Index by Keyword

generalized symmetric, band storage: Purpose
generalized symmetric, full storage: Purpose
generalized symmetric, packed storage: Purpose
least squares: Purpose
singular value problems: Purpose
symmetric tridiagonal: Purpose
symmetric, band storage: Purpose
symmetric, full storage: Purpose
symmetric, packed storage: Purpose

Gaussian elimination with row interchanges

band storage: Purpose | Purpose
dense storage: Purpose | Purpose
tridiagonal: Purpose | Purpose

inverse iteration

LDL decomposition

full storage: Purpose

LDL decomposition

full storage: Purpose

LDL decomposition

packed storage: Purpose

LDL decomposition

packed storage: Purpose

Pal-Walker-Kahan

QR

Arguments | Arguments

RRR

Purpose | Purpose

Schur decomposition

see Schur

UDU decomposition

full storage: Purpose

UDU decomposition

full storage: Purpose

UDU decomposition

packed storage: Purpose

UDU decomposition

packed storage: Purpose

ALLOCATABLE attribute

ALLOCATE statement

arguments

assumed-shape arrays: Array Arguments
description: Argument Descriptions
descriptions: Argument Descriptions
illegal value: Error Handling
optional: Design of the LAPACK95 | Optional Arguments
order of: Order of Arguments
rank: Design of the LAPACK95

arrays

allocatable: Design of the LAPACK95 | Example 1
assumed-shape: LAPACK95 | Design of the LAPACK95 | Design of the LAPACK95 | Array Arguments
empty: Design of the LAPACK95
passing subsections: Design of the LAPACK95

ATLAS

LAPACK and the BLAS | BLAS | Performance Tables

automatic allocation

Computational Routines for the | Computational Routines for the

auxiliary

enquiry function ILAENV: Optimal Value of the
routines: Levels of Routines | How to call an

backward error

bounds: Linear Equations

backward transformation

balanced pair of matrices

balancing

Purpose | Computational Routines for the

transformation: Purpose

band

form

see band storage

storage

Availability of Software via

scheme: Example 1 | Example 1 | Example 1

Basic Linear Algebra Subprograms

see BLAS

bidiagonal

factor: Computational Routines for the
form: Computational Routines for the
matrices: Matrix Storage Schemes | Matrix Storage Schemes

BLAS

Preface | Performance Tables

library: BLAS
model implementation: BLAS
optimized: BLAS
vendor implementation: BLAS

block

algorithms: Preface | Optimal Value of the
size: Incorporating Machine Dependencies | Performance Tables

bug reports

Support

Bunch-Kaufman

see algorithms

call LAPACK95 routines

Example 1 | Example 2

CD-ROM

Cholesky

see algorithms, decomposition and factorization

column equilibration

Example (from Program LA_GBSVX_EXAMPLE)

commercial use

Commercial Use

complex

conjugate pairs: Nonsymmetric Eigenproblems (NEP) | Generalized Nonsymmetric Eigenproblems (GNEP)
Hermitian: Linear Equations
Schur factorization: Nonsymmetric Eigenproblems (NEP)
symmetric: Linear Equations

computation

failure: Error Handling

computational routines

Problems that LAPACK95 can | Problems that LAPACK95 can | Levels of Routines | Design of Interfaces for

condition number

Linear Equations | Purpose

eigenvalues

generalized nonsymmetric: Purpose | Purpose
nonsymmetric: Arguments

eigenvectors

generalized nonsymmetric: Purpose | Purpose
nonsymmetric: Arguments
right: Computational Routines for the

invariant subspace

nonsymmetric: Purpose

selected eigenvalues

nonsymmetric: Purpose

specified eigenvalues

condition number of the system

complex general

band: Purpose
dense: Purpose | General Linear Systems
triangular band: Triangular Linear Systems
triangular matrix: Triangular Linear Systems
triangular packed: Triangular Linear Systems
tridiagonal: Purpose

complex Hermitian

band storage: Symmetric/Hermitian Positive Definite Linear
dense: Symmetric/Hermitian Positive Definite Linear
indefinite, full storage: Purpose | Symmetric Indefinite Linear Systems
indefinite, packed storage: Purpose | Symmetric Indefinite Linear Systems
packed storage: Symmetric/Hermitian Positive Definite Linear
positive definite, band storage: Purpose
positive definite, full storage: Purpose
positive definite, packed storage: Purpose
positive definite, tridiagonal: Purpose
tridiagonal: Symmetric/Hermitian Positive Definite Linear

complex symmetric

indefinite, full storage: Purpose | Symmetric Indefinite Linear Systems
indefinite, packed storage: Purpose | Symmetric Indefinite Linear Systems

general band

real general

band: Purpose
dense: Purpose | General Linear Systems
triangular band: Triangular Linear Systems
triangular matrix: Triangular Linear Systems
triangular packed: Triangular Linear Systems
tridiagonal: Purpose

real symmetric

dense: Symmetric/Hermitian Positive Definite Linear
dense, band storage: Symmetric/Hermitian Positive Definite Linear
indefinite, full storage: Purpose | Symmetric Indefinite Linear Systems
indefinite, packed storage: Purpose | Symmetric Indefinite Linear Systems
packed storage: Symmetric/Hermitian Positive Definite Linear
positive definite, band storage: Purpose
positive definite, full storage: Purpose
positive definite, packed storage: Purpose
positive definite, tridiagonal: Purpose
tridiagonal: Symmetric/Hermitian Positive Definite Linear

tridiagonal

constructing LAPACK routines

LAPACK and the BLAS

conventional storage

Matrix Storage Schemes

Cosine-Sine decomposition

CPU_TIME

CXML

data types

debugging

hints, installation: Installation Debugging Hints
release_notes: Installation Debugging Hints

