Index

absolute error , ,

absolute gap , ,

accuracy ,

accuracy

high , , ,

Active Messages

algorithmic

coherence

reliability , ,

repeatability

algorithms, block-partitioned ,

alignment restrictions

AM-II, see Active Messages

angle between vectors and subspaces , , , , , , , ,

arguments

BERR

description conventions , , ,

descriptor , , , , ,

DIAG ,

dimensions

FERR ,

global

global column index , , ,

global input

global output

global row index , , ,

IA and JA ,

INFO , ,

local

local input

local output

LWORK

options

order of

RCOND

SIDE

TRANS

UPLO

work space

ARPACK

array argument descriptions

block cyclic arrays

block-column and block-row arrays

array descriptor , , , , , ,

array descriptor

block , ,

block cyclic

CTXT_

definition of

DLEN_

DTYPE_ ,

example

LLD_

M_ and N_ ,

MB_ and NB_ ,

out-of-core

RSRC_ and CSRC_

auxiliary routines ,

auxiliary routines, index of: see Appendix A

avoiding poor performance

backward error , , , , , ,

backward stability , ,

backward stability

componentwise

normwise

band matrix, distribution of

bandwidth

Berkeley NOW

bidiagonal form , ,

bidiagonal matrix, distribution of

BLACS ,

BLACS

BLACS_ABORT ,

BLACS_BARRIER

BLACS_EXIT

BLACS_GRIDEXIT ,

BLACS_GRIDINFO

BLACS_GRIDINIT

BLACS_SET , ,

C interface

context

context handle

efficiency ,

Fortran 77 interface

prebuilt libraries, availability of

quick reference guide: see Appendix D

BLAS , , ,

BLAS

Level 1

Level 2

Level 3

block-column distribution , ,

block-partitioned algorithms , , ,

block-row distribution , ,

block cyclic distribution ,

blocking factor, see block size

block size ,

block size

size of ,

bug reports

bug reports

checklist

bug reports

mailing alias

C

C

C

C

C

C

CAPSS

checklist, high performance

chordal distance

cluster

eigenvalues

singular values

clusters of workstations

coefficient band matrix

coefficient matrix , , , ,

coefficient matrix

distribution of , ,

coefficient tridiagonal matrix ,

coherence , ,

column-major order

column pivoting (QR)

