
, Eigenproblem and Generalized Symmetric Eigenproblem
, computational and simple/expert driver routines
prec complex
file clapack/timing/zseptim.in
for SMALL Data file for timing the complex Symmetric
, Eigenproblem and Generalized Symmetric Eigenproblem
, computational and simple/expert driver routines
prec doublecomplex
file clapack/timing/ssvdtim.in
for SMALL Data file for timing the real Singular Value
, Decomposition computational and simple/expert driver routines
prec single
file clapack/timing/dsvdtim.in
for SMALL Data file for timing the real Singular Value
, Decomposition computational and simple/expert driver routines
prec double
file clapack/timing/csvdtim.in
for SMALL Data file for timing the complex Singular Value
, Decomposition computational and simple/expert driver routines
prec complex
file clapack/timing/zsvdtim.in
for SMALL Data file for timing the complex Singular Value
, Decomposition computational and simple/expert driver routines
prec doublecomplex
#######################################
# Index for clapack/timing/lin #
#######################################
file clapack/timing/lin/index
for This index
file clapack/timing/lin/ilaenv.c
for Special version used in conjunction with XLAENV
file clapack/timing/lin/xlaenv.c
for Resets ILAENV values for timing purposes
# ==========================================
# Available Linear Equation Timing Routines
# ==========================================
file clapack/timing/lin/stimaa.c
for Timing program driver for linear equation timing
prec single
file clapack/timing/lin/dtimaa.c
for Timing program driver for linear equation timing
prec double
file clapack/timing/lin/ctimaa.c
for Timing program driver for linear equation timing
prec complex
file clapack/timing/lin/ztimaa.c
for Timing program driver for linear equation timing
prec doublecomplex
# ===
file clapack/timing/lin/seispk.c
for Instrumented eispack routines used in timing comparisons
prec single
file clapack/timing/lin/deispk.c
for Instrumented eispack routines used in timing comparisons
prec double
# ===
file clapack/timing/lin/slinpk.c
for Instrumented linpack routines used in timing comparisons
prec single
file clapack/timing/lin/dlinpk.c
for Instrumented linpack routines used in timing comparisons
prec double
file clapack/timing/lin/clinpk.c
for Instrumented linpack routines used in timing comparisons
prec complex
file clapack/timing/lin/zlinpk.c
for Instrumented linpack routines used in timing comparisons
prec doublecomplex
# ===
file clapack/timing/lin/stimmg.c
for Generates a toeplitz test matrix
prec single
file clapack/timing/lin/dtimmg.c
for Generates a toeplitz test matrix
prec double
file clapack/timing/lin/ctimmg.c
for Generates a toeplitz test matrix
prec complex
file clapack/timing/lin/ztimmg.c
for Generates a toeplitz test matrix
prec doublecomplex
# ===
file clapack/timing/lin/stimb2.c
for Times the BLAS 2 routines
prec single
file clapack/timing/lin/dtimb2.c
for Times the BLAS 2 routines
prec double
file clapack/timing/lin/ctimb2.c
for Times the BLAS 2 routines
prec complex
file clapack/timing/lin/ztimb2.c
for Times the BLAS 2 routines
prec doublecomplex
file clapack/timing/lin/stimb3.c
for Times the BLAS 3 routines
prec single
file clapack/timing/lin/dtimb3.c
for Times the BLAS 3 routines
prec double
file clapack/timing/lin/ctimb3.c
for Times the BLAS 3 routines
prec complex
file clapack/timing/lin/ztimb3.c
for Times the BLAS 3 routines
prec doublecomplex
file clapack/timing/lin/stimmm.c
for Times SGEMM
prec single
file clapack/timing/lin/dtimmm.c
for Times DGEMM
prec double
file clapack/timing/lin/ctimmm.c
for Times CGEMM
prec complex
file clapack/timing/lin/ztimmm.c
for Times ZGEMM
prec doublecomplex
file clapack/timing/lin/stimmv.c
for Times individual BLAS 2 routines
prec single
file clapack/timing/lin/dtimmv.c
for Times individual BLAS 2 routines
prec double
file clapack/timing/lin/ctimmv.c
for Times individual BLAS 2 routines
prec complex
file clapack/timing/lin/ztimmv.c
for Times individual BLAS 2 routines
prec doublecomplex
# ===
file clapack/timing/lin/stimbr.c
for Times SGEBRD, SORGBR, and SORMBR
prec single
file clapack/timing/lin/dtimbr.c
for Times DGEBRD, DORGBR, and DORMBR
prec double
file clapack/timing/lin/ctimbr.c
for Times CGEBRD, CUNGBR, and CUNMBR
prec complex
file clapack/timing/lin/ztimbr.c
for Times ZGEBRD, ZUNGBR, and ZUNMBR
prec doublecomplex
# ===
file clapack/timing/lin/stimgb.c
for Times SGBTRF and SGBTRS
prec single
file clapack/timing/lin/dtimgb.c
for Times DGBTRF and DGBTRS
prec double
file clapack/timing/lin/ctimgb.c
for Times CGBTRF and CGBTRS
prec complex
file clapack/timing/lin/ztimgb.c
for Times ZGBTRF and ZGBTRS
prec doublecomplex
# ===
file clapack/timing/lin/stimge.c
for Times SGETRF, SGETRS, and SGETRI
prec single
file clapack/timing/lin/dtimge.c
for Times DGETRF, DGETRS, and DGETRI
prec double
file clapack/timing/lin/ctimge.c
for Times CGETRF, CGETRS, and CGETRI
prec complex
file clapack/timing/lin/ztimge.c
for Times ZGETRF, ZGETRS, and ZGETRI
prec doublecomplex
# ===
file clapack/timing/lin/stimgt.c
for Times SGTTRF, -TRS, -SV, and -SL.
prec single
file clapack/timing/lin/dtimgt.c
for Times DGTTRF, -TRS, -SV, and -SL.
prec double
file clapack/timing/lin/ctimgt.c
for Times CGTTRF, -TRS, -SV, and -SL.
prec complex
file clapack/timing/lin/ztimgt.c
for Times ZGTTRF, -TRS, -SV, and -SL.
prec doublecomplex
# ===
file clapack/timing/lin/stimhr.c
for Times the LAPACK routines SGEHRD, SORGHR, and SORMHR,
, and the EISPACK routine ORTHES
prec single
file clapack/timing/lin/dtimhr.c
for Times the LAPACK routines DGEHRD, DORGHR, and DORMHR,
, and the EISPACK routine ORTHES
prec double
file clapack/timing/lin/ctimhr.c
for Times the LAPACK routines CGEHRD, CUNGHR, and CUNMHR
prec complex
file clapack/timing/lin/ztimhr.c
for Times the LAPACK routines ZGEHRD, ZUNGHR, and ZUNMHR
prec doublecomplex
# ===
file clapack/timing/lin/stimlq.c
for Times the LAPACK routines to perform the LQ factorization
, (SGELQF, SORGLQ, SORMLQ)
prec single
file clapack/timing/lin/dtimlq.c
for Times the LAPACK routines to perform the LQ factorization
, (DGELQF, DORGLQ, DORMLQ)
prec double
file clapack/timing/lin/ctimlq.c
for Times the LAPACK routines to perform the LQ factorization
, (CGELQF, CUNGLQ, CUNMLQ)
prec complex
file clapack/timing/lin/ztimlq.c
for Times the LAPACK routines to perform the LQ factorization
, (ZGELQF, ZUNGLQ, ZUNMLQ)
prec doublecomplex
# ===
file clapack/timing/lin/stimpb.c
for Times SPBTRF and SPBTRS
prec single
file clapack/timing/lin/dtimpb.c
for Times DPBTRF and DPBTRS
prec double
file clapack/timing/lin/ctimpb.c
for Times CPBTRF and CPBTRS
prec complex
file clapack/timing/lin/ztimpb.c
for Times ZPBTRF and ZPBTRS
prec doublecomplex
# ===
file clapack/timing/lin/stimpo.c
for Times SPOTRF, SPOTRS, and SPOTRI
prec single
file clapack/timing/lin/dtimpo.c
for Times DPOTRF, DPOTRS, and DPOTRI
prec double
file clapack/timing/lin/ctimpo.c
for Times CPOTRF, CPOTRS, and CPOTRI
prec complex
file clapack/timing/lin/ztimpo.c
for Times ZPOTRF, ZPOTRS, and ZPOTRI
prec doublecomplex
# ===
file clapack/timing/lin/stimpp.c
for Times SPPTRF, SPPTRS, and SPPTRI
prec single
file clapack/timing/lin/dtimpp.c
for Times DPPTRF, DPPTRS, and DPPTRI
prec double
file clapack/timing/lin/ctimpp.c
for Times CPPTRF, CPPTRS, and CPPTRI
prec complex
file clapack/timing/lin/ztimpp.c
for Times ZPPTRF, ZPPTRS, and ZPPTRI
prec doublecomplex
# ===
file clapack/timing/lin/stimpt.c
for Times SPTTRF, -TRS, -SV, and -SL.
prec single
file clapack/timing/lin/dtimpt.c
for Times DPTTRF, -TRS, -SV, and -SL.
prec double
file clapack/timing/lin/ctimpt.c
for Times CPTTRF, -TRS, -SV, and -SL.
prec complex
file clapack/timing/lin/ztimpt.c
for Times ZPTTRF, -TRS, -SV, and -SL.
prec doublecomplex
# ===
file clapack/timing/lin/stimql.c
for Times the LAPACK routines to perform the QL factorization
, (SGEQLF, SORGQL, SORMQL)
prec single
file clapack/timing/lin/dtimql.c
for Times the LAPACK routines to perform the QL factorization
, (DGEQLF, DORGQL, DORMQL)
prec double
file clapack/timing/lin/ctimql.c
for Times the LAPACK routines to perform the QL factorization
, (CGEQLF, CUNGQL, CUNMQL)
prec complex
file clapack/timing/lin/ztimql.c
for Times the LAPACK routines to perform the QL factorization
, (ZGEQLF, ZUNGQL, ZUNMQL)
prec doublecomplex
# ===
file clapack/timing/lin/stimqp.c
for Times the LAPACK routines to perform the QR factorization
, with column pivoting (SGEQPF)
prec single
file clapack/timing/lin/dtimqp.c
for Times the LAPACK routines to perform the QR factorization
, with column pivoting (DGEQPF)
prec double
file clapack/timing/lin/ctimqp.c
for Times the LAPACK routines to perform the QR factorization
, with column pivoting (CGEQPF)
prec complex
file clapack/timing/lin/ztimqp.c
for Times the LAPACK routines to perform the QR factorization
, with column pivoting (ZGEQPF)
prec doublecomplex
# ===
file clapack/timing/lin/stimqr.c
for Times the LAPACK routines to perform the QR factorization
, (SGEQRF, SORGQR, SORMQR)
prec single
file clapack/timing/lin/dtimqr.c
for Times the LAPACK routines to perform the QR factorization
, (DGEQRF, DORGQR, DORMQR)
prec double
file clapack/timing/lin/ctimqr.c
for Times the LAPACK routines to perform the QR factorization
, (CGEQRF, CUNGQR, CUNMQR)
prec complex
file clapack/timing/lin/ztimqr.c
for Times the LAPACK routines to perform the QR factorization
, (ZGEQRF, ZUNGQR, ZUNMQR)
prec doublecomplex
# ===
file clapack/timing/lin/stimrq.c
for Times the LAPACK routines to perform the RQ factorization
, (SGERQF, SORGRQ, SORMRQ)
prec single
file clapack/timing/lin/dtimrq.c
for Times the LAPACK routines to perform the RQ factorization
, (DGERQF, DORGRQ, DORMRQ)
prec double
file clapack/timing/lin/ctimrq.c
for Times the LAPACK routines to perform the RQ factorization
, (CGERQF, CUNGRQ, CUNMRQ)
prec complex
file clapack/timing/lin/ztimrq.c
for Times the LAPACK routines to perform the RQ factorization
, (ZGERQF, ZUNGRQ, ZUNMRQ)
prec doublecomplex
# ===
file clapack/timing/lin/stimsp.c
for Times SSPTRF, SSPTRS, and SSPTRI
prec single
file clapack/timing/lin/dtimsp.c
for Times DSPTRF, DSPTRS, and DSPTRI
prec double
file clapack/timing/lin/ctimsp.c
for Times CSPTRF, CSPTRS, and CSPTRI
prec complex
file clapack/timing/lin/ztimsp.c
for Times ZSPTRF, ZSPTRS, and ZSPTRI
prec doublecomplex
file clapack/timing/lin/ctimhp.c
for Times CHPTRF, CHPTRS, and CHPTRI
prec complex
file clapack/timing/lin/ztimhp.c
for Times ZHPTRF, ZHPTRS, and ZHPTRI
prec doublecomplex
# ===
file clapack/timing/lin/stimsy.c
for Times SSYTRF, SSYTRS, and SSYTRI
prec single
file clapack/timing/lin/dtimsy.c
for Times DSYTRF, DSYTRS, and DSYTRI
prec double
file clapack/timing/lin/ctimsy.c
for Times CSYTRF, CSYTRS, and CSYTRI
prec complex
file clapack/timing/lin/ztimsy.c
for Times ZSYTRF, ZSYTRS, and ZSYTRI
prec doublecomplex
file clapack/timing/lin/ctimhe.c
for Times CHETRF, CHETRS, and CHETRI
prec complex
file clapack/timing/lin/ztimhe.c
for Times ZHETRF, ZHETRS, and ZHETRI
prec doublecomplex
# ===
file clapack/timing/lin/stimtb.c
for Times STBTRS
prec single
file clapack/timing/lin/dtimtb.c
for Times DTBTRS
prec double
file clapack/timing/lin/ctimtb.c
for Times CTBTRS
prec complex
file clapack/timing/lin/ztimtb.c
for Times ZTBTRS
prec doublecomplex
# ===
file clapack/timing/lin/stimtd.c
for Times the LAPACK routines SSYTRD, SORGTR, and SORMTR,
, and the EISPACK routine TRED1
prec single
file clapack/timing/lin/dtimtd.c
for Times the LAPACK routines DSYTRD, DORGTR, and DORMTR,
, and the EISPACK routine TRED1
prec double
file clapack/timing/lin/ctimtd.c
for Times the LAPACK routines CHETRD, CUNGTR, and CUNMTR
prec complex
file clapack/timing/lin/ztimtd.c
for Times the LAPACK routines ZHETRD, ZUNGTR, and ZUNMTR
prec doublecomplex
# ===
file clapack/timing/lin/stimtp.c
for Times STPTRI and STPTRS
prec single
file clapack/timing/lin/dtimtp.c
for Times DTPTRI and DTPTRS
prec double
file clapack/timing/lin/ctimtp.c
for Times CTPTRI and CTPTRS
prec complex
file clapack/timing/lin/ztimtp.c
for Times ZTPTRI and ZTPTRS
prec doublecomplex
# ===
file clapack/timing/lin/stimtr.c
for Times STRTRI and STRTRS
prec single
file clapack/timing/lin/dtimtr.c
for Times DTRTRI and DTRTRS
prec double
file clapack/timing/lin/ctimtr.c
for Times CTRTRI and CTRTRS
prec complex
file clapack/timing/lin/ztimtr.c
for Times ZTRTRI and ZTRTRS
prec doublecomplex
file clapack/util/f2c.h
file commercial/aimms
for AIMMS
keywords algebraic modeling
file commercial/delisoft
for Delisoft Ltd, Finland
file commercial/fptsoftware
for quad and double quad precision libraries for Windows C compilers
by Steve Turato http://www.fptsoftware.com/
file commercial/greenmtn
for CrayFishpack and GMS Real FFT
by Green Mountain Software
file commercial/harmonic
for O-Matrix, A high-performance Visual Data Analysis environment
by Harmonic Software Inc. http://world.std.com/~harmonic
file commercial/hiq
for HiQ (interactive problem-solving environment for Macintosh)
file commercial/imsl.html
for Visual Numerics (former IMSL and Precision Visuals)
file commercial/mathematica.html
for Mathematica
keywords Wolfram Research, mathematics, software
file commercial/mathworks.html
for Mathtools, MathWorks, Matlab
file commercial/mlab
for description and ordering information for MLAB
keywords mathematics, statistics, modeling, differential equations, linear algebra
file commercial/nag
for Numerical Algorithms Group
file commercial/nr
for Numerical Recipes
file commercial/peda
for GrafEq
by Pedagoguery Software http://www.cafe.net/peda/
alg display of interval evaluation on tensor grid
file commercial/ve
for Visual Engineering
keywords visualization and presentation
file commercial/windward
for Windward Technologies, Inc. (WTI)
by TomAird@aol.com PWSmith@aol.com
file commercial/lau
for "A Numerical Library in C for Scientists and Engineers", CRC Press
by H. T. Lau
file commercial/softintegration
for Ch: An embeddable C/C++ interpreter for 2D/3D plotting, numerical computing and scripting
by softintegration.com (Wayne W. Cheng)
file confdb/soda95/prog.html
for program for SODA, San Francisco, January 22-24, 1995
file confdb/soda95/prog.html
for program for SODA, San Francisco, January 22-24, 1995
file confdb/soda95/prog.html
for program for SODA, San Francisco, January 22-24, 1995
file conformal/cap
for conformal mapping of circular arc polygons
by P. Bjorstad and E. Grosse
ref SIAM J Scientific Computing 8,19-32
rel ok
age experimental
file conformal/scpack
for Schwarz-Christoffel conformal mapping, disk to polygon
prec single
by L. N. Trefethen
ref SCPACK User's Guide, Internal Report 24, ICASE, NASA Langley, 1983.
rel excellent
age stable
gams i2b4, p
lang fortran
file conformal/scpdbl
for Schwarz-Christoffel conformal mapping, disk to polygon
prec double
by L. N. Trefethen
ref SCPACK User's Guide, Internal Report 24, ICASE, NASA Langley, 1983.
rel excellent
age stable
gams i2b4, p
lang fortran
file conformal/scdoc
for users guide for conformal/scpack
by L. N. Trefethen
file conformal/sclibdbl
for requisite utility routines for conformal/scpack
prec double
by L. N. Trefethen
file conformal/testdbl
for three tests for conformal/scpack
prec double
by L. N. Trefethen
file conformal/sclib
for requisite utility routines for conformal/scpack
prec single
by L. N. Trefethen
file conformal/tests
for three tests for conformal/scpack
prec single
by L. N. Trefethen
file conformal/kirch1
for free-streamline flows code for conformal/scpdbl
by L. N. Trefethen
gams i2b4, p, z
lang fortran
file conformal/gearlike
for conformal mapping from the unit disk to a gear-like domain
, consisting of concentric circular arcs and radial line segments.
by Kent Pearce
ref SIAM J Sci and Stat Comp.
gams p
lang fortran
file conformal/gearplot
for plotting output of conformal/gearlike using DISSPLA
by Kent Pearce
file conformal/confpack
for The CONFPACK subroutine library
size 412 kB
alg Symm's integral equation
by Gutknecht and Hough
ref David M. Hough, August 1990, "User's Guide to CONFPACK, Version 1.0", IPS Research Report No. 90-11. ETH-Zentrum, Ch-8092 Zurich, Switzerland.
# CONFPACK 1.0, 6 Apr 1991 by ftp from 129.132.17.1 in Zurich.
see linpack, quadpack
# send isamax sasum saxpy sdot sgeco sgefa sgedi sgesl sscal sswap from linpack.
# send qaws qawse qc25s qcheb qk15w qmaco qmomo qsort qwgts from quadpack.
# But netlib has slatec version of quadpack, this code uses book version!
# We'll fix this when we get a chance.
# Martin Gutknecht mhg@ips.ethz.ch or na.gutknecht@na-net.ornl.gov
# David Hough mtx005@cck.cov.ac.uk or na.dhough@na-net.ornl.gov
gams i2b4, p
lang fortran
file conformal/pargen
for preprocessor program PARGEN for conformal/confpack
file conformal/confdrivers
for 10 example driver programs for conformal/confpack
file conformal/readme
lib contin/manpak
for Computations on Implicitly Defined Manifolds
by W. C. Rheinboldt
# also: algebraically explicit differential algebraic equations (DAEs)
file contin/pcon61.f
title PITCON 6.1
for continuation and limit points
by Werner Rheinboldt and John Burkardt, University of Pittsburgh.
, wcrhein@vms.cis.pitt.edu burkardt@psc.edu
prec single
age stable
gams f2
file contin/dpcon61.f
title PITCON 6.1
for continuation and limit points
by Werner Rheinboldt and John Burkardt, University of Pittsburgh.
, wcrhein@vms.cis.pitt.edu burkardt@psc.edu
prec double
age stable
gams f2
file contin/pcon61subs.f
for LINPACK routines needed by contin/pcon61.f
prec single
file contin/pcon61subd.f
for LINPACK routines needed by contin/dpcon61.f
prec double
file contin/pcprb1.f
for sample problem for contin/pcon61.f
file contin/pcprb2.f
for sample problem for contin/pcon61.f
file contin/pcprb3.f
for sample problem for contin/pcon61.f
file contin/pcprb4.f
for sample problem for contin/pcon61.f
file contin/pcprb5.f
for sample problem for contin/pcon61.f
file contin/pcprb6.f
for sample problem for contin/pcon61.f
file contin/pcprb7.f
for sample problem for contin/pcon61.f
file contin/pcprb8.f
for sample problem for contin/pcon61.f
file contin/abcon.f
for predictor-corrector continuation
alg variable order Adams-Bashforth
by Bruce N. Lundberg and Aubrey B. Poore; lundberg@math.colostate.edu
prec single
age research
file contin/changes
file contin/manpak/manpak.f
for submanifolds implicitly defined by a system of nonlinear equations
file contin/manpak/manaux.f
for support of MANPAK and DAEPAK.
file contin/manpak/daepak.shar
for subroutines based on MANPAK and MANAUX for solving
, differential algebraic equations (DAEs) in which either the
, algebraic equations and/or the algebraic variables are explicitly specified.
file contin/manpak/drivers.shar
for sample drivers for the DAE solvers in daepak.shar
file contin/manpak/readme
file control/darex_f.tgz
file crc/guide
for how to set up files for mirroring by netlib
file crc/mirror.ps
for rationale for "Repository Mirroring"
by Eric Grosse
ref ACM TOMS, March 1995
lib crc/man
for man pages for crc and related commands
file crc/crc.c
for computing file checksums (POSIX.2)
by James W. Williams, Eric Grosse
file crc/lsr.c
for recursive ls, in same format as crc.c
by Eric Grosse
file crc/lsr-plan9.c
for recursive ls, in same format as crc.c
by Eric Grosse
file crc/nightly
for sample cron job to update checksums crc.gz
file crc/makefile
file crc/masterslave.c
for comparing the output of crc.c from two locations
by Eric Grosse
file crc/mirror.c
for executing the output of masterslave.c
by Eric Grosse
file crc/plausible.c
for cautious people might want to check masterslave's output
by Eric Grosse
file crc/suffix.c
for deciding when a file is suitable for compression
by Eric Grosse
file crc/suffix.h
for header for suffix.c
by Eric Grosse
file crc/util.c
for creating directories, reporting errors
by Eric Grosse
file crc/zopen.c
for like fopen(f,"r"), except for compressed files
by tps@chem.ucsd.edu (Tom Stockfisch)
ref Jan 18 1990 netnews/comp.sys.sgi
file crc/mirror-net
for sample script for slave to synchronize against master
by Eric Grosse
lang sh
file crc/chktime
for use after mirror ftp, to update times if lengths and checksums agree
by Eric Grosse
lang sh
file crc/htmlunz.c
for use after mirror ftp, if your mirror doesn't offer compressed files
by Eric Grosse
lib crc/net
for file list for directories at netlib@research.bell-labs.com
# generated nightly at research.bell-labs.com and elsewhere
# for frequent updates, please use binary ftp rather than email
lib crc/ornl
for file list for directories at netlib@ornl.gov
# generated nightly at research.bell-labs.com and elsewhere
# for frequent updates, please use binary ftp rather than email
lib crc/nac
for file list for directories at netlib@nac.no
# generated nightly at research.bell-labs.com and elsewhere
# for frequent updates, please use binary ftp rather than email
file crc/oldlsr.c
for recursive ls, in same format at crc.c
# deprecated, K&R version of lsr.c
by Eric Grosse
file crc/oldmasterslave.c
for comparing the output of crc.c from two locations
# deprecated, K&R version of masterslave.c
by Eric Grosse
file crc/oldmirror.c
for executing the output of masterslave.c
# deprecated, K&R version of mirror.c
by Eric Grosse
file crc/mkfile
file crc/oldplausible.c
file crc/changes
file crc/sedit
file crc/ls-lr_to_lsr-t.c
file crc/md5sum.c
for cryptographically verifying files
by Dave Presotto
alg RSA Data Security, Inc. MD5 Message-Digest Algorithm
file crc/netlib-bl.html
for PGP key used to sign MD5 checksums at netlib.bell-labs.com
by Eric Grosse
file crc/man/crc.1
lang formatted ASCII text
file crc/man/lsr.1
lang formatted ASCII text
file crc/man/masterslave.1
lang formatted ASCII text
file crc/man/mirror.1
lang formatted ASCII text
file crc/man/crc.man
lang troff
file crc/man/lsr.man
lang troff
file crc/man/masterslave.man
lang troff
file crc/man/mirror.man
lang troff
file crc/net/net
for file list for directories with master copy at netlib@netlib.bell-labs.com
, generated nightly at netlib.bell-labs.com
size 209 kB
file crc/net/ornl
for file list for directories with master copy at netlib@netlib.org
, generated nightly at netlib.bell-labs.com
size 506 kB
file crc/net/nac
for file list for directories with master copy at netlib@netlib.no
, generated nightly at netlib.bell-labs.com
file crc/net/compressed
for list of file suffixes that are already compressed
file crc/net/quis_custodiet
for checksums of the checksums
, "Quis custodiet ipsos custodes?" Juvenal, Satires
file cumulvs/README
file cumulvs/CUMULVS1.1.1.src.tgz
file ddsv/readme
for overview of ddsv
file ddsv/slpsubhalf.f
for software to measure the performance of routines SGEFA and
, SGESL from the Linpack package.
file ddsv/linpacks
for software to run the "Linpack Benchmark"
file ddsv/sblas1
for single precision Level 1 BLAS
file ddsv/dblas1
for double precision Level 1 BLAS
file ddsv/cblas1
for complex precision Level 1 BLAS
file ddsv/zblas1
for double complex precision Level 1 BLAS
file ddsv/sblas2
for single precision Level 2 BLAS
file ddsv/dblas2
for double precision Level 2 BLAS
file ddsv/cblas2
for complex precision Level 2 BLAS
file ddsv/zblas2
for double complex precision Level 2 BLAS
file ddsv/sblas3
for single precision Level 3 BLAS
file ddsv/dblas3
for double precision Level 3 BLAS
file ddsv/cblas3
for complex precision Level 3 BLAS
file ddsv/zblas3
for double complex precision Level 3 BLAS
file ddsv/slus.f
for single precision versions of different blocked
, LU decomposition algorithms
file ddsv/schol.f
for single precision versions of different blocked
, Cholesky decomposition algorithms
file ddsv/sqrs.f
for single precision versions of different blocked
, QR decomposition algorithms
file ddsv/benchm.f
for a benchmark program for performance test for Fortran loops.
, The program executes a number of Fortran DO-loops and lists
, the execution times for different loop lengths, the Mflops-rates
, and the performance parameters R-inf and n-half.
file ddsv/pcg3d.f
for a preconditioned conjugate gradient code for 3D problems.
file dierckx/ex/dapasu
file dierckx/ex/dapogr
file dierckx/ex/dapola
file dierckx/ex/daregr
file dierckx/ex/daspgr
file dierckx/ex/dasphe
file dierckx/ex/dasurf
file dierckx/ex/mnbisp.f
file dierckx/ex/mncloc.f
file dierckx/ex/mncoco.f
file dierckx/ex/mnconc.f
file dierckx/ex/mncosp.f
file dierckx/ex/mncual.f
file dierckx/ex/mncuev.f
file dierckx/ex/mncurf.f
file dierckx/ex/mndbin.f
file dierckx/ex/mnevpo.f
file dierckx/ex/mnfour.f
file dierckx/ex/mninst.f
file dierckx/ex/mnpade.f
file dierckx/ex/mnparc.f
file dierckx/ex/mnpasu.f
file dierckx/ex/mnperc.f
file dierckx/ex/mnpogr.f
file dierckx/ex/mnpola.f
file dierckx/ex/mnprof.f
file dierckx/ex/mnregr.f
file dierckx/ex/mnspal.f
file dierckx/ex/mnspde.f
file dierckx/ex/mnspev.f
file dierckx/ex/mnspgr.f
file dierckx/ex/mnsphe.f
file dierckx/ex/mnspin.f
file dierckx/ex/mnspro.f
file dierckx/ex/mnsuev.f
file dierckx/ex/mnsurf.f
#======== Curve fitting routines ======
file dierckx/curfit.f
for general curve fitting
gams k1a1a1, k5, l8g, l8h
file dierckx/percur.f
for curve fitting with periodic splines
gams k1a1a1, k5, l8g, l8h
file dierckx/parcur.f
for smoothing of parametric curves
gams k1a1a1, k5, l8g, l8h
file dierckx/clocur.f
for smoothing of closed curves
gams k1a1a1, k5, l8g, l8h
file dierckx/concur.f
for smoothing with end point derivative constraints
gams k1a1a1, k5, l8g, l8h
file dierckx/cocosp.f
for least-squares fitting with convexity constraints
gams k1a2a
file dierckx/concon.f
for automatic smoothing with convexity constraints
gams k5, k1a2a
#======== Curve application routines ======
file dierckx/splev.f
for evaluation of a spline function
gams e3a1, k6a1
file dierckx/splder.f
for derivative calculation of a spline function
gams e3a2, k6a2
file dierckx/spalde.f
for all derivatives of a spline function
gams e3a2, k6a2
file dierckx/curev.f
for evaluation of a spline curve
gams e3a1, k6a1
file dierckx/cualde.f
for all derivatives of a spline curve
gams k6a2
file dierckx/insert.f
for inserting a knot into a given spline
gams e3a3, k6c
file dierckx/splint.f
for integration of a spline function
gams e3a3, k6a3
file dierckx/fourco.f
for fourier coefficients of a cubic spline
gams e3d, k6d
file dierckx/sproot.f
for the zeros of a cubic spline
gams e3d, f1b, k6d
#======== Surface fitting routines ======
file dierckx/surfit.f
for surface fitting to scattered data
gams k1a1b, k5, l8g, l8h
file dierckx/regrid.f
for surface fitting to data on a rectangular grid
gams k1a1b, k5, l8g, l8h
file dierckx/polar.f
for surface fitting using generalized polar coordinates
gams k1a1b, k5, l8g, l8h
file dierckx/pogrid.f
for surface fitting to data on a polar grid
gams k1a1b, k5, l8g, l8h
file dierckx/sphere.f
for surface fitting using spherical coordinates
gams k1a1b, k5, l8g, l8h
file dierckx/spgrid.f
for surface fitting to data on a spherical grid
gams k1a1b, k5, l8g, l8h
file dierckx/parsur.f
for parametric surface fitting to data on a grid
gams k1a1b, k5, l8g, l8h
#======== Surface application routines ======
file dierckx/bispev.f
for evaluation of a bivariate spline function
gams k6a1
file dierckx/parder.f
for partial derivatives of a bivariate spline
gams e3a2, k6a2
file dierckx/dblint.f
for integration of a bivariate spline
gams e3a3, k6a3
file dierckx/profil.f
for cross sections of a bivariate spline
gams e3d, k6d
file dierckx/evapol.f
for evaluation of a polar spline
gams e3a1, k6a1
file dierckx/surev.f
for evaluation of a parametric spline surface
gams e3a1, k6a1
lib dierckx/ex
for test programs for each of the 29 main routines
# This index file only describes the top-level routines.
# The remaining FITPACK programs are lower level routines either called directly
# or indirectly by one or more of the user-level routines below. Their names all
# begin with the initials fp (fpader, fpadno,...) to avoid confusion with other
# possible user-supplied routines.
file dierckx/fpader.f
file dierckx/fpadno.f
file dierckx/fpadpo.f
file dierckx/fpback.f
file dierckx/fpbacp.f
file dierckx/fpbfout.f
file dierckx/fpbisp.f
file dierckx/fpbspl.f
file dierckx/fpchec.f
file dierckx/fpched.f
file dierckx/fpchep.f
file dierckx/fpclos.f
file dierckx/fpcoco.f
file dierckx/fpcons.f
file dierckx/fpcosp.f
file dierckx/fpcsin.f
file dierckx/fpcurf.f
file dierckx/fpcuro.f
file dierckx/fpcyt1.f
file dierckx/fpcyt2.f
file dierckx/fpdeno.f
file dierckx/fpdisc.f
file dierckx/fpfrno.f
file dierckx/fpgivs.f
file dierckx/fpgrdi.f
file dierckx/fpgrpa.f
file dierckx/fpgrre.f
file dierckx/fpgrsp.f
file dierckx/fpinst.f
file dierckx/fpintb.f
file dierckx/fpknot.f
file dierckx/fpopdi.f
file dierckx/fpopsp.f
file dierckx/fporde.f
file dierckx/fppara.f
file dierckx/fppasu.f
file dierckx/fpperi.f
file dierckx/fppocu.f
file dierckx/fppogr.f
file dierckx/fppola.f
file dierckx/fprank.f
file dierckx/fprati.f
file dierckx/fpregr.f
file dierckx/fprota.f
file dierckx/fprppo.f
file dierckx/fprpsp.f
file dierckx/fpseno.f
file dierckx/fpspgr.f
file dierckx/fpsphe.f
file dierckx/fpsuev.f
file dierckx/fpsurf.f
file dierckx/fpsysy.f
file dierckx/fptrnp.f
file dierckx/fptrpe.f
file dierckx/readme
# no longer free distributed, but rather a commercial package
file domino/readme
for overview of domino
file domino/conofacepc
for domino conoface for an IBM-PC (lattice C)
file domino/conofaces
for domino conoface for a Sun workstation
file domino/conofacevcc
for domino conoface for a Z80 (Vandata vcc compiler)
file domino/conofacevu
for domino conoface for a Vax (Berkeley Unix)
file domino/conofacevv
for domino conoface for a Vax (VMS)
file domino/doc
for documentation on how to create conoface and proface as well as notes
on linking node programs in Fortran
file domino/source
for system for multiple task/processor scheduling, communicating and handling
# The files in this directory comprise a version of double-precision
# EISPACK that has been tuned to take advantage of the cache, the vector
# registers, and the vectorizing compiler of the ibm 3090-vf.
# This version is the work of Augustin Dubrulle of IBM's Palo Alto
# Scientific Center.
# For more details, see the paper by Cline and Meyering in the
# directory, ../paper.
file eispack/3090vf/double/README
file eispack/3090vf/double/bakvec.f
file eispack/3090vf/double/balanc.f
file eispack/3090vf/double/balbak.f
file eispack/3090vf/double/bandr.f
file eispack/3090vf/double/bandv.f
file eispack/3090vf/double/bisect.f
file eispack/3090vf/double/bqr.f
file eispack/3090vf/double/cbabk2.f
file eispack/3090vf/double/cbal.f
file eispack/3090vf/double/cdiv.f
file eispack/3090vf/double/cg.f
file eispack/3090vf/double/ch.f
file eispack/3090vf/double/cinvit.f
file eispack/3090vf/double/combak.f
file eispack/3090vf/double/comhes.f
file eispack/3090vf/double/comlr.f
file eispack/3090vf/double/comlr2.f
file eispack/3090vf/double/comqr.f
file eispack/3090vf/double/comqr2.f
file eispack/3090vf/double/cortb.f
file eispack/3090vf/double/corth.f
file eispack/3090vf/double/csroot.f
file eispack/3090vf/double/dsc16.f
file eispack/3090vf/double/elmbak.f
file eispack/3090vf/double/elmhes.f
file eispack/3090vf/double/eltran.f
file eispack/3090vf/double/epslon.f
file eispack/3090vf/double/figi.f
file eispack/3090vf/double/figi2.f
file eispack/3090vf/double/hqr.f
file eispack/3090vf/double/hqr2.f
file eispack/3090vf/double/htrib3.f
file eispack/3090vf/double/htribk.f
file eispack/3090vf/double/htrid3.f
file eispack/3090vf/double/htridi.f
file eispack/3090vf/double/imtql1.f
file eispack/3090vf/double/imtql2.f
file eispack/3090vf/double/imtqlv.f
file eispack/3090vf/double/invit.f
file eispack/3090vf/double/kachel.f
file eispack/3090vf/double/minfit.f
file eispack/3090vf/double/ortbak.f
file eispack/3090vf/double/orthes.f
file eispack/3090vf/double/ortran.f
file eispack/3090vf/double/pythag.f
file eispack/3090vf/double/qzhes.f
file eispack/3090vf/double/qzit.f
file eispack/3090vf/double/qzval.f
file eispack/3090vf/double/qzvec.f
file eispack/3090vf/double/ratqr.f
file eispack/3090vf/double/rebak.f
file eispack/3090vf/double/rebakb.f
file eispack/3090vf/double/reduc.f
file eispack/3090vf/double/reduc2.f
file eispack/3090vf/double/rg.f
file eispack/3090vf/double/rgg.f
file eispack/3090vf/double/rs.f
file eispack/3090vf/double/rsb.f
file eispack/3090vf/double/rsg.f
file eispack/3090vf/double/rsgab.f
file eispack/3090vf/double/rsgba.f
file eispack/3090vf/double/rsm.f
file eispack/3090vf/double/rsp.f
file eispack/3090vf/double/rst.f
file eispack/3090vf/double/rt.f
file eispack/3090vf/double/svd.f
file eispack/3090vf/double/tinvit.f
file eispack/3090vf/double/tql1.f
file eispack/3090vf/double/tql2.f
file eispack/3090vf/double/tqlrat.f
file eispack/3090vf/double/trbak1.f
file eispack/3090vf/double/trbak3.f
file eispack/3090vf/double/tred1.f
file eispack/3090vf/double/tred2.f
file eispack/3090vf/double/tred3.f
file eispack/3090vf/double/tridib.f
file eispack/3090vf/double/tsturm.f
# The files here comprise a version of EISPACK that has been tuned to
# take advantage of the cache, the vector registers, and the vectorizing
# compiler of the IBM 3090-VF. Some of these files were not modified at
# all (from the original EISPACK versions), but are included here for
# completeness.
lib eispack/3090vf/paper
for description of changes to eispack
by Cline and Meyering
lib eispack/3090vf/single
prec single
by Cline and Meyering
lib eispack/3090vf/double
prec double
by Augustin Dubrulle
# Thus to get the file double precision vectorized tql2 subroutine, say
# send tql2 from eispack/3090vf/d.
# To get the corresponding single precision, say
# send tql2 from eispack/3090vf/s.
# Because the code contains a few IBM-specific constructions not understood
# by the compiler here, netlib can not provide its customary dependency
# analysis. So you have to ask for each subroutine individually. For a
# list of subroutines, see the index for (standard) eispack.
#
# Patches posted to the na-digest have been applied to the appropriate
# files. For details, "send changes from eispack/3090vf/s".
#
# A. Cline and J. Meyering, "Converting EISPACK to run efficiently on
# a vector processor", Tech. Memo., Pleasant Valley Software,
# Austin TX, 1989.
#
# A.A. Dubrulle, "A version of EISPACK for the IBM 3090VF", TR G320-3510,
# IBM Scientific Center, Palo Alto CA, 1988.
file eispack/3090vf/paper/ibm.tex
file eispack/3090vf/paper/ibm.ps
# The files in this directory comprise a version of single-precision
# EISPACK that has been tuned to take advantage of the cache, the vector
# registers, and the vectorizing compiler of the ibm 3090-vf. Some of
# these files were not modified at all (from the original EISPACK versions),
# but are included here for completeness.
# The patches posted to the netlib mailing list have been
# applied to the appropriate files. See the file NETLIB_PATCHES.
# For more details, see the paper by Cline and Meyering in the
# directory, ../paper.
file eispack/3090vf/single/NETLIB-PATCHES
file eispack/3090vf/single/README
file eispack/3090vf/single/bakvec.f
file eispack/3090vf/single/balanc.f
file eispack/3090vf/single/balbak.f
file eispack/3090vf/single/bandr.f
file eispack/3090vf/single/bandv.f
file eispack/3090vf/single/bisect.f
file eispack/3090vf/single/bqr.f
file eispack/3090vf/single/cbabk2.f
file eispack/3090vf/single/cbal.f
file eispack/3090vf/single/cdiv.f
file eispack/3090vf/single/cg.f
file eispack/3090vf/single/ch.f
file eispack/3090vf/single/cinvit.f
file eispack/3090vf/single/combak.f
file eispack/3090vf/single/comhes.f
file eispack/3090vf/single/comlr.f
file eispack/3090vf/single/comlr2.f
file eispack/3090vf/single/comqr.f
file eispack/3090vf/single/comqr2.f
file eispack/3090vf/single/cortb.f
file eispack/3090vf/single/corth.f
file eispack/3090vf/single/csroot.f
file eispack/3090vf/single/elmbak.f
file eispack/3090vf/single/elmhes.f
file eispack/3090vf/single/eltran.f
file eispack/3090vf/single/epslon.f
file eispack/3090vf/single/figi.f
file eispack/3090vf/single/figi2.f
file eispack/3090vf/single/hqr.f
file eispack/3090vf/single/hqr2.f
file eispack/3090vf/single/htrib3.f
file eispack/3090vf/single/htribk.f
file eispack/3090vf/single/htrid3.f
file eispack/3090vf/single/htridi.f
file eispack/3090vf/single/imtql1.f
file eispack/3090vf/single/imtql2.f
file eispack/3090vf/single/imtqlv.f
file eispack/3090vf/single/invit.f
file eispack/3090vf/single/minfit.f
file eispack/3090vf/single/ortbak.f
file eispack/3090vf/single/orthes.f
file eispack/3090vf/single/ortran.f
file eispack/3090vf/single/pythag.f
file eispack/3090vf/single/qzhes.f
file eispack/3090vf/single/qzit.f
file eispack/3090vf/single/qzval.f
file eispack/3090vf/single/qzvec.f
file eispack/3090vf/single/ratqr.f
file eispack/3090vf/single/rebak.f
file eispack/3090vf/single/rebakb.f
file eispack/3090vf/single/reduc.f
file eispack/3090vf/single/reduc2.f
file eispack/3090vf/single/rg.f
file eispack/3090vf/single/rgg.f
file eispack/3090vf/single/rs.f
file eispack/3090vf/single/rsb.f
file eispack/3090vf/single/rsg.f
file eispack/3090vf/single/rsgab.f
file eispack/3090vf/single/rsgba.f
file eispack/3090vf/single/rsm.f
file eispack/3090vf/single/rsp.f
file eispack/3090vf/single/rst.f
file eispack/3090vf/single/rt.f
file eispack/3090vf/single/svd.f
file eispack/3090vf/single/tinvit.f
file eispack/3090vf/single/tql1.f
file eispack/3090vf/single/tql2.f
file eispack/3090vf/single/tqlrat.f
file eispack/3090vf/single/trbak1.f
file eispack/3090vf/single/trbak3.f
file eispack/3090vf/single/tred1.f
file eispack/3090vf/single/tred2.f
file eispack/3090vf/single/tred3.f
file eispack/3090vf/single/tridib.f
file eispack/3090vf/single/tsturm.f
file eispack/archives/readme
file eispack/archives/eispack_alpha.tgz
file eispack/archives/eispack_hppa.tgz
file eispack/archives/eispack_irix64-64.tgz
file eispack/archives/eispack_irix64-n32.tgz
file eispack/archives/eispack_linux.tgz
file eispack/archives/eispack_rs6k.tgz
file eispack/archives/eispack_solaris.tgz
file eispack/ex/rteispak.f
file eispack/readme
for overview of eispack
lib eispack/3090vf
by Cline, Dubrulle, and Meyering
for vectorizing on an IBM 3090-VF computer
, These codes might be a useful starting point
, for vectorized versions on other computers as well.
lib eispack/ex
for This directory contains a complete set of
, testing routines for eispack.
file eispack/bakvec.f
gams D4c4
for back transformation, sign-symmetric matrix
file eispack/balanc.f
gams D4c1a
for scaling, general matrix
file eispack/balbak.f
gams D4c4
for back scaling, general matrix
file eispack/bandr.f
gams D4c1b1
for reduction, symmetric band matrix
file eispack/bandv.f
gams D4c3
for some eigenvectors, symmetric band matrix
file eispack/bisect.f
gams D4a5,D4c2a
for some eigenvalues, symmetric tridiagonal matrix
file eispack/bqr.f
gams D4a6
for some eigenvalues, symmetric band matrix
file eispack/cbabk2.f
gams D4c4
for back scaling, complex matrix
file eispack/cbal.f
gams D4c1a
for scaling, complex matrix
file eispack/cg.f
gams D4a4
for find eigenvalues and eigenvectors, complex general matrix
file eispack/ch.f
gams D4a3
for find eigenvalues and eigenvectors, complex Hermitian matrix
file eispack/cinvit.f
gams D4c2b
for some eigenvectors, complex Hessenberg matrix
file eispack/combak.f
gams D4c4
for back transformation, complex matrix
file eispack/comhes.f
gams D4c1b2
for reduction, complex matrix
file eispack/comlr.f
gams D4c2b
for all eigenvalues, complex Hessenberg matrix
file eispack/comlr2.f
gams D4c2b
for all eigenvalues and eigenvectors, complex Hessenberg matrix
file eispack/comqr.f
gams D4c2b
for all eigenvalues, complex Hessenberg matrix
file eispack/comqr2.f
gams D4c2b
for all eigenvalues and eigenvectors, complex Hessenberg matrix
file eispack/cortb.f
gams D4c4
for back transformation, complex matrix
file eispack/corth.f
gams D4c1b2
for reduction, complex matrix
file eispack/elmbak.f
gams D4c4
for back transformation, real matrix
file eispack/elmhes.f
gams D4c1b2
for reduction, real matrix
file eispack/eltran.f
gams D4c4
for reduction, real matrix
file eispack/figi.f
gams D4c1c
for reduction, sign-symmetric matrix
file eispack/figi2.f
gams D4c1c
for reduction, sign-symmetric matrix
file eispack/hqr.f
gams D4c2b
for all eigenvalues, real Hessenberg matrix
file eispack/hqr2.f
gams D4c2b
for all eigenvalues and eigenvectors, real Hessenberg matrix
file eispack/htrib3.f
gams D4c4
for back transformation, Hermitian packed matrix
file eispack/htribk.f
gams D4c4
for back transformation, Hermitian matrix
file eispack/htrid3.f
gams D4c1b1
for reduction, Hermitian packed matrix
file eispack/htridi.f
gams D4c1b1
for reduction, Hermitian matrix
file eispack/imtql1.f
gams D4a5,D4c2a
for all eigenvalues, symmetric tridiagonal matrix
file eispack/imtql2.f
gams D4a5,D4c2a
for all eigenvalues and eigenvectors, symmetric tridiagonal matrix
file eispack/imtqlv.f
gams D4a5,D4c2a
for all eigenvalues, symmetric tridiagonal matrix
file eispack/invit.f
gams D4c2b
for some eigenvectors, real Hessenberg matrix
file eispack/minfit.f
gams D6
for least squares, real matrix
file eispack/ortbak.f
gams D4c4
for back transformation, real matrix
file eispack/orthes.f
gams D4c1b2
for reduction, real matrix
file eispack/ortran.f
gams D4c4
for reduction, real matrix
file eispack/qzhes.f
gams D4c1b3
for reduction, generalized matrix
file eispack/qzit.f
gams D4c1b3
for further reduction, generalized Hessenberg matrix
file eispack/qzval.f
gams D4c2c
for all eigenvalues, generalized Hessenberg matrix
file eispack/qzvec.f
gams D4c3
for all eigenvectors, generalized Hessenberg matrix
file eispack/ratqr.f
gams D4a5,D4c2a
for some eigenvalues, symmetric tridiagonal matrix
file eispack/rebak.f
gams D4c4
for back transformation, symmetric generalized matrix
file eispack/rebakb.f
gams D4c4
for back transformation, symmetric generalized matrix
file eispack/reduc.f
gams D4c1c
for reduction, symmetric generalized matrix
file eispack/reduc2.f
gams D4c1c
for reduction, symmetric generalized matrix
file eispack/rg.f
gams D4a2
for find eigenvalues and eigenvectors, general matrix
file eispack/rgg.f
gams D4b2
for find eigenvalues and eigenvectors, generalized matrix
file eispack/rs.f
gams D4a1
for find eigenvalues and eigenvectors, symmetric matrix
file eispack/rsb.f
gams D4a6
for find eigenvalues and eigenvectors, band symmetric matrix
file eispack/rsg.f
gams D4b1
for find eigenvalues and eigenvectors, generalized symmetric matrix
file eispack/rsgab.f
gams D4b1
for find eigenvalues and eigenvectors, generalized symmetric matrix
file eispack/rsgba.f
gams D4b1
for find eigenvalues and eigenvectors, generalized symmetric matrix
file eispack/rsm.f
for find eigenvalues and eigenvectors, symmetric matrix
file eispack/rsp.f
gams D4a1
for find eigenvalues and eigenvectors, packed symmetric matrix
file eispack/rst.f
gams D4a5
for find eigenvalues and eigenvectors, tridiagonal symmetric matrix
file eispack/rt.f
gams D4a5
for find eigenvalues and eigenvectors, sign-symmetric tridiagonal matrix
file eispack/svd.f
gams D6
for singular value decomposition, real matrix
file eispack/tinvit.f
gams D4c3
for some eigenvectors, symmetric tridiagonal matrix
file eispack/tql1.f
gams D4a5,D4c2a
for all eigenvalues, symmetric tridiagonal matrix
file eispack/tql2.f
gams D4a5,D4c2a
for all eigenvalues and eigenvectors, symmetric tridiagonal matrix
file eispack/tqlrat.f
gams D4a5,D4c2a
for all eigenvalues, symmetric tridiagonal matrix
file eispack/trbak1.f
gams D4c4
for back transformation, symmetric matrix
file eispack/trbak3.f
gams D4c4
for back transformation, packed symmetric matrix
file eispack/tred1.f
gams D4c1b1
for reduction, symmetric matrix
file eispack/tred2.f
gams D4c1b1
for reduction, symmetric matrix
file eispack/tred3.f
gams D4c1b1
for reduction, packed symmetric matrix
file eispack/tridib.f
gams D4a5,D4c2a
for some eigenvalues, symmetric tridiagonal matrix
file eispack/tsturm.f
gams D4a5,D4c2a
for some eigenvalues and eigenvectors, symmetric tridiagonal matrix
file elefunt/alog.f
for test of alog and alog10
prec single
gams c4a
file elefunt/asin.f
for test of asin and acos
prec single
gams c4a
file elefunt/atan.f
for test of atan
prec single
gams c4a
file elefunt/dasin.f
for test of dasin and dacos
prec double
gams c4a
file elefunt/datan.f
for test of datan
prec double
gams c4a
file elefunt/dexp.f
for test of exponential
prec double
gams c4a
file elefunt/dlog.f
for test of dlog and dlog10
prec double
gams c4a
file elefunt/dmachar.f
for environmental parameters
prec double
file elefunt/dpower.f
for test of dpower
prec double
gams c2
file elefunt/dsin.f
for test of dsin and dcos
prec double
gams c4a
file elefunt/dsinh.f
for test of dsinh and dcosh
prec double
gams c4c
file elefunt/dsqrt.f
for test of dsqrt
prec double
gams c2
file elefunt/dtan.f
for test of dtan and dcotan
prec double
gams c4a
file elefunt/dtanh.f
for test of dtanh
prec double
gams c4c
file elefunt/exp.f
for test of exponential
prec single
gams c4a
file elefunt/machar.f
for floating point environmental parameters
prec single/double
file elefunt/machar.c
for floating point environmental parameters
prec single/double
file elefunt/machar-basic
lang Basic
for floating point environmental parameters
prec single/double
file elefunt/power.f
for test of power
prec single
gams c2
file elefunt/sin.f
for test of sin and cos
prec single
gams c4a
file elefunt/sinh.f
for test of sinh and cosh
prec single
gams c4c
file elefunt/sqrt.f
for test of sqrt
prec single
gams c2
file elefunt/tan.f
for test of tan and cotan
prec single
gams c4a
file elefunt/tanh.f
for test of tanh
prec single
gams c4c
file elefunt/makefile
file env/links.html
for pointers to related resources on the web, e.g. Algae
file env/yorick.tar.gz
for developing simulations codes and pre- and post-processors
by David H. Munro
lang Standard C
# *** This is a pre-release of yorick-1.0, which will come out soon. ***
# Yorick is an interpreted language like Basic or Lisp, but far faster.
# * A C-like language, but without declarative statements. Operations
# between arrays produce array results, which is one reason for
# Yorick's high speed. Scientific computing and numerical analysis
# are the goals of most Yorick programs.
# * An X window system interactive graphics package. Concentrates on
# x-y plots and filling and contouring quadrilateral meshes. Also
# handles cell arrays. Hardcopy to binary CGM or PostScript files.
# A separate CGM browser is included.
# * Yorick's binary file package can read or write floating point
# formats foreign to the machine where Yorick is running. Thus, you
# can share binary files freely on heterogeneous networks.
# * A library of functions written in the Yorick language. These
# include Bessel, gamma, and related functions, multiple key sorting,
# spline, rational function, and least squares fitting, and routines
# to read and write netCDF files.
# * Provisions for embedding compiled subroutines and functions within
# a Yorick interpreter. A compiled package which solves matrices and
# performs FFTs is supplied.
size 1.4 MB
# (NOT AVAILABLE BY EMAIL)
file env/yorick.readme
file env/mathomatic.zip
for simple symbolic algebra (low degree polynomial equations)
name mathomatic algebraic equation processor
by George Gesslein II
# primitive compared to Maple, but it's free and you get source
lang C
The current URL for
Templates for the Solution of Algebraic Eigenvalue Problems
is http://www.cs.ucdavis.edu/~bai/ET/contents.html.
file f2c/changes
file f2c/f2c.1
lang man page
file f2c/f2c.1t
lang troff -man source for man page
file f2c/f2c.h
file f2c/f2c.ps
lang Postscript
file f2c/f2c.pdf
file f2c/fc
lang Bourne shell script
file f2c/getopt.c
for Source for "getopt" command used by fc (for systems lacking getopt)
file f2c/index
file f2c/libf77
lang C (bundle of source)
file f2c/libi77
lang C (bundle of source)
file f2c/libf2c.zip
for combined libf77, libi77, with several makefile variants
size 102 KB
# DO NOT REQUEST BY EMAIL, USE FTP!
lib f2c/msdos
for MS-DOS f2c binaries (ftp only)
lib f2c/mswin
for Win32 f2c binaries (ftp only)
lib f2c/src
for f2c source
file f2c/README
file f2c/msdos/README
file f2c/msdos/f2c.exe.gz
for conventional-memory MSDOS version of f2c (compiled by Borland C++ 4.02)
file f2c/msdos/f2cx.exe.gz
for extended-memory MSDOS version of f2c (compiled by Symantec C/C++)
file f2c/msdos/ccb.bat
for compilation of f2c.exe (for people curious about how it was done)
file f2c/msdos/ccs.bat
for compilation of f2cx.exe (for people curious about how it was done)
file f2c/msdos/ccm.bat
file f2c/msdos/etime.exe.gz
file f2c/msdos/xsum.executable (uncompressed MSDOS version of xsum)
file f2c/mswin/README
file f2c/mswin/f2c.exe.gz
for Win32 console version of f2c (compiled by MSVC++ 6.0)
file f2c/mswin/makefile.vc
for compiling f2c.exe by MSVC++
# ====== index for f2c/src ======
# NOTE: The E-mail request "send all from f2c/src" retrieves the
# complete f2c source (sans libraries).
# The remaining files in this directory are the component modules
# of "all from f2c/src", so you can request just the modules that
# have changed since last you updated your f2c source. You can
# tell what has changed by looking at the timestamps at the end
# of "readme from f2c".
file f2c/src/cds.c
file f2c/src/data.c
file f2c/src/defines.h
file f2c/src/defs.h
file f2c/src/equiv.c
file f2c/src/error.c
file f2c/src/exec.c
file f2c/src/expr.c
file f2c/src/f2c.1
file f2c/src/f2c.1t
file f2c/src/f2c.h
file f2c/src/format.c
file f2c/src/format.h
file f2c/src/formatdata.c
file f2c/src/ftypes.h
file f2c/src/gram.c
file f2c/src/gram.dcl
file f2c/src/gram.exec
file f2c/src/gram.expr
file f2c/src/gram.head
file f2c/src/gram.io
file f2c/src/init.c
file f2c/src/intr.c
file f2c/src/io.c
file f2c/src/iob.h
file f2c/src/lex.c
file f2c/src/machdefs.h
file f2c/src/main.c
file f2c/src/makefile.u
file f2c/src/makefile.vc
file f2c/src/malloc.c
file f2c/src/mem.c
file f2c/src/memset.c
file f2c/src/misc.c
file f2c/src/mkfile.plan9
for making f2c under plan 9 (mk -f mkfile.plan9)
file f2c/src/names.c
file f2c/src/names.h
file f2c/src/niceprintf.c
file f2c/src/niceprintf.h
file f2c/src/notice
file f2c/src/output.c
file f2c/src/output.h
file f2c/src/p1defs.h
file f2c/src/p1output.c
file f2c/src/parse.h
file f2c/src/parse_args.c
file f2c/src/pccdefs.h
file f2c/src/pread.c
file f2c/src/proc.c
file f2c/src/put.c
file f2c/src/putpcc.c
file f2c/src/sysdep.c
file f2c/src/sysdep.h
file f2c/src/sysdeptest.c
file f2c/src/tokens
file f2c/src/tokdefs.h
file f2c/src/usignal.h
file f2c/src/vax.c
file f2c/src/version.c
file f2c/src/xsum.c
file f2c/src/xsum0.out
file f2c/src/Notice
file f2c/src/README
file f2c/src/readme
file fdlibm/fdlibm.h
file fdlibm/index
file fdlibm/e_acos.c
file fdlibm/e_acosh.c
file fdlibm/e_asin.c
file fdlibm/e_atan2.c
file fdlibm/e_atanh.c
file fdlibm/e_cosh.c
file fdlibm/e_exp.c
file fdlibm/e_fmod.c
file fdlibm/e_gamma.c
file fdlibm/e_gamma_r.c
file fdlibm/e_hypot.c
file fdlibm/e_j0.c
file fdlibm/e_j1.c
file fdlibm/e_jn.c
file fdlibm/e_lgamma.c
file fdlibm/e_lgamma_r.c
file fdlibm/e_log.c
file fdlibm/e_log10.c
file fdlibm/e_pow.c
file fdlibm/e_rem_pio2.c
file fdlibm/e_remainder.c
file fdlibm/e_scalb.c
file fdlibm/e_sinh.c
file fdlibm/e_sqrt.c
file fdlibm/k_cos.c
file fdlibm/k_rem_pio2.c
file fdlibm/k_sin.c
file fdlibm/k_standard.c
file fdlibm/k_tan.c
file fdlibm/makefile
file fdlibm/s_asinh.c
file fdlibm/s_atan.c
file fdlibm/s_cbrt.c
file fdlibm/s_ceil.c
file fdlibm/s_copysign.c
file fdlibm/s_cos.c
file fdlibm/s_erf.c
file fdlibm/s_expm1.c
file fdlibm/s_fabs.c
file fdlibm/s_finite.c
file fdlibm/s_floor.c
file fdlibm/s_frexp.c
file fdlibm/s_ilogb.c
file fdlibm/s_isnan.c
file fdlibm/s_ldexp.c
file fdlibm/s_lib_version.c
file fdlibm/s_log1p.c
file fdlibm/s_logb.c
file fdlibm/s_matherr.c
file fdlibm/s_modf.c
file fdlibm/s_nextafter.c
file fdlibm/s_rint.c
file fdlibm/s_scalbn.c
file fdlibm/s_signgam.c
file fdlibm/s_significand.c
file fdlibm/s_sin.c
file fdlibm/s_tan.c
file fdlibm/s_tanh.c
file fdlibm/w_acos.c
file fdlibm/w_acosh.c
file fdlibm/w_asin.c
file fdlibm/w_atan2.c
file fdlibm/w_atanh.c
file fdlibm/w_cosh.c
file fdlibm/w_exp.c
file fdlibm/w_fmod.c
file fdlibm/w_gamma.c
file fdlibm/w_gamma_r.c
file fdlibm/w_hypot.c
file fdlibm/w_j0.c
file fdlibm/w_j1.c
file fdlibm/w_jn.c
file fdlibm/w_lgamma.c
file fdlibm/w_lgamma_r.c
file fdlibm/w_log.c
file fdlibm/w_log10.c
file fdlibm/w_pow.c
file fdlibm/w_remainder.c
file fdlibm/w_scalb.c
file fdlibm/w_sinh.c
file fdlibm/w_sqrt.c
file fdlibm/readme
file fftpack/links.html
for related resources
file fftpack/doc
for user guide for fftpack
file fftpack/fft.c
for C translation of much of fftpack
prec single
by Monty
gams J1a
lang C
file fftpack/dp.tgz
for double precision clone of fftpack
by Hugh C. Pumphrey
prec double
lang Fortran
gams J1a
file fftpack/jfftpack.tgz
for Java translation of fftpack
by Baoshe Zhang baoshe.zhang@uleth.ca
lang Java
gams J1a
file fftpack/cfftb.f
gams J1a2
for FFT, backward transform (synthesis) of a complex Fourier coefficient array
file fftpack/cfftf.f
gams J1a2
for FFT, forward transform of a complex periodic sequence
file fftpack/cosqf.f
gams J1a3
for FFT, forward cosine transform with odd wave numbers
file fftpack/cost.f
gams J1a3
for FFT, discrete cosine transform of a real even sequence
file fftpack/ezfftb.f
gams J1a1
for FFT, backward transform (synthesis) of a real Fourier coefficient array, simplified and slower version of (fftpack/rfftb)
file fftpack/ezfftf.f
gams J1a1
for FFT, forward transform of a real periodic sequence, simplified and slower version of (fftpack/rfftf)
file fftpack/rfftb.f
gams J1a1
for FFT, backward transform (synthesis) of a real Fourier coefficient array
file fftpack/rfftf.f
gams J1a1
for FFT, forward transform of a real periodic sequence
file fftpack/sinqb.f
gams J1a3
for FFT, backward sine transform (synthesis) with odd wave numbers
file fftpack/sinqf.f
gams J1a3
for FFT, forward sine transform with odd wave numbers
file fftpack/sint.f
gams J1a3
for FFT, discrete sine transform of a real odd sequence
file fftpack/cffti.f
gams -0-
for initialization routine for (fftpack/cfftf) and (fftpack/cfftb)
file fftpack/cosqb.f
gams J1a3
for FFT, backward cosine transform (synthesis) with odd wave numbers
file fftpack/cosqi.f
gams -0-
for initialization routine for (fftpack/cosqf) and (fftpack/cosqb)
file fftpack/ezffti.f
for initialization routine for (fftpack/ezfftf) and (fftpack/ezfftb)
file fftpack/costi.f
gams -0-
for initialization routine for (fftpack/cost)
file fftpack/rffti.f
gams J1a1
for initialization routine for (fftpack/rfftf) and (ftpack/rfftb)
file fftpack/sinqi.f
gams -0-
for initialization routtine for (fftpack/sinqf) and (fftpack/sinqb)
file fftpack/sinti.f
gams -0-
for initialization routine for (fftpack/sint)
file fftpack/cfftb1.f
file fftpack/cfftf1.f
file fftpack/cffti1.f
file fftpack/changes
file fftpack/cosqb1.f
file fftpack/cosqf1.f
file fftpack/ezfft1.f
file fftpack/fftpack.mail
file fftpack/passb.f
file fftpack/passb2.f
file fftpack/passb3.f
file fftpack/passb4.f
file fftpack/passb5.f
file fftpack/passf.f
file fftpack/passf2.f
file fftpack/passf3.f
file fftpack/passf4.f
file fftpack/passf5.f
file fftpack/radb2.f
file fftpack/radb3.f
file fftpack/radb4.f
file fftpack/radb5.f
file fftpack/radbg.f
file fftpack/radf2.f
file fftpack/radf3.f
file fftpack/radf4.f
file fftpack/radf5.f
file fftpack/radfg.f
file fftpack/rfftb1.f
file fftpack/rfftf1.f
file fftpack/rffti1.f
file fftpack/sint1.f
file fftpack/test.f
file fishpack/hwscrt.f
for solves the standard Helmholtz 5-point approximation in Cartesian coordinates using a centered finite difference grid
gams i2b1a1a
file fishpack/hwsplr.f
for solves a Helmholtz 5-point approximation in polar coordinates using a centered finite difference grid
gams i2b1a1a
file fishpack/hwscyl.f
for solves a modified Helmholtz 5-point approximation in cylindrical coordinates using a centered finite difference grid
gams i2b1a1a
file fishpack/hwsssp.f
for solves a Helmholtz 5-point approximation in spherical coordinates and on the surface of the unit sphere using a centered finite difference grid
gams i2b1a1a
file fishpack/hwscsp.f
for solves modified Helmholtz 5-point approximation in spherical coordinate assuming axis symmetry and using a centered finite difference grid
gams i2b1a1a
file fishpack/hstcrt.f
for solves the standard Helmholtz 5-point approximation in Cartesian coordinates using a staggered finite difference grid
gams i2b1a1a
file fishpack/hstplr.f
for solves a Helmholtz 5-point approximation in polar coordinates using a staggered finite difference grid
gams i2b1a1a
file fishpack/hstcyl.f
for solves a modified Helmholtz 5-point approximation in cylindrical coordinates using a staggered finite difference grid
gams i2b1a1a
file fishpack/hstssp.f
for solves a Helmholtz 5-point approximation in spherical coordinates and on the surface of the unit sphere using a staggered finite difference grid
gams i2b1a1a
file fishpack/hstcsp.f
for solves a modified Helmholtz 5-point approximation in spherical coordinates assuming axis symmetry
gams i2b1a1a
file fishpack/hw3crt.f
for solves the standard Helmholtz 7-point approximation in Cartesian coordinates using a centered finite difference grid
gams i2b1a1a
file fishpack/sepx4.f
for discretizes and solves 2nd and optionally 4th order approximations to separable elliptic PDEs with constant coefficients in one direction
gams i2b1a1a, i2b1a2
file fishpack/sepeli.f
for discretizes and solves 2nd and optionally 4th order approximations on a uniform grid to a separable elliptic PDE on a rectangle
gams i2b1a1a, i2b1a2
file fishpack/genbun.f
for solves the linear system of equations resulting from an approximation to 2-dimensional elliptic PDEs with constant coefficients in one direction
gams i2b4b
file fishpack/blktri.f
for solves block tridiagonal linear systems arising from approximations to separable 2-dimensional elliptic PDEs
gams i2b4b
file fishpack/poistg.f
for solves a block tridiagonal linear system arising from staggered grid approximations to 2-dimensional elliptic PDEs with constant coefficients
gams d2a4, i2b4b
file fishpack/pois3d.f
for solves a block tridiagonal linear system of equations arising from approximations to 3-dimensional elliptic PDEs in a box
gams d2a4, i2b4b
file fishpack/cmgnbn.f
for solves a complex block tridiagonal linear system arising from approximations to separable complex 2-dimensional elliptic PDEs
gams i2b4b
file fishpack/cblktr.f
for solves a complex block tridiagonal linear system arising from approximations to separable complex 2-dimensional elliptic PDEs
gams i2b4b
lib fishpack/ex
file fishpack/bcrh.f
file fishpack/blktr1.f
file fishpack/bsrh.f
file fishpack/cblkt1.f
file fishpack/ccmpb.f
file fishpack/changes
file fishpack/chkpr4.f
file fishpack/chkprm.f
file fishpack/chksn4.f
file fishpack/chksng.f
file fishpack/cmpcsg.f
file fishpack/cmpmrg.f
file fishpack/cmposd.f
file fishpack/cmposn.f
file fishpack/cmposp.f
file fishpack/cmptr3.f
file fishpack/cmptrx.f
file fishpack/cofx.f
file fishpack/cofx4.f
file fishpack/cofy.f
file fishpack/compb.f
file fishpack/cosgen.f
file fishpack/cpadd.f
file fishpack/cproc.f
file fishpack/cprocp.f
file fishpack/cprod.f
file fishpack/cprodp.f
file fishpack/defe4.f
file fishpack/defer.f
file fishpack/dx.f
file fishpack/dx4.f
file fishpack/dy.f
file fishpack/dy4.f
file fishpack/epmach.f
file fishpack/hstcs1.f
file fishpack/hwscs1.f
file fishpack/hwsss1.f
file fishpack/indxa.f
file fishpack/indxb.f
file fishpack/indxc.f
file fishpack/inxca.f
file fishpack/inxcb.f
file fishpack/inxcc.f
file fishpack/merge.f
file fishpack/minso4.f
file fishpack/minsol.f
file fishpack/ortho4.f
file fishpack/orthog.f
file fishpack/pgsf.f
file fishpack/pimach.f
file fishpack/poisd2.f
file fishpack/poisn2.f
file fishpack/poisp2.f
file fishpack/pos3d1.f
file fishpack/postg2.f
file fishpack/ppadd.f
file fishpack/ppgsf.f
file fishpack/pppsf.f
file fishpack/ppsgf.f
file fishpack/ppspf.f
file fishpack/proc.f
file fishpack/procp.f
file fishpack/prod.f
file fishpack/prodp.f
file fishpack/psgf.f
file fishpack/speli4.f
file fishpack/spelip.f
file fishpack/store.f
file fishpack/tevlc.f
file fishpack/tevls.f
file fishpack/tri3.f
file fishpack/trid.f
file fishpack/tris4.f
file fishpack/trisp.f
file fishpack/trix.f
file fitpack/all
for spline under tension
# Interested parties can obtain the entire package on disk or tape
# from Pleasant Valley Software, 8603 Altus Cove, Austin TX (USA),
# 78759 at a cost of $495 US. A 340 page manual is available for
# $30 US per copy. The package includes examples and machine
# readable documentation.
# 512-345-7645
# Alan Kaylor Cline
file floppy/contents.html
for Online manual for floppy and flow; viewable using Mosaic or any other
World Wide Web browser. (included in tar files)
file floppy/floppy7.tgz
for FLOPPY is a software tool that takes as input a file of FORTRAN 77
, code and checks it according to various "coding conventions". Floppy
, can "tidy" the source FORTRAN, producing a new file with indented
, DO-loops, block IF-s, and so on. Floppy can be used to generate HTML
, from the Fortran program. In this case, a new file is written where each
, module and include file name in the source Fortran is replaced by an
, HTML Anchor. The format of the source is preserved when the
, document is browsed by an HTML browser. FLOPPY can also be used
, to write a binary summary file which is then used as input to the FLOW
, program.
by Julian J. Bunn, julian@vxcern.cern.ch.
file floppy/flow3.tgz
for The FLOW program takes the binary summary file produced by
, FLOPPY, and can produce various reports on the structure of the
, original FORTRAN program.
by Julian J. Bunn, julian@vxcern.cern.ch.
lib floppy/win32
for win32 versions of the floppy package
, FLOPPY is a software tool that takes as input a file of FORTRAN 77
, code and checks it according to various "coding conventions". Floppy
, can "tidy" the source FORTRAN, producing a new file with indented
, DO-loops, block IF-s, and so on. Floppy can be used to generate HTML
, from the Fortran program. In this case, a new file is written where each
, module and include file name in the source Fortran is replaced by an
, HTML Anchor. The format of the source is preserved when the
, document is browsed by an HTML browser. FLOPPY can also be used
, to write a binary summary file which is then used as input to the FLOW
, program.
by Julian J. Bunn, julian@vxcern.cern.ch.
file floppy/win32/floppy.zip
for win32 version of the floppy program
, FLOPPY is a software tool that takes as input a file of FORTRAN 77
, code and checks it according to various "coding conventions". Floppy
, can "tidy" the source FORTRAN, producing a new file with indented
, DO-loops, block IF-s, and so on. Floppy can be used to generate HTML
, from the Fortran program. In this case, a new file is written where each
, module and include file name in the source Fortran is replaced by an
, HTML Anchor. The format of the source is preserved when the
, document is browsed by an HTML browser. FLOPPY can also be used
, to write a binary summary file which is then used as input to the FLOW
, program.