decomposition

Cholesky

band storage: Symmetric/Hermitian Positive Definite Linear
packed storage: Symmetric/Hermitian Positive Definite Linear
tridiagonal: Symmetric/Hermitian Positive Definite Linear

singular values

Purpose

deflating subspace

Generalized Nonsymmetric Eigenproblems (GNEP) | Generalized Nonsymmetric Eigenproblems (GNEP) | Arguments | Example (from Program LA_GGESX_EXAMPLE)

derived types

Generalized Symmetric Definite Eigenproblems

diagonal

block: Computational Routines for the | Computational Routines for the
blocks: Nonsymmetric Eigenproblems (NEP) | Generalized Nonsymmetric Eigenproblems (GNEP) | Computational Routines for the
elements: Symmetric Eigenproblems (SEP) | Argument Descriptions
entries: Generalized Singular Value Decomposition
matrices: Symmetric Eigenproblems (SEP) | Singular Value Decomposition (SVD) | Generalized Symmetric Definite Eigenproblems | Generalized Singular Value Decomposition | Generalized Singular Value Decomposition

divide and conquer

driver: Symmetric Eigenproblems (SEP)
least squares: Linear Least Squares (LLS) | Linear Least Squares (LLS)
method: Computational Routines for the
SVD: Singular Value Decomposition (SVD)

DLAMCH

LA_LAMCH Interfaces

documentation, structure

Structure of the Documentation

driver routines

Problems that LAPACK95 can | Problems that LAPACK95 can | Levels of Routines | Driver Routines | Performance Tables

divide and conquer

Linear Least Squares (LLS) | Singular Value Decomposition (SVD) | Generalized Symmetric Definite Eigenproblems

expert

Linear Equations | Generalized Symmetric Definite Eigenproblems

generalized

least squares: Generalized Linear Least Squares
nonsymmetric eigenvalue problem: Generalized Nonsymmetric Eigenproblems (GNEP) | Generalized Nonsymmetric Eigenproblems (GNEP)
SVD: Generalized Singular Value Decomposition
symmetric definite eigenvalue problem: Generalized Symmetric Definite Eigenproblems

linear

equations: Linear Equations
least squares: Linear Least Squares (LLS)

nonsymmetric eigenvalue problem

Linear Equations | Generalized Symmetric Definite Eigenproblems

simple

effective rank of matrix

Purpose

eigenvalue problem

Problems that LAPACK95 can

ill-conditioned: Generalized Nonsymmetric Eigenproblems (GNEP)
regular: Generalized Nonsymmetric Eigenproblems (GNEP)
singular: Generalized Nonsymmetric Eigenproblems (GNEP)

eigenvalues

Symmetric Eigenproblems (SEP) | Symmetric Eigenproblems (SEP)

all

generalized nonsymmetric: Purpose
generalized symmetric, band storage: Purpose
generalized symmetric, full storage: Purpose
generalized symmetric, packed storage: Purpose
nonsymmetric: Purpose | Purpose
symmetric tridiagonal: Purpose
symmetric, band storage: Purpose
symmetric, full storage: Purpose
symmetric, packed storage: Purpose

approximate

generalized symmetric, band storage: Arguments
generalized symmetric, full storage: Arguments | Arguments
symmetric tridiagonal: Arguments | Arguments
symmetric, band storage: Arguments
symmetric, full storage: Arguments | Arguments
symmetric, packed storage: Arguments

condition number

nonsymmetric: Purpose | Arguments

divide and conquer method

generalized

ordering of: Generalized Nonsymmetric Eigenproblems (GNEP)

nontrivial

ordering of

Pal-Walker-Kahan algorithm

reciprocal condition numbers

Computational Routines for the | Computational Routines for the

selected

complex Hermitian: Computational Routines for the
generalized nonsymmetric: Purpose | Purpose | Purpose
generalized symmetric, band storage: Purpose
generalized symmetric, full storage: Purpose
generalized symmetric, packed storage: Purpose
nonsymmetric: Purpose | Purpose
real symmetric: Computational Routines for the
symmetric tridiagonal: Purpose | Purpose
symmetric, band storage: Purpose
symmetric, full storage: Purpose | Purpose
symmetric, packed storage: Purpose

selected cluster

symmetric

positive definite tridiagonal matrix: Computational Routines for the
tridiagonal matrix: Computational Routines for the

trivial

eigenvectors

all

generalized nonsymmetric: Purpose
generalized symmetric, band storage: Purpose
generalized symmetric, full storage: Purpose
generalized symmetric, packed storage: Purpose
nonsymmetric: Purpose | Purpose
symmetric tridiagonal: Purpose
symmetric, band storage: Purpose
symmetric, full storage: Purpose
symmetric, packed storage: Purpose

complex conjugate pairs

nonsymmetric: Arguments | Arguments

condition number

nonsymmetric: Purpose | Arguments

left

generalized: Computational Routines for the
nonsymmetric: Purpose | Purpose

NEP

normalized

nonsymmetric: Purpose

orthogonal

generalized symmetric, band storage: Arguments
generalized symmetric, full storage: Arguments
generalized symmetric, packed storage: Arguments

reciprocal condition numbers

right

generalized: Computational Routines for the
nonsymmetric: Purpose | Purpose

scaled

nonsymmetric: Purpose | Arguments | Purpose

selected

complex Hermitian: Computational Routines for the
generalized nonsymmetric: Purpose | Purpose | Purpose
generalized symmetric, band storage: Purpose
generalized symmetric, full storage: Purpose
generalized