commercial use

communication bandwidth

communication deadlock

communication latency

communicator, MPI

complete orthogonal factorization

computational routines , ,

Computational Routines, index of: see Appendix A

computers, see distributed memory computers

condensed form, reduction to

condition number , , , , , , , , , ,

condition number

estimate ,

context, BLACS

context handle

coprocessor

CoWs ,

CSRC_, see array descriptor

CTXT_, see array descriptor

data distribution

data distribution

block

block cyclic ,

block-column , ,

block-row , ,

general band matrix ,

general tridiagonal matrix ,

symmetric band matrix

symmetric positive definite band matrix

symmetric positive definite tridiagonal matrix

symmetric tridiagonal matrix

DDISNA ,

deadlock

debugging

alignment restrictions

errata.blacs ,

errata.scalapack ,

INFO > 0

INFO < 0

INFO < 0

INFO > 0

synchronization points

TOOLS

workspace requirements

debugging hints

application

installation

debug level BLACS

decomposition, see data distribution

DESC_, see array descriptor

descriptor , , , , ,

descriptor, see array descriptor

determining the size of local arrays , ,

diagonally dominant-like , , ,

distributed across process columns

distributed across process rows

distributed matrix

distributed matrix, partitioning of

distributed memory , , , , ,

distributed memory computers ,

distributed memory standards

distributed vector

distribution, see data distribution

DLEN_, see array descriptor

documentation

documentation

installation guide ,

documentation, structure

downloading instructions

driver routine

generalized symmetric definite eigenvalue problem

linear equations

linear least squares

SVD

driver routine, symmetric eigenvalue problem

driver routines , ,

driver routines

expert ,

simple ,

driver routines, index of: see Appendix A

DSTEQR2

DTYPE_, see array descriptor

E() ,

effective rank

efficiency

efficiency

BLACS

BLAS

block-partitioned algorithms

efficiency, transportable

eigendecomposition

blocked form

symmetric

eigenvalue , , , , ,

eigenvalue

error bound , , , , ,

GSEP

SEP

eigenvalue problem

generalized symmetric

generalized symmetric/Hermitian

eigenvalue problem,symmetric/Hermitian

eigenvalue problems

large scale

large sparse

nonsymmetric

eigenvalue problems, symmetric/Hermitian

eigenvector , ,

eigenvector

error bound , , , , ,

GSEP ,

left

right

SEP

elementary Householder matrix, see Householder matrix , , , , ,

elementary reflector, see Householder matrix , , , ,

equilibration ,

errata

BLACS

ScaLAPACK and PBLAS

error

absolute , ,

analysis

backward , , , , , ,

measurement of

measurement of

matrix ,

scalar ,

subspace ,

vector ,

relative , , , , , , ,

error bounds

generalized symmetric definite eigenproblem ,

linear equations ,

linear least squares ,

singular value decomposition ,

symmetric eigenproblem ,

error handler, BLACS

error handler, PBLAS ,

error handler, PXERBLA ,

example program

how to execute

HPF

output, using MPICH

output, using PVM

ScaLAPACK (PDGESV) ,

expert driver

expert driver, see driver routines, expert ,

External Data Representation (XDR)

F

F

factorizations, see matrix factorizations

failures

failures

common causes

error handling

INFO

FDDI

Fiber Distributed Data Interface (FDDI)

floating-point arithmetic

floating-point arithmetic

gradual underflow

infinity

NaN

Not-a-Number

overflow , , , , , , , , ,

relative machine precision ,

roundoff error

subnormal numbers

underflow , , ,

floating-point arithmetic, IEEE standard , , , , ,

flop counts, for ScaLAPACK drivers

forward error

forward stability ,

functionality

gang scheduler,

gap , ,

generalized eigenproblem, symmetric definite

generalized orthogonal factorization

global

global

matrix

software components

variables ,

global column index (JA)

global column index (JA) ,

global input

globally blocking receive

global output

global row index (IA) , ,

glossary

GQR , , ,

granularity, of computation , , ,

grid, see process grid

GRQ ,

GSEP

guidelines, for high performance

Hermitian eigenvalue problem, see eigenvalue problems

Hessenberg form

Hessenberg form

reduction to

upper

heterogeneity

heterogeneous environment

heterogeneous network

heterogeneous software issues

algorithmic integrity ,

machine parameters (PxLAMCH)

hierarchical memory , ,

homepage

BLACS

MPI

netlib

PBLAS

PVM

ScaLAPACK ,

homogeneous network

Householder matrix ,

Householder matrix

complex

Householder transformation - blocked form

Householder vector

HPF

DISTRIBUTE , , , , , , , , ,

example program

interface LA_GELS

interface LA_GEMM

interface LA_GESV

interface LA_POSV

interface to ScaLAPACK ,

LA_GELS

LA_GEMM

LA_GESV

LA_POSV

PROCESSORS

ICTXT

ICTXT, see BLACS

ill-conditioned

ill-posed

incoherence

infinity

INFO

input error

installation

installation

PxLAMCH

insufficient workspace

invariant subspaces

error bound

inverse iteration

inverting matrix, using factorization

isoefficiency

isogranularity

iterative refinement

LAPACK

latency ,

layout, see data distribution

lcm(P,P)

LDL factorization

leading dimension, see local array

linear equations

linear least squares problem

linear least squares problem

linear least squares problem , ,

linear least squares problem

full rank

overdetermined ,

rank-deficient , ,

underdetermined

linear systems, solution of ,

LLD_, see array descriptor

LLS ,

load balance

LOC()

LOC()

LOC()

LOC()

LOC()