,
, The FLOW program takes the binary summary file produced by
, FLOPPY, and can produce various reports on the structure of the
, original FORTRAN program.
size 413k
by Julian J. Bunn, julian@vxcern.cern.ch.
file fmm/readme
for overview of fmm
file fmm/decomp.f
for decomposes a matrix by Gaussian elimination and estimates the
, condition of the matrix
prec double
file fmm/solve.f
for solution of linear system, A*x = b, do not use if (fmm/decomp) has
, detected a singularity
prec double
file fmm/quanc8.f
for estimate the integral of f(x) in a finite interval, user provided
, tolerance using an automatic adaptive routine based on the 8-panel
, Newton-Cotes rule
prec double
file fmm/rkf45.f
for Fehlberg fourth-fifth order Runge-Kutta method
prec double
file fmm/spline.f
for compute the coefficients for a cubic interpolating spline
prec double
file fmm/seval.f
for evaluate a cubic interpolating spline
prec double
file fmm/svd.f
for determines the singular value decomposition, SVD, of a real
, rectangular matrix, using Householder bidiagonalization and a variant
, of the QR algorithm
prec double
file fmm/fmin.f
for an approximation to the point where a user function attains a minimum
, on an interval is determined
prec double
file fmm/urand.f
for is a uniform random number generator based on theory and suggestions
, given in D.E. Knuth (1969), Vol 2
prec double
file fmm/zeroin.f
for find a zero of a user function in an interval
prec double
file fn/acos.f
gams C4a
for arc cosine
file fn/acosh.f
gams C4c
for arc hyperbolic cosine
file fn/ai.f
gams C10d
for Airy function
file fn/aid.f
gams C10d
for derivative of Airy function
file fn/aide.f
gams C10d
for derivative of expontential scaled Airy function
file fn/aie.f
gams C10d
for exponential scaled Airy function
file fn/aint.f
gams C1
for truncate real to an integral value
file fn/albeta.f
gams C7b
for log beta function
file fn/algams.f
gams C7a
for log gamma function with sign
file fn/ali.f
gams C5
for logarithmic integral
file fn/alngam.f
gams C7a
for log absolute gamma function
file fn/alnrel.f
gams C4b
for relative error logarithm
file fn/alog.f
gams C4b
for natural logarithm
file fn/alog10.f
gams C4b
for common logarithm
file fn/asin.f
gams C4a
for arc sine
file fn/asinh.f
gams C4c
for arc hyperbolic sine
file fn/atan.f
gams C4a
for arc tangent
file fn/atan2.f
gams C4a
for quadrant correct arc tangent
file fn/atanh.f
gams C4c
for arc hyperbolic tangent
file fn/besi0.f
gams C10b1
for modified Bessel function of first kind, order zero
file fn/besi0e.f
gams C10b1
for exponential scaled modified Bessel function, first kind, order zero
file fn/besi1.f
gams C10b1
for modified Bessel function of first kind, order one
file fn/besi1e.f
gams C10b1
for exponential scaled modified Bessel function of first kind, order one
file fn/besj0.f
gams C10a1
for Bessel function of first kind, order zero
file fn/besj1.f
gams C10a1
for Bessel function of first kind, order one
file fn/besk0.f
gams C10b1
for modified Bessel function of third kind, order zero
file fn/besk0e.f
gams C10b1
for exponential scaled modified Bessel function, third kind, order zero
file fn/besk1.f
gams C10b1
for modified Bessel function of third kind, order one
file fn/besk1e.f
gams C10b1
for exponential scaled modified Bessel function, third kind, order one
file fn/beskes.f
gams C10b3
for sequence of exponential scaled modified Bessel function, third kind
file fn/besks.f
gams C10b3
for sequence of n modified Bessel function of third kind
file fn/besy0.f
gams C10a1
for Bessel function of second kind, order zero
file fn/besy1.f
gams C10a1
for Bessel function of second kind, order one
file fn/beta.f
gams C7b
for beta function
file fn/betai.f
gams C7f
for incomplete beta function
file fn/bi.f
gams C10d
for Airy function of second kind, bAiry function
file fn/bid.f
gams C10d
for derivative of Airy function of second kind
file fn/bide.f
gams C10d
for derivative of exponential scaled Airy function of second kind
file fn/bie.f
gams C10d
for exponential scaled Airy function of second kind
file fn/c8lgmc.f
for complex log gamma correction term
file fn/c9lgmc.f
for complex log gamma correction term
file fn/c9ln2r.f
for complex relative error logarithm from second order
file fn/cabs.f
gams C19
for absolute value of complex number
file fn/cacos.f
gams C4a
for complex arc cosine
file fn/cacosh.f
gams C4c
for complex arc hyperbolic cosine
file fn/carg.f
gams A4a
for argument (angle) of complex number
file fn/casin.f
gams C4a
for complex arc sine
file fn/casinh.f
gams C4c
for complex arc hyperbolic sine
file fn/catan.f
gams C4a
for complex arc tangent
file fn/catan2.f
gams C4a
for complex quadrant correct arc tangent
file fn/catanh.f
gams C4c
for complex arc hyperbolic tangent
file fn/cbeta.f
gams C7b
for complex beta function
file fn/cbrt.f
gams C2
for cube root
file fn/ccbrt.f
gams C2
for complex cube root
file fn/ccos.f
gams C4a
for complex cosine
file fn/ccosh.f
gams C4c
for complex hyperbolic cosine
file fn/ccot.f
gams C4a
for complex cotangent
file fn/cexp.f
gams C4b
for complex exponential function
file fn/cexprl.f
gams C4b
for complex relative error exp from first order
file fn/cgamma.f
gams C7a
for complex gamma function
file fn/cgamr.f
gams C7a
for complex reciprocal gamma function
file fn/chi.f
gams C6
for hyperbolic cosine integral
file fn/chu.f
gams C11
for confluent hypergeometric function, logarithmic solution
file fn/ci.f
gams C6
for cosine integral
file fn/cin.f
gams C6
for cosine integral inverse
file fn/cinh.f
gams C6
for hyperbolic cosine integral inverse
file fn/clbeta.f
gams C7b
for complex log beta function
file fn/clngam.f
gams C7a
for complex log gamma function
file fn/clnrel.f
gams C4b
for complex relative error logarithm
file fn/clog.f
gams C4b
for complex natural logarithm
file fn/clog10.f
gams C4b
for complex common logarithm
file fn/comp1.f
for compare single and double precision functions
file fn/comp2.f
for compare single and double precision functions
file fn/comp3.f
for compare single and double precision functions
file fn/cos.f
gams C4a
for cosine
file fn/cosdg.f
gams C4a
for cosine, degree
file fn/cosh.f
gams C4c
for hyperbolic cosine
file fn/cot.f
gams C4a
for cotangent
file fn/cpsi.f
gams C7c
for complex digamma function
file fn/csevl.f
gams C3a2
for Chebyshev series
file fn/csin.f
gams C4a
for complex sine
file fn/csinh.f
gams C4c
for complex hyperbolic sine
file fn/csqrt.f
gams C2
for complex square root
file fn/ctan.f
gams C4a
for complex tangent
file fn/ctanh.f
gams C4c
for complex hyperbolic tangent
file fn/d9atn1.f
for arc tangent from first order
prec double
file fn/d9gaml.f
for gamma under and overflow limits
prec double
file fn/d9lgmc.f
for log gamma correction term
prec double
file fn/d9ln2r.f
for relative error logarithm from second order
prec double
file fn/d9pak.f
for pack number
prec double
file fn/d9upak.f
for subroutine to unpack number
prec double
file fn/dacos.f
gams C4a
for arc cosine
prec double
file fn/dacosh.f
gams C4c
for arc hyperbolic cosine
prec double
file fn/dai.f
gams C10d
for Airy function
prec double
file fn/daid.f
gams C10d
for derivative of Airy function
file fn/daide.f
gams C10d
for derivative of exp scaled Airy function
file fn/daie.f
gams C10d
for exp scaled Airy function
prec double
file fn/dasin.f
gams C4a
for arc sine
prec double
file fn/dasinh.f
gams C4c
for arc hyperbolic sine
prec double
file fn/datan.f
gams C4a
for arc tangent
prec double
file fn/datan2.f
gams C4a
for quadrant correct arc tangent
prec double
file fn/datanh.f
gams C4c
for arc hyperbolic tangent
prec double
file fn/daws.f
gams C8c
for Dawson function
file fn/dbesi0.f
gams C10b1
for modified Bessel function of first kind, order zero
prec double
file fn/dbesi1.f
gams C10b1
for modified Bessel function of first kind, order one
prec double
file fn/dbesj0.f
gams C10a1
for Bessel function of first kind, order zero
prec double
file fn/dbesj1.f
gams C10a1
for Bessel function of first kind, order one
prec double
file fn/dbesk0.f
gams C10b1
for modified Bessel function of third kind, order zero
prec double
file fn/dbesk1.f
gams C10b1
for modified Bessel function of third kind, order one
prec double
file fn/dbesks.f
gams C10b3
for sequence of n modified Bessel function, third kind
prec double
file fn/dbesy0.f
gams C10a1
for Bessel function of second kind, order zero
prec double
file fn/dbesy1.f
gams C10a1
for Bessel function of second kind, order one
prec double
file fn/dbeta.f
gams C7b
for beta function
prec double
file fn/dbetai.f
gams C7f
for incomplete beta function
prec double
file fn/dbi.f
gams C10d
for Airy function of second kind, bAiry function
prec double
file fn/dbid.f
gams C10d
for derivative of Airy function of second kind
file fn/dbide.f
gams C10d
for derivative of exp scaled Airy function of second kind
file fn/dbie.f
gams C10d
for exp scaled Airy function of second kind
prec double
file fn/dbsi0e.f
gams C10b1
for exp scaled modified Bessel, first kind, order zero
prec double
file fn/dbsi1e.f
gams C10b1
for exp scaled modified Bessel, first kind, order one
prec double
file fn/dbsk0e.f
gams C10b1
for exp scaled modified Bessel, third kind, order zero
prec double
file fn/dbsk1e.f
gams C10b1
for exp scaled modified Bessel, third kind, order one
prec double
file fn/dbskes.f
gams C10b3
for sequence n exp scaled modified Bessel, third kind
prec double
file fn/dcbrt.f
gams C2
for cube root
prec double
file fn/dchi.f
gams C6
for hyperbolic cosine integral
file fn/dchu.f
gams C11
for confluent hypergeometric function, log solution
prec double
file fn/dci.f
gams C6
for cosine integral
prec double
file fn/dcin.f
gams C6
for cosine integral inverse
prec double
file fn/dcinh.f
gams C6
for hyperbolic cosine integral inverse
prec double
file fn/dcos.f
gams C4a
for cosine
prec double
file fn/dcosdg.f
gams C4a
for cosine, degree
prec double
file fn/dcosh.f
gams C4c
for hyperbolic cosine
prec double
file fn/dcot.f
gams C4a
for cotangent
prec double
file fn/dcsevl.f
gams C3a2
for Chebyshev series
prec double
file fn/ddaws.f
gams C8c
for Dawson function
prec double
file fn/de1.f
gams C5
for exponential integral
prec double
file fn/dei.f
gams C5
for exponential integral
prec double
file fn/derf.f
gams C8a,L5a1e
for error function
prec double
file fn/derfc.f
gams C8a,L5a1e
for complementary error function
prec double
file fn/dexp.f
gams C4b
for exponential function
prec double
file fn/dexprl.f
gams C4b
for relative error exp from first order
prec double
file fn/dfac.f
gams C1
for factorial
prec double
file fn/dgami.f
gams C7e
for incomplete gamma function
prec double
file fn/dgamic.f
gams C7e
for complementary incomplete gamma function
prec double
file fn/dgamit.f
gams C7e
for Tricomi incomplete gamma function
prec double
file fn/dgamma.f
gams C7a
for gamma function
prec double
file fn/dgamr.f
gams C7a
for reciprocal gamma function
prec double
file fn/dint.f
gams C1
for truncate double precision to integral value
prec double
file fn/dlbeta.f
gams C7b
for log beta function
prec double
file fn/dlgams.f
gams C7a
for log gamma function with sign
prec double
file fn/dli.f
gams C5
for logarithmic integral
prec double
file fn/dlngam.f
gams C7a
for log absolute gamma function
prec double
file fn/dlnrel.f
gams C4b
for relative error logarithm
prec double
file fn/dlog.f
gams C4b
for natural logarithm
prec double
file fn/dlog10.f
gams C4b
for common logarithm
prec double
file fn/dpoch.f
gams C7a
for Pochhammer generalized symbol
prec double
file fn/dpsi.f
gams C7c
for psi or digamma function
prec double
file fn/dshi.f
gams C6
for hyperbolic sine integral
prec double
file fn/dsi.f
gams C6
for sine integral
prec double
file fn/dsin.f
gams C4a
for sine
prec double
file fn/dsindg.f
gams C4a
for sine, degree
prec double
file fn/dsinh.f
gams C4c
for hyperbolic sine
prec double
file fn/dspenc.f
gams C5
for Spence function, related to dilogarithm
prec double
file fn/dsqrt.f
gams C2
for square root
prec double
file fn/dtan.f
gams C4a
for tangent
prec double
file fn/dtanh.f
gams C4c
for hyperbolic tangent
prec double
file fn/e1.f
gams C5
for exponential integral
file fn/ei.f
gams C5
for exponential integral
file fn/erf.f
gams C8a,L5a1e
for error function
file fn/erfc.f
gams C8a,L5a1e
for complementary error function
file fn/exp.f
gams C4b
for exponential function
file fn/exprel.f
gams C4b
for relative error exp from first order
file fn/fac.f
gams C1
for factorial
file fn/gami.f
gams C7e
for incomplete gamma function
file fn/gamic.f
gams C7e
for complementary incomplete gamma function
file fn/gamit.f
gams C7e
for tricomi incomplete gamma function
file fn/gamma.f
gams C7a
for gamma function
file fn/gamr.f
gams C7a
for reciprocal gamma function
file fn/initds.f
gams C3a2
for initialize orthogonal polynomial series
prec double
file fn/inits.f
gams C3a2
for initialize orthogonal polynomial series
file fn/poch.f
gams C7a
for Pochhammer generalized symbol
file fn/psi.f
gams C7c
for psi or digamma function
file fn/r9atn1.f
for arc tangent from first order
file fn/r9gaml.f
for gamma under and overflow limits
file fn/r9lgmc.f
for log gamma correction term
file fn/r9ln2r.f
for relative error logarithm from second order
file fn/r9pak.f
for pack floating point number
file fn/r9upak.f
for unpack floating point number
file fn/rand.f
gams L6a21
for portable uniform random numbers
file fn/randgs.f
gams L6a14
for portable normal random numbers
file fn/random.f
gams L6a21
for portable uniform random numbers
file fn/ranf.f
gams L6a21
for portable uniform random numbers
file fn/shi.f
gams C6
for hyperbolic sine integral
file fn/si.f
gams C6
for sine integral
file fn/sin.f
gams C4a
for sine
file fn/sindg.f
gams C4a
for sine in degree
file fn/sinh.f
gams C4c
for hyperbolic sine
file fn/spenc.f
gams C5
for Spence function, related to dilogarithm
file fn/sqrt.f
gams C2
for square root
file fn/tan.f
gams C4a
for tangent
file fn/tanh.f
gams C4c
for hyperbolic tangent
file fn/binom.f
gams C1
for binomial fac(n)/(fac(m)*fac(n-m))
file fn/dbinom.f
gams C1
for binomial fac(n)/(fac(m)*fac(n-m))
prec double
file fn/poch1.f
gams C7a
for Pochhammer generalized symbol, (poch(a, x)-1)/x
file fn/dpoch1.f
gams C7a
for Pochhammer generalized symbol, (poch(a, x)-1)/x
prec double
lib fn/Deleted
for machine constants, stack that duplicate supported routines in port
file fn/c0lgmc.f
file fn/changes
file fn/d9admp.f
file fn/d9aimp.f
file fn/d9b0mp.f
file fn/d9b1mp.f
file fn/d9chm.f
file fn/d9chu.f
file fn/d9gmic.f
file fn/d9gmit.f
file fn/d9knus.f
file fn/d9lgic.f
file fn/d9lgit.f
file fn/d9sifg.f
file fn/e9rint.f
file fn/entsrc.f
file fn/eprint.f
file fn/erroff.f
file fn/i0tk00.f
file fn/i8save.f
file fn/istkgt.f
file fn/istkin.f
file fn/istkmd.f
file fn/istkpr.f
file fn/istkqu.f
file fn/istkrl.f
file fn/istkst.f
file fn/nerror.f
file fn/r9admp.f
file fn/r9aimp.f
file fn/r9chm.f
file fn/r9chu.f
file fn/r9gmic.f
file fn/r9gmit.f
file fn/r9knus.f
file fn/r9lgic.f
file fn/r9lgit.f
file fn/r9sifg.f
file fn/retsrc.f
file fn/s88fmt.f
file fn/s9comp.f
file fn/seterr.f
file fn/seteru.f
file fn/slatec_index
# ======================================================================
# Fortran M, Version 1.0 Date: February 3, 1994
# ======================================================================
#
# --------------------------
# Available software/reports:
# --------------------------
file fortran-m/fm_v1.0.tgz
for This is the Fortran M compiler
, and user manual in tar compressed form (1545886 bytes).
file fortran-m/fm_prog_v1.0.ps.gz
for This is a compressed tar
, file of the user manual "Programming in Fortran M"
, in postscript format (127675 bytes).
file fortran-m/fm_prog_v1.0.tgz
for This is a compressed tar
, file of the user manual "Programming in Fortran M"
, in latex format (64447 bytes).
lib fortran-m/reports
for Subdirectory containing various Fortran M-related papers
, and technical reports
# *******************
# Questions/comments? Direct email to fortran-m@mcs.anl.gov
# *******************
# Ian Foster
# Robert Olson
# Steven Tuecke
# ======================================================================
# ******************
# WHAT IS Fortran M?
# ******************
# Fortran M is a small set of extensions to Fortran 77 that supports
# a modular approach to the design of message-passing programs. It has
# the following features.
# (1) Modularity. Programs are constructed by using explicitly-declared
# communication channels to plug together program modules called
# processes. A process can encapsulate common data, subprocesses, and
# internal communication.
# (2) Safety. Operations on channels are restricted so as to guarantee
# deterministic execution, even in dynamic computations that create and
# delete processes and channels. Channels are typed, so a compiler can
# check for correct usage.
# (3) Architecture Independence. The mapping of processes to processors
# can be specified with respect to a virtual computer with size and
# shape different from that of the target computer. Mapping is
# specified by annotations that influence performance but not
# correctness.
# (4) Efficiency. Fortran M can be compiled efficiently for
# uniprocessors, shared-memory computers, distributed-memory computers,
# and networks of workstations. Because message passing is incorporated
# into the language, a compiler can optimize communication as well as
# computation.
# Compatability libraries are available that allow the integration of
# message-passing programs into an Fortran M framework. Send mail to
# fortran-m@mcs.anl.gov for details. A compilation system that
# integrates Fortran M and HPF is under development in collaboration
# with Syracuse University.
# For more information, see the user manual or use World Wide Web at
# address
# http://www.mcs.anl.gov/fortran-m
# (WWW is a distributed multimedia system, accessible for example
# via NCSA XMosaic.) The server currently provides FM tutorial slides,
# the FM manual, application case studies, and programming examples.
# Fortran M has been funded in part by NSF and DOE.
# ======================================================================
# This directory contains the following Fortran M-related reports:
file fortran-m/reports/fortran-m.ps.gz
for Fortran M: A Language for Modular Parallel Programming
, Preprint MCS-P327-0992, Argonne National Lab.
size 127337 bytes
by Ian Foster and Mani Chandy
file fortran-m/reports/fortran-m.tgz
for Fortran M: A Language for Modular Parallel Programming
, Preprint MCS-P327-0992, Argonne National Lab.
size 84201 bytes.
by Ian Foster and Mani Chandy
file fortran-m/reports/determinism.ps.gz
for A Deterministic Notation for Cooperating Processes
, MCS-P346-0193, Argonne National Lab.
by Mani Chandy and Ian Foster
size 76843 bytes.
file fortran-m/reports/determinism.tgz
for A Deterministic Notation for Cooperating Processes
, Preprint MCS-P346-0193, Argonne National Lab.
by Mani Chandy and Ian Foster
size 36455 bytes.
file fortran-m/reports/shpcc94.ps.gz
for A Compilation System that Integrates High Performance Fortran and
, Fortran M (extended abstract)
, Proc. 1994 Scalable High Performance Computing Conference (to appear).
by Ian Foster, Bhaven Avalani, Alok Choudhary, and Ming Xu
size 46813 bytes.
file fortran-m/reports/shpcc94.tgz
for A Compilation System that Integrates High Performance Fortran and
, Fortran M (extended abstract)
, Proc. 1994 Scalable High Performance Computing Conference (to appear).
by Ian Foster, Bhaven Avalani, Alok Choudhary, and Ming Xu
size 22690 bytes.
file fortran-m/reports/ijsa.ps.gz
for Integrated Support for Task and Data Parallelism
, International Journal of Supercomputer Applications (to appear).
by Mani Chandy, Ian Foster, Ken Kennedy, Charles Koelbel, and Chau-Wen Tseng
size 93419 bytes.
file fortran-m/reports/ijsa.tgz
for Integrated Support for Task and Data Parallelism
, International Journal of Supercomputer Applications (to appear).
by Mani Chandy, Ian Foster, Ken Kennedy, Charles Koelbel, and Chau-Wen Tseng
size 36086 bytes.
file fortran-m/reports/definition.ps.gz
by Ian Foster and Mani Chandy
for Fortran M Language Definition
, Technical Report ANL-93/28, Argonne National Lab, 1993.
size 42547 bytes.
file fortran-m/reports/definition.tgz
by Ian Foster and Mani Chandy
for Fortran M Language Definition
, Technical Report ANL-93/28, Argonne National Lab, 1993.
size 10485 bytes.
file fortran/links.html
for related resources
file fortran/s2d.shar
for converting between Fortran single and double precision
by Jim Meyering, Univ. Texas
gams s1
lang C
# shar of uuencode of gzip of gzip of tar (sic)
file fortran/ftnchek.tgz
for detecting unused, uninitialized, and undeclared variables
by moniot@dsm.fordham.edu (Robert Moniot)
gams s2
# compressed binary file, not available by email
size 1MB
file fortran/fdfpp.tgz
for fdfpp, a Fortran-aware variant of the cpp preprocessor
by Sun Microsystems Inc. (fpp-comments@devpro.Eng.sun.com)
lang C
# compressed binary file, not available by email
size 57 kB
file fortran/fdfpp-martin.tgz
for minor variant of fdfpp using autoconf
by Martin Wilck
file fp/links.html
for related resources
file fp/dtoa.c
by David Gay
for ANSI C or C++ source for functions strtod and dtoa that do
, decimal-to-binary and binary-to-decimal conversions. Comments
, at the beginning describe various preprocessor variables that
, can be defined to make this code work with binary IEEE, VAX,
, or IBM-mainframe arithmetic. A paper is available at
, http://cm.bell-labs.com/cm/cs/doc/90/4-10.ps.gz
file fp/g_fmt.c
by David Gay
for ANSI C or C++ source for function g_fmt(char *, double):
, with help from dtoa, g_fmt(buf, x) sets buf to the shortest
, decimal string that correctly rounds to x and returns buf.
file fp/rnd_prod.s
, Assembly code, usable under UNIX UTS System V Release 2.6b,
, that uses IBM-mainframe extended-precision floating-point
, instructions to compute rounded products and quotients.
file fp/testbase
by Vern Paxson
for announcing ftp access for test program
file fp/changes
file fp/ucbtest.tgz
for testing certain difficult cases of IEEE 754 floating-point arithmetic
by dgh@validgh.com (David G. Hough) et al.
lang C
size 1 megabyte
# Retrieve by ftp or http, not email.
file fp/fp2.tgz
for formal definitions and theorems, with proofs, about floating-point
, numbers, for use with Coq (http://coq.inria.fr/).
file fp/gdtoa.tgz
for generalization of dtoa.c to other IEEE and IEEE-like precisions
, (float, extended, quad) and "double double". Rounding
, directions may be specified; decimal -> interval is an alternative.
file fp/p9fmt.tgz
for Unix port of the Plan 9 formatted I/O package
by Rob Pike and Ken Thompson
lang C
# see also toms/642.
file gcv/sbart.r
for univariate smoothing spline automatically choosing the smoothing parameter by minimizing generalized cross validation
lang Ratfor language with comments
by Finbarr O'Sullivan
ref "Comments on Dr. Silverman's Paper", J. Royal Statistical Society B (1985) 47, pp.39-40
file gcv/sbart.f
for univariate smoothing spline automatically choosing the smoothing parameter by minimizing generalized cross validation
lang Fortran language with NO comments
by Finbarr O'Sullivan
ref "Comments on Dr. Silverman's Paper", J. Royal Statistical Society B (1985) 47, pp.39-40
file gcv/bart.shar
for smoothing spline
by Finbarr O'Sullivan
size 200 kB
file gcv/gcvspl
for B-spline data smoothing using generalized cross-validation and mean squared prediction or explicit user smoothing
by H.J. Woltring, University of Nijmegen, Philips Medical Systems, Eindhoven (The Netherlands)
# Natural B-spline data smoothing subroutine, using the Generalized Cross-
# Validation and Mean-Squared Prediction Error Criteria of Craven & Wahba
# (1979). Alternatively, the amount of smoothing can be given explicitly, or
# it can be based on the effective number of degrees of freedom in the
# smoothing process as defined by Wahba (1980). The model assumes
# uncorrelated, additive noise and essentially smooth, underlying functions.
# The noise may be non-stationary, and the independent co-ordinates may be
# spaced non-equidistantly. Multiple datasets, with common independent
# variables and weight factors are accomodated. A full description of the
# package is provided in: H.J. Woltring (1986), A FORTRAN package for
# generalized, cross-validatory spline smoothing and differentiation.
# Advances in Engineering Software 8(2):104-113
file gcv/gcv1
title gcvpack release 2, part 1
for generalized cross validation, also requires (gcv/gcv2)
by D. Bates, M. Lindstrom, G. Wahba and B. Yandell Univ Wisconsin-Madison
ref "GCVPACK-ROUTINES FOR GENERALIZED CROSS VALIDATION", TR 775(rev.), October, 1986.
# Uses: dcopy dasum dqrsl dtrco dtrsl ddot dswap dqrdc dchdc dsvdc from linpack and the blas.
# If you have problems or questions, please mail details to
# gcvpack@stat.wisc.edu
# We may be contacted individually as follows:
# bates@stat.wisc.edu - Douglas Bates
# lindstro@stat.wisc.edu - Mary Lindstrom
# wahba@stat.wisc.edu - Grace Wahba
# yandell@stat.wisc.edu - Brian Yandell
file gcv/gcv2
title gcvpack release 2, part 2
see gcv/gcv1
file gcv/gcvdoc
for error codes and update notices for (gcv/gcv1) and (gcv/gcv2)
see gcv/gcv1
file gcv/rkpk.shar
title RKPACK
for smoothing spline by generalized cross validation or generalized maximum likelihood
lang ratfor
by C. Gu, University of Wisconsin-Madison [gu@stat.wisc.edu]
ref SIAM J. Sci. Stat. Comp. 12, 383-398.
alg Householder tridiagonalization with distributed truncation
size 305 kB
file gcv/rkpk.tex
file gcv/changes
file gcv/vspline
for non-parametric estimate of a smooth vector-valued function from noisy measurements
by Jeff Fessler, Stanford University
lang C
alg generalization of (scalar) cubic-spline smoothing
ref "Non-parametric fixed-interval smoothing with vector splines", IEEE ASSP
file gcv/grkpack.shar
title GRKPACK
for smoothing spline ANOVA for data from exponential families
lang ratfor
by Yuedong Wang, University of Michigan [yuedong@umich.edu]
ref Tech. Rep. 940, University of Wisconsin-Madison, Dept. of Statistics.
alg generalization of RKPACK
size 721 kB
file gmat/readme
for overview of gmat
file gmat/gmat.tgz
for documentation for the GMAT multiprocessing Timeline and Stategraph tools
, It includes example data files
, for both logging styles (CRI and NLTSS { same as the Cray
, Compatibility library on the Alliant FX/8 }). The README file
, has appropriate instructions and information.
size 52139 bytes
file gmat/stategraph.tgz
for source code for the GMAT Stategraph Analysis tool
, This tool analyzes multiprocessing log
, files as an inheritance tree of tasks. Code for both Sunview and
, X-Window (R3 & R4 - Athena toolkit) implementations is included.
size 128981 bytes
file gmat/timeline.tgz
for source for the GMAT Timeline tool
, This tool analyzes multiprocessing log files as a flowing
, sequence of events for multiple concurrent tasks. Code for both Sunview
, and X-Window (R3 & R4 - Athena toolkit) implementations is included.
size 181374 bytes
# All of the following files are binary, unsuitable for email.
# Instead, use "ftp netlib.att.com" to retrieve.
# Most of the binaries (Sun, HP, RS6000) are linked
# with dynamic libraries. This can cause error messages
# on machines that lack the libraries, or that have
# older versions of them than the ones I linked against.
# If this causes too many complaints, I can replace them
# with statically linked binaries (which are usually
# much larger). dmg@research.att.com
# Mac users are reported to use "macgzip".
file gnu/gzip/src.tar
for gzip source
size 799 kB
file gnu/gzip/cray.unicos.executable
for gzip for Crays running UNICOS (built on a YMP)
file gnu/gzip/dec5000.executable
for gzip for DECStation 5000
file gnu/gzip/dos.executable
for gzip for MS-DOS (compiled by Microsoft C 6.0A)
file gnu/gzip/hp.executable
for gzip for HP 9000
file gnu/gzip/rs6000.executable
for gzip for IBM Risc System 6000
file gnu/gzip/sgi.executable
for gzip for SGI machines (ELF format)
file gnu/gzip/sgicoff.executable
for gzip for SGI machines (the old COFF format)
file gnu/gzip/sun.executable
for gzip for Sun Sparc
file gnu/gzip/win32.executable
for gzip for MS Windows NT and W9x
file gnu/gzip/readme
file gnu/links.html
for other resources, like the Ghostscript viewer of PostScript
file gnu/copying
for GNU General Public License (version 2, June 1991)
lib gnu/gzip
for source for gzip and some machine-specific executable versions:
, gzip is a program for compressing and uncompressing files.
, See gzip/readme for more details. File "copying" gives
, general conditions for copying gzip.
# These are large, binary files unsuitable for email.
, Use ftp or the Web to download.
file go/gaussq.f
gams H2c
for weights for Gaussian quadrature rules
prec double
file go/sgausq.f
gams H2c
for weights for Gaussian quadrature rules
prec single
file go/zeroin.f
gams F1b
for univariate zero-finding
by Brent
prec double
file go/seroin.f
gams F1b
for univariate zero-finding
by Brent
prec single
file go/fmin.f
gams G1a1a
for univariate minimization
by Brent
prec double
file go/sfmin.f
gams G1a1a
for univariate minimization
by Brent
prec single
file go/ibmblas
gams D1a
for IBM assembly language level-1 BLAS
file go/lowess.f
gams L8h
for smoothing scatterplots by locally weighted regression
by Bill Cleveland
file go/fft.f
gams J1b
for complex FFT 1D, 2D, 3D
prec single
by Singleton 1968
file go/realtr.f
gams J1a1
for real FFT
prec single
by Singleton 1968
file go/ffts.b
gams J1b
for complex FFT 1D, 2D, 3D
lang Limbo
by Singleton 1968, trans. Eric Grosse
file go/ffts.m
for header file for ffts.b
file go/fft-olesen.tar.gz
gams J1b
for complex FFT 1D, 2D, 3D
lang C, Fortran90
by Singleton 1968, trans. Mark Olesen, Michael Steffens
file go/pfort
title PFORT Verifier
gams S2
for checking adherence to the 1966 standard.
size 283 kB
file go/underwood.f
for sparse symmetric eigenproblems
alg iterative block Lanczos
by Richard Ray Underwood
, retyped by Cheryl M. M. Carey
prec double
, actually REAL*8 but maybe your compiler can cope
file go/underwood-out
for sample output of go/underwood.f
file go/accuracy
file graphics/links.html
for related resources
file graphics/haines
for database constructor programs for testing ray tracer efficiency
by Eric Haines
file graphics/rainbow.c
for equally spaced colors, primarily for level plots
by Eric Grosse
ref "Automatic Choice of Colors for Level Plots", AT&T Bell Labs, Murray Hill NJ 07974
file graphics/hotiron.c
for sample driver for rainbow, also defining "hot iron" and "zebra"
by Eric Grosse
file graphics/tk_colorscale.c
for another sample driver, useful with Tcl/Tk
by Eric Grosse
file graphics/cie.c
for CIE 1931 colour matching functions
by Tom Duff
file graphics/conic
by J. Hu & T. Pavlidis
ref "Function Plotting using Conic Splines," IEEE CGNA, January 1991.
for adaptive fitting of a function using relatively few conic segments
file graphics/xfarbe.taz.uu
for area filled, labelled contour plot of grid data for X displays and PostScript
by A. Preusser
alg Akima bicubic
size 336 kB
file graphics/video.signals
for notes on video signal formats
by Tom Duff
file graphics/plotterf90.tgz
for Fortran90 wrapper for Postscript line drawing
by Masao Kodama
file harwell/ma30ad.f
file harwell/ma30bd.f
file harwell/ma30cd.f
file hence/hence-2.0-doc-html/hence-2.0-doc.html
for HeNCE User Manual and Installation Guide in HTML format (root doc).
lang html
keywords visual,parallel,computation,graph,PVM,Heterogeneous
by hence@cs.utk.edu
file hence/readme
for Overview of HeNCE
see hence-2.0-doc.ps.gz
file hence/HeNCE-2.0-examples.tgz
for Example programs for HeNCE 2.0.
lang HeNCE
age experimental
file hence/HeNCE-2.0-src.tgz
for Complete source code to HeNCE environment
size 296 KB
age experimental
file hence/HeNCE-2.0-doc.ps.gz
title HeNCE 2.0 User Manual and Installation Guide
size 116 KB
lang PostScript
keywords visual,parallel,computation,graph,PVM,Heterogeneous
lib hence/old-hence
for Out-of-date versions of the HeNCE visual parallel programming environment
age old
lib hence/hence-2.0-doc-html
title HeNCE 2.0 User Manual and Installation Guide
lang HTML
file hence/old-hence/readme
for overview of hence
file hence/old-hence/hence1.4.tgz
for HeNCE source code (supports either pvm2.4.2 or pvm3.x)
size 1.8 megabytes
file hence/old-hence/hence-1.4-changes
for changes from version 1.3 to 1.4 of HeNCE
file hence/old-hence/read-me.pvm3
for notes on HeNCE 1.4 support for pvm3
file hence/old-hence/hence1.3.tgz
for HeNCE source code
size 1.8 megabytes
file hence/old-hence/1.3-to-1.3.1.patch
for patches to allow HeNCE 1.3 to compile/run on SGIs & PMAX w/Ultrix 4.3
file hence/old-hence/hence-1.3-changes
for changes from version 1.2 to 1.3 of HeNCE
file hence/old-hence/faq
for answers to frequently asked questions about HeNCE
file hence/old-hence/buglist
for known bugs in the current release of the HeNCE
, Please check here before reporting a bug. When reporting a bug
, give explicit steps which will reproduce the bug. Also include
, o the machine type you are running on (vendor, model),
, o the operating system version (ie ULTRIX V4.1),
, o the Version of X windows (R4, R5, IBM's...), and
, o the window manager you're using
file hence/old-hence/porting-status
for list of machines HeNCE 1.4 runs on (last update: May 16 1993)
file hence/old-hence/hug.ps
for The HeNCE User's Guide
lang PostScript form
size 540 kilobytes
, This version of the HeNCE User's Guide has been reformatted to
, make it easier to print on postscript printers with limited memory.
file hence/old-hence/hug.tgz
for unencoded source code for HeNCE User's Guide (XNETLIB USERS ONLY)
file hence/old-hence/sc91.ps
for paper from Supercomputing 91 describing HeNCE
lang PostScript
size 756 kilobytes
file hence/old-hence/sc91.tgz
size 49 kilobytes
file hence/old-hence/short.ps
for short description of HeNCE
lang PostScript
file hence/old-hence/short.ps.z.uu
file hompack/hompack90.tar.gz
ref TOMS 777
gams f2
lang Fortran90
file hompack/readme
for overview of hompack
file hompack/fixpdf.f
for dense Jacobian
alg ODE-based
gams f2
file hompack/fixpds.f
for sparse Jacobian
alg ODE-based
gams f2
file hompack/fixpnf.f
for dense Jacobian
alg normal flow
gams f2
file hompack/fixpns.f
for sparse Jacobian
alg normal flow
gams f2
file hompack/fixpqf.f
for dense Jacobian
alg augmented Jacobian
gams f2
file hompack/fixpqs.f
for sparse Jacobian
alg augmented Jacobian
gams f2
file hompack/polsys.f
for all (complex) solutions to a system of n polynomial equations
, in n unknowns with real coefficients. Can return solutions at
, infinity if requested.
gams f2
file hompack/changes
file hompack/dcpose.f
file hompack/divp.f
file hompack/f.f
file hompack/ffunp.f
file hompack/fjac.f
file hompack/fjacs.f
file hompack/fode.f
file hompack/fodeds.f
file hompack/gfunp.f
file hompack/gmfads.f
file hompack/hfun1p.f
file hompack/hfunp.f
file hompack/initp.f
file hompack/innhp.dat
file hompack/mainf.f
file hompack/mainp.f
file hompack/mains.f
file hompack/mfacds.f
file hompack/mulp.f
file hompack/multds.f
file hompack/odoc.for
file hompack/otputp.f
file hompack/pcgds.f
file hompack/pcgns.f
file hompack/pcgqs.f
file hompack/polyp.f
file hompack/powp.f
file hompack/qimuds.f
file hompack/qrfaqf.f
file hompack/qrslqf.f
file hompack/rho.f
file hompack/rhoa.f
file hompack/rhojac.f
file hompack/rhojs.f
file hompack/root.f
file hompack/rootnf.f
file hompack/rootns.f
file hompack/rootqf.f
file hompack/rootqs.f
file hompack/sclgnp.f
file hompack/sintrp.f
file hompack/solvds.f
file hompack/stepds.f
file hompack/stepnf.f
file hompack/stepns.f
file hompack/stepqf.f
file hompack/stepqs.f
file hompack/steps.f
file hompack/strptp.f
file hompack/tangnf.f
file hompack/tangns.f
file hompack/tangqf.f
file hompack/tangqs.f
file hompack/upqrqf.f
file hpf/readme
for overview of HPF
file hpf/hpf-v10-final.ps.gz
for HPF Language Specification, Version 1.0, May 3, 1993.
, Superceded by Version 1.1 but remains available for historical
, purposes.
file hpf/jod-v10-final.ps.gz
for HPF Journal of Development, Version 1.0, May 3, 1993.
, Contains proposals considered for but not included in HPF 1.0.
file hpf/hpf-v11.ps.gz
for HPF Language Specification, Version 1.1, November 10, 1994.
, Contains all the technical features proposed for the version
, of HPF known as HPF 1.1.
file hpf/hpf-v20-final.ps.gz
for HPF Language Specification, Version 2.0, January 31, 1997.
, Contains the HPF 2.0 Language and the HPF 2.0 Approved Extensions.
file hypercube/readme
for overview of hypercube
file hypercube/ipsc-error-handle
for floating point exception handling on Intel iPSC hypercube
# Cascade Software Availability
# Cascade Version SUN0.9 June 23, 1988
#
# Two groups of software are available under the cascade sublibrary of netlib.
# These are the cascade subroutine library, and the cascade tools, which are a
# group of programs which can be called either as subroutines or as commands
# from a Unix shell or VMS/DCL. The main programs use routines from the
# subroutine library.
#
# The cascade subroutine library's subroutines and functions are documented in
# the manual "Cascade Library Users' Guide", available via netlib by requesting
# "send cascade_users_guide.ps from cascade" in postscript form.
#
# The cascade tools are documented in the manual "Cascade Tools and Knowledge
# Base", available via netlib by requesting "send cascade_tools_and_kb.ps from
# cascade" in postscript form.
#
# These files, as well as a suite of examples, are also available as Unix
# compressed tar-format files via anonymous login to hickory.engr.utk.edu at The
# University of Tennessee, Knoxville. If you are using a Unix system, the
# Makefiles for libcascade.a (the cascade subroutine library) and
# libcascadetools.a (the cascade tools library) are appended at the end of this
# message; they will have to be modified to work at your site, since they are
# intended to be invoked from the cascade distribution tape Makefile.
#
# The network-available software is a part of the cascade expert system for
# multivariable controller design using the LQG/LTR methodology. The complete
# distribution is available on Sun 1/4" (60Mbyte or 150Mbyte) or Sun 8mm tapes,
# as a tar file, only. The expert system requires the Quintus Prolog
# development environment for compilation and execution. The cascade
# distribution tape and/or printed documentation is available from J. D.
# Birdwell at the address below; a fee is charged to cover the cost of media
# and duplication. The cascade expert system and tools are known to work only
# on Sun 3 workstations at the present time.
#
# No warranty is made concerning the quality of the cascade software or its
# applicability. The software available as a part of netlib has been placed in
# the public domain by the authors, as a part of the cascade development
# project, sponsored by the U.S. Department of Energy. Several authors
# contributed to this project; they are cited in the manuals.
#
# The cascade tools require several include files which netlib will not
# automatically send; to receive them, request:
# send Parameter.f from cascade
# send dpcommon.f from cascade
# send dpcom.f from cascade
# send commands.h from cascade
# You will also need the main program for the tools, headercode.c, in order
# to invoke the tools from the command line:
# send headercode.c from cascade
#
# For further information, contact:
#
# J. D. Birdwell
# Department of Electrical and Computer Engineering
# The University of Tennessee
# Knoxville, TN 37996-2100
#
# e-mail: birdwell@hickory.engr.utk.edu or birdwell@utkux1.bitnet
#
# ========================================================================
#
# Contents of the Cascade Subroutine Library
#
# Special Functions
##
file ieeecss/cascade/ahcon.f
for "ad-hoc" controllability calculation
file ieeecss/cascade/gauss.f
for Gaussian pseudo-random number generator
file ieeecss/cascade/gfba.f
for general frequency balancing algorithm
file ieeecss/cascade/icnvrt.f
for integer <-> character conversion
file ieeecss/cascade/rand.f
for uniformly distributed pseudo-random numbers on [0,1]
#
# Regulator and Filter Design Software
##
file ieeecss/cascade/ckbf.f
for continuous time Kalman filter design program
file ieeecss/cascade/creg.f
for continuous time LQR design program
#
# Riccati Equation Solver
#
# The following routines comprise RICPACK, written by Arnold and Laub;
# some of the code is based upon other work, as referenced in the
# documentation. the main entry points are ricsol and fbgain.
##
file ieeecss/cascade/cmprs.f
for forms a compressed matrix pencil for the GARE
file ieeecss/cascade/exchqz.f
for exchange diagonal blocks of the upper Hessenberg pencil a-s*b
file ieeecss/cascade/fbgain.f
for find the optimal gain from the GARE solution, discrete or conts
file ieeecss/cascade/giv.f
for forms a Givens rotation
file ieeecss/cascade/newt.f
for Newton iteration to GARE solution
file ieeecss/cascade/order.f
for reorders diagonal blocks of Hessenberg pencil a-s*b
file ieeecss/cascade/resid.f
for calculate GARE residual and its 1-norm
file ieeecss/cascade/ricsol.f
for calculates GARE solution, discrete or continuous time
file ieeecss/cascade/rinv.f
for used in solution to continuous time GARE
file ieeecss/cascade/rotc.f
for Givens rotation on columns
file ieeecss/cascade/rotr.f
for Givens rotation on rows
file ieeecss/cascade/sepest.f
for used to estimate condition
file ieeecss/cascade/sequiv.f
for used to form compressed problem
#
# Frequency Response Computations
##
file ieeecss/cascade/dfrmg.f
for calculate frequency response at single frequency
file ieeecss/cascade/dhetr.f
for reduction of submatrix of real general matrix to up. Hess. form
file ieeecss/cascade/zheco.f
for lu factor & condition estimate of up. Hess. matrix
file ieeecss/cascade/zhefa.f
for lu factor of upper Hessenberg matrix
file ieeecss/cascade/zhesl.f
for solve complex upper Hessenberg system H*X=B
#
# Matrix Exponential Routines
##
file ieeecss/cascade/pade.f
for calculate approx. of exp(a*t) and several integrals
file ieeecss/cascade/pade8m.f
for calculate approx. of exp(a)
#
# Computation of Poles and Zeros
##
file ieeecss/cascade/eigen.f
for find eigenvalues and eigenvectors of real general matrix
file ieeecss/cascade/housh.f
for a Householder transformation
file ieeecss/cascade/mvzero.f
for computes finite multivariable zeros of a conts linear system
file ieeecss/cascade/pivot.f
for finds maximal element of vector and its location
file ieeecss/cascade/rduce.f
for extracts a reduced system with same transmission zeros
file ieeecss/cascade/tr1.f
for a Householder transformation
file ieeecss/cascade/tr2.f
for a Householder transformation
file ieeecss/cascade/zeros.f
for extract pencil defining zeros of original system
#
# Ward's Balancing Routines
##
file ieeecss/cascade/balgbk.f
for back transform eigenvectors to original problem
file ieeecss/cascade/balgen.f
for balance generalized eigenproblem
file ieeecss/cascade/balinv.f
for inverse transformation of balanc (eispack)
file ieeecss/cascade/gradbk.f
for back transform eigenvectors from gradeq
file ieeecss/cascade/gradeq.f
for grade the submatrices of A and B
file ieeecss/cascade/qzhesw.f
for first step of QZ algorithm
file ieeecss/cascade/qzitw.f
for second step of QZ algorithm
file ieeecss/cascade/reduce.f
for reduce order of generalized eigenproblem if possible
file ieeecss/cascade/scalbk.f
for back transform from reduce and/or scaleg
file ieeecss/cascade/scaleg.f
for scale original problem
#
# Lyapunov Equation Solvers
##
file ieeecss/cascade/dstslv.f
for solve A'*X*A - X = C, C symmetric & A up. RSF
file ieeecss/cascade/lypcnd.f
for solve F'*X + X*F + H = 0 by Bartels-Stewart
file ieeecss/cascade/lypdsd.f
for solve F'*X*F - X = H by modified Bartels-Stewart
file ieeecss/cascade/symslv.f
for solve A'*X + X*A + C = 0, C symmetrix & A up. RSF
file ieeecss/cascade/hqrort.f
for compute up. real Schur form (RSF); mod of HQR2
#
# Linear Equation Solvers
##
file ieeecss/cascade/gausel.f
for Gaussian elimination
file ieeecss/cascade/lineq.f
for solves A*X=B for B a vector w/ cond. est.; uses dgecom and dgeslm
file ieeecss/cascade/mlineq.f
for solves A*X=B for B a matrix w/ cond. est.; uses dgecom and dgeslm
file ieeecss/cascade/mpinv.f
for calculate Moore-Penrose pseudo-inverse of real gen. A
#
# Modified LINPACK Routines
##
file ieeecss/cascade/dgecom.f
for lu decomposition w/ cond. est.
file ieeecss/cascade/dgefam.f
for lu decomposition
file ieeecss/cascade/dgeslm.f
for solution of A*X=B using lu factors
#
# Input / Output Routines
#
# Note: see the Cascade Tools and Knowledge Base
# manual (cascade_tools_and_kb.ps) for file formats.
##
file ieeecss/cascade/insys.f
for read a system container file
file ieeecss/cascade/filext.f
for modifies a file name by adding or changing an extension
file ieeecss/cascade/fmout.f
for formatted matrix output
file ieeecss/cascade/mout.f
for free format ascii matrix output
file ieeecss/cascade/outsys.f
for writes a system container file
#
# Basic Matrix Manipulation Routines
##
file ieeecss/cascade/cpycol.f
for copy a column of a matrix (vector)
file ieeecss/cascade/d1nrm.f
for compute 1-norm of a matrix
file ieeecss/cascade/dcl1.f
for function to return 1-type magnitude of complex number
file ieeecss/cascade/fnorm.f
for compute Frobenius or Euclidean matrix norm of square matrix
file ieeecss/cascade/madd.f
for matrix addition
file ieeecss/cascade/mmul.f
for matrix multiplication
file ieeecss/cascade/mqf.f
for symmetric matrix product, X'*S*X
file ieeecss/cascade/mqfa.f
for symmetric matrix product, X'*X
file ieeecss/cascade/mqfwo.f
for symmetric matrix product, X'*S*X, stored in S
file ieeecss/cascade/mscale.f
for scalar matrix product, a*X
file ieeecss/cascade/msub.f
for matrix subtraction
file ieeecss/cascade/mula.f
for matrix product, A*B, stored in A
file ieeecss/cascade/mulb.f
for matrix product, A*B, stored in B
file ieeecss/cascade/mulwoa.f
for matrix product, A*B, stored in A
file ieeecss/cascade/mulwob.f
for matrix product, A*B, stored in B
file ieeecss/cascade/save.f
for copy a matrix
file ieeecss/cascade/symprd.f
for symmetric matrix product, X'*A*X
file ieeecss/cascade/trnata.f
for replace a matrix in an array with its transpose (in place)
file ieeecss/cascade/trnatb.f
for form matrix transpose
file ieeecss/cascade/xty.f
for matrix product, X'*Y
file ieeecss/cascade/xyt.f
for matrix product, X*Y'
file ieeecss/cascade/zl1nrm.f
for compute 1-norm of complex vector and scale vector by its norm
#
# ========================================================================
#
# The Cascade Tools
#
# Note: These tools are intended primarily for use by the cascade expert
# system, which implements a version of the LQG/LTR multivariable controller
# design methodology. All of the tools can be run from the Unix or VMS/DCL
# command line, but some are not very useful except to the expert system. The
# tools can also be called as subroutines in other programs. As commands, all
# the tools expect command line arguments providing parameters and necessary
# files. These are provided as elements of the argument lists when the tools
# are accessed as subroutines. File formats and the command line formats are
# described in the manual. All the tools require several include files in
# order to compile, which define limits on array and matrix sizes and other
# parameters. The tool contained in the file "svplot.f" requires the cgs/ncar
# graphics library, but can be modified to use any low-order line graphics
# library.
#
# The tools all use a common command line parser, contained in the file
# "headercode.c". The commands to be built into headercode are defined in
# "commands.h", included in headercode.c. There is currently a problem with
# this code's execution on Sun 4 machines. If you wish the patch when it
# becomes available, contact J. D. Birdwell, birdwell@hickory.engr.utk.edu.
# Notification will be available only via e-mail. The tools are linked with
# headercode.c into one large file, and, on Unix, links are defined from the
# toolname (e.g. aolsys) to the headercode executable. Which tool is to be
# executed is determined by the name of this link. On VMS systems, a command
# definition file is required; contact J. D. Birdwell for its availability.
# The tools were originally developed under a VMS/DCL environment, but have
# since been ported to Unix The command line software may or may not work
# under recent releases of VMS; it has not been tested.
#
# headercode.c main program used to access all tools from the command line
##
file ieeecss/cascade/aolsys.f
for Analyze Open Loop System
file ieeecss/cascade/auginp.f
for Augment at Input
file ieeecss/cascade/augout.f
for Augment at Output
file ieeecss/cascade/augsqr.f
for Augment-Square
file ieeecss/cascade/balsvd.f
for Balance Singular Values
file ieeecss/cascade/dlohi.f
for Decide Low or High
file ieeecss/cascade/evlbnd.f
for Evaluate Bounds
file ieeecss/cascade/exmsys.f
for Examine System
file ieeecss/cascade/kbf.f
for KBF
file ieeecss/cascade/kbffwc.f
for KBF Find Wcmin
file ieeecss/cascade/lqr.f
for LQR
file ieeecss/cascade/lqrfwc.f
for LQR Find Wcmin
file ieeecss/cascade/ltrkbf.f
for LTR using KBF
file ieeecss/cascade/ltrlqr.f
for LTR using LQR
file ieeecss/cascade/makbnd.f
for Make Bounds
file ieeecss/cascade/makmat.f
for Make Matrices
file ieeecss/cascade/rankv.f
for Rank of V
file ieeecss/cascade/svplot.f
for Svplot and Bounds
file ieeecss/readme
for overview of ieeecss
file ieeecss/ahcon.f
file ieeecss/balgbk.f
lib ieeecss/cascade
by J. D. Birdwell
for "Computer-Aided Systems and Control Analysis and Design Environment";
# Cascade Version SUN0.9 June 23, 1988
file ieeecss/sqred.tgz
alg Van Loan's "square reduced" algorithm
for calculating all eigenvalues of a Hamiltonian matrix;
by Ralph Byers.
# version dated Wed Oct 4 15:41:54 1989
file ijsa/contributors
file image/morph.tgz
for 2D and 3D Mathematical Morphology
by Richard Alan Peters II, Electrical Engineering, Vanderbilt
, (615) 322-7924 rap2@vuse.vanderbilt.edu
, Mathematical morphology is a powerful tool for image analysis and enhancement.
, Morphological operators are shape-dependent, nonlinear image transforms such
, as erosion, dilation, opening, closing, and rank filters.
, The mathematical operators are defined in $n$ dimensions so it is possible to
, create programs that will operate on 1D signals, 2D images, or 3D datasets
, using exactly the same concepts.
size 379 kB
file intercom/readme
file intercom/readme.html
# There are four packages in the ITPACK directory for solving
# large sparse linear systems by iterative methods: ITPACK 2C (single
# precision), ITPACK 2C (double precision), ITPACKV 2D (a vectorized
# version of ITPACK 2C for the Cray Y-MP and similar vector computers),
# and NSPCG. ITPACK 2C and ITPACKV 2D are intended for symmetric and
# positive-definite matrix problems. NSPCG has preconditioners and
# polynomial accelerators for nonsymmetric matrix problems as well.
# Only single precision versions are available for ITPACKV 2D
# and NSPCG. Machine-dependent constants and the timing function may
# need to be modified by the user when installing the packages for a
# particular computer. They are located in routines DFAULT and TIMER in
# all four packages.
file itpack/dsrc2c.f
for ITPACK 2C source code
prec double
gams d2b4
size 302 kB
file itpack/dtst2c.f
for testing routine for ITPACK 2C
prec double
file itpack/info.tex
for information about CNA iterative packages
lang LaTeX
file itpack/nspcg1.f
for NSPCG source code, part 1
gams d2a4, d2b4
size 270 kB
file itpack/nspcg2.f
for NSPCG source code, part 2
gams d2a4, d2b4
size 216 kB
file itpack/nspcg3.f
for NSPCG source code, part 3
gams d2a4, d2b4
size 303 kB
file itpack/nspcg4.f
for NSPCG source code, part 4
gams d2a4, d2b4
size 279 kB
file itpack/nspcg5.f
for NSPCG source code, part 5
gams d2a4, d2b4
file itpack/quick.tex
for Quick Reference Guide for NSPCG (formatted with LaTeX)
file itpack/src2c.f
for ITPACK 2C source code
prec single
gams d2b4
size 301 kB
file itpack/srcv2d.f
for ITPACKV 2D source code (vectorized for Cray Y-MP)
gams d2b4
size 230 kB
file itpack/tst2c.f
for testing routine for s.p. ITPACK 2C
file itpack/tstnsp1.f
for testing program 1 for NSPCG
file itpack/tstnsp2.f
for testing program 2 for NSPCG
file itpack/tstnsp3.f
for testing program 3 for NSPCG
file itpack/tstnsp4.f
for testing program 4 for NSPCG
file itpack/tstnsp5.f
for testing program 5 for NSPCG
file itpack/tstv2d.f
for testing routine for ITPACKV 2D
file itpack/user2c.tex
for ITPACK 2C User's Guide
lang LaTeX
file itpack/usernsp.tex
for NSPCG User's Guide
lang LaTeX
size 208 kB
file itpack/userv2d.tex
for ITPACKV 2D User's Guide
lang LaTeX
file jakef/readme
for initial remarks about jakef/jakeff
file jakef/doc
for documentation for (jakef/jakeff)
file jakef/supportf
for necessary support routines for (jakef/jakeff)
file jakef/jakeff
for a precompiler to generate Fortran code for evaluation of gradients or
, Jacobians given Fortran code to evaluate a scalar or vector function
size 200 kilobytes
file java/f2j/f2j-0.8.tgz
for f2j Fortran-to-Java Source Code (tgz archive)
by Keith Seymour
size 453k
file java/f2j/f2j-0.8.zip
for f2j Fortran-to-Java Source Code (zip archive)
by Keith Seymour
size 493k
file java/f2j/jlapack-0.8.tgz
for JLAPACK source and class files (tgz archive)
by Keith Seymour
size 1.3M
file java/f2j/jlapack-0.8.zip
for JLAPACK source and class files (zip archive)
by Keith Seymour
size 1.3M
file java/f2j/jlapack-0.8-javadoc.tgz
for javadoc of JLAPACK source code (tgz archive)
by Keith Seymour
size 1.3M
file java/f2j/jlapack-0.8-javadoc.zip
for javadoc of JLAPACK source code (zip archive)
by Keith Seymour
size 5.8M
file java/f2j/jlapack-0.8-testers.tgz
for source & class files for JLAPACK test routines (tgz archive)
by Keith Seymour
size 965k
file java/f2j/jlapack-0.8-testers.zip
for source & class files for JLAPACK test routines (zip archive)
by Keith Seymour
size 976k
file java/f2j/jlapack-0.8-strict.tgz
for JLAPACK source and class files usingjava.lang.StrictMath and/or strictfp (tgz archive)
by Keith Seymour
size 5.2M
file java/f2j/jlapack-0.8-strict.zip
for JLAPACK source and class files using java.lang.StrictMath and/or strictfp (zip archive)
by Keith Seymour
size 5.2M
file java/f2j/jlapack-0.6.tgz
for JLAPACK source and class files
by Keith Seymour , David Doolin
size 706k
file java/f2j/jlapack_apidoc-0.6.tgz
for javadoc of JLAPACK source code
by Keith Seymour , David Doolin
size 5075k
file java/f2j/jlapack_testers-0.6.tgz
for source & class files for JLAPACK test routines
by Keith Seymour , David Doolin
size 706k
file java/JavaComplex.tgz
for Complex number class for Java. Complex numbers are not
, part of the Java standard libraries.
size 98k
by Alexander Anderson
lang java
file java/fmg.tgz
for a Java 1.1 package that implements the Full Multigrid Algorithm
, for solving linear elliptic parital differential equations on regular
, cubic domains in 3D.
size 173k
by Gerald Loeffler
lang java
lib java/f2j
for the Fortran 2 Java collection
file kincaid-cheney/elimit.f
for Example of a slowly converging sequence
ref text 10
file kincaid-cheney/sqrt2.f
for Example of a rapidly converging sequence
ref text 10
file kincaid-cheney/nest.f
for Nested multiplication
ref text 14
file kincaid-cheney/epsi.f
for Approximate value of machine precision
ref text 36
file kincaid-cheney/depsi.f
for Approximate value of double precision machine precision
ref text 36
file kincaid-cheney/ex2s22.f
for Loss of significance
ref text 43-44
file kincaid-cheney/unstab1.f
for Example of an unstable sequence
ref text 49
file kincaid-cheney/unstab2.f
for Example of another unstable sequence
ref text 50
file kincaid-cheney/instab.f
for Example of numerical instability
ref text 50
file kincaid-cheney/ex1s31.f
for Bisection method to find root of exp(x) = sinx (bisect)
ref text 58-59
file kincaid-cheney/ex1s32.f
for Newton's method example
ref text 65
file kincaid-cheney/ex2s32.f
for Simple Newton's method
ref text 68
file kincaid-cheney/ex3s32.f
for Implicit function example
ref text 69-70
file kincaid-cheney/ex1s33.f
for Secant method example (f )
ref text 76
file kincaid-cheney/ex3s34.f
for Contractive mapping example
ref text 83-84
file kincaid-cheney/ex3s35.f
for Horner's method example
ref text 93
file kincaid-cheney/ex6s35.f
for Newton's method on a given polynomial (horner)
ref text 94
file kincaid-cheney/ex7s35.f
for Bairstow's method example
ref text 99
file kincaid-cheney/laguerre.f
for Laguerre's method example
ref text 102
file kincaid-cheney/forsub.f
for Forward substitution example
ref text 127
file kincaid-cheney/bacsub.f
for Backward substitution example
ref text 127
file kincaid-cheney/pforsub.f
for Forward substitution for a permuted system
ref text 128
file kincaid-cheney/pbacsub.f
for Backward substitution for a permuted system
ref text 128
file kincaid-cheney/genlu.f
for General LU-factorization example
ref text 130
file kincaid-cheney/doolt.f
for Doolittle's-factorization example
ref text 131
file kincaid-cheney/cholsky.f
for Cholesky-factorization example
ref text 134
file kincaid-cheney/bgauss.f
for Basic Gaussian elimination
ref text 143
file kincaid-cheney/pbgauss.f
for Basic Gaussian elimination with pivoting
ref text 145
file kincaid-cheney/gauss.f
for Gaussian elimination with scaled row pivoting
ref text 148
file kincaid-cheney/paxeb.f
for Solves Lz = Pb and then Ux = z (gauss)
ref text 150
file kincaid-cheney/yaec.f
for Solves UT z = c and then LTPy = z (gauss)
ref text 151
file kincaid-cheney/tri.f
for Tridiagonal system solver (tri)
ref text 155
file kincaid-cheney/ex1s45.f
for Neumann series example (setI, mult, store, add, prt)
ref text 173
file kincaid-cheney/ex2s45.f
for Gaussian elimination followed by iterative improvement (residual, gauss, solve)
ref text 175
file kincaid-cheney/ex1s46.f
for Example of Jacobi and Gauss-Seidel methods
ref text 182
file kincaid-cheney/ex2s46.f
for Richardson method example (with scaling)
ref text 184
file kincaid-cheney/jacobi.f
for Jacobi method example (with scaling)
ref text 186
file kincaid-cheney/ex3s46.f
for Gauss-Seidel method (with scaling)
ref text 190
file kincaid-cheney/ex6s46.f
for Chebyshev acceleration example (extrap, cheb, vnorm)
ref text 200
file kincaid-cheney/steepd.f
for Steepest descent method example (prod, mult)
ref text 207
file kincaid-cheney/cg.f
for Conjugate gradient method (prod, residual, mult)
ref text 211
file kincaid-cheney/pcg.f
for Jacobi preconditioned conjugate gradient method (prod, residual, mult)
ref text 217
file kincaid-cheney/ex1s51.f
for Power method example (dot, prod, store, norm, normal)
ref text 231
file kincaid-cheney/poweracc.f
for Power method with Aitken acceleration (dot, prod, store, norm, normal)
ref text 231
file kincaid-cheney/ex2s51.f
for Inverse power method example (gauss, dot, prod, store, norm, normal, solve)
ref text 233
file kincaid-cheney/ipoweracc.f
for Inverse power method with Aitken acceleration (gauss, dot, prod, store, norm, normal, solve)
ref text 233
file kincaid-cheney/ex1s52.f
for Schur factorization example (prtmtx, mult)
ref text 239
file kincaid-cheney/qrshif.f
for Modified Gram-Schmidt example (prtmtx, mgs, mult)
ref text 248
file kincaid-cheney/ex1s53.f
for QR-factorization using Householder transformations (QRfac, setoI, prtmtx, UtimesA, findV, prod, formU, formW, trans, mult)
ref text 253-255
file kincaid-cheney/ex2s55.f
for QR-factorization example (QRfac, setoI, prtmtx, UtimesA, findV, prod, formU, formW, trans, mult, copy, scale)
ref text 272-273
file kincaid-cheney/ex3s55.f
for Shifted QR-factorization example (submtx, shiftA, unshiftA, hess, QRfac, setoI, prtmtx, UtimesA, findU, findV, prod, formU, formW, Trans, mult, copy, scale)
ref text 274
file kincaid-cheney/coef.f
for Coefficients in the Newton form of a polynomial
ref text 280-281
file kincaid-cheney/fft.f
for Fast Fourier transform example (f )
ref text 419
file kincaid-cheney/adapta.f
for Adaptive approximation example (f, max)
ref text 426-428
file kincaid-cheney/ex1s71.f
for Derivative approximations: forward difference formula
ref text 431-432
file kincaid-cheney/ex2s71.f
for Derivative approximation: central difference
ref text 434
file kincaid-cheney/ex5s71.f
for Derivative approximation: Richardson extrapolation
ref text 437-438
file kincaid-cheney/ex6s71.f
for Richardson extrapolation
ref text 440-441
file kincaid-cheney/gauss5.f
for Gaussian five-point quadrature example
ref text 459
file kincaid-cheney/romberg.f
for Romberg extrapolation
ref text 468
file kincaid-cheney/adapt.f
for Adaptive quadrature
ref text 475
file kincaid-cheney/taylor.f
for Taylor-series method
ref text 492
file kincaid-cheney/rk4.f
for Runge-Kutta method (f, u)
ref text 501-502
file kincaid-cheney/rkfelberg.f
for Runge-Kutta-Fehlberg method (f )
ref text 503-505
file kincaid-cheney/taysys.f
for Taylor series for systems
ref text 526-527
file kincaid-cheney/exs91.f
for Boundary value problem (BVP): Explicit method example (a, b, vnorm)
ref text 576
file kincaid-cheney/exs92.f
for BVP: Implicit method example (tri, unorm)
ref text 582
file kincaid-cheney/exs93.f
for Finite difference method (g )
ref text 589
file kincaid-cheney/ex3s96.f
for BVP: Method of characteristics (f, g, df, tu)
ref text 613
file kincaid-cheney/mgrid1.f
for Multigrid method example (vnorm)
ref text 624
file kincaid-cheney/exs98.f
for Damping of errors
ref text 625
file kincaid-cheney/mgrid2.f
for Multigrid method V-cycle (vnorm)
ref text 630
file kincaid-cheney/code-info.tex
for introduction
file kincaid-cheney/code-info.tty
for introduction
file kincaid-cheney/shar
for entire library
file kincaid-cheney/changes
file la-net/call94.text
for call for papers, FIFTH SIAM CONFERENCE ON APPLIED LINEAR ALGEBRA
, June 15-18, 1994, Snowbird, Utah
lib lanczos/vol2
for chapters of "Lanczos Algorithms" book volume 2
by Jane Cullum cullumj@lanl.gov and Ralph Willoughby
file lanczos/vol2.pdf.gz
for same as lanczos/vol2, but as a single large PDF file
size 1.6MB
file lanczos/vol2.ps.gz
for same as vol2.pdf.gz, but PostScript instead of PDF
size 800kB
file lanczos/hleval
for distinct eigenvalue of a Hermitian matrix using Lanczos tridiagonalization without reorthogonalization
file lanczos/leval
for distinct eigenvalues of a real symmetric matrix using Lanczos tridiagonalization
file lanczos/lsval
for distinct singular values of a real, rectangular matrix using Lanczos tridiagonalization
file lanczos/hlemult
for internal routines to generate real symmetric tridiagonal matrices for (lanczos/hleval) and (lanczos/hlevec)
file lanczos/hlevec
for eigenvectors of a Hermitian matrix, called with the eigenvalues from (lanczos/hleval)
file lanczos/levec
for eigenvectors of a real symmetric matrix, called with the eigenvalues from (lanczos/leval)
file lanczos/lemult
for internal routines to generate real symmetric tridiagonal matrices for (lanczos/leval) and (lanczos/levec)
file lanczos/lesub
for internal routines for (lanczos/leval) and (lanczos/levec)
file lanczos/lsvec
for singular vectors of a real, rectangular matrix using singular values from (lanczos/lsval)
file lanczos/lsmult
for internal routines to generate real symmetric tridiagonal matrices for (lanczos/lsval) and (lanczos/lsvec)
file lanczos/lssub
for internal routines for (lanczos/lsval) and (lanczos/lsvec)
file lanczos/levalhed
for documentation for Lanczos real and Hermetian eigenvalue/eigenvector codes
file lanczos/lsvalhed
for documentation for singular value/vector Lanczos codes
file lanczos/data
for input/output file definitions and sample input files for (lanczos/leval) and (lanczos/levec)
file lanczos/hlevalio
for list of i/o files and sample input for (lanczos/hleval)
file lanczos/hlevecio
for list of i/o files and sample input for (lanczos/hlevec)
file lanczos/levalio
for list of i/o files and sample input for (lanczos/leval)
file lanczos/levecio
for list of i/o files and sample input for (lanczos/levec)
file lanczos/lsvalio
for list of i/o files and sample input for (lanczos/lsval)
file lanczos/lsvecio
for list of i/o files and sample input for (lanczos/lsvec)
# for lgval and lgmult, contact Jane Cullum directly.
file lanczos/changes
file lanczos/errata
file lanczos/foo
file lanczos/foo2
file lanczos/foo3
file lanczos/jane1
file lanczos/jane2
file lanczos/jane3
file lanczos/jane4
file lanczos/levaled
file lanczos/lsvaled
file lanczos/lump
file lanczos/message
file lanczos/ralph1
file lanczos/ralph2
file lanczos/singed
file lanczos/xxx
file lanczos/vol2/Chp_1_Overview.pdf
file lanczos/vol2/Chp_2_RealSymmetric.pdf
file lanczos/vol2/Chp_3_Hermitian.pdf
file lanczos/vol2/Chp_4_FactoredInverses.pdf
file lanczos/vol2/Chp_5_RealSymmGen.pdf
file lanczos/vol2/Chp_6_SingularValues.pdf
file lanczos/vol2/Chp_7_ComplexSymmetric.pdf
file lanczos/vol2/Chp_89_BlockLanczos.pdf
file lanczos/vol2/Refs_Vol1_Errata.pdf
# ======== index for lanz =======
# LANZ: Software for Solving the Large Sparse Symmetric Generalized Eigenproblem
# Mark T. Jones, Argonne National Laboratory, Argonne, Illinois 60439-4844
# Merrell L. Patrick, Duke University, Durham, North Carolina 27706
#
# LANZ solves the symmetric generalized eigenproblem,
# \begin{equation}
# Kx=\lambda Mx,
# \end{equation}
# where $K$ is symmetric positive definite and $M$ is
# positive semi-definite. It is also capable of solving
# \begin{equation}
# Kx=-\lambda Mx,
# \end{equation}
# where $M$ can be indefinite.
# It can find either 1) all
# the eigenpairs in a user-specified range, or 2) the $p$ eigenpairs
# closest to some user-specified value, $\sigma$.
#
# The LANZ package was developed to run efficiently on a range of
# architectures, including vector and parallel computers.
#
# LANZ is an implementation of the algorithm described in
# \cite{jones:lanczos}. The heart of LANZ is
# the Lanczos algorithm used with spectral transformations
# similar to those described in \cite{nour-omid:implement}. LANZ uses
# the partial reorthogonalization algorithm, originally proposed
# in \cite{simon:partial}, and expanded upon in \cite{parlett:semi_ortho},
# to maintain semi-orthogonality among the Lanczos vectors.
# In addition, LANZ uses a dynamic shifting algorithm to accelerate
# convergence to desired eigenpairs in a slightly different fashion
# than in \cite{boeing:small_lan_report}.
#
# \bibitem{jones:lanczos}
# {\sc Jones, M.~T., and Patrick, M.~L.}
# \newblock {The Use of Lanczos's Method to Solve the Large Generalized
# Symmetric Definite Eigenvalue Problem}.
# \newblock Technical Report 89-67, Institute for Computer Applications in
# Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA,
# 1989.
# \bibitem{nour-omid:implement}
# {\sc Nour-Omid, B., Parlett, B.~N., Ericsson, T., and Jensen, P.~S.}
# \newblock {How to Implement the Spectral Transformation}.
# \newblock {\em Mathematics of Computation 48}, 178 (April 1987), 663--673.
# \bibitem{simon:partial}
# {\sc Simon, H.~D.}
# \newblock {The Lanczos Algorithm With Partial Reorthogonalization}.
# \newblock {\em Mathematics of Computation 42}, 165 (January 1984), 115--142.
# \bibitem{parlett:semi_ortho}
# {\sc Parlett, B.~N., Nour-Omid, B., and Liu, Z.~A.}
# \newblock {How to Maintain Semi-Orthogonality Among Lanczos Vectors}.
# \newblock {PAM-420}, Center for Pure and Applied Mathematics, University of
# California, Berkeley, July, 1988.
# \bibitem{boeing:small_lan_report}
# {\sc Grimes, R.~G., Lewis, J.~G., and Simon, H.~D.}
# \newblock {The Implementation of a Block Lanczos Algorithm with
# Reorthogonalization Methods}.
# \newblock {ETA-TR-91}, Boeing Computer Servies, Seattle, WA, May, 1988.
file lanz/lanz_file1.tgz
for code, documentation, makefiles, etc.
size 51 kilobytes
file lanz/lanz_file2.tgz
for code, documentation, makefiles, etc.
size 169 kilobytes
file lanz/lanz_file3
for just code, no documentation
size 464 kilobytes
lang Fortran
file lanz/lanz_file4
size 4 kilobytes
lang C
# Installation of LANZ, depending on your architecture, may take up
# to 3.5mb of disk space. After installing LANZ, if you desire, you
# can delete all but one or two files created by the installation
# process.
# For detailed information on LAPACK++, please refer to the URL:
# http://math.nist.gov/lapack++
file lapack++/overview.ps
for "LAPACK++: A Design Overview of Object-Oriented Extensions
, for High Performance Linear Algebra," J. J. Dongarra,
, R. Pozo, David W. Walker
size 272 kB
file lapack++/classref.ps
for Class reference guide
size 115 kB
file lapack++/install.ps
for Release notes and Installation manual for LAPACK++
size 167k kB
file lapack++/user.ps
for User Guide for LAPACK++
size 278 kB
file lapack++/lapack++.tgz
for source code for LAPACK++
size 66 kB
file lapack++/readme
file lapack/archives/readme
file lapack/archives/lapack_alpha.tgz
file lapack/archives/lapack_linux.tgz
file lapack/archives/lapack_rs6k.tgz
file lapack/archives/lapack_solaris.tgz
file lapack/archives/lapack_win32.zip
# ---------------------------------
# Available SIMPLE DRIVER routines:
# ---------------------------------
file lapack/complex/cgbsv.f
prec complex
CGBSV computes the solution to a complex system of linear equations
A * X = B, where A is a band matrix of order N with KL subdiagonals
and KU superdiagonals, and X and B are N-by-NRHS matrices.
The LU decomposition with partial pivoting and row interchanges is
used to factor A as A = L * U, where L is a product of permutation
and unit lower triangular matrices with KL subdiagonals, and U is
upper triangular with KL+KU superdiagonals. The factored form of A
is then used to solve the system of equations A * X = B.
file lapack/complex/cgees.f
prec complex
CGEES computes for an N-by-N complex nonsymmetric matrix A, the
eigenvalues, the Schur form T, and, optionally, the matrix of Schur
vectors Z. This gives the Schur factorization A = Z*T*(Z**H).
Optionally, it also orders the eigenvalues on the diagonal of the
Schur form so that selected eigenvalues are at the top left.
The leading columns of Z then form an orthonormal basis for the
invariant subspace corresponding to the selected eigenvalues.
A complex matrix is in Schur form if it is upper triangular.
file lapack/complex/cgeev.f
prec complex
CGEEV computes for an N-by-N complex nonsymmetric matrix A, the
eigenvalues and, optionally, the left and/or right eigenvectors.
The right eigenvector v(j) of A satisfies
A * v(j) = lambda(j) * v(j)
where lambda(j) is its eigenvalue.
The left eigenvector u(j) of A satisfies
u(j)**H * A = lambda(j) * u(j)**H
where u(j)**H denotes the conjugate transpose of u(j).
The computed eigenvectors are normalized to have Euclidean norm
equal to 1 and largest component real.
file lapack/complex/cgegs.f
prec complex
This routine is deprecated and has been replaced by routine CGGES.
CGEGS computes the eigenvalues, Schur form, and, optionally, the
left and or/right Schur vectors of a complex matrix pair (A,B).
Given two square matrices A and B, the generalized Schur
factorization has the form
A = Q*S*Z**H, B = Q*T*Z**H
where Q and Z are unitary matrices and S and T are upper triangular.
The columns of Q are the left Schur vectors
and the columns of Z are the right Schur vectors.
If only the eigenvalues of (A,B) are needed, the driver routine
CGEGV should be used instead. See CGEGV for a description of the
eigenvalues of the generalized nonsymmetric eigenvalue problem
(GNEP).
file lapack/complex/cgegv.f
prec complex
This routine is deprecated and has been replaced by routine CGGEV.
CGEGV computes the eigenvalues and, optionally, the left and/or right
eigenvectors of a complex matrix pair (A,B).
Given two square matrices A and B,
the generalized nonsymmetric eigenvalue problem (GNEP) is to find the
eigenvalues lambda and corresponding (non-zero) eigenvectors x such
that
A*x = lambda*B*x.
An alternate form is to find the eigenvalues mu and corresponding
eigenvectors y such that
mu*A*y = B*y.
These two forms are equivalent with mu = 1/lambda and x = y if
neither lambda nor mu is zero. In order to deal with the case that
lambda or mu is zero or small, two values alpha and beta are returned
for each eigenvalue, such that lambda = alpha/beta and
mu = beta/alpha.
The vectors x and y in the above equations are right eigenvectors of
the matrix pair (A,B). Vectors u and v satisfying
u**H*A = lambda*u**H*B or mu*v**H*A = v**H*B
are left eigenvectors of (A,B).
Note: this routine performs "full balancing" on A and B -- see
"Further Details", below.
file lapack/complex/cgels.f
prec complex
CGELS solves overdetermined or underdetermined complex linear systems
involving an M-by-N matrix A, or its conjugate-transpose, using a QR
or LQ factorization of A. It is assumed that A has full rank.
The following options are provided:
1. If TRANS = 'N' and m >= n: find the least squares solution of
an overdetermined system, i.e., solve the least squares problem
minimize || B - A*X ||.
2. If TRANS = 'N' and m < n: find the minimum norm solution of
an underdetermined system A * X = B.