LOC()

local

local

software components

variables ,

local array

local array

determining the size of , ,

local leading dimension

local input

locally blocking send

local output

LQ factorization

LU factorization

LU factorization

matrix types

LWORK

LWORK WORK(1)

LWORK query

M_, see array descriptor

machine precision ,

matrix factorizations

Cholesky ,

complete orthogonal

generalized orthogonal

generalized QR ,

generalized RQ

LDL

LQ ,

LU

orthogonal ,

QL

QR , ,

RQ

matrix inversion ,

matrix of right-hand-side vectors

matrix of solution vectors

matrix partitioning

matrix sign function

MB_, see array descriptor

memory hierarchy , ,

message-passing libraries

MPI ,

MPL ,

NX ,

PVM ,

message coprocessor

message passing, see distributed memory

MIMD ,

minimum norm least squares solution

minimum norm solution

minimum norm solution , ,

MPI , , , ,

MPI

communicator

homepage

reference implementation (MPICH)

MPICH

MPL ,

Multiple Instruction Multiple Data (MIMD)

Multiple Instruction Multiple Data (MIMD)

MYCOL , ,

MYROW , ,

N_, see array descriptor

naming scheme

naming scheme

auxiliary

driver and computational

NaN

NB_, see array descriptor

NBRHS

netlib

netlib

homepage

mirror repositories

networks of workstations

nonrepeatability

nonsymmetric eigenproblem

norm

Frobenius norm

matrix

two norm

vector

Not-a-Number

notation, table of

NoWs ,

NPCOL, see P

NPROCS, see P

NPROW, see P

NRHS

numerical error, sources of

numerical error, sources of

input error

roundoff error ,

NX ,

optimal block size, determination of

orthogonal (unitary) factorizations ,

orthogonal (unitary) transformation ,

orthogonal factorization, generalized

orthogonal matrix ,

out-of-core linear solvers

overdetermined system , ,

overflow , , , , , , , ,

P , ,

P

P

P

P

P_ARPACK

parallel efficiency ,

parallelizing BLAS-based programs: see Appendix B

parallelizing LAPACK-based programs: see Appendix B

ParPre

partial pivoting

partitioning unit, see block size ,