3. If TRANS = 'C' and m >= n: find the minimum norm solution of
an undetermined system A**H * X = B.
4. If TRANS = 'C' and m < n: find the least squares solution of
an overdetermined system, i.e., solve the least squares problem
minimize || B - A**H * X ||.
Several right hand side vectors b and solution vectors x can be
handled in a single call; they are stored as the columns of the
M-by-NRHS right hand side matrix B and the N-by-NRHS solution
matrix X.
file lapack/complex/cgelsd.f
prec complex
CGELSD computes the minimum-norm solution to a real linear least
squares problem:
minimize 2-norm(| b - A*x |)
using the singular value decomposition (SVD) of A. A is an M-by-N
matrix which may be rank-deficient.
Several right hand side vectors b and solution vectors x can be
handled in a single call; they are stored as the columns of the
M-by-NRHS right hand side matrix B and the N-by-NRHS solution
matrix X.
The problem is solved in three steps:
(1) Reduce the coefficient matrix A to bidiagonal form with
Householder tranformations, reducing the original problem
into a "bidiagonal least squares problem" (BLS)
(2) Solve the BLS using a divide and conquer approach.
(3) Apply back all the Householder tranformations to solve
the original least squares problem.
The effective rank of A is determined by treating as zero those
singular values which are less than RCOND times the largest singular
value.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/complex/cgelss.f
prec complex
CGELSS computes the minimum norm solution to a complex linear
least squares problem:
Minimize 2-norm(| b - A*x |).
using the singular value decomposition (SVD) of A. A is an M-by-N
matrix which may be rank-deficient.
Several right hand side vectors b and solution vectors x can be
handled in a single call; they are stored as the columns of the
M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix
X.
The effective rank of A is determined by treating as zero those
singular values which are less than RCOND times the largest singular
value.
file lapack/complex/cgelsy.f
prec complex
CGELSY computes the minimum-norm solution to a complex linear least
squares problem:
minimize || A * X - B ||
using a complete orthogonal factorization of A. A is an M-by-N
matrix which may be rank-deficient.
Several right hand side vectors b and solution vectors x can be
handled in a single call; they are stored as the columns of the
M-by-NRHS right hand side matrix B and the N-by-NRHS solution
matrix X.
The routine first computes a QR factorization with column pivoting:
A * P = Q * [ R11 R12 ]
[ 0 R22 ]
with R11 defined as the largest leading submatrix whose estimated
condition number is less than 1/RCOND. The order of R11, RANK,
is the effective rank of A.
Then, R22 is considered to be negligible, and R12 is annihilated
by unitary transformations from the right, arriving at the
complete orthogonal factorization:
A * P = Q * [ T11 0 ] * Z
[ 0 0 ]
The minimum-norm solution is then
X = P * Z' [ inv(T11)*Q1'*B ]
[ 0 ]
where Q1 consists of the first RANK columns of Q.
This routine is basically identical to the original xGELSX except
three differences:
o The permutation of matrix B (the right hand side) is faster and
more simple.
o The call to the subroutine xGEQPF has been substituted by the
the call to the subroutine xGEQP3. This subroutine is a Blas-3
version of the QR factorization with column pivoting.
o Matrix B (the right hand side) is updated with Blas-3.
file lapack/complex/cgesdd.f
prec complex
CGESDD computes the singular value decomposition (SVD) of a complex
M-by-N matrix A, optionally computing the left and/or right singular
vectors, by using divide-and-conquer method. The SVD is written
A = U * SIGMA * conjugate-transpose(V)
where SIGMA is an M-by-N matrix which is zero except for its
min(m,n) diagonal elements, U is an M-by-M unitary matrix, and
V is an N-by-N unitary matrix. The diagonal elements of SIGMA
are the singular values of A; they are real and non-negative, and
are returned in descending order. The first min(m,n) columns of
U and V are the left and right singular vectors of A.
Note that the routine returns VT = V**H, not V.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/complex/cgesv.f
prec complex
CGESV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N matrix and X and B are N-by-NRHS matrices.
The LU decomposition with partial pivoting and row interchanges is
used to factor A as
A = P * L * U,
where P is a permutation matrix, L is unit lower triangular, and U is
upper triangular. The factored form of A is then used to solve the
system of equations A * X = B.
file lapack/complex/cgesvd.f
prec complex
CGESVD computes the singular value decomposition (SVD) of a complex
M-by-N matrix A, optionally computing the left and/or right singular
vectors. The SVD is written
A = U * SIGMA * conjugate-transpose(V)
where SIGMA is an M-by-N matrix which is zero except for its
min(m,n) diagonal elements, U is an M-by-M unitary matrix, and
V is an N-by-N unitary matrix. The diagonal elements of SIGMA
are the singular values of A; they are real and non-negative, and
are returned in descending order. The first min(m,n) columns of
U and V are the left and right singular vectors of A.
Note that the routine returns V**H, not V.
file lapack/complex/cgges.f
prec complex
CGGES computes for a pair of N-by-N complex nonsymmetric matrices
(A,B), the generalized eigenvalues, the generalized complex Schur
form (S, T), and optionally left and/or right Schur vectors (VSL
and VSR). This gives the generalized Schur factorization
(A,B) = ( (VSL)*S*(VSR)**H, (VSL)*T*(VSR)**H )
where (VSR)**H is the conjugate-transpose of VSR.
Optionally, it also orders the eigenvalues so that a selected cluster
of eigenvalues appears in the leading diagonal blocks of the upper
triangular matrix S and the upper triangular matrix T. The leading
columns of VSL and VSR then form an unitary basis for the
corresponding left and right eigenspaces (deflating subspaces).
(If only the generalized eigenvalues are needed, use the driver
CGGEV instead, which is faster.)
A generalized eigenvalue for a pair of matrices (A,B) is a scalar w
or a ratio alpha/beta = w, such that A - w*B is singular. It is
usually represented as the pair (alpha,beta), as there is a
reasonable interpretation for beta=0, and even for both being zero.
A pair of matrices (S,T) is in generalized complex Schur form if S
and T are upper triangular and, in addition, the diagonal elements
of T are non-negative real numbers.
file lapack/complex/cggev.f
prec complex
CGGEV computes for a pair of N-by-N complex nonsymmetric matrices
(A,B), the generalized eigenvalues, and optionally, the left and/or
right generalized eigenvectors.
A generalized eigenvalue for a pair of matrices (A,B) is a scalar
lambda or a ratio alpha/beta = lambda, such that A - lambda*B is
singular. It is usually represented as the pair (alpha,beta), as
there is a reasonable interpretation for beta=0, and even for both
being zero.
The right generalized eigenvector v(j) corresponding to the
generalized eigenvalue lambda(j) of (A,B) satisfies
A * v(j) = lambda(j) * B * v(j).
The left generalized eigenvector u(j) corresponding to the
generalized eigenvalues lambda(j) of (A,B) satisfies
u(j)**H * A = lambda(j) * u(j)**H * B
where u(j)**H is the conjugate-transpose of u(j).
file lapack/complex/cggglm.f
prec complex
CGGGLM solves a general Gauss-Markov linear model (GLM) problem:
minimize || y ||_2 subject to d = A*x + B*y
x
where A is an N-by-M matrix, B is an N-by-P matrix, and d is a
given N-vector. It is assumed that M <= N <= M+P, and
rank(A) = M and rank( A B ) = N.
Under these assumptions, the constrained equation is always
consistent, and there is a unique solution x and a minimal 2-norm
solution y, which is obtained using a generalized QR factorization
of the matrices (A, B) given by
A = Q*(R), B = Q*T*Z.
(0)
In particular, if matrix B is square nonsingular, then the problem
GLM is equivalent to the following weighted linear least squares
problem
minimize || inv(B)*(d-A*x) ||_2
x
where inv(B) denotes the inverse of B.
file lapack/complex/cgglse.f
prec complex
CGGLSE solves the linear equality-constrained least squares (LSE)
problem:
minimize || c - A*x ||_2 subject to B*x = d
where A is an M-by-N matrix, B is a P-by-N matrix, c is a given
M-vector, and d is a given P-vector. It is assumed that
P <= N <= M+P, and
rank(B) = P and rank( (A) ) = N.
( (B) )
These conditions ensure that the LSE problem has a unique solution,
which is obtained using a generalized RQ factorization of the
matrices (B, A) given by
B = (0 R)*Q, A = Z*T*Q.
file lapack/complex/cggsvd.f
prec complex
CGGSVD computes the generalized singular value decomposition (GSVD)
of an M-by-N complex matrix A and P-by-N complex matrix B:
U'*A*Q = D1*( 0 R ), V'*B*Q = D2*( 0 R )
where U, V and Q are unitary matrices, and Z' means the conjugate
transpose of Z. Let K+L = the effective numerical rank of the
matrix (A',B')', then R is a (K+L)-by-(K+L) nonsingular upper
triangular matrix, D1 and D2 are M-by-(K+L) and P-by-(K+L) "diagonal"
matrices and of the following structures, respectively:
If M-K-L >= 0,
K L
D1 = K ( I 0 )
L ( 0 C )
M-K-L ( 0 0 )
K L
D2 = L ( 0 S )
P-L ( 0 0 )
N-K-L K L
( 0 R ) = K ( 0 R11 R12 )
L ( 0 0 R22 )
where
C = diag( ALPHA(K+1), ... , ALPHA(K+L) ),
S = diag( BETA(K+1), ... , BETA(K+L) ),
C**2 + S**2 = I.
R is stored in A(1:K+L,N-K-L+1:N) on exit.
If M-K-L < 0,
K M-K K+L-M
D1 = K ( I 0 0 )
M-K ( 0 C 0 )
K M-K K+L-M
D2 = M-K ( 0 S 0 )
K+L-M ( 0 0 I )
P-L ( 0 0 0 )
N-K-L K M-K K+L-M
( 0 R ) = K ( 0 R11 R12 R13 )
M-K ( 0 0 R22 R23 )
K+L-M ( 0 0 0 R33 )
where
C = diag( ALPHA(K+1), ... , ALPHA(M) ),
S = diag( BETA(K+1), ... , BETA(M) ),
C**2 + S**2 = I.
(R11 R12 R13 ) is stored in A(1:M, N-K-L+1:N), and R33 is stored
( 0 R22 R23 )
in B(M-K+1:L,N+M-K-L+1:N) on exit.
The routine computes C, S, R, and optionally the unitary
transformation matrices U, V and Q.
In particular, if B is an N-by-N nonsingular matrix, then the GSVD of
A and B implicitly gives the SVD of A*inv(B):
A*inv(B) = U*(D1*inv(D2))*V'.
If ( A',B')' has orthnormal columns, then the GSVD of A and B is also
equal to the CS decomposition of A and B. Furthermore, the GSVD can
be used to derive the solution of the eigenvalue problem:
A'*A x = lambda* B'*B x.
In some literature, the GSVD of A and B is presented in the form
U'*A*X = ( 0 D1 ), V'*B*X = ( 0 D2 )
where U and V are orthogonal and X is nonsingular, and D1 and D2 are
``diagonal''. The former GSVD form can be converted to the latter
form by taking the nonsingular matrix X as
X = Q*( I 0 )
( 0 inv(R) )
file lapack/complex/chbev.f
prec complex
CHBEV computes all the eigenvalues and, optionally, eigenvectors of
a complex Hermitian band matrix A.
file lapack/complex/chbevd.f
prec complex
CHBEVD computes all the eigenvalues and, optionally, eigenvectors of
a complex Hermitian band matrix A. If eigenvectors are desired, it
uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/complex/chbgv.f
prec complex
CHBGV computes all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite banded eigenproblem, of
the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian
and banded, and B is also positive definite.
file lapack/complex/chbgvd.f
prec complex
CHBGVD computes all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite banded eigenproblem, of
the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian
and banded, and B is also positive definite. If eigenvectors are
desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/complex/cheev.f
prec complex
CHEEV computes all eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A.
file lapack/complex/cheevd.f
prec complex
CHEEVD computes all eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A. If eigenvectors are desired, it uses a
divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/complex/cheevr.f
prec complex
CHEEVR computes selected eigenvalues and, optionally, eigenvectors
of a complex Hermitian matrix A. Eigenvalues and eigenvectors can
be selected by specifying either a range of values or a range of
indices for the desired eigenvalues.
CHEEVR first reduces the matrix A to tridiagonal form T with a call
to CHETRD. Then, whenever possible, CHEEVR calls CSTEMR to compute
the eigenspectrum using Relatively Robust Representations. CSTEMR
computes eigenvalues by the dqds algorithm, while orthogonal
eigenvectors are computed from various "good" L D L^T representations
(also known as Relatively Robust Representations). Gram-Schmidt
orthogonalization is avoided as far as possible. More specifically,
the various steps of the algorithm are as follows.
For each unreduced block (submatrix) of T,
(a) Compute T - sigma I = L D L^T, so that L and D
define all the wanted eigenvalues to high relative accuracy.
This means that small relative changes in the entries of D and L
cause only small relative changes in the eigenvalues and
eigenvectors. The standard (unfactored) representation of the
tridiagonal matrix T does not have this property in general.
(b) Compute the eigenvalues to suitable accuracy.
If the eigenvectors are desired, the algorithm attains full
accuracy of the computed eigenvalues only right before
the corresponding vectors have to be computed, see steps c) and d).
(c) For each cluster of close eigenvalues, select a new
shift close to the cluster, find a new factorization, and refine
the shifted eigenvalues to suitable accuracy.
(d) For each eigenvalue with a large enough relative separation compute
the corresponding eigenvector by forming a rank revealing twisted
factorization. Go back to (c) for any clusters that remain.
The desired accuracy of the output can be specified by the input
parameter ABSTOL.
For more details, see DSTEMR's documentation and:
- Inderjit S. Dhillon and Beresford N. Parlett: "Multiple representations
to compute orthogonal eigenvectors of symmetric tridiagonal matrices,"
Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004.
- Inderjit Dhillon and Beresford Parlett: "Orthogonal Eigenvectors and
Relative Gaps," SIAM Journal on Matrix Analysis and Applications, Vol. 25,
2004. Also LAPACK Working Note 154.
- Inderjit Dhillon: "A new O(n^2) algorithm for the symmetric
tridiagonal eigenvalue/eigenvector problem",
Computer Science Division Technical Report No. UCB/CSD-97-971,
UC Berkeley, May 1997.
Note 1 : CHEEVR calls CSTEMR when the full spectrum is requested
on machines which conform to the ieee-754 floating point standard.
CHEEVR calls SSTEBZ and CSTEIN on non-ieee machines and
when partial spectrum requests are made.
Normal execution of CSTEMR may create NaNs and infinities and
hence may abort due to a floating point exception in environments
which do not handle NaNs and infinities in the ieee standard default
manner.
file lapack/complex/chegv.f
prec complex
CHEGV computes all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
Here A and B are assumed to be Hermitian and B is also
positive definite.
file lapack/complex/chegvd.f
prec complex
CHEGVD computes all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be Hermitian and B is also positive definite.
If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/complex/chesv.f
prec complex
CHESV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
matrices.
The diagonal pivoting method is used to factor A as
A = U * D * U**H, if UPLO = 'U', or
A = L * D * L**H, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and D is Hermitian and block diagonal with
1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then
used to solve the system of equations A * X = B.
file lapack/complex/chpev.f
prec complex
CHPEV computes all the eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix in packed storage.
file lapack/complex/chpevd.f
prec complex
CHPEVD computes all the eigenvalues and, optionally, eigenvectors of
a complex Hermitian matrix A in packed storage. If eigenvectors are
desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/complex/chpgv.f
prec complex
CHPGV computes all the eigenvalues and, optionally, the eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
Here A and B are assumed to be Hermitian, stored in packed format,
and B is also positive definite.
file lapack/complex/chpgvd.f
prec complex
CHPGVD computes all the eigenvalues and, optionally, the eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be Hermitian, stored in packed format, and B is also
positive definite.
If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/complex/chpsv.f
prec complex
CHPSV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N Hermitian matrix stored in packed format and X
and B are N-by-NRHS matrices.
The diagonal pivoting method is used to factor A as
A = U * D * U**H, if UPLO = 'U', or
A = L * D * L**H, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, D is Hermitian and block diagonal with 1-by-1
and 2-by-2 diagonal blocks. The factored form of A is then used to
solve the system of equations A * X = B.
file lapack/complex/cpbsv.f
prec complex
CPBSV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N Hermitian positive definite band matrix and X
and B are N-by-NRHS matrices.
The Cholesky decomposition is used to factor A as
A = U**H * U, if UPLO = 'U', or
A = L * L**H, if UPLO = 'L',
where U is an upper triangular band matrix, and L is a lower
triangular band matrix, with the same number of superdiagonals or
subdiagonals as A. The factored form of A is then used to solve the
system of equations A * X = B.
file lapack/complex/cposv.f
prec complex
CPOSV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N Hermitian positive definite matrix and X and B
are N-by-NRHS matrices.
The Cholesky decomposition is used to factor A as
A = U**H* U, if UPLO = 'U', or
A = L * L**H, if UPLO = 'L',
where U is an upper triangular matrix and L is a lower triangular
matrix. The factored form of A is then used to solve the system of
equations A * X = B.
file lapack/complex/cppsv.f
prec complex
CPPSV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N Hermitian positive definite matrix stored in
packed format and X and B are N-by-NRHS matrices.
The Cholesky decomposition is used to factor A as
A = U**H* U, if UPLO = 'U', or
A = L * L**H, if UPLO = 'L',
where U is an upper triangular matrix and L is a lower triangular
matrix. The factored form of A is then used to solve the system of
equations A * X = B.
file lapack/complex/cspsv.f
prec complex
CSPSV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N symmetric matrix stored in packed format and X
and B are N-by-NRHS matrices.
The diagonal pivoting method is used to factor A as
A = U * D * U**T, if UPLO = 'U', or
A = L * D * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, D is symmetric and block diagonal with 1-by-1
and 2-by-2 diagonal blocks. The factored form of A is then used to
solve the system of equations A * X = B.
file lapack/complex/cstemr.f
prec complex
CSTEMR computes selected eigenvalues and, optionally, eigenvectors
of a real symmetric tridiagonal matrix T. Any such unreduced matrix has
a well defined set of pairwise different real eigenvalues, the corresponding
real eigenvectors are pairwise orthogonal.
The spectrum may be computed either completely or partially by specifying
either an interval (VL,VU] or a range of indices IL:IU for the desired
eigenvalues.
Depending on the number of desired eigenvalues, these are computed either
by bisection or the dqds algorithm. Numerically orthogonal eigenvectors are
computed by the use of various suitable L D L^T factorizations near clusters
of close eigenvalues (referred to as RRRs, Relatively Robust
Representations). An informal sketch of the algorithm follows.
For each unreduced block (submatrix) of T,
(a) Compute T - sigma I = L D L^T, so that L and D
define all the wanted eigenvalues to high relative accuracy.
This means that small relative changes in the entries of D and L
cause only small relative changes in the eigenvalues and
eigenvectors. The standard (unfactored) representation of the
tridiagonal matrix T does not have this property in general.
(b) Compute the eigenvalues to suitable accuracy.
If the eigenvectors are desired, the algorithm attains full
accuracy of the computed eigenvalues only right before
the corresponding vectors have to be computed, see steps c) and d).
(c) For each cluster of close eigenvalues, select a new
shift close to the cluster, find a new factorization, and refine
the shifted eigenvalues to suitable accuracy.
(d) For each eigenvalue with a large enough relative separation compute
the corresponding eigenvector by forming a rank revealing twisted
factorization. Go back to (c) for any clusters that remain.
For more details, see:
- Inderjit S. Dhillon and Beresford N. Parlett: "Multiple representations
to compute orthogonal eigenvectors of symmetric tridiagonal matrices,"
Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004.
- Inderjit Dhillon and Beresford Parlett: "Orthogonal Eigenvectors and
Relative Gaps," SIAM Journal on Matrix Analysis and Applications, Vol. 25,
2004. Also LAPACK Working Note 154.
- Inderjit Dhillon: "A new O(n^2) algorithm for the symmetric
tridiagonal eigenvalue/eigenvector problem",
Computer Science Division Technical Report No. UCB/CSD-97-971,
UC Berkeley, May 1997.
Further Details
1.CSTEMR works only on machines which follow IEEE-754
floating-point standard in their handling of infinities and NaNs.
This permits the use of efficient inner loops avoiding a check for
zero divisors.
2. LAPACK routines can be used to reduce a complex Hermitean matrix to
real symmetric tridiagonal form.
(Any complex Hermitean tridiagonal matrix has real values on its diagonal
and potentially complex numbers on its off-diagonals. By applying a
similarity transform with an appropriate diagonal matrix
diag(1,e^{i \phy_1}, ... , e^{i \phy_{n-1}}), the complex Hermitean
matrix can be transformed into a real symmetric matrix and complex
arithmetic can be entirely avoided.)
While the eigenvectors of the real symmetric tridiagonal matrix are real,
the eigenvectors of original complex Hermitean matrix have complex entries
in general.
Since LAPACK drivers overwrite the matrix data with the eigenvectors,
CSTEMR accepts complex workspace to facilitate interoperability
with CUNMTR or CUPMTR.
file lapack/complex/csysv.f
prec complex
CSYSV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
matrices.
The diagonal pivoting method is used to factor A as
A = U * D * U**T, if UPLO = 'U', or
A = L * D * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and D is symmetric and block diagonal with
1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then
used to solve the system of equations A * X = B.
# ---------------------------------
# Available EXPERT DRIVER routines:
# ---------------------------------
file lapack/complex/cgbsvx.f
prec complex
CGBSVX uses the LU factorization to compute the solution to a complex
system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
where A is a band matrix of order N with KL subdiagonals and KU
superdiagonals, and X and B are N-by-NRHS matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed by this subroutine:
1. If FACT = 'E', real scaling factors are computed to equilibrate
the system:
TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B
TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N')
or diag(C)*B (if TRANS = 'T' or 'C').
2. If FACT = 'N' or 'E', the LU decomposition is used to factor the
matrix A (after equilibration if FACT = 'E') as
A = L * U,
where L is a product of permutation and unit lower triangular
matrices with KL subdiagonals, and U is upper triangular with
KL+KU superdiagonals.
3. If some U(i,i)=0, so that U is exactly singular, then the routine
returns with INFO = i. Otherwise, the factored form of A is used
to estimate the condition number of the matrix A. If the
reciprocal of the condition number is less than machine precision,
INFO = N+1 is returned as a warning, but the routine still goes on
to solve for X and compute error bounds as described below.
4. The system of equations is solved for X using the factored form
of A.
5. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
6. If equilibration was used, the matrix X is premultiplied by
diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
that it solves the original system before equilibration.
file lapack/complex/cgbsvxx.f
prec complex
CGBSVXX uses the LU factorization to compute the solution to a
complex system of linear equations A * X = B, where A is an
N-by-N matrix and X and B are N-by-NRHS matrices.
If requested, both normwise and maximum componentwise error bounds
are returned. CGBSVXX will return a solution with a tiny
guaranteed error (O(eps) where eps is the working machine
precision) unless the matrix is very ill-conditioned, in which
case a warning is returned. Relevant condition numbers also are
calculated and returned.
CGBSVXX accepts user-provided factorizations and equilibration
factors; see the definitions of the FACT and EQUED options.
Solving with refinement and using a factorization from a previous
CGBSVXX call will also produce a solution with either O(eps)
errors or warnings, but we cannot make that claim for general
user-provided factorizations and equilibration factors if they
differ from what CGBSVXX would itself produce.
Description
===========
The following steps are performed:
1. If FACT = 'E', real scaling factors are computed to equilibrate
the system:
TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B
TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N')
or diag(C)*B (if TRANS = 'T' or 'C').
2. If FACT = 'N' or 'E', the LU decomposition is used to factor
the matrix A (after equilibration if FACT = 'E') as
A = P * L * U,
where P is a permutation matrix, L is a unit lower triangular
matrix, and U is upper triangular.
3. If some U(i,i)=0, so that U is exactly singular, then the
routine returns with INFO = i. Otherwise, the factored form of A
is used to estimate the condition number of the matrix A (see
argument RCOND). If the reciprocal of the condition number is less
than machine precision, the routine still goes on to solve for X
and compute error bounds as described below.
4. The system of equations is solved for X using the factored form
of A.
5. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero),
the routine will use iterative refinement to try to get a small
error and error bounds. Refinement calculates the residual to at
least twice the working precision.
6. If equilibration was used, the matrix X is premultiplied by
diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
that it solves the original system before equilibration.
file lapack/complex/cgeesx.f
prec complex
CGEESX computes for an N-by-N complex nonsymmetric matrix A, the
eigenvalues, the Schur form T, and, optionally, the matrix of Schur
vectors Z. This gives the Schur factorization A = Z*T*(Z**H).
Optionally, it also orders the eigenvalues on the diagonal of the
Schur form so that selected eigenvalues are at the top left;
computes a reciprocal condition number for the average of the
selected eigenvalues (RCONDE); and computes a reciprocal condition
number for the right invariant subspace corresponding to the
selected eigenvalues (RCONDV). The leading columns of Z form an
orthonormal basis for this invariant subspace.
For further explanation of the reciprocal condition numbers RCONDE
and RCONDV, see Section 4.10 of the LAPACK Users' Guide (where
these quantities are called s and sep respectively).
A complex matrix is in Schur form if it is upper triangular.
file lapack/complex/cgeevx.f
prec complex
CGEEVX computes for an N-by-N complex nonsymmetric matrix A, the
eigenvalues and, optionally, the left and/or right eigenvectors.
Optionally also, it computes a balancing transformation to improve
the conditioning of the eigenvalues and eigenvectors (ILO, IHI,
SCALE, and ABNRM), reciprocal condition numbers for the eigenvalues
(RCONDE), and reciprocal condition numbers for the right
eigenvectors (RCONDV).
The right eigenvector v(j) of A satisfies
A * v(j) = lambda(j) * v(j)
where lambda(j) is its eigenvalue.
The left eigenvector u(j) of A satisfies
u(j)**H * A = lambda(j) * u(j)**H
where u(j)**H denotes the conjugate transpose of u(j).
The computed eigenvectors are normalized to have Euclidean norm
equal to 1 and largest component real.
Balancing a matrix means permuting the rows and columns to make it
more nearly upper triangular, and applying a diagonal similarity
transformation D * A * D**(-1), where D is a diagonal matrix, to
make its rows and columns closer in norm and the condition numbers
of its eigenvalues and eigenvectors smaller. The computed
reciprocal condition numbers correspond to the balanced matrix.
Permuting rows and columns will not change the condition numbers
(in exact arithmetic) but diagonal scaling will. For further
explanation of balancing, see section 4.10.2 of the LAPACK
Users' Guide.
file lapack/complex/cgelsx.f
prec complex
This routine is deprecated and has been replaced by routine CGELSY.
CGELSX computes the minimum-norm solution to a complex linear least
squares problem:
minimize || A * X - B ||
using a complete orthogonal factorization of A. A is an M-by-N
matrix which may be rank-deficient.
Several right hand side vectors b and solution vectors x can be
handled in a single call; they are stored as the columns of the
M-by-NRHS right hand side matrix B and the N-by-NRHS solution
matrix X.
The routine first computes a QR factorization with column pivoting:
A * P = Q * [ R11 R12 ]
[ 0 R22 ]
with R11 defined as the largest leading submatrix whose estimated
condition number is less than 1/RCOND. The order of R11, RANK,
is the effective rank of A.
Then, R22 is considered to be negligible, and R12 is annihilated
by unitary transformations from the right, arriving at the
complete orthogonal factorization:
A * P = Q * [ T11 0 ] * Z
[ 0 0 ]
The minimum-norm solution is then
X = P * Z' [ inv(T11)*Q1'*B ]
[ 0 ]
where Q1 consists of the first RANK columns of Q.
file lapack/complex/cgesvx.f
prec complex
CGESVX uses the LU factorization to compute the solution to a complex
system of linear equations
A * X = B,
where A is an N-by-N matrix and X and B are N-by-NRHS matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed:
1. If FACT = 'E', real scaling factors are computed to equilibrate
the system:
TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B
TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N')
or diag(C)*B (if TRANS = 'T' or 'C').
2. If FACT = 'N' or 'E', the LU decomposition is used to factor the
matrix A (after equilibration if FACT = 'E') as
A = P * L * U,
where P is a permutation matrix, L is a unit lower triangular
matrix, and U is upper triangular.
3. If some U(i,i)=0, so that U is exactly singular, then the routine
returns with INFO = i. Otherwise, the factored form of A is used
to estimate the condition number of the matrix A. If the
reciprocal of the condition number is less than machine precision,
INFO = N+1 is returned as a warning, but the routine still goes on
to solve for X and compute error bounds as described below.
4. The system of equations is solved for X using the factored form
of A.
5. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
6. If equilibration was used, the matrix X is premultiplied by
diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
that it solves the original system before equilibration.
file lapack/complex/cgesvxx.f
prec complex
CGESVXX uses the LU factorization to compute the solution to a
complex system of linear equations A * X = B, where A is an
N-by-N matrix and X and B are N-by-NRHS matrices.
If requested, both normwise and maximum componentwise error bounds
are returned. CGESVXX will return a solution with a tiny
guaranteed error (O(eps) where eps is the working machine
precision) unless the matrix is very ill-conditioned, in which
case a warning is returned. Relevant condition numbers also are
calculated and returned.
CGESVXX accepts user-provided factorizations and equilibration
factors; see the definitions of the FACT and EQUED options.
Solving with refinement and using a factorization from a previous
CGESVXX call will also produce a solution with either O(eps)
errors or warnings, but we cannot make that claim for general
user-provided factorizations and equilibration factors if they
differ from what CGESVXX would itself produce.
Description
===========
The following steps are performed:
1. If FACT = 'E', real scaling factors are computed to equilibrate
the system:
TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B
TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N')
or diag(C)*B (if TRANS = 'T' or 'C').
2. If FACT = 'N' or 'E', the LU decomposition is used to factor
the matrix A (after equilibration if FACT = 'E') as
A = P * L * U,
where P is a permutation matrix, L is a unit lower triangular
matrix, and U is upper triangular.
3. If some U(i,i)=0, so that U is exactly singular, then the
routine returns with INFO = i. Otherwise, the factored form of A
is used to estimate the condition number of the matrix A (see
argument RCOND). If the reciprocal of the condition number is less
than machine precision, the routine still goes on to solve for X
and compute error bounds as described below.
4. The system of equations is solved for X using the factored form
of A.
5. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero),
the routine will use iterative refinement to try to get a small
error and error bounds. Refinement calculates the residual to at
least twice the working precision.
6. If equilibration was used, the matrix X is premultiplied by
diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
that it solves the original system before equilibration.
file lapack/complex/cggesx.f
prec complex
CGGESX computes for a pair of N-by-N complex nonsymmetric matrices
(A,B), the generalized eigenvalues, the complex Schur form (S,T),
and, optionally, the left and/or right matrices of Schur vectors (VSL
and VSR). This gives the generalized Schur factorization
(A,B) = ( (VSL) S (VSR)**H, (VSL) T (VSR)**H )
where (VSR)**H is the conjugate-transpose of VSR.
Optionally, it also orders the eigenvalues so that a selected cluster
of eigenvalues appears in the leading diagonal blocks of the upper
triangular matrix S and the upper triangular matrix T; computes
a reciprocal condition number for the average of the selected
eigenvalues (RCONDE); and computes a reciprocal condition number for
the right and left deflating subspaces corresponding to the selected
eigenvalues (RCONDV). The leading columns of VSL and VSR then form
an orthonormal basis for the corresponding left and right eigenspaces
(deflating subspaces).
A generalized eigenvalue for a pair of matrices (A,B) is a scalar w
or a ratio alpha/beta = w, such that A - w*B is singular. It is
usually represented as the pair (alpha,beta), as there is a
reasonable interpretation for beta=0 or for both being zero.
A pair of matrices (S,T) is in generalized complex Schur form if T is
upper triangular with non-negative diagonal and S is upper
triangular.
file lapack/complex/cggevx.f
prec complex
CGGEVX computes for a pair of N-by-N complex nonsymmetric matrices
(A,B) the generalized eigenvalues, and optionally, the left and/or
right generalized eigenvectors.
Optionally, it also computes a balancing transformation to improve
the conditioning of the eigenvalues and eigenvectors (ILO, IHI,
LSCALE, RSCALE, ABNRM, and BBNRM), reciprocal condition numbers for
the eigenvalues (RCONDE), and reciprocal condition numbers for the
right eigenvectors (RCONDV).
A generalized eigenvalue for a pair of matrices (A,B) is a scalar
lambda or a ratio alpha/beta = lambda, such that A - lambda*B is
singular. It is usually represented as the pair (alpha,beta), as
there is a reasonable interpretation for beta=0, and even for both
being zero.
The right eigenvector v(j) corresponding to the eigenvalue lambda(j)
of (A,B) satisfies
A * v(j) = lambda(j) * B * v(j) .
The left eigenvector u(j) corresponding to the eigenvalue lambda(j)
of (A,B) satisfies
u(j)**H * A = lambda(j) * u(j)**H * B.
where u(j)**H is the conjugate-transpose of u(j).
file lapack/complex/chbevx.f
prec complex
CHBEVX computes selected eigenvalues and, optionally, eigenvectors
of a complex Hermitian band matrix A. Eigenvalues and eigenvectors
can be selected by specifying either a range of values or a range of
indices for the desired eigenvalues.
file lapack/complex/chbgvx.f
prec complex
CHBGVX computes all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite banded eigenproblem, of
the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian
and banded, and B is also positive definite. Eigenvalues and
eigenvectors can be selected by specifying either all eigenvalues,
a range of values or a range of indices for the desired eigenvalues.
file lapack/complex/cheevx.f
prec complex
CHEEVX computes selected eigenvalues and, optionally, eigenvectors
of a complex Hermitian matrix A. Eigenvalues and eigenvectors can
be selected by specifying either a range of values or a range of
indices for the desired eigenvalues.
file lapack/complex/chegvx.f
prec complex
CHEGVX computes selected eigenvalues, and optionally, eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be Hermitian and B is also positive definite.
Eigenvalues and eigenvectors can be selected by specifying either a
range of values or a range of indices for the desired eigenvalues.
file lapack/complex/chesvx.f
prec complex
CHESVX uses the diagonal pivoting factorization to compute the
solution to a complex system of linear equations A * X = B,
where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed:
1. If FACT = 'N', the diagonal pivoting method is used to factor A.
The form of the factorization is
A = U * D * U**H, if UPLO = 'U', or
A = L * D * L**H, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and D is Hermitian and block diagonal with
1-by-1 and 2-by-2 diagonal blocks.
2. If some D(i,i)=0, so that D is exactly singular, then the routine
returns with INFO = i. Otherwise, the factored form of A is used
to estimate the condition number of the matrix A. If the
reciprocal of the condition number is less than machine precision,
INFO = N+1 is returned as a warning, but the routine still goes on
to solve for X and compute error bounds as described below.
3. The system of equations is solved for X using the factored form
of A.
4. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
file lapack/complex/chesvxx.f
prec complex
CHESVXX uses the diagonal pivoting factorization to compute the
solution to a complex system of linear equations A * X = B, where
A is an N-by-N symmetric matrix and X and B are N-by-NRHS
matrices.
If requested, both normwise and maximum componentwise error bounds
are returned. CHESVXX will return a solution with a tiny
guaranteed error (O(eps) where eps is the working machine
precision) unless the matrix is very ill-conditioned, in which
case a warning is returned. Relevant condition numbers also are
calculated and returned.
CHESVXX accepts user-provided factorizations and equilibration
factors; see the definitions of the FACT and EQUED options.
Solving with refinement and using a factorization from a previous
CHESVXX call will also produce a solution with either O(eps)
errors or warnings, but we cannot make that claim for general
user-provided factorizations and equilibration factors if they
differ from what CHESVXX would itself produce.
Description
===========
The following steps are performed:
1. If FACT = 'E', real scaling factors are computed to equilibrate
the system:
diag(S)*A*diag(S) *inv(diag(S))*X = diag(S)*B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(S)*A*diag(S) and B by diag(S)*B.
2. If FACT = 'N' or 'E', the LU decomposition is used to factor
the matrix A (after equilibration if FACT = 'E') as
A = U * D * U**T, if UPLO = 'U', or
A = L * D * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and D is symmetric and block diagonal with
1-by-1 and 2-by-2 diagonal blocks.
3. If some D(i,i)=0, so that D is exactly singular, then the
routine returns with INFO = i. Otherwise, the factored form of A
is used to estimate the condition number of the matrix A (see
argument RCOND). If the reciprocal of the condition number is
less than machine precision, the routine still goes on to solve
for X and compute error bounds as described below.
4. The system of equations is solved for X using the factored form
of A.
5. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero),
the routine will use iterative refinement to try to get a small
error and error bounds. Refinement calculates the residual to at
least twice the working precision.
6. If equilibration was used, the matrix X is premultiplied by
diag(R) so that it solves the original system before
equilibration.
file lapack/complex/chpevx.f
prec complex
CHPEVX computes selected eigenvalues and, optionally, eigenvectors
of a complex Hermitian matrix A in packed storage.
Eigenvalues/vectors can be selected by specifying either a range of
values or a range of indices for the desired eigenvalues.
file lapack/complex/chpgvx.f
prec complex
CHPGVX computes selected eigenvalues and, optionally, eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be Hermitian, stored in packed format, and B is also
positive definite. Eigenvalues and eigenvectors can be selected by
specifying either a range of values or a range of indices for the
desired eigenvalues.
file lapack/complex/chpsvx.f
prec complex
CHPSVX uses the diagonal pivoting factorization A = U*D*U**H or
A = L*D*L**H to compute the solution to a complex system of linear
equations A * X = B, where A is an N-by-N Hermitian matrix stored
in packed format and X and B are N-by-NRHS matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed:
1. If FACT = 'N', the diagonal pivoting method is used to factor A as
A = U * D * U**H, if UPLO = 'U', or
A = L * D * L**H, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices and D is Hermitian and block diagonal with
1-by-1 and 2-by-2 diagonal blocks.
2. If some D(i,i)=0, so that D is exactly singular, then the routine
returns with INFO = i. Otherwise, the factored form of A is used
to estimate the condition number of the matrix A. If the
reciprocal of the condition number is less than machine precision,
INFO = N+1 is returned as a warning, but the routine still goes on
to solve for X and compute error bounds as described below.
3. The system of equations is solved for X using the factored form
of A.
4. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
file lapack/complex/cpbsvx.f
prec complex
CPBSVX uses the Cholesky factorization A = U**H*U or A = L*L**H to
compute the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N Hermitian positive definite band matrix and X
and B are N-by-NRHS matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed:
1. If FACT = 'E', real scaling factors are computed to equilibrate
the system:
diag(S) * A * diag(S) * inv(diag(S)) * X = diag(S) * B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(S)*A*diag(S) and B by diag(S)*B.
2. If FACT = 'N' or 'E', the Cholesky decomposition is used to
factor the matrix A (after equilibration if FACT = 'E') as
A = U**H * U, if UPLO = 'U', or
A = L * L**H, if UPLO = 'L',
where U is an upper triangular band matrix, and L is a lower
triangular band matrix.
3. If the leading i-by-i principal minor is not positive definite,
then the routine returns with INFO = i. Otherwise, the factored
form of A is used to estimate the condition number of the matrix
A. If the reciprocal of the condition number is less than machine
precision, INFO = N+1 is returned as a warning, but the routine
still goes on to solve for X and compute error bounds as
described below.
4. The system of equations is solved for X using the factored form
of A.
5. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
6. If equilibration was used, the matrix X is premultiplied by
diag(S) so that it solves the original system before
equilibration.
file lapack/complex/cposvx.f
prec complex
CPOSVX uses the Cholesky factorization A = U**H*U or A = L*L**H to
compute the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N Hermitian positive definite matrix and X and B
are N-by-NRHS matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed:
1. If FACT = 'E', real scaling factors are computed to equilibrate
the system:
diag(S) * A * diag(S) * inv(diag(S)) * X = diag(S) * B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(S)*A*diag(S) and B by diag(S)*B.
2. If FACT = 'N' or 'E', the Cholesky decomposition is used to
factor the matrix A (after equilibration if FACT = 'E') as
A = U**H* U, if UPLO = 'U', or
A = L * L**H, if UPLO = 'L',
where U is an upper triangular matrix and L is a lower triangular
matrix.
3. If the leading i-by-i principal minor is not positive definite,
then the routine returns with INFO = i. Otherwise, the factored
form of A is used to estimate the condition number of the matrix
A. If the reciprocal of the condition number is less than machine
precision, INFO = N+1 is returned as a warning, but the routine
still goes on to solve for X and compute error bounds as
described below.
4. The system of equations is solved for X using the factored form
of A.
5. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
6. If equilibration was used, the matrix X is premultiplied by
diag(S) so that it solves the original system before
equilibration.
file lapack/complex/cposvxx.f
prec complex
CPOSVXX uses the Cholesky factorization A = U**T*U or A = L*L**T
to compute the solution to a complex system of linear equations
A * X = B, where A is an N-by-N symmetric positive definite matrix
and X and B are N-by-NRHS matrices.
If requested, both normwise and maximum componentwise error bounds
are returned. CPOSVXX will return a solution with a tiny
guaranteed error (O(eps) where eps is the working machine
precision) unless the matrix is very ill-conditioned, in which
case a warning is returned. Relevant condition numbers also are
calculated and returned.
CPOSVXX accepts user-provided factorizations and equilibration
factors; see the definitions of the FACT and EQUED options.
Solving with refinement and using a factorization from a previous
CPOSVXX call will also produce a solution with either O(eps)
errors or warnings, but we cannot make that claim for general
user-provided factorizations and equilibration factors if they
differ from what CPOSVXX would itself produce.
Description
===========
The following steps are performed:
1. If FACT = 'E', real scaling factors are computed to equilibrate
the system:
diag(S)*A*diag(S) *inv(diag(S))*X = diag(S)*B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(S)*A*diag(S) and B by diag(S)*B.
2. If FACT = 'N' or 'E', the Cholesky decomposition is used to
factor the matrix A (after equilibration if FACT = 'E') as
A = U**T* U, if UPLO = 'U', or
A = L * L**T, if UPLO = 'L',
where U is an upper triangular matrix and L is a lower triangular
matrix.
3. If the leading i-by-i principal minor is not positive definite,
then the routine returns with INFO = i. Otherwise, the factored
form of A is used to estimate the condition number of the matrix
A (see argument RCOND). If the reciprocal of the condition number
is less than machine precision, the routine still goes on to solve
for X and compute error bounds as described below.
4. The system of equations is solved for X using the factored form
of A.
5. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero),
the routine will use iterative refinement to try to get a small
error and error bounds. Refinement calculates the residual to at
least twice the working precision.
6. If equilibration was used, the matrix X is premultiplied by
diag(S) so that it solves the original system before
equilibration.
file lapack/complex/cppsvx.f
prec complex
CPPSVX uses the Cholesky factorization A = U**H*U or A = L*L**H to
compute the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N Hermitian positive definite matrix stored in
packed format and X and B are N-by-NRHS matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed:
1. If FACT = 'E', real scaling factors are computed to equilibrate
the system:
diag(S) * A * diag(S) * inv(diag(S)) * X = diag(S) * B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(S)*A*diag(S) and B by diag(S)*B.
2. If FACT = 'N' or 'E', the Cholesky decomposition is used to
factor the matrix A (after equilibration if FACT = 'E') as
A = U'* U , if UPLO = 'U', or
A = L * L', if UPLO = 'L',
where U is an upper triangular matrix, L is a lower triangular
matrix, and ' indicates conjugate transpose.
3. If the leading i-by-i principal minor is not positive definite,
then the routine returns with INFO = i. Otherwise, the factored
form of A is used to estimate the condition number of the matrix
A. If the reciprocal of the condition number is less than machine
precision, INFO = N+1 is returned as a warning, but the routine
still goes on to solve for X and compute error bounds as
described below.
4. The system of equations is solved for X using the factored form
of A.
5. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
6. If equilibration was used, the matrix X is premultiplied by
diag(S) so that it solves the original system before
equilibration.
file lapack/complex/cspsvx.f
prec complex
CSPSVX uses the diagonal pivoting factorization A = U*D*U**T or
A = L*D*L**T to compute the solution to a complex system of linear
equations A * X = B, where A is an N-by-N symmetric matrix stored
in packed format and X and B are N-by-NRHS matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed:
1. If FACT = 'N', the diagonal pivoting method is used to factor A as
A = U * D * U**T, if UPLO = 'U', or
A = L * D * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices and D is symmetric and block diagonal with
1-by-1 and 2-by-2 diagonal blocks.
2. If some D(i,i)=0, so that D is exactly singular, then the routine
returns with INFO = i. Otherwise, the factored form of A is used
to estimate the condition number of the matrix A. If the
reciprocal of the condition number is less than machine precision,
INFO = N+1 is returned as a warning, but the routine still goes on
to solve for X and compute error bounds as described below.
3. The system of equations is solved for X using the factored form
of A.
4. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
file lapack/complex/csysvx.f
prec complex
CSYSVX uses the diagonal pivoting factorization to compute the
solution to a complex system of linear equations A * X = B,
where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed:
1. If FACT = 'N', the diagonal pivoting method is used to factor A.
The form of the factorization is
A = U * D * U**T, if UPLO = 'U', or
A = L * D * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and D is symmetric and block diagonal with
1-by-1 and 2-by-2 diagonal blocks.
2. If some D(i,i)=0, so that D is exactly singular, then the routine
returns with INFO = i. Otherwise, the factored form of A is used
to estimate the condition number of the matrix A. If the
reciprocal of the condition number is less than machine precision,
INFO = N+1 is returned as a warning, but the routine still goes on
to solve for X and compute error bounds as described below.
3. The system of equations is solved for X using the factored form
of A.
4. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
file lapack/complex/csysvxx.f
prec complex
CSYSVXX uses the diagonal pivoting factorization to compute the
solution to a complex system of linear equations A * X = B, where
A is an N-by-N symmetric matrix and X and B are N-by-NRHS
matrices.
If requested, both normwise and maximum componentwise error bounds
are returned. CSYSVXX will return a solution with a tiny
guaranteed error (O(eps) where eps is the working machine
precision) unless the matrix is very ill-conditioned, in which
case a warning is returned. Relevant condition numbers also are
calculated and returned.
CSYSVXX accepts user-provided factorizations and equilibration
factors; see the definitions of the FACT and EQUED options.
Solving with refinement and using a factorization from a previous
CSYSVXX call will also produce a solution with either O(eps)
errors or warnings, but we cannot make that claim for general
user-provided factorizations and equilibration factors if they
differ from what CSYSVXX would itself produce.
Description
===========
The following steps are performed:
1. If FACT = 'E', real scaling factors are computed to equilibrate
the system:
diag(S)*A*diag(S) *inv(diag(S))*X = diag(S)*B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(S)*A*diag(S) and B by diag(S)*B.
2. If FACT = 'N' or 'E', the LU decomposition is used to factor
the matrix A (after equilibration if FACT = 'E') as
A = U * D * U**T, if UPLO = 'U', or
A = L * D * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and D is symmetric and block diagonal with
1-by-1 and 2-by-2 diagonal blocks.
3. If some D(i,i)=0, so that D is exactly singular, then the
routine returns with INFO = i. Otherwise, the factored form of A
is used to estimate the condition number of the matrix A (see
argument RCOND). If the reciprocal of the condition number is
less than machine precision, the routine still goes on to solve
for X and compute error bounds as described below.
4. The system of equations is solved for X using the factored form
of A.
5. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero),
the routine will use iterative refinement to try to get a small
error and error bounds. Refinement calculates the residual to at
least twice the working precision.
6. If equilibration was used, the matrix X is premultiplied by
diag(R) so that it solves the original system before
equilibration.
# ---------------------------------
# Available SIMPLE DRIVER routines:
# ---------------------------------
file lapack/complex16/zcgesv.f
prec complex16
ZCGESV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N matrix and X and B are N-by-NRHS matrices.
ZCGESV first attempts to factorize the matrix in COMPLEX and use this
factorization within an iterative refinement procedure to produce a
solution with COMPLEX*16 normwise backward error quality (see below).
If the approach fails the method switches to a COMPLEX*16
factorization and solve.
The iterative refinement is not going to be a winning strategy if
the ratio COMPLEX performance over COMPLEX*16 performance is too
small. A reasonable strategy should take the number of right-hand
sides and the size of the matrix into account. This might be done
with a call to ILAENV in the future. Up to now, we always try
iterative refinement.
The iterative refinement process is stopped if
ITER > ITERMAX
or for all the RHS we have:
RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX
where
o ITER is the number of the current iteration in the iterative
refinement process
o RNRM is the infinity-norm of the residual
o XNRM is the infinity-norm of the solution
o ANRM is the infinity-operator-norm of the matrix A
o EPS is the machine epsilon returned by DLAMCH('Epsilon')
The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00
respectively.
file lapack/complex16/zcposv.f
prec complex16
ZCPOSV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N Hermitian positive definite matrix and X and B
are N-by-NRHS matrices.
ZCPOSV first attempts to factorize the matrix in COMPLEX and use this
factorization within an iterative refinement procedure to produce a
solution with COMPLEX*16 normwise backward error quality (see below).
If the approach fails the method switches to a COMPLEX*16
factorization and solve.
The iterative refinement is not going to be a winning strategy if
the ratio COMPLEX performance over COMPLEX*16 performance is too
small. A reasonable strategy should take the number of right-hand
sides and the size of the matrix into account. This might be done
with a call to ILAENV in the future. Up to now, we always try
iterative refinement.
The iterative refinement process is stopped if
ITER > ITERMAX
or for all the RHS we have:
RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX
where
o ITER is the number of the current iteration in the iterative
refinement process
o RNRM is the infinity-norm of the residual
o XNRM is the infinity-norm of the solution
o ANRM is the infinity-operator-norm of the matrix A
o EPS is the machine epsilon returned by DLAMCH('Epsilon')
The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00
respectively.
file lapack/complex16/zgbsv.f
prec complex16
ZGBSV computes the solution to a complex system of linear equations
A * X = B, where A is a band matrix of order N with KL subdiagonals
and KU superdiagonals, and X and B are N-by-NRHS matrices.
The LU decomposition with partial pivoting and row interchanges is
used to factor A as A = L * U, where L is a product of permutation
and unit lower triangular matrices with KL subdiagonals, and U is
upper triangular with KL+KU superdiagonals. The factored form of A
is then used to solve the system of equations A * X = B.
file lapack/complex16/zgees.f
prec complex16
ZGEES computes for an N-by-N complex nonsymmetric matrix A, the
eigenvalues, the Schur form T, and, optionally, the matrix of Schur
vectors Z. This gives the Schur factorization A = Z*T*(Z**H).
Optionally, it also orders the eigenvalues on the diagonal of the
Schur form so that selected eigenvalues are at the top left.
The leading columns of Z then form an orthonormal basis for the
invariant subspace corresponding to the selected eigenvalues.
A complex matrix is in Schur form if it is upper triangular.
file lapack/complex16/zgeev.f
prec complex16
ZGEEV computes for an N-by-N complex nonsymmetric matrix A, the
eigenvalues and, optionally, the left and/or right eigenvectors.
The right eigenvector v(j) of A satisfies
A * v(j) = lambda(j) * v(j)
where lambda(j) is its eigenvalue.
The left eigenvector u(j) of A satisfies
u(j)**H * A = lambda(j) * u(j)**H
where u(j)**H denotes the conjugate transpose of u(j).
The computed eigenvectors are normalized to have Euclidean norm
equal to 1 and largest component real.
file lapack/complex16/zgegs.f
prec complex16
This routine is deprecated and has been replaced by routine ZGGES.
ZGEGS computes the eigenvalues, Schur form, and, optionally, the
left and or/right Schur vectors of a complex matrix pair (A,B).
Given two square matrices A and B, the generalized Schur
factorization has the form
A = Q*S*Z**H, B = Q*T*Z**H
where Q and Z are unitary matrices and S and T are upper triangular.
The columns of Q are the left Schur vectors
and the columns of Z are the right Schur vectors.
If only the eigenvalues of (A,B) are needed, the driver routine
ZGEGV should be used instead. See ZGEGV for a description of the
eigenvalues of the generalized nonsymmetric eigenvalue problem
(GNEP).
file lapack/complex16/zgegv.f
prec complex16
This routine is deprecated and has been replaced by routine ZGGEV.
ZGEGV computes the eigenvalues and, optionally, the left and/or right
eigenvectors of a complex matrix pair (A,B).
Given two square matrices A and B,
the generalized nonsymmetric eigenvalue problem (GNEP) is to find the
eigenvalues lambda and corresponding (non-zero) eigenvectors x such
that
A*x = lambda*B*x.
An alternate form is to find the eigenvalues mu and corresponding
eigenvectors y such that
mu*A*y = B*y.
These two forms are equivalent with mu = 1/lambda and x = y if
neither lambda nor mu is zero. In order to deal with the case that
lambda or mu is zero or small, two values alpha and beta are returned
for each eigenvalue, such that lambda = alpha/beta and
mu = beta/alpha.
The vectors x and y in the above equations are right eigenvectors of
the matrix pair (A,B). Vectors u and v satisfying
u**H*A = lambda*u**H*B or mu*v**H*A = v**H*B
are left eigenvectors of (A,B).
Note: this routine performs "full balancing" on A and B -- see
"Further Details", below.
file lapack/complex16/zgels.f
prec complex16
ZGELS solves overdetermined or underdetermined complex linear systems
involving an M-by-N matrix A, or its conjugate-transpose, using a QR
or LQ factorization of A. It is assumed that A has full rank.
The following options are provided:
1. If TRANS = 'N' and m >= n: find the least squares solution of
an overdetermined system, i.e., solve the least squares problem
minimize || B - A*X ||.
2. If TRANS = 'N' and m < n: find the minimum norm solution of
an underdetermined system A * X = B.
3. If TRANS = 'C' and m >= n: find the minimum norm solution of
an undetermined system A**H * X = B.
4. If TRANS = 'C' and m < n: find the least squares solution of
an overdetermined system, i.e., solve the least squares problem
minimize || B - A**H * X ||.
Several right hand side vectors b and solution vectors x can be
handled in a single call; they are stored as the columns of the
M-by-NRHS right hand side matrix B and the N-by-NRHS solution
matrix X.
file lapack/complex16/zgelsd.f
prec complex16
ZGELSD computes the minimum-norm solution to a real linear least
squares problem:
minimize 2-norm(| b - A*x |)
using the singular value decomposition (SVD) of A. A is an M-by-N
matrix which may be rank-deficient.
Several right hand side vectors b and solution vectors x can be
handled in a single call; they are stored as the columns of the
M-by-NRHS right hand side matrix B and the N-by-NRHS solution
matrix X.
The problem is solved in three steps:
(1) Reduce the coefficient matrix A to bidiagonal form with
Householder tranformations, reducing the original problem
into a "bidiagonal least squares problem" (BLS)
(2) Solve the BLS using a divide and conquer approach.
(3) Apply back all the Householder tranformations to solve
the original least squares problem.
The effective rank of A is determined by treating as zero those
singular values which are less than RCOND times the largest singular
value.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/complex16/zgelss.f
prec complex16
ZGELSS computes the minimum norm solution to a complex linear
least squares problem:
Minimize 2-norm(| b - A*x |).
using the singular value decomposition (SVD) of A. A is an M-by-N
matrix which may be rank-deficient.
Several right hand side vectors b and solution vectors x can be
handled in a single call; they are stored as the columns of the
M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix
X.
The effective rank of A is determined by treating as zero those
singular values which are less than RCOND times the largest singular
value.
file lapack/complex16/zgelsy.f
prec complex16
ZGELSY computes the minimum-norm solution to a complex linear least
squares problem:
minimize || A * X - B ||
using a complete orthogonal factorization of A. A is an M-by-N
matrix which may be rank-deficient.
Several right hand side vectors b and solution vectors x can be
handled in a single call; they are stored as the columns of the
M-by-NRHS right hand side matrix B and the N-by-NRHS solution
matrix X.
The routine first computes a QR factorization with column pivoting:
A * P = Q * [ R11 R12 ]
[ 0 R22 ]
with R11 defined as the largest leading submatrix whose estimated
condition number is less than 1/RCOND. The order of R11, RANK,
is the effective rank of A.
Then, R22 is considered to be negligible, and R12 is annihilated
by unitary transformations from the right, arriving at the
complete orthogonal factorization:
A * P = Q * [ T11 0 ] * Z
[ 0 0 ]
The minimum-norm solution is then
X = P * Z' [ inv(T11)*Q1'*B ]
[ 0 ]
where Q1 consists of the first RANK columns of Q.
This routine is basically identical to the original xGELSX except
three differences:
o The permutation of matrix B (the right hand side) is faster and
more simple.
o The call to the subroutine xGEQPF has been substituted by the
the call to the subroutine xGEQP3. This subroutine is a Blas-3
version of the QR factorization with column pivoting.
o Matrix B (the right hand side) is updated with Blas-3.
file lapack/complex16/zgesdd.f
prec complex16
ZGESDD computes the singular value decomposition (SVD) of a complex
M-by-N matrix A, optionally computing the left and/or right singular
vectors, by using divide-and-conquer method. The SVD is written
A = U * SIGMA * conjugate-transpose(V)
where SIGMA is an M-by-N matrix which is zero except for its
min(m,n) diagonal elements, U is an M-by-M unitary matrix, and
V is an N-by-N unitary matrix. The diagonal elements of SIGMA
are the singular values of A; they are real and non-negative, and
are returned in descending order. The first min(m,n) columns of
U and V are the left and right singular vectors of A.
Note that the routine returns VT = V**H, not V.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/complex16/zgesv.f
prec complex16
ZGESV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N matrix and X and B are N-by-NRHS matrices.
The LU decomposition with partial pivoting and row interchanges is
used to factor A as
A = P * L * U,
where P is a permutation matrix, L is unit lower triangular, and U is
upper triangular. The factored form of A is then used to solve the
system of equations A * X = B.
file lapack/complex16/zgesvd.f
prec complex16
ZGESVD computes the singular value decomposition (SVD) of a complex
M-by-N matrix A, optionally computing the left and/or right singular
vectors. The SVD is written
A = U * SIGMA * conjugate-transpose(V)
where SIGMA is an M-by-N matrix which is zero except for its
min(m,n) diagonal elements, U is an M-by-M unitary matrix, and
V is an N-by-N unitary matrix. The diagonal elements of SIGMA
are the singular values of A; they are real and non-negative, and
are returned in descending order. The first min(m,n) columns of
U and V are the left and right singular vectors of A.
Note that the routine returns V**H, not V.
file lapack/complex16/zgges.f
prec complex16
ZGGES computes for a pair of N-by-N complex nonsymmetric matrices
(A,B), the generalized eigenvalues, the generalized complex Schur
form (S, T), and optionally left and/or right Schur vectors (VSL
and VSR). This gives the generalized Schur factorization
(A,B) = ( (VSL)*S*(VSR)**H, (VSL)*T*(VSR)**H )
where (VSR)**H is the conjugate-transpose of VSR.
Optionally, it also orders the eigenvalues so that a selected cluster
of eigenvalues appears in the leading diagonal blocks of the upper
triangular matrix S and the upper triangular matrix T. The leading
columns of VSL and VSR then form an unitary basis for the
corresponding left and right eigenspaces (deflating subspaces).
(If only the generalized eigenvalues are needed, use the driver
ZGGEV instead, which is faster.)
A generalized eigenvalue for a pair of matrices (A,B) is a scalar w
or a ratio alpha/beta = w, such that A - w*B is singular. It is
usually represented as the pair (alpha,beta), as there is a
reasonable interpretation for beta=0, and even for both being zero.
A pair of matrices (S,T) is in generalized complex Schur form if S
and T are upper triangular and, in addition, the diagonal elements
of T are non-negative real numbers.
file lapack/complex16/zggev.f
prec complex16
ZGGEV computes for a pair of N-by-N complex nonsymmetric matrices
(A,B), the generalized eigenvalues, and optionally, the left and/or
right generalized eigenvectors.
A generalized eigenvalue for a pair of matrices (A,B) is a scalar
lambda or a ratio alpha/beta = lambda, such that A - lambda*B is
singular. It is usually represented as the pair (alpha,beta), as
there is a reasonable interpretation for beta=0, and even for both
being zero.
The right generalized eigenvector v(j) corresponding to the
generalized eigenvalue lambda(j) of (A,B) satisfies
A * v(j) = lambda(j) * B * v(j).
The left generalized eigenvector u(j) corresponding to the
generalized eigenvalues lambda(j) of (A,B) satisfies
u(j)**H * A = lambda(j) * u(j)**H * B
where u(j)**H is the conjugate-transpose of u(j).
file lapack/complex16/zggglm.f
prec complex16
ZGGGLM solves a general Gauss-Markov linear model (GLM) problem:
minimize || y ||_2 subject to d = A*x + B*y
x
where A is an N-by-M matrix, B is an N-by-P matrix, and d is a
given N-vector. It is assumed that M <= N <= M+P, and
rank(A) = M and rank( A B ) = N.
Under these assumptions, the constrained equation is always
consistent, and there is a unique solution x and a minimal 2-norm
solution y, which is obtained using a generalized QR factorization
of the matrices (A, B) given by
A = Q*(R), B = Q*T*Z.
(0)
In particular, if matrix B is square nonsingular, then the problem
GLM is equivalent to the following weighted linear least squares
problem
minimize || inv(B)*(d-A*x) ||_2
x
where inv(B) denotes the inverse of B.
file lapack/complex16/zgglse.f
prec complex16
ZGGLSE solves the linear equality-constrained least squares (LSE)
problem:
minimize || c - A*x ||_2 subject to B*x = d
where A is an M-by-N matrix, B is a P-by-N matrix, c is a given
M-vector, and d is a given P-vector. It is assumed that
P <= N <= M+P, and
rank(B) = P and rank( ( A ) ) = N.
( ( B ) )
These conditions ensure that the LSE problem has a unique solution,
which is obtained using a generalized RQ factorization of the
matrices (B, A) given by
B = (0 R)*Q, A = Z*T*Q.
file lapack/complex16/zggsvd.f
prec complex16
ZGGSVD computes the generalized singular value decomposition (GSVD)
of an M-by-N complex matrix A and P-by-N complex matrix B:
U'*A*Q = D1*( 0 R ), V'*B*Q = D2*( 0 R )
where U, V and Q are unitary matrices, and Z' means the conjugate
transpose of Z. Let K+L = the effective numerical rank of the
matrix (A',B')', then R is a (K+L)-by-(K+L) nonsingular upper
triangular matrix, D1 and D2 are M-by-(K+L) and P-by-(K+L) "diagonal"
matrices and of the following structures, respectively:
If M-K-L >= 0,
K L
D1 = K ( I 0 )
L ( 0 C )
M-K-L ( 0 0 )
K L
D2 = L ( 0 S )
P-L ( 0 0 )
N-K-L K L
( 0 R ) = K ( 0 R11 R12 )
L ( 0 0 R22 )
where
C = diag( ALPHA(K+1), ... , ALPHA(K+L) ),
S = diag( BETA(K+1), ... , BETA(K+L) ),
C**2 + S**2 = I.
R is stored in A(1:K+L,N-K-L+1:N) on exit.
If M-K-L < 0,
K M-K K+L-M
D1 = K ( I 0 0 )
M-K ( 0 C 0 )
K M-K K+L-M
D2 = M-K ( 0 S 0 )
K+L-M ( 0 0 I )
P-L ( 0 0 0 )
N-K-L K M-K K+L-M
( 0 R ) = K ( 0 R11 R12 R13 )
M-K ( 0 0 R22 R23 )
K+L-M ( 0 0 0 R33 )
where
C = diag( ALPHA(K+1), ... , ALPHA(M) ),
S = diag( BETA(K+1), ... , BETA(M) ),
C**2 + S**2 = I.
(R11 R12 R13 ) is stored in A(1:M, N-K-L+1:N), and R33 is stored
( 0 R22 R23 )
in B(M-K+1:L,N+M-K-L+1:N) on exit.
The routine computes C, S, R, and optionally the unitary
transformation matrices U, V and Q.
In particular, if B is an N-by-N nonsingular matrix, then the GSVD of
A and B implicitly gives the SVD of A*inv(B):
A*inv(B) = U*(D1*inv(D2))*V'.
If ( A',B')' has orthnormal columns, then the GSVD of A and B is also
equal to the CS decomposition of A and B. Furthermore, the GSVD can
be used to derive the solution of the eigenvalue problem:
A'*A x = lambda* B'*B x.
In some literature, the GSVD of A and B is presented in the form
U'*A*X = ( 0 D1 ), V'*B*X = ( 0 D2 )
where U and V are orthogonal and X is nonsingular, and D1 and D2 are
``diagonal''. The former GSVD form can be converted to the latter
form by taking the nonsingular matrix X as
X = Q*( I 0 )
( 0 inv(R) )
file lapack/complex16/zhbev.f
prec complex16
ZHBEV computes all the eigenvalues and, optionally, eigenvectors of
a complex Hermitian band matrix A.
file lapack/complex16/zhbevd.f
prec complex16
ZHBEVD computes all the eigenvalues and, optionally, eigenvectors of
a complex Hermitian band matrix A. If eigenvectors are desired, it
uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/complex16/zhbgv.f
prec complex16
ZHBGV computes all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite banded eigenproblem, of
the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian
and banded, and B is also positive definite.
file lapack/complex16/zhbgvd.f
prec complex16
ZHBGVD computes all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite banded eigenproblem, of
the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian
and banded, and B is also positive definite. If eigenvectors are
desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/complex16/zheev.f
prec complex16
ZHEEV computes all eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A.
file lapack/complex16/zheevd.f
prec complex16
ZHEEVD computes all eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A. If eigenvectors are desired, it uses a
divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/complex16/zheevr.f
prec complex16
ZHEEVR computes selected eigenvalues and, optionally, eigenvectors
of a complex Hermitian matrix A. Eigenvalues and eigenvectors can
be selected by specifying either a range of values or a range of
indices for the desired eigenvalues.
ZHEEVR first reduces the matrix A to tridiagonal form T with a call
to ZHETRD. Then, whenever possible, ZHEEVR calls ZSTEMR to compute
eigenspectrum using Relatively Robust Representations. ZSTEMR
computes eigenvalues by the dqds algorithm, while orthogonal
eigenvectors are computed from various "good" L D L^T representations
(also known as Relatively Robust Representations). Gram-Schmidt
orthogonalization is avoided as far as possible. More specifically,
the various steps of the algorithm are as follows.
For each unreduced block (submatrix) of T,
(a) Compute T - sigma I = L D L^T, so that L and D
define all the wanted eigenvalues to high relative accuracy.
This means that small relative changes in the entries of D and L
cause only small relative changes in the eigenvalues and
eigenvectors. The standard (unfactored) representation of the
tridiagonal matrix T does not have this property in general.
(b) Compute the eigenvalues to suitable accuracy.
If the eigenvectors are desired, the algorithm attains full
accuracy of the computed eigenvalues only right before
the corresponding vectors have to be computed, see steps c) and d).
(c) For each cluster of close eigenvalues, select a new
shift close to the cluster, find a new factorization, and refine
the shifted eigenvalues to suitable accuracy.
(d) For each eigenvalue with a large enough relative separation compute
the corresponding eigenvector by forming a rank revealing twisted
factorization. Go back to (c) for any clusters that remain.
The desired accuracy of the output can be specified by the input
parameter ABSTOL.
For more details, see DSTEMR's documentation and:
- Inderjit S. Dhillon and Beresford N. Parlett: "Multiple representations
to compute orthogonal eigenvectors of symmetric tridiagonal matrices,"
Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004.
- Inderjit Dhillon and Beresford Parlett: "Orthogonal Eigenvectors and
Relative Gaps," SIAM Journal on Matrix Analysis and Applications, Vol. 25,
2004. Also LAPACK Working Note 154.
- Inderjit Dhillon: "A new O(n^2) algorithm for the symmetric
tridiagonal eigenvalue/eigenvector problem",
Computer Science Division Technical Report No. UCB/CSD-97-971,
UC Berkeley, May 1997.
Note 1 : ZHEEVR calls ZSTEMR when the full spectrum is requested
on machines which conform to the ieee-754 floating point standard.
ZHEEVR calls DSTEBZ and ZSTEIN on non-ieee machines and
when partial spectrum requests are made.
Normal execution of ZSTEMR may create NaNs and infinities and
hence may abort due to a floating point exception in environments
which do not handle NaNs and infinities in the ieee standard default
manner.
file lapack/complex16/zhegv.f
prec complex16
ZHEGV computes all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
Here A and B are assumed to be Hermitian and B is also
positive definite.
file lapack/complex16/zhegvd.f
prec complex16
ZHEGVD computes all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be Hermitian and B is also positive definite.
If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/complex16/zhesv.f
prec complex16
ZHESV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
matrices.
The diagonal pivoting method is used to factor A as
A = U * D * U**H, if UPLO = 'U', or
A = L * D * L**H, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and D is Hermitian and block diagonal with
1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then
used to solve the system of equations A * X = B.
file lapack/complex16/zhpev.f
prec complex16
ZHPEV computes all the eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix in packed storage.
file lapack/complex16/zhpevd.f
prec complex16
ZHPEVD computes all the eigenvalues and, optionally, eigenvectors of
a complex Hermitian matrix A in packed storage. If eigenvectors are
desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/complex16/zhpgv.f
prec complex16
ZHPGV computes all the eigenvalues and, optionally, the eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
Here A and B are assumed to be Hermitian, stored in packed format,
and B is also positive definite.
file lapack/complex16/zhpgvd.f
prec complex16
ZHPGVD computes all the eigenvalues and, optionally, the eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be Hermitian, stored in packed format, and B is also
positive definite.
If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/complex16/zhpsv.f
prec complex16
ZHPSV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N Hermitian matrix stored in packed format and X
and B are N-by-NRHS matrices.
The diagonal pivoting method is used to factor A as
A = U * D * U**H, if UPLO = 'U', or
A = L * D * L**H, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, D is Hermitian and block diagonal with 1-by-1
and 2-by-2 diagonal blocks. The factored form of A is then used to
solve the system of equations A * X = B.
file lapack/complex16/zpbsv.f
prec complex16
ZPBSV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N Hermitian positive definite band matrix and X
and B are N-by-NRHS matrices.
The Cholesky decomposition is used to factor A as
A = U**H * U, if UPLO = 'U', or
A = L * L**H, if UPLO = 'L',
where U is an upper triangular band matrix, and L is a lower
triangular band matrix, with the same number of superdiagonals or
subdiagonals as A. The factored form of A is then used to solve the
system of equations A * X = B.
file lapack/complex16/zposv.f
prec complex16
ZPOSV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N Hermitian positive definite matrix and X and B
are N-by-NRHS matrices.
The Cholesky decomposition is used to factor A as
A = U**H* U, if UPLO = 'U', or
A = L * L**H, if UPLO = 'L',
where U is an upper triangular matrix and L is a lower triangular
matrix. The factored form of A is then used to solve the system of
equations A * X = B.
file lapack/complex16/zppsv.f
prec complex16
ZPPSV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N Hermitian positive definite matrix stored in
packed format and X and B are N-by-NRHS matrices.
The Cholesky decomposition is used to factor A as
A = U**H* U, if UPLO = 'U', or
A = L * L**H, if UPLO = 'L',
where U is an upper triangular matrix and L is a lower triangular
matrix. The factored form of A is then used to solve the system of
equations A * X = B.
file lapack/complex16/zspsv.f
prec complex16
ZSPSV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N symmetric matrix stored in packed format and X
and B are N-by-NRHS matrices.
The diagonal pivoting method is used to factor A as
A = U * D * U**T, if UPLO = 'U', or
A = L * D * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, D is symmetric and block diagonal with 1-by-1
and 2-by-2 diagonal blocks. The factored form of A is then used to
solve the system of equations A * X = B.
file lapack/complex16/zstemr.f
prec complex16
ZSTEMR computes selected eigenvalues and, optionally, eigenvectors
of a real symmetric tridiagonal matrix T. Any such unreduced matrix has
a well defined set of pairwise different real eigenvalues, the corresponding
real eigenvectors are pairwise orthogonal.
The spectrum may be computed either completely or partially by specifying
either an interval (VL,VU] or a range of indices IL:IU for the desired
eigenvalues.
Depending on the number of desired eigenvalues, these are computed either
by bisection or the dqds algorithm. Numerically orthogonal eigenvectors are
computed by the use of various suitable L D L^T factorizations near clusters
of close eigenvalues (referred to as RRRs, Relatively Robust
Representations). An informal sketch of the algorithm follows.
For each unreduced block (submatrix) of T,
(a) Compute T - sigma I = L D L^T, so that L and D
define all the wanted eigenvalues to high relative accuracy.
This means that small relative changes in the entries of D and L
cause only small relative changes in the eigenvalues and
eigenvectors. The standard (unfactored) representation of the
tridiagonal matrix T does not have this property in general.
(b) Compute the eigenvalues to suitable accuracy.
If the eigenvectors are desired, the algorithm attains full
accuracy of the computed eigenvalues only right before
the corresponding vectors have to be computed, see steps c) and d).
(c) For each cluster of close eigenvalues, select a new
shift close to the cluster, find a new factorization, and refine
the shifted eigenvalues to suitable accuracy.
(d) For each eigenvalue with a large enough relative separation compute
the corresponding eigenvector by forming a rank revealing twisted
factorization. Go back to (c) for any clusters that remain.
For more details, see:
- Inderjit S. Dhillon and Beresford N. Parlett: "Multiple representations
to compute orthogonal eigenvectors of symmetric tridiagonal matrices,"
Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004.
- Inderjit Dhillon and Beresford Parlett: "Orthogonal Eigenvectors and
Relative Gaps," SIAM Journal on Matrix Analysis and Applications, Vol. 25,
2004. Also LAPACK Working Note 154.
- Inderjit Dhillon: "A new O(n^2) algorithm for the symmetric
tridiagonal eigenvalue/eigenvector problem",
Computer Science Division Technical Report No. UCB/CSD-97-971,
UC Berkeley, May 1997.
Further Details
1.ZSTEMR works only on machines which follow IEEE-754
floating-point standard in their handling of infinities and NaNs.
This permits the use of efficient inner loops avoiding a check for
zero divisors.
2. LAPACK routines can be used to reduce a complex Hermitean matrix to
real symmetric tridiagonal form.
(Any complex Hermitean tridiagonal matrix has real values on its diagonal
and potentially complex numbers on its off-diagonals. By applying a
similarity transform with an appropriate diagonal matrix
diag(1,e^{i \phy_1}, ... , e^{i \phy_{n-1}}), the complex Hermitean
matrix can be transformed into a real symmetric matrix and complex
arithmetic can be entirely avoided.)
While the eigenvectors of the real symmetric tridiagonal matrix are real,
the eigenvectors of original complex Hermitean matrix have complex entries
in general.
Since LAPACK drivers overwrite the matrix data with the eigenvectors,
ZSTEMR accepts complex workspace to facilitate interoperability
with ZUNMTR or ZUPMTR.
file lapack/complex16/zsysv.f
prec complex16
ZSYSV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
matrices.
The diagonal pivoting method is used to factor A as
A = U * D * U**T, if UPLO = 'U', or
A = L * D * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and D is symmetric and block diagonal with
1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then
used to solve the system of equations A * X = B.
# ---------------------------------
# Available EXPERT DRIVER routines:
# ---------------------------------
file lapack/complex16/zgbsvx.f
prec complex16
ZGBSVX uses the LU factorization to compute the solution to a complex
system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
where A is a band matrix of order N with KL subdiagonals and KU
superdiagonals, and X and B are N-by-NRHS matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed by this subroutine:
1. If FACT = 'E', real scaling factors are computed to equilibrate
the system:
TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B
TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N')
or diag(C)*B (if TRANS = 'T' or 'C').
2. If FACT = 'N' or 'E', the LU decomposition is used to factor the
matrix A (after equilibration if FACT = 'E') as
A = L * U,
where L is a product of permutation and unit lower triangular
matrices with KL subdiagonals, and U is upper triangular with
KL+KU superdiagonals.
3. If some U(i,i)=0, so that U is exactly singular, then the routine
returns with INFO = i. Otherwise, the factored form of A is used
to estimate the condition number of the matrix A. If the
reciprocal of the condition number is less than machine precision,
INFO = N+1 is returned as a warning, but the routine still goes on
to solve for X and compute error bounds as described below.
4. The system of equations is solved for X using the factored form
of A.
5. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
6. If equilibration was used, the matrix X is premultiplied by
diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
that it solves the original system before equilibration.
file lapack/complex16/zgbsvxx.f
prec complex16
ZGBSVXX uses the LU factorization to compute the solution to a
complex*16 system of linear equations A * X = B, where A is an
N-by-N matrix and X and B are N-by-NRHS matrices.
If requested, both normwise and maximum componentwise error bounds
are returned. ZGBSVXX will return a solution with a tiny
guaranteed error (O(eps) where eps is the working machine
precision) unless the matrix is very ill-conditioned, in which
case a warning is returned. Relevant condition numbers also are
calculated and returned.
ZGBSVXX accepts user-provided factorizations and equilibration
factors; see the definitions of the FACT and EQUED options.
Solving with refinement and using a factorization from a previous
ZGBSVXX call will also produce a solution with either O(eps)
errors or warnings, but we cannot make that claim for general
user-provided factorizations and equilibration factors if they
differ from what ZGBSVXX would itself produce.
Description
===========
The following steps are performed:
1. If FACT = 'E', double precision scaling factors are computed to equilibrate
the system:
TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B
TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N')
or diag(C)*B (if TRANS = 'T' or 'C').
2. If FACT = 'N' or 'E', the LU decomposition is used to factor
the matrix A (after equilibration if FACT = 'E') as
A = P * L * U,
where P is a permutation matrix, L is a unit lower triangular
matrix, and U is upper triangular.
3. If some U(i,i)=0, so that U is exactly singular, then the
routine returns with INFO = i. Otherwise, the factored form of A
is used to estimate the condition number of the matrix A (see
argument RCOND). If the reciprocal of the condition number is less
than machine precision, the routine still goes on to solve for X
and compute error bounds as described below.
4. The system of equations is solved for X using the factored form
of A.
5. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero),
the routine will use iterative refinement to try to get a small
error and error bounds. Refinement calculates the residual to at
least twice the working precision.
6. If equilibration was used, the matrix X is premultiplied by
diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
that it solves the original system before equilibration.
file lapack/complex16/zgeesx.f
prec complex16
ZGEESX computes for an N-by-N complex nonsymmetric matrix A, the
eigenvalues, the Schur form T, and, optionally, the matrix of Schur
vectors Z. This gives the Schur factorization A = Z*T*(Z**H).
Optionally, it also orders the eigenvalues on the diagonal of the
Schur form so that selected eigenvalues are at the top left;
computes a reciprocal condition number for the average of the
selected eigenvalues (RCONDE); and computes a reciprocal condition
number for the right invariant subspace corresponding to the
selected eigenvalues (RCONDV). The leading columns of Z form an
orthonormal basis for this invariant subspace.
For further explanation of the reciprocal condition numbers RCONDE
and RCONDV, see Section 4.10 of the LAPACK Users' Guide (where
these quantities are called s and sep respectively).
A complex matrix is in Schur form if it is upper triangular.
file lapack/complex16/zgeevx.f
prec complex16
ZGEEVX computes for an N-by-N complex nonsymmetric matrix A, the
eigenvalues and, optionally, the left and/or right eigenvectors.
Optionally also, it computes a balancing transformation to improve
the conditioning of the eigenvalues and eigenvectors (ILO, IHI,
SCALE, and ABNRM), reciprocal condition numbers for the eigenvalues
(RCONDE), and reciprocal condition numbers for the right
eigenvectors (RCONDV).
The right eigenvector v(j) of A satisfies
A * v(j) = lambda(j) * v(j)
where lambda(j) is its eigenvalue.
The left eigenvector u(j) of A satisfies
u(j)**H * A = lambda(j) * u(j)**H
where u(j)**H denotes the conjugate transpose of u(j).
The computed eigenvectors are normalized to have Euclidean norm
equal to 1 and largest component real.
Balancing a matrix means permuting the rows and columns to make it
more nearly upper triangular, and applying a diagonal similarity
transformation D * A * D**(-1), where D is a diagonal matrix, to
make its rows and columns closer in norm and the condition numbers
of its eigenvalues and eigenvectors smaller. The computed
reciprocal condition numbers correspond to the balanced matrix.
Permuting rows and columns will not change the condition numbers
(in exact arithmetic) but diagonal scaling will. For further
explanation of balancing, see section 4.10.2 of the LAPACK
Users' Guide.
file lapack/complex16/zgelsx.f
prec complex16
This routine is deprecated and has been replaced by routine ZGELSY.
ZGELSX computes the minimum-norm solution to a complex linear least
squares problem:
minimize || A * X - B ||
using a complete orthogonal factorization of A. A is an M-by-N
matrix which may be rank-deficient.
Several right hand side vectors b and solution vectors x can be
handled in a single call; they are stored as the columns of the
M-by-NRHS right hand side matrix B and the N-by-NRHS solution
matrix X.
The routine first computes a QR factorization with column pivoting:
A * P = Q * [ R11 R12 ]
[ 0 R22 ]
with R11 defined as the largest leading submatrix whose estimated
condition number is less than 1/RCOND. The order of R11, RANK,
is the effective rank of A.
Then, R22 is considered to be negligible, and R12 is annihilated
by unitary transformations from the right, arriving at the
complete orthogonal factorization:
A * P = Q * [ T11 0 ] * Z
[ 0 0 ]
The minimum-norm solution is then
X = P * Z' [ inv(T11)*Q1'*B ]
[ 0 ]
where Q1 consists of the first RANK columns of Q.
file lapack/complex16/zgesvx.f
prec complex16
ZGESVX uses the LU factorization to compute the solution to a complex
system of linear equations
A * X = B,
where A is an N-by-N matrix and X and B are N-by-NRHS matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed:
1. If FACT = 'E', real scaling factors are computed to equilibrate
the system:
TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B
TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N')
or diag(C)*B (if TRANS = 'T' or 'C').
2. If FACT = 'N' or 'E', the LU decomposition is used to factor the
matrix A (after equilibration if FACT = 'E') as
A = P * L * U,
where P is a permutation matrix, L is a unit lower triangular
matrix, and U is upper triangular.
3. If some U(i,i)=0, so that U is exactly singular, then the routine
returns with INFO = i. Otherwise, the factored form of A is used
to estimate the condition number of the matrix A. If the
reciprocal of the condition number is less than machine precision,
INFO = N+1 is returned as a warning, but the routine still goes on
to solve for X and compute error bounds as described below.
4. The system of equations is solved for X using the factored form
of A.
5. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
6. If equilibration was used, the matrix X is premultiplied by
diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
that it solves the original system before equilibration.
file lapack/complex16/zgesvxx.f
prec complex16
ZGESVXX uses the LU factorization to compute the solution to a
complex*16 system of linear equations A * X = B, where A is an
N-by-N matrix and X and B are N-by-NRHS matrices.
If requested, both normwise and maximum componentwise error bounds
are returned. ZGESVXX will return a solution with a tiny
guaranteed error (O(eps) where eps is the working machine
precision) unless the matrix is very ill-conditioned, in which
case a warning is returned. Relevant condition numbers also are
calculated and returned.
ZGESVXX accepts user-provided factorizations and equilibration
factors; see the definitions of the FACT and EQUED options.
Solving with refinement and using a factorization from a previous
ZGESVXX call will also produce a solution with either O(eps)
errors or warnings, but we cannot make that claim for general
user-provided factorizations and equilibration factors if they
differ from what ZGESVXX would itself produce.
Description
===========
The following steps are performed:
1. If FACT = 'E', double precision scaling factors are computed to equilibrate
the system:
TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B
TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N')
or diag(C)*B (if TRANS = 'T' or 'C').
2. If FACT = 'N' or 'E', the LU decomposition is used to factor
the matrix A (after equilibration if FACT = 'E') as
A = P * L * U,
where P is a permutation matrix, L is a unit lower triangular
matrix, and U is upper triangular.
3. If some U(i,i)=0, so that U is exactly singular, then the
routine returns with INFO = i. Otherwise, the factored form of A
is used to estimate the condition number of the matrix A (see
argument RCOND). If the reciprocal of the condition number is less
than machine precision, the routine still goes on to solve for X
and compute error bounds as described below.
4. The system of equations is solved for X using the factored form
of A.
5. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero),
the routine will use iterative refinement to try to get a small
error and error bounds. Refinement calculates the residual to at
least twice the working precision.
6. If equilibration was used, the matrix X is premultiplied by
diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
that it solves the original system before equilibration.
file lapack/complex16/zggesx.f
prec complex16
ZGGESX computes for a pair of N-by-N complex nonsymmetric matrices
(A,B), the generalized eigenvalues, the complex Schur form (S,T),
and, optionally, the left and/or right matrices of Schur vectors (VSL
and VSR). This gives the generalized Schur factorization
(A,B) = ( (VSL) S (VSR)**H, (VSL) T (VSR)**H )
where (VSR)**H is the conjugate-transpose of VSR.
Optionally, it also orders the eigenvalues so that a selected cluster
of eigenvalues appears in the leading diagonal blocks of the upper
triangular matrix S and the upper triangular matrix T; computes
a reciprocal condition number for the average of the selected
eigenvalues (RCONDE); and computes a reciprocal condition number for
the right and left deflating subspaces corresponding to the selected
eigenvalues (RCONDV). The leading columns of VSL and VSR then form
an orthonormal basis for the corresponding left and right eigenspaces
(deflating subspaces).
A generalized eigenvalue for a pair of matrices (A,B) is a scalar w
or a ratio alpha/beta = w, such that A - w*B is singular. It is
usually represented as the pair (alpha,beta), as there is a
reasonable interpretation for beta=0 or for both being zero.
A pair of matrices (S,T) is in generalized complex Schur form if T is
upper triangular with non-negative diagonal and S is upper
triangular.
file lapack/complex16/zggevx.f
prec complex16
ZGGEVX computes for a pair of N-by-N complex nonsymmetric matrices
(A,B) the generalized eigenvalues, and optionally, the left and/or
right generalized eigenvectors.
Optionally, it also computes a balancing transformation to improve
the conditioning of the eigenvalues and eigenvectors (ILO, IHI,
LSCALE, RSCALE, ABNRM, and BBNRM), reciprocal condition numbers for
the eigenvalues (RCONDE), and reciprocal condition numbers for the
right eigenvectors (RCONDV).
A generalized eigenvalue for a pair of matrices (A,B) is a scalar
lambda or a ratio alpha/beta = lambda, such that A - lambda*B is
singular. It is usually represented as the pair (alpha,beta), as
there is a reasonable interpretation for beta=0, and even for both
being zero.
The right eigenvector v(j) corresponding to the eigenvalue lambda(j)
of (A,B) satisfies
A * v(j) = lambda(j) * B * v(j) .
The left eigenvector u(j) corresponding to the eigenvalue lambda(j)
of (A,B) satisfies
u(j)**H * A = lambda(j) * u(j)**H * B.
where u(j)**H is the conjugate-transpose of u(j).
file lapack/complex16/zhbevx.f
prec complex16
ZHBEVX computes selected eigenvalues and, optionally, eigenvectors
of a complex Hermitian band matrix A. Eigenvalues and eigenvectors
can be selected by specifying either a range of values or a range of
indices for the desired eigenvalues.
file lapack/complex16/zhbgvx.f
prec complex16
ZHBGVX computes all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite banded eigenproblem, of
the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian
and banded, and B is also positive definite. Eigenvalues and
eigenvectors can be selected by specifying either all eigenvalues,
a range of values or a range of indices for the desired eigenvalues.
file lapack/complex16/zheevx.f
prec complex16
ZHEEVX computes selected eigenvalues and, optionally, eigenvectors
of a complex Hermitian matrix A. Eigenvalues and eigenvectors can
be selected by specifying either a range of values or a range of
indices for the desired eigenvalues.
file lapack/complex16/zhegvx.f
prec complex16
ZHEGVX computes selected eigenvalues, and optionally, eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be Hermitian and B is also positive definite.
Eigenvalues and eigenvectors can be selected by specifying either a
range of values or a range of indices for the desired eigenvalues.
file lapack/complex16/zhesvx.f
prec complex16
ZHESVX uses the diagonal pivoting factorization to compute the
solution to a complex system of linear equations A * X = B,
where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed:
1. If FACT = 'N', the diagonal pivoting method is used to factor A.
The form of the factorization is
A = U * D * U**H, if UPLO = 'U', or
A = L * D * L**H, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and D is Hermitian and block diagonal with
1-by-1 and 2-by-2 diagonal blocks.
2. If some D(i,i)=0, so that D is exactly singular, then the routine
returns with INFO = i. Otherwise, the factored form of A is used
to estimate the condition number of the matrix A. If the
reciprocal of the condition number is less than machine precision,
INFO = N+1 is returned as a warning, but the routine still goes on
to solve for X and compute error bounds as described below.
3. The system of equations is solved for X using the factored form
of A.
4. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
file lapack/complex16/zhesvxx.f
prec complex16
ZHESVXX uses the diagonal pivoting factorization to compute the
solution to a complex*16 system of linear equations A * X = B, where
A is an N-by-N symmetric matrix and X and B are N-by-NRHS
matrices.
If requested, both normwise and maximum componentwise error bounds
are returned. ZHESVXX will return a solution with a tiny
guaranteed error (O(eps) where eps is the working machine
precision) unless the matrix is very ill-conditioned, in which
case a warning is returned. Relevant condition numbers also are
calculated and returned.
ZHESVXX accepts user-provided factorizations and equilibration
factors; see the definitions of the FACT and EQUED options.
Solving with refinement and using a factorization from a previous
ZHESVXX call will also produce a solution with either O(eps)
errors or warnings, but we cannot make that claim for general
user-provided factorizations and equilibration factors if they
differ from what ZHESVXX would itself produce.
Description
===========
The following steps are performed:
1. If FACT = 'E', double precision scaling factors are computed to equilibrate
the system:
diag(S)*A*diag(S) *inv(diag(S))*X = diag(S)*B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(S)*A*diag(S) and B by diag(S)*B.
2. If FACT = 'N' or 'E', the LU decomposition is used to factor
the matrix A (after equilibration if FACT = 'E') as
A = U * D * U**T, if UPLO = 'U', or
A = L * D * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and D is symmetric and block diagonal with
1-by-1 and 2-by-2 diagonal blocks.
3. If some D(i,i)=0, so that D is exactly singular, then the
routine returns with INFO = i. Otherwise, the factored form of A
is used to estimate the condition number of the matrix A (see
argument RCOND). If the reciprocal of the condition number is
less than machine precision, the routine still goes on to solve
for X and compute error bounds as described below.
4. The system of equations is solved for X using the factored form
of A.
5. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero),
the routine will use iterative refinement to try to get a small
error and error bounds. Refinement calculates the residual to at
least twice the working precision.
6. If equilibration was used, the matrix X is premultiplied by
diag(R) so that it solves the original system before
equilibration.
file lapack/complex16/zhpevx.f
prec complex16
ZHPEVX computes selected eigenvalues and, optionally, eigenvectors
of a complex Hermitian matrix A in packed storage.
Eigenvalues/vectors can be selected by specifying either a range of
values or a range of indices for the desired eigenvalues.
file lapack/complex16/zhpgvx.f
prec complex16
ZHPGVX computes selected eigenvalues and, optionally, eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be Hermitian, stored in packed format, and B is also
positive definite. Eigenvalues and eigenvectors can be selected by
specifying either a range of values or a range of indices for the
desired eigenvalues.
file lapack/complex16/zhpsvx.f
prec complex16
ZHPSVX uses the diagonal pivoting factorization A = U*D*U**H or
A = L*D*L**H to compute the solution to a complex system of linear
equations A * X = B, where A is an N-by-N Hermitian matrix stored
in packed format and X and B are N-by-NRHS matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed:
1. If FACT = 'N', the diagonal pivoting method is used to factor A as
A = U * D * U**H, if UPLO = 'U', or
A = L * D * L**H, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices and D is Hermitian and block diagonal with
1-by-1 and 2-by-2 diagonal blocks.
2. If some D(i,i)=0, so that D is exactly singular, then the routine
returns with INFO = i. Otherwise, the factored form of A is used
to estimate the condition number of the matrix A. If the
reciprocal of the condition number is less than machine precision,
INFO = N+1 is returned as a warning, but the routine still goes on
to solve for X and compute error bounds as described below.
3. The system of equations is solved for X using the factored form
of A.
4. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
file lapack/complex16/zpbsvx.f
prec complex16
ZPBSVX uses the Cholesky factorization A = U**H*U or A = L*L**H to
compute the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N Hermitian positive definite band matrix and X
and B are N-by-NRHS matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed:
1. If FACT = 'E', real scaling factors are computed to equilibrate
the system:
diag(S) * A * diag(S) * inv(diag(S)) * X = diag(S) * B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(S)*A*diag(S) and B by diag(S)*B.
2. If FACT = 'N' or 'E', the Cholesky decomposition is used to
factor the matrix A (after equilibration if FACT = 'E') as
A = U**H * U, if UPLO = 'U', or
A = L * L**H, if UPLO = 'L',
where U is an upper triangular band matrix, and L is a lower
triangular band matrix.
3. If the leading i-by-i principal minor is not positive definite,
then the routine returns with INFO = i. Otherwise, the factored
form of A is used to estimate the condition number of the matrix
A. If the reciprocal of the condition number is less than machine
precision, INFO = N+1 is returned as a warning, but the routine
still goes on to solve for X and compute error bounds as
described below.
4. The system of equations is solved for X using the factored form
of A.
5. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
6. If equilibration was used, the matrix X is premultiplied by
diag(S) so that it solves the original system before
equilibration.
file lapack/complex16/zposvx.f
prec complex16
ZPOSVX uses the Cholesky factorization A = U**H*U or A = L*L**H to
compute the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N Hermitian positive definite matrix and X and B
are N-by-NRHS matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed:
1. If FACT = 'E', real scaling factors are computed to equilibrate
the system:
diag(S) * A * diag(S) * inv(diag(S)) * X = diag(S) * B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(S)*A*diag(S) and B by diag(S)*B.
2. If FACT = 'N' or 'E', the Cholesky decomposition is used to
factor the matrix A (after equilibration if FACT = 'E') as
A = U**H* U, if UPLO = 'U', or
A = L * L**H, if UPLO = 'L',
where U is an upper triangular matrix and L is a lower triangular
matrix.
3. If the leading i-by-i principal minor is not positive definite,
then the routine returns with INFO = i. Otherwise, the factored
form of A is used to estimate the condition number of the matrix
A. If the reciprocal of the condition number is less than machine
precision, INFO = N+1 is returned as a warning, but the routine
still goes on to solve for X and compute error bounds as
described below.
4. The system of equations is solved for X using the factored form
of A.
5. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
6. If equilibration was used, the matrix X is premultiplied by
diag(S) so that it solves the original system before
equilibration.
file lapack/complex16/zposvxx.f
prec complex16
ZPOSVXX uses the Cholesky factorization A = U**T*U or A = L*L**T
to compute the solution to a complex*16 system of linear equations
A * X = B, where A is an N-by-N symmetric positive definite matrix
and X and B are N-by-NRHS matrices.
If requested, both normwise and maximum componentwise error bounds
are returned. ZPOSVXX will return a solution with a tiny
guaranteed error (O(eps) where eps is the working machine
precision) unless the matrix is very ill-conditioned, in which
case a warning is returned. Relevant condition numbers also are
calculated and returned.
ZPOSVXX accepts user-provided factorizations and equilibration
factors; see the definitions of the FACT and EQUED options.
Solving with refinement and using a factorization from a previous
ZPOSVXX call will also produce a solution with either O(eps)
errors or warnings, but we cannot make that claim for general
user-provided factorizations and equilibration factors if they
differ from what ZPOSVXX would itself produce.
Description
===========
The following steps are performed:
1. If FACT = 'E', double precision scaling factors are computed to equilibrate
the system:
diag(S)*A*diag(S) *inv(diag(S))*X = diag(S)*B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(S)*A*diag(S) and B by diag(S)*B.
2. If FACT = 'N' or 'E', the Cholesky decomposition is used to
factor the matrix A (after equilibration if FACT = 'E') as
A = U**T* U, if UPLO = 'U', or
A = L * L**T, if UPLO = 'L',
where U is an upper triangular matrix and L is a lower triangular
matrix.
3. If the leading i-by-i principal minor is not positive definite,
then the routine returns with INFO = i. Otherwise, the factored
form of A is used to estimate the condition number of the matrix
A (see argument RCOND). If the reciprocal of the condition number
is less than machine precision, the routine still goes on to solve
for X and compute error bounds as described below.
4. The system of equations is solved for X using the factored form
of A.
5. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero),
the routine will use iterative refinement to try to get a small
error and error bounds. Refinement calculates the residual to at
least twice the working precision.
6. If equilibration was used, the matrix X is premultiplied by
diag(S) so that it solves the original system before
equilibration.
file lapack/complex16/zppsvx.f
prec complex16
ZPPSVX uses the Cholesky factorization A = U**H*U or A = L*L**H to
compute the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N Hermitian positive definite matrix stored in
packed format and X and B are N-by-NRHS matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed:
1. If FACT = 'E', real scaling factors are computed to equilibrate
the system:
diag(S) * A * diag(S) * inv(diag(S)) * X = diag(S) * B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(S)*A*diag(S) and B by diag(S)*B.
2. If FACT = 'N' or 'E', the Cholesky decomposition is used to
factor the matrix A (after equilibration if FACT = 'E') as
A = U'* U , if UPLO = 'U', or
A = L * L', if UPLO = 'L',
where U is an upper triangular matrix, L is a lower triangular
matrix, and ' indicates conjugate transpose.
3. If the leading i-by-i principal minor is not positive definite,
then the routine returns with INFO = i. Otherwise, the factored
form of A is used to estimate the condition number of the matrix
A. If the reciprocal of the condition number is less than machine
precision, INFO = N+1 is returned as a warning, but the routine
still goes on to solve for X and compute error bounds as
described below.
4. The system of equations is solved for X using the factored form
of A.
5. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
6. If equilibration was used, the matrix X is premultiplied by
diag(S) so that it solves the original system before
equilibration.
file lapack/complex16/zspsvx.f
prec complex16
ZSPSVX uses the diagonal pivoting factorization A = U*D*U**T or
A = L*D*L**T to compute the solution to a complex system of linear
equations A * X = B, where A is an N-by-N symmetric matrix stored
in packed format and X and B are N-by-NRHS matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed:
1. If FACT = 'N', the diagonal pivoting method is used to factor A as
A = U * D * U**T, if UPLO = 'U', or
A = L * D * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices and D is symmetric and block diagonal with
1-by-1 and 2-by-2 diagonal blocks.
2. If some D(i,i)=0, so that D is exactly singular, then the routine
returns with INFO = i. Otherwise, the factored form of A is used
to estimate the condition number of the matrix A. If the
reciprocal of the condition number is less than machine precision,
INFO = N+1 is returned as a warning, but the routine still goes on
to solve for X and compute error bounds as described below.
3. The system of equations is solved for X using the factored form
of A.
4. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
file lapack/complex16/zsysvx.f
prec complex16
ZSYSVX uses the diagonal pivoting factorization to compute the
solution to a complex system of linear equations A * X = B,
where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed:
1. If FACT = 'N', the diagonal pivoting method is used to factor A.
The form of the factorization is
A = U * D * U**T, if UPLO = 'U', or
A = L * D * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and D is symmetric and block diagonal with
1-by-1 and 2-by-2 diagonal blocks.
2. If some D(i,i)=0, so that D is exactly singular, then the routine
returns with INFO = i. Otherwise, the factored form of A is used
to estimate the condition number of the matrix A. If the
reciprocal of the condition number is less than machine precision,
INFO = N+1 is returned as a warning, but the routine still goes on
to solve for X and compute error bounds as described below.
3. The system of equations is solved for X using the factored form
of A.
4. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
file lapack/complex16/zsysvxx.f
prec complex16
ZSYSVXX uses the diagonal pivoting factorization to compute the
solution to a complex*16 system of linear equations A * X = B, where
A is an N-by-N symmetric matrix and X and B are N-by-NRHS
matrices.
If requested, both normwise and maximum componentwise error bounds
are returned. ZSYSVXX will return a solution with a tiny
guaranteed error (O(eps) where eps is the working machine
precision) unless the matrix is very ill-conditioned, in which
case a warning is returned. Relevant condition numbers also are
calculated and returned.
ZSYSVXX accepts user-provided factorizations and equilibration
factors; see the definitions of the FACT and EQUED options.
Solving with refinement and using a factorization from a previous
ZSYSVXX call will also produce a solution with either O(eps)
errors or warnings, but we cannot make that claim for general
user-provided factorizations and equilibration factors if they
differ from what ZSYSVXX would itself produce.
Description
===========
The following steps are performed:
1. If FACT = 'E', double precision scaling factors are computed to equilibrate
the system:
diag(S)*A*diag(S) *inv(diag(S))*X = diag(S)*B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(S)*A*diag(S) and B by diag(S)*B.
2. If FACT = 'N' or 'E', the LU decomposition is used to factor
the matrix A (after equilibration if FACT = 'E') as
A = U * D * U**T, if UPLO = 'U', or
A = L * D * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and D is symmetric and block diagonal with
1-by-1 and 2-by-2 diagonal blocks.
3. If some D(i,i)=0, so that D is exactly singular, then the
routine returns with INFO = i. Otherwise, the factored form of A
is used to estimate the condition number of the matrix A (see
argument RCOND). If the reciprocal of the condition number is
less than machine precision, the routine still goes on to solve
for X and compute error bounds as described below.
4. The system of equations is solved for X using the factored form
of A.
5. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero),
the routine will use iterative refinement to try to get a small
error and error bounds. Refinement calculates the residual to at
least twice the working precision.
6. If equilibration was used, the matrix X is premultiplied by
diag(R) so that it solves the original system before
equilibration.
# ---------------------------------
# Available SIMPLE DRIVER routines:
# ---------------------------------
file lapack/double/dgbsv.f
prec double
DGBSV computes the solution to a real system of linear equations
A * X = B, where A is a band matrix of order N with KL subdiagonals
and KU superdiagonals, and X and B are N-by-NRHS matrices.
The LU decomposition with partial pivoting and row interchanges is
used to factor A as A = L * U, where L is a product of permutation
and unit lower triangular matrices with KL subdiagonals, and U is
upper triangular with KL+KU superdiagonals. The factored form of A
is then used to solve the system of equations A * X = B.
file lapack/double/dgees.f
prec double
DGEES computes for an N-by-N real nonsymmetric matrix A, the
eigenvalues, the real Schur form T, and, optionally, the matrix of
Schur vectors Z. This gives the Schur factorization A = Z*T*(Z**T).
Optionally, it also orders the eigenvalues on the diagonal of the
real Schur form so that selected eigenvalues are at the top left.
The leading columns of Z then form an orthonormal basis for the
invariant subspace corresponding to the selected eigenvalues.
A matrix is in real Schur form if it is upper quasi-triangular with
1-by-1 and 2-by-2 blocks. 2-by-2 blocks will be standardized in the
form
[ a b ]
[ c a ]
where b*c < 0. The eigenvalues of such a block are a +- sqrt(bc).
file lapack/double/dgeev.f
prec double
DGEEV computes for an N-by-N real nonsymmetric matrix A, the
eigenvalues and, optionally, the left and/or right eigenvectors.
The right eigenvector v(j) of A satisfies
A * v(j) = lambda(j) * v(j)
where lambda(j) is its eigenvalue.
The left eigenvector u(j) of A satisfies
u(j)**H * A = lambda(j) * u(j)**H
where u(j)**H denotes the conjugate transpose of u(j).
The computed eigenvectors are normalized to have Euclidean norm
equal to 1 and largest component real.
file lapack/double/dgegs.f
prec double
This routine is deprecated and has been replaced by routine DGGES.
DGEGS computes the eigenvalues, real Schur form, and, optionally,
left and or/right Schur vectors of a real matrix pair (A,B).
Given two square matrices A and B, the generalized real Schur
factorization has the form
A = Q*S*Z**T, B = Q*T*Z**T
where Q and Z are orthogonal matrices, T is upper triangular, and S
is an upper quasi-triangular matrix with 1-by-1 and 2-by-2 diagonal
blocks, the 2-by-2 blocks corresponding to complex conjugate pairs
of eigenvalues of (A,B). The columns of Q are the left Schur vectors
and the columns of Z are the right Schur vectors.
If only the eigenvalues of (A,B) are needed, the driver routine
DGEGV should be used instead. See DGEGV for a description of the
eigenvalues of the generalized nonsymmetric eigenvalue problem
(GNEP).
file lapack/double/dgegv.f
prec double
This routine is deprecated and has been replaced by routine DGGEV.
DGEGV computes the eigenvalues and, optionally, the left and/or right
eigenvectors of a real matrix pair (A,B).
Given two square matrices A and B,
the generalized nonsymmetric eigenvalue problem (GNEP) is to find the
eigenvalues lambda and corresponding (non-zero) eigenvectors x such
that
A*x = lambda*B*x.
An alternate form is to find the eigenvalues mu and corresponding
eigenvectors y such that
mu*A*y = B*y.
These two forms are equivalent with mu = 1/lambda and x = y if
neither lambda nor mu is zero. In order to deal with the case that
lambda or mu is zero or small, two values alpha and beta are returned
for each eigenvalue, such that lambda = alpha/beta and
mu = beta/alpha.
The vectors x and y in the above equations are right eigenvectors of
the matrix pair (A,B). Vectors u and v satisfying
u**H*A = lambda*u**H*B or mu*v**H*A = v**H*B
are left eigenvectors of (A,B).
Note: this routine performs "full balancing" on A and B -- see
"Further Details", below.
file lapack/double/dgels.f
prec double
DGELS solves overdetermined or underdetermined real linear systems
involving an M-by-N matrix A, or its transpose, using a QR or LQ
factorization of A. It is assumed that A has full rank.
The following options are provided:
1. If TRANS = 'N' and m >= n: find the least squares solution of
an overdetermined system, i.e., solve the least squares problem
minimize || B - A*X ||.
2. If TRANS = 'N' and m < n: find the minimum norm solution of
an underdetermined system A * X = B.
3. If TRANS = 'T' and m >= n: find the minimum norm solution of
an undetermined system A**T * X = B.
4. If TRANS = 'T' and m < n: find the least squares solution of
an overdetermined system, i.e., solve the least squares problem
minimize || B - A**T * X ||.
Several right hand side vectors b and solution vectors x can be
handled in a single call; they are stored as the columns of the
M-by-NRHS right hand side matrix B and the N-by-NRHS solution
matrix X.
file lapack/double/dgelsd.f
prec double
DGELSD computes the minimum-norm solution to a real linear least
squares problem:
minimize 2-norm(| b - A*x |)
using the singular value decomposition (SVD) of A. A is an M-by-N
matrix which may be rank-deficient.
Several right hand side vectors b and solution vectors x can be
handled in a single call; they are stored as the columns of the
M-by-NRHS right hand side matrix B and the N-by-NRHS solution
matrix X.
The problem is solved in three steps:
(1) Reduce the coefficient matrix A to bidiagonal form with
Householder transformations, reducing the original problem
into a "bidiagonal least squares problem" (BLS)
(2) Solve the BLS using a divide and conquer approach.
(3) Apply back all the Householder tranformations to solve
the original least squares problem.
The effective rank of A is determined by treating as zero those
singular values which are less than RCOND times the largest singular
value.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/double/dgelss.f
prec double
DGELSS computes the minimum norm solution to a real linear least
squares problem:
Minimize 2-norm(| b - A*x |).
using the singular value decomposition (SVD) of A. A is an M-by-N
matrix which may be rank-deficient.
Several right hand side vectors b and solution vectors x can be
handled in a single call; they are stored as the columns of the
M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix
X.
The effective rank of A is determined by treating as zero those
singular values which are less than RCOND times the largest singular
value.
file lapack/double/dgelsy.f
prec double
DGELSY computes the minimum-norm solution to a real linear least
squares problem:
minimize || A * X - B ||
using a complete orthogonal factorization of A. A is an M-by-N
matrix which may be rank-deficient.
Several right hand side vectors b and solution vectors x can be
handled in a single call; they are stored as the columns of the
M-by-NRHS right hand side matrix B and the N-by-NRHS solution
matrix X.
The routine first computes a QR factorization with column pivoting:
A * P = Q * [ R11 R12 ]
[ 0 R22 ]
with R11 defined as the largest leading submatrix whose estimated
condition number is less than 1/RCOND. The order of R11, RANK,
is the effective rank of A.
Then, R22 is considered to be negligible, and R12 is annihilated
by orthogonal transformations from the right, arriving at the
complete orthogonal factorization:
A * P = Q * [ T11 0 ] * Z
[ 0 0 ]
The minimum-norm solution is then
X = P * Z' [ inv(T11)*Q1'*B ]
[ 0 ]
where Q1 consists of the first RANK columns of Q.
This routine is basically identical to the original xGELSX except
three differences:
o The call to the subroutine xGEQPF has been substituted by the
the call to the subroutine xGEQP3. This subroutine is a Blas-3
version of the QR factorization with column pivoting.
o Matrix B (the right hand side) is updated with Blas-3.
o The permutation of matrix B (the right hand side) is faster and
more simple.
file lapack/double/dgesdd.f
prec double
DGESDD computes the singular value decomposition (SVD) of a real
M-by-N matrix A, optionally computing the left and right singular
vectors. If singular vectors are desired, it uses a
divide-and-conquer algorithm.
The SVD is written
A = U * SIGMA * transpose(V)
where SIGMA is an M-by-N matrix which is zero except for its
min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and
V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA
are the singular values of A; they are real and non-negative, and
are returned in descending order. The first min(m,n) columns of
U and V are the left and right singular vectors of A.
Note that the routine returns VT = V**T, not V.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/double/dgesv.f
prec double
DGESV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N matrix and X and B are N-by-NRHS matrices.
The LU decomposition with partial pivoting and row interchanges is
used to factor A as
A = P * L * U,
where P is a permutation matrix, L is unit lower triangular, and U is
upper triangular. The factored form of A is then used to solve the
system of equations A * X = B.
file lapack/double/dgesvd.f
prec double
DGESVD computes the singular value decomposition (SVD) of a real
M-by-N matrix A, optionally computing the left and/or right singular
vectors. The SVD is written
A = U * SIGMA * transpose(V)
where SIGMA is an M-by-N matrix which is zero except for its
min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and
V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA
are the singular values of A; they are real and non-negative, and
are returned in descending order. The first min(m,n) columns of
U and V are the left and right singular vectors of A.
Note that the routine returns V**T, not V.
file lapack/double/dgges.f
prec double
DGGES computes for a pair of N-by-N real nonsymmetric matrices (A,B),
the generalized eigenvalues, the generalized real Schur form (S,T),
optionally, the left and/or right matrices of Schur vectors (VSL and
VSR). This gives the generalized Schur factorization
(A,B) = ( (VSL)*S*(VSR)**T, (VSL)*T*(VSR)**T )
Optionally, it also orders the eigenvalues so that a selected cluster
of eigenvalues appears in the leading diagonal blocks of the upper
quasi-triangular matrix S and the upper triangular matrix T.The
leading columns of VSL and VSR then form an orthonormal basis for the
corresponding left and right eigenspaces (deflating subspaces).
(If only the generalized eigenvalues are needed, use the driver
DGGEV instead, which is faster.)
A generalized eigenvalue for a pair of matrices (A,B) is a scalar w
or a ratio alpha/beta = w, such that A - w*B is singular. It is
usually represented as the pair (alpha,beta), as there is a
reasonable interpretation for beta=0 or both being zero.
A pair of matrices (S,T) is in generalized real Schur form if T is
upper triangular with non-negative diagonal and S is block upper
triangular with 1-by-1 and 2-by-2 blocks. 1-by-1 blocks correspond
to real generalized eigenvalues, while 2-by-2 blocks of S will be
"standardized" by making the corresponding elements of T have the
form:
[ a 0 ]
[ 0 b ]
and the pair of corresponding 2-by-2 blocks in S and T will have a
complex conjugate pair of generalized eigenvalues.
file lapack/double/dggev.f
prec double
DGGEV computes for a pair of N-by-N real nonsymmetric matrices (A,B)
the generalized eigenvalues, and optionally, the left and/or right
generalized eigenvectors.
A generalized eigenvalue for a pair of matrices (A,B) is a scalar
lambda or a ratio alpha/beta = lambda, such that A - lambda*B is
singular. It is usually represented as the pair (alpha,beta), as
there is a reasonable interpretation for beta=0, and even for both
being zero.
The right eigenvector v(j) corresponding to the eigenvalue lambda(j)
of (A,B) satisfies
A * v(j) = lambda(j) * B * v(j).
The left eigenvector u(j) corresponding to the eigenvalue lambda(j)
of (A,B) satisfies
u(j)**H * A = lambda(j) * u(j)**H * B .
where u(j)**H is the conjugate-transpose of u(j).
file lapack/double/dggglm.f
prec double
DGGGLM solves a general Gauss-Markov linear model (GLM) problem:
minimize || y ||_2 subject to d = A*x + B*y
x
where A is an N-by-M matrix, B is an N-by-P matrix, and d is a
given N-vector. It is assumed that M <= N <= M+P, and
rank(A) = M and rank( A B ) = N.
Under these assumptions, the constrained equation is always
consistent, and there is a unique solution x and a minimal 2-norm
solution y, which is obtained using a generalized QR factorization
of the matrices (A, B) given by
A = Q*(R), B = Q*T*Z.
(0)
In particular, if matrix B is square nonsingular, then the problem
GLM is equivalent to the following weighted linear least squares
problem
minimize || inv(B)*(d-A*x) ||_2
x
where inv(B) denotes the inverse of B.
file lapack/double/dgglse.f
prec double
DGGLSE solves the linear equality-constrained least squares (LSE)
problem:
minimize || c - A*x ||_2 subject to B*x = d
where A is an M-by-N matrix, B is a P-by-N matrix, c is a given
M-vector, and d is a given P-vector. It is assumed that
P <= N <= M+P, and
rank(B) = P and rank( (A) ) = N.
( (B) )
These conditions ensure that the LSE problem has a unique solution,
which is obtained using a generalized RQ factorization of the
matrices (B, A) given by
B = (0 R)*Q, A = Z*T*Q.
file lapack/double/dggsvd.f
prec double
DGGSVD computes the generalized singular value decomposition (GSVD)
of an M-by-N real matrix A and P-by-N real matrix B:
U'*A*Q = D1*( 0 R ), V'*B*Q = D2*( 0 R )
where U, V and Q are orthogonal matrices, and Z' is the transpose
of Z. Let K+L = the effective numerical rank of the matrix (A',B')',
then R is a K+L-by-K+L nonsingular upper triangular matrix, D1 and
D2 are M-by-(K+L) and P-by-(K+L) "diagonal" matrices and of the
following structures, respectively:
If M-K-L >= 0,
K L
D1 = K ( I 0 )
L ( 0 C )
M-K-L ( 0 0 )
K L
D2 = L ( 0 S )
P-L ( 0 0 )
N-K-L K L
( 0 R ) = K ( 0 R11 R12 )
L ( 0 0 R22 )
where
C = diag( ALPHA(K+1), ... , ALPHA(K+L) ),
S = diag( BETA(K+1), ... , BETA(K+L) ),
C**2 + S**2 = I.
R is stored in A(1:K+L,N-K-L+1:N) on exit.
If M-K-L < 0,
K M-K K+L-M
D1 = K ( I 0 0 )
M-K ( 0 C 0 )
K M-K K+L-M
D2 = M-K ( 0 S 0 )
K+L-M ( 0 0 I )
P-L ( 0 0 0 )
N-K-L K M-K K+L-M
( 0 R ) = K ( 0 R11 R12 R13 )
M-K ( 0 0 R22 R23 )
K+L-M ( 0 0 0 R33 )
where
C = diag( ALPHA(K+1), ... , ALPHA(M) ),
S = diag( BETA(K+1), ... , BETA(M) ),
C**2 + S**2 = I.
(R11 R12 R13 ) is stored in A(1:M, N-K-L+1:N), and R33 is stored
( 0 R22 R23 )
in B(M-K+1:L,N+M-K-L+1:N) on exit.
The routine computes C, S, R, and optionally the orthogonal
transformation matrices U, V and Q.
In particular, if B is an N-by-N nonsingular matrix, then the GSVD of
A and B implicitly gives the SVD of A*inv(B):
A*inv(B) = U*(D1*inv(D2))*V'.
If ( A',B')' has orthonormal columns, then the GSVD of A and B is
also equal to the CS decomposition of A and B. Furthermore, the GSVD
can be used to derive the solution of the eigenvalue problem:
A'*A x = lambda* B'*B x.
In some literature, the GSVD of A and B is presented in the form
U'*A*X = ( 0 D1 ), V'*B*X = ( 0 D2 )
where U and V are orthogonal and X is nonsingular, D1 and D2 are
``diagonal''. The former GSVD form can be converted to the latter
form by taking the nonsingular matrix X as
X = Q*( I 0 )
( 0 inv(R) ).
file lapack/double/dpbsv.f
prec double
DPBSV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric positive definite band matrix and X
and B are N-by-NRHS matrices.
The Cholesky decomposition is used to factor A as
A = U**T * U, if UPLO = 'U', or
A = L * L**T, if UPLO = 'L',
where U is an upper triangular band matrix, and L is a lower
triangular band matrix, with the same number of superdiagonals or
subdiagonals as A. The factored form of A is then used to solve the
system of equations A * X = B.
file lapack/double/dposv.f
prec double
DPOSV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric positive definite matrix and X and B
are N-by-NRHS matrices.
The Cholesky decomposition is used to factor A as
A = U**T* U, if UPLO = 'U', or
A = L * L**T, if UPLO = 'L',
where U is an upper triangular matrix and L is a lower triangular
matrix. The factored form of A is then used to solve the system of
equations A * X = B.
file lapack/double/dppsv.f
prec double
DPPSV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric positive definite matrix stored in
packed format and X and B are N-by-NRHS matrices.
The Cholesky decomposition is used to factor A as
A = U**T* U, if UPLO = 'U', or
A = L * L**T, if UPLO = 'L',
where U is an upper triangular matrix and L is a lower triangular
matrix. The factored form of A is then used to solve the system of
equations A * X = B.
file lapack/double/dsbev.f
prec double
DSBEV computes all the eigenvalues and, optionally, eigenvectors of
a real symmetric band matrix A.
file lapack/double/dsbevd.f
prec double
DSBEVD computes all the eigenvalues and, optionally, eigenvectors of
a real symmetric band matrix A. If eigenvectors are desired, it uses
a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/double/dsbgv.f
prec double
DSBGV computes all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite banded eigenproblem, of
the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric
and banded, and B is also positive definite.
file lapack/double/dsbgvd.f
prec double
DSBGVD computes all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite banded eigenproblem, of the
form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric and
banded, and B is also positive definite. If eigenvectors are
desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/double/dsgesv.f
prec double
DSGESV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N matrix and X and B are N-by-NRHS matrices.
DSGESV first attempts to factorize the matrix in SINGLE PRECISION
and use this factorization within an iterative refinement procedure
to produce a solution with DOUBLE PRECISION normwise backward error
quality (see below). If the approach fails the method switches to a
DOUBLE PRECISION factorization and solve.
The iterative refinement is not going to be a winning strategy if
the ratio SINGLE PRECISION performance over DOUBLE PRECISION
performance is too small. A reasonable strategy should take the
number of right-hand sides and the size of the matrix into account.
This might be done with a call to ILAENV in the future. Up to now, we
always try iterative refinement.
The iterative refinement process is stopped if
ITER > ITERMAX
or for all the RHS we have:
RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX
where
o ITER is the number of the current iteration in the iterative
refinement process
o RNRM is the infinity-norm of the residual
o XNRM is the infinity-norm of the solution
o ANRM is the infinity-operator-norm of the matrix A
o EPS is the machine epsilon returned by DLAMCH('Epsilon')
The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00
respectively.
file lapack/double/dspev.f
prec double
DSPEV computes all the eigenvalues and, optionally, eigenvectors of a
real symmetric matrix A in packed storage.
file lapack/double/dspevd.f
prec double
DSPEVD computes all the eigenvalues and, optionally, eigenvectors
of a real symmetric matrix A in packed storage. If eigenvectors are
desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/double/dspgv.f
prec double
DSPGV computes all the eigenvalues and, optionally, the eigenvectors
of a real generalized symmetric-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
Here A and B are assumed to be symmetric, stored in packed format,
and B is also positive definite.
file lapack/double/dspgvd.f
prec double
DSPGVD computes all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be symmetric, stored in packed format, and B is also
positive definite.
If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/double/dsposv.f
prec double
DSPOSV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric positive definite matrix and X and B
are N-by-NRHS matrices.
DSPOSV first attempts to factorize the matrix in SINGLE PRECISION
and use this factorization within an iterative refinement procedure
to produce a solution with DOUBLE PRECISION normwise backward error
quality (see below). If the approach fails the method switches to a
DOUBLE PRECISION factorization and solve.
The iterative refinement is not going to be a winning strategy if
the ratio SINGLE PRECISION performance over DOUBLE PRECISION
performance is too small. A reasonable strategy should take the
number of right-hand sides and the size of the matrix into account.
This might be done with a call to ILAENV in the future. Up to now, we
always try iterative refinement.
The iterative refinement process is stopped if
ITER > ITERMAX
or for all the RHS we have:
RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX
where
o ITER is the number of the current iteration in the iterative
refinement process
o RNRM is the infinity-norm of the residual
o XNRM is the infinity-norm of the solution
o ANRM is the infinity-operator-norm of the matrix A
o EPS is the machine epsilon returned by DLAMCH('Epsilon')
The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00
respectively.
file lapack/double/dspsv.f
prec double
DSPSV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric matrix stored in packed format and X
and B are N-by-NRHS matrices.
The diagonal pivoting method is used to factor A as
A = U * D * U**T, if UPLO = 'U', or
A = L * D * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, D is symmetric and block diagonal with 1-by-1
and 2-by-2 diagonal blocks. The factored form of A is then used to
solve the system of equations A * X = B.
file lapack/double/dstedc.f
prec double
DSTEDC computes all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the divide and conquer method.
The eigenvectors of a full or band real symmetric matrix can also be
found if DSYTRD or DSPTRD or DSBTRD has been used to reduce this
matrix to tridiagonal form.
This code makes very mild assumptions about floating point
arithmetic. It will work on machines with a guard digit in
add/subtract, or on those binary machines without guard digits
which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none. See DLAED3 for details.
file lapack/double/dstev.f
prec double
DSTEV computes all eigenvalues and, optionally, eigenvectors of a
real symmetric tridiagonal matrix A.
file lapack/double/dstevd.f
prec double
DSTEVD computes all eigenvalues and, optionally, eigenvectors of a
real symmetric tridiagonal matrix. If eigenvectors are desired, it
uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/double/dstevr.f
prec double
DSTEVR computes selected eigenvalues and, optionally, eigenvectors
of a real symmetric tridiagonal matrix T. Eigenvalues and
eigenvectors can be selected by specifying either a range of values
or a range of indices for the desired eigenvalues.
Whenever possible, DSTEVR calls DSTEMR to compute the
eigenspectrum using Relatively Robust Representations. DSTEMR
computes eigenvalues by the dqds algorithm, while orthogonal
eigenvectors are computed from various "good" L D L^T representations
(also known as Relatively Robust Representations). Gram-Schmidt
orthogonalization is avoided as far as possible. More specifically,
the various steps of the algorithm are as follows. For the i-th
unreduced block of T,
(a) Compute T - sigma_i = L_i D_i L_i^T, such that L_i D_i L_i^T
is a relatively robust representation,
(b) Compute the eigenvalues, lambda_j, of L_i D_i L_i^T to high
relative accuracy by the dqds algorithm,
(c) If there is a cluster of close eigenvalues, "choose" sigma_i
close to the cluster, and go to step (a),
(d) Given the approximate eigenvalue lambda_j of L_i D_i L_i^T,
compute the corresponding eigenvector by forming a
rank-revealing twisted factorization.
The desired accuracy of the output can be specified by the input
parameter ABSTOL.
For more details, see "A new O(n^2) algorithm for the symmetric
tridiagonal eigenvalue/eigenvector problem", by Inderjit Dhillon,
Computer Science Division Technical Report No. UCB//CSD-97-971,
UC Berkeley, May 1997.
Note 1 : DSTEVR calls DSTEMR when the full spectrum is requested
on machines which conform to the ieee-754 floating point standard.
DSTEVR calls DSTEBZ and DSTEIN on non-ieee machines and
when partial spectrum requests are made.
Normal execution of DSTEMR may create NaNs and infinities and
hence may abort due to a floating point exception in environments
which do not handle NaNs and infinities in the ieee standard default
manner.
file lapack/double/dsyev.f
prec double
DSYEV computes all eigenvalues and, optionally, eigenvectors of a
real symmetric matrix A.
file lapack/double/dsyevd.f
prec double
DSYEVD computes all eigenvalues and, optionally, eigenvectors of a
real symmetric matrix A. If eigenvectors are desired, it uses a
divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Because of large use of BLAS of level 3, DSYEVD needs N**2 more
workspace than DSYEVX.
file lapack/double/dsyevr.f
prec double
DSYEVR computes selected eigenvalues and, optionally, eigenvectors
of a real symmetric matrix A. Eigenvalues and eigenvectors can be
selected by specifying either a range of values or a range of
indices for the desired eigenvalues.
DSYEVR first reduces the matrix A to tridiagonal form T with a call
to DSYTRD. Then, whenever possible, DSYEVR calls DSTEMR to compute
the eigenspectrum using Relatively Robust Representations. DSTEMR
computes eigenvalues by the dqds algorithm, while orthogonal
eigenvectors are computed from various "good" L D L^T representations
(also known as Relatively Robust Representations). Gram-Schmidt
orthogonalization is avoided as far as possible. More specifically,
the various steps of the algorithm are as follows.
For each unreduced block (submatrix) of T,
(a) Compute T - sigma I = L D L^T, so that L and D
define all the wanted eigenvalues to high relative accuracy.
This means that small relative changes in the entries of D and L
cause only small relative changes in the eigenvalues and
eigenvectors. The standard (unfactored) representation of the
tridiagonal matrix T does not have this property in general.
(b) Compute the eigenvalues to suitable accuracy.
If the eigenvectors are desired, the algorithm attains full
accuracy of the computed eigenvalues only right before
the corresponding vectors have to be computed, see steps c) and d).
(c) For each cluster of close eigenvalues, select a new
shift close to the cluster, find a new factorization, and refine
the shifted eigenvalues to suitable accuracy.
(d) For each eigenvalue with a large enough relative separation compute
the corresponding eigenvector by forming a rank revealing twisted
factorization. Go back to (c) for any clusters that remain.
The desired accuracy of the output can be specified by the input
parameter ABSTOL.
For more details, see DSTEMR's documentation and:
- Inderjit S. Dhillon and Beresford N. Parlett: "Multiple representations
to compute orthogonal eigenvectors of symmetric tridiagonal matrices,"
Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004.
- Inderjit Dhillon and Beresford Parlett: "Orthogonal Eigenvectors and
Relative Gaps," SIAM Journal on Matrix Analysis and Applications, Vol. 25,
2004. Also LAPACK Working Note 154.
- Inderjit Dhillon: "A new O(n^2) algorithm for the symmetric
tridiagonal eigenvalue/eigenvector problem",
Computer Science Division Technical Report No. UCB/CSD-97-971,
UC Berkeley, May 1997.
Note 1 : DSYEVR calls DSTEMR when the full spectrum is requested
on machines which conform to the ieee-754 floating point standard.
DSYEVR calls DSTEBZ and SSTEIN on non-ieee machines and
when partial spectrum requests are made.
Normal execution of DSTEMR may create NaNs and infinities and
hence may abort due to a floating point exception in environments
which do not handle NaNs and infinities in the ieee standard default
manner.
file lapack/double/dsygv.f
prec double
DSYGV computes all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
Here A and B are assumed to be symmetric and B is also
positive definite.
file lapack/double/dsygvd.f
prec double
DSYGVD computes all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be symmetric and B is also positive definite.
If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/double/dsysv.f
prec double
DSYSV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
matrices.
The diagonal pivoting method is used to factor A as
A = U * D * U**T, if UPLO = 'U', or
A = L * D * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and D is symmetric and block diagonal with
1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then
used to solve the system of equations A * X = B.
# ---------------------------------
# Available EXPERT DRIVER routines:
# ---------------------------------
file lapack/double/dgbsvx.f
prec double
DGBSVX uses the LU factorization to compute the solution to a real
system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
where A is a band matrix of order N with KL subdiagonals and KU
superdiagonals, and X and B are N-by-NRHS matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed by this subroutine:
1. If FACT = 'E', real scaling factors are computed to equilibrate
the system:
TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B
TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N')
or diag(C)*B (if TRANS = 'T' or 'C').
2. If FACT = 'N' or 'E', the LU decomposition is used to factor the
matrix A (after equilibration if FACT = 'E') as
A = L * U,
where L is a product of permutation and unit lower triangular
matrices with KL subdiagonals, and U is upper triangular with
KL+KU superdiagonals.
3. If some U(i,i)=0, so that U is exactly singular, then the routine
returns with INFO = i. Otherwise, the factored form of A is used
to estimate the condition number of the matrix A. If the
reciprocal of the condition number is less than machine precision,
INFO = N+1 is returned as a warning, but the routine still goes on
to solve for X and compute error bounds as described below.
4. The system of equations is solved for X using the factored form
of A.
5. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
6. If equilibration was used, the matrix X is premultiplied by
diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
that it solves the original system before equilibration.
file lapack/double/dgbsvxx.f
prec double
DGBSVXX uses the LU factorization to compute the solution to a
double precision system of linear equations A * X = B, where A is an
N-by-N matrix and X and B are N-by-NRHS matrices.
If requested, both normwise and maximum componentwise error bounds
are returned. DGBSVXX will return a solution with a tiny
guaranteed error (O(eps) where eps is the working machine
precision) unless the matrix is very ill-conditioned, in which
case a warning is returned. Relevant condition numbers also are
calculated and returned.
DGBSVXX accepts user-provided factorizations and equilibration
factors; see the definitions of the FACT and EQUED options.
Solving with refinement and using a factorization from a previous
DGBSVXX call will also produce a solution with either O(eps)
errors or warnings, but we cannot make that claim for general
user-provided factorizations and equilibration factors if they
differ from what DGBSVXX would itself produce.
Description
===========
The following steps are performed:
1. If FACT = 'E', double precision scaling factors are computed to equilibrate
the system:
TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B
TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N')
or diag(C)*B (if TRANS = 'T' or 'C').
2. If FACT = 'N' or 'E', the LU decomposition is used to factor
the matrix A (after equilibration if FACT = 'E') as
A = P * L * U,
where P is a permutation matrix, L is a unit lower triangular
matrix, and U is upper triangular.
3. If some U(i,i)=0, so that U is exactly singular, then the
routine returns with INFO = i. Otherwise, the factored form of A
is used to estimate the condition number of the matrix A (see
argument RCOND). If the reciprocal of the condition number is less
than machine precision, the routine still goes on to solve for X
and compute error bounds as described below.
4. The system of equations is solved for X using the factored form
of A.
5. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero),
the routine will use iterative refinement to try to get a small
error and error bounds. Refinement calculates the residual to at
least twice the working precision.
6. If equilibration was used, the matrix X is premultiplied by
diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
that it solves the original system before equilibration.
file lapack/double/dgeesx.f
prec double
DGEESX computes for an N-by-N real nonsymmetric matrix A, the
eigenvalues, the real Schur form T, and, optionally, the matrix of
Schur vectors Z. This gives the Schur factorization A = Z*T*(Z**T).
Optionally, it also orders the eigenvalues on the diagonal of the
real Schur form so that selected eigenvalues are at the top left;
computes a reciprocal condition number for the average of the
selected eigenvalues (RCONDE); and computes a reciprocal condition
number for the right invariant subspace corresponding to the
selected eigenvalues (RCONDV). The leading columns of Z form an
orthonormal basis for this invariant subspace.
For further explanation of the reciprocal condition numbers RCONDE
and RCONDV, see Section 4.10 of the LAPACK Users' Guide (where
these quantities are called s and sep respectively).
A real matrix is in real Schur form if it is upper quasi-triangular
with 1-by-1 and 2-by-2 blocks. 2-by-2 blocks will be standardized in
the form
[ a b ]
[ c a ]
where b*c < 0. The eigenvalues of such a block are a +- sqrt(bc).
file lapack/double/dgeevx.f
prec double
DGEEVX computes for an N-by-N real nonsymmetric matrix A, the
eigenvalues and, optionally, the left and/or right eigenvectors.
Optionally also, it computes a balancing transformation to improve
the conditioning of the eigenvalues and eigenvectors (ILO, IHI,
SCALE, and ABNRM), reciprocal condition numbers for the eigenvalues
(RCONDE), and reciprocal condition numbers for the right
eigenvectors (RCONDV).
The right eigenvector v(j) of A satisfies
A * v(j) = lambda(j) * v(j)
where lambda(j) is its eigenvalue.
The left eigenvector u(j) of A satisfies
u(j)**H * A = lambda(j) * u(j)**H
where u(j)**H denotes the conjugate transpose of u(j).
The computed eigenvectors are normalized to have Euclidean norm
equal to 1 and largest component real.
Balancing a matrix means permuting the rows and columns to make it
more nearly upper triangular, and applying a diagonal similarity
transformation D * A * D**(-1), where D is a diagonal matrix, to
make its rows and columns closer in norm and the condition numbers
of its eigenvalues and eigenvectors smaller. The computed
reciprocal condition numbers correspond to the balanced matrix.
Permuting rows and columns will not change the condition numbers
(in exact arithmetic) but diagonal scaling will. For further
explanation of balancing, see section 4.10.2 of the LAPACK
Users' Guide.
file lapack/double/dgelsx.f
prec double
This routine is deprecated and has been replaced by routine DGELSY.
DGELSX computes the minimum-norm solution to a real linear least
squares problem:
minimize || A * X - B ||
using a complete orthogonal factorization of A. A is an M-by-N
matrix which may be rank-deficient.
Several right hand side vectors b and solution vectors x can be
handled in a single call; they are stored as the columns of the
M-by-NRHS right hand side matrix B and the N-by-NRHS solution
matrix X.
The routine first computes a QR factorization with column pivoting:
A * P = Q * [ R11 R12 ]
[ 0 R22 ]
with R11 defined as the largest leading submatrix whose estimated
condition number is less than 1/RCOND. The order of R11, RANK,
is the effective rank of A.
Then, R22 is considered to be negligible, and R12 is annihilated
by orthogonal transformations from the right, arriving at the
complete orthogonal factorization:
A * P = Q * [ T11 0 ] * Z
[ 0 0 ]
The minimum-norm solution is then
X = P * Z' [ inv(T11)*Q1'*B ]
[ 0 ]
where Q1 consists of the first RANK columns of Q.
file lapack/double/dgesvx.f
prec double
DGESVX uses the LU factorization to compute the solution to a real
system of linear equations
A * X = B,
where A is an N-by-N matrix and X and B are N-by-NRHS matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed:
1. If FACT = 'E', real scaling factors are computed to equilibrate
the system:
TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B
TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N')
or diag(C)*B (if TRANS = 'T' or 'C').
2. If FACT = 'N' or 'E', the LU decomposition is used to factor the
matrix A (after equilibration if FACT = 'E') as
A = P * L * U,
where P is a permutation matrix, L is a unit lower triangular
matrix, and U is upper triangular.
3. If some U(i,i)=0, so that U is exactly singular, then the routine
returns with INFO = i. Otherwise, the factored form of A is used
to estimate the condition number of the matrix A. If the
reciprocal of the condition number is less than machine precision,
INFO = N+1 is returned as a warning, but the routine still goes on
to solve for X and compute error bounds as described below.
4. The system of equations is solved for X using the factored form
of A.
5. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
6. If equilibration was used, the matrix X is premultiplied by
diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
that it solves the original system before equilibration.
file lapack/double/dgesvxx.f
prec double
DGESVXX uses the LU factorization to compute the solution to a
double precision system of linear equations A * X = B, where A is an
N-by-N matrix and X and B are N-by-NRHS matrices.
If requested, both normwise and maximum componentwise error bounds
are returned. DGESVXX will return a solution with a tiny
guaranteed error (O(eps) where eps is the working machine
precision) unless the matrix is very ill-conditioned, in which
case a warning is returned. Relevant condition numbers also are
calculated and returned.
DGESVXX accepts user-provided factorizations and equilibration
factors; see the definitions of the FACT and EQUED options.
Solving with refinement and using a factorization from a previous
DGESVXX call will also produce a solution with either O(eps)
errors or warnings, but we cannot make that claim for general
user-provided factorizations and equilibration factors if they
differ from what DGESVXX would itself produce.
Description
===========
The following steps are performed:
1. If FACT = 'E', double precision scaling factors are computed to equilibrate
the system:
TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B
TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N')
or diag(C)*B (if TRANS = 'T' or 'C').
2. If FACT = 'N' or 'E', the LU decomposition is used to factor
the matrix A (after equilibration if FACT = 'E') as
A = P * L * U,
where P is a permutation matrix, L is a unit lower triangular
matrix, and U is upper triangular.
3. If some U(i,i)=0, so that U is exactly singular, then the
routine returns with INFO = i. Otherwise, the factored form of A
is used to estimate the condition number of the matrix A (see
argument RCOND). If the reciprocal of the condition number is less
than machine precision, the routine still goes on to solve for X
and compute error bounds as described below.
4. The system of equations is solved for X using the factored form
of A.
5. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero),
the routine will use iterative refinement to try to get a small
error and error bounds. Refinement calculates the residual to at
least twice the working precision.
6. If equilibration was used, the matrix X is premultiplied by
diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
that it solves the original system before equilibration.
file lapack/double/dggesx.f
prec double
DGGESX computes for a pair of N-by-N real nonsymmetric matrices
(A,B), the generalized eigenvalues, the real Schur form (S,T), and,
optionally, the left and/or right matrices of Schur vectors (VSL and
VSR). This gives the generalized Schur factorization
(A,B) = ( (VSL) S (VSR)**T, (VSL) T (VSR)**T )
Optionally, it also orders the eigenvalues so that a selected cluster
of eigenvalues appears in the leading diagonal blocks of the upper
quasi-triangular matrix S and the upper triangular matrix T; computes
a reciprocal condition number for the average of the selected
eigenvalues (RCONDE); and computes a reciprocal condition number for
the right and left deflating subspaces corresponding to the selected
eigenvalues (RCONDV). The leading columns of VSL and VSR then form
an orthonormal basis for the corresponding left and right eigenspaces
(deflating subspaces).
A generalized eigenvalue for a pair of matrices (A,B) is a scalar w
or a ratio alpha/beta = w, such that A - w*B is singular. It is
usually represented as the pair (alpha,beta), as there is a
reasonable interpretation for beta=0 or for both being zero.
A pair of matrices (S,T) is in generalized real Schur form if T is
upper triangular with non-negative diagonal and S is block upper
triangular with 1-by-1 and 2-by-2 blocks. 1-by-1 blocks correspond
to real generalized eigenvalues, while 2-by-2 blocks of S will be
"standardized" by making the corresponding elements of T have the
form:
[ a 0 ]
[ 0 b ]
and the pair of corresponding 2-by-2 blocks in S and T will have a
complex conjugate pair of generalized eigenvalues.
file lapack/double/dggevx.f
prec double
DGGEVX computes for a pair of N-by-N real nonsymmetric matrices (A,B)
the generalized eigenvalues, and optionally, the left and/or right
generalized eigenvectors.
Optionally also, it computes a balancing transformation to improve
the conditioning of the eigenvalues and eigenvectors (ILO, IHI,
LSCALE, RSCALE, ABNRM, and BBNRM), reciprocal condition numbers for
the eigenvalues (RCONDE), and reciprocal condition numbers for the
right eigenvectors (RCONDV).
A generalized eigenvalue for a pair of matrices (A,B) is a scalar
lambda or a ratio alpha/beta = lambda, such that A - lambda*B is
singular. It is usually represented as the pair (alpha,beta), as
there is a reasonable interpretation for beta=0, and even for both
being zero.
The right eigenvector v(j) corresponding to the eigenvalue lambda(j)
of (A,B) satisfies
A * v(j) = lambda(j) * B * v(j) .
The left eigenvector u(j) corresponding to the eigenvalue lambda(j)
of (A,B) satisfies
u(j)**H * A = lambda(j) * u(j)**H * B.
where u(j)**H is the conjugate-transpose of u(j).
file lapack/double/dpbsvx.f
prec double
DPBSVX uses the Cholesky factorization A = U**T*U or A = L*L**T to
compute the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric positive definite band matrix and X
and B are N-by-NRHS matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed:
1. If FACT = 'E', real scaling factors are computed to equilibrate
the system:
diag(S) * A * diag(S) * inv(diag(S)) * X = diag(S) * B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(S)*A*diag(S) and B by diag(S)*B.
2. If FACT = 'N' or 'E', the Cholesky decomposition is used to
factor the matrix A (after equilibration if FACT = 'E') as
A = U**T * U, if UPLO = 'U', or
A = L * L**T, if UPLO = 'L',
where U is an upper triangular band matrix, and L is a lower
triangular band matrix.
3. If the leading i-by-i principal minor is not positive definite,
then the routine returns with INFO = i. Otherwise, the factored
form of A is used to estimate the condition number of the matrix
A. If the reciprocal of the condition number is less than machine
precision, INFO = N+1 is returned as a warning, but the routine
still goes on to solve for X and compute error bounds as
described below.
4. The system of equations is solved for X using the factored form
of A.
5. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
6. If equilibration was used, the matrix X is premultiplied by
diag(S) so that it solves the original system before
equilibration.
file lapack/double/dposvx.f
prec double
DPOSVX uses the Cholesky factorization A = U**T*U or A = L*L**T to
compute the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric positive definite matrix and X and B
are N-by-NRHS matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed:
1. If FACT = 'E', real scaling factors are computed to equilibrate
the system:
diag(S) * A * diag(S) * inv(diag(S)) * X = diag(S) * B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(S)*A*diag(S) and B by diag(S)*B.
2. If FACT = 'N' or 'E', the Cholesky decomposition is used to
factor the matrix A (after equilibration if FACT = 'E') as
A = U**T* U, if UPLO = 'U', or
A = L * L**T, if UPLO = 'L',
where U is an upper triangular matrix and L is a lower triangular
matrix.
3. If the leading i-by-i principal minor is not positive definite,
then the routine returns with INFO = i. Otherwise, the factored
form of A is used to estimate the condition number of the matrix
A. If the reciprocal of the condition number is less than machine
precision, INFO = N+1 is returned as a warning, but the routine
still goes on to solve for X and compute error bounds as
described below.
4. The system of equations is solved for X using the factored form
of A.
5. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
6. If equilibration was used, the matrix X is premultiplied by
diag(S) so that it solves the original system before
equilibration.
file lapack/double/dposvxx.f
prec double
DPOSVXX uses the Cholesky factorization A = U**T*U or A = L*L**T
to compute the solution to a double precision system of linear equations
A * X = B, where A is an N-by-N symmetric positive definite matrix
and X and B are N-by-NRHS matrices.
If requested, both normwise and maximum componentwise error bounds
are returned. DPOSVXX will return a solution with a tiny
guaranteed error (O(eps) where eps is the working machine
precision) unless the matrix is very ill-conditioned, in which
case a warning is returned. Relevant condition numbers also are
calculated and returned.
DPOSVXX accepts user-provided factorizations and equilibration
factors; see the definitions of the FACT and EQUED options.
Solving with refinement and using a factorization from a previous
DPOSVXX call will also produce a solution with either O(eps)
errors or warnings, but we cannot make that claim for general
user-provided factorizations and equilibration factors if they
differ from what DPOSVXX would itself produce.
Description
===========
The following steps are performed:
1. If FACT = 'E', double precision scaling factors are computed to equilibrate
the system:
diag(S)*A*diag(S) *inv(diag(S))*X = diag(S)*B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(S)*A*diag(S) and B by diag(S)*B.
2. If FACT = 'N' or 'E', the Cholesky decomposition is used to
factor the matrix A (after equilibration if FACT = 'E') as
A = U**T* U, if UPLO = 'U', or
A = L * L**T, if UPLO = 'L',
where U is an upper triangular matrix and L is a lower triangular
matrix.
3. If the leading i-by-i principal minor is not positive definite,
then the routine returns with INFO = i. Otherwise, the factored
form of A is used to estimate the condition number of the matrix
A (see argument RCOND). If the reciprocal of the condition number
is less than machine precision, the routine still goes on to solve
for X and compute error bounds as described below.
4. The system of equations is solved for X using the factored form
of A.
5. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero),
the routine will use iterative refinement to try to get a small
error and error bounds. Refinement calculates the residual to at
least twice the working precision.
6. If equilibration was used, the matrix X is premultiplied by
diag(S) so that it solves the original system before
equilibration.
file lapack/double/dppsvx.f
prec double
DPPSVX uses the Cholesky factorization A = U**T*U or A = L*L**T to
compute the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric positive definite matrix stored in
packed format and X and B are N-by-NRHS matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed:
1. If FACT = 'E', real scaling factors are computed to equilibrate
the system:
diag(S) * A * diag(S) * inv(diag(S)) * X = diag(S) * B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(S)*A*diag(S) and B by diag(S)*B.
2. If FACT = 'N' or 'E', the Cholesky decomposition is used to
factor the matrix A (after equilibration if FACT = 'E') as
A = U**T* U, if UPLO = 'U', or
A = L * L**T, if UPLO = 'L',
where U is an upper triangular matrix and L is a lower triangular
matrix.
3. If the leading i-by-i principal minor is not positive definite,
then the routine returns with INFO = i. Otherwise, the factored
form of A is used to estimate the condition number of the matrix
A. If the reciprocal of the condition number is less than machine
precision, INFO = N+1 is returned as a warning, but the routine
still goes on to solve for X and compute error bounds as
described below.
4. The system of equations is solved for X using the factored form
of A.
5. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
6. If equilibration was used, the matrix X is premultiplied by
diag(S) so that it solves the original system before
equilibration.
file lapack/double/dsbevx.f
prec double
DSBEVX computes selected eigenvalues and, optionally, eigenvectors
of a real symmetric band matrix A. Eigenvalues and eigenvectors can
be selected by specifying either a range of values or a range of
indices for the desired eigenvalues.
file lapack/double/dsbgvx.f
prec double
DSBGVX computes selected eigenvalues, and optionally, eigenvectors
of a real generalized symmetric-definite banded eigenproblem, of
the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric
and banded, and B is also positive definite. Eigenvalues and
eigenvectors can be selected by specifying either all eigenvalues,
a range of values or a range of indices for the desired eigenvalues.
file lapack/double/dspevx.f
prec double
DSPEVX computes selected eigenvalues and, optionally, eigenvectors
of a real symmetric matrix A in packed storage. Eigenvalues/vectors
can be selected by specifying either a range of values or a range of
indices for the desired eigenvalues.
file lapack/double/dspgvx.f
prec double
DSPGVX computes selected eigenvalues, and optionally, eigenvectors
of a real generalized symmetric-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A
and B are assumed to be symmetric, stored in packed storage, and B
is also positive definite. Eigenvalues and eigenvectors can be
selected by specifying either a range of values or a range of indices
for the desired eigenvalues.
file lapack/double/dspsvx.f
prec double
DSPSVX uses the diagonal pivoting factorization A = U*D*U**T or
A = L*D*L**T to compute the solution to a real system of linear
equations A * X = B, where A is an N-by-N symmetric matrix stored
in packed format and X and B are N-by-NRHS matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed:
1. If FACT = 'N', the diagonal pivoting method is used to factor A as
A = U * D * U**T, if UPLO = 'U', or
A = L * D * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices and D is symmetric and block diagonal with
1-by-1 and 2-by-2 diagonal blocks.
2. If some D(i,i)=0, so that D is exactly singular, then the routine
returns with INFO = i. Otherwise, the factored form of A is used
to estimate the condition number of the matrix A. If the
reciprocal of the condition number is less than machine precision,
INFO = N+1 is returned as a warning, but the routine still goes on
to solve for X and compute error bounds as described below.
3. The system of equations is solved for X using the factored form
of A.
4. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
file lapack/double/dstevx.f
prec double
DSTEVX computes selected eigenvalues and, optionally, eigenvectors
of a real symmetric tridiagonal matrix A. Eigenvalues and
eigenvectors can be selected by specifying either a range of values
or a range of indices for the desired eigenvalues.
file lapack/double/dsyevx.f
prec double
DSYEVX computes selected eigenvalues and, optionally, eigenvectors
of a real symmetric matrix A. Eigenvalues and eigenvectors can be
selected by specifying either a range of values or a range of indices
for the desired eigenvalues.
file lapack/double/dsygvx.f
prec double
DSYGVX computes selected eigenvalues, and optionally, eigenvectors
of a real generalized symmetric-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A
and B are assumed to be symmetric and B is also positive definite.
Eigenvalues and eigenvectors can be selected by specifying either a
range of values or a range of indices for the desired eigenvalues.
file lapack/double/dsysvx.f
prec double
DSYSVX uses the diagonal pivoting factorization to compute the
solution to a real system of linear equations A * X = B,
where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed:
1. If FACT = 'N', the diagonal pivoting method is used to factor A.
The form of the factorization is
A = U * D * U**T, if UPLO = 'U', or
A = L * D * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and D is symmetric and block diagonal with
1-by-1 and 2-by-2 diagonal blocks.
2. If some D(i,i)=0, so that D is exactly singular, then the routine
returns with INFO = i. Otherwise, the factored form of A is used
to estimate the condition number of the matrix A. If the
reciprocal of the condition number is less than machine precision,
INFO = N+1 is returned as a warning, but the routine still goes on
to solve for X and compute error bounds as described below.
3. The system of equations is solved for X using the factored form
of A.
4. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
file lapack/essl/cci.tgz
file lapack/lawns/lawn19_scan.pdf
file lapack/lawns/lawn47.ps
file lapack/lawns/lawn48.ps
file lapack/lawns/lawn49.ps
file lapack/lawns/lawn53.ps
file lapack/lawns/lawn54.ps
file lapack/lawns/lawn55.ps
file lapack/lawns/lawn56.tgz
file lapack/lawns/lawn56.ps
file lapack/lawns/lawn57.tgz
file lapack/lawns/lawn57.ps
file lapack/lawns/lawn58.tgz
file lapack/lawns/lawn58.ps
file lapack/lawns/lawn59.ps
file lapack/lawns/lawn60.ps
file lapack/lawns/lawn61.ps
file lapack/lawns/lawn62.ps
file lapack/lawns/lawn63.ps
file lapack/lawns/lawn64.ps
file lapack/lawns/lawn65.ps
file lapack/lawns/lawn66.ps
file lapack/lawns/lawn67.ps
file lapack/lawns/lawn68.ps
file lapack/lawns/lawn69.ps
file lapack/lawns/lawn70.ps
file lapack/lawns/lawn71.ps
file lapack/lawns/lawn72.ps
file lapack/lawns/lawn73.ps
file lapack/lawns/lawn75.ps
file lapack/lawns/lawn76.ps
file lapack/lawns/lawn77.ps
file lapack/lawns/lawn78.ps
file lapack/lawns/lawn79.ps
file lapack/lawns/lawn80.ps
file lapack/lawns/lawn81.ps
file lapack/lawns/lawn82.ps
file lapack/lawns/lawn83.ps
file lapack/lawns/lawn84.ps
file lapack/lawns/lawn85.ps
file lapack/lawns/lawn86.ps
file lapack/lawns/lawn87.ps
file lapack/lawns/lawn89.ps
file lapack/lawns/lawn90.ps
file lapack/lawns/lawn91.ps
file lapack/lawns/lawn92.ps
file lapack/lawns/lawn93.ps
file lapack/lawns/lawn94.ps
file lapack/lawns/lawn95.ps
file lapack/lawns/lawn96.ps
file lapack/lawns/lawn97.ps
file lapack/lawns/lawn98.ps
file lapack/lawns/lawn101.ps
file lapack/lawns/lawn102.ps
file lapack/lawns/lawn104.ps
file lapack/lawns/lawn105.ps
file lapack/lawns/lawn106.ps
file lapack/lawns/lawn107.ps
file lapack/lawns/lawn108.ps
file lapack/lawns/lawn109.ps
file lapack/lawns/lawn110.ps
file lapack/lawns/lawn111.ps
file lapack/lawns/lawn112.ps
file lapack/lawns/lawn113.ps
file lapack/lawns/lawn114.ps
file lapack/lawns/lawn115.ps
file lapack/lawns/lawn116.ps
file lapack/lawns/lawn117.ps
file lapack/lawns/lawn118.ps
file lapack/lawns/lawn119.ps
file lapack/lawns/lawn120.ps
file lapack/lawns/lawn121.ps
file lapack/lawns/lawn125.ps
file lapack/lawns/lawn154.ps
file lapack/lawns/lawn155.ps
file lapack/lawns/lawn156.ps
file lapack/lawns/lawn158.ps
file lapack/lawns/lawn160.ps
file lapack/lawns/lawn164.ps
file lapack/lawns/lawn165.ps
file lapack/lawnspdf/lawn47.pdf
file lapack/lawnspdf/lawn48.pdf
file lapack/lawnspdf/lawn49.pdf
file lapack/lawnspdf/lawn53.pdf
file lapack/lawnspdf/lawn54.pdf
file lapack/lawnspdf/lawn55.pdf
file lapack/lawnspdf/lawn56.pdf
file lapack/lawnspdf/lawn57.pdf
file lapack/lawnspdf/lawn58.pdf
file lapack/lawnspdf/lawn59.pdf
file lapack/lawnspdf/lawn60.pdf
file lapack/lawnspdf/lawn61.pdf
file lapack/lawnspdf/lawn62.pdf
file lapack/lawnspdf/lawn63.pdf
file lapack/lawnspdf/lawn64.pdf
file lapack/lawnspdf/lawn65.pdf
file lapack/lawnspdf/lawn66.pdf
file lapack/lawnspdf/lawn67.pdf
file lapack/lawnspdf/lawn68.pdf
file lapack/lawnspdf/lawn69.pdf
file lapack/lawnspdf/lawn70.pdf
file lapack/lawnspdf/lawn71.pdf
file lapack/lawnspdf/lawn72.pdf
file lapack/lawnspdf/lawn73.pdf
file lapack/lawnspdf/lawn75.pdf
file lapack/lawnspdf/lawn76.pdf
file lapack/lawnspdf/lawn77.pdf
file lapack/lawnspdf/lawn78.pdf
file lapack/lawnspdf/lawn79.pdf
file lapack/lawnspdf/lawn80.pdf
file lapack/lawnspdf/lawn81.pdf
file lapack/lawnspdf/lawn82.pdf
file lapack/lawnspdf/lawn83.pdf
file lapack/lawnspdf/lawn84.pdf
file lapack/lawnspdf/lawn85.pdf
file lapack/lawnspdf/lawn86.pdf
file lapack/lawnspdf/lawn87.pdf
file lapack/lawnspdf/lawn89.pdf
file lapack/lawnspdf/lawn90.pdf
file lapack/lawnspdf/lawn91.pdf
file lapack/lawnspdf/lawn92.pdf
file lapack/lawnspdf/lawn93.pdf
file lapack/lawnspdf/lawn94.pdf
file lapack/lawnspdf/lawn95.pdf
file lapack/lawnspdf/lawn96.pdf
file lapack/lawnspdf/lawn97.pdf
file lapack/lawnspdf/lawn98.pdf
file lapack/lawnspdf/lawn101.pdf
file lapack/lawnspdf/lawn102.pdf
file lapack/lawnspdf/lawn104.pdf
file lapack/lawnspdf/lawn105.pdf
file lapack/lawnspdf/lawn106.pdf
file lapack/lawnspdf/lawn107.pdf
file lapack/lawnspdf/lawn108.pdf
file lapack/lawnspdf/lawn109.pdf
file lapack/lawnspdf/lawn110.pdf
file lapack/lawnspdf/lawn111.pdf
file lapack/lawnspdf/lawn112.pdf
file lapack/lawnspdf/lawn113.pdf
file lapack/lawnspdf/lawn114.pdf
file lapack/lawnspdf/lawn115.pdf
file lapack/lawnspdf/lawn116.pdf
file lapack/lawnspdf/lawn117.pdf
file lapack/lawnspdf/lawn118.pdf
file lapack/lawnspdf/lawn119.pdf
file lapack/lawnspdf/lawn120.pdf
file lapack/lawnspdf/lawn121.pdf
file lapack/lawnspdf/lawn125.pdf
file lapack/lawnspdf/lawn139.pdf
file lapack/lawnspdf/lawn140.pdf
file lapack/lawnspdf/lawn141.pdf
file lapack/lawnspdf/lawn142.pdf
file lapack/lawnspdf/lawn144.pdf
file lapack/lawnspdf/lawn145.pdf
file lapack/lawnspdf/lawn146.pdf
file lapack/lawnspdf/lawn147.pdf
file lapack/lawnspdf/lawn148.pdf
file lapack/lawnspdf/lawn149.pdf
file lapack/lawnspdf/lawn150.pdf
file lapack/lawnspdf/lawn151.pdf
file lapack/lawnspdf/lawn152.pdf
file lapack/lawnspdf/lawn153.pdf
# ======================================================================
# LAPACK, Version 1.0 Date: February 29, 1992
# LAPACK, Version 1.0a Date: June 30, 1992
# LAPACK, Version 1.0b Date: October 31, 1992
# LAPACK, Version 1.1 Date: March 31, 1993
# LAPACK, Version 2.0 Date: September 30, 1994
# LAPACK, Version 3.0 Date: June 30, 1999
# LAPACK, Version 3.0 (update) Date: October 31, 1999
# LAPACK, Version 3.0 (update) Date: May 31, 2000
# LAPACK, Version 3.1 Date: November 12, 2006
# LAPACK, Version 3.1.1 Date: February 26, 2007
# LAPACK, Version 3.2 Date: November 18, 2008
# LAPACK, Version 3.2.1 Date: April 17, 2009
# LAPACK, Version 3.2.2 Date: June 30, 2010
# LAPACK, Version 3.3.0 Date: Nov 14, 2010
# ======================================================================
#
# -------------------
# SVN Access:
# -------------------
svn co http://icl.cs.utk.edu/svn/lapack-dev/lapack/trunk
# -------------------
# Available software:
# -------------------
file lapack/lapack.tgz
for LAPACK, version 3.3.0
, All revisions included.
, Please refer to lapack-3.3.0.html file for release notes on release 3.3.0
, Updated: November 14, 2010
--> NEW: Standard C language APIs for LAPACK ( collaboration LAPACK and INTEL Math Kernel Library)
file lapack/lapacke.tgz
for LAPACK C INTERFACE, version 1.0.0.009
, Corresponds to Intel MKL 10.3 product
, Updated: November 14, 2010
file lapack/lapack-3.2.2.tgz
for LAPACK, version 3.2.2
, This is the package without html pages and manpages (installation and testing) in tar gzip form. All revisions included.
, This cannot be retrieved via email.
, Please refer to lapack-3.2.2.html file for release notes on release 3.2.2
, Updated: June 30, 2010
file lapack/lapack-3.2.1-CMAKE.zip
file lapack/lapack-3.2.1-CMAKE.tgz
for LAPACK, version 3.2.1 CMAKE package
, for UNIX Make, MAC xcode, Windows (Nmake, Visual Studio all versions) 32 or 64 bits.
, [REQUIRE CMAKE - http://www.cmake.org/ Running doc: http://www.cmake.org/cmake/help/runningcmake.html]
, FEEDBACK WELCOME --> http://icl.cs.utk.edu/lapack-forum
, Please refer to lapack-3.2.1.html file for release notes on release 3.2.1
, Updated: January 26, 2010
file lapack/lapack-3.2.1.tgz
for LAPACK, version 3.2.1
, This is the package without html pages and manpages (installation and testing) in tar gzip form. All revisions included.
, This cannot be retrieved via email.
, Please refer to lapack-3.2.1.html file for release notes on release 3.2.1
, Updated: April 17, 2009
file lapack/lapack-3.2.tgz
for LAPACK, version 3.2
, This is the package without html pages and manpages (installation and testing) in tar gzip form. All revisions included.
, This cannot be retrieved via email.
, Please refer to lapack-3.2.html file for release notes on release 3.2
, Updated: November 18, 2008
file lapack/lapack-3.1.1.tgz
for LAPACK, version 3.1.1
, This is the COMPLETE package (installation, testing, manpages and html) in tar gzip form (10407 Kbytes). All revisions included.
, This cannot be retrieved via email.
, Updated: February 26, 2007
file lapack/lapack-lite-3.1.1.tgz
for LAPACK, version 3.1.1
, This is the package without html pages and manpages (installation and testing) in tar gzip form (5332 Kbytes). All revisions included.
, This cannot be retrieved via email.
, Updated: February 26, 2007
file lapack/lapack-3.0.tgz
for LAPACK, version 3.0 + UPDATES
, This is the COMPLETE package
, (installation, testing, and timing) in tar gzip
, form (4991992 bytes). All revisions included.
, This cannot be retrieved via email.
, Updated: May 31, 2000
ref http://icl.cs.utk.edu/lapack-for-windows/
for LAPACK 3.1.1 for Windows
file lapack/update.tgz
for UPDATE (tar gzipped) file for LAPACK, version 3.0
, Instructions: cd LAPACK; gunzip -c update.tgz | tar xvf -
, Updated: May 31, 2000
ref http://www.amd.com/acml
for ACML AMD Core Math Library
ref http://www.intel.com/software/products/mkl
for Intel Math Kernel Library
, The AMD Core Math Library (ACML) and the Intel Math Kernel Library
, (Intel MKL) includes BLAS, LAPACK, and ScaLAPACK, which are designed
, to be used by a wide range of software developers to obtain excellent
, performance from their applications running on AMD and Intel platforms.
# -------------------
# Individual Routines:
# -------------------
lib lapack/explore-html
for Explore LAPACK code by routine
lib lapack/single
for single precision real LAPACK routines
prec single
lib lapack/double
for double precision real LAPACK routines
prec double
lib lapack/complex
for single precision complex LAPACK routines
prec complex
lib lapack/complex16
for double precision complex LAPACK routines
prec doublecomplex
lib lapack/util
for LAPACK utility routines
lib lapack/testing
for Subdirectory containing the testing routines for lapack.
lib lapack/timing
for Subdirectory containing the timing routines for lapack.
# -------------------------
# Prebuilt LAPACK libraries:
# -------------------------
lib lapack/archives
for Subdirectory containing prebuilt LAPACK libraries
, !! Being updated for LAPACK, version 3.0 + PATCH!!
# --------------
# Documentation:
# --------------
lib lapack/lug/
, HTML version of the LAPACK Users' Guide, Third Edition
file lapack/lapack-3.2
for Text file explaining the changes that were made to the
, LAPACK software in version 3.2.
, Please refer to lapack-3.2.html file for release notes on release 3.2
file lapack/lapack-3.1.1.changes
for Text file explaining the changes that were made to the
, LAPACK software in version 3.1.1.
, Please refer to lapack-3.1.1.changes.html file for release notes on release 3.1.1
file lapack/lapack-3.1.0.changes
for Text file explaining the changes that were made to the
, LAPACK software in version 3.1.0.
, Please refer to lapack-3.1.0.changes.html file for release notes on release 3.1.0
file lapack/release_notes.html
for ** RELEASE_NOTES webpage for LAPACK **
, List of known problems, bugs, and compiler errors, as
, well as ERRATA for the LAPACK Users' Guide and the
, LAPACK code itself.
, Last UPDATED: July 10, 2001
file lapack/lapackqref.ps
for LAPACK Quick Reference Guide to the Driver Routines
, (VERSION 3.0)
lib lapack/lawn81/
, HTML version of "Quick Installation Guide for LAPACK"
file lapack/lawns/lawn81.ps
for LAPACK Working Note 81: Quick Installation Guide for LAPACK
, on Unix Systems
, (25 pages)
, Updated: June, 1999. (VERSION 3.0)
lib lapack/lawn41/
, HTML version of "LAPACK Installation Guide"
file lapack/lawns/lawn41.ps
for LAPACK Working Note 41: LAPACK Installation Guide
, (149 pages)
, Updated: June, 1999 (VERSION 3.0)
file lapack/manpages.tgz
for This is a gzip tar
, file of the manual pages for the LAPACK 3.2.0 driver and
, computational routines.
, (1016997 bytes). This cannot be retrieved via email.
# ------------------------------
# LAPACK Working Notes in ps/pdf:
# ------------------------------
lib lapack/lawns
for Subdirectory containing the LAPACK Working Notes
, To find out what is available and retrieve a postscript copy
, of these reports, send mail in the form:
, send index from lapack/lawns
, send lawnxx from lapack/lawns
, These reports are kept only at netlib@www.netlib.org
lib lapack/lawnspdf
for Subdirectory containing pdf versions of the LAPACK Working Notes
, To find out what is available and retrieve a postscript copy
, of these reports, send mail in the form:
, send index from lapack/lawnspdf
, send lawnxx from lapack/lawnspdf
, These reports are kept only at netlib@www.netlib.org
# -----------------
# Related Projects:
# -----------------
# For the Fortran95 interface to LAPACK see directory lapack95
lib lapack95
for LAPACK95 is the Fortran95 interface to LAPACK.
by Jerzy Wasniewski
# For the Fortran-to-Java LAPACK see directory java/f2j/
lib java/f2j
for JLAPACK
# For an f2c'ed conversion of LAPACK see directory clapack
lib clapack
for CLAPACK. An f2c'ed conversion of LAPACK.
# For a distributed-memory implementation of LAPACK see directory scalapack
lib scalapack
for ScaLAPACK. A portable implementation of some of the core
, routines in LAPACK across MPI, PVM, Intel Paragon, IBM SP, and SGI O2K.
# For a c++ implementation of LAPACK see directory lapack++
lib lapack++
for LAPACK++. LAPACK extensions for high performance linear
, algebra computations. This version includes support for solving
, linear systems using LU, Cholesky, and QR matrix factorizations.
by Roldan Pozo
lib lapack/essl
for Subdirectory containing CCI (Call Conversion Interface) for
, LAPACK/ESSL.
, See lawn82 for more information.
#
# This directory contains previous releases/versions of LAPACK, only
# for purposes of historical reference or comparison.
#
# WARNING: Be aware that known bugs exist in these tar files,
# and have been fixed in subsequent versions! As a
# result, these tar files should never be used for a
# current LAPACK installation!
#
# The definitive distribution tar file for LAPACK is:
# http://www.netlib.org/lapack/lapack.tgz
# This is the tar file that should always be used for an up-to-date
# installation of LAPACK.
#
# ======================================================================
# LAPACK, Version 1.0 Date: February 29, 1992
# LAPACK, Version 1.0a Date: June 30, 1992
# LAPACK, Version 1.0b Date: October 31, 1992
# LAPACK, Version 1.1 Date: March 31, 1993
# LAPACK, Version 2.0 Date: September 30, 1994
# LAPACK, Version 3.0 Date: June 30, 1999
# LAPACK, Version 3.0 (update) Date: October 31, 1999
# LAPACK, Version 3.0 (update) Date: May 31, 2000
# ======================================================================
#
file lapack/releases/lapack2.0.tgz
for LAPACK, version 2.0
, Date: September 30, 1994
file lapack/releases/lapack1.1.tgz
for LAPACK, version 1.1
, Date: March 31, 1993
file lapack/releases/lapack1.0b.tgz
for LAPACK, version 1.0b
, Date: October 31, 1992
file lapack/releases/lapack1.0a.tgz
for LAPACK, version 1.0a
, Date: June 30, 1992
file lapack/releases/lapack1.0.tgz
for LAPACK, version 1.0
, Date: February 29, 1992
#######################################
# LAPACK rpm files for Linux #
#######################################
# This directory contains LAPACK rpms for RedHat Linux
# and Debian Linux.
#
# (Thanks to Andrew Lumsdaine from UND for the RedHat rpms! :) )
# rpms for RedHat Linux
#
# Note that you will need to link with library -lg2c !!
# /usr/lib/gcc-lib/i386-redhat-linux/2.96/libg2c.a
file lapack/rpms/lapack-3_0-2_src.rpm
file lapack/rpms/lapack-3_0-2_i386.rpm
file lapack/rpms/blas-3_0-2_i386.rpm
file lapack/rpms/blas-man-3_0-2_i386.rpm
file lapack/rpms/lapack-man-3_0-2_i386.rpm
# debs for Debian Linux
#
# Refer to http://www.debian.org/Packages/frozen/libs/lapack.html
GENRATING INDEX FOR SINGLE PRECISION
# ---------------------------------
# Available SIMPLE DRIVER routines:
# ---------------------------------
file lapack/single/sgbsv.f
prec single
SGBSV computes the solution to a real system of linear equations
A * X = B, where A is a band matrix of order N with KL subdiagonals
and KU superdiagonals, and X and B are N-by-NRHS matrices.
The LU decomposition with partial pivoting and row interchanges is
used to factor A as A = L * U, where L is a product of permutation
and unit lower triangular matrices with KL subdiagonals, and U is
upper triangular with KL+KU superdiagonals. The factored form of A
is then used to solve the system of equations A * X = B.
file lapack/single/sgees.f
prec single
SGEES computes for an N-by-N real nonsymmetric matrix A, the
eigenvalues, the real Schur form T, and, optionally, the matrix of
Schur vectors Z. This gives the Schur factorization A = Z*T*(Z**T).
Optionally, it also orders the eigenvalues on the diagonal of the
real Schur form so that selected eigenvalues are at the top left.
The leading columns of Z then form an orthonormal basis for the
invariant subspace corresponding to the selected eigenvalues.
A matrix is in real Schur form if it is upper quasi-triangular with
1-by-1 and 2-by-2 blocks. 2-by-2 blocks will be standardized in the
form
[ a b ]
[ c a ]
where b*c < 0. The eigenvalues of such a block are a +- sqrt(bc).
file lapack/single/sgeev.f
prec single
SGEEV computes for an N-by-N real nonsymmetric matrix A, the
eigenvalues and, optionally, the left and/or right eigenvectors.
The right eigenvector v(j) of A satisfies
A * v(j) = lambda(j) * v(j)
where lambda(j) is its eigenvalue.
The left eigenvector u(j) of A satisfies
u(j)**H * A = lambda(j) * u(j)**H
where u(j)**H denotes the conjugate transpose of u(j).
The computed eigenvectors are normalized to have Euclidean norm
equal to 1 and largest component real.
file lapack/single/sgegs.f
prec single
This routine is deprecated and has been replaced by routine SGGES.
SGEGS computes the eigenvalues, real Schur form, and, optionally,
left and or/right Schur vectors of a real matrix pair (A,B).
Given two square matrices A and B, the generalized real Schur
factorization has the form
A = Q*S*Z**T, B = Q*T*Z**T
where Q and Z are orthogonal matrices, T is upper triangular, and S
is an upper quasi-triangular matrix with 1-by-1 and 2-by-2 diagonal
blocks, the 2-by-2 blocks corresponding to complex conjugate pairs
of eigenvalues of (A,B). The columns of Q are the left Schur vectors
and the columns of Z are the right Schur vectors.
If only the eigenvalues of (A,B) are needed, the driver routine
SGEGV should be used instead. See SGEGV for a description of the
eigenvalues of the generalized nonsymmetric eigenvalue problem
(GNEP).
file lapack/single/sgegv.f
prec single
This routine is deprecated and has been replaced by routine SGGEV.
SGEGV computes the eigenvalues and, optionally, the left and/or right
eigenvectors of a real matrix pair (A,B).
Given two square matrices A and B,
the generalized nonsymmetric eigenvalue problem (GNEP) is to find the
eigenvalues lambda and corresponding (non-zero) eigenvectors x such
that
A*x = lambda*B*x.
An alternate form is to find the eigenvalues mu and corresponding
eigenvectors y such that
mu*A*y = B*y.
These two forms are equivalent with mu = 1/lambda and x = y if
neither lambda nor mu is zero. In order to deal with the case that
lambda or mu is zero or small, two values alpha and beta are returned
for each eigenvalue, such that lambda = alpha/beta and
mu = beta/alpha.
The vectors x and y in the above equations are right eigenvectors of
the matrix pair (A,B). Vectors u and v satisfying
u**H*A = lambda*u**H*B or mu*v**H*A = v**H*B
are left eigenvectors of (A,B).
Note: this routine performs "full balancing" on A and B -- see
"Further Details", below.
file lapack/single/sgels.f
prec single
SGELS solves overdetermined or underdetermined real linear systems
involving an M-by-N matrix A, or its transpose, using a QR or LQ
factorization of A. It is assumed that A has full rank.
The following options are provided:
1. If TRANS = 'N' and m >= n: find the least squares solution of
an overdetermined system, i.e., solve the least squares problem
minimize || B - A*X ||.
2. If TRANS = 'N' and m < n: find the minimum norm solution of
an underdetermined system A * X = B.
3. If TRANS = 'T' and m >= n: find the minimum norm solution of
an undetermined system A**T * X = B.
4. If TRANS = 'T' and m < n: find the least squares solution of
an overdetermined system, i.e., solve the least squares problem
minimize || B - A**T * X ||.
Several right hand side vectors b and solution vectors x can be
handled in a single call; they are stored as the columns of the
M-by-NRHS right hand side matrix B and the N-by-NRHS solution
matrix X.
file lapack/single/sgelsd.f
prec single
SGELSD computes the minimum-norm solution to a real linear least
squares problem:
minimize 2-norm(| b - A*x |)
using the singular value decomposition (SVD) of A. A is an M-by-N
matrix which may be rank-deficient.
Several right hand side vectors b and solution vectors x can be
handled in a single call; they are stored as the columns of the
M-by-NRHS right hand side matrix B and the N-by-NRHS solution
matrix X.
The problem is solved in three steps:
(1) Reduce the coefficient matrix A to bidiagonal form with
Householder transformations, reducing the original problem
into a "bidiagonal least squares problem" (BLS)
(2) Solve the BLS using a divide and conquer approach.
(3) Apply back all the Householder tranformations to solve
the original least squares problem.
The effective rank of A is determined by treating as zero those
singular values which are less than RCOND times the largest singular
value.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/single/sgelss.f
prec single
SGELSS computes the minimum norm solution to a real linear least
squares problem:
Minimize 2-norm(| b - A*x |).
using the singular value decomposition (SVD) of A. A is an M-by-N
matrix which may be rank-deficient.
Several right hand side vectors b and solution vectors x can be
handled in a single call; they are stored as the columns of the
M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix
X.
The effective rank of A is determined by treating as zero those
singular values which are less than RCOND times the largest singular
value.
file lapack/single/sgelsy.f
prec single
SGELSY computes the minimum-norm solution to a real linear least
squares problem:
minimize || A * X - B ||
using a complete orthogonal factorization of A. A is an M-by-N
matrix which may be rank-deficient.
Several right hand side vectors b and solution vectors x can be
handled in a single call; they are stored as the columns of the
M-by-NRHS right hand side matrix B and the N-by-NRHS solution
matrix X.
The routine first computes a QR factorization with column pivoting:
A * P = Q * [ R11 R12 ]
[ 0 R22 ]
with R11 defined as the largest leading submatrix whose estimated
condition number is less than 1/RCOND. The order of R11, RANK,
is the effective rank of A.
Then, R22 is considered to be negligible, and R12 is annihilated
by orthogonal transformations from the right, arriving at the
complete orthogonal factorization:
A * P = Q * [ T11 0 ] * Z
[ 0 0 ]
The minimum-norm solution is then
X = P * Z' [ inv(T11)*Q1'*B ]
[ 0 ]
where Q1 consists of the first RANK columns of Q.
This routine is basically identical to the original xGELSX except
three differences:
o The call to the subroutine xGEQPF has been substituted by the
the call to the subroutine xGEQP3. This subroutine is a Blas-3
version of the QR factorization with column pivoting.
o Matrix B (the right hand side) is updated with Blas-3.
o The permutation of matrix B (the right hand side) is faster and
more simple.
file lapack/single/sgesdd.f
prec single
SGESDD computes the singular value decomposition (SVD) of a real
M-by-N matrix A, optionally computing the left and right singular
vectors. If singular vectors are desired, it uses a
divide-and-conquer algorithm.
The SVD is written
A = U * SIGMA * transpose(V)
where SIGMA is an M-by-N matrix which is zero except for its
min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and
V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA
are the singular values of A; they are real and non-negative, and
are returned in descending order. The first min(m,n) columns of
U and V are the left and right singular vectors of A.
Note that the routine returns VT = V**T, not V.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/single/sgesv.f
prec single
SGESV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N matrix and X and B are N-by-NRHS matrices.
The LU decomposition with partial pivoting and row interchanges is
used to factor A as
A = P * L * U,
where P is a permutation matrix, L is unit lower triangular, and U is
upper triangular. The factored form of A is then used to solve the
system of equations A * X = B.
file lapack/single/sgesvd.f
prec single
SGESVD computes the singular value decomposition (SVD) of a real
M-by-N matrix A, optionally computing the left and/or right singular
vectors. The SVD is written
A = U * SIGMA * transpose(V)
where SIGMA is an M-by-N matrix which is zero except for its
min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and
V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA
are the singular values of A; they are real and non-negative, and
are returned in descending order. The first min(m,n) columns of
U and V are the left and right singular vectors of A.
Note that the routine returns V**T, not V.
file lapack/single/sgges.f
prec single
SGGES computes for a pair of N-by-N real nonsymmetric matrices (A,B),
the generalized eigenvalues, the generalized real Schur form (S,T),
optionally, the left and/or right matrices of Schur vectors (VSL and
VSR). This gives the generalized Schur factorization
(A,B) = ( (VSL)*S*(VSR)**T, (VSL)*T*(VSR)**T )
Optionally, it also orders the eigenvalues so that a selected cluster
of eigenvalues appears in the leading diagonal blocks of the upper
quasi-triangular matrix S and the upper triangular matrix T.The
leading columns of VSL and VSR then form an orthonormal basis for the
corresponding left and right eigenspaces (deflating subspaces).
(If only the generalized eigenvalues are needed, use the driver
SGGEV instead, which is faster.)
A generalized eigenvalue for a pair of matrices (A,B) is a scalar w
or a ratio alpha/beta = w, such that A - w*B is singular. It is
usually represented as the pair (alpha,beta), as there is a
reasonable interpretation for beta=0 or both being zero.
A pair of matrices (S,T) is in generalized real Schur form if T is
upper triangular with non-negative diagonal and S is block upper
triangular with 1-by-1 and 2-by-2 blocks. 1-by-1 blocks correspond
to real generalized eigenvalues, while 2-by-2 blocks of S will be
"standardized" by making the corresponding elements of T have the
form:
[ a 0 ]
[ 0 b ]
and the pair of corresponding 2-by-2 blocks in S and T will have a
complex conjugate pair of generalized eigenvalues.
file lapack/single/sggev.f
prec single
SGGEV computes for a pair of N-by-N real nonsymmetric matrices (A,B)
the generalized eigenvalues, and optionally, the left and/or right
generalized eigenvectors.
A generalized eigenvalue for a pair of matrices (A,B) is a scalar
lambda or a ratio alpha/beta = lambda, such that A - lambda*B is
singular. It is usually represented as the pair (alpha,beta), as
there is a reasonable interpretation for beta=0, and even for both
being zero.
The right eigenvector v(j) corresponding to the eigenvalue lambda(j)
of (A,B) satisfies
A * v(j) = lambda(j) * B * v(j).
The left eigenvector u(j) corresponding to the eigenvalue lambda(j)
of (A,B) satisfies
u(j)**H * A = lambda(j) * u(j)**H * B .
where u(j)**H is the conjugate-transpose of u(j).
file lapack/single/sggglm.f
prec single
SGGGLM solves a general Gauss-Markov linear model (GLM) problem:
minimize || y ||_2 subject to d = A*x + B*y
x
where A is an N-by-M matrix, B is an N-by-P matrix, and d is a
given N-vector. It is assumed that M <= N <= M+P, and
rank(A) = M and rank( A B ) = N.
Under these assumptions, the constrained equation is always
consistent, and there is a unique solution x and a minimal 2-norm
solution y, which is obtained using a generalized QR factorization
of the matrices (A, B) given by
A = Q*(R), B = Q*T*Z.
(0)
In particular, if matrix B is square nonsingular, then the problem
GLM is equivalent to the following weighted linear least squares
problem
minimize || inv(B)*(d-A*x) ||_2
x
where inv(B) denotes the inverse of B.
file lapack/single/sgglse.f
prec single
SGGLSE solves the linear equality-constrained least squares (LSE)
problem:
minimize || c - A*x ||_2 subject to B*x = d
where A is an M-by-N matrix, B is a P-by-N matrix, c is a given
M-vector, and d is a given P-vector. It is assumed that
P <= N <= M+P, and
rank(B) = P and rank( (A) ) = N.
( (B) )
These conditions ensure that the LSE problem has a unique solution,
which is obtained using a generalized RQ factorization of the
matrices (B, A) given by
B = (0 R)*Q, A = Z*T*Q.
file lapack/single/sggsvd.f
prec single
SGGSVD computes the generalized singular value decomposition (GSVD)
of an M-by-N real matrix A and P-by-N real matrix B:
U'*A*Q = D1*( 0 R ), V'*B*Q = D2*( 0 R )
where U, V and Q are orthogonal matrices, and Z' is the transpose
of Z. Let K+L = the effective numerical rank of the matrix (A',B')',
then R is a K+L-by-K+L nonsingular upper triangular matrix, D1 and
D2 are M-by-(K+L) and P-by-(K+L) "diagonal" matrices and of the
following structures, respectively:
If M-K-L >= 0,
K L
D1 = K ( I 0 )
L ( 0 C )
M-K-L ( 0 0 )
K L
D2 = L ( 0 S )
P-L ( 0 0 )
N-K-L K L
( 0 R ) = K ( 0 R11 R12 )
L ( 0 0 R22 )
where
C = diag( ALPHA(K+1), ... , ALPHA(K+L) ),
S = diag( BETA(K+1), ... , BETA(K+L) ),
C**2 + S**2 = I.
R is stored in A(1:K+L,N-K-L+1:N) on exit.
If M-K-L < 0,
K M-K K+L-M
D1 = K ( I 0 0 )
M-K ( 0 C 0 )
K M-K K+L-M
D2 = M-K ( 0 S 0 )
K+L-M ( 0 0 I )
P-L ( 0 0 0 )
N-K-L K M-K K+L-M
( 0 R ) = K ( 0 R11 R12 R13 )
M-K ( 0 0 R22 R23 )
K+L-M ( 0 0 0 R33 )
where
C = diag( ALPHA(K+1), ... , ALPHA(M) ),
S = diag( BETA(K+1), ... , BETA(M) ),
C**2 + S**2 = I.
(R11 R12 R13 ) is stored in A(1:M, N-K-L+1:N), and R33 is stored
( 0 R22 R23 )
in B(M-K+1:L,N+M-K-L+1:N) on exit.
The routine computes C, S, R, and optionally the orthogonal
transformation matrices U, V and Q.
In particular, if B is an N-by-N nonsingular matrix, then the GSVD of
A and B implicitly gives the SVD of A*inv(B):
A*inv(B) = U*(D1*inv(D2))*V'.
If ( A',B')' has orthonormal columns, then the GSVD of A and B is
also equal to the CS decomposition of A and B. Furthermore, the GSVD
can be used to derive the solution of the eigenvalue problem:
A'*A x = lambda* B'*B x.
In some literature, the GSVD of A and B is presented in the form
U'*A*X = ( 0 D1 ), V'*B*X = ( 0 D2 )
where U and V are orthogonal and X is nonsingular, D1 and D2 are
``diagonal''. The former GSVD form can be converted to the latter
form by taking the nonsingular matrix X as
X = Q*( I 0 )
( 0 inv(R) ).
file lapack/single/spbsv.f
prec single
SPBSV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric positive definite band matrix and X
and B are N-by-NRHS matrices.
The Cholesky decomposition is used to factor A as
A = U**T * U, if UPLO = 'U', or
A = L * L**T, if UPLO = 'L',
where U is an upper triangular band matrix, and L is a lower
triangular band matrix, with the same number of superdiagonals or
subdiagonals as A. The factored form of A is then used to solve the
system of equations A * X = B.
file lapack/single/sposv.f
prec single
SPOSV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric positive definite matrix and X and B
are N-by-NRHS matrices.
The Cholesky decomposition is used to factor A as
A = U**T* U, if UPLO = 'U', or
A = L * L**T, if UPLO = 'L',
where U is an upper triangular matrix and L is a lower triangular
matrix. The factored form of A is then used to solve the system of
equations A * X = B.
file lapack/single/sppsv.f
prec single
SPPSV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric positive definite matrix stored in
packed format and X and B are N-by-NRHS matrices.
The Cholesky decomposition is used to factor A as
A = U**T* U, if UPLO = 'U', or
A = L * L**T, if UPLO = 'L',
where U is an upper triangular matrix and L is a lower triangular
matrix. The factored form of A is then used to solve the system of
equations A * X = B.
file lapack/single/ssbev.f
prec single
SSBEV computes all the eigenvalues and, optionally, eigenvectors of
a real symmetric band matrix A.
file lapack/single/ssbevd.f
prec single
SSBEVD computes all the eigenvalues and, optionally, eigenvectors of
a real symmetric band matrix A. If eigenvectors are desired, it uses
a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/single/ssbgv.f
prec single
SSBGV computes all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite banded eigenproblem, of
the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric
and banded, and B is also positive definite.
file lapack/single/ssbgvd.f
prec single
SSBGVD computes all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite banded eigenproblem, of the
form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric and
banded, and B is also positive definite. If eigenvectors are
desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/single/sspev.f
prec single
SSPEV computes all the eigenvalues and, optionally, eigenvectors of a
real symmetric matrix A in packed storage.
file lapack/single/sspevd.f
prec single
SSPEVD computes all the eigenvalues and, optionally, eigenvectors
of a real symmetric matrix A in packed storage. If eigenvectors are
desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/single/sspgv.f
prec single
SSPGV computes all the eigenvalues and, optionally, the eigenvectors
of a real generalized symmetric-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
Here A and B are assumed to be symmetric, stored in packed format,
and B is also positive definite.
file lapack/single/sspgvd.f
prec single
SSPGVD computes all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be symmetric, stored in packed format, and B is also
positive definite.
If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/single/sspsv.f
prec single
SSPSV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric matrix stored in packed format and X
and B are N-by-NRHS matrices.
The diagonal pivoting method is used to factor A as
A = U * D * U**T, if UPLO = 'U', or
A = L * D * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, D is symmetric and block diagonal with 1-by-1
and 2-by-2 diagonal blocks. The factored form of A is then used to
solve the system of equations A * X = B.
file lapack/single/sstedc.f
prec single
SSTEDC computes all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the divide and conquer method.
The eigenvectors of a full or band real symmetric matrix can also be
found if SSYTRD or SSPTRD or SSBTRD has been used to reduce this
matrix to tridiagonal form.
This code makes very mild assumptions about floating point
arithmetic. It will work on machines with a guard digit in
add/subtract, or on those binary machines without guard digits
which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none. See SLAED3 for details.
file lapack/single/sstev.f
prec single
SSTEV computes all eigenvalues and, optionally, eigenvectors of a
real symmetric tridiagonal matrix A.
file lapack/single/sstevd.f
prec single
SSTEVD computes all eigenvalues and, optionally, eigenvectors of a
real symmetric tridiagonal matrix. If eigenvectors are desired, it
uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/single/sstevr.f
prec single
SSTEVR computes selected eigenvalues and, optionally, eigenvectors
of a real symmetric tridiagonal matrix T. Eigenvalues and
eigenvectors can be selected by specifying either a range of values
or a range of indices for the desired eigenvalues.
Whenever possible, SSTEVR calls SSTEMR to compute the
eigenspectrum using Relatively Robust Representations. SSTEMR
computes eigenvalues by the dqds algorithm, while orthogonal
eigenvectors are computed from various "good" L D L^T representations
(also known as Relatively Robust Representations). Gram-Schmidt
orthogonalization is avoided as far as possible. More specifically,
the various steps of the algorithm are as follows. For the i-th
unreduced block of T,
(a) Compute T - sigma_i = L_i D_i L_i^T, such that L_i D_i L_i^T
is a relatively robust representation,
(b) Compute the eigenvalues, lambda_j, of L_i D_i L_i^T to high
relative accuracy by the dqds algorithm,
(c) If there is a cluster of close eigenvalues, "choose" sigma_i
close to the cluster, and go to step (a),
(d) Given the approximate eigenvalue lambda_j of L_i D_i L_i^T,
compute the corresponding eigenvector by forming a
rank-revealing twisted factorization.
The desired accuracy of the output can be specified by the input
parameter ABSTOL.
For more details, see "A new O(n^2) algorithm for the symmetric
tridiagonal eigenvalue/eigenvector problem", by Inderjit Dhillon,
Computer Science Division Technical Report No. UCB//CSD-97-971,
UC Berkeley, May 1997.
Note 1 : SSTEVR calls SSTEMR when the full spectrum is requested
on machines which conform to the ieee-754 floating point standard.
SSTEVR calls SSTEBZ and SSTEIN on non-ieee machines and
when partial spectrum requests are made.
Normal execution of SSTEMR may create NaNs and infinities and
hence may abort due to a floating point exception in environments
which do not handle NaNs and infinities in the ieee standard default
manner.
file lapack/single/ssyev.f
prec single
SSYEV computes all eigenvalues and, optionally, eigenvectors of a
real symmetric matrix A.
file lapack/single/ssyevd.f
prec single
SSYEVD computes all eigenvalues and, optionally, eigenvectors of a
real symmetric matrix A. If eigenvectors are desired, it uses a
divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Because of large use of BLAS of level 3, SSYEVD needs N**2 more
workspace than SSYEVX.
file lapack/single/ssyevr.f
prec single
SSYEVR computes selected eigenvalues and, optionally, eigenvectors
of a real symmetric matrix A. Eigenvalues and eigenvectors can be
selected by specifying either a range of values or a range of
indices for the desired eigenvalues.
SSYEVR first reduces the matrix A to tridiagonal form T with a call
to SSYTRD. Then, whenever possible, SSYEVR calls SSTEMR to compute
the eigenspectrum using Relatively Robust Representations. SSTEMR
computes eigenvalues by the dqds algorithm, while orthogonal
eigenvectors are computed from various "good" L D L^T representations
(also known as Relatively Robust Representations). Gram-Schmidt
orthogonalization is avoided as far as possible. More specifically,
the various steps of the algorithm are as follows.
For each unreduced block (submatrix) of T,
(a) Compute T - sigma I = L D L^T, so that L and D
define all the wanted eigenvalues to high relative accuracy.
This means that small relative changes in the entries of D and L
cause only small relative changes in the eigenvalues and
eigenvectors. The standard (unfactored) representation of the
tridiagonal matrix T does not have this property in general.
(b) Compute the eigenvalues to suitable accuracy.
If the eigenvectors are desired, the algorithm attains full
accuracy of the computed eigenvalues only right before
the corresponding vectors have to be computed, see steps c) and d).
(c) For each cluster of close eigenvalues, select a new
shift close to the cluster, find a new factorization, and refine
the shifted eigenvalues to suitable accuracy.
(d) For each eigenvalue with a large enough relative separation compute
the corresponding eigenvector by forming a rank revealing twisted
factorization. Go back to (c) for any clusters that remain.
The desired accuracy of the output can be specified by the input
parameter ABSTOL.
For more details, see SSTEMR's documentation and:
- Inderjit S. Dhillon and Beresford N. Parlett: "Multiple representations
to compute orthogonal eigenvectors of symmetric tridiagonal matrices,"
Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004.
- Inderjit Dhillon and Beresford Parlett: "Orthogonal Eigenvectors and
Relative Gaps," SIAM Journal on Matrix Analysis and Applications, Vol. 25,
2004. Also LAPACK Working Note 154.
- Inderjit Dhillon: "A new O(n^2) algorithm for the symmetric
tridiagonal eigenvalue/eigenvector problem",
Computer Science Division Technical Report No. UCB/CSD-97-971,
UC Berkeley, May 1997.
Note 1 : SSYEVR calls SSTEMR when the full spectrum is requested
on machines which conform to the ieee-754 floating point standard.
SSYEVR calls SSTEBZ and SSTEIN on non-ieee machines and
when partial spectrum requests are made.
Normal execution of SSTEMR may create NaNs and infinities and
hence may abort due to a floating point exception in environments
which do not handle NaNs and infinities in the ieee standard default
manner.
file lapack/single/ssygv.f
prec single
SSYGV computes all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
Here A and B are assumed to be symmetric and B is also
positive definite.
file lapack/single/ssygvd.f
prec single
SSYGVD computes all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be symmetric and B is also positive definite.
If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
file lapack/single/ssysv.f
prec single
SSYSV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
matrices.
The diagonal pivoting method is used to factor A as
A = U * D * U**T, if UPLO = 'U', or
A = L * D * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and D is symmetric and block diagonal with
1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then
used to solve the system of equations A * X = B.
# ---------------------------------
# Available EXPERT DRIVER routines:
# ---------------------------------
file lapack/single/sgbsvx.f
prec single
SGBSVX uses the LU factorization to compute the solution to a real
system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
where A is a band matrix of order N with KL subdiagonals and KU
superdiagonals, and X and B are N-by-NRHS matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed by this subroutine:
1. If FACT = 'E', real scaling factors are computed to equilibrate
the system:
TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B
TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N')
or diag(C)*B (if TRANS = 'T' or 'C').
2. If FACT = 'N' or 'E', the LU decomposition is used to factor the
matrix A (after equilibration if FACT = 'E') as
A = L * U,
where L is a product of permutation and unit lower triangular
matrices with KL subdiagonals, and U is upper triangular with
KL+KU superdiagonals.
3. If some U(i,i)=0, so that U is exactly singular, then the routine
returns with INFO = i. Otherwise, the factored form of A is used
to estimate the condition number of the matrix A. If the
reciprocal of the condition number is less than machine precision,
INFO = N+1 is returned as a warning, but the routine still goes on
to solve for X and compute error bounds as described below.
4. The system of equations is solved for X using the factored form
of A.
5. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
6. If equilibration was used, the matrix X is premultiplied by
diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
that it solves the original system before equilibration.
file lapack/single/sgbsvxx.f
prec single
SGBSVXX uses the LU factorization to compute the solution to a
real system of linear equations A * X = B, where A is an
N-by-N matrix and X and B are N-by-NRHS matrices.
If requested, both normwise and maximum componentwise error bounds
are returned. SGBSVXX will return a solution with a tiny
guaranteed error (O(eps) where eps is the working machine
precision) unless the matrix is very ill-conditioned, in which
case a warning is returned. Relevant condition numbers also are
calculated and returned.
SGBSVXX accepts user-provided factorizations and equilibration
factors; see the definitions of the FACT and EQUED options.
Solving with refinement and using a factorization from a previous
SGBSVXX call will also produce a solution with either O(eps)
errors or warnings, but we cannot make that claim for general
user-provided factorizations and equilibration factors if they
differ from what SGBSVXX would itself produce.
Description
===========
The following steps are performed:
1. If FACT = 'E', real scaling factors are computed to equilibrate
the system:
TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B
TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N')
or diag(C)*B (if TRANS = 'T' or 'C').
2. If FACT = 'N' or 'E', the LU decomposition is used to factor
the matrix A (after equilibration if FACT = 'E') as
A = P * L * U,
where P is a permutation matrix, L is a unit lower triangular
matrix, and U is upper triangular.
3. If some U(i,i)=0, so that U is exactly singular, then the
routine returns with INFO = i. Otherwise, the factored form of A
is used to estimate the condition number of the matrix A (see
argument RCOND). If the reciprocal of the condition number is less
than machine precision, the routine still goes on to solve for X
and compute error bounds as described below.
4. The system of equations is solved for X using the factored form
of A.
5. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero),
the routine will use iterative refinement to try to get a small
error and error bounds. Refinement calculates the residual to at
least twice the working precision.
6. If equilibration was used, the matrix X is premultiplied by
diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
that it solves the original system before equilibration.
file lapack/single/sgeesx.f
prec single
SGEESX computes for an N-by-N real nonsymmetric matrix A, the
eigenvalues, the real Schur form T, and, optionally, the matrix of
Schur vectors Z. This gives the Schur factorization A = Z*T*(Z**T).
Optionally, it also orders the eigenvalues on the diagonal of the
real Schur form so that selected eigenvalues are at the top left;
computes a reciprocal condition number for the average of the
selected eigenvalues (RCONDE); and computes a reciprocal condition
number for the right invariant subspace corresponding to the
selected eigenvalues (RCONDV). The leading columns of Z form an
orthonormal basis for this invariant subspace.
For further explanation of the reciprocal condition numbers RCONDE
and RCONDV, see Section 4.10 of the LAPACK Users' Guide (where
these quantities are called s and sep respectively).
A real matrix is in real Schur form if it is upper quasi-triangular
with 1-by-1 and 2-by-2 blocks. 2-by-2 blocks will be standardized in
the form
[ a b ]
[ c a ]
where b*c < 0. The eigenvalues of such a block are a +- sqrt(bc).
file lapack/single/sgeevx.f
prec single
SGEEVX computes for an N-by-N real nonsymmetric matrix A, the
eigenvalues and, optionally, the left and/or right eigenvectors.
Optionally also, it computes a balancing transformation to improve
the conditioning of the eigenvalues and eigenvectors (ILO, IHI,
SCALE, and ABNRM), reciprocal condition numbers for the eigenvalues
(RCONDE), and reciprocal condition numbers for the right
eigenvectors (RCONDV).
The right eigenvector v(j) of A satisfies
A * v(j) = lambda(j) * v(j)
where lambda(j) is its eigenvalue.
The left eigenvector u(j) of A satisfies
u(j)**H * A = lambda(j) * u(j)**H
where u(j)**H denotes the conjugate transpose of u(j).
The computed eigenvectors are normalized to have Euclidean norm
equal to 1 and largest component real.
Balancing a matrix means permuting the rows and columns to make it
more nearly upper triangular, and applying a diagonal similarity
transformation D * A * D**(-1), where D is a diagonal matrix, to
make its rows and columns closer in norm and the condition numbers
of its eigenvalues and eigenvectors smaller. The computed
reciprocal condition numbers correspond to the balanced matrix.
Permuting rows and columns will not change the condition numbers
(in exact arithmetic) but diagonal scaling will. For further
explanation of balancing, see section 4.10.2 of the LAPACK
Users' Guide.
file lapack/single/sgelsx.f
prec single
This routine is deprecated and has been replaced by routine SGELSY.
SGELSX computes the minimum-norm solution to a real linear least
squares problem:
minimize || A * X - B ||
using a complete orthogonal factorization of A. A is an M-by-N
matrix which may be rank-deficient.
Several right hand side vectors b and solution vectors x can be
handled in a single call; they are stored as the columns of the
M-by-NRHS right hand side matrix B and the N-by-NRHS solution
matrix X.
The routine first computes a QR factorization with column pivoting:
A * P = Q * [ R11 R12 ]
[ 0 R22 ]
with R11 defined as the largest leading submatrix whose estimated
condition number is less than 1/RCOND. The order of R11, RANK,
is the effective rank of A.
Then, R22 is considered to be negligible, and R12 is annihilated
by orthogonal transformations from the right, arriving at the
complete orthogonal factorization:
A * P = Q * [ T11 0 ] * Z
[ 0 0 ]
The minimum-norm solution is then
X = P * Z' [ inv(T11)*Q1'*B ]
[ 0 ]
where Q1 consists of the first RANK columns of Q.
file lapack/single/sgesvx.f
prec single
SGESVX uses the LU factorization to compute the solution to a real
system of linear equations
A * X = B,
where A is an N-by-N matrix and X and B are N-by-NRHS matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed:
1. If FACT = 'E', real scaling factors are computed to equilibrate
the system:
TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B
TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N')
or diag(C)*B (if TRANS = 'T' or 'C').
2. If FACT = 'N' or 'E', the LU decomposition is used to factor the
matrix A (after equilibration if FACT = 'E') as
A = P * L * U,
where P is a permutation matrix, L is a unit lower triangular
matrix, and U is upper triangular.
3. If some U(i,i)=0, so that U is exactly singular, then the routine
returns with INFO = i. Otherwise, the factored form of A is used
to estimate the condition number of the matrix A. If the
reciprocal of the condition number is less than machine precision,
INFO = N+1 is returned as a warning, but the routine still goes on
to solve for X and compute error bounds as described below.
4. The system of equations is solved for X using the factored form
of A.
5. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
6. If equilibration was used, the matrix X is premultiplied by
diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
that it solves the original system before equilibration.
file lapack/single/sgesvxx.f
prec single
SGESVXX uses the LU factorization to compute the solution to a
real system of linear equations A * X = B, where A is an
N-by-N matrix and X and B are N-by-NRHS matrices.
If requested, both normwise and maximum componentwise error bounds
are returned. SGESVXX will return a solution with a tiny
guaranteed error (O(eps) where eps is the working machine
precision) unless the matrix is very ill-conditioned, in which
case a warning is returned. Relevant condition numbers also are
calculated and returned.
SGESVXX accepts user-provided factorizations and equilibration
factors; see the definitions of the FACT and EQUED options.
Solving with refinement and using a factorization from a previous
SGESVXX call will also produce a solution with either O(eps)
errors or warnings, but we cannot make that claim for general
user-provided factorizations and equilibration factors if they
differ from what SGESVXX would itself produce.
Description
===========
The following steps are performed:
1. If FACT = 'E', real scaling factors are computed to equilibrate
the system:
TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B
TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N')
or diag(C)*B (if TRANS = 'T' or 'C').
2. If FACT = 'N' or 'E', the LU decomposition is used to factor
the matrix A (after equilibration if FACT = 'E') as
A = P * L * U,
where P is a permutation matrix, L is a unit lower triangular
matrix, and U is upper triangular.
3. If some U(i,i)=0, so that U is exactly singular, then the
routine returns with INFO = i. Otherwise, the factored form of A
is used to estimate the condition number of the matrix A (see
argument RCOND). If the reciprocal of the condition number is less
than machine precision, the routine still goes on to solve for X
and compute error bounds as described below.
4. The system of equations is solved for X using the factored form
of A.
5. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero),
the routine will use iterative refinement to try to get a small
error and error bounds. Refinement calculates the residual to at
least twice the working precision.
6. If equilibration was used, the matrix X is premultiplied by
diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so
that it solves the original system before equilibration.
file lapack/single/sggesx.f
prec single
SGGESX computes for a pair of N-by-N real nonsymmetric matrices
(A,B), the generalized eigenvalues, the real Schur form (S,T), and,
optionally, the left and/or right matrices of Schur vectors (VSL and
VSR). This gives the generalized Schur factorization
(A,B) = ( (VSL) S (VSR)**T, (VSL) T (VSR)**T )
Optionally, it also orders the eigenvalues so that a selected cluster
of eigenvalues appears in the leading diagonal blocks of the upper
quasi-triangular matrix S and the upper triangular matrix T; computes
a reciprocal condition number for the average of the selected
eigenvalues (RCONDE); and computes a reciprocal condition number for
the right and left deflating subspaces corresponding to the selected
eigenvalues (RCONDV). The leading columns of VSL and VSR then form
an orthonormal basis for the corresponding left and right eigenspaces
(deflating subspaces).
A generalized eigenvalue for a pair of matrices (A,B) is a scalar w
or a ratio alpha/beta = w, such that A - w*B is singular. It is
usually represented as the pair (alpha,beta), as there is a
reasonable interpretation for beta=0 or for both being zero.
A pair of matrices (S,T) is in generalized real Schur form if T is
upper triangular with non-negative diagonal and S is block upper
triangular with 1-by-1 and 2-by-2 blocks. 1-by-1 blocks correspond
to real generalized eigenvalues, while 2-by-2 blocks of S will be
"standardized" by making the corresponding elements of T have the
form:
[ a 0 ]
[ 0 b ]
and the pair of corresponding 2-by-2 blocks in S and T will have a
complex conjugate pair of generalized eigenvalues.
file lapack/single/sggevx.f
prec single
SGGEVX computes for a pair of N-by-N real nonsymmetric matrices (A,B)
the generalized eigenvalues, and optionally, the left and/or right
generalized eigenvectors.
Optionally also, it computes a balancing transformation to improve
the conditioning of the eigenvalues and eigenvectors (ILO, IHI,
LSCALE, RSCALE, ABNRM, and BBNRM), reciprocal condition numbers for
the eigenvalues (RCONDE), and reciprocal condition numbers for the
right eigenvectors (RCONDV).
A generalized eigenvalue for a pair of matrices (A,B) is a scalar
lambda or a ratio alpha/beta = lambda, such that A - lambda*B is
singular. It is usually represented as the pair (alpha,beta), as
there is a reasonable interpretation for beta=0, and even for both
being zero.
The right eigenvector v(j) corresponding to the eigenvalue lambda(j)
of (A,B) satisfies
A * v(j) = lambda(j) * B * v(j) .
The left eigenvector u(j) corresponding to the eigenvalue lambda(j)
of (A,B) satisfies
u(j)**H * A = lambda(j) * u(j)**H * B.
where u(j)**H is the conjugate-transpose of u(j).
file lapack/single/spbsvx.f
prec single
SPBSVX uses the Cholesky factorization A = U**T*U or A = L*L**T to
compute the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric positive definite band matrix and X
and B are N-by-NRHS matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed:
1. If FACT = 'E', real scaling factors are computed to equilibrate
the system:
diag(S) * A * diag(S) * inv(diag(S)) * X = diag(S) * B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(S)*A*diag(S) and B by diag(S)*B.
2. If FACT = 'N' or 'E', the Cholesky decomposition is used to
factor the matrix A (after equilibration if FACT = 'E') as
A = U**T * U, if UPLO = 'U', or
A = L * L**T, if UPLO = 'L',
where U is an upper triangular band matrix, and L is a lower
triangular band matrix.
3. If the leading i-by-i principal minor is not positive definite,
then the routine returns with INFO = i. Otherwise, the factored
form of A is used to estimate the condition number of the matrix
A. If the reciprocal of the condition number is less than machine
precision, INFO = N+1 is returned as a warning, but the routine
still goes on to solve for X and compute error bounds as
described below.
4. The system of equations is solved for X using the factored form
of A.
5. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
6. If equilibration was used, the matrix X is premultiplied by
diag(S) so that it solves the original system before
equilibration.
file lapack/single/sposvx.f
prec single
SPOSVX uses the Cholesky factorization A = U**T*U or A = L*L**T to
compute the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric positive definite matrix and X and B
are N-by-NRHS matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed:
1. If FACT = 'E', real scaling factors are computed to equilibrate
the system:
diag(S) * A * diag(S) * inv(diag(S)) * X = diag(S) * B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(S)*A*diag(S) and B by diag(S)*B.
2. If FACT = 'N' or 'E', the Cholesky decomposition is used to
factor the matrix A (after equilibration if FACT = 'E') as
A = U**T* U, if UPLO = 'U', or
A = L * L**T, if UPLO = 'L',
where U is an upper triangular matrix and L is a lower triangular
matrix.
3. If the leading i-by-i principal minor is not positive definite,
then the routine returns with INFO = i. Otherwise, the factored
form of A is used to estimate the condition number of the matrix
A. If the reciprocal of the condition number is less than machine
precision, INFO = N+1 is returned as a warning, but the routine
still goes on to solve for X and compute error bounds as
described below.
4. The system of equations is solved for X using the factored form
of A.
5. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
6. If equilibration was used, the matrix X is premultiplied by
diag(S) so that it solves the original system before
equilibration.
file lapack/single/sposvxx.f
prec single
SPOSVXX uses the Cholesky factorization A = U**T*U or A = L*L**T
to compute the solution to a real system of linear equations
A * X = B, where A is an N-by-N symmetric positive definite matrix
and X and B are N-by-NRHS matrices.
If requested, both normwise and maximum componentwise error bounds
are returned. SPOSVXX will return a solution with a tiny
guaranteed error (O(eps) where eps is the working machine
precision) unless the matrix is very ill-conditioned, in which
case a warning is returned. Relevant condition numbers also are
calculated and returned.
SPOSVXX accepts user-provided factorizations and equilibration
factors; see the definitions of the FACT and EQUED options.
Solving with refinement and using a factorization from a previous
SPOSVXX call will also produce a solution with either O(eps)
errors or warnings, but we cannot make that claim for general
user-provided factorizations and equilibration factors if they
differ from what SPOSVXX would itself produce.
Description
===========
The following steps are performed:
1. If FACT = 'E', real scaling factors are computed to equilibrate
the system:
diag(S)*A*diag(S) *inv(diag(S))*X = diag(S)*B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(S)*A*diag(S) and B by diag(S)*B.
2. If FACT = 'N' or 'E', the Cholesky decomposition is used to
factor the matrix A (after equilibration if FACT = 'E') as
A = U**T* U, if UPLO = 'U', or
A = L * L**T, if UPLO = 'L',
where U is an upper triangular matrix and L is a lower triangular
matrix.
3. If the leading i-by-i principal minor is not positive definite,
then the routine returns with INFO = i. Otherwise, the factored
form of A is used to estimate the condition number of the matrix
A (see argument RCOND). If the reciprocal of the condition number
is less than machine precision, the routine still goes on to solve
for X and compute error bounds as described below.
4. The system of equations is solved for X using the factored form
of A.
5. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero),
the routine will use iterative refinement to try to get a small
error and error bounds. Refinement calculates the residual to at
least twice the working precision.
6. If equilibration was used, the matrix X is premultiplied by
diag(S) so that it solves the original system before
equilibration.
file lapack/single/sppsvx.f
prec single
SPPSVX uses the Cholesky factorization A = U**T*U or A = L*L**T to
compute the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric positive definite matrix stored in
packed format and X and B are N-by-NRHS matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed:
1. If FACT = 'E', real scaling factors are computed to equilibrate
the system:
diag(S) * A * diag(S) * inv(diag(S)) * X = diag(S) * B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(S)*A*diag(S) and B by diag(S)*B.
2. If FACT = 'N' or 'E', the Cholesky decomposition is used to
factor the matrix A (after equilibration if FACT = 'E') as
A = U**T* U, if UPLO = 'U', or
A = L * L**T, if UPLO = 'L',
where U is an upper triangular matrix and L is a lower triangular
matrix.
3. If the leading i-by-i principal minor is not positive definite,
then the routine returns with INFO = i. Otherwise, the factored
form of A is used to estimate the condition number of the matrix
A. If the reciprocal of the condition number is less than machine
precision, INFO = N+1 is returned as a warning, but the routine
still goes on to solve for X and compute error bounds as
described below.
4. The system of equations is solved for X using the factored form
of A.
5. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
6. If equilibration was used, the matrix X is premultiplied by
diag(S) so that it solves the original system before
equilibration.
file lapack/single/ssbevx.f
prec single
SSBEVX computes selected eigenvalues and, optionally, eigenvectors
of a real symmetric band matrix A. Eigenvalues and eigenvectors can
be selected by specifying either a range of values or a range of
indices for the desired eigenvalues.
file lapack/single/ssbgvx.f
prec single
SSBGVX computes selected eigenvalues, and optionally, eigenvectors
of a real generalized symmetric-definite banded eigenproblem, of
the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric
and banded, and B is also positive definite. Eigenvalues and
eigenvectors can be selected by specifying either all eigenvalues,
a range of values or a range of indices for the desired eigenvalues.
file lapack/single/sspevx.f
prec single
SSPEVX computes selected eigenvalues and, optionally, eigenvectors
of a real symmetric matrix A in packed storage. Eigenvalues/vectors
can be selected by specifying either a range of values or a range of
indices for the desired eigenvalues.
file lapack/single/sspgvx.f
prec single
SSPGVX computes selected eigenvalues, and optionally, eigenvectors
of a real generalized symmetric-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A
and B are assumed to be symmetric, stored in packed storage, and B
is also positive definite. Eigenvalues and eigenvectors can be
selected by specifying either a range of values or a range of indices
for the desired eigenvalues.
file lapack/single/sspsvx.f
prec single
SSPSVX uses the diagonal pivoting factorization A = U*D*U**T or
A = L*D*L**T to compute the solution to a real system of linear
equations A * X = B, where A is an N-by-N symmetric matrix stored
in packed format and X and B are N-by-NRHS matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed:
1. If FACT = 'N', the diagonal pivoting method is used to factor A as
A = U * D * U**T, if UPLO = 'U', or
A = L * D * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices and D is symmetric and block diagonal with
1-by-1 and 2-by-2 diagonal blocks.
2. If some D(i,i)=0, so that D is exactly singular, then the routine
returns with INFO = i. Otherwise, the factored form of A is used
to estimate the condition number of the matrix A. If the
reciprocal of the condition number is less than machine precision,
INFO = N+1 is returned as a warning, but the routine still goes on
to solve for X and compute error bounds as described below.
3. The system of equations is solved for X using the factored form
of A.
4. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
file lapack/single/sstevx.f
prec single
SSTEVX computes selected eigenvalues and, optionally, eigenvectors
of a real symmetric tridiagonal matrix A. Eigenvalues and
eigenvectors can be selected by specifying either a range of values
or a range of indices for the desired eigenvalues.
file lapack/single/ssyevx.f
prec single
SSYEVX computes selected eigenvalues and, optionally, eigenvectors
of a real symmetric matrix A. Eigenvalues and eigenvectors can be
selected by specifying either a range of values or a range of indices
for the desired eigenvalues.
file lapack/single/ssygvx.f
prec single
SSYGVX computes selected eigenvalues, and optionally, eigenvectors
of a real generalized symmetric-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A
and B are assumed to be symmetric and B is also positive definite.
Eigenvalues and eigenvectors can be selected by specifying either a
range of values or a range of indices for the desired eigenvalues.
file lapack/single/ssysvx.f
prec single
SSYSVX uses the diagonal pivoting factorization to compute the
solution to a real system of linear equations A * X = B,
where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
matrices.
Error bounds on the solution and a condition estimate are also
provided.
Description
===========
The following steps are performed:
1. If FACT = 'N', the diagonal pivoting method is used to factor A.
The form of the factorization is
A = U * D * U**T, if UPLO = 'U', or
A = L * D * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and D is symmetric and block diagonal with
1-by-1 and 2-by-2 diagonal blocks.
2. If some D(i,i)=0, so that D is exactly singular, then the routine
returns with INFO = i. Otherwise, the factored form of A is used
to estimate the condition number of the matrix A. If the
reciprocal of the condition number is less than machine precision,
INFO = N+1 is returned as a warning, but the routine still goes on
to solve for X and compute error bounds as described below.
3. The system of equations is solved for X using the factored form
of A.
4. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
# --------------------------------------------------------
# Available SIMPLE and DIVIDE AND CONQUER DRIVER routines:
# --------------------------------------------------------
file lapack/single/sgesv.f
prec single
for Solves a general system of linear equations AX=B.
gams d2a1
file lapack/single/sgbsv.f
prec single
for Solves a general banded system of linear equations AX=B.
gams d2a2
file lapack/single/sgtsv.f
prec single
for Solves a general tridiagonal system of linear equations AX=B.
gams d2a2a
file lapack/single/sposv.f
prec single
for Solves a symmetric positive definite system of linear
, equations AX=B.
gams d2b1b
file lapack/single/sppsv.f
prec single
for Solves a symmetric positive definite system of linear
, equations AX=B, where A is held in packed storage.
gams d2b1b
file lapack/single/spbsv.f
prec single
for Solves a symmetric positive definite banded system
, of linear equations AX=B.
gams d2b2
file lapack/single/sptsv.f
prec single
for Solves a symmetric positive definite tridiagonal system
, of linear equations AX=B.
gams d2b2a
file lapack/single/ssysv.f
prec single
for Solves a real symmetric indefinite system of linear equations AX=B.
gams d2b1a
file lapack/single/sspsv.f
prec single
for Solves a real symmetric indefinite system of linear equations AX=B,
, where A is held in packed storage.
gams d2b1a
file lapack/single/sgels.f
prec single
for Computes the least squares solution to an over-determined system
, of linear equations, A X=B or A**H X=B, or the minimum norm
, solution of an under-determined system, where A is a general
, rectangular matrix of full rank, using a QR or LQ factorization
, of A.
gams d9a1
file lapack/single/sgelsd.f
prec single
for Computes the least squares solution to an over-determined system
, of linear equations, A X=B or A**H X=B, or the minimum norm
, solution of an under-determined system, using a divide and conquer
, method, where A is a general rectangular matrix of full rank,
, using a QR or LQ factorization of A.
gams d9a1
file lapack/single/sgglse.f
prec single
for Solves the LSE (Constrained Linear Least Squares Problem) using
, the GRQ (Generalized RQ) factorization
gams d9b1
file lapack/single/sggglm.f
prec single
for Solves the GLM (Generalized Linear Regression Model) using
, the GQR (Generalized QR) factorization
file lapack/single/ssyev.f
prec single
for Computes all eigenvalues, and optionally, eigenvectors of a real
, symmetric matrix.
gams d4a1
file lapack/single/ssyevd.f
prec single
for Computes all eigenvalues, and optionally, eigenvectors of a real
, symmetric matrix. If eigenvectors are desired, it uses a divide
, and conquer algorithm.
gams d4a1
file lapack/single/sspev.f
prec single
for Computes all eigenvalues, and optionally, eigenvectors of a real
, symmetric matrix in packed storage.
gams d4a1
file lapack/single/sspevd.f
prec single
for Computes all eigenvalues, and optionally, eigenvectors of a real
, symmetric matrix in packed storage. If eigenvectors are desired,
, it uses a divide and conquer algorithm.
gams d4a1
file lapack/single/ssbev.f
prec single
for Computes all eigenvalues, and optionally, eigenvectors of a real
, symmetric band matrix.
gams d4a1, d4a6
file lapack/single/ssbevd.f
prec single
for Computes all eigenvalues, and optionally, eigenvectors of a real
, symmetric band matrix. If eigenvectors are desired, it uses a
, divide and conquer algorithm.
gams d4a1, d4a6
file lapack/single/sstev.f
prec single
for Computes all eigenvalues, and optionally, eigenvectors of a real
, symmetric tridiagonal matrix.
gams d4a1, d4a5
file lapack/single/sstevd.f
prec single
for Computes all eigenvalues, and optionally, eigenvectors of a real
, symmetric tridiagonal matrix. If eigenvectors are desired, it uses
, a divide and conquer algorithm.
gams d4a1, d4a5
file lapack/single/sgees.f
prec single
for Computes the eigenvalues and Schur factorization of a general
, matrix, and orders the factorization so that selected eigenvalues
, are at the top left of the Schur form.
gams d4a2
file lapack/single/sgeev.f
prec single
for Computes the eigenvalues and left and right eigenvectors of
, a general matrix.
gams d4a2
file lapack/single/sgesvd.f
prec single
for Computes the singular value decomposition (SVD) of a general
, rectangular matrix.
gams d6
file lapack/single/sgesdd.f
prec single
for Computes the singular value decomposition (SVD) of a general
, rectangular matrix using divide-and-conquer.
gams d6
file lapack/single/ssygv.f
prec single
for Computes all eigenvalues and the eigenvectors of a generalized
, symmetric-definite generalized eigenproblem,
, Ax= lambda Bx, ABx= lambda x, or BAx= lambda x.
gams d4b1
file lapack/single/ssygvd.f
prec single
for Computes all eigenvalues and the eigenvectors of a generalized
, symmetric-definite generalized eigenproblem,
, Ax= lambda Bx, ABx= lambda x, or BAx= lambda x.
, If eigenvectors are desired, it uses a divide and conquer algorithm.
gams d4b1
file lapack/single/sspgv.f
prec single
for Computes all eigenvalues and eigenvectors of a generalized
, symmetric-definite generalized eigenproblem, Ax= lambda
, Bx, ABx= lambda x, or BAx= lambda x, where A and B are in packed
, storage.
gams d4b1
file lapack/single/sspgvd.f
prec single
for Computes all eigenvalues and eigenvectors of a generalized
, symmetric-definite generalized eigenproblem, Ax= lambda
, Bx, ABx= lambda x, or BAx= lambda x, where A and B are in packed
, storage.
, If eigenvectors are desired, it uses a divide and conquer algorithm.
gams d4b1
file lapack/single/ssbgv.f
prec single
for Computes all the eigenvalues, and optionally, the eigenvectors
, of a real generalized symmetric-definite banded eigenproblem, of
, the form A*x=(lambda)*B*x. A and B are assumed to be symmetric
, and banded, and B is also positive definite.
file lapack/single/ssbgvd.f
prec single
for Computes all the eigenvalues, and optionally, the eigenvectors
, of a real generalized symmetric-definite banded eigenproblem, of
, the form A*x=(lambda)*B*x. A and B are assumed to be symmetric
, and banded, and B is also positive definite.
, If eigenvectors are desired, it uses a divide and conquer algorithm.
file lapack/single/sgegs.f
prec single
for Computes the generalized eigenvalues, Schur form, and left and/or
, right Schur vectors for a pair of nonsymmetric matrices
file lapack/single/sgges.f
prec single
for Computes the generalized eigenvalues, Schur form, and left and/or
, right Schur vectors for a pair of nonsymmetric matrices
file lapack/single/sgegv.f
prec single
for Computes the generalized eigenvalues, and left and/or right
, generalized eigenvectors for a pair of nonsymmetric matrices
file lapack/single/sggev.f
prec single
for Computes the generalized eigenvalues, and left and/or right
, generalized eigenvectors for a pair of nonsymmetric matrices
file lapack/single/sggsvd.f
prec single
for Computes the Generalized Singular Value Decomposition
# -----------------------------------------
# Available EXPERT and RRR DRIVER routines:
# -----------------------------------------
file lapack/single/sgesvx.f
prec single
for Solves a general system of linear equations AX=B, A**T X=B
, or A**H X=B, and provides an estimate of the condition number
, and error bounds on the solution.
gams d2a1
file lapack/single/sgbsvx.f
prec single
for Solves a general banded system of linear equations AX=B,
, A**T X=B or A**H X=B, and provides an estimate of the condition
, number and error bounds on the solution.
gams d2a2
file lapack/single/sgtsvx.f
prec single
for Solves a general tridiagonal system of linear equations AX=B,
, A**T X=B or A**H X=B, and provides an estimate of the condition
, number and error bounds on the solution.
gams d2a2a
file lapack/single/sposvx.f
prec single
for Solves a symmetric positive definite system of linear
, equations AX=B, and provides an estimate of the condition number
, and error bounds on the solution.
gams d2b1b
file lapack/single/sppsvx.f
prec single
for Solves a symmetric positive definite system of linear
, equations AX=B, where A is held in packed storage, and provides
, an estimate of the condition number and error bounds on the
, solution.
gams d2b1b
file lapack/single/spbsvx.f
prec single
for Solves a symmetric positive definite banded system
, of linear equations AX=B, and provides an estimate of the condition
, number and error bounds on the solution.
gams d2b2
file lapack/single/sptsvx.f
prec single
for Solves a symmetric positive definite tridiagonal
, system of linear equations AX=B, and provides an estimate of
, the condition number and error bounds on the solution.
gams d2b2a
file lapack/single/ssysvx.f
prec single
for Solves a real symmetric
, indefinite system of linear equations AX=B, and provides an
, estimate of the condition number and error bounds on the solution.
gams d2b1a
file lapack/single/sspsvx.f
prec single
for Solves a real symmetric
, indefinite system of linear equations AX=B, where A is held
, in packed storage, and provides an estimate of the condition
, number and error bounds on the solution.
gams d2b1a
file lapack/single/sgelsx.f
prec single
for Computes the minimum norm least squares solution to an over-
, or under-determined system of linear equations A X=B, using a
, complete orthogonal factorization of A.
gams d9a1
file lapack/single/sgelsy.f
prec single
for Computes the minimum norm least squares solution to an over-
, or under-determined system of linear equations A X=B, using a
, complete orthogonal factorization of A.
gams d9a1
file lapack/single/sgelss.f
prec single
for Computes the minimum norm least squares solution to an over-
, or under-determined system of linear equations A X=B, using
, the singular value decomposition of A.
gams d9a1
file lapack/single/ssyevx.f
prec single
for Computes selected eigenvalues and eigenvectors of a symmetric matrix.
gams d4a1
file lapack/single/ssyevr.f
prec single
for Computes selected eigenvalues, and optionally, eigenvectors of a real
, symmetric matrix. Eigenvalues are computed by the dqds
, algorithm, and eigenvectors are computed from various "good" LDL^T
, representations (also known as Relatively Robust Representations).
gams d4a1, d4a5
file lapack/single/ssygvx.f
prec single
for Computes selected eigenvalues, and optionally, the eigenvectors of
, a generalized symmetric-definite generalized eigenproblem,
, Ax= lambda Bx, ABx= lambda x, or BAx= lambda x.
gams d4b1
file lapack/single/sspevx.f
prec single
for Computes selected eigenvalues and eigenvectors of a
, symmetric matrix in packed storage.
gams d4a1
file lapack/single/sspgvx.f
prec single
for Computes selected eigenvalues, and optionally, eigenvectors of
, a generalized symmetric-definite generalized eigenproblem, Ax= lambda
, Bx, ABx= lambda x, or BAx= lambda x, where A and B are in packed
, storage.
gams d4b1
file lapack/single/ssbevx.f
prec single
for Computes selected eigenvalues and eigenvectors of a
, symmetric band matrix.
gams d4a1, d4a6
file lapack/single/ssbgvx.f
prec single
for Computes selected eigenvalues, and optionally, the eigenvectors
, of a real generalized symmetric-definite banded eigenproblem, of
, the form A*x=(lambda)*B*x. A and B are assumed to be symmetric
, and banded, and B is also positive definite.
file lapack/single/sstevx.f
prec single
for Computes selected eigenvalues and eigenvectors of a real
, symmetric tridiagonal matrix.
gams d4a1, d4a5
file lapack/single/sstevr.f
prec single
for Computes selected eigenvalues, and optionally, eigenvectors of a real
, symmetric tridiagonal matrix. Eigenvalues are computed by the dqds
, algorithm, and eigenvectors are computed from various "good" LDL^T
, representations (also known as Relatively Robust Representations).
gams d4a1, d4a5
file lapack/single/sgeesx.f
prec single
for Computes the eigenvalues and Schur factorization of a general
, matrix, orders the factorization so that selected eigenvalues
, are at the top left of the Schur form, and computes reciprocal
, condition numbers for the average of the selected eigenvalues,
, and for the associated right invariant subspace.
gams d4a2
file lapack/single/sggesx.f
prec single
for Computes the generalized eigenvalues, the real Schur form, and,
, optionally, the left and/or right matrices of Schur vectors.
file lapack/single/sgeevx.f
prec single
for Computes the eigenvalues and left and right eigenvectors of
, a general matrix, with preliminary balancing of the matrix,
, and computes reciprocal condition numbers for the eigenvalues
, and right eigenvectors.
gams d4a2
file lapack/single/sggevx.f
prec single
for Computes the generalized eigenvalues, and optionally, the left
, and/or right generalized eigenvectors.