PBLAS ,

PBLAS

converting from the BLAS to: see Appendix B

error handling

PDGEMM

PDGEMV

PSGEMM

PSGEMV

quick reference guide: see Appendix D

PCDBSV

PCDBTRF , ,

PCDBTRS ,

PCDTSV

PCDTTRF , ,

PCDTTRS ,

PCGBSV

PCGBTRF , ,

PCGBTRS ,

PCGEBRD

PCGECON ,

PCGEEQU

PCGEHRD

PCGELQF ,

PCGELS , ,

PCGEMR2D

PCGEQLF

PCGEQPF

PCGEQRF , ,

PCGERFS ,

PCGERQF

PCGESVD , , ,

PCGESVX , ,

PCGETRF

PCGETRI

PCGETRS

PCGGQRF

PCGGRQF

PCHEEVX , , ,

PCHEGST

PCHEGVX , , , ,

PCHETRD

PCHETRF

PCHETRS

PCPBSV

PCPBTRF , ,

PCPBTRS ,

PCPOCON , ,

PCPOEQU

PCPORFS ,

PCPOSV ,

PCPOSVX ,

PCPOTRF

PCPOTRI

PCPOTRS

PCPTSV

PCPTTRF

PCPTTRS

PCSTEIN ,

PCTRCON , ,

PCTRMR2D

PCTRRFS ,

PCTRTRI

PCTRTRS , ,

PCTZRZF

PCUNGLQ

PCUNGQR ,

PCUNMBR

PCUNMHR

PCUNMLQ

PCUNMQR , , ,

PCUNMRZ

PCUNMTR

PDDBSV

PDDBTRF , ,

PDDBTRS ,

PDDTSV

PDDTTRF , ,

PDDTTRS ,

PDGBSV

PDGBTRF , ,

PDGBTRS ,

PDGEBRD ,

PDGECON ,

PDGEEQU

PDGEHRD ,

PDGELQF ,

PDGELS , , ,

PDGEMR2D

PDGEQLF

PDGEQPF

PDGEQRF , ,

PDGERFS ,

PDGERQF

PDGESV ,

PDGESVD , , , , , ,

PDGESVX , , ,

PDGETRF

PDGETRI

PDGETRS

PDGGQRF

PDGGRQF

PDLAHQR ,

PDLAMCH ,

PDORGLQ

PDORGQR ,

PDORMBR ,

PDORMHR

PDORMLQ ,

PDORMQR , , ,

PDORMRZ

PDORMTR

PDPBSV

PDPBTRF , ,

PDPBTRS ,

PDPOCON , ,

PDPOEQU

PDPORFS ,

PDPOSV , ,

PDPOSVX ,

PDPOTRF

PDPOTRI

PDPOTRS

PDPTSV

PDPTTRF

PDPTTRS

PDSTEBZ ,

PDSTEIN ,

PDSYEV , , , ,

PDSYEVX , , , , , ,

PDSYGST

PDSYGVX , , , ,

PDSYR2K

PDSYTRD ,

PDTRCON , ,

PDTRMR2D

PDTRRFS ,

PDTRTRI

PDTRTRS , ,

PDTZRZF

peak performance

performance , ,

performance

diagnosing poor

evaluation of

improvement guidelines

PDLAHQR

PSGELS/PDGELS

PSGEMM/PDGEMM

PSGEMV/PDGEMV

PSGESV/PDGESV

PSGESVD/PDGESVD

PSPOSV/PDPOSV

PSSYEV/PDSYEV

PSSYEVX/PDSYEVX

recommendations

tuning

performance guidelines

PETSc

PIGEMR2D

PITRMR2D

pivoting

column (QR)

partial

poor performance

PoPCs

portability , , , ,

prebuilt libraries

blacs

scalapack

process

column coordinate (MYCOL)

row coordinate (MYROW)