# ---------------------------------
# Available COMPUTATIONAL routines:
# ---------------------------------
file lapack/single/sbdsdc.f
prec single
for Computes the singular value decomposition (SVD) of a real bidiagonal
, matrix, using a divide and conquer method.
gams d6
file lapack/single/sbdsqr.f
prec single
for Computes the singular value decomposition (SVD) of a real bidiagonal
, matrix, using the bidiagonal QR algorithm.
gams d6
file lapack/single/sdisna.f
prec single
for Computes the reciprocal condition numbers for the eigenvectors of a
, real symmetric or complex Hermitian matrix or for the left or right
, singular vectors of a general matrix.
file lapack/single/sgbbrd.f
prec single
, Reduces a general band matrix to real upper bidiagonal form
, by an orthogonal transformation.
file lapack/single/sgbcon.f
prec single
for Estimates the reciprocal of the condition number of a general
, band matrix, in either the 1-norm or the infinity-norm, using
, the LU factorization computed by SGBTRF.
gams d2a2
file lapack/single/sgbequ.f
prec single
for Computes row and column scalings to equilibrate a general band
, matrix and reduce its condition number.
gams d2a2
file lapack/single/sgbrfs.f
prec single
for Improves the computed solution to a general banded system of
, linear equations AX=B, A**T X=B or A**H X=B, and provides forward
, and backward error bounds for the solution.
gams d2a2
file lapack/single/sgbtrf.f
prec single
for Computes an LU factorization of a general band matrix, using
, partial pivoting with row interchanges.
gams d2a2
file lapack/single/sgbtrs.f
prec single
for Solves a general banded system of linear equations AX=B,
, A**T X=B or A**H X=B, using the LU factorization computed
, by SGBTRF.
gams d2a2
file lapack/single/sgebak.f
prec single
for Transforms eigenvectors of a balanced matrix to those of the
, original matrix supplied to SGEBAL.
gams d4c4
file lapack/single/sgebal.f
prec single
for Balances a general matrix in order to improve the accuracy
, of computed eigenvalues.
gams d4c1a
file lapack/single/sgebrd.f
prec single
for Reduces a general rectangular matrix to real bidiagonal form
, by an orthogonal transformation.
gams d6
file lapack/single/sgecon.f
prec single
for Estimates the reciprocal of the condition number of a general
, matrix, in either the 1-norm or the infinity-norm, using the
, LU factorization computed by SGETRF.
gams d2a1
file lapack/single/sgeequ.f
prec single
for Computes row and column scalings to equilibrate a general
, rectangular matrix and reduce its condition number.
gams d2a1
file lapack/single/sgehrd.f
prec single
for Reduces a general matrix to upper Hessenberg form by an
, orthogonal similarity transformation.
gams d4c1b2
file lapack/single/sgelqf.f
prec single
for Computes an LQ factorization of a general rectangular matrix.
gams d5
file lapack/single/sgeqlf.f
prec single
for Computes a QL factorization of a general rectangular matrix.
gams d5
file lapack/single/sgeqp3.f
prec single
for Computes a QR factorization with column pivoting of a general
, rectangular matrix using Level 3 BLAS.
gams d5
file lapack/single/sgeqpf.f
prec single
for Computes a QR factorization with column pivoting of a general
, rectangular matrix.
gams d5
file lapack/single/sgeqrf.f
prec single
for Computes a QR factorization of a general rectangular matrix.
gams d5
file lapack/single/sgerfs.f
prec single
for Improves the computed solution to a general system of linear
, equations AX=B, A**T X=B or A**H X=B, and provides forward and
, backward error bounds for the solution.
gams d2a1
file lapack/single/sgerqf.f
prec single
for Computes an RQ factorization of a general rectangular matrix.
gams d5
file lapack/single/sgetrf.f
prec single
for Computes an LU factorization of a general matrix, using partial
, pivoting with row interchanges.
gams d2a1
file lapack/single/sgetri.f
prec single
for Computes the inverse of a general matrix, using the LU factorization
, computed by SGETRF.
gams d2a1
file lapack/single/sgetrs.f
prec single
for Solves a general system of linear equations AX=B, A**T X=B
, or A**H X=B, using the LU factorization computed by SGETRF.
gams d2a1
file lapack/single/sggbak.f
prec single
For Forms the right or left eigenvectors of the generalized eigenvalue
, problem by backward transformation on the computed eigenvectors of
, the balanced pair of matrices output by SGGBAL.
file lapack/single/sggbal.f
prec single
For Balances a pair of general real matrices for the generalized
, eigenvalue problem A x = lambda B x.
file lapack/single/sgghrd.f
prec single
for Reduces a pair of real matrices to generalized upper
, Hessenberg form using orthogonal transformations
file lapack/single/sggqrf.f
prec single
for Computes a generalized QR factorization of a pair of matrices.
file lapack/single/sggrqf.f
prec single
for Computes a generalized RQ factorization of a pair of matrices.
file lapack/single/sggsvp.f
prec single
for Computes orthogonal matrices as a preprocessing step
, for computing the generalized singular value decomposition
file lapack/single/sgtcon.f
prec single
for Estimates the reciprocal of the condition number of a general
, tridiagonal matrix, in either the 1-norm or the infinity-norm,
, using the LU factorization computed by SGTTRF.
gams d2a2a
file lapack/single/sgtrfs.f
prec single
for Improves the computed solution to a general tridiagonal system
, of linear equations AX=B, A**T X=B or A**H X=B, and provides
, forward and backward error bounds for the solution.
gams d2a2a
file lapack/single/sgttrf.f
prec single
for Computes an LU factorization of a general tridiagonal matrix,
, using partial pivoting with row interchanges.
gams d2a2a
file lapack/single/sgttrs.f
prec single
for Solves a general tridiagonal system of linear equations AX=B,
, A**T X=B or A**H X=B, using the LU factorization computed by
, SGTTRF.
gams d2a2a
file lapack/single/shgeqz.f
prec single
for Implements a single-/double-shift version of the QZ method for
, finding the generalized eigenvalues of the equation
, det(A - w(i) B) = 0
file lapack/single/shsein.f
prec single
for Computes specified right and/or left eigenvectors of an upper
, Hessenberg matrix by inverse iteration.
gams d4c3
file lapack/single/shseqr.f
prec single
for Computes the eigenvalues and Schur factorization of an upper
, Hessenberg matrix, using the multishift QR algorithm.
gams d4c2b
file lapack/single/sopgtr.f
prec single
for Generates the orthogonal transformation matrix from
, a reduction to tridiagonal form determined by SSPTRD.
gams d4c1b1
file lapack/single/sopmtr.f
prec single
for Multiplies a general matrix by the orthogonal
, transformation matrix from a reduction to tridiagonal form
, determined by SSPTRD.
gams d4c4
file lapack/single/sorgbr.f
prec single
for Generates the orthogonal transformation matrices from
, a reduction to bidiagonal form determined by SGEBRD.
gams d6
file lapack/single/sorghr.f
prec single
for Generates the orthogonal transformation matrix from
, a reduction to Hessenberg form determined by SGEHRD.
gams d4c1b2
file lapack/single/sorglq.f
prec single
for Generates all or part of the orthogonal matrix Q from
, an LQ factorization determined by SGELQF.
gams d5
file lapack/single/sorgql.f
prec single
for Generates all or part of the orthogonal matrix Q from
, a QL factorization determined by SGEQLF.
gams d5
file lapack/single/sorgqr.f
prec single
for Generates all or part of the orthogonal matrix Q from
, a QR factorization determined by SGEQRF.
gams d5
file lapack/single/sorgrq.f
prec single
for Generates all or part of the orthogonal matrix Q from
, an RQ factorization determined by SGERQF.
gams d5
file lapack/single/sorgtr.f
prec single
for Generates the orthogonal transformation matrix from
, a reduction to tridiagonal form determined by SSYTRD.
gams d4c1b1
file lapack/single/sormbr.f
prec single
for Multiplies a general matrix by one of the orthogonal
, transformation matrices from a reduction to bidiagonal form
, determined by SGEBRD.
gams d6
file lapack/single/sormhr.f
prec single
for Multiplies a general matrix by the orthogonal transformation
, matrix from a reduction to Hessenberg form determined by SGEHRD.
gams d4c4
file lapack/single/sormlq.f
prec single
for Multiplies a general matrix by the orthogonal matrix
, from an LQ factorization determined by SGELQF.
gams d5
file lapack/single/sormql.f
prec single
for Multiplies a general matrix by the orthogonal matrix
, from a QL factorization determined by SGEQLF.
gams d5
file lapack/single/sormqr.f
prec single
for Multiplies a general matrix by the orthogonal matrix
, from a QR factorization determined by SGEQRF.
gams d5
file lapack/single/sormr3.f
prec single
for Multiples a general matrix by the orthogonal matrix
, from an RZ factorization determined by STZRZF.
file lapack/single/sormrq.f
prec single
for Multiplies a general matrix by the orthogonal matrix
, from an RQ factorization determined by SGERQF.
gams d5
file lapack/single/sormrz.f
prec single
for Multiples a general matrix by the orthogonal matrix
, from an RZ factorization determined by STZRZF.
file lapack/single/sormtr.f
prec single
for Multiplies a general matrix by the orthogonal
, transformation matrix from a reduction to tridiagonal form
, determined by SSYTRD.
gams d4c4
file lapack/single/spbcon.f
prec single
for Estimates the reciprocal of the condition number of a
, symmetric positive definite band matrix, using the
, Cholesky factorization computed by SPBTRF.
gams d2b2
file lapack/single/spbequ.f
prec single
for Computes row and column scalings to equilibrate a symmetric
, positive definite band matrix and reduce its condition number.
gams d2b2
file lapack/single/spbrfs.f
prec single
for Improves the computed solution to a symmetric positive
, definite banded system of linear equations AX=B, and provides
, forward and backward error bounds for the solution.
gams d2b2
file lapack/single/spbstf.f
prec single
for Computes a split Cholesky factorization of a real symmetric positive
, definite band matrix.
file lapack/single/spbtrf.f
prec single
for Computes the Cholesky factorization of a symmetric
, positive definite band matrix.
gams d2b2
file lapack/single/spbtrs.f
prec single
for Solves a symmetric positive definite banded system
, of linear equations AX=B, using the Cholesky factorization
, computed by SPBTRF.
gams d2b2
file lapack/single/spocon.f
prec single
for Estimates the reciprocal of the condition number of a
, symmetric positive definite matrix, using the
, Cholesky factorization computed by SPOTRF.
gams d2b1b
file lapack/single/spoequ.f
prec single
for Computes row and column scalings to equilibrate a symmetric
, positive definite matrix and reduce its condition number.
gams d2b1b
file lapack/single/sporfs.f
prec single
for Improves the computed solution to a symmetric positive
, definite system of linear equations AX=B, and provides forward
, and backward error bounds for the solution.
gams d2b1b
file lapack/single/spotrf.f
prec single
for Computes the Cholesky factorization of a symmetric
, positive definite matrix.
gams d2b1b
file lapack/single/spotri.f
prec single
for Computes the inverse of a symmetric positive definite
, matrix, using the Cholesky factorization computed by SPOTRF.
gams d2b1b
file lapack/single/spotrs.f
prec single
for Solves a symmetric positive definite system of linear
, equations AX=B, using the Cholesky factorization computed by
, SPOTRF.
gams d2b1b
file lapack/single/sppcon.f
prec single
for Estimates the reciprocal of the condition number of a
, symmetric positive definite matrix in packed storage,
, using the Cholesky factorization computed by SPPTRF.
gams d2b1b
file lapack/single/sppequ.f
prec single
for Computes row and column scalings to equilibrate a symmetric
, positive definite matrix in packed storage and reduce its condition
, number.
gams d2b1b
file lapack/single/spprfs.f
prec single
for Improves the computed solution to a symmetric positive
, definite system of linear equations AX=B, where A is held in
, packed storage, and provides forward and backward error bounds
, for the solution.
gams d2b1b
file lapack/single/spptrf.f
prec single
for Computes the Cholesky factorization of a symmetric
, positive definite matrix in packed storage.
gams d2b1b
file lapack/single/spptri.f
prec single
for Computes the inverse of a symmetric positive definite
, matrix in packed storage, using the Cholesky factorization computed
, by SPPTRF.
gams d2b1b
file lapack/single/spptrs.f
prec single
for Solves a symmetric positive definite system of linear
, equations AX=B, where A is held in packed storage, using the
, Cholesky factorization computed by SPPTRF.
gams d2b1b
file lapack/single/sptcon.f
prec single
for Computes the reciprocal of the condition number of a
, symmetric positive definite tridiagonal matrix,
, using the LDL**H factorization computed by SPTTRF.
gams d2b2a
file lapack/single/spteqr.f
prec single
for Computes all eigenvalues and eigenvectors of a real symmetric
, positive definite tridiagonal matrix, by computing the SVD of
, its bidiagonal Cholesky factor.
gams d4c2a
file lapack/single/sptrfs.f
prec single
for Improves the computed solution to a symmetric positive
, definite tridiagonal system of linear equations AX=B, and provides
, forward and backward error bounds for the solution.
gams d2b2a
file lapack/single/spttrf.f
prec single
for Computes the LDL**H factorization of a symmetric
, positive definite tridiagonal matrix.
gams d2b2a
file lapack/single/spttrs.f
prec single
for Solves a symmetric positive definite tridiagonal
, system of linear equations, using the LDL**H factorization
, computed by SPTTRF.
gams d2b2a
file lapack/single/ssbgst.f
prec single
for Reduces a real symmetric-definite banded generalized eigenproblem
, A x = lambda B x to standard form, where B has been factorized by
, SPBSTF (Crawford's algorithm).
file lapack/single/ssbtrd.f
prec single
for Reduces a symmetric band matrix to real symmetric
, tridiagonal form by an orthogonal similarity transformation.
gams d4c1b1
file lapack/single/sspcon.f
prec single
for Estimates the reciprocal of the condition number of a
, real symmetric indefinite
, matrix in packed storage, using the factorization computed
, by SSPTRF.
gams d2b1a
file lapack/single/sspgst.f
prec single
for Reduces a symmetric-definite generalized eigenproblem
, Ax= lambda Bx, ABx= lambda x, or BAx= lambda x, to standard
, form, where A and B are held in packed storage, and B has been
, factorized by SPPTRF.
gams d4c1c
file lapack/single/ssprfs.f
prec single
for Improves the computed solution to a real
, symmetric indefinite system of linear equations
, AX=B, where A is held in packed storage, and provides forward
, and backward error bounds for the solution.
gams d2b1a
file lapack/single/ssptrd.f
prec single
for Reduces a symmetric matrix in packed storage to real
, symmetric tridiagonal form by an orthogonal similarity
, transformation.
gams d4c1b1
file lapack/single/ssptrf.f
prec single
for Computes the factorization of a real
, symmetric-indefinite matrix in packed storage,
, using the diagonal pivoting method.
gams d2b1a
file lapack/single/ssptri.f
prec single
for Computes the inverse of a real symmetric
, indefinite matrix in packed storage, using the factorization
, computed by SSPTRF.
gams d2b1a
file lapack/single/ssptrs.f
prec single
for Solves a real symmetric
, indefinite system of linear equations AX=B, where A is held
, in packed storage, using the factorization computed
, by SSPTRF.
gams d2b1a
file lapack/single/sstebz.f
prec single
for Computes selected eigenvalues of a real symmetric tridiagonal
, matrix by bisection.
gams d4c2a
file lapack/single/sstedc.f
prec single
for Computes all eigenvalues and, optionally, eigenvectors of a
, symmetric tridiagonal matrix using the divide and conquer algorithm.
file lapack/single/sstegr.f
prec single
for Computes selected eigenvalues and, optionally, eigenvectors of a
, symmetric tridiagonal matrix. The eigenvalues are computed by the
, dqds algorithm, while eigenvectors are computed from various "good"
, LDL^T representations (also known as Relatively Robust Representations.)
file lapack/single/sstein.f
prec single
for Computes selected eigenvectors of a real symmetric tridiagonal
, matrix by inverse iteration.
gams d4c3
file lapack/single/ssteqr.f
prec single
for Computes all eigenvalues and eigenvectors of a real symmetric
, tridiagonal matrix, using the implicit QL or QR algorithm.
gams d4a1, d4a5, d4c2a
file lapack/single/ssterf.f
prec single
for Computes all eigenvalues of a real symmetric tridiagonal matrix,
, using a root-free variant of the QL or QR algorithm.
gams d4c2a
file lapack/single/ssycon.f
prec single
for Estimates the reciprocal of the condition number of a
, real symmetric indefinite matrix,
, using the factorization computed by SSYTRF.
gams d2b1a
file lapack/single/ssygst.f
prec single
for Reduces a symmetric-definite generalized eigenproblem
, Ax= lambda Bx, ABx= lambda x, or BAx= lambda x, to standard
, form, where B has been factorized by SPOTRF.
gams d4c1c
file lapack/single/ssyrfs.f
prec single
for Improves the computed solution to a real
, symmetric indefinite system of linear equations
, AX=B, and provides forward and backward error bounds for the
, solution.
gams d2b1a
file lapack/single/ssytrd.f
prec single
for Reduces a symmetric matrix to real symmetric tridiagonal
, form by an orthogonal similarity transformation.
gams d4c1b1
file lapack/single/ssytrf.f
prec single
for Computes the factorization of a real symmetric-indefinite matrix,
, using the diagonal pivoting method.
gams d2b1a
file lapack/single/ssytri.f
prec single
for Computes the inverse of a real symmetric indefinite matrix,
, using the factorization computed by SSYTRF.
gams d2b1a
file lapack/single/ssytrs.f
prec single
for Solves a real symmetric indefinite system of linear equations AX=B,
, using the factorization computed by SSPTRF.
gams d2b1a
file lapack/single/stbcon.f
prec single
for Estimates the reciprocal of the condition number of a triangular
, band matrix, in either the 1-norm or the infinity-norm.
gams d2a2, d2a3
file lapack/single/stbrfs.f
prec single
for Provides forward and backward error bounds for the solution
, of a triangular banded system of linear equations AX=B,
, A**T X=B or A**H X=B.
gams d2a2, d2a3
file lapack/single/stbtrs.f
prec single
for Solves a triangular banded system of linear equations AX=B,
, A**T X=B or A**H X=B.
gams d2a2, d2a3
file lapack/single/stgevc.f
prec single
for Computes some or all of the right and/or left generalized eigenvectors
, of a pair of upper triangular matrices.
gams d4b2
file lapack/single/stgexc.f
prec single
for Reorders the generalized real Schur decomposition of a real
, matrix pair (A,B) using an orthogonal equivalence transformation
, so that the diagonal block of (A,B) with row index IFST is moved
, to row ILST.
file lapack/single/stgsen.f
prec single
for Reorders the generalized real Schur decomposition of a real
, matrix pair (A, B) so that a selected cluster of eigenvalues
, appears in the leading diagonal blocks of the upper quasi-triangular
, matrix A and the upper triangular B.
file lapack/single/stgsja.f
prec single
for Computes the generalized singular value decomposition of two real
, upper triangular (or trapezoidal) matrices as output by SGGSVP.
gams d6
file lapack/single/stgsna.f
prec single
for Estimates reciprocal condition numbers for specified
, eigenvalues and/or eigenvectors of a matrix pair (A, B) in
, generalized real Schur canonical form, as returned by SGGES.
file lapack/single/stgsyl.f
prec single
for Solves the generalized Sylvester equation.
file lapack/single/stpcon.f
prec single
for Estimates the reciprocal of the condition number of a triangular
, matrix in packed storage, in either the 1-norm or the infinity-norm.
gams d2a3
file lapack/single/stprfs.f
prec single
for Provides forward and backward error bounds for the solution
, of a triangular system of linear equations AX=B, A**T X=B or
, A**H X=B, where A is held in packed storage.
gams d2a3
file lapack/single/stptri.f
prec single
for Computes the inverse of a triangular matrix in packed storage.
gams d2a3
file lapack/single/stptrs.f
prec single
for Solves a triangular system of linear equations AX=B,
, A**T X=B or A**H X=B, where A is held in packed storage.
gams d2a3
file lapack/single/strcon.f
prec single
for Estimates the reciprocal of the condition number of a triangular
, matrix, in either the 1-norm or the infinity-norm.
gams d2a3
file lapack/single/strevc.f
prec single
for Computes some or all of the right and/or left eigenvectors of
, an upper quasi-triangular matrix.
gams d4c3
file lapack/single/strexc.f
prec single
for Reorders the Schur factorization of a matrix by an orthogonal
, similarity transformation.
gams d4c
file lapack/single/strrfs.f
prec single
for Provides forward and backward error bounds for the solution
, of a triangular system of linear equations A X=B, A**T X=B or
, A**H X=B.
gams d2a3
file lapack/single/strsen.f
prec single
for Reorders the Schur factorization of a matrix in order to find
, an orthonormal basis of a right invariant subspace corresponding
, to selected eigenvalues, and returns reciprocal condition numbers
, (sensitivities) of the average of the cluster of eigenvalues
, and of the invariant subspace.
gams d4c
file lapack/single/strsna.f
prec single
for Estimates the reciprocal condition numbers (sensitivities)
, of selected eigenvalues and eigenvectors of an upper
, quasi-triangular matrix.
gams d4c
file lapack/single/strsyl.f
prec single
for Solves the Sylvester matrix equation A X +/- X B=C where A
, and B are upper quasi-triangular, and may be transposed.
gams d8
file lapack/single/strtri.f
prec single
for Computes the inverse of a triangular matrix.
gams d2a3
file lapack/single/strtrs.f
prec single
for Solves a triangular system of linear equations AX=B,
, A**T X=B or A**H X=B.
gams d2a3
file lapack/single/stzrqf.f
prec single
for Computes an RQ factorization of an upper trapezoidal matrix.
gams d5
file lapack/single/stzrzf.f
prec single
for Computes an RZ factorization of an upper trapezoidal matrix
, (blocked version of STZRQF).
#######################################
# Index for lapack/testing/eig #
#######################################
file xerbla.f
for Special version of this routine used in testing
file ilaenv.f
for Special version of this routine for testing and timing purposes
file xlaenv.f
for Resets ILAENV values for testing purposes
# ==========================================
# Available Eigenproblem Testing Routines
# ==========================================
file schkee.f
for Test program driver for eigenproblem testing
prec single
file dchkee.f
for Test program driver for eigenproblem testing
prec double
file cchkee.f
for Test program driver for eigenproblem testing
prec complex
file zchkee.f
for Test program driver for eigenproblem testing
prec doublecomplex
# ===
file schkbb.f
for Checks the banded SVD routine SGBBRD
prec single
file dchkbb.f
for Checks the banded SVD routine DGBBRD
prec double
file cchkbb.f
for Checks the banded SVD routine CGBBRD
prec complex
file zchkbb.f
for Checks the banded SVD routine ZGBBRD
prec doublecomplex
file schkbd.f
for Checks the SVD routines (SGEBRD, SORGBR, SBDSQR, SBDSDC)
prec single
file dchkbd.f
for Checks the SVD routines (DGEBRD, DORGBR, DBDSQR, DBDSDC)
prec double
file cchkbd.f
for Checks the SVD routines (CGEBRD, CUNGBR, CBDSQR, CBDSDC)
prec complex, doublecomplex
file zchkbd.f
for Checks the SVD routines (ZGEBRD, ZUNGBR, ZBDSQR, ZBDSDC)
prec doublecomplex
file sdrvbd.f
for Checks the SVD driver SGESVD and SGESDD
prec single
file ddrvbd.f
for Checks the SVD driver DGESVD and DGESDD
prec double
file cdrvbd.f
for Checks the SVD driver CGESVD and CGESDD
prec complex
file zdrvbd.f
for Checks the SVD driver ZGESVD and ZGESDD
prec doublecomplex
file serrbd.f
for Tests the error exits for SGEBRD,SORGBR,SORMBR,SBDSQR,SBDSDC
prec single
file derrbd.f
for Tests the error exits for DGEBRD,DORGBR,DORMBR,DBDSQR,DBDSDC
prec double
file cerrbd.f
for Tests the error exits for CGEBRD,CUNGBR,CUNMBR,CBDSQR,CBDSDC
prec complex
file zerrbd.f
for Tests the error exits for ZGEBRD,ZUNGBR,ZUNMBR,ZBDSQR,ZBDSDC
prec doublecomplex
# ===
file schkbk.f
for Tests SGEBAK
prec single
file dchkbk.f
for Tests DGEBAK
prec double
file cchkbk.f
for Tests CGEBAK
prec complex
file zchkbk.f
for Tests ZGEBAK
prec doublecomplex
# ===
file schkbl.f
for Tests SGEBAL
prec single
file dchkbl.f
for Tests DGEBAL
prec double
file cchkbl.f
for Tests CGEBAL
prec complex
file zchkbl.f
for Tests ZGEBAL
prec doublecomplex
# ===
file schkec.f
for Tests the eigen- condition estimation routines, STRSYL, STREXC, STRSNA, STRSEN
prec single
file dchkec.f
for Tests the eigen- condition estimation routines, DTRSYL, DTREXC, DTRSNA, DTRSEN
prec double
file cchkec.f
for Tests the eigen- condition estimation routines, CTRSYL, CTREXC, CTRSNA, CTRSEN
prec complex
file zchkec.f
for Tests the eigen- condition estimation routines, ZTRSYL, ZTREXC, ZTRSNA, ZTRSEN
prec doublecomplex
file serrec.f
for Tests the error exits for the eigen- condition estimation, routines (STRSYL, STREXC, STRSNA, STRSEN)
prec single
file derrec.f
for Tests the error exits for the eigen- condition estimation, routines (DTRSYL, DTREXC, DTRSNA, DTRSEN)
prec double
file cerrec.f
for Tests the error exits for the eigen- condition estimation, routines (CTRSYL, CTREXC, CTRSNA, CTRSEN)
prec complex
file zerrec.f
for Tests the error exits for the eigen- condition estimation, routines (ZTRSYL, ZTREXC, ZTRSNA, ZTRSEN)
prec doublecomplex
# ===
file schkgg.f
for Tests SGGHRD, SHGEQZ, and STGEVC
prec single
file dchkgg.f
for Tests DGGHRD, DHGEQZ, and DTGEVC
prec double
file cchkgg.f
for Tests CGGHRD, CHGEQZ, and CTGEVC
prec complex
file zchkgg.f
for Tests ZGGHRD, ZHGEQZ, and ZTGEVC
prec doublecomplex
file sdrvgg.f
for Tests SGEGS and SGEGV
prec single
file ddrvgg.f
for Tests DGEGS and DGEGV
prec double
file cdrvgg.f
for Tests CGEGS and CGEGV
prec complex
file zdrvgg.f
for Tests ZGEGS and ZGEGV
prec doublecomplex
file serrgg.f
for Tests the error exits for SGGHRD, SHGEQZ, and STGEVC
prec single
file derrgg.f
for Tests the error exits for DGGHRD, DHGEQZ, and DTGEVC
prec double
file cerrgg.f
for Tests the error exits for CGGHRD, CHGEQZ, and CTGEVC
prec complex
file zerrgg.f
for Tests the error exits for ZGGHRD, ZHGEQZ, and ZTGEVC
prec doublecomplex
# ===
file schkgk.f
for Testing SGGBAK
prec single
file dchkgk.f
for Testing DGGBAK
prec double
file cchkgk.f
for Testing CGGBAK
prec complex
file zchkgk.f
for Testing ZGGBAK
prec doublecomplex
# ===
file schkgl.f
for Testing SGGBAL
prec single
file dchkgl.f
for Testing DGGBAL
prec double
file cchkgl.f
for Testing CGGBAL
prec complex
file zchkgl.f
for Testing ZGGBAL
prec doublecomplex
# ===
file schkhs.f
for Checks the nonsymmetric eigenvalue problem routines, (SGEHRD, SORGHR, SORMHR, SHSEQR, STREVC, and SHSEIN)
prec single
file dchkhs.f
for Checks the nonsymmetric eigenvalue problem routines, (DGEHRD, DORGHR, DORMHR, DHSEQR, DTREVC, and DHSEIN)
prec double
file cchkhs.f
for Checks the nonsymmetric eigenvalue problem routines, (CGEHRD, CUNGHR, CUNMHR, CHSEQR, CTREVC, and CHSEIN)
prec complex
file zchkhs.f
for Checks the nonsymmetric eigenvalue problem routines, (ZGEHRD, ZUNGHR, ZUNMHR, ZHSEQR, ZTREVC, and ZHSEIN)
prec doublecomplex
file serrhs.f
for Tests the error exits for SGEHRD, SORGHR, SORMHR, SHSEQR, SHSEIN, and STREVC
prec single
file derrhs.f
for Tests the error exits for DGEHRD, DORGHR, DORMHR, DHSEQR, DHSEIN, and DTREVC
prec double
file cerrhs.f
for Tests the error exits for CGEHRD, CUNGHR, CUNMHR, CHSEQR, CHSEIN, and CTREVC
prec complex
file zerrhs.f
for Tests the error exits for ZGEHRD, ZUNGHR, ZUNMHR, ZHSEQR, ZHSEIN, and ZTREVC
prec doublecomplex
file sdrges.f
for Tests the driver routine SGGES
prec single
file ddrges.f
for Tests the driver routine DGGES
prec double
file cdrges.f
for Tests the driver routine CGGES
prec complex
file zdrges.f
for Tests the driver routine ZGGES
prec doublecomplex
file sdrgev.f
for Tests the driver routine SGGEV
prec single
file ddrgev.f
for Tests the driver routine DGGEV
prec double
file cdrgev.f
for Tests the driver routine CGGEV
prec complex
file zdrgev.f
for Tests the driver routine ZGGEV
prec doublecomplex
file sdrgsx.f
for Tests the driver routine SGGESX
prec single
file ddrgsx.f
for Tests the driver routine DGGESX
prec double
file cdrgsx.f
for Tests the driver routine CGGESX
prec complex
file zdrgsx.f
for Tests the driver routine ZGGESX
prec doublecomplex
file sdrgvx.f
for Tests the driver routine SGGEVX
prec single
file ddrgvx.f
for Tests the driver routine DGGEVX
prec double
file cdrgvx.f
for Tests the driver routine CGGEVX
prec complex
file zdrgvx.f
for Tests the driver routine ZGGEVX
prec doublecomplex
file sdrves.f
for Checks the nonsymmetric eigenvalue (Schur form) problem, driver SGEES
prec single
file ddrves.f
for Checks the nonsymmetric eigenvalue (Schur form) problem, driver DGEES
prec double
file cdrves.f
for Checks the nonsymmetric eigenvalue (Schur form) problem, driver CGEES
prec complex
file zdrves.f
for Checks the nonsymmetric eigenvalue (Schur form) problem, driver ZGEES
prec doublecomplex
file sdrvsx.f
for Checks the nonsymmetric eigenvalue (Schur form) problem, expert driver SGEESX
prec single
file ddrvsx.f
for Checks the nonsymmetric eigenvalue (Schur form) problem, expert driver DGEESX
prec double
file cdrvsx.f
for Checks the nonsymmetric eigenvalue (Schur form) problem, expert driver CGEESX
prec complex
file zdrvsx.f
for Checks the nonsymmetric eigenvalue (Schur form) problem, expert driver ZGEESX
prec doublecomplex
file sdrvev.f
for Checks the nonsymmetric eigenvalue problem driver SGEEV
prec single
file ddrvev.f
for Checks the nonsymmetric eigenvalue problem driver DGEEV
prec double
file cdrvev.f
for Checks the nonsymmetric eigenvalue problem driver CGEEV
prec complex
file zdrvev.f
for Checks the nonsymmetric eigenvalue problem driver ZGEEV
prec doublecomplex
file sdrvvx.f
for Checks the nonsymmetric eigenvalue problem expert driver SGEEVX
prec single
file ddrvvx.f
for Checks the nonsymmetric eigenvalue problem expert driver DGEEVX
prec double
file cdrvvx.f
for Checks the nonsymmetric eigenvalue problem expert driver CGEEVX
prec complex
file zdrvvx.f
for Checks the nonsymmetric eigenvalue problem expert driver ZGEEVX
prec doublecomplex
file serred.f
for Tests the error exits for the eigenvalue driver routines
, (SGEEV,SGEES,SGEEVX,SGEESX,SGESVD,SGESDD)
prec single
file derred.f
for Tests the error exits for the eigenvalue driver routines
, (DGEEV,DGEES,DGEEVX,DGEESX,DGESVD,DGESDD)
prec double
file cerred.f
for Tests the error exits for the eigenvalue driver routines (CGEEV,CGEES,CGEEVX,CGEESX,CGESVD,CGESDD)
prec complex
file zerred.f
for Tests the error exits for the eigenvalue driver routines (ZGEEV,ZGEES,ZGEEVX,ZGEESX,ZGESVD,ZGESDD)
prec doublecomplex
# ===
file schksb.f
for Tests SSBTRD (the reduction of a symmetric band matrix to tridiagonal form, used with the symmetric eigenvalue problem
prec single
file dchksb.f
for Tests DSBTRD (the reduction of a symmetric band matrix to tridiagonal form, used with the symmetric eigenvalue problem
prec double
file cchkhb.f
for Tests CHBTRD (the reduction of a Hermitian band matrix to tridiagonal form), used with the Hermitian eigenvalue problem
prec complex
file zchkhb.f
for Tests ZHBTRD (the reduction of a Hermitian band matrix to tridiagonal form), used with the Hermitian eigenvalue problem
prec doublecomplex
# ===
file schkst.f
for Checks the symmetric eigenvalue problem routines (SSYTRD,SSPTRD,SORGTR,SOPGTR,SSTEQR,SSTERF,SPTEQR,SSTEBZ,SSTEIN,SSTEDC,SSTEGR)
prec single
file dchkst.f
for Checks the symmetric eigenvalue problem routines (DSYTRD,DSPTRD,DORGTR,DOPGTR,DSTEQR,DSTERF,DPTEQR,DSTEBZ,DSTEIN,DSTEDC,DSTEGR)
prec double
file cchkst.f
for Checks the (complex) hermitian eigenvalue problem routines (CHETRD,CHPTRD,CUNGTR,CUPGTR,SSTERF,CPTEQR,SSTEBZ,CSTEIN,CSTEDC,CSTEGR)
prec complex
file zchkst.f
for Checks the (complex) hermitian eigenvalue problem routines (ZHETRD,ZHPTRD,ZUNGTR,ZUPGTR,DSTERF,ZPTEQR,DSTEBZ,ZSTEIN,ZSTEDC,ZSTEGR)
prec doublecomplex
file sdrvst.f
for Checks the symmetric eigenvalue problem drivers (SSTEV,SSTEVD,SSTEVX,SSYEV,SSYEVD,SSYEVX,SSPEV,SSPEVD,SSPEVX,SSBEV,SSBEVD,SSBEVX)
prec single
file ddrvst.f
for Checks the symmetric eigenvalue problem drivers (DSTEV,DSTEVD,DSTEVX,DSYEV,DSYEVD,DSYEVX,DSPEV,DSPEVD,DSPEVX,DSBEV,DSBEVD,DSBEVX)
prec double
file cdrvst.f
for Checks the Hermitian eigenvalue problem drivers (CHEEV,CHEEVD,CHEEVX,CHPEV,CHPEVD,CHPEVX,CHBEV,CHBEVD,CHBEVX)
prec complex
file zdrvst.f
for Checks the Hermitian eigenvalue problem drivers (ZHEEV,ZHEEVD,ZHEEVX,ZHPEV,ZHPEVD,ZHPEVX,ZHBEV,ZHBEVD,ZHBEVX)
prec doublecomplex
file serrst.f
for Tests the error exits for SSYTRD,SORGTR,SORMTR,SSPTRD,SOPGTR,SOPMTR,SSTEQR,SSTERF,SSTEBZ,SSTEIN,SPTEQR,SSBTRD,SSYEV,SSYEVX,SSYEVD,
, SSYEVR,SSBEV,SSBEVX,SSBEVD,SSPEV,SSPEVX,SSPEVD,SSTEV,SSTEVX,SSTEVD,SSTEVR and SSTEDC.
prec single
file derrst.f
for Tests the error exits for DSYTRD,DORGTR,DORMTR,DSPTRD,DOPGTR,DOPMTR,DSTEQR,DSTERF,DSTEBZ,DSTEIN,DPTEQR,DSBTRD,DSYEV,DSYEVX,DSYEVD,
, DSYEVR,DSBEV,DSBEVX,DSBEVD,DSPEV,DSPEVX,DSPEVD,DSTEV,DSTEVX,DSTEVD,DSTEVR and DSTEDC.
prec double
file cerrst.f
for Tests the error exits for CHETRD,CUNGTR,CUNMTR,CHPTRD,CUPGTR,CUPMTR,CSTEQR,CSTEIN,CPTEQR,CHBTRD,CHEEV,CHEEVR,CHEEVX,CHEEVD,CHBEV,
, CHBEVX,CHBEVD,CHPEV,CHPEVX,CHPEVD and CSTEDC.
prec complex
file zerrst.f
for Tests the error exits for ZHETRD,ZUNGTR,ZUNMTR,ZHPTRD,ZUPGTR,ZUPMTR,ZSTEQR,ZSTEIN,ZPTEQR,ZHBTRD,ZHEEV,ZHEEVR,ZHEEVX,ZHEEVD,ZHBEV,
, ZHBEVX,ZHBEVD,ZHPEV,ZHPEVX,ZHPEVD and ZSTEDC.
prec doublecomplex
file sdrvsg.f
for Checks the symmetric generalized eigenvalue problem routines(SSYGV,SSYGVD,SSYGVX,SSPGV,SSPGVD,SSPGVX,SSBGV,SSBGVD,SSBGVX)
prec single
file ddrvsg.f
for Checks the symmetric generalized eigenvalue problem routines (DSYGV,DSYGVD,DSYGVX,DSPGV,DSPGVD,DSPGVX,DSBGV,DSBGVD,DSBGVX)
prec double
file cdrvsg.f
for Checks the complex hermitian generalized eigenvalue problem routines (CHEGV,CHEGVD,CHEGVX,CHPGV,CHPGVD,CHPGVX,CHBGV,CHBGVD,CHBGVX)
prec complex
file zdrvsg.f
for Checks the complex hermitian generalized eigenvalue problem routines (ZHEGV,ZHEGVD,ZHEGVX,ZHPGV,ZHPGVD,ZHPGVX,ZHBGV,ZHBGVD,ZHBGVX)
prec doublecomplex
# ===
file sckglm.f
for Tests SGGGLM
prec single
file dckglm.f
for Tests DGGGLM
prec double
file cckglm.f
for Tests CGGGLM
prec complex
file zckglm.f
for Tests ZGGGLM
prec doublecomplex
# ===
file sckgqr.f
for Tests SGGQRF and SGGRQF
prec single
file dckgqr.f
for Tests DGGQRF and DGGRQF
prec double
file cckgqr.f
for Tests CGGQRF and CGGRQF
prec complex
file zckgqr.f
for Tests ZGGQRF and ZGGRQF
prec doublecomplex
# ===
file sckgsv.f
for Tests SGGSVD
prec single
file dckgsv.f
for Tests DGGSVD
prec double
file cckgsv.f
for Tests CGGSVD
prec complex
file zckgsv.f
for Tests ZGGSVD
prec doublecomplex
# ===
file scklse.f
for Tests SGGLSE
prec single
file dcklse.f
for Tests DGGLSE
prec double
file ccklse.f
for Tests CGGLSE
prec complex
file zcklse.f
for Tests ZGGLSE
prec doublecomplex
#######################################
# index for lapack/testing #
#######################################
lib eig
for Subdirectory of Eigenproblem Testing
lib lin
for Subdirectory of Linear Equation Testing
lib matgen
for Subdirectory of Matrix Generation Routines (used in testing
, and timing directories)
# =======================================
# Input Files for Linear Equation Testing
# =======================================
file stest.in
for Data file for linear equations/linear least squares test programs
prec single
file dtest.in
for Data file for linear equations/linear least squares test programs
prec double
file ctest.in
for Data file for linear equations/linear least squares test programs
prec complex
file ztest.in
for Data file for linear equations/linear least squares test programs
prec doublecomplex
file dstest.in
for Data file for linear equations test programs using iterative refinement
prec double / single
file zctest.in
for Data file for linear equations test programs using iterative refinement
prec doublecomplex / complex
file stest_rfp.in
for Data file for linear equations/linear least squares test programs
prec single
file dtest_rfp.in
for Data file for linear equations/linear least squares test programs using rfp format
prec double
file ctest.in
for Data file for linear equations/linear least squares test programs using rfp format
prec complex
file ztest_rfp.in
for Data file for linear equations/linear least squares test programs using rfp format
prec doublecomplex
# =======================================
# Input Files for Eigenproblem Testing
# =======================================
file nep.in
for Data file for testing the (s,d,c,z) Nonsymmetric Eigenproblem computational routines
prec single, double, complex, doublecomplex
file sep.in
for Data file for testing the (s,d,c,z) Symmetric Eigenproblem computational and simple/expert driver routines
prec single, double, complex, doublecomplex
file svd.in
for Data file for testing the (s,d,c,z) Singular Value Decomposition computational and simple/expert driver routines
prec single, double, complex, doublecomplex
file sec.in
for Data file for testing real Eigen Condition Routines
prec single
file dec.in
for Data file for testing real Eigen Condition Routines
prec double
file cec.in
for Data file for testing complex Eigen Condition Routines
prec complex
file zec.in
for Data file for testing complex Eigen Condition Routines
prec doublecomplex
file sed.in
for Data file for testing real Nonsymmetric Eigenvalue Driver
prec single
file ded.in
for Data file for testing real Nonsymmetric Eigenvalue Driver
prec double
file ced.in
for Data file for testing complex Nonsymmetric Eigenvalue Driver
prec complex
file zed.in
for Data file for testing complex Nonsymmetric Eigenvalue Driver
prec doublecomplex
file sgd.in
for Data file for testing the real Nonsymmetric Generalized Eigenvalue Problem drivers
prec single
file dgd.in
for Data file for testing the real Nonsymmetric Generalized Eigenvalue Problem drivers
prec double
file cgd.in
for Data file for testing the complex Nonsymmetric Generalized Eigenvalue Problem drivers
prec complex
file zgd.in
for Data file for testing the complex Nonsymmetric Generalized Eigenvalue Problem drivers
prec doublecomplex
file sgg.in
for Data file for testing the real Nonsymmetric Generalized Eigenvalue Problem routines
prec single
file dgg.in
for Data file for testing the real Nonsymmetric Generalized Eigenvalue Problem routines
prec double
file cgg.in
for Data file for testing the complex Nonsymmetric Generalized Eigenvalue Problem routines
prec complex
file zgg.in
for Data file for testing the complex Nonsymmetric Generalized Eigenvalue Problem routines
prec doublecomplex
file ssb.in
for Data file for testing real Symmetric Banded Eigenvalue Problem routines
prec single
file dsb.in
for Data file for testing real Symmetric Banded Eigenvalue Problem routines
prec double
file csb.in
for Data file for testing complex Symmetric Banded Eigenvalue Problem routines
prec complex
file zsb.in
for Data file for testing complex Symmetric Banded Eigenvalue Problem routines
prec doublecomplex
file ssg.in
for Data file for testing real Symmetric Generalized Eigenvalue Problem routines
prec single
file dsg.in
for Data file for testing real Symmetric Generalized Eigenvalue Problem routines
prec double
file csg.in
for Data file for testing complex Symmetric Generalized Eigenvalue Problem routines
prec complex
file zsg.in
for Data file for testing complex Symmetric Generalized Eigenvalue Problem routines
prec doublecomplex
file sbal.in
for Data file for testing SGEBAL
prec single
file dbal.in
for Data file for testing DGEBAL
prec double
file cbal.in
for Data file for testing CGEBAL
prec complex
file zbal.in
for Data file for testing ZGEBAL
prec doublecomplex
file sbak.in
for Data file for testing SGEBAK
prec single
file dbak.in
for Data file for testing DGEBAK
prec double
file cbak.in
for Data file for testing CGEBAK
prec complex
file zbak.in
for Data file for testing ZGEBAK
prec doublecomplex
file sgbal.in
for Data file for testing SGGBAL
prec single
file dgbal.in
for Data file for testing DGGBAL
prec double
file cgbal.in
for Data file for testing CGGBAL
prec complex
file zgbal.in
for Data file for testing ZGGBAL
prec doublecomplex
file sgbak.in
for Data file for testing SGGBAK
prec single
file dgbak.in
for Data file for testing DGGBAK
prec double
file cgbak.in
for Data file for testing CGGBAK
prec complex
file zgbak.in
for Data file for testing ZGGBAK
prec doublecomplex
file sbb.in
for Data file for testing banded SVD routines
prec single
file dbb.in
for Data file for testing banded SVD routines
prec double
file cbb.in
for Data file for testing banded SVD routines
prec complex
file zbb.in
for Data file for testing banded SVD routines
prec complex16
file glm.in
for Data file for testing the (s, d, c, z) GLM routines
prec single, double, complex, doublecomplex
file gqr.in
for Data file for testing the (s, d, c, z) GQR and GRQ routines
prec single, double, complex, doublecomplex
file gsv.in
for Data file for testing the (s, d, c, z) GSVD routines
prec single, double, complex, doublecomplex
file lse.in
for Data file for testing the (s, d, c, z) LSE routines
prec single, double, complex, doublecomplex
######################################
# Index for lapack/testing/lin #
######################################
file xerbla.f
for: Special version of this routine used in testing
file ilaenv.f
for: Special version used in conjunction with XLAENV
file xlaenv.f
for: Resets ILAENV values for testing purposes
==========================================
Available Linear Equation Testing Routines
==========================================
file schkaa.f
for Test program driver for linear equation testing
prec single
file dchkaa.f
for Test program driver for linear equation testing
prec double
file cchkaa.f
for Test program driver for linear equation testing
prec complex
file zchkaa.f
for Test program driver for linear equation testing
prec doublecomplex
file dchkab.f
for Test program driver for linear equation testing using iterative refinement
prec double/ single
file zchkab.f
for Test program driver for linear equation testing using iterative refinement
prec doublecomplex / complex
# ===
file schkeq.f
for Tests equilibration routines (SGEEQU, SGBEQU, SPOEQU, SPPEQU and SPBEQU)
prec single
file dchkeq.f
for Tests equilibration routines (DGEEQU, DGBEQU, DPOEQU,DPPEQU and DPBEQU)
prec double
file cchkeq.f
for Tests equilibration routines (CGEEQU, CGBEQU)
prec complex
file zchkeq.f
for Tests equilibration routines (ZGEEQU, ZGBEQU)
prec doublecomplex
===
file schkgb.f
for Tests SGBTRF, SGBTRS, SGBRFS, and SGBCON
prec single
file dchkgb.f
for Tests DGBTRF, DGBTRS, DGBRFS, and DGBCON
prec double
file cchkgb.f
for Tests CGBTRF, CGBTRS, CGBRFS, and CGBCON
prec complex
file zchkgb.f
for Tests ZGBTRF, ZGBTRS, ZGBRFS, and ZGBCON
prec doublecomplex
file sdrvgb.f
for Tests the driver routines SGBSV and SGBSVX
prec single
file ddrvgb.f
for Tests the driver routines DGBSV and DGBSVX
prec double
file cdrvgb.f
for Tests the driver routines CGBSV and CGBSVX
prec complex
file zdrvgb.f
for Tests the driver routines ZGBSV and ZGBSVX
prec doublecomplex
file schkge.f
for Tests SGETRF, SGETRI, SGETRS, SGERFS, and SGECON
prec single
file dchkge.f
for Tests DGETRF, DGETRI, DGETRS, DGERFS, and DGECON
prec double
file cchkge.f
for Tests CGETRF, CGETRI, CGETRS, CGERFS, and CGECON
prec complex
file zchkge.f
for Tests ZGETRF, ZGETRI, ZGETRS, ZGERFS, and ZGECON
prec doublecomplex
file sdrvge.f
for Tests the driver routines SGESV and SGESVX
prec single
file ddrvge.f
for Tests the driver routines DGESV and DGESVX
prec double
file ddrvab.f
for Tests the driver routines DSGESV and DSGESVX
prec double/ single
file cdrvge.f
for Tests the driver routines CGESV and CGESVX
prec complex
file zdrvge.f
for Tests the driver routines ZGESV and ZGESVX
prec doublecomplex
file zdrvab.f
for Tests the driver routines ZCGESV and ZCGESVX
prec doublecomplex / complex
file serrge.f
for Tests the error exits for the SGE- and SGB- routines
prec single
file derrge.f
for Tests the error exits for the DGE- and DGB- routines
prec double
file derrab.f
for Tests the error exits for the DSGE- routines
prec double / single
file cerrge.f
for Tests the error exits for the CGE- and CGB- routines
prec complex
file zerrge.f
for Tests the error exits for the ZGE- and ZGB- routines
prec doublecomplex
file zerrab.f
for Tests the error exits for the ZCGE- routines
prec doublecomplex / complex
# ===
file schkgt.f
for Tests SGTTRF, SGTTRS, SGTRFS, and SGTCON
prec single
file dchkgt.f
for Tests DGTTRF, DGTTRS, DGTRFS, and DGTCON
prec double
file cchkgt.f
for Tests CGTTRF, CGTTRS, CGTRFS, and CGTCON
prec complex
file zchkgt.f
for Tests ZGTTRF, ZGTTRS, ZGTRFS, and ZGTCON
prec doublecomplex
file sdrvgt.f
for Tests SGTSV and SGTSVX
prec single
file ddrvgt.f
for Tests DGTSV and DGTSVX
prec double
file cdrvgt.f
for Tests CGTSV and CGTSVX
prec complex
file zdrvgt.f
for Tests ZGTSV and ZGTSVX
prec doublecomplex
file serrgt.f
for Tests the error exits for the tridiagonal routines (SGT- and SPT-)
prec single
file derrgt.f
for Tests the error exits for the tridiagonal routines (DGT- and DPT-)
prec double
file cerrgt.f
for Tests the error exits for the tridiagonal routines (CGT- and CPT-)
prec complex
file zerrgt.f
for Tests the error exits for the tridiagonal routines (ZGT- and ZPT-)
prec doublecomplex
===
file schklq.f
for Tests SGELQF, SORGLQ and SORMLQ
prec single
file dchklq.f
for Tests DGELQF, DORGLQ and DORMLQ
prec double
file cchklq.f
for Tests CGELQF, CUNGLQ and CUNMLQ
prec complex
file zchklq.f
for Tests ZGELQF, ZUNGLQ and ZUNMLQ
prec doublecomplex
file serrlq.f
for Tests the error exits for the LQ routines
prec single
file derrlq.f
for Tests the error exits for the LQ routines
prec double
file cerrlq.f
for Tests the error exits for the LQ routines
prec complex
file zerrlq.f
for Tests the error exits for the LQ routines
prec doublecomplex
# ===
file sdrvls.f
for Tests SGELS, SGELSD, SGELSS, SGELSX, SGELSY
prec single
file ddrvls.f
for Tests DGELS, DGELSD, DGELSS, DGELSX, DGELSY
prec double
file cdrvls.f
for Tests CGELS, CGELSD, CGELSS, CGELSX, CGELSY
prec complex
file zdrvls.f
for Tests ZGELS, ZGELSD, ZGELSS, ZGELSX, ZGELSY
prec doublecomplex
file serrls.f
for Tests the error exits for the LS routines
prec single
file derrls.f
for Tests the error exits for the LS routines
prec double
file cerrls.f
for Tests the error exits for the LS routines
prec complex
file zerrls.f
for Tests the error exits for the LS routines
prec doublecomplex
# ===
file schkpb.f
for Tests SPBTRF, SPBTRS, SPBRFS, and SPBCON
prec single
file dchkpb.f
for Tests DPBTRF, DPBTRS, DPBRFS, and DPBCON
prec double
file cchkpb.f
for Tests CPBTRF, CPBTRS, CPBRFS, and CPBCON
prec complex
file zchkpb.f
for Tests ZPBTRF, ZPBTRS, ZPBRFS, and ZPBCON
prec doublecomplex
file sdrvpb.f
for Tests the driver routines SPBSV and SPBSVX
prec single
file ddrvpb.f
for Tests the driver routines DPBSV and DPBSVX
prec double
file cdrvpb.f
for Tests the driver routines CPBSV and CPBSVX
prec complex
file zdrvpb.f
for Tests the driver routines ZPBSV and ZPBSVX
prec doublecomplex
file schkpo.f
for Tests SPOTRF, SPOTRI, SPOTRS, SPORFS, and SPOCON
prec single
file dchkpo.f
for Tests DPOTRF, DPOTRI, DPOTRS, DPORFS, and DPOCON
prec double
file cchkpo.f
for Tests CPOTRF, CPOTRI, CPOTRS, CPORFS, and CPOCON
prec complex
file zchkpo.f
for Tests ZPOTRF, ZPOTRI, ZPOTRS, ZPORFS, and ZPOCON
prec doublecomplex
file sdrvpo.f
for Tests the driver routines SPOSV and SPOSVX
prec single
file ddrvpo.f
for Tests the driver routines DPOSV and DPOSVX
prec double
file cdrvpo.f
for Tests the driver routines CPOSV and CPOSVX
prec complex
file zdrvpo.f
for Tests the driver routines ZPOSV and ZPOSVX
prec doublecomplex
file schkpp.f
for Tests SPPTRF, SPPTRI, SPPTRS, SPPRFS, and SPPCON
prec single
file dchkpp.f
for Tests DPPTRF, DPPTRI, DPPTRS, DPPRFS, and DPPCON
prec double
file cchkpp.f
for Tests CPPTRF, CPPTRI, CPPTRS, CPPRFS, and CPPCON
prec complex
file zchkpp.f
for Tests ZPPTRF, ZPPTRI, ZPPTRS, ZPPRFS, and ZPPCON
prec doublecomplex
file sdrvpp.f
for Tests the driver routines SPPSV and SPPSVX
prec single
file ddrvpp.f
for Tests the driver routines DPPSV and DPPSVX
prec double
file cdrvpp.f
for Tests the driver routines CPPSV and CPPSVX
prec complex
file zdrvpp.f
for Tests the driver routines ZPPSV and ZPPSVX
prec doublecomplex
file serrpo.f
for Tests the error exits for the (SPB-, SPO-, SPP-) routines
prec single
file derrpo.f
for Tests the error exits for the (DPB-, DPO-, DPP-) routines
prec double
file cerrpo.f
for Tests the error exits for the (CPB-, CPO-, CPP-) routines
prec complex
file zerrpo.f
for Tests the error exits for the (ZPB-, ZPO-, ZPP-) routines
prec doublecomplex
# ===
file schkpt.f
for Tests SPTTRF, SPTTRS, SPTRFS, and SPTCON
prec single
file dchkpt.f
for Tests DPTTRF, DPTTRS, DPTRFS, and DPTCON
prec double
file cchkpt.f
for Tests CPTTRF, CPTTRS, CPTRFS, and CPTCON
prec complex
file zchkpt.f
for Tests ZPTTRF, ZPTTRS, ZPTRFS, and ZPTCON
prec doublecomplex
file sdrvpt.f
for Tests SPTSV and SPTSVX
prec single
file ddrvpt.f
for Tests DPTSV and DPTSVX
prec double
file cdrvpt.f
for Tests CPTSV and CPTSVX
prec complex
file zdrvpt.f
for Tests ZPTSV and ZPTSVX
prec doublecomplex
# ===
file schkql.f
for Tests SGEQLF, SORGQL and SORMQL
prec single
file dchkql.f
for Tests DGEQLF, DORGQL and DORMQL
prec double
file cchkql.f
for Tests CGEQLF, CUNGQL and CUNMQL
prec complex
file zchkql.f
for Tests ZGEQLF, ZUNGQL and ZUNMQL
prec doublecomplex
file serrql.f
for Tests the error exits for the QL routines
prec single
file derrql.f
for Tests the error exits for the QL routines
prec double
file cerrql.f
for Tests the error exits for the QL routines
prec complex
file zerrql.f
for Tests the error exits for the QL routines
prec doublecomplex
# ===
file schkqp.f
for Tests SGEQPF
prec single
file dchkqp.f
for Tests DGEQPF
prec double
file cchkqp.f
for Tests CGEQPF
prec complex
file zchkqp.f
for Tests ZGEQPF
prec doublecomplex
file schkq3.f
for Tests SGEQP3
prec single
file dchkq3.f
for Tests DGEQP3
prec double
file cchkq3.f
for Tests CGEQP3
prec complex
file zchkq3.f
for Tests ZGEQP3
prec doublecomplex
file serrqp.f
for Tests the error exits for SGEQPF and SGEQP3
prec single
file derrqp.f
for Tests the error exits for DGEQPF and DGEQP3
prec double
file cerrqp.f
for Tests the error exits for CGEQPF and CGEQP3
prec complex
file zerrqp.f
for Tests the error exits for ZGEQPF and ZGEQP3
prec doublecomplex
# ===
file schkqr.f
for Tests SGEQRF, SORGQR and SORMQR
prec single
file dchkqr.f
for Tests DGEQRF, DORGQR and DORMQR
prec double
file cchkqr.f
for Tests CGEQRF, CUNGQR and CUNMQR
prec complex
file zchkqr.f
for Tests ZGEQRF, ZUNGQR and ZUNMQR
prec doublecomplex
file serrqr.f
for Tests the error exits for the QR routines
prec single
file derrqr.f
for Tests the error exits for the QR routines
prec double
file cerrqr.f
for Tests the error exits for the QR routines
prec complex
file zerrqr.f
for Tests the error exits for the QR routines
prec doublecomplex
# ===
file schkrq.f
for Tests SGERQF, SORGRQ and SORMRQ
prec single
file dchkrq.f
for Tests DGERQF, DORGRQ and DORMRQ
prec double
file cchkrq.f
for Tests CGERQF, CUNGRQ and CUNMRQ
prec complex
file zchkrq.f
for Tests ZGERQF, ZUNGRQ and ZUNMRQ
prec doublecomplex
file serrrq.f
for Tests the error exits for the RQ routines
prec single
file derrrq.f
for Tests the error exits for the RQ routines
prec double
file cerrrq.f
for Tests the error exits for the RQ routines
prec complex
file zerrrq.f
for Tests the error exits for the RQ routines
prec doublecomplex
# ===
file schksp.f
for Tests SSPTRF, SSPTRI, SSPTRS, SSPRFS, and SSPCON
prec single
file dchksp.f
for Tests DSPTRF, DSPTRI, DSPTRS, DSPRFS, and DSPCON
prec double
file cchksp.f
for Tests CSPTRF, CSPTRI, CSPTRS, CSPRFS, and CSPCON
prec complex
file zchksp.f
for Tests ZSPTRF, ZSPTRI, ZSPTRS, ZSPRFS, and ZSPCON
prec doublecomplex
file cchkhp.f
for Tests CHPTRF, CHPTRI, CHPTRS, CHPRFS, and CHPCON
prec complex
file zchkhp.f
for Tests ZHPTRF, ZHPTRI, ZHPTRS, ZHPRFS, and ZHPCON
prec doublecomplex
file sdrvsp.f
for Tests the driver routines SSPSV and SSPSVX
prec single
file ddrvsp.f
for Tests the driver routines DSPSV and DSPSVX
prec double
file cdrvsp.f
for Tests the driver routines CSPSV and CSPSVX
prec complex
file zdrvsp.f
for Tests the driver routines ZSPSV and ZSPSVX
prec doublecomplex
file cdrvhp.f
for Tests the driver routines CHPSV and CHPSVX
prec complex
file zdrvhp.f
for Tests the driver routines ZHPSV and ZHPSVX
prec doublecomplex
file schksy.f
for Tests SSYTRF, SSYTRI, SSYTRS, SSYRFS, and SSYCON
prec single
file dchksy.f
for Tests DSYTRF, DSYTRI, DSYTRS, DSYRFS, and DSYCON
prec double
file cchksy.f
for Tests CSYTRF, CSYTRI, CSYTRS, CSYRFS, and CSYCON
prec complex
file zchksy.f
for Tests ZSYTRF, ZSYTRI, ZSYTRS, ZSYRFS, and ZSYCON
prec doublecomplex
file cchkhe.f
for Tests CHETRF, CHETRI, CHETRS, CHERFS, and CHECON
prec complex
file zchkhe.f
for Tests ZHETRF, ZHETRI, ZHETRS, ZHERFS, and ZHECON
prec doublecomplex
file sdrvsy.f
for Tests the driver routines SSYSV and SSYSVX
prec single
file ddrvsy.f
for Tests the driver routines DSYSV and DSYSVX
prec double
file cdrvsy.f
for Tests the driver routines SSYSV and SSYSVX
prec complex
file zdrvsy.f
for Tests the driver routines ZSYSV and ZSYSVX
prec doublecomplex
file cdrvhe.f
for Tests the driver routines CHESV and CHESVX
prec complex
file zdrvhe.f
for Tests the driver routines ZHESV and ZHESVX
prec doublecomplex
file serrsy.f
for Tests the error exits for the (SSP- and SSY-) routines
prec single
file derrsy.f
for Tests the error exits for the (DSP- and DSY-) routines
prec double
file cerrsy.f
for Tests the error exits for the (DSP- and DSY-) routines
prec complex
file zerrsy.f
for Tests the error exits for the (DSP- and DSY-) routines
prec doublecomplex
file cerrhe.f
for Tests the error exits for the (CHE- and CHP-) routines
prec complex
file zerrhe.f
for Tests the error exits for the (ZHE- and ZHP-) routines
prec doublecomplex
# ===
file schktb.f
for Tests STBTRI, STBTRS, STBRFS, and STBCON, and SLATBS
prec single
file dchktb.f
for Tests DTBTRI, DTBTRS, DTBRFS, and DTBCON, and DLATBS
prec double
file cchktb.f
for Tests CTBTRI, CTBTRS, CTBRFS, and CTBCON, and CLATBS
prec complex
file zchktb.f
for Tests ZTBTRI, ZTBTRS, ZTBRFS, and ZTBCON, and ZLATBS
prec doublecomplex
file schktp.f
for Tests STPTRI, STPTRS, STPRFS, and STPCON, and SLATPS
prec single
file dchktp.f
for Tests DTPTRI, DTPTRS, DTPRFS, and DTPCON, and DLATPS
prec double
file cchktp.f
for Tests CTPTRI, CTPTRS, CTPRFS, and CTPCON, and CLATPS
prec complex
file zchktp.f
for Tests ZTPTRI, ZTPTRS, ZTPRFS, and ZTPCON, and ZLATPS
prec doublecomplex
file schktr.f
for Tests STRTRI, STRTRS, STRRFS, and STRCON, and SLATRS
prec single
file dchktr.f
for Tests DTRTRI, DTRTRS, DTRRFS, and DTRCON, and DLATRS
prec double
file cchktr.f
for Tests CTRTRI, CTRTRS, CTRRFS, and CTRCON, and CLATRS
prec complex
file zchktr.f
for Tests ZTRTRI, ZTRTRS, ZTRRFS, and ZTRCON, and ZLATRS
prec doublecomplex
file serrtr.f
for Tests the error exits for the -TR routines
prec single
file derrtr.f
for Tests the error exits for the -TR routines
prec double
file cerrtr.f
for Tests the error exits for the -TR routines
prec complex
file zerrtr.f
for Tests the error exits for the -TR routines
prec doublecomplex
# ===
file schktz.f
for Tests STZRQF and STZRZF
prec single
file dchktz.f
for Tests DTZRQF and DTZRZF
prec double
file cchktz.f
for Tests CTZRQF and CTZRZF
prec complex
file zchktz.f
for Tests ZTZRQF and ZTZRZF
prec doublecomplex
file serrtz.f
for Tests the error exits for STZRQF and STZRZF
prec single
file derrtz.f
for Tests the error exits for DTZRQF and DTZRZF
prec double
file cerrtz.f
for Tests the error exits for CTZRQF and CTZRZF
prec complex
file zerrtz.f
for Tests the error exits for ZTZRQF and ZTZRZF
prec doublecomplex
# ===
file serrvx.f
for Tests the error exits for the (-SV and -SVX) routines
prec single
file derrvx.f
for Tests the error exits for the (-SV and -SVX) routines
prec double
file cerrvx.f
for Tests the error exits for the (-SV and -SVX) routines
prec complex
file zerrvx.f
for Tests the error exits for the (-SV and -SVX) routines
prec doublecomplex
==========================================
Other Available Testing Routines
==========================================
file sgelqs.f
for Compute a minimum norm solution using the LQ, factorization computed by SGELQF
prec single
file dgelqs.f
for Compute a minimum norm solution using the LQ, factorization computed by DGELQF
prec double
file cgelqs.f
for Compute a minimum norm solution using the LQ, factorization computed by CGELQF
prec complex
file zgelqs.f
for Compute a minimum norm solztion using the LQ, factorization computed by ZGELQF
prec doublecomplex
file sgeqls.f
for Solve the least squares problem using the QL, factorization computed by SGEQLF
prec single
file dgeqls.f
for Solve the least squares problem using the QL, factorization computed by DGEQLF
prec double
file cgeqls.f
for Solve the least squares problem using the QL, factorization computed by CGEQLF
prec complex
file zgeqls.f
for Solve the least squares problem using the QL, factorization computed by ZGEQLF
prec doublecomplex
file sgeqrs.f
for Solve the least squares problem using the QR, factorization computed by SGEQRF
prec single
file dgeqrs.f
for Solve the least squares problem using the QR, factorization computed by DGEQRF
prec double
file cgeqrs.f
for Solve the least squares problem using the QR,factorization computed by CGEQRF
prec complex
file zgeqrs.f
for Solve the least squares problem using the QR, factorization computed by ZGEQRF
prec doublecomplex
file sgerqs.f
for Compute a minimum-norm solution using the RQ, factorization computed by SGERQF
prec single
file dgerqs.f
for Compute a minimum-norm solution using the RQ, factorization computed by DGERQF
prec double
file cgerqs.f
for Compute a minimum-norm solution using the RQ, factorization computed by CGERQF
prec complex
file zgerqs.f
for Compute a minimum-norm solution using the RQ, factorization computed by ZGERQF
prec doublecomplex
======== index for lapack/testing/matgen =========
file lapack/testing/matgen/slagge.f
for Generates a real general matrix
prec single
file lapack/testing/matgen/dlagge.f
for Generates a real general matrix
prec double
file lapack/testing/matgen/clagge.f
for Generates a complex general matrix
prec complex
file lapack/testing/matgen/zlagge.f
for Generates a complex general matrix
prec doublecomplex
file lapack/testing/matgen/slagsy.f
for Generates a real symmetric matrix
prec single
file lapack/testing/matgen/dlagsy.f
for Generates a real symmetric matrix
prec double
file lapack/testing/matgen/clagsy.f
for Generates a complex symmetric matrix
prec complex
file lapack/testing/matgen/zlagsy.f
for Generates a complex symmetric matrix
prec doublecomplex
file lapack/testing/matgen/claghe.f
for Generates a complex Hermitian matrix
prec complex
file lapack/testing/matgen/zlaghe.f
for Generates a complex Hermitian matrix
prec doublecomplex
file lapack/testing/matgen/slakf2.f
for Forms a matrix of Kronecker products
prec single
file lapack/testing/matgen/dlakf2.f
for Forms a matrix of Kronecker products
prec double
file lapack/testing/matgen/clakf2.f
for Forms a matrix of Kronecker products
prec complex
file lapack/testing/matgen/zlakf2.f
for Forms a matrix of Kronecker products
prec doublecomplex
file lapack/testing/matgen/slaran.f
for Returns a random real number from a uniform (0,1) distribution
prec single
file lapack/testing/matgen/dlaran.f
for Returns a random real number from a uniform (0,1) distribution
prec double
file lapack/testing/matgen/slarge.f
for Pre- and post-multiples a real general matrix with a random orthogonal matrix
prec single
file lapack/testing/matgen/dlarge.f
for Pre- and post-multiples a real general matrix with a random orthogonal matrix
prec double
file lapack/testing/matgen/clarge.f
for Pre- and post-multiples a complex general matrix with a random unitary matrix
prec complex
file lapack/testing/matgen/zlarge.f
for Pre- and post-multiples a complex general matrix with a random unitary matrix
prec doublecomplex
file lapack/testing/matgen/slarnd.f
for Returns a random real number from a uniform or normal distribution
prec single
file lapack/testing/matgen/dlarnd.f
for Returns a random real number from a uniform or normal distribution
prec double
file lapack/testing/matgen/clarnd.f
for Returns a random complex number from a uniform or normal distribution
prec complex
file lapack/testing/matgen/zlarnd.f
for Returns a random complex number from a uniform or normal distribution
prec doublecomplex
file lapack/testing/matgen/slaror.f
for Pre- or post-multiplies a real general matrix by a random orthogonal matrix
prec single
file lapack/testing/matgen/dlaror.f
for Pre- or post-multiplies a real general matrix by a random orthogonal matrix
prec double
file lapack/testing/matgen/claror.f
for Pre- or post-multiplies a complex general matrix by a random unitary matrix
prec complex
file lapack/testing/matgen/zlaror.f
for Pre- or post-multiplies a complex general matrix by a random unitary matrix
prec doublecomplex
file lapack/testing/matgen/slarot.f
for Applies a (Givens) rotation to two adjacent rows or columns, where one element of the first and/or last column/row may be
, a separate variable.
prec single
file lapack/testing/matgen/dlarot.f
for Applies a (Givens) rotation to two adjacent rows or columns, where one element of the first and/or last column/row may be
, a separate variable.
prec double
file lapack/testing/matgen/clarot.f
for Applies a (Givens) rotation to two adjacent rows or columns, where one element of the first and/or last column/row may be
, a separate variable.
prec complex
file lapack/testing/matgen/zlarot.f
for Applies a (Givens) rotation to two adjacent rows or columns, where one element of the first and/or last column/row may be
, a separate variable.
prec doublecomplex
file lapack/testing/matgen/slatm1.f
for Called by SLATMR to generate random test matrices
prec single
file lapack/testing/matgen/dlatm1.f
for Called by DLATMR to generate random test matrices
prec double
file lapack/testing/matgen/clatm1.f
for Called by CLATMR to generate random test matrices
prec complex
file lapack/testing/matgen/zlatm1.f
for Called by ZLATMR to generate random test matrices
prec doublecomplex
file lapack/testing/matgen/slatm2.f
for Called by SLATMR to generate random test matrices
prec single
file lapack/testing/matgen/dlatm2.f
for Called by DLATMR to generate random test matrices
prec double
file lapack/testing/matgen/clatm2.f
for Called by CLATMR to generate random test matrices
prec complex
file lapack/testing/matgen/zlatm2.f
for Called by ZLATMR to generate random test matrices
prec doublecomplex
file lapack/testing/matgen/slatm3.f
for Called by SLATMR to generate random test matrices
prec single
file lapack/testing/matgen/dlatm3.f
for Called by DLATMR to generate random test matrices
prec double
file lapack/testing/matgen/clatm3.f
for Called by CLATMR to generate random test matrices
prec complex
file lapack/testing/matgen/zlatm3.f
for Called by ZLATMR to generate random test matrices
prec doublecomplex
file lapack/testing/matgen/slatm5.f
for Generates matrices involved in the Generalized Sylvester equation
prec single
file lapack/testing/matgen/dlatm5.f
for Generates matrices involved in the Generalized Sylvester equation
prec double
file lapack/testing/matgen/clatm5.f
for Generates matrices involved in the Generalized Sylvester equation
prec complex
file lapack/testing/matgen/zlatm5.f
for Generates matrices involved in the Generalized Sylvester equation
prec doublecomplex
file lapack/testing/matgen/slatm6.f
for Generates test matrices for the generalized eigenvalue problem
prec single
file lapack/testing/matgen/dlatm6.f
for Generates test matrices for the generalized eigenvalue problem
prec double
file lapack/testing/matgen/clatm6.f
for Generates test matrices for the generalized eigenvalue problem
prec complex
file lapack/testing/matgen/zlatm6.f
for Generates test matrices for the generalized eigenvalue problem
prec doublecomplex
file lapack/testing/matgen/slatme.f
for Generates random non-symmetric square matrices with specified eigenvalues
prec single
file lapack/testing/matgen/dlatme.f
for Generates random non-symmetric square matrices with specified eigenvalues
prec double
file lapack/testing/matgen/clatme.f
for Generates random non-symmetric square matrices with specified eigenvalues
prec complex
file lapack/testing/matgen/zlatme.f
for Generates random non-symmetric square matrices with specified eigenvalues
prec doublecomplex
file lapack/testing/matgen/slatmr.f
for Generates random matrices of various types
prec single
file lapack/testing/matgen/dlatmr.f
for Generates random matrices of various types
prec double
file lapack/testing/matgen/clatmr.f
for Generates random matrices of various types
prec complex
file lapack/testing/matgen/zlatmr.f
for Generates random matrices of various types
prec doublecomplex
file lapack/testing/matgen/slatms.f
for generates random matrices with specified singular values (or symmetric with specified eigenvalues)
prec single
file lapack/testing/matgen/dlatms.f
for generates random matrices with specified singular values (or symmetric with specified eigenvalues)
prec double
file lapack/testing/matgen/clatms.f
for generates random matrices with specified singular values (or Hermitian with specified eigenvalues)
prec complex
file lapack/testing/matgen/zlatms.f
for generates random matrices with specified singular values (or Hermitian with specified eigenvalues)
prec doublecomplex
#########################################
# Index for lapack/timing/eig/eigsrc #
#########################################
# ===================================================
# Available Instrumented Eigenproblem LAPACK Routines
# ===================================================
file lapack/timing/eig/eigsrc/sbdsdc.f
for instrumented SBDSDC to count operations
prec single
file lapack/timing/eig/eigsrc/dbdsdc.f
for instrumented DBDSDC to count operations
prec double
file lapack/timing/eig/eigsrc/cbdsdc.f
for instrumented CBDSDC to count operations
prec complex
file lapack/timing/eig/eigsrc/zbdsdc.f
for instrumented ZBDSDC to count operations
prec doublecomplex
file lapack/timing/eig/eigsrc/sbdsqr.f
for instrumented SBDSQR to count operations
prec single
file lapack/timing/eig/eigsrc/dbdsqr.f
for instrumented DBDSQR to count operations
prec double
file lapack/timing/eig/eigsrc/cbdsqr.f
for instrumented CBDSQR to count operations
prec complex
file lapack/timing/eig/eigsrc/zbdsqr.f
for instrumented ZBDSQR to count operations
prec doublecomplex
file lapack/timing/eig/eigsrc/sgesdd.f
for instrumented SGESDD to count operations
prec single
file lapack/timing/eig/eigsrc/dgesdd.f
for instrumented DGESDD to count operations
prec double
file lapack/timing/eig/eigsrc/cgesdd.f
for instrumented CGESDD to count operations
prec complex
file lapack/timing/eig/eigsrc/zgesdd.f
for instrumented ZGESDD to count operations
prec doublecomplex
file lapack/timing/eig/eigsrc/sgghrd.f
for instrumented SGGHRD to count operations
prec single
file lapack/timing/eig/eigsrc/dgghrd.f
for instrumented DGGHRD to count operations
prec double
file lapack/timing/eig/eigsrc/cgghrd.f
for instrumented CGGHRD to count operations
prec complex
file lapack/timing/eig/eigsrc/zgghrd.f
for instrumented ZGGHRD to count operations
prec doublecomplex
file lapack/timing/eig/eigsrc/shgeqz.f
for instrumented SHGEQZ to count operations
prec single
file lapack/timing/eig/eigsrc/dhgeqz.f
for instrumented DHGEQZ to count operations
prec double
file lapack/timing/eig/eigsrc/chgeqz.f
for instrumented CHGEQZ to count operations
prec complex
file lapack/timing/eig/eigsrc/zhgeqz.f
for instrumented ZHGEQZ to count operations
prec doublecomplex
file lapack/timing/eig/eigsrc/shsein.f
for instrumented SHSEIN to count operations
prec single
file lapack/timing/eig/eigsrc/dhsein.f
for instrumented DHSEIN to count operations
prec double
file lapack/timing/eig/eigsrc/chsein.f
for instrumented CHSEIN to count operations
prec complex
file lapack/timing/eig/eigsrc/zhsein.f
for instrumented ZHSEIN to count operations
prec doublecomplex
file lapack/timing/eig/eigsrc/shseqr.f
for instrumented SHSEQR to count operations
prec single
file lapack/timing/eig/eigsrc/dhseqr.f
for instrumented DHSEQR to count operations
prec double
file lapack/timing/eig/eigsrc/chseqr.f
for instrumented CHSEQR to count operations
prec complex
file lapack/timing/eig/eigsrc/zhseqr.f
for instrumented ZHSEQR to count operations
prec doublecomplex
file lapack/timing/eig/eigsrc/slaebz.f
for instrumented SLAEBZ to count operations
prec single
file lapack/timing/eig/eigsrc/dlaebz.f
for instrumented DLAEBZ to count operations
prec double
file lapack/timing/eig/eigsrc/slaed0.f
for instrumented SLAED0 to count operations
prec single
file lapack/timing/eig/eigsrc/dlaed0.f
for instrumented DLAED0 to count operations
prec double
file lapack/timing/eig/eigsrc/claed0.f
for instrumented CLAED0 to count operations
prec complex
file lapack/timing/eig/eigsrc/zlaed0.f
for instrumented ZLAED0 to count operations
prec doublecomplex
file lapack/timing/eig/eigsrc/slaed1.f
for instrumented SLAED1 to count operations
prec single
file lapack/timing/eig/eigsrc/dlaed1.f
for instrumented DLAED1 to count operations
prec double
file lapack/timing/eig/eigsrc/slaed2.f
for instrumented SLAED2 to count operations
prec single
file lapack/timing/eig/eigsrc/dlaed2.f
for instrumented DLAED2 to count operations
prec double
file lapack/timing/eig/eigsrc/slaed3.f
for instrumented SLAED3 to count operations
prec single
file lapack/timing/eig/eigsrc/dlaed3.f
for instrumented DLAED3 to count operations
prec double
file lapack/timing/eig/eigsrc/slaed4.f
for instrumented SLAED4 to count operations
prec single
file lapack/timing/eig/eigsrc/dlaed4.f
for instrumented DLAED4 to count operations
prec double
file lapack/timing/eig/eigsrc/slaed5.f
for instrumented SLAED5 to count operations
prec single
file lapack/timing/eig/eigsrc/dlaed5.f
for instrumented DLAED5 to count operations
prec double
file lapack/timing/eig/eigsrc/slaed6.f
for instrumented SLAED6 to count operations
prec single
file lapack/timing/eig/eigsrc/dlaed6.f
for instrumented DLAED6 to count operations
prec double
file lapack/timing/eig/eigsrc/slaed7.f
for instrumented SLAED7 to count operations
prec single
file lapack/timing/eig/eigsrc/dlaed7.f
for instrumented DLAED7 to count operations
prec double
file lapack/timing/eig/eigsrc/claed7.f
for instrumented CLAED7 to count operations
prec complex
file lapack/timing/eig/eigsrc/zlaed7.f
for instrumented ZLAED7 to count operations
prec doublecomplex
file lapack/timing/eig/eigsrc/slaed8.f
for instrumented SLAED8 to count operations
prec single
file lapack/timing/eig/eigsrc/dlaed8.f
for instrumented DLAED8 to count operations
prec double
file lapack/timing/eig/eigsrc/claed8.f
for instrumented CLAED8 to count operations
prec complex
file lapack/timing/eig/eigsrc/zlaed8.f
for instrumented ZLAED8 to count operations
prec doublecomplex
file lapack/timing/eig/eigsrc/slaed9.f
for instrumented SLAED9 to count operations
prec single
file lapack/timing/eig/eigsrc/dlaed9.f
for instrumented DLAED9 to count operations
prec double
file lapack/timing/eig/eigsrc/slaeda.f
for instrumented SLAEDA to count operations
prec single
file lapack/timing/eig/eigsrc/dlaeda.f
for instrumented DLAEDA to count operations
prec double
file lapack/timing/eig/eigsrc/slaein.f
for instrumented SLAEIN to count operations
prec single
file lapack/timing/eig/eigsrc/dlaein.f
for instrumented DLAEIN to count operations
prec double
file lapack/timing/eig/eigsrc/claein.f
for instrumented CLAEIN to count operations
prec complex
file lapack/timing/eig/eigsrc/zlaein.f
for instrumented ZLAEIN to count operations
prec doublecomplex
file lapack/timing/eig/eigsrc/slahqr.f
for instrumented SLAHQR to count operations
prec single
file lapack/timing/eig/eigsrc/dlahqr.f
for instrumented DLAHQR to count operations
prec double
file lapack/timing/eig/eigsrc/clahqr.f
for instrumented CLAHQR to count operations
prec complex
file lapack/timing/eig/eigsrc/zlahqr.f
for instrumented ZLAHQR to count operations
prec doublecomplex
file lapack/timing/eig/eigsrc/slar1v.f
for instrumented SLAR1V to count operations
prec single
file lapack/timing/eig/eigsrc/dlar1v.f
for instrumented DLAR1V to count operations
prec double
file lapack/timing/eig/eigsrc/clar1v.f
for instrumented CLAR1V to count operations
prec complex
file lapack/timing/eig/eigsrc/zlar1v.f
for instrumented ZLAR1V to count operations
prec doublecomplex
file lapack/timing/eig/eigsrc/slarrb.f
for instrumented SLARRB to count operations
prec single
file lapack/timing/eig/eigsrc/dlarrb.f
for instrumented DLARRB to count operations
prec double
file lapack/timing/eig/eigsrc/slarre.f
for instrumented SLARRE to count operations
prec single
file lapack/timing/eig/eigsrc/dlarre.f
for instrumented DLARRE to count operations
prec double
file lapack/timing/eig/eigsrc/slarrf.f
for instrumented SLARRF to count operations
prec single
file lapack/timing/eig/eigsrc/dlarrf.f
for instrumented DLARRF to count operations
prec double
file lapack/timing/eig/eigsrc/slarrv.f
for instrumented SLARRV to count operations
prec single
file lapack/timing/eig/eigsrc/dlarrv.f
for instrumented DLARRV to count operations
prec double
file lapack/timing/eig/eigsrc/clarrv.f
for instrumented CLARRV to count operations
prec complex
file lapack/timing/eig/eigsrc/zlarrv.f
for instrumented ZLARRV to count operations
prec doublecomplex
file lapack/timing/eig/eigsrc/slasd0.f
for instrumented SLASD0 to count operations
prec single
file lapack/timing/eig/eigsrc/dlasd0.f
for instrumented DLASD0 to count operations
prec double
file lapack/timing/eig/eigsrc/slasd1.f
for instrumented SLASD1 to count operations
prec single
file lapack/timing/eig/eigsrc/dlasd1.f
for instrumented DLASD1 to count operations
prec double
file lapack/timing/eig/eigsrc/slasd2.f
for instrumented SLASD2 to count operations
prec single
file lapack/timing/eig/eigsrc/dlasd2.f
for instrumented DLASD2 to count operations
prec double
file lapack/timing/eig/eigsrc/slasd3.f
for instrumented SLASD3 to count operations
prec single
file lapack/timing/eig/eigsrc/dlasd3.f
for instrumented DLASD3 to count operations
prec double
file lapack/timing/eig/eigsrc/slasd4.f
for instrumented SLASD4 to count operations
prec single
file lapack/timing/eig/eigsrc/dlasd4.f
for instrumented DLASD4 to count operations
prec double
file lapack/timing/eig/eigsrc/slasd5.f
for instrumented SLASD5 to count operations
prec single
file lapack/timing/eig/eigsrc/dlasd5.f
for instrumented DLASD5 to count operations
prec double
file lapack/timing/eig/eigsrc/slasd6.f
for instrumented SLASD6 to count operations
prec single
file lapack/timing/eig/eigsrc/dlasd6.f
for instrumented DLASD6 to count operations
prec double
file lapack/timing/eig/eigsrc/slasd7.f
for instrumented SLASD7 to count operations
prec single
file lapack/timing/eig/eigsrc/dlasd7.f
for instrumented DLASD7 to count operations
prec double
file lapack/timing/eig/eigsrc/slasd8.f
for instrumented SLASD8 to count operations
prec single
file lapack/timing/eig/eigsrc/dlasd8.f
for instrumented DLASD8 to count operations
prec double
file lapack/timing/eig/eigsrc/slasda.f
for instrumented SLASDA to count operations
prec single
file lapack/timing/eig/eigsrc/dlasda.f
for instrumented DLASDA to count operations
prec double
file lapack/timing/eig/eigsrc/slasdq.f
for instrumented SLASDQ to count operations
prec single
file lapack/timing/eig/eigsrc/dlasdq.f
for instrumented DLASDQ to count operations
prec double
file lapack/timing/eig/eigsrc/slasdt.f
for instrumented SLASDT to count operations
prec single
file lapack/timing/eig/eigsrc/dlasdt.f
for instrumented DLASDT to count operations
prec double
file lapack/timing/eig/eigsrc/slasq1.f
for instrumented SLASQ1 to count operations
prec single
file lapack/timing/eig/eigsrc/dlasq1.f
for instrumented DLASQ1 to count operations
prec double
file lapack/timing/eig/eigsrc/slasq2.f
for instrumented SLASQ2 to count operations
prec single
file lapack/timing/eig/eigsrc/dlasq2.f
for instrumented DLASQ2 to count operations
prec double
file lapack/timing/eig/eigsrc/slasq3.f
for instrumented SLASQ3 to count operations
prec single
file lapack/timing/eig/eigsrc/dlasq3.f
for instrumented DLASQ3 to count operations
prec double
file lapack/timing/eig/eigsrc/slasq4.f
for instrumented SLASQ4 to count operations
prec single
file lapack/timing/eig/eigsrc/dlasq4.f
for instrumented DLASQ4 to count operations
prec double
file lapack/timing/eig/eigsrc/slasq5.f
for instrumented SLASQ5 to count operations
prec single
file lapack/timing/eig/eigsrc/dlasq5.f
for instrumented DLASQ5 to count operations
prec double
file lapack/timing/eig/eigsrc/slasq6.f
for instrumented SLASQ6 to count operations
prec single
file lapack/timing/eig/eigsrc/dlasq6.f
for instrumented DLASQ6 to count operations
prec double
file lapack/timing/eig/eigsrc/spteqr.f
for instrumented SPTEQR to count operations
prec single
file lapack/timing/eig/eigsrc/dpteqr.f
for instrumented DPTEQR to count operations
prec double
file lapack/timing/eig/eigsrc/cpteqr.f
for instrumented CPTEQR to count operations
prec complex
file lapack/timing/eig/eigsrc/zpteqr.f
for instrumented ZPTEQR to count operations
prec doublecomplex
file lapack/timing/eig/eigsrc/sstebz.f
for instrumented SSTEBZ to count operations
prec single
file lapack/timing/eig/eigsrc/dstebz.f
for instrumented DSTEBZ to count operations
prec double
file lapack/timing/eig/eigsrc/sstedc.f
for instrumented SSTEDC to count operations
prec single
file lapack/timing/eig/eigsrc/dstedc.f
for instrumented DSTEDC to count operations
prec double
file lapack/timing/eig/eigsrc/cstedc.f
for instrumented CSTEDC to count operations
prec complex
file lapack/timing/eig/eigsrc/zstedc.f
for instrumented ZSTEDC to count operations
prec doublecomplex
file lapack/timing/eig/eigsrc/sstegr.f
for instrumented SSTEGR to count operations
prec single
file lapack/timing/eig/eigsrc/dstegr.f
for instrumented DSTEGR to count operations
prec double
file lapack/timing/eig/eigsrc/cstegr.f
for instrumented CSTEGR to count operations
prec complex
file lapack/timing/eig/eigsrc/zstegr.f
for instrumented ZSTEGR to count operations
prec doublecomplex
file lapack/timing/eig/eigsrc/sstein.f
for instrumented SSTEIN to count operations
prec single
file lapack/timing/eig/eigsrc/dstein.f
for instrumented DSTEIN to count operations
prec double
file lapack/timing/eig/eigsrc/cstein.f
for instrumented CSTEIN to count operations
prec complex
file lapack/timing/eig/eigsrc/zstein.f
for instrumented ZSTEIN to count operations
prec doublecomplex
file lapack/timing/eig/eigsrc/ssteqr.f
for instrumented SSTEQR to count operations
prec single
file lapack/timing/eig/eigsrc/dsteqr.f
for instrumented DSTEQR to count operations
prec double
file lapack/timing/eig/eigsrc/csteqr.f
for instrumented CSTEQR to count operations
prec complex
file lapack/timing/eig/eigsrc/zsteqr.f
for instrumented ZSTEQR to count operations
prec doublecomplex
file lapack/timing/eig/eigsrc/ssterf.f
for instrumented SSTERF to count operations
prec single
file lapack/timing/eig/eigsrc/dsterf.f
for instrumented DSTERF to count operations
prec double
file lapack/timing/eig/eigsrc/stgevc.f
for instrumented STGEVC to count operations
prec single
file lapack/timing/eig/eigsrc/dtgevc.f
for instrumented DTGEVC to count operations
prec double
file lapack/timing/eig/eigsrc/ctgevc.f
for instrumented CTGEVC to count operations
prec complex
file lapack/timing/eig/eigsrc/ztgevc.f
for instrumented ZTGEVC to count operations
prec doublecomplex
file lapack/timing/eig/eigsrc/strevc.f
for instrumented STREVC to count operations
prec single
file lapack/timing/eig/eigsrc/dtrevc.f
for instrumented DTREVC to count operations
prec double
file lapack/timing/eig/eigsrc/ctrevc.f
for instrumented CTREVC to count operations
prec complex
file lapack/timing/eig/eigsrc/ztrevc.f
for instrumented ZTREVC to count operations
prec doublecomplex
#######################################
# Index for lapack/timing/eig #
#######################################
file lapack/timing/eig/index
for This index
lib lapack/timing/eig/eigsrc
for Subdirectory containing instrumented LAPACK routines
file lapack/timing/eig/ilaenv.f
for Special version to be used in conjunction with XLAENV
file lapack/timing/eig/xlaenv.f
for Resets ILAENV values for timing purposes
# ==========================================
# Available Eigenproblem Timing Routines
# ==========================================
file lapack/timing/eig/stimee.f
for Timing program driver for eigenvalue problem timing
prec single
file lapack/timing/eig/dtimee.f
for Timing program driver for eigenvalue problem timing
prec double
file lapack/timing/eig/ctimee.f
for Timing program driver for eigenvalue problem timing
prec complex
file lapack/timing/eig/ztimee.f
for Timing program driver for eigenvalue problem timing
prec doublecomplex
# ===
file lapack/timing/eig/seispack.f
for Instrumented EISPACK routines used for timing purposes
prec single
file lapack/timing/eig/deispack.f
for Instrumented EISPACK routines used for timing purposes
prec double
file lapack/timing/eig/ceispack.f
for Instrumented EISPACK routines used for timing purposes
prec complex
file lapack/timing/eig/zeispack.f
for Instrumented EISPACK routines used for timing purposes
prec doublecomplex
# ===
file lapack/timing/eig/stim21.f
for Times the nonsymmetric eigenvalue problem LAPACK routines
, (SGEHRD, SHSEQR, STREVC, SHSEIN)
prec single
file lapack/timing/eig/dtim21.f
for Times the nonsymmetric eigenvalue problem LAPACK routines
, (DGEHRD, DHSEQR, DTREVC, DHSEIN)
prec double
file lapack/timing/eig/ctim21.f
for Times the nonsymmetric eigenvalue problem LAPACK routines
, (CGEHRD, CHSEQR, CTREVC, CHSEIN)
prec complex
file lapack/timing/eig/ztim21.f
for Times the nonsymmetric eigenvalue problem LAPACK routines
, (ZGEHRD, ZHSEQR, ZTREVC, ZHSEIN)
prec doublecomplex
# ===
file lapack/timing/eig/stim22.f
for Times the symmetric eigenvalue problem LAPACK routines
, (SSYTRD, SORGTR, SORMTR, SSTEQR, SSTERF, SPTEQR, SSTEBZ,
, SSTEIN, SSTEDC, SSTEGR)
prec single
file lapack/timing/eig/dtim22.f
for Times the symmetric eigenvalue problem LAPACK routines
, (DSYTRD, DORGTR, DORMTR, DSTEQR, DSTERF, DPTEQR, DSTEBZ,
, DSTEIN, DSTEDC, DSTEGR)
prec double
file lapack/timing/eig/ctim22.f
for Times the symmetric eigenvalue problem LAPACK routines
, (CHETRD, CSTEQR, CUNGTR+CSTEQR, CPTEQR, CUNGTR+CPTEQR,
, SSTEBZ+CSTEIN+CUNMTR, CUNGTR+CSTEDC, CSTEDC, CSTEGR)
prec complex
file lapack/timing/eig/ztim22.f
for Times the symmetric eigenvalue problem LAPACK routines
, (ZHETRD, ZSTEQR, ZUNGTR+ZSTEQR, ZPTEQR, ZUNGTR+ZPTEQR,
, DSTEBZ+ZSTEIN+ZUNMTR, ZUNGTR+ZSTEDC, ZSTEDC, ZSTEGR)
prec doublecomplex
# ===
file lapack/timing/eig/stim26.f
for Times the singular value decomposition LAPACK routines
, (SGEBRD, SBDSQR, SGEBRD+SBDSQR, SGEBRD+SORGBR+SBDSQR,
, SBDSDC, SGESDD)
prec single
file lapack/timing/eig/dtim26.f
for Times the singular value decomposition LAPACK routines
, (DGEBRD, DBDSQR, DGEBRD+DBDSQR, DGEBRD+DORGBR+DBDSQR,
, DBDSDC, DGESDD)
prec double
file lapack/timing/eig/ctim26.f
for Times the singular value decomposition LAPACK routines
, (CGEBRD, CBDSQR, CGEBRD+CBDSQR, CGEBRD+CUNGBR+CBDSQR,
, CGESDD)
prec complex
file lapack/timing/eig/ztim26.f
for Times the singular value decomposition LAPACK routines
, (ZGEBRD, ZBDSQR, ZGEBRD+ZBDSQR, ZGEBRD+ZUNGBR+ZBDSQR,
, ZGESDD)
prec doublecomplex
# ===
file lapack/timing/eig/stim51.f
for Times the generalized nonsymmetric eigenvalue problem LAPACK
, routines (SGGHRD+SGEQRF, SHGEQZ, STGEVC)
prec single
file lapack/timing/eig/dtim51.f
for Times the generalized nonsymmetric eigenvalue problem LAPACK
, routines (DGGHRD+DGEQRF, DHGEQZ, DTGEVC)
prec double
file lapack/timing/eig/ctim51.f
for Times the generalized nonsymmetric eigenvalue problem LAPACK
, routines (CGGHRD+CGEQRF, CHGEQZ, CTGEVC)
prec complex
file lapack/timing/eig/ztim51.f
for Times the generalized nonsymmetric eigenvalue problem LAPACK
, routines (ZGGHRD+ZGEQRF, ZHGEQZ, ZTGEVC)
prec doublecomplex
file lapack/timing/timing.tgz
for This is a gzip tar file of the timing directory
, (1059485 bytes).
, This cannot be retrieved via email.
#######################################
# Index for lapack/timing #
#######################################
lib lapack/timing/eig
for Subdirectory of Eigenproblem Timing
lib lapack/timing/lin
for Subdirectory of Linear Equation Timing
file lapack/timing/large.tgz
for Tar-gzipped file of LARGE timing data files (xBLASA.in, xBLASB.in,
, xBLASC.in, xTIME.in, xBAND.in, xTIME2.in, xGEPTIM.in,
, xNEPTIM.in, xSEPTIM.in, and xSVDTIM.in)
prec single, double, complex, doublecomplex
# ====
# NOTE: SMALL and LARGE refer to the size of the matrices being
# ==== generated. Because of nondifferentiation between upper
# and lowercase letters, the LARGE data set can only be obtained
# via the large.tgz file.
# =======================================
# Input Files for BLAS Timing
# =======================================
file lapack/timing/sblasa.in
for SMALL Data file for timing BLAS (parameters M, N, and K)
, with K small
prec single
file lapack/timing/dblasa.in
for SMALL Data file for timing BLAS (parameters M, N, and K)
, with K small
prec double
file lapack/timing/cblasa.in
for SMALL Data file for timing BLAS (parameters M, N, and K)
, with K small
prec complex
file lapack/timing/zblasa.in
for SMALL Data file for timing BLAS (parameters M, N, and K)
, with K small
prec doublecomplex
file lapack/timing/sblasb.in
for SMALL Data file for timing BLAS (parameters M, N, and K)
, with M small
prec single
file lapack/timing/dblasb.in
for SMALL Data file for timing BLAS (parameters M, N, and K)
, with M small
prec double
file lapack/timing/cblasb.in
for SMALL Data file for timing BLAS (parameters M, N, and K)
, with M small
prec complex
file lapack/timing/zblasb.in
for SMALL Data file for timing BLAS (parameters M, N, and K)
, with M small
prec doublecomplex
file lapack/timing/sblasc.in
for SMALL Data file for timing BLAS (parameters M, N, and K)
, with N small
prec single
file lapack/timing/dblasc.in
for SMALL Data file for timing BLAS (parameters M, N, and K)
, with N small
prec double
file lapack/timing/cblasc.in
for SMALL Data file for timing BLAS (parameters M, N, and K)
, with N small
prec complex
file lapack/timing/zblasc.in
for SMALL Data file for timing BLAS (parameters M, N, and K)
, with N small
prec doublecomplex
# =======================================
# Input Files for Linear Equation Timing
# =======================================
file lapack/timing/stime.in
for SMALL Data file for timing square real linear
, equations/linear least squares routines
prec single
file lapack/timing/dtime.in
for SMALL Data file for timing square real linear
, equations/linear least squares routines
prec double
file lapack/timing/ctime.in
for SMALL Data file for timing square complex linear
, equations/linear least squares routines
prec complex
file lapack/timing/ztime.in
for SMALL Data file for timing square complex linear
, equations/linear least squares routines
prec doublecomplex
file lapack/timing/sband.in
for SMALL Data file for timing banded real linear
, equations/linear least squares routines
prec single, double, complex, doublecomplex
file lapack/timing/dband.in
for SMALL Data file for timing banded real linear
, equations/linear least squares routines
prec double
file lapack/timing/cband.in
for SMALL Data file for timing banded complex linear
, equations/linear least squares routines
prec complex
file lapack/timing/zband.in
for SMALL Data file for timing banded complex linear
, equations/linear least squares routines
prec doublecomplex
file lapack/timing/stime2.in
for SMALL Data file for timing rectangular real linear
, equations/least squares routines
prec single
file lapack/timing/dtime2.in
for SMALL Data file for timing rectangular real linear
, equations/least squares routines
prec double
file lapack/timing/ctime2.in
for SMALL Data file for timing rectangular complex linear
, equations/least squares routines
prec complex
file lapack/timing/ztime2.in
for SMALL Data file for timing rectangular complex linear
, equations/least squares routines
prec doublecomplex
# =======================================
# Input Files for Eigenproblem Timing
# =======================================
file lapack/timing/sgeptim.in
for SMALL Data file for timing the real Generalized
, Nonsymmetric Eigenproblem computational and simple driver routines
prec single
file lapack/timing/dgeptim.in
for SMALL Data file for timing the real Generalized
, Nonsymmetric Eigenproblem computational and simple driver routines
prec double
file lapack/timing/cgeptim.in
for SMALL Data file for timing the complex Generalized
, Nonsymmetric Eigenproblem computational and simple driver routines
prec complex
file lapack/timing/zgeptim.in
for SMALL Data file for timing the complex Generalized
, Nonsymmetric Eigenproblem computational and simple driver routines
prec doublecomplex
file lapack/timing/sneptim.in
for SMALL Data file for timing the real Nonsymmetric
, Eigenproblem computational and simple/expert driver routines
prec single
file lapack/timing/dneptim.in
for SMALL Data file for timing the real Nonsymmetric
, Eigenproblem computational and simple/expert driver routines
prec double
file lapack/timing/cneptim.in
for SMALL Data file for timing the complex Nonsymmetric
, Eigenproblem computational and simple/expert driver routines
prec complex
file lapack/timing/zneptim.in
for SMALL Data file for timing the complex Nonsymmetric
, Eigenproblem computational and simple/expert driver routines
prec doublecomplex
file lapack/timing/sseptim.in
for SMALL Data file for timing the real Symmetric
, Eigenproblem and Generalized Symmetric Eigenproblem
, computational and simple/expert driver routines
prec single
file lapack/timing/dseptim.in
for SMALL Data file for timing the real Symmetric
, Eigenproblem and Generalized Symmetric Eigenproblem
, computational and simple/expert driver routines
prec double
file lapack/timing/cseptim.in
for SMALL Data file for timing the complex Symmetric
, Eigenproblem and Generalized Symmetric Eigenproblem
, computational and simple/expert driver routines
prec complex
file lapack/timing/zseptim.in
for SMALL Data file for timing the complex Symmetric
, Eigenproblem and Generalized Symmetric Eigenproblem
, computational and simple/expert driver routines
prec doublecomplex
file lapack/timing/ssvdtim.in
for SMALL Data file for timing the real Singular Value
, Decomposition computational and simple/expert driver routines
prec single
file lapack/timing/dsvdtim.in
for SMALL Data file for timing the real Singular Value
, Decomposition computational and simple/expert driver routines
prec double
file lapack/timing/csvdtim.in
for SMALL Data file for timing the complex Singular Value
, Decomposition computational and simple/expert driver routines
prec complex
file lapack/timing/zsvdtim.in
for SMALL Data file for timing the complex Singular Value
, Decomposition computational and simple/expert driver routines
prec doublecomplex
#######################################
# Index for lapack/timing/lin #
#######################################
file lapack/timing/lin/index
for This index
lib lapack/timing/lin/linsrc
for Subdirectory containing instrumented LAPACK routines
file lapack/timing/lin/ilaenv.f
for Special version used in conjunction with XLAENV
file lapack/timing/lin/xlaenv.f
for Resets ILAENV values for timing purposes
# ==========================================
# Available Linear Equation Timing Routines
# ==========================================
file lapack/timing/lin/stimaa.f
for Timing program driver for linear equation timing
prec single
file lapack/timing/lin/dtimaa.f
for Timing program driver for linear equation timing
prec double
file lapack/timing/lin/ctimaa.f
for Timing program driver for linear equation timing
prec complex
file lapack/timing/lin/ztimaa.f
for Timing program driver for linear equation timing
prec doublecomplex
# ===
file lapack/timing/lin/seispk.f
for Instrumented eispack routines used in timing comparisons
prec single
file lapack/timing/lin/deispk.f
for Instrumented eispack routines used in timing comparisons
prec double
# ===
file lapack/timing/lin/slinpk.f
for Instrumented linpack routines used in timing comparisons
prec single
file lapack/timing/lin/dlinpk.f
for Instrumented linpack routines used in timing comparisons
prec double
file lapack/timing/lin/clinpk.f
for Instrumented linpack routines used in timing comparisons
prec complex
file lapack/timing/lin/zlinpk.f
for Instrumented linpack routines used in timing comparisons
prec doublecomplex
# ===
file lapack/timing/lin/stimmg.f
for Generates a toeplitz test matrix
prec single
file lapack/timing/lin/dtimmg.f
for Generates a toeplitz test matrix
prec double
file lapack/timing/lin/ctimmg.f
for Generates a toeplitz test matrix
prec complex
file lapack/timing/lin/ztimmg.f
for Generates a toeplitz test matrix
prec doublecomplex
# ===
file lapack/timing/lin/stimb2.f
for Times the BLAS 2 routines
prec single
file lapack/timing/lin/dtimb2.f
for Times the BLAS 2 routines
prec double
file lapack/timing/lin/ctimb2.f
for Times the BLAS 2 routines
prec complex
file lapack/timing/lin/ztimb2.f
for Times the BLAS 2 routines
prec doublecomplex
file lapack/timing/lin/stimb3.f
for Times the BLAS 3 routines
prec single
file lapack/timing/lin/dtimb3.f
for Times the BLAS 3 routines
prec double
file lapack/timing/lin/ctimb3.f
for Times the BLAS 3 routines
prec complex
file lapack/timing/lin/ztimb3.f
for Times the BLAS 3 routines
prec doublecomplex
file lapack/timing/lin/stimmm.f
for Times SGEMM
prec single
file lapack/timing/lin/dtimmm.f
for Times DGEMM
prec double
file lapack/timing/lin/ctimmm.f
for Times CGEMM
prec complex
file lapack/timing/lin/ztimmm.f
for Times ZGEMM
prec doublecomplex
file lapack/timing/lin/stimmv.f
for Times individual BLAS 2 routines
prec single
file lapack/timing/lin/dtimmv.f
for Times individual BLAS 2 routines
prec double
file lapack/timing/lin/ctimmv.f
for Times individual BLAS 2 routines
prec complex
file lapack/timing/lin/ztimmv.f
for Times individual BLAS 2 routines
prec doublecomplex
# ===
file lapack/timing/lin/stimbr.f
for Times SGEBRD, SORGBR, and SORMBR
prec single
file lapack/timing/lin/dtimbr.f
for Times DGEBRD, DORGBR, and DORMBR
prec double
file lapack/timing/lin/ctimbr.f
for Times CGEBRD, CUNGBR, and CUNMBR
prec complex
file lapack/timing/lin/ztimbr.f
for Times ZGEBRD, ZUNGBR, and ZUNMBR
prec doublecomplex
# ===
file lapack/timing/lin/stimgb.f
for Times SGBTRF and SGBTRS
prec single
file lapack/timing/lin/dtimgb.f
for Times DGBTRF and DGBTRS
prec double
file lapack/timing/lin/ctimgb.f
for Times CGBTRF and CGBTRS
prec complex
file lapack/timing/lin/ztimgb.f
for Times ZGBTRF and ZGBTRS
prec doublecomplex
# ===
file lapack/timing/lin/stimge.f
for Times SGETRF, SGETRS, and SGETRI
prec single
file lapack/timing/lin/dtimge.f
for Times DGETRF, DGETRS, and DGETRI
prec double
file lapack/timing/lin/ctimge.f
for Times CGETRF, CGETRS, and CGETRI
prec complex
file lapack/timing/lin/ztimge.f
for Times ZGETRF, ZGETRS, and ZGETRI
prec doublecomplex
# ===
file lapack/timing/lin/stimgt.f
for Times SGTTRF, -TRS, -SV, and -SL.
prec single
file lapack/timing/lin/dtimgt.f
for Times DGTTRF, -TRS, -SV, and -SL.
prec double
file lapack/timing/lin/ctimgt.f
for Times CGTTRF, -TRS, -SV, and -SL.
prec complex
file lapack/timing/lin/ztimgt.f
for Times ZGTTRF, -TRS, -SV, and -SL.
prec doublecomplex
# ===
file lapack/timing/lin/stimhr.f
for Times the LAPACK routines SGEHRD, SORGHR, and SORMHR,
, and the EISPACK routine ORTHES
prec single
file lapack/timing/lin/dtimhr.f
for Times the LAPACK routines DGEHRD, DORGHR, and DORMHR,
, and the EISPACK routine ORTHES
prec double
file lapack/timing/lin/ctimhr.f
for Times the LAPACK routines CGEHRD, CUNGHR, and CUNMHR
prec complex
file lapack/timing/lin/ztimhr.f
for Times the LAPACK routines ZGEHRD, ZUNGHR, and ZUNMHR
prec doublecomplex
# ===
file lapack/timing/lin/stimlq.f
for Times the LAPACK routines to perform the LQ factorization
, (SGELQF, SORGLQ, SORMLQ)
prec single
file lapack/timing/lin/dtimlq.f
for Times the LAPACK routines to perform the LQ factorization
, (DGELQF, DORGLQ, DORMLQ)
prec double
file lapack/timing/lin/ctimlq.f
for Times the LAPACK routines to perform the LQ factorization
, (CGELQF, CUNGLQ, CUNMLQ)
prec complex
file lapack/timing/lin/ztimlq.f
for Times the LAPACK routines to perform the LQ factorization
, (ZGELQF, ZUNGLQ, ZUNMLQ)
prec doublecomplex
# ===
file lapack/timing/lin/stimls.f
for Times the LAPACK routines to perform least squares
, (SGELS, SGELSD, SGELSS, SGELSX, SGELSY)
prec single
file lapack/timing/lin/dtimls.f
for Times the LAPACK routines to perform least squares
, (DGELS, DGELSD, DGELSS, DGELSX, DGELSY)
prec double
file lapack/timing/lin/ctimls.f
for Times the LAPACK routines to perform least squares
, (CGELS, CGELSD, CGELSS, CGELSX, CGELSY)
prec complex
file lapack/timing/lin/ztimls.f
for Times the LAPACK routines to perform least squares
, (ZGELS, ZGELSD, ZGELSS, ZGELSX, ZGELSY)
prec doublecomplex
# ===
file lapack/timing/lin/stimpb.f
for Times SPBTRF and SPBTRS
prec single
file lapack/timing/lin/dtimpb.f
for Times DPBTRF and DPBTRS
prec double
file lapack/timing/lin/ctimpb.f
for Times CPBTRF and CPBTRS
prec complex
file lapack/timing/lin/ztimpb.f
for Times ZPBTRF and ZPBTRS
prec doublecomplex
# ===
file lapack/timing/lin/stimpo.f
for Times SPOTRF, SPOTRS, and SPOTRI
prec single
file lapack/timing/lin/dtimpo.f
for Times DPOTRF, DPOTRS, and DPOTRI
prec double
file lapack/timing/lin/ctimpo.f
for Times CPOTRF, CPOTRS, and CPOTRI
prec complex
file lapack/timing/lin/ztimpo.f
for Times ZPOTRF, ZPOTRS, and ZPOTRI
prec doublecomplex
# ===
file lapack/timing/lin/stimpp.f
for Times SPPTRF, SPPTRS, and SPPTRI
prec single
file lapack/timing/lin/dtimpp.f
for Times DPPTRF, DPPTRS, and DPPTRI
prec double
file lapack/timing/lin/ctimpp.f
for Times CPPTRF, CPPTRS, and CPPTRI
prec complex
file lapack/timing/lin/ztimpp.f
for Times ZPPTRF, ZPPTRS, and ZPPTRI
prec doublecomplex
# ===
file lapack/timing/lin/stimpt.f
for Times SPTTRF, -TRS, -SV, and -SL.
prec single
file lapack/timing/lin/dtimpt.f
for Times DPTTRF, -TRS, -SV, and -SL.
prec double
file lapack/timing/lin/ctimpt.f
for Times CPTTRF, -TRS, -SV, and -SL.
prec complex
file lapack/timing/lin/ztimpt.f
for Times ZPTTRF, -TRS, -SV, and -SL.
prec doublecomplex
# ===
file lapack/timing/lin/stimql.f
for Times the LAPACK routines to perform the QL factorization
, (SGEQLF, SORGQL, SORMQL)
prec single
file lapack/timing/lin/dtimql.f
for Times the LAPACK routines to perform the QL factorization
, (DGEQLF, DORGQL, DORMQL)
prec double
file lapack/timing/lin/ctimql.f
for Times the LAPACK routines to perform the QL factorization
, (CGEQLF, CUNGQL, CUNMQL)
prec complex
file lapack/timing/lin/ztimql.f
for Times the LAPACK routines to perform the QL factorization
, (ZGEQLF, ZUNGQL, ZUNMQL)
prec doublecomplex
# ===
file lapack/timing/lin/stimqp.f
for Times the LAPACK routines to perform the QR factorization
, with column pivoting (SGEQPF)
prec single
file lapack/timing/lin/dtimqp.f
for Times the LAPACK routines to perform the QR factorization
, with column pivoting (DGEQPF)
prec double
file lapack/timing/lin/ctimqp.f
for Times the LAPACK routines to perform the QR factorization
, with column pivoting (CGEQPF)
prec complex
file lapack/timing/lin/ztimqp.f
for Times the LAPACK routines to perform the QR factorization
, with column pivoting (ZGEQPF)
prec doublecomplex
file lapack/timing/lin/stimq3.f
for Times the LAPACK routines to perform the QR factorization
, with column pivoting (SGEQP3)
prec single
file lapack/timing/lin/dtimq3.f
for Times the LAPACK routines to perform the QR factorization
, with column pivoting (DGEQP3)
prec double
file lapack/timing/lin/ctimq3.f
for Times the LAPACK routines to perform the QR factorization
, with column pivoting (CGEQP3)
prec complex
file lapack/timing/lin/ztimq3.f
for Times the LAPACK routines to perform the QR factorization
, with column pivoting (ZGEQP3)
prec doublecomplex
# ===
file lapack/timing/lin/stimqr.f
for Times the LAPACK routines to perform the QR factorization
, (SGEQRF, SORGQR, SORMQR)
prec single
file lapack/timing/lin/dtimqr.f
for Times the LAPACK routines to perform the QR factorization
, (DGEQRF, DORGQR, DORMQR)
prec double
file lapack/timing/lin/ctimqr.f
for Times the LAPACK routines to perform the QR factorization
, (CGEQRF, CUNGQR, CUNMQR)
prec complex
file lapack/timing/lin/ztimqr.f
for Times the LAPACK routines to perform the QR factorization
, (ZGEQRF, ZUNGQR, ZUNMQR)
prec doublecomplex
# ===
file lapack/timing/lin/stimrq.f
for Times the LAPACK routines to perform the RQ factorization
, (SGERQF, SORGRQ, SORMRQ)
prec single
file lapack/timing/lin/dtimrq.f
for Times the LAPACK routines to perform the RQ factorization
, (DGERQF, DORGRQ, DORMRQ)
prec double
file lapack/timing/lin/ctimrq.f
for Times the LAPACK routines to perform the RQ factorization
, (CGERQF, CUNGRQ, CUNMRQ)
prec complex
file lapack/timing/lin/ztimrq.f
for Times the LAPACK routines to perform the RQ factorization
, (ZGERQF, ZUNGRQ, ZUNMRQ)
prec doublecomplex
# ===
file lapack/timing/lin/stimsp.f
for Times SSPTRF, SSPTRS, and SSPTRI
prec single
file lapack/timing/lin/dtimsp.f
for Times DSPTRF, DSPTRS, and DSPTRI
prec double
file lapack/timing/lin/ctimsp.f
for Times CSPTRF, CSPTRS, and CSPTRI
prec complex
file lapack/timing/lin/ztimsp.f
for Times ZSPTRF, ZSPTRS, and ZSPTRI
prec doublecomplex
file lapack/timing/lin/ctimhp.f
for Times CHPTRF, CHPTRS, and CHPTRI
prec complex
file lapack/timing/lin/ztimhp.f
for Times ZHPTRF, ZHPTRS, and ZHPTRI
prec doublecomplex
# ===
file lapack/timing/lin/stimsy.f
for Times SSYTRF, SSYTRS, and SSYTRI
prec single
file lapack/timing/lin/dtimsy.f
for Times DSYTRF, DSYTRS, and DSYTRI
prec double
file lapack/timing/lin/ctimsy.f
for Times CSYTRF, CSYTRS, and CSYTRI
prec complex
file lapack/timing/lin/ztimsy.f
for Times ZSYTRF, ZSYTRS, and ZSYTRI
prec doublecomplex
file lapack/timing/lin/ctimhe.f
for Times CHETRF, CHETRS, and CHETRI
prec complex
file lapack/timing/lin/ztimhe.f
for Times ZHETRF, ZHETRS, and ZHETRI
prec doublecomplex
# ===
file lapack/timing/lin/stimtb.f
for Times STBTRS
prec single
file lapack/timing/lin/dtimtb.f
for Times DTBTRS
prec double
file lapack/timing/lin/ctimtb.f
for Times CTBTRS
prec complex
file lapack/timing/lin/ztimtb.f
for Times ZTBTRS
prec doublecomplex
# ===
file lapack/timing/lin/stimtd.f
for Times the LAPACK routines SSYTRD, SORGTR, and SORMTR,
, and the EISPACK routine TRED1
prec single
file lapack/timing/lin/dtimtd.f
for Times the LAPACK routines DSYTRD, DORGTR, and DORMTR,
, and the EISPACK routine TRED1
prec double
file lapack/timing/lin/ctimtd.f
for Times the LAPACK routines CHETRD, CUNGTR, and CUNMTR
prec complex
file lapack/timing/lin/ztimtd.f
for Times the LAPACK routines ZHETRD, ZUNGTR, and ZUNMTR
prec doublecomplex
# ===
file lapack/timing/lin/stimtp.f
for Times STPTRI and STPTRS
prec single
file lapack/timing/lin/dtimtp.f
for Times DTPTRI and DTPTRS
prec double
file lapack/timing/lin/ctimtp.f
for Times CTPTRI and CTPTRS
prec complex
file lapack/timing/lin/ztimtp.f
for Times ZTPTRI and ZTPTRS
prec doublecomplex
# ===
file lapack/timing/lin/stimtr.f
for Times STRTRI and STRTRS
prec single
file lapack/timing/lin/dtimtr.f
for Times DTRTRI and DTRTRS
prec double
file lapack/timing/lin/ctimtr.f
for Times CTRTRI and CTRTRS
prec complex
file lapack/timing/lin/ztimtr.f
for Times ZTRTRI and ZTRTRS
prec doublecomplex
#########################################
# Index for lapack/timing/lin/linsrc #
#########################################
# ==========================================
# Available Instrumented LIN LAPACK Routines
# ==========================================
file lapack/timing/lin/linsrc/sgels.f
for instrumented SGELS to count operations
prec single
file lapack/timing/lin/linsrc/dgels.f
for instrumented DGELS to count operations
prec double
file lapack/timing/lin/linsrc/cgels.f
for instrumented CGELS to count operations
prec complex
file lapack/timing/lin/linsrc/zgels.f
for instrumented ZGELS to count operations
prec doublecomplex
file lapack/timing/lin/linsrc/sgelsd.f
for instrumented SGELSD to count operations
prec single
file lapack/timing/lin/linsrc/dgelsd.f
for instrumented DGELSD to count operations
prec double
file lapack/timing/lin/linsrc/cgelsd.f
for instrumented CGELSD to count operations
prec complex
file lapack/timing/lin/linsrc/zgelsd.f
for instrumented ZGELSD to count operations
prec doublecomplex
file lapack/timing/lin/linsrc/sgelss.f
for instrumented SGELSS to count operations
prec single
file lapack/timing/lin/linsrc/dgelss.f
for instrumented DGELSS to count operations
prec double
file lapack/timing/lin/linsrc/cgelss.f
for instrumented CGELSS to count operations
prec complex
file lapack/timing/lin/linsrc/zgelss.f
for instrumented ZGELSS to count operations
prec doublecomplex
file lapack/timing/lin/linsrc/sgelsx.f
for instrumented SGELSX to count operations
prec single
file lapack/timing/lin/linsrc/dgelsx.f
for instrumented DGELSX to count operations
prec double
file lapack/timing/lin/linsrc/cgelsx.f
for instrumented CGELSX to count operations
prec complex
file lapack/timing/lin/linsrc/zgelsx.f
for instrumented ZGELSX to count operations
prec doublecomplex
file lapack/timing/lin/linsrc/sgelsy.f
for instrumented SGELSY to count operations
prec single
file lapack/timing/lin/linsrc/dgelsy.f
for instrumented DGELSY to count operations
prec double
file lapack/timing/lin/linsrc/cgelsy.f
for instrumented CGELSY to count operations
prec complex
file lapack/timing/lin/linsrc/zgelsy.f
for instrumented ZGELSY to count operations
prec doublecomplex
file lapack/timing/lin/linsrc/slaic1.f
for instrumented SLAIC1 to count operations
prec single
file lapack/timing/lin/linsrc/dlaic1.f
for instrumented DLAIC1 to count operations
prec double
file lapack/timing/lin/linsrc/claic1.f
for instrumented CLAIC1 to count operations
prec complex
file lapack/timing/lin/linsrc/zlaic1.f
for instrumented ZLAIC1 to count operations
prec doublecomplex
file lapack/timing/lin/linsrc/slals0.f
for instrumented SLALS0 to count operations
prec single
file lapack/timing/lin/linsrc/dlals0.f
for instrumented DLALS0 to count operations
prec double
file lapack/timing/lin/linsrc/clals0.f
for instrumented CLALS0 to count operations
prec complex
file lapack/timing/lin/linsrc/zlals0.f
for instrumented ZLALS0 to count operations
prec doublecomplex
file lapack/timing/lin/linsrc/slalsa.f
for instrumented SLALSA to count operations
prec single
file lapack/timing/lin/linsrc/dlalsa.f
for instrumented DLALSA to count operations
prec double
file lapack/timing/lin/linsrc/clalsa.f
for instrumented CLALSA to count operations
prec complex
file lapack/timing/lin/linsrc/zlalsa.f
for instrumented ZLALSA to count operations
prec doublecomplex
file lapack/timing/lin/linsrc/slalsd.f
for instrumented SLALSD to count operations
prec single
file lapack/timing/lin/linsrc/dlalsd.f
for instrumented DLALSD to count operations
prec double
file lapack/timing/lin/linsrc/clalsd.f
for instrumented CLALSD to count operations
prec complex
file lapack/timing/lin/linsrc/zlalsd.f
for instrumented ZLALSD to count operations
prec doublecomplex
file lapack/util/ilaver.f
# ======================================================================
# LAPACK3E Version: 1.2, September 10, 2003
#
# LAPACK3E is an update to LAPACK version 3.0 enhanced with selected
# features of Fortran 90. It is compatible with both the Fortran 77
# interfaces of LAPACK 3 and the Fortran 90 interfaces of LAPACK 95.
# ======================================================================
# -------------------
# Available software:
# -------------------
file lapack3e/LAPACK3E.1.2.tar.gz
for LAPACK3E.1.2
, LAPACK3E.1.2 source code in gzip'ed tar format
size 3.8mb
file lapack3e/LAPACK3E.tar.gz
for LAPACK3E
, LAPACK3E source code in gzip'ed tar format
size 3.7mb
# -------------------
# Library Files:
# -------------------
file lapack3e/liblapack3e_IBM.a.gz
for LAPACK3E
, LAPACK3E library compiled for a Power3 IBM SP
size 3.0mb
file lapack3e/liblapack3e_SUN.a.gz
for LAPACK3E
, LAPACK3E library compiled for a SUN
size 3.5mb
file lapack3e/liblapack3e_T3E.a.gz
for LAPACK3E
, LAPACK3E library compiled for a CRAY T3E
size 3.1mb
# -------------------
# Documentation:
# -------------------
file lapack3e/FoCM.pdf
for LAPACK3E
, Presentation on LAPACK3E from the Foundations of
, Computational Mathematics meeting in Minneapolis,
, workshop on Numerical Linear Algebra, Aug. 2002
file lapack3e/lawn158.pdf
for LAPACK3E
, Technical report on LAPACK3E
file lapack95/lapack95.tgz
file lapack95/lapack95_linux_redhat.tgz
file lapack/lawns/lawn138.ps
file lapack/lawns/lawn134.ps
file lapack/lawns/lawn117.ps
file laso/readme
for overview of laso
file laso/dilaso.f
for all eigenvalues and eigenvectors of a sparse symmetric matrix outside
an excluded interval, block Lanczos with orthogonalization
prec double
gams d4a1, d4a7
file laso/silaso.f
for all eigenvalues and eigenvectors of a sparse symmetric matrix outside
an excluded interval, block Lanczos with orthogonalization
prec single
gams d4a1, d4a7
file laso/dnlaso.f
for a few eigenvalues and eigenvectors of a sparse symmetric matrix from
either end of the spectrum, block Lanczos with orthogonalization
prec double
gams d4a1, d4a7
file laso/snlaso.f
for a few eigenvalues and eigenvectors of a sparse symmetric matrix from
either end of the spectrum, block Lanczos with orthogonalization
prec single
gams d4a1, d4a7
file laso/doc
for user manual for the LASO package
file laso/lanczos3
for sample driver program for the LASO package
file lawson-hanson/all
for programs from "Solving Least Squares Problems," SIAM Publications
lang Fortran77, Fortran90
# BNDACC
# BNDSOL
# DIFF
# G1
# G2
# GEN
# H12
# HFTI
# LDP
# MFEOUT
# NNLS
# QRBD
# SVA
# SVDRS
# BVLS
file linalg/amd/readme
for readme for approximate minimum degree ordering routines
by Timothy A. Davis (University of Florida, email: davis@cise.ufl.edu),
, Patrick Amestoy, Iain S. Duff, and John K. Reid
file linalg/amd/amdatr.f
for approximate minimum degree ordering of a sparse symmetric matrix
, (upper bound on true degree)
by Timothy A. Davis, Patrick Amestoy, Iain S. Duff, and John K. Reid
alg approximate minimum degree ordering
file linalg/amd/amdbar.f
for approximate minimum degree ordering of a sparse symmetric matrix
, (upper bound on external degree)
by Timothy A. Davis, Patrick Amestoy, Iain S. Duff, and John K. Reid
alg approximate minimum degree ordering
file linalg/amd/amdexa.f
for approximate minimum degree ordering of a sparse symmetric matrix
, (exact external degree)
by Timothy A. Davis, Patrick Amestoy, Iain S. Duff, and John K. Reid
alg approximate minimum degree ordering
file linalg/amd/amdhaf.f
for approximate minimum degree ordering of a sparse symmetric matrix
, ("half-and-half" degree)
by Timothy A. Davis, Patrick Amestoy, Iain S. Duff, and John K. Reid
alg approximate minimum degree ordering
file linalg/amd/amdhat.f
for approximate minimum degree ordering of a sparse symmetric matrix
, (Gilbert, Moler, and Schreiber bound on external degree)
by Timothy A. Davis, Patrick Amestoy, Iain S. Duff, and John K. Reid
alg approximate minimum degree ordering
file linalg/amd/amdpre.f
for the amdpre routine is a preprocessor to amdbar. It removes dense rows
, and columns from the matrix prior to ordering by amdbar and can thus
, be much faster than amdbar alone.
size 164k
by Timothy A. Davis and Joseph L. Carmen
file linalg/amd/amdpre.ps
for a technical report describing the amdpre routine
by Timothy A. Davis and Joseph L. Carmen
file linalg/amd/amdtru.f
for approximate minimum degree ordering of a sparse symmetric matrix
, (exact true degree)
by Timothy A. Davis, Patrick Amestoy, Iain S. Duff, and John K. Reid
alg approximate minimum degree ordering
file linalg/amd/amdbar.m
for Matlab V5 interface for amdbar.f (amdbarmex.f also needed)
by Timothy A. Davis
alg approximate minimum degree ordering
file linalg/amd/amdbarmex.f
for Matlab V5 interface for amdbar.f (amdbar.m also needed)
by Timothy A. Davis
alg approximate minimum degree ordering
file linalg/amd/amdbar_demo.m
for Demo for the Matlab V5 interface for amdbar
by Timothy A. Davis
alg approximate minimum degree ordering
file linalg/colamd/readme
file linalg/colamd/colamd1.0.tar.gz
file linalg/colamd/colamd.c
file linalg/colamd/colamd.h
file linalg/colamd/colamd.m
file linalg/colamd/colamd_demo.m
file linalg/colamd/colamdtree.m
file linalg/colamd/startup.m
file linalg/colamd/symamd.m
file linalg/colamd/symamdmex.c
file linalg/colamd/symamdtree.m
file linalg/amli.tgz
file linalg/pcg.tgz
file linalg/qmr/cpyrit.doc
file linalg/spooles/spooles.2.2.html
for web page for spooles. look here first.
date 1/28/99
file linalg/spooles/spooles.2.2.tgz
size 4.5Mb
date 1/28/99
lang c
contact Cleve Ashcraft
for SPOOLES is a library for solving sparse linear systems of equations.
, see spooles.2..html (listed above) for more information.
file linalg/spooles/AllInOne.ps.gz
size 110k
date 4/8/99
file linalg/spooles/Eigen.ps.gz
size 501k
date 1/28/99
file linalg/spooles/Install.ps.gz
size 487k
date 1/28/99
file linalg/spooles/LinSol.ps.gz
size 503k
date 1/28/99
file linalg/spooles/Ordering.ps.gz
size 593k
date 1/28/99
file linalg/spooles/PP99.ps.gz
size 596k
date 1/28/99
file linalg/spooles/ReferenceManual.ps.gz
size 1.2Mb
date 1/28/99
file linpack/archives/readme
file linpack/archives/linpack_alpha.tgz
file linpack/archives/linpack_hppa.tgz
file linpack/archives/linpack_irix64-64.tgz
file linpack/archives/linpack_irix64-n32.tgz
file linpack/archives/linpack_linux.tgz
file linpack/archives/linpack_rs6k.tgz
file linpack/archives/linpack_solaris.tgz
####################################
# Index for linpack/chk #
####################################
file linpack/chk/bandcray.f
for matrix decomposition for banded positive definite matrices
file linpack/chk/ch.f
for Test program to check the xHICO, xHIFA, xHISL, xHIDI, xHPCO,
, xHPFA, xHPSL, and xHPDI Hermitian routines (where x is only
, replaced by C or Z)
prec complex
file linpack/chk/zh.f
for Test program to check the xHICO, xHIFA, xHISL, xHIDI, xHPCO,
, xHPFA, xHPSL, and xHPDI Hermitian routines (where x is only
, replaced by C or Z)
prec double complex
file linpack/chk/sch.f
for Test program to check the xCHDC routines
prec single
file linpack/chk/dch.f
for Test program to check the xCHDC routines
prec double
file linpack/chk/cch.f
for Test program to check the xCHDC routines
prec complex
file linpack/chk/zch.f
for Test program to check the xCHDC routines
prec double complex
file linpack/chk/sex.f
for Test program to check the xCHEX routines
prec single
file linpack/chk/dex.f
for Test program to check the xCHEX routines
prec double
file linpack/chk/cex.f
for Test program to check the xCHEX routines
prec complex
file linpack/chk/zex.f
for Test program to check the xCHEX routines
prec double complex
file linpack/chk/sg.f
for Test program to check the xGECO, xGEFA, xGESL, xGEDI, xGBCO,
, xGBFA, xGBSL, and xGBDI routines
prec single
file linpack/chk/dg.f
for Test program to check the xGECO, xGEFA, xGESL, xGEDI, xGBCO,
, xGBFA, xGBSL, and xGBDI routines
prec double
file linpack/chk/cg.f
for Test program to check the xGECO, xGEFA, xGESL, xGEDI, xGBCO,
, xGBFA, xGBSL, and xGBDI routines
prec complex
file linpack/chk/zg.f
for Test program to check the xGECO, xGEFA, xGESL, xGEDI, xGBCO,
, xGBFA, xGBSL, and xGBDI routines
prec double complex
file linpack/chk/sgt.f
for Test program to check the xGTSL and xPTSL routines
prec single
file linpack/chk/dgt.f
for Test program to check the xGTSL and xPTSL routines
prec double
file linpack/chk/cgt.f
for Test program to check the xGTSL and xPTSL routines
prec complex
file linpack/chk/zgt.f
for Test program to check the xGTSL and xPTSL routines
prec double complex
file linpack/chk/sp.f
for Test program to check the xPOCO, xPOFA, xPOSL, xPODI, xPPCO,
, xPPFA, xPPSL, xPPDI, xPBCO, xPBFA, xPBSL, and xPBDI routines
prec single
file linpack/chk/dp.f
for Test program to check the xPOCO, xPOFA, xPOSL, xPODI, xPPCO,
, xPPFA, xPPSL, xPPDI, xPBCO, xPBFA, xPBSL, and xPBDI routines
prec double
file linpack/chk/cp.f
for Test program to check the xPOCO, xPOFA, xPOSL, xPODI, xPPCO,
, xPPFA, xPPSL, xPPDI, xPBCO, xPBFA, xPBSL, and xPBDI routines
prec complex
file linpack/chk/zp.f
for Test program to check the xPOCO, xPOFA, xPOSL, xPODI, xPPCO,
, xPPFA, xPPSL, xPPDI, xPBCO, xPBFA, xPBSL, and xPBDI routines
prec double complex
file linpack/chk/sqr.f
for Test program to check the xQRDC and xQRSL routines
prec single
file linpack/chk/dqr.f
for Test program to check the xQRDC and xQRSL routines
prec double
file linpack/chk/cqr.f
for Test program to check the xQRDC and xQRSL routines
prec complex
file linpack/chk/zqr.f
for Test program to check the xQRDC and xQRSL routines
prec double complex
file linpack/chk/ss.f
for Test program to check the xSICO, xSIFA, xSISL, xSIDI, xSPCO,
, xSPFA, xSPSL, and xSPDI routines
prec single
file linpack/chk/ds.f
for Test program to check the xSICO, xSIFA, xSISL, xSIDI, xSPCO,
, xSPFA, xSPSL, and xSPDI routines
prec double
file linpack/chk/cs.f
for Test program to check the xSICO, xSIFA, xSISL, xSIDI, xSPCO,
, xSPFA, xSPSL, and xSPDI routines
prec complex
file linpack/chk/zs.f
for Test program to check the xSICO, xSIFA, xSISL, xSIDI, xSPCO,
, xSPFA, xSPSL, and xSPDI routines
prec double complex
file linpack/chk/ssv.f
for Test program to check the xSVDC routines
prec single
file linpack/chk/dsv.f
for Test program to check the xSVDC routines
prec double
file linpack/chk/csv.f
for Test program to check the xSVDC routines
prec complex, double complex
file linpack/chk/zsv.f
for Test program to check the xSVDC routines
prec double complex
file linpack/chk/st.f
for Test program to check the xTRCO and xTRSL routines
prec single
file linpack/chk/dt.f
for Test program to check the xTRCO and xTRSL routines
prec double
file linpack/chk/ct.f
for Test program to check the xTRCO and xTRSL routines
prec complex
file linpack/chk/zt.f
for Test program to check the xTRCO and xTRSL routines
prec double complex
file linpack/chk/sud.f
for Test program to check the xCHDD routines
prec single
file linpack/chk/dud.f
for Test program to check the xCHDD routines
prec double
file linpack/chk/cud.f
for Test program to check the xCHDD routines
prec complex
file linpack/chk/zud.f
for Test program to check the xCHDD routines
prec double complex
# Netlib Index for LINPACK
#
# NOTE:
# 1. Entries are arranged in alphabetical order by the real routine name.
# (If you are looking for a specific complex Hermitian routine, you
# will find it listed with its real symmetric equivalent.)
# 2. Specifications for pairs of real and complex routines have been
# merged. In a few cases, specifications of three routines have been
# merged, one for real symmetric, one for complex symmetric, and one
# for complex Hermitian matrices.
# 3. Specifications are given only for single precision routines. To
# adapt them for the double precision version of the software, simply
# interpret REAL as DOUBLE PRECISION and COMPLEX and COMPLEX*16 (or
# DOUBLE COMPLEX).
file linpack/readme
for README file for LINPACK
lib linpack/chk
for test drivers for LINPACK
file linpack/schdc.f
gams D2b1b
for computes the Cholesky decomposition of a positive definite matrix,
, a pivoting option allows the user to estimate the condition of a
, positive definite matrix or determine the rank of a positive
, semidefinite matrix
prec single
file linpack/dchdc.f
gams D2b1b
for computes the Cholesky decomposition of a positive definite matrix,
, a pivoting option allows the user to estimate the condition of a
, positive definite matrix or determine the rank of a positive
, semidefinite matrix
prec double
file linpack/cchdc.f
gams D2d1b
for computes the Cholesky decomposition of a positive definite matrix,
, a pivoting option allows the user to estimate the condition of a
, positive definite matrix or determine the rank of a positive
, semidefinite matrix
prec complex
file linpack/zchdc.f
gams D2d1b
for computes the Cholesky decomposition of a positive definite matrix,
, a pivoting option allows the user to estimate the condition of a
, positive definite matrix or determine the rank of a positive
, semidefinite matrix
prec doublecomplex
file linpack/schdd.f
gams D7b
for downdates an augmented Cholesky decomposition or the triangular
, factor of an augmented QR decomposition
prec single
file linpack/dchdd.f
gams D7b
for downdates an augmented Cholesky decomposition or the triangular
, factor of an augmented QR decomposition
prec double
file linpack/cchdd.f
gams D7b
for downdates an augmented Cholesky decomposition or the triangular
, factor of an augmented QR decomposition
prec complex
file linpack/zchdd.f
gams D7b
for downdates an augmented Cholesky decomposition or the triangular
, factor of an augmented QR decomposition
prec doublecomplex
file linpack/schex.f
gams D7b
for updates the Cholesky factorization
prec single
file linpack/dchex.f
gams D7b
for updates the Cholesky factorization
prec double
file linpack/cchex.f
gams D7b
for updates the Cholesky factorization
prec complex
file linpack/zchex.f
gams D7b
for updates the Cholesky factorization
prec doublecomplex
file linpack/schud.f
gams D7b
for updates an augmented Cholesky decomposition or the triangular
, part of an augmented QR decomposition
prec single
file linpack/dchud.f
gams D7b
for updates an augmented Cholesky decomposition or the triangular
, part of an augmented QR decomposition
prec double
file linpack/cchud.f
gams D7b
for updates an augmented Cholesky decomposition or the triangular
, part of an augmented QR decomposition
prec complex
file linpack/zchud.f
gams D7b
for updates an augmented Cholesky decomposition or the triangular
, part of an augmented QR decomposition
prec doublecomplex
file linpack/sgbco.f
gams D2a2
for factors a real band matrix by Gaussian elimination and
, estimates the condition number of the matrix
prec single
file linpack/dgbco.f
gams D2a2
for factors a real band matrix by Gaussian elimination and
, estimates the condition number of the matrix
prec double
file linpack/cgbco.f
gams D2c2
for factors a complex band matrix by Gaussian elimination and
, estimates the condition number of the matrix
prec complex
file linpack/zgbco.f
gams D2c2
for factors a complex band matrix by Gaussian elimination and
, estimates the condition number of the matrix
prec doublecomplex
file linpack/sgbdi.f
gams D3a2
for computes the determinant of a band matrix using the factors
, computed by (linpack/sgbco) or (linpack/sgbfa), if the inverse
, is needed use (linpack/sgbsl) n times
prec single
file linpack/dgbdi.f
gams D3a2
for computes the determinant of a band matrix using the factors
, computed by (linpack/dgbco) or (linpack/dgbfa), if the inverse
, is needed use (linpack/dgbsl) n times
prec double
file linpack/cgbdi.f
gams D3c2
for computes the determinant of a band matrix using the factors
, computed by (linpack/cgbco) or (linpack/cgbfa), if the inverse
, is needed use (linpack/cgbsl) n times
prec complex
file linpack/zgbdi.f
gams D3c2
for computes the determinant of a band matrix using the factors
, computed by (linpack/zgbco) or (linpack/zgbfa), if the inverse
, is needed use (linpack/zgbsl) n times
prec doublecomplex
file linpack/sgbfa.f
gams D2a2
for factors a band matrix by elimination
prec single
file linpack/dgbfa.f
gams D2a2
for factors a band matrix by elimination
prec double
file linpack/cgbfa.f
gams D2c2
for factors a band matrix by elimination
prec complex
file linpack/zgbfa.f
gams D2c2
for factors a band matrix by elimination
prec doublecomplex
file linpack/sgbsl.f
gams D2a2
for solves the real band system Ax = b or trans(A)x = b using
, the factors computed by (linpack/sgbco) or (linpack/sgbfa)
prec single
file linpack/dgbsl.f
gams D2a2
for solves the real band system Ax = b or trans(A)x = b using
, the factors computed by (linpack/dgbco) or (linpack/dgbfa)
prec double
file linpack/cgbsl.f
gams D2c2
for solves the complex band system Ax = b or trans(A)x = b using
, the factors computed by (linpack/cgbco) or (linpack/cgbfa)
prec complex
file linpack/zgbsl.f
gams D2c2
for solves the complex band system Ax = b or trans(A)x = b using
, the factors computed by (linpack/zgbco) or (linpack/zgbfa)
prec doublecomplex
file linpack/sgeco.f
gams D2a1
for factors a matrix by Gaussian elimination and estimates the
, condition number of the matrix
prec single
file linpack/dgeco.f
gams D2a1
for factors a matrix by Gaussian elimination and estimates the
, condition number of the matrix
prec double
file linpack/cgeco.f
gams D2c1
for factors a matrix by Gaussian elimination and estimates the
, condition number of the matrix
prec complex
file linpack/zgeco.f
gams D2c1
for factors a matrix by Gaussian elimination and estimates the
, condition number of the matrix
prec doublecomplex
file linpack/sgedi.f
gams D3a1, D2a1
for computes the determinant and inverse of a matrix using the
, factors computed by (linpack/sgeco) or (linpack/sgefa)
prec single
file linpack/dgedi.f
gams D3a1, D2a1
for computes the determinant and inverse of a matrix using the
, factors computed by (linpack/dgeco) or (linpack/dgefa)
prec double
file linpack/cgedi.f
gams D2c1, D3c1
for computes the determinant and inverse of a matrix using the
, factors computed by (linpack/cgeco) or (linpack/cgefa)
prec complex
file linpack/zgedi.f
gams D2c1, D3c1
for computes the determinant and inverse of a matrix using the
, factors computed by (linpack/zgeco) or (linpack/zgefa)
prec doublecomplex
file linpack/sgefa.f
gams D2a1
for factors a real matrix by Gaussian elimination
prec single
file linpack/dgefa.f
gams D2a1
for factors a real matrix by Gaussian elimination
prec double
file linpack/cgefa.f
gams D2c1
for factors a complex matrix by Gaussian elimination
prec complex
file linpack/zgefa.f
gams D2c1
for factors a complex matrix by Gaussian elimination
prec doublecomplex
file linpack/sgesl.f
gams D2a1
for solves the real system Ax = b or trans(A)x = b using
, the factors computed by (linpack/sgeco) or (linpack/sgefa)
prec single
file linpack/dgesl.f
gams D2a1
for solves the real system Ax = b or trans(A)x = b using
, the factors computed by (linpack/dgeco) or (linpack/dgefa)
prec double
file linpack/cgesl.f
gams D2c1
for solves the complex system Ax = b or trans(A)x = b using
, the factors computed by (linpack/cgeco) or (linpack/cgefa)
prec complex
file linpack/zgesl.f
gams D2c1
for solves the complex system Ax = b or trans(A)x = b using
, the factors computed by (linpack/zgeco) or (linpack/zgefa)
prec doublecomplex
file linpack/sgtsl.f
gams D2a2a
for given a general tridiagonal matrix and a right hand side will
, find the solution
prec single
file linpack/dgtsl.f
gams D2a2a
for given a general tridiagonal matrix and a right hand side will
, find the solution
prec double
file linpack/cgtsl.f
gams D2c2a
for given a general tridiagonal matrix and a right hand side will
, find the solution
prec complex
file linpack/zgtsl.f
gams D2c2a
for given a general tridiagonal matrix and a right hand side will
, find the solution
prec doublecomplex
file linpack/spbco.f
gams D2b2
for factors a real symmetric positive definite matrix stored
, in band form and estimates the condition of the matrix
prec single
file linpack/dpbco.f
gams D2b2
for factors a real symmetric positive definite matrix stored
, in band form and estimates the condition of the matrix
prec double
file linpack/cpbco.f
gams D2d2
for factors a complex hermitian positive definite matrix stored
, in band form and estimates the condition of the matrix
prec complex
file linpack/zpbco.f
gams D2d2
for factors a complex hermitian positive definite matrix stored
, in band form and estimates the condition of the matrix
prec doublecomplex
file linpack/spbdi.f
gams D3b2
for computes the determinant of a real symmetric positive
, definite band matrix using the factors computed by (linpack/spbco)
, or (linpack/spbfa), if the inverse is needed use (linpack/spbsl)
, n times
prec single
file linpack/dpbdi.f
gams D3b2
for computes the determinant of a real symmetric positive
, definite band matrix using the factors computed by (linpack/dpbco)
, or (linpack/dpbfa), if the inverse is needed use (linpack/dpbsl)
, n times
prec double
file linpack/cpbdi.f
gams D3d2
for computes the determinant of a complex hermitian positive
, definite band matrix using the factors computed by (linpack/cpbco)
, or (linpack/cpbfa), if the inverse is needed use (linpack/cpbsl)
, n times
prec complex
file linpack/zpbdi.f
gams D3d2
for computes the determinant of a complex hermitian positive
, definite band matrix using the factors computed by (linpack/zpbco)
, or (linpack/zpbfa), if the inverse is needed use (linpack/zpbsl)
, n times
prec doublecomplex
file linpack/spbfa.f
gams D2b2
for factors a real symmetric positive definite matrix stored
, in band form
prec single
file linpack/dpbfa.f
gams D2b2
for factors a real symmetric positive definite matrix stored
, in band form
prec double
file linpack/cpbfa.f
gams D2d2
for factors a complex hermitian positive definite matrix stored
, in band form
prec complex
file linpack/zpbfa.f
gams D2d2
for factors a complex hermitian positive definite matrix stored
, in band form
prec doublecomplex
file linpack/spbsl.f
gams D2b2
for solves the real symmetric positive definite band system
, Ax = b using the factors computed by (linpack/spbco) or (linpack/spbfa)
prec single
file linpack/dpbsl.f
gams D2b2
for solves the real symmetric positive definite band system
, Ax = b using the factors computed by (linpack/dpbco) or (linpack/dpbfa)
prec double
file linpack/cpbsl.f
gams D2d2
for solves the complex hermitian positive definite band system
, Ax = b using the factors computed by (linpack/cpbco) or (linpack/cpbfa)
prec complex
file linpack/zpbsl.f
gams D2d2
for solves the complex hermitian positive definite band system
, Ax = b using the factors computed by (linpack/zpbco) or (linpack/zpbfa)
prec doublecomplex
file linpack/spoco.f
gams D2b1b
for factors a real symmetric positive definite matrix and
, estimates the condition number of the matrix
prec single
file linpack/dpoco.f
gams D2b1b
for factors a real symmetric positive definite matrix and
, estimates the condition number of the matrix
prec double
file linpack/cpoco.f
gams D2d1b
for factors a complex hermitian positive definite matrix and
, estimates the condition number of the matrix
prec complex
file linpack/zpoco.f
gams D2d1b
for factors a complex hermitian positive definite matrix and
, estimates the condition number of the matrix
prec doublecomplex
file linpack/spodi.f
gams D2b1b,D3b1b
for computes the determinant and inverse of a certain real
, symmetric positive definite matrix using the factors computed by
, (linpack/spoco), (linpack/spofa) or (linpack/sqrdc)
prec single
file linpack/dpodi.f
gams D2b1b,D3b1b
for computes the determinant and inverse of a certain real
, symmetric positive definite matrix using the factors computed by
, (linpack/dpoco), (linpack/dpofa) or (linpack/dqrdc)
prec double
file linpack/cpodi.f
gams D2d1b, D3d1b
for computes the determinant and inverse of a certain complex
, hermitian positive definite matrix using the factors computed by
, (linpack/cpoco), (linpack/cpofa) or (linpack/cqrdc)
prec complex
file linpack/zpodi.f
gams D2d1b, D3d1b
for computes the determinant and inverse of a certain complex
, hermitian positive definite matrix using the factors computed by
, (linpack/zpoco), (linpack/zpofa) or (linpack/zqrdc)
prec doublecomplex
file linpack/spofa.f
gams D2b1b
for factors a real symmetric positive definite matrix
prec single
file linpack/dpofa.f
gams D2b1b
for factors a real symmetric positive definite matrix
prec double
file linpack/cpofa.f
gams D2d1b
for factors a complex hermitian positive definite matrix
prec complex
file linpack/zpofa.f
gams D2d1b
for factors a complex hermitian positive definite matrix
prec doublecomplex
file linpack/sposl.f
gams D2b1b
for solves the real symmetric positive definite system
, Ax = b using the factors computed by (linpack/spoco) or
, (linpack/spofa)
prec single
file linpack/dposl.f
gams D2b1b
for solves the real symmetric positive definite system
, Ax = b using the factors computed by (linpack/dpoco) or
, (linpack/dpofa)
prec double
file linpack/cposl.f
gams D2d1b
for solves the complex hermitian positive definite system
, Ax = b using the factors computed by (linpack/cpoco) or
, (linpack/cpofa)
prec complex
file linpack/zposl.f
gams D2d1b
for solves the complex hermitian positive definite system
, Ax = b using the factors computed by (linpack/zpoco) or
, (linpack/zpofa)
prec doublecomplex
file linpack/sppco.f
gams D2b1b
for factors a real symmetric positive definite matrix stored
, in packed form and estimates the condition number of the matrix
prec single
file linpack/dppco.f
gams D2b1b
for factors a real symmetric positive definite matrix stored
, in packed form and estimates the condition number of the matrix
prec double
file linpack/cppco.f
gams D2d1b
for factors a complex hermitian positive definite matrix stored
, in packed form and estimates the condition number of the matrix
prec complex
file linpack/zppco.f
gams D2d1b
for factors a complex hermitian positive definite matrix stored
, in packed form and estimates the condition number of the matrix
prec doublecomplex
file linpack/sppdi.f
gams D2b1b,D3b1b
for computes the determinant and inverse of a real symmetric
, positive definite matrix using the factors computed by
, (linpack/sppco) or (linpack/sppfa)
prec single
file linpack/dppdi.f
gams D2b1b,D3b1b
for computes the determinant and inverse of a real symmetric
, positive definite matrix using the factors computed by
, (linpack/dppco) or (linpack/dppfa)
prec double
file linpack/cppdi.f
gams D2d1b, D3d1b
for computes the determinant and inverse of a complex hermitian
, positive definite matrix using the factors computed by
, (linpack/cppco) or (linpack/cppfa)
prec complex
file linpack/zppdi.f
gams D2d1b, D3d1b
for computes the determinant and inverse of a complex hermitian
, positive definite matrix using the factors computed by
, (linpack/zppco) or (linpack/zppfa)
prec doublecomplex
file linpack/sppfa.f
gams D2b1b
for factors a real symmetric positive definite matrix stored
, in packed form
prec single
file linpack/dppfa.f
gams D2b1b
for factors a real symmetric positive definite matrix stored
, in packed form
prec double
file linpack/cppfa.f
gams D2d1b
for factors a complex hermitian positive definite matrix stored
, in packed form
prec complex
file linpack/zppfa.f
gams D2d1b
for factors a complex hermitian positive definite matrix stored
, in packed form
prec doublecomplex
file linpack/sppsl.f
gams D2b1b
for solves the real symmetric positive definite system
, Ax = b using the factors computed by (linpack/sppco) or
, (linpack/sppfa)
prec single
file linpack/dppsl.f
gams D2b1b
for solves the real symmetric positive definite system
, Ax = b using the factors computed by (linpack/dppco) or
, (linpack/dppfa)
prec double
file linpack/cppsl.f
gams D2d1b
for solves the complex hermitian positive definite system
, Ax = b using the factors computed by (linpack/cppco) or
, (linpack/cppfa)
prec complex
file linpack/zppsl.f
gams D2d1b
for solves the complex hermitian positive definite system
, Ax = b using the factors computed by (linpack/zppco) or
, (linpack/zppfa)
prec doublecomplex
file linpack/sptsl.f
gams D2b2a
for given a positive definite tridiagonal matrix and a right hand
, side will find the solution
prec single
file linpack/dptsl.f
gams D2b2a
for given a positive definite tridiagonal matrix and a right hand
, side will find the solution
prec double
file linpack/cptsl.f
gams D2d2a
for given a positive definite tridiagonal matrix and a right hand
, side will find the solution
prec complex
file linpack/zptsl.f
gams D2d2a
for given a positive definite tridiagonal matrix and a right hand
, side will find the solution
prec doublecomplex
file linpack/sqrdc.f
gams D5
for uses Householder transformations to compute the QR factorization,
, column pivoting based on the 2-norms of the reduced columns may
, be performed at the user's option
prec single
file linpack/dqrdc.f
gams D5
for uses Householder transformations to compute the QR factorization,
, column pivoting based on the 2-norms of the reduced columns may
, be performed at the user's option
prec double
file linpack/cqrdc.f
gams D5
for uses Householder transformations to compute the QR factorization,
, column pivoting based on the 2-norms of the reduced columns may
, be performed at the user's option
prec complex
file linpack/zqrdc.f
gams D5
for uses Householder transformations to compute the QR factorization,
, column pivoting based on the 2-norms of the reduced columns may
, be performed at the user's option
prec doublecomplex
file linpack/sqrsl.f
gams D2a1, D9a1
for applies the output of (linpack/sqrdc) to compute coordinate
, transformations, projections, and least squares solutions
prec single
file linpack/dqrsl.f
gams D2a1, D9a1
for applies the output of (linpack/dqrdc) to compute coordinate
, transformations, projections, and least squares solutions
prec double
file linpack/cqrsl.f
gams D9a1, D2c1
for applies the output of (linpack/cqrdc) to compute coordinate
, transformations, projections, and least squares solutions
prec complex
file linpack/zqrsl.f
gams D9a1, D2c1
for applies the output of (linpack/zqrdc) to compute coordinate
, transformations, projections, and least squares solutions
prec doublecomplex
file linpack/ssico.f
gams D2b1a
for factors a real symmetric matrix by elimination with symmetric
, pivoting and estimates the condition number of the matrix
prec single
file linpack/dsico.f
gams D2b1a
for factors a real symmetric matrix by elimination with symmetric
, pivoting and estimates the condition number of the matrix
prec double
file linpack/csico.f
gams D2c1
for factors a complex symmetric matrix by eliminatin with symmetric
, pivoting and estimates the condition number of the matrix
prec complex
file linpack/zsico.f
gams D2c1
for factors a complex symmetric matrix by eliminatin with symmetric
, pivoting and estimates the condition number of the matrix
prec doublecomplex
file linpack/chico.f
gams D2d1a
for factors a complex Hermitian matrix by elimination with symmetric
, pivoting and estimates the condition number of the matrix
prec complex
file linpack/zhico.f
gams D2d1a
for factors a complex Hermitian matrix by elimination with symmetric
, pivoting and estimates the condition number of the matrix
prec doublecomplex
file linpack/ssidi.f
gams D2b1a, D3b1a
for computes the determinant, inertia and inverse of a real symmetric
, matrix using the factors from linpack/ssifa
prec single
file linpack/dsidi.f
gams D2b1a, D3b1a
for computes the determinant, inertia and inverse of a real symmetric
, matrix using the factors from linpack/dsifa
prec double
file linpack/csidi.f
gams D2c1, D3c1
for computes the determinant, inertia and inverse of a complex symmetric
, matrix using the factors from linpack/csifa
prec complex
file linpack/zsidi.f
gams D2c1, D3c1
for computes the determinant, inertia and inverse of a complex symmetric
, matrix using the factors from linpack/zsifa
prec doublecomplex
file linpack/chidi.f
gams D2d1a, D3d1a
for computes the determinant, inertia and inverse of a complex
, Hermitian matrix using the factors from linpack/chifa
prec complex
file linpack/zhidi.f
gams D2d1a, D3d1a
for computes the determinant, inertia and inverse of a complex
, Hermitian matrix using the factors from linpack/zhifa)