process column

process grid ,

process grid

initialization ,

mapping (column-major) ,

mapping (row-major) ,

mapping (user-defined) ,

obtaining BLACS context

P

P

shape ,

process mesh, see process grid

processor

process row

prototype codes

prototype codes

HPF interface to ScaLAPACK

prototype codes

matrix sign function ,

out-of-core linear solvers

SuperLU

PSDBSV

PSDBTRF , ,

PSDBTRS ,

PSDTSV

PSDTTRF , ,

PSDTTRS ,

PSGBSV

PSGBTRF , ,

PSGBTRS ,

PSGEBRD ,

PSGECON ,

PSGEEQU

PSGEHRD ,

PSGELQF ,

PSGELS , , ,

PSGEMR2D

PSGEQLF

PSGEQPF

PSGEQRF , ,

PSGERFS ,

PSGERQF

PSGESV , ,

PSGESVD , , , , , ,

PSGESVX , , , , ,

PSGETRF

PSGETRI

PSGETRS

PSGGQRF

PSGGRQF

PSLAHQR ,

PSLAMCH ,

PSORGLQ

PSORGQR ,

PSORMBR ,

PSORMHR

PSORMLQ ,

PSORMQR , , ,

PSORMRZ

PSORMTR

PSPBSV

PSPBTRF , ,

PSPBTRS ,

PSPOCON , ,

PSPOEQU

PSPORFS ,

PSPOSV , ,

PSPOSVX ,

PSPOTRF

PSPOTRI

PSPOTRS

PSPTSV

PSPTTRF

PSPTTRS

PSSTEBZ ,

PSSTEIN ,

PSSYEV , , , ,

PSSYEVX , , , , , ,

PSSYGST

PSSYGVX , , , ,

PSSYR2K

PSSYTRD ,

PSTRCON , ,

PSTRMR2D

PSTRRFS ,

PSTRTRI

PSTRTRS , ,

PSTZRZF

PVM , , ,

PVM

homepage

PXERBLA , ,

PZDBSV

PZDBTRF , ,

PZDBTRS ,

PZDTSV

PZDTTRF , ,

PZDTTRS ,

PZGBSV

PZGBTRF , ,

PZGBTRS ,

PZGEBRD

PZGECON ,

PZGEEQU

PZGEHRD

PZGELQF ,

PZGELS , ,

PZGEMR2D

PZGEQLF

PZGEQPF

PZGEQRF , ,

PZGERFS ,

PZGERQF

PZGESVD , , ,

PZGESVX , ,

PZGETRF

PZGETRI

PZGETRS

PZGGQRF

PZGGRQF

PZHEEVX , , ,

PZHEGST

PZHEGVX , , , ,

PZHETRD

PZHETRF

PZHETRS

PZPBSV

PZPBTRF , ,

PZPBTRS ,

PZPOCON , ,

PZPOEQU

PZPORFS ,

PZPOSV ,

PZPOSVX ,

PZPOTRF

PZPOTRI

PZPOTRS

PZPTSV

PZPTTRF

PZPTTRS

PZSTEIN ,

PZTRCON , ,

PZTRMR2D

PZTRRFS ,

PZTRTRI

PZTRTRS , ,

PZTZRZF

PZUNGLQ

PZUNGQR ,

PZUNMBR

PZUNMHR

PZUNMLQ

PZUNMQR , , ,

PZUNMRZ

PZUNMTR

QL algorithm

implicit

QL factorization

QR algorithm

implicit

QR factorization ,

QR factorization

blocked form

generalized (GQR) ,

with pivoting ,

query

quick reference guides: see Appendix D

rank

rank-deficient, see linear least squares problem

redistribution routines

PxGEMR2D

PxTRMR2D

reduction

bidiagonal

standard form

tridiagonal

upper Hessenberg

relative error , , , , , , ,

relative machine precision

reliability, see test suites ,

repeatability ,

repeatability

enforcement of (BLACS_SET)

replicated across process columns

replicated across process rows

replicated and distributed

replicated vector ,

reporting bugs, see bug reports ,

right-hand-side matrix

roundoff error ,

RQ factorization

RQ factorization

generalized (GRQ) ,

RSRC_, see array descriptor

rule of thumb

scalability , , ,

ScaLAPACK

commercial use of

converting from LAPACK to: see Appendix B

prebuilt libraries, availability of

quick reference guide: see Appendix D

scaling

Schur factorization

Schur form

Schur vectors

scope ,

scope

groupings of processes

in communication

of a variable

within a process grid

scoped operation

SDISNA ,

SEP ,

simple driver, see driver routines, simple ,

Single Program Multiple Data (SPMD)

singular value

singular value decomposition (SVD)

singular value decomposition (SVD)

singular value

error bound ,

singular vector

error bound ,

singular vectors

left ,

right ,

software hierarchy

software standards

software standards

distributed memory

solution matrix

spectral factorization

SPMD

SSTEQR2

stability ,

stability

backward , , , ,

forward

standard form

storage scheme

general tridiagonal

Hermitian ,

orthogonal or unitary matrices

symmetric

symmetric tridiagonal

triangular

submatrix access

subspaces

angle between

subspaces, angle between , , , , , , ,

suggestions for reading

SuperLU, see prototype codes

support

SVD

Sylvester equation

symmetric eigenproblem

T() ,

T()

t

t

t

t

t

T

t

t, see latency

t

t

t

terminology

test suites , , , , , , , , ,

thread of execution, see process

throughput, see bandwidth

TOOLS

DESCINIT

NUMROC

PxLAPRNT

SL_INIT

transportable efficiency

tridiagonal form , , , , ,

tridiagonal matrix, distribution of

troubleshooting

tuning

underdetermined system , ,

underflow , , ,

unitary matrix ,

upper Hessenberg form

utility routines

workspace query

World Wide Web

wrong results

WWW

XDR