prec doublecomplex
file linpack/ssifa.f
gams D2b1a
for factors a real symmetric matrix by elimination with symmetric
, pivoting
prec single
file linpack/dsifa.f
gams D2b1a
for factors a real symmetric matrix by elimination with symmetric
, pivoting
prec double
file linpack/csifa.f
gams D2c1
for factors a complex symmetric matrix
, by elimination with symmetric pivoting
prec complex
file linpack/zsifa.f
gams D2c1
for factors a complex symmetric matrix
, by elimination with symmetric pivoting
prec doublecomplex
file linpack/chifa.f
gams D2d1a
for factors a complex Hermitian matrix
, by elimination with symmetric pivoting
prec complex
file linpack/zhifa.f
gams D2d1a
for factors a complex Hermitian matrix
, by elimination with symmetric pivoting
prec doublecomplex
file linpack/ssisl.f
gams D2b1a
for solves the real symmetric system
, Ax = b using the factors computed by linpack/ssifa
prec single
file linpack/dsisl.f
gams D2b1a
for solves the real symmetric system
, Ax = b using the factors computed by linpack/dsifa
prec double
file linpack/csisl.f
gams D2c1
for solves the complex symmetric system
, Ax = b using the factors computed by linpack/csifa
prec complex
file linpack/zsisl.f
gams D2c1
for solves the complex symmetric system
, Ax = b using the factors computed by linpack/zsifa
prec doublecomplex
file linpack/chisl.f
gams D2d1a
for solves the complex Hermitian system
, Ax = b using the factors computed by linpack/chifa
prec complex
file linpack/zhisl.f
gams D2d1a
for solves the complex Hermitian system
, Ax = b using the factors computed by linpack/zhifa
prec doublecomplex
file linpack/sspco.f
gams D2b1a
for factors a real symmetric matrix
, stored in packed form by elimination with symmetric pivoting and
, estimates the condition number of the matrix
prec single
file linpack/dspco.f
gams D2b1a
for factors a real symmetric matrix
, stored in packed form by elimination with symmetric pivoting and
, estimates the condition number of the matrix
prec double
file linpack/cspco.f
gams D2c1
for factors a complex symmetric matrix
, stored in packed form by elimination with symmetric pivoting and
, estimates the condition number of the matrix
prec complex
file linpack/zspco.f
gams D2c1
for factors a complex symmetric matrix
, stored in packed form by elimination with symmetric pivoting and
, estimates the condition number of the matrix
prec doublecomplex
file linpack/chpco.f
gams D2d1a
for factors a complex Hermitian matrix
, stored in packed form by elimination with symmetric pivoting and
, estimates the condition number of the matrix
prec complex
file linpack/zhpco.f
gams D2d1a
for factors a complex Hermitian matrix
, stored in packed form by elimination with symmetric pivoting and
, estimates the condition number of the matrix
prec doublecomplex
file linpack/sspdi.f
gams D2b1a, D3b1a
for computes the determinant, inertia and inverse of a
, real symmetric matrix using the factors from linpack/sspfa,
, where the matrix is stored in packed form
prec single
file linpack/dspdi.f
gams D2b1a, D3b1a
for computes the determinant, inertia and inverse of a
, real symmetric matrix using the factors from linpack/dspfa,
, where the matrix is stored in packed form
prec double
file linpack/cspdi.f
gams D2c1, D3c1
for computes the determinant, inertia and inverse of a
, complex symmetric matrix using the factors from linpack/cspfa,
, where the matrix is stored in packed form
prec complex
file linpack/zspdi.f
gams D2c1, D3c1
for computes the determinant, inertia and inverse of a
, complex symmetric matrix using the factors from linpack/zspfa,
, where the matrix is stored in packed form
prec doublecomplex
file linpack/chpdi.f
gams D2d1a, D3d1a
for computes the determinant, inertia and inverse of a
, complex Hermitian matrix using the factors from linpack/chpfa,
, where the matrix is stored in packed form
prec complex
file linpack/zhpdi.f
gams D2d1a, D3d1a
for computes the determinant, inertia and inverse of a
, complex Hermitian matrix using the factors from linpack/zhpfa,
, where the matrix is stored in packed form
prec doublecomplex
file linpack/sspfa.f
gams D2b1a
for factors a real symmetric matrix
, stored in packed form by elimination with symmetric pivoting
prec single
file linpack/dspfa.f
gams D2b1a
for factors a real symmetric matrix
, stored in packed form by elimination with symmetric pivoting
prec double
file linpack/cspfa.f
gams D2c1
for factors a complex symmetric matrix
, stored in packed form by elimination with symmetric pivoting
prec complex
file linpack/zspfa.f
gams D2c1
for factors a complex symmetric matrix
, stored in packed form by elimination with symmetric pivoting
prec doublecomplex
file linpack/chpfa.f
gams D2d1a
for factors a complex Hermitian matrix
, stored in packed form by elimination with symmetric pivoting
prec complex
file linpack/zhpfa.f
gams D2d1a
for factors a complex Hermitian matrix
, stored in packed form by elimination with symmetric pivoting
prec doublecomplex
file linpack/sspsl.f
gams D2b1a
for solves the real symmetric system
, Ax = b using the factors computed by linpack/sspfa
prec single
file linpack/dspsl.f
gams D2b1a
for solves the real symmetric system
, Ax = b using the factors computed by linpack/dspfa
prec double
file linpack/cspsl.f
gams D2c1
for solves the complex symmetric system
, Ax = b using the factors computed by linpack/cspfa
prec complex
file linpack/zspsl.f
gams D2c1
for solves the complex symmetric system
, Ax = b using the factors computed by linpack/zspfa
prec doublecomplex
file linpack/chpsl.f
gams D2d1a
for solves the complex Hermitian system
, Ax = b using the factors computed by linpack/chpfa
prec complex
file linpack/zhpsl.f
gams D2d1a
for solves the complex Hermitian system
, Ax = b using the factors computed by linpack/zhpfa
prec doublecomplex
file linpack/ssvdc.f
gams D6
for reduces a real matrix to diagonal form by orthogonal/unitary
, transformations
prec single
file linpack/dsvdc.f
gams D6
for reduces a real matrix to diagonal form by orthogonal/unitary
, transformations
prec double
file linpack/csvdc.f
gams D6
for reduces a complex matrix to diagonal form by orthogonal/unitary
, transformations
prec complex
file linpack/zsvdc.f
gams D6
for reduces a complex matrix to diagonal form by orthogonal/unitary
, transformations
prec doublecomplex
file linpack/strco.f
gams D2a3
for estimates the condition number of a triangular matrix
prec single
file linpack/dtrco.f
gams D2a3
for estimates the condition number of a triangular matrix
prec double
file linpack/ctrco.f
gams D2c3
for estimates the condition number of a triangular matrix
prec complex
file linpack/ztrco.f
gams D2c3
for estimates the condition number of a triangular matrix
prec doublecomplex
file linpack/strdi.f
gams D2a3, D3a3
for computes the determinant and inverse of a triangular matrix
prec single
file linpack/dtrdi.f
gams D2a3, D3a3
for computes the determinant and inverse of a triangular matrix
prec double
file linpack/ctrdi.f
gams D2c3, D3c3
for computes the determinant and inverse of a triangular matrix
prec complex
file linpack/ztrdi.f
gams D2c3, D3c3
for computes the determinant and inverse of a triangular matrix
prec doublecomplex
file linpack/strsl.f
gams D2a3
for solves systems of the form Tx = b or trans(T)x = b where T is
, a triangular matrix of order n, trans(T) denotes the transpose
, of the matrix T
prec single
file linpack/dtrsl.f
gams D2a3
for solves systems of the form Tx = b or trans(T)x = b where T is
, a triangular matrix of order n, trans(T) denotes the transpose
, of the matrix T
prec double
file linpack/ctrsl.f
gams D2c3
for solves systems of the form Tx = b or trans(T)x = b where T is
, a triangular matrix of order n, trans(T) denotes the transpose
, of the matrix T
prec complex
file linpack/ztrsl.f
gams D2c3
for solves systems of the form Tx = b or trans(T)x = b where T is
, a triangular matrix of order n, trans(T) denotes the transpose
, of the matrix T
prec doublecomplex
file list/imsl
for IMSL library keyword index
file list/nag
for NAG library keyword index
file list/port
for PORT library keyword index
file list/siam
for SIAM journal table of contents
# complete for SISSC; very incomplete for others
# ===== LP/DATA index =====
# NOTE: The former "index from lp/data" is now "readme from lp/data".
# It contains details on the following files.
file lp/data/25fv47
lang compressed MPS
file lp/data/80bau3b
lang compressed MPS
size 298 kB
file lp/data/adlittle
lang compressed MPS
file lp/data/afiro
lang compressed MPS
file lp/data/agg
lang compressed MPS
file lp/data/agg2
lang compressed MPS
file lp/data/agg3
lang compressed MPS
file lp/data/ascii
for list of ASCII characters that can appear in compressed MPS files
file lp/data/bandm
lang compressed MPS
file lp/data/beaconfd
lang compressed MPS
file lp/data/blend
lang compressed MPS
file lp/data/bnl1
lang compressed MPS
file lp/data/bnl2
lang compressed MPS
file lp/data/boeing1
lang compressed MPS
file lp/data/boeing2
lang compressed MPS
file lp/data/bore3d
lang compressed MPS
file lp/data/brandy
lang compressed MPS
file lp/data/capri
lang compressed MPS
file lp/data/changes
for summary of changes to this directory
file lp/data/cycle
lang compressed MPS
file lp/data/czprob
lang compressed MPS
file lp/data/d2q06c
lang compressed MPS
size 258 kB
file lp/data/d6cube
lang compressed MPS
file lp/data/degen2
lang compressed MPS
file lp/data/degen3
lang compressed MPS
file lp/data/dfl001
lang compressed MPS
size 353 kB
file lp/data/e226
lang compressed MPS
file lp/data/emps.c
for C source for EMPS (to uncompress the compressed MPS files)
file lp/data/emps.exe.gz
for Win32 "emps.exe", compiled by MS VC++ 6.0, linked with setargv.obj
file lp/data/emps.f
for Fortran source for EMPS (to uncompress the compressed MPS files)
file lp/data/etamacro
lang compressed MPS
file lp/data/fffff800
lang compressed MPS
file lp/data/finnis
lang compressed MPS
file lp/data/fit1d
lang compressed MPS
file lp/data/fit1p
lang compressed MPS
file lp/data/fit2d
lang compressed MPS
size 482 kB
file lp/data/fit2p
lang compressed MPS
size 439 kB
file lp/data/forplan
lang compressed MPS
file lp/data/ganges
lang compressed MPS
file lp/data/gfrd-pnc
lang compressed MPS
file lp/data/greenbea
lang compressed MPS
size 235 kB
file lp/data/greenbeb
lang compressed MPS
size 235 kB
file lp/data/grow15
lang compressed MPS
file lp/data/grow22
lang compressed MPS
file lp/data/grow7
lang compressed MPS
file lp/data/israel
lang compressed MPS
file lp/data/kb2
lang compressed MPS
lib lp/data/kennington
for Kennington test problems
file lp/data/lotfi
lang compressed MPS
file lp/data/maros
lang compressed MPS
file lp/data/maros-r7
lang compressed MPS
size 746 kB
file lp/data/minos
for notes on MINOS 5.0 on problems supplied by Michael Saunders
file lp/data/modszk1
lang compressed MPS
file lp/data/mpc.src
for bundle of source for mpc, the program that compresses MPS files
file lp/data/nesm
lang compressed MPS
file lp/data/perold
lang compressed MPS
file lp/data/pilot
lang compressed MPS
size 278 kB
file lp/data/pilot.ja
lang compressed MPS
file lp/data/pilot.we
lang compressed MPS
file lp/data/pilot4
lang compressed MPS
file lp/data/pilot87
lang compressed MPS
size 514 kB
file lp/data/pilotnov
lang compressed MPS
file lp/data/recipe
lang compressed MPS
file lp/data/sc105
lang compressed MPS
file lp/data/sc205
lang compressed MPS
file lp/data/sc50a
lang compressed MPS
file lp/data/sc50b
lang compressed MPS
file lp/data/scagr25
lang compressed MPS
file lp/data/scagr7
lang compressed MPS
file lp/data/scfxm1
lang compressed MPS
file lp/data/scfxm2
lang compressed MPS
file lp/data/scfxm3
lang compressed MPS
file lp/data/scorpion
lang compressed MPS
file lp/data/scrs8
lang compressed MPS
file lp/data/scsd1
lang compressed MPS
file lp/data/scsd6
lang compressed MPS
file lp/data/scsd8
lang compressed MPS
file lp/data/sctap1
lang compressed MPS
file lp/data/sctap2
lang compressed MPS
file lp/data/sctap3
lang compressed MPS
file lp/data/seba
lang compressed MPS
file lp/data/share1b
lang compressed MPS
file lp/data/share2b
lang compressed MPS
file lp/data/shell
lang compressed MPS
file lp/data/ship04l
lang compressed MPS
file lp/data/ship04s
lang compressed MPS
file lp/data/ship08l
lang compressed MPS
file lp/data/ship08s
lang compressed MPS
file lp/data/ship12l
lang compressed MPS
file lp/data/ship12s
lang compressed MPS
file lp/data/sierra
lang compressed MPS
file lp/data/stair
lang compressed MPS
file lp/data/standata
lang compressed MPS
file lp/data/standgub
lang compressed MPS with GUB markers
file lp/data/standmps
lang compressed MPS
file lp/data/stocfor1
lang compressed MPS
file lp/data/stocfor2
lang compressed MPS
file lp/data/stocfor3
for bundle of Fortran source and data for problem STOCFOR3
size 227 kB
file lp/data/stocfor3.old
for previous version (prior to 4 Feb. 1993) of lp/data/stocfor3
file lp/data/truss
for bundle of Fortran source and data for problem TRUSS
file lp/data/tuff
lang compressed MPS
file lp/data/vtp.base
lang compressed MPS
file lp/data/wood1p
lang compressed MPS
size 328 kB
file lp/data/woodw
lang compressed MPS
size 240 kB
file lp/data/readme
file lp/data/nams.ps.gz
for COAL Newsletter announcement (updated, with current "readme")
# ===== LP/DATA/KENNINGTON index
file lp/data/kennington/cre-a.gz
lang compressed MPS
file lp/data/kennington/cre-b.gz
lang compressed MPS
size 538 kB
file lp/data/kennington/cre-c.gz
lang compressed MPS
file lp/data/kennington/cre-d.gz
lang compressed MPS
size 505 kB
file lp/data/kennington/ken-07.gz
lang compressed MPS
size 78 kB
file lp/data/kennington/ken-11.gz
lang compressed MPS
size 449 kB
file lp/data/kennington/ken-13.gz
lang compressed MPS
size 865 kB
file lp/data/kennington/ken-18.gz
lang compressed MPS
size 2.9 MB
file lp/data/kennington/osa-07.gz
lang compressed MPS
size 349 kB
file lp/data/kennington/osa-14.gz
lang compressed MPS
size 733 kB
file lp/data/kennington/osa-30.gz
lang compressed MPS
size 1.3 MB
file lp/data/kennington/osa-60.gz
lang compressed MPS
size 3.0 MB
file lp/data/kennington/pds-02.gz
lang compressed MPS
size 67 kB
file lp/data/kennington/pds-06.gz
lang compressed MPS
size 262 kB
file lp/data/kennington/pds-10.gz
lang compressed MPS
size 445 kB
file lp/data/kennington/pds-20.gz
lang compressed MPS
size 946 kB
file lp/data/kennington/readme
# ===== LP/GENERATORS index =====
file lp/generators/netgen
lang Fortran
for NETGEN (Darwin Klingman's generator for transportation networks
, and assignment problems, along with data for generating 50 problems).
file lp/generators/gnetgen
lang Fortran
for GNETGEN (Fred Glover's modification of NETGEN into a generator for
, generalized network flow problems, with input data by M. Ramamurti
, for 15 specific problem instances).
file lp/generators/qap
lang Fortran
for Terri Johnson's generator for linearized quadratic assignment
, problems, with input data for QAP8, QAP12, and QAP15.
file lp/generators/changes
file lp/generators/qap/newlp.f
for Terri Johnson's generator for linearized quadratic assignment problems.
file lp/generators/qap/data.8
file lp/generators/qap/data.12
file lp/generators/qap/data.15
lib lp/data
for a set of test problems in MPS format.
lib lp/generators
for programs that generate linear programming test problems
lib lp/infeas
for infeasible linear programming test problems
# ===== LP/INFEAS index =====
file lp/infeas/ceria3d
lang compressed MPS
file lp/infeas/chemcom
lang compressed MPS
file lp/infeas/cplex1
lang compressed MPS
file lp/infeas/cplex2
lang compressed MPS
file lp/infeas/forest6
lang compressed MPS
file lp/infeas/galenet
lang compressed MPS
file lp/infeas/greenbea
lang compressed MPS
size 258 kB
file lp/infeas/itest2
lang compressed MPS
file lp/infeas/itest6
lang compressed MPS
file lp/infeas/klein1
lang compressed MPS
file lp/infeas/klein2
lang compressed MPS
file lp/infeas/klein3
lang compressed MPS
file lp/infeas/mondou2
lang compressed MPS
file lp/infeas/qual
lang compressed MPS
file lp/infeas/reactor
lang compressed MPS
file lp/infeas/readme
lang compressed MPS
file lp/infeas/refinery
lang compressed MPS
file lp/infeas/vol1
lang compressed MPS
file lp/infeas/woodinfe
lang compressed MPS
file lp/infeas/bgdbg1
file lp/infeas/bgetam
file lp/infeas/bgindy
size 446 kB
file lp/infeas/bgprtr
file lp/infeas/box1
file lp/infeas/ex72a
file lp/infeas/ex73a
file lp/infeas/gosh
size 622 kB
file lp/infeas/gran
file lp/infeas/pang
file lp/infeas/pilot4i
file lp/infeas/changes
file lyapack/lyapack.tar.gz
file lyapack/README
file lyapack/guide.ps
file lyapack/guide.pdf
file machines/readme
for overview of machines
file machines/alliant.tex
file machines/amdahl.tex
file machines/ametek.tex
file machines/amt.tex
file machines/ardent.tex
file machines/bbn.tex
file machines/cdc190.tex
file machines/cdc205.tex
file machines/convex.tex
file machines/cray1.tex
file machines/cray2.tex
file machines/cray3.tex
file machines/crayea.tex
file machines/crayxmp.tex
file machines/crayymp.tex
file machines/culler.tex
file machines/cyberplus.tex
file machines/cydrome.tex
file machines/elxsi.tex
file machines/encore.tex
file machines/eta10.tex
file machines/flex.tex
file machines/fps1.tex
file machines/fps2.tex
file machines/fps3.tex
file machines/fps4.tex
file machines/fpst.tex
file machines/galaxy.tex
file machines/goodyear.tex
file machines/gould.tex
file machines/hitachi.tex
file machines/ibm3090.tex
file machines/intel.tex
file machines/ip1.tex
file machines/isis.tex
file machines/ksr.tex
file machines/loral.tex
file machines/machines.tex
file machines/meiko.tex
file machines/multiflow.tex
file machines/myrias.tex
file machines/nas.tex
file machines/ncube.tex
file machines/nec.tex
file machines/prevec.tex
file machines/printex
file machines/ps2000.tex
file machines/saxpy.tex
file machines/scs.tex
file machines/sequent.tex
file machines/sequent2.tex
file machines/sgi.tex
file machines/star.tex
file machines/startech.tex
file machines/stellar.tex
file machines/supertek.tex
file machines/tmc.tex
file machines/unisys.tex
# Index for magic/doc
file magic/doc/MaGIC_doc.tex
lang tex
file magic/doc/Titlepage.tex
lang tex
file magic/doc/algebra.tex
lang tex
file magic/doc/algorithm.tex
lang tex
file magic/doc/biblio.tex
lang tex
file magic/doc/gfile
file magic/doc/installation.tex
lang tex
file magic/doc/mg_header.tex
lang tex
file magic/doc/overview.tex
lang tex
file magic/doc/results.tex
lang tex
file magic/doc/user_guide.tex
lang tex
file magic/doc/xmagic.ps
lang postscript
# Index for magic
# November 13, 1989
lib magic/doc
lib magic/monmacs
for parts of the Argonne Monitor Macros package which are relevant to MaGIC.
lib magic/mstuff
for help files (called *.show) and data
file magic/magic.u
file magic/magic.h
file magic/magic.m4
file magic/makefile
file magic/readme
file magic/tr.c
file magic/dialog.c
file magic/isom.c
file magic/lid.c
file magic/logic.c
file magic/logic_io_p.c
file magic/logic_io_s.c
file magic/logic_set.c
file magic/logic_test.c
file magic/magic.man
file magic/mp_parse.c
file magic/setup.c
# MaGIC is a program which finds matrices for implication
# connectives for various types of logics. MaGIC has been
# written by John Slaney from the Automated Reasoning Project,
# The Research School of Social Sciences, The Australian
# National University.
#
# _I_n_s_t_a_l_l_a_t_i_o_n
#
# This version of magic has been written using the
# Argonne Monitor Macros package for portable parallel pro-
# gramming. The part required to compile magic has been
# attached so that you do not have to have these macros
# installed on your system.
#
# Before compilation and installation edit the Makefile
# in the main directory of magic. On most systems only the top
# few lines of the Makefile may require editing. And so: BIN
# defines where magic's binaries will go, MAGLIB defines the
# directory in which magic's auxiliary files will be
# installed. The manual will be installed in
# $(MANROOT)/man$(MANSECT) as magic.$(MANSECT).Z, and the for-
# matted version of the manual will go to
# $(MANROOT)/cat$(MANSECT). If you intend to place the auxili-
# ary files and manual pages in different locations you should
# edit magic.man so that the manual page would properly point
# to file locations, and that the manual section (which is
# "L") is also correct. Also, remember that under Dynix the
# manual is compressed. If you don't run Dynix you will have
# to comment out two lines from the installation part which
# compress the manual.
#
# On our system binary files and manual pages are
# writable to the group. This is reflected in variables
# MANDMDE, MANMODE, and BINMODE - modify these if you don't
# want the group to be allowed to write on magic's binaries
# and libraries.
#
# To read the command line, magic uses AT&T's function
# getopt. Under Dynix this means that you will have to use
# -lseq library during linking. Make sure that -lseq is
# included in CLIBS if you run Dynix.
#
# The Argonne Monitor Macros reside in ./monmacs. They
# will be made during installation. If you prefer to use your
# own version of these macros - redefine MACDIR to point to
# your directory. Note that these are the macros for Sequent
# Symmetry. You will have to use different sets of macros for
# different machines.
#
# Once you are happy with the Makefile, type
#
# make
#
# and then if there were no problems with compilation and
# linking, type
#
# make install
#
# to install magic, magic's libraries and the manual page.
#
# To clean up the source directory type
#
# make clean
#
# To remove magic, its libraries and manual pages type
#
# make deinstall
#
#
# _R_u_n_n_i_n_g _m_a_g_i_c
#
# Refer to the documentation in ./doc which describes how
# to run magic. These documents should be formatted with
# LaTeX. There is one ecial in the file ./doc/user_guide.tex.
# It works fine with with dvi2ps, which is part of tex82 dis-
# tribution. The file which is included is ./doc/xmagic.ps.
# To format the documentation change to ./doc and type
#
# latex MaGIC
#
# or
#
# format
#
#
# Note that you can also run magic over the network using
# an X Windows based front end: xmagic.
#
# _M_a_i_n_t_e_n_a_n_c_e _o_f _M_a_G_I_C
#
# In case of problems with installation and/or running of
# magic contact John Slaney or Gustav Meglicki from the
#
# Automated Reasoning Project,
# The Research School of Social Sciences,
# The Australian National University,
# G.P.O. Box 4, Canberra, A.C.T. 2601,
# Australia
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
# November 13, 1989
#
#
#
file magic/monmacs/Makefile
file magic/monmacs/c.m4.monmacs
file magic/monmacs/c.m4.smacs
file magic/monmacs/cputm.U
file magic/monmacs/cputm.c
file magic/monmacs/inmain
file magic/monmacs/rec.U
file magic/monmacs/send.U
file magic/monmacs/shmem.U
file magic/monmacs/soctest.c
file magic/monmacs/sox.U
file magic/monmacs/trace.U
file magic/monmacs/xptrace.c
file magic/mstuff/AX.show
file magic/mstuff/BTW.show
file magic/mstuff/FDL.show
file magic/mstuff/LOG.show
file magic/mstuff/MEN.show
file magic/mstuff/OUT.show
file magic/mstuff/WFF.show
file magic/mstuff/ba.16
file magic/mstuff/dl.10
file magic/mstuff/dln.10
file magic/mstuff/dln.14
file magic/mstuff/l.8
file magic/mstuff/ln.10
file magic/mstuff/po.6
file magic/mstuff/pon.7
file magic/mstuff/pont.8
file magic/mstuff/pot.7
file magic/mstuff/tn.16
file magic/mstuff/to.12
file maspar/f90/dblas/dasum.f
for sum of absolute values
prec double real
gams D1a3a
file maspar/f90/dblas/daxpy.f
for y = a*x + y
prec double real
gams D1a7
file maspar/f90/dblas/dcopy.f
for copy x into y
prec double real
gams D1a5
file maspar/f90/dblas/ddot.f
for dot product
prec double real
gams D1a4
file maspar/f90/dblas/dgbmv.f
for matrix vector multiply
prec double real
gams D1b4
file maspar/f90/dblas/dgemm.f
for matrix matrix multiply
prec double real
gams D1b6
file maspar/f90/dblas/dgemv.f
for matrix vector multiply
prec double real
gams D1b4
file maspar/f90/dblas/dger.f
for rank one update to a matrix
prec double real
gams D1b5
file maspar/f90/dblas/dnrm2.f
for Euclidean norm
prec double real
gams D1a3b
file maspar/f90/dblas/drot.f
for apply Givens rotation
prec double real
gams D1a8
file maspar/f90/dblas/drotg.f
for setup Givens rotation
prec double real
gams D1b10
file maspar/f90/dblas/dsbmv.f
for matrix vector multiply
prec double real
gams D1b4
file maspar/f90/dblas/dscal.f
for x = a*x
prec double real
gams D1a6
file maspar/f90/dblas/dspmv.f
for matrix vector multiply
prec double real
gams D1b4
file maspar/f90/dblas/dspr.f
for rank one update to a matrix
prec double real
gams D1b5
file maspar/f90/dblas/dspr2.f
for rank two update to a matrix
prec double real
gams D1b5
file maspar/f90/dblas/dswap.f
for swap x and y
prec double real
gams D1a5
file maspar/f90/dblas/dsymm.f
for matrix matrix multiply
prec double real
gams D1b6
file maspar/f90/dblas/dsymv.f
for matrix vector multiply
prec double real
gams D1b4
file maspar/f90/dblas/dsyr.f
for rank one update to a matrix
prec double real
gams D1b5
file maspar/f90/dblas/dsyr2.f
for rank two update to a matrix
prec double real
gams D1b5
file maspar/f90/dblas/dsyr2k.f
for rank-2k update to a matrix
prec double real
gams D1b5
file maspar/f90/dblas/dsyrk.f
for rank-k update to a matrix
prec double real
gams D1b5
file maspar/f90/dblas/dtbmv.f
for matrix vector multiply
prec double real
gams D1b4
file maspar/f90/dblas/dtbsv.f
for solving certain triangular matrix problems
prec double real
gams D2a3,D2a2
file maspar/f90/dblas/dtpmv.f
for matrix vector multiply
prec double real
gams D1b4
file maspar/f90/dblas/dtpsv.f
for solving certain triangular matrix problems
prec double real
gams D2a3
file maspar/f90/dblas/dtrmm.f
for matrix matrix multiply
prec double real
gams D1b6
file maspar/f90/dblas/dtrmv.f
for matrix vector multiply
prec double real
gams D1b4
file maspar/f90/dblas/dtrsm.f
for solving triangular matrix with many right--hand-sides
prec double real
gams D2a3
file maspar/f90/dblas/dtrsv.f
for solving certain triangular matrix problems
prec double real
gams D2a3
file maspar/f90/dblas/idamax.f
for index of max abs value
prec double real
gams D1a2,D1a3c,N5a
file maspar/f90/dblas/degad.f
file maspar/f90/dblas/dfillo.f
file maspar/f90/dblas/dpacku.f
file maspar/f90/dblas/lsame.f
file maspar/f90/dblas/xerbla.f
file maspar/f90/dblas/makefile
file maspar/f90/dblas/readme
lib maspar/f90/dblas
for purely Fortran version of BLAS library
prec double real
by Petter Bjorstad, Erik Boman, Jeremy Cook, Hans Munthe-Kaas, Tor Sorevik
lang Fortran90
lib maspar/f90/sblas
for purely Fortran version of BLAS library
prec single real
by Petter Bjorstad, Erik Boman, Jeremy Cook, Hans Munthe-Kaas, Tor Sorevik
lang Fortran90
file maspar/f90/readme
file maspar/f90/sblas/isamax.f
for index of max abs value
prec single real
gams D1a2,D1a3c,N5a
file maspar/f90/sblas/sasum.f
for sum of absolute values
prec single real
gams D1a3a
file maspar/f90/sblas/saxpy.f
for y = a*x + y
prec single real
gams D1a7
file maspar/f90/sblas/scopy.f
for copy x into y
prec single real
gams D1a5
file maspar/f90/sblas/sdot.f
for dot product
prec single real
gams D1a4
file maspar/f90/sblas/sgbmv.f
for matrix vector multiply
prec single real
gams D1b4
file maspar/f90/sblas/sgemm.f
for matrix matrix multiply
prec single real
gams D1b6
file maspar/f90/sblas/sgemv.f
for matrix vector multiply
prec single real
gams D1b4
file maspar/f90/sblas/sger.f
for rank one update to a matrix
prec single real
gams D1b5
file maspar/f90/sblas/snrm2.f
for Euclidean norm
prec single real
gams D1a3b
file maspar/f90/sblas/srot.f
for apply Givens rotation
prec single real
gams D1a8
file maspar/f90/sblas/srotg.f
for setup Givens rotation
prec single real
gams D1b10
file maspar/f90/sblas/ssbmv.f
for matrix vector multiply
prec single real
gams D1b4
file maspar/f90/sblas/sscal.f
for x = a*x
prec single real
gams D1a6
file maspar/f90/sblas/sspmv.f
for matrix vector multiply
prec single real
gams D1b4
file maspar/f90/sblas/sspr.f
for rank one update to a matrix
prec single real
gams D1b5
file maspar/f90/sblas/sspr2.f
for rank two update to a matrix
prec single real
gams D1b5
file maspar/f90/sblas/sswap.f
for swap x and y
prec single real
gams D1a5
file maspar/f90/sblas/ssymm.f
for matrix matrix multiply
prec single real
gams D1b6
file maspar/f90/sblas/ssymv.f
for matrix vector multiply
prec single real
gams D1b4
file maspar/f90/sblas/ssyr.f
for rank one update to a matrix
prec single real
gams D1b5
file maspar/f90/sblas/ssyr2.f
for rank two update to a matrix
prec single real
gams D1b5
file maspar/f90/sblas/ssyr2k.f
for rank-2k update to a matrix
prec single real
gams D1b5
file maspar/f90/sblas/ssyrk.f
for rank-k update to a matrix
prec single real
gams D1b5
file maspar/f90/sblas/stbmv.f
for matrix vector multiply
prec single real
gams D1b4
file maspar/f90/sblas/stbsv.f
for solving certain triangular matrix problems
prec single real
gams D2a3,D2a2
file maspar/f90/sblas/stpmv.f
for matrix vector multiply
prec single real
gams D1b4
file maspar/f90/sblas/stpsv.f
for solving certain triangular matrix problems
prec single real
gams D2a3
file maspar/f90/sblas/strmm.f
for matrix matrix multiply
prec single real
gams D1b6
file maspar/f90/sblas/strmv.f
for matrix vector multiply
prec single real
gams D1b4
file maspar/f90/sblas/strsm.f
for solving triangular matrix with many right--hand-sides
prec single real
gams D2a3
file maspar/f90/sblas/strsv.f
for solving certain triangular matrix problems
prec single real
gams D2a3
file maspar/f90/sblas/lsame.f
file maspar/f90/sblas/segad.f
file maspar/f90/sblas/sfillo.f
file maspar/f90/sblas/spacku.f
file maspar/f90/sblas/xerbla.f
file maspar/f90/sblas/makefile
file maspar/f90/sblas/readme
lib maspar/f90
for purely Fortran version of library
by Petter Bjorstad, Erik Boman, Jeremy Cook, Hans Munthe-Kaas, Tor Sorevik
lang Fortran90
lib maspar/mpl
for mixed MPL and Fortran version of library (sometimes faster than maspar/f90)
by Petter Bjorstad, Erik Boman, Jeremy Cook, Hans Munthe-Kaas, Tor Sorevik
lang Fortran90, MPL
file maspar/readme
file maspar/mpl/dblas/dasum.f
for sum of absolute values
prec double real
gams D1a3a
file maspar/mpl/dblas/daxpy.f
for y = a*x + y
prec double real
gams D1a7
file maspar/mpl/dblas/dcopy.f
for copy x into y
prec double real
gams D1a5
file maspar/mpl/dblas/ddot.f
for dot product
prec double real
gams D1a4
file maspar/mpl/dblas/dgbmv.f
for matrix vector multiply
prec double real
gams D1b4
file maspar/mpl/dblas/dgemm.f
for matrix matrix multiply
prec double real
gams D1b6
file maspar/mpl/dblas/dgemv.f
for matrix vector multiply
prec double real
gams D1b4
file maspar/mpl/dblas/dger.f
for rank one update to a matrix
prec double real
gams D1b5
file maspar/mpl/dblas/dnrm2.f
for Euclidean norm
prec double real
gams D1a3b
file maspar/mpl/dblas/drot.f
for apply Givens rotation
prec double real
gams D1a8
file maspar/mpl/dblas/drotg.f
for setup Givens rotation
prec double real
gams D1b10
file maspar/mpl/dblas/dsbmv.f
for matrix vector multiply
prec double real
gams D1b4
file maspar/mpl/dblas/dscal.f
for x = a*x
prec double real
gams D1a6
file maspar/mpl/dblas/dspmv.f
for matrix vector multiply
prec double real
gams D1b4
file maspar/mpl/dblas/dspr.f
for rank one update to a matrix
prec double real
gams D1b5
file maspar/mpl/dblas/dspr2.f
for rank two update to a matrix
prec double real
gams D1b5
file maspar/mpl/dblas/dswap.f
for swap x and y
prec double real
gams D1a5
file maspar/mpl/dblas/dsymm.f
for matrix matrix multiply
prec double real
gams D1b6
file maspar/mpl/dblas/dsymv.f
for matrix vector multiply
prec double real
gams D1b4
file maspar/mpl/dblas/dsyr.f
for rank one update to a matrix
prec double real
gams D1b5
file maspar/mpl/dblas/dsyr2.f
for rank two update to a matrix
prec double real
gams D1b5
file maspar/mpl/dblas/dsyr2k.f
for rank-2k update to a matrix
prec double real
gams D1b5
file maspar/mpl/dblas/dsyrk.f
for rank-k update to a matrix
prec double real
gams D1b5
file maspar/mpl/dblas/dtbmv.f
for matrix vector multiply
prec double real
gams D1b4
file maspar/mpl/dblas/dtbsv.f
for solving certain triangular matrix problems
prec double real
gams D2a3,D2a2
file maspar/mpl/dblas/dtpmv.f
for matrix vector multiply
prec double real
gams D1b4
file maspar/mpl/dblas/dtpsv.f
for solving certain triangular matrix problems
prec double real
gams D2a3
file maspar/mpl/dblas/dtrmm.f
for matrix matrix multiply
prec double real
gams D1b6
file maspar/mpl/dblas/dtrmv.f
for matrix vector multiply
prec double real
gams D1b4
file maspar/mpl/dblas/dtrsm.f
for solving triangular matrix with many right--hand-sides
prec double real
gams D2a3
file maspar/mpl/dblas/dtrsv.f
for solving certain triangular matrix problems
prec double real
gams D2a3
file maspar/mpl/dblas/idamax.f
for index of max abs value
prec double real
gams D1a2,D1a3c,N5a
file maspar/mpl/dblas/degad.f
file maspar/mpl/dblas/dfillo.f
file maspar/mpl/dblas/dpacku.f
file maspar/mpl/dblas/lsame.f
file maspar/mpl/dblas/xerbla.f
file maspar/mpl/dblas/MPL_DAXPY.m
file maspar/mpl/dblas/MPL_DCOPY.m
file maspar/mpl/dblas/MPL_DGEMM1.m
file maspar/mpl/dblas/MPL_DGEMV1.m
file maspar/mpl/dblas/MPL_DGEMV2.m
file maspar/mpl/dblas/MPL_DGER.m
file maspar/mpl/dblas/MPL_DSCAL.m
file maspar/mpl/dblas/MPL_DSWAP.m
file maspar/mpl/dblas/MPL_DTRSM_LON.m
file maspar/mpl/dblas/MPL_DTRSM_UPN.m
file maspar/mpl/dblas/MPL_DTRSV_LO.m
file maspar/mpl/dblas/MPL_DTRSV_UP.m
file maspar/mpl/dblas/MPL_IDAMAX.m
file maspar/mpl/dblas/mpl_daxpy.m
file maspar/mpl/dblas/mpl_dcopy.m
file maspar/mpl/dblas/mpl_dgemm1.m
file maspar/mpl/dblas/mpl_dger.m
file maspar/mpl/dblas/mpl_dgemv1.m
file maspar/mpl/dblas/mpl_dgemv2.m
file maspar/mpl/dblas/mpl_dlrsolve.m
file maspar/mpl/dblas/mpl_dlssolve.m
file maspar/mpl/dblas/mpl_dscal.m
file maspar/mpl/dblas/mpl_dswap.m
file maspar/mpl/dblas/mpl_dtri_rln.m
file maspar/mpl/dblas/mplwrap
file maspar/mpl/dblas/mpl_dtri_run.m
file maspar/mpl/dblas/mpl_dtri_sln.m
file maspar/mpl/dblas/mpl_dtri_sun.m
file maspar/mpl/dblas/mpl_dtrsm_lon.m
file maspar/mpl/dblas/mpl_dtrsm_upn.m
file maspar/mpl/dblas/mpl_dtrsv_lo.m
file maspar/mpl/dblas/mpl_dtrsv_up.m
file maspar/mpl/dblas/mpl_dursolve.m
file maspar/mpl/dblas/mpl_dussolve.m
file maspar/mpl/dblas/mpl_idamax.m
file maspar/mpl/dblas/mpl_rec_dmul.m
file maspar/mpl/dblas/mpl_rec_dps.m
file maspar/mpl/dblas/mpl_sq_dmul.m
file maspar/mpl/dblas/mpl_sq_dps.m
file maspar/mpl/dblas/mpl_blas.h
file maspar/mpl/dblas/makefile
file maspar/mpl/dblas/readme
lib maspar/mpl/dblas
for Mixed Fortran90/MPL version of BLAS library
prec double real
by Petter Bjorstad, Erik Boman, Jeremy Cook, Hans Munthe-Kaas, Tor Sorevik
lang Fortran90
lib maspar/mpl/sblas
for Mixed Fortran90/MPL version of BLAS library
prec single real
by Petter Bjorstad, Erik Boman, Jeremy Cook, Hans Munthe-Kaas, Tor Sorevik
lang Fortran90
lib maspar/mpl/p3pack
for Permutation of Data
prec double real int
by Hans Munthe-Kaas
lang Fortran90, MPL
lib maspar/mpl/spfft
for Fast Fourier Transforms
prec double real
by Hans Munthe-Kaas
lang Fortran90, MPL
file maspar/mpl/readme
file maspar/mpl/p3pack/genutil.h
file maspar/mpl/p3pack/hpftest.f
file maspar/mpl/p3pack/makefile
file maspar/mpl/p3pack/mpltest.m
file maspar/mpl/p3pack/p3pack.doc
file maspar/mpl/p3pack/p3pack.h
file maspar/mpl/p3pack/p3pack.m
file maspar/mpl/p3pack/p3wrap.m
file maspar/mpl/sblas/isamax.f
for index of max abs value
prec single real
gams D1a2,D1a3c,N5a
file maspar/mpl/sblas/sasum.f
for sum of absolute values
prec single real
gams D1a3a
file maspar/mpl/sblas/saxpy.f
for y = a*x + y
prec single real
gams D1a7
file maspar/mpl/sblas/scopy.f
for copy x into y
prec single real
gams D1a5
file maspar/mpl/sblas/sdot.f
for dot product
prec single real
gams D1a4
file maspar/mpl/sblas/sgbmv.f
for matrix vector multiply
prec single real
gams D1b4
file maspar/mpl/sblas/sgemm.f
for matrix matrix multiply
prec single real
gams D1b6
file maspar/mpl/sblas/sgemv.f
for matrix vector multiply
prec single real
gams D1b4
file maspar/mpl/sblas/sger.f
for rank one update to a matrix
prec single real
gams D1b5
file maspar/mpl/sblas/snrm2.f
for Euclidean norm
prec single real
gams D1a3b
file maspar/mpl/sblas/srot.f
for apply Givens rotation
prec single real
gams D1a8
file maspar/mpl/sblas/srotg.f
for setup Givens rotation
prec single real
gams D1b10
file maspar/mpl/sblas/ssbmv.f
for matrix vector multiply
prec single real
gams D1b4
file maspar/mpl/sblas/sscal.f
for x = a*x
prec single real
gams D1a6
file maspar/mpl/sblas/sspmv.f
for matrix vector multiply
prec single real
gams D1b4
file maspar/mpl/sblas/sspr.f
for rank one update to a matrix
prec single real
gams D1b5
file maspar/mpl/sblas/sspr2.f
for rank two update to a matrix
prec single real
gams D1b5
file maspar/mpl/sblas/sswap.f
for swap x and y
prec single real
gams D1a5
file maspar/mpl/sblas/ssymm.f
for matrix matrix multiply
prec single real
gams D1b6
file maspar/mpl/sblas/ssymv.f
for matrix vector multiply
prec single real
gams D1b4
file maspar/mpl/sblas/ssyr.f
for rank one update to a matrix
prec single real
gams D1b5
file maspar/mpl/sblas/ssyr2.f
for rank two update to a matrix
prec single real
gams D1b5
file maspar/mpl/sblas/ssyr2k.f
for rank-2k update to a matrix
prec single real
gams D1b5
file maspar/mpl/sblas/ssyrk.f
for rank-k update to a matrix
prec single real
gams D1b5
file maspar/mpl/sblas/stbmv.f
for matrix vector multiply
prec single real
gams D1b4
file maspar/mpl/sblas/stbsv.f
for solving certain triangular matrix problems
prec single real
gams D2a3,D2a2
file maspar/mpl/sblas/stpmv.f
for matrix vector multiply
prec single real
gams D1b4
file maspar/mpl/sblas/stpsv.f
for solving certain triangular matrix problems
prec single real
gams D2a3
file maspar/mpl/sblas/strmm.f
for matrix matrix multiply
prec single real
gams D1b6
file maspar/mpl/sblas/strmv.f
for matrix vector multiply
prec single real
gams D1b4
file maspar/mpl/sblas/strsm.f
for solving triangular matrix with many right--hand-sides
prec single real
gams D2a3
file maspar/mpl/sblas/strsv.f
for solving certain triangular matrix problems
prec single real
gams D2a3
file maspar/mpl/sblas/lsame.f
file maspar/mpl/sblas/segad.f
file maspar/mpl/sblas/sfillo.f
file maspar/mpl/sblas/spacku.f
file maspar/mpl/sblas/xerbla.f
file maspar/mpl/sblas/MPL_ISAMAX.m
file maspar/mpl/sblas/MPL_SAXPY.m
file maspar/mpl/sblas/MPL_SCOPY.m
file maspar/mpl/sblas/MPL_SGEMM1.m
file maspar/mpl/sblas/MPL_SGEMV1.m
file maspar/mpl/sblas/MPL_SGEMV2.m
file maspar/mpl/sblas/MPL_SGER.m
file maspar/mpl/sblas/MPL_SSCAL.m
file maspar/mpl/sblas/MPL_SSWAP.m
file maspar/mpl/sblas/MPL_STRSM_LON.m
file maspar/mpl/sblas/MPL_STRSM_UPN.m
file maspar/mpl/sblas/MPL_STRSV_LO.m
file maspar/mpl/sblas/MPL_STRSV_UP.m
file maspar/mpl/sblas/mpl_isamax.m
file maspar/mpl/sblas/mpl_rec_smul.m
file maspar/mpl/sblas/mpl_rec_sps.m
file maspar/mpl/sblas/mpl_saxpy.m
file maspar/mpl/sblas/mpl_scopy.m
file maspar/mpl/sblas/mpl_sgemm1.m
file maspar/mpl/sblas/mpl_sgemv1.m
file maspar/mpl/sblas/mpl_sgemv2.m
file maspar/mpl/sblas/mpl_sger.m
file maspar/mpl/sblas/mpl_slrsolve.m
file maspar/mpl/sblas/mpl_slssolve.m
file maspar/mpl/sblas/mpl_sq_smul.m
file maspar/mpl/sblas/mpl_sq_sps.m
file maspar/mpl/sblas/mpl_sscal.m
file maspar/mpl/sblas/mpl_sswap.m
file maspar/mpl/sblas/mpl_stri_rln.m
file maspar/mpl/sblas/mpl_stri_run.m
file maspar/mpl/sblas/mpl_stri_sln.m
file maspar/mpl/sblas/mpl_stri_sun.m
file maspar/mpl/sblas/mpl_strsm_lon.m
file maspar/mpl/sblas/mpl_strsm_upn.m
file maspar/mpl/sblas/mpl_strsv_lo.m
file maspar/mpl/sblas/mpl_strsv_up.m
file maspar/mpl/sblas/mpl_sursolve.m
file maspar/mpl/sblas/mpl_sussolve.m
file maspar/mpl/sblas/makefile
file maspar/mpl/sblas/mpl_blas.h
file maspar/mpl/sblas/mplwrap
file maspar/mpl/sblas/readme
file maspar/mpl/spfft/fftwrap.m
for Fast Fourier Transform routines callable from Fortran
prec single and double real (for complex transforms)
file maspar/mpl/spfft/spfft.m
for Fast Fourier Transform routines from MPL
prec single and double real (for complex transforms)
file maspar/mpl/spfft/mpltest.m
for test programs in mpl for FFT's
prec single and double (for complex transforms)
file maspar/mpl/spfft/hpftest.f
for test program in Fortran for FFT's
prec single and double real (for complex transforms)
file maspar/mpl/spfft/hpftest2.f
for test program in Fortran for FFT's
prec single and double real (for complex transforms)
file maspar/mpl/spfft/hpftest3.f
for test program in Fortran for FFT's
prec single and double real (for complex transforms)
file maspar/mpl/spfft/genutil.h
file maspar/mpl/spfft/makefile
file maspar/mpl/spfft/p3pack.h
file maspar/mpl/spfft/p3pack.m
file maspar/mpl/spfft/realtest.m
file maspar/mpl/spfft/spfft.doc
file maspar/mpl/spfft/spfft.h
file maspar/mpl/spfft/spfftOptim.h
file maspar/mpl/spfft/testcodes.doc
lib a
for algorithms for numerical approximation
editor Eric Grosse
master ornl.gov
lib access
for netlib access tools, such as unshar
editor Eric Grosse
master ornl.gov
lib aicm
for selected material from Advances in Computational Mathematics
# journal published by Baltzer
master ornl.gov
lib alliant
for programs collected from Alliant users
editor Jack Dongarra
master ornl.gov
lib amos
for Bessel functions of complex argument and nonnegative order
, The Bessel functions H1, H2, I, J, K, and Y, as well as the
, Airy functions Ai, Bi, and their derivatives are provided.
, Exponential scaling and sequence generation are optional.
by D.E. Amos
ref ACM TOMS 12 (1986) 265-273 algorithm 644
master ornl.gov
lib ampl
for linear and nonlinear programming.
editor David Gay
master ornl.gov
lib anl-reports
for Reports from the MCS division at Argonne
editor Jack Dongarra
master ornl.gov
lib apollo
for programs collected from Apollo users.
editor Jack Dongarra
master ornl.gov
lib arpack
for large-scale eigenvalue problems
master ornl.gov
lib atlas
for Autmatically Tuned Linear Algebra Subroutines
by Clint Whaley
master ornl.gov
contact atlas@cs.utk.edu
lib benchmark
for contains benchmark programs and the table of Linpack timings.
editor Jack Dongarra
master ornl.gov
lib bib
for bibliographies: Golub and Van Loan, 2nd ed.
editor Eric Grosse
master ornl.gov
lib bibnet
for BibNet -- Netlib Bibliography Project
# This initiative is a step toward sharing information electronically,
# and it will allow scientists to:
# - provide complete and updated information on their own work,
# - have an efficient pointer to publications and ongoing research, and
# - simplify the work of preparing publications.
editor Stefano Foresti, Nelson H. F. Beebe, Eric Grosse
master ornl.gov
lib bihar
for biharmonic equation in rectangular geometry and polar coordinates
by Petter Bjorstad
master nac.no
lib blacs
for Basic Linear Algebra Communication Subprograms
editor Clint Whaley
contact blacs@cs.utk.edu
master ornl.gov
lib blas
for blas (level 1, 2 and 3) and machine constants
rel excellent
age stable
editor Jack Dongarra
master ornl.gov
lib blast
for Communications of the BLAST mailing lists
editor Jack Dongarra
master ornl.gov
lib bmp
for Brent's multiple precision package
master ornl.gov
lib c++
for miscellaneous codes in C++
editor Eric Grosse
master ornl.gov
lib c
for miscellaneous codes written in C
# Not all C software is in this "miscellaneous" library.
# If it clearly fits into domain specific library, it is assigned there.
# The principal contents at present is the c/meschach subdirectory
# by David Stewart covering linear algebra and utilities. See
# c/index for details.
editor Eric Grosse
master ornl.gov
lib cephes
for special functions and IEEE floating point arithmetic
by Stephen L. Moshier
lang C
master ornl.gov
lib chammp
for DOE Computer Hardware, Advanced Mathematics and Model Physics program
editor Jack Dongarra
master ornl.gov
lib cheney-kincaid
by Ward Cheney & David Kincaid
ref Numerical Mathematics and Computing, 2nd ed., 1985.
master ornl.gov
lib clapack
for C version of LAPACK
by J. Demmel and Xiaoye Li
rel pre-release
lang C
master ornl.gov
lib commercial
for advertising material for commercial math software
editor ehg@research.bell-labs.com
master ornl.gov
lib confdb
for conferences database
editor Shirley Browne
contact conferences@cs.utk.edu
master ornl.gov
lib conformal
for the "parameter problem" associated with conformal mapping
editor Eric Grosse
master ornl.gov
lib contin
for continuation and limit points
editor Eric Grosse
master ornl.gov
lib control
for generation of examples of continuous-time algebraic Riccati equations
by Benner, Laub, and Mehrmann
prec double
lang fortran
gams D8, F2, G3, G4a
master ornl.gov
lib crc
for checksums for netlib files
editor Eric Grosse
master ornl.gov
lib cumulvs
for CUMULVS is an infrastructure library that allows a programmer to
, easily extract data from a running parallel simulation and send the
, data to a visualization package. CUMULVS includes the capability to
, steer user-defined parameters in a distributed simulation.
master ornl.gov
contact cumulvs@msr.epm.ornl.gov
lib ddsv
for "Linear Algebra Computations on Vector and Parallel Computers"
by Jack Dongarra, Iain Duff, Danny Sorensen, and Henk Van der Vorst.
master ornl.gov
lib dierckx
for spline fitting routines for various kinds of data and geometries
by Paul Dierckx
# Comp Sci, K. U. Leuven, Celestijnenlaan 200A, B-3001 Heverlee, Belgium
# also called fitpack, but no connection with Alan Cline's library
master ornl.gov
lib diffpack
# removed; Diffpack is now a commercial package
by www.nobjects.com
master ornl.gov
lib domino
for multiple tasks to communicate and schedule local tasks for execution.
, These tasks may be on a single processor or spread among multiple
, processors connected by a message-passing network.
by O'Leary, Stewart, Van de Geijn, University of Maryland
lang C, assembler
master ornl.gov
lib eispack
for eigenvalues and eigenvectors
, A collection of Fortran subroutines that compute the eigenvalues
, and eigenvectors of nine classes of matrices. The package can
, determine the eigensystems of complex general, complex Hermitian,
, real general, real symmetric, real symmetric band, real symmetric
, tridiagonal, special real tridiagonal, generalized real, and
, generalized real symmetric matrices. In addition, there are two
, routines which use the singular value decomposition to solve
, certain least squares problems.
by NATS Project at Argonne National Laboratory
prec double
see seispack
rel excellent
age stable
ref B.T. Smith, J.M. Boyle, J.J. Dongarra, B.S. Garbow, Y. Ikebe,
, V.C. Klema, and C.B. Moler. Matrix Eigensystem Routines -
, EISPACK Guide, volume 6 of Lecture Notes in Computer Science,
, Springer-Verlag, Berlin, 1976.
,
, B.S. Garbow, J.M. Boyle, J.J. Dongarra, and C.B. Moler.
, Matrix Eigensystem Routines - EISPACK Guide Extension, volume 51 of
, Lecture Notes in Computer Science, Springer-Verlag, Berlin, 1977.
master ornl.gov
lib elefunt
for testing elementary function programs provided with Fortran compilers
ref Software Manual for the Elementary Functions, Prentice Hall, 1980.
by W. J. Cody and W. Waite
master ornl.gov
lib env
for integrated problem solving environments
editor Eric Grosse
master ornl.gov
lib etemplates
for Electronic templates
master ornl.gov
lib f2c
for converting Fortran to C
by Feldman, Gay, Maimone, and Schryer
editor David Gay
master ornl.gov
gams s1
lib fdlibm
for C math library for machines that support IEEE 754 floating-point
by Kwok C Ng
# Version: 5.3
# Maintained-hy: fdlibm-comments@sun.com
# Platforms: Require ANSI C compiler with IEEE 754 style arithmetic
# Copying-Policy: Freely Redistributable
# Keywords: libm,exp,log,sin,cos,floating-point,IEEE754
master ornl.gov
lib fftpack
for Fast Fourier Transform of periodic and other symmetric sequences
# This package consists of programs which perform Fast Fourier
# Transforms for both complex and real periodic sequences and
# certain other symmetric sequences.
by Paul Swarztrauber, NCAR.
see double precision version in bihar
rel excellent
age stable
master ornl.gov
lib fishpack
for finite differences for elliptic boundary value problems.
by Paul Swarztrauber and Roland Sweet.
# CRAYFISHPAK is an expanded version of FISHPAK that has been totally
# rewritten for vector computers, on which order of magnitude speedups
# have been commonly observed. For more information, see
# http://www.greenmtn.com/software
rel excellent
age stable
master ornl.gov
lib fitpack
for splines under tension. (an early version)
by Alan K. Cline
# For a current copy and for other routines, contact:
# Pleasant Valley Software, 8603 Altus Cove, Austin TX 78759, USA
master ornl.gov
lib floppy
for fortan code syntax and flow control checker
master ornl.gov
lib fmm
ref Computer Methods for Mathematical Computations
by George Forsythe, Mike Malcolm, and Cleve Moler.
prec double
see sfmm
master ornl.gov
lib fn
for special functions
by Wayne Fullerton
master ornl.gov
lib fortran-m
for small set of extensions to f77 that supports modular message-passing
editor Jack Dongarra
master ornl.gov
lib fortran
for tools specific to Fortran: a single/double converter; static debugger
master ornl.gov
lib fp
for floating point arithmetic
editor David Gay
master ornl.gov
lib gcv
for Generalized Cross Validation spline smoothing
editor Eric Grosse
master ornl.gov
lib gmat
for multi-processing Time Line and State Graph tools.
by Mark Seager (LLNL Oct 8, 1987)
master ornl.gov
contact werner@ramius.llnl.gov (Nancy Werner) 26 Oct 90
lib gnu
for utilities useful to netlib clients, covered by GNU public license
editor David Gay
master ornl.gov
lib go
for Golden Oldies: widely used, but not in standard libraries.
# Nominations welcome!
rel excellent
age old
editor Eric Grosse
master ornl.gov
lib graphics
for scientific visualization
editor Eric Grosse
master ornl.gov
lib harwell
for sparse unsymmetric matrix routine MA28 from the Harwell library
editor Iain Duff
master ornl.gov
lib hence
for Heterogenous Network Computing Environment, a visual parallel
, programming environment
keywords visual,parallel,computation,graph,PVM,Heterogeneous
editor Peter Newton
contact hence@cs.utk.edu
master ornl.gov
lib hompack
for solving nonlinear systems of equations by homotopy methods
# fixed point, zero finding, and general homotopy curve tracking problems,
# utilizing both dense and sparse Jacobian matrices;
# ODE-based, normal flow, and augmented Jacobian.
by Layne T. Watson ltw@vtopus.cs.vt.edu (703) 231-7540
# Department of Computer Science, VPI & SU, Blacksburg, VA 24061
master ornl.gov
lib hpf
for HPF language specifications
by High Performance Fortran Forum
master ornl.gov
lib hypercube
master ornl.gov
editor Jack Dongarra
lib ieeecss
for IEEE / Control Systems Society
# sqred, Van Loan's "square reduced" algorithm.
# Systems and Control Analysis and Design Environment by J. D. Birdwell.
editor Jack Dongarra
master ornl.gov
lib ijsa
for International Journal of Supercomputer Applications
editor Jack Dongarra
master ornl.gov
lib image
for image processing
editor Eric Grosse
master ornl.gov
see popi, a/blur
lib intercom
for Interprocessor Collective Communications (InterCom) Library
by Mike Barnett, David Payne, Satya Gupta, Lance Shuler,
, Robert van de Geijn, and Jerrell Watts
contact intercom@cs.utexas.edu
editor Jack Dongarra
master ornl.gov
lib itpack
for Iterative Linear System Solvers
# Jacobi method, SOR, SSOR with conjugate gradient acceleration
# or with Chebyshev (semi-iteration - SI) acceleration.
by Young and Kincaid and the group at U of Texas.
# kincaid@cs.utexas.edu oppe@scri1.scri.fsu.edu joubert@cs.utexas.edu
# Center for Numerical Analysis; (512) 471-1242
# RLM Bldg. 13.150; University of Texas at Austin; Austin TX 78713-8510
editor Bill Coughran
master ornl.gov
lib jakef
for automatic differentiation
, a precompiler that analyses a given Fortran77 source code for
, the evaluation of a scalar or vector function and then generates an
, expanded Fortran subroutine that simultaneously evaluates the gradient
, or Jacobian respectively. For scalar functions the ratio between the
, run-time of the resulting gradient routine and that of the original
, evaluation routine is never greater than a fixed bound of about five.
, The storage requirement may be considerable as it is also proportional
, to the run-time of the original routine. Since no differencing is done
, the partial derivative values obtained are exact up to round-off errors.
by A. Griewank, Argonne National Laboratory 12/1/88.
master ornl.gov
lib java
for miscellaneous codes written in java
, Not all java software is in this "miscellaneous" library.
, If it clearly fits into a domain specific library then it is
, assigned there instead.
editor Jeremy Millar (millar@cs.utk.edu)
master ornl.gov
lib kincaid-cheney
by Ward Cheney & David Kincaid
ref Numerical Analysis: The Mathematics of Scientific Computing, 1990.
master ornl.gov
lib la-net
for SIAG/LA news and conference arrangements
editor John Gilbert
master ornl.gov
lib lanczos
for a few eigenvalues/eigenvectors of a large (sparse) symmetric matrix
# real symmetric and Hermitian matrices
# singular values and vectors of real, rectangular matrices
by Jane Cullum and Ralph A. Willoughby, IBM Yorktown 914-945-1589
ref Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Birkhauser
# Additional codes, for factored inverses, real symmetric generalized
# problems, complex symmetric problems and real symmetric block codes
# are available from the authors.
master ornl.gov
see go/underwood.f
lib lanz
for Large Sparse Symmetric Generalized Eigenproblem
by Mark T. Jones and Merrell L. Patrick
master ornl.gov
see go/underwood.f
gams d4b1
lib lapack++
for the c++ version of lapack (see www.netlib.org/lapack/)
rel excellent
age research
ref LAPACK Users' Guide, May 1992, available from SIAM;
, 3600 University City Science Center;
, Philadelphia, PA 19104-2688; 215-382-9800, FAX 215-386-7999;
, service@siam.org
master ornl.gov
contact lapack@cs.utk.edu
lib lapack
for the most common problems in numerical linear algebra
, linear equations, linear least squares problems, eigenvalue problems,
, and singular value problems. It has been designed to be efficient
, on a wide range of modern high-performance computers.
by Ed Anderson, Z. Bai, Chris Bischof, Jim Demmel, Jack Dongarra,
, Jeremy Du Croz, Anne Greenbaum, Sven Hammarling, Alan McKenney,
, Susan Ostrouchov, and Danny Sorensen
rel excellent
age research
ref LAPACK Users' Guide, May 1992, available from SIAM;
, 3600 University City Science Center;
, Philadelphia, PA 19104-2688; 215-382-9800, FAX 215-386-7999;
, service@siam.org
master ornl.gov
contact lapack@cs.utk.edu
lib lapack3e
for update to lapack v3.0 enhanced with features of fortran 90
editor Ed Anderson
contact lapack@cs.utk.edu
master ornl.gov
lib lapack90
for Fortran90 interface for LAPACK
by J. J. Dongarra, J. Du Croz, S. Hammarling, J. Wasniewski,
, A. Zemla
age experimental
ref LAPACK Working Note 101: A Proposal for a Fortran 90 Interface
, for LAPACK (http://www.netlib.org/lapack/lawns/lawn101.ps)
master ornl.gov
contact lapack@cs.utk.edu
lib laso
for a few eigenvalues/eigenvectors of a large (sparse) symmetric matrix
alg Lanczos
by David Scott
master ornl.gov
see go/underwood.f
lib lawson-hanson
for least squares
by C. Lawson and R. Hanson
ref "Solving Least Squares Problems," SIAM Publications
lang Fortran77, Fortran90
master ornl.gov
lib linalg
for various functions complementing the bigger linear algebra libraries
editor Jack Dongarra
master ornl.gov
lib linpack
for linear equations and linear least squares problems
, linear systems whose matrices are general, banded, symmetric
, indefinite, symmetric positive definite, triangular, and tridiagonal
, square. In addition, the package computes the QR and singular value
, decompositions of rectangular matrices and applies them to least
, squares problems.
by Jack Dongarra ,
, Jim Bunch, Cleve Moler and Pete Stewart.
rel excellent
age stable
ref J. Bunch, J. Dongarra, C. Moler, and G.W. Stewart. LINPACK User's
, Guide. SIAM, Philadelphia, PA, 1979.
master ornl.gov
lib list
for various databases searched by netlib's "find" and "who is" commands.
# By default, "find" searches a large collection of one-line descriptions
# of netlib items. You can also search in some proprietary libraries
# by sending a request of the form
# find bessel from imsl nag port.
# Of course, you can't get the actual source code from netlib!
# By default, "whois" searches the SIAM Membership List and the "nalist"
# files. Use the form
# whois Ed Block.
lib lp
for linear programming test problems
editor David Gay
master ornl.gov
lib lyapack
for Riccati and Lyapunov eqations, optimal control
lib machines
for information on high performance computers
editor Jack Dongarra
master ornl.gov
lib magic
for finding matrices for implication connectives
editor Jack Dongarra
master ornl.gov
lib maspar
for MasPar-specific libraries and tools
editor Petter Bjorstad
master nac.no
lib mds
for multidimensional scaling
editor kruskal@research.bell-labs.com
master ornl.gov
lib microscope
for looking closely at functions
# Given an interpolation or approximation scheme, it
# allows the following questions, among others, to be answered:
# Does the scheme interpolate? How often is it
# differentiable? What functions does it reproduce exactly? If
# the scheme is polynomial, what is its polynomial degree? Where
# is the smoothness of a function reduced? Where are the bugs in
# a FORTRAN implementation?
by Peter Alfeld and Bill Harris, Dept. Math., University of Utah
# 801-581-6842 or 801-581-6851
master ornl.gov
lib minpack
for nonlinear equations and nonlinear least squares problems.
, Five algorithmic paths each include a core subroutine and an
, easy-to-use driver. The algorithms proceed either from an analytic
, specification of the Jacobian matrix or directly from the problem
, functions. The paths include facilities for systems of equations
, with a banded Jacobian matrix, for least squares problems with a
, large amount of data, and for checking the consistency of the
, Jacobian matrix with the functions.
by Jorge More', Burt Garbow, and Ken Hillstrom at Argonne National Laboratory.
prec double
see sminpack
master ornl.gov
lib misc
for various stuff collected over time
editor Jack Dongarra
master ornl.gov
lib mpfun
for multiple precision arithmetic
by David Bailey
master ornl.gov
lib mpi
for message passing interface draft standard.
editor Jack Dongarra
master ornl.gov
lib mpicl
for MPICL is a subroutine library for collecting information
on communication and user-defined events in message-passing
parallel programs written in C or FORTRAN.
contact Pat Worley
lib na-digest-html
for html versions of the NA-Digests and a search interface
editor Cleve Moler (moler@mathworks.com)
master ornl.gov
lib na-digest
for archives of the numerical interest mailing group
editor Cleve Moler
lib napack
for linear algebra and optimization
# A collection of Fortran subroutines to solve linear systems,
# to estimate the condition number or the norm of a matrix,
# to compute determinants, to multiply a matrix by a vector,
# to invert a matrix, to solve least squares problems, to perform
# unconstrained minimization, to compute eigenvalues, eigenvectors,
# the singular value decomposition, or the QR decomposition.
# The package has special routines for general, band, symmetric,
# indefinite, tridiagonal, upper Hessenberg, and circulant matrices.
by Bill Hager
# Mathematics, Univ. Florida, Gainesville, FL 32611, hager@math.ufl.edu
ref Applied Numerical Linear Algebra, Prentice-Hall, 1988.
master ornl.gov
lib netsolve
for The motivation behind NetSolve was to devise a fast,
, efficient, easy-to-use system to effectively solve large
, computational problems, regardless of the type of
, computer one happens to be using. Issues such as
, Networking, Heterogeneity, Portability Numerical
, Computing Fault Tolerance Load Balancing are all dealt
, with by the system freeing the user to focus on other
, aspects of the application. NetSolve has been designed
, to overcome hardware and software restrictions so that
, resources can be available to any user anywhere on the
, network.
editor Dorian Arnold, University of Tennessee
contact netsolve@cs.utk.edu
master ornl.gov
lib news
for netlib column for SIAM News
lang LaTeX
by Eric Grosse
master ornl.gov
lib numeralgo
for algorithms from the new journal "Numerical Algorithms"
master ornl.gov
lib ode
for initial and boundary value ordinary differential equation solvers
# colsys, dverk, rksuite, ode
editor Eric Grosse
master ornl.gov
lib odepack
for ODE package (LSODE, LSODES, LSODA, LSODAR, LSODPK, LSODKR, LSODI, LSOIBT, LSODIS)
by Alan Hindmarsh and others
prec single, double
lang Fortran
see sodepack
master ornl.gov
lib odrpack
for Orthogonal Distance Regression
by Boggs Byrd Rogers Schnabel
# A portable collection of Fortran subprograms for fitting a model to
# data. It is designed primarily for instances when the independent
# as well as the dependent variables have significant errors,
# implementing a highly efficient algorithm for solving the weighted
# orthogonal distance regression problem, i.e., for minimizing the
# sum of the squares of the weighted orthogonal distances between
# each data point and the curve described by the model equation.
master ornl.gov
lib opt
for nonlinear optimization and zero-finding
editor David Gay
master ornl.gov
lib p4
for parallel programming system.
# subroutines and macors for writing portable parallel
# programs in Frtran or C for execution on a wide variety of parallel
# machines and workstation networks.
by Rusty Lusk, Argonne National Laboratory
contact p4@mcs.anl.gov
master ornl.gov
lib paragraph
for graphical display of message-passing multiprocessor architectures.
by Jennifer Etheridge and Michael Heath, Oak Ridge National Lab.
master ornl.gov
lib paranoia
for exploring the floating point system on your computer.
by Kahan, Berkeley
editor David Gay
master ornl.gov
lib parkbench
for parallel benchmark working group
editor Jack Dongarra
master ornl.gov
lib parmacs
for parallel programmming macros for monitors and send/receive
by Rusty Lusk, Argonne National Lab (lusk@anl-mcs.arpa)
master ornl.gov
lib pascal
for miscellaneous codes written in Pascal
# At present, codes from J.C. Nash, Compact Numerical Methods for
# Computers: Linear Algebra and Function Minimisation, Second Edition
# Adam Hilger: Bristol & American Institute of Physics: New York, 1990
editor Eric Grosse
master ornl.gov
lib pdes
for partial differential equation packages
editor Bill Coughran
master ornl.gov
lib performance
lib photo
for snapshots from numerical analysis conferences (contributions welcome)
editor ehg@research.bell-labs.com
master ornl.gov
lib picl
for PICL is a subroutine library that implements a generic
message-passing interface on a variety of multiprocessors.
editor Pat Worley
master ornl.gov
master ornl.gov
lib pltmg
for elliptic partial differential equations in general regions of the plane
# It features adaptive local mesh
# refinement, multigrid iteration, and a pseudo-arclength
# continuation option for parameter dependencies. The package
# includes an initial mesh generator and several graphics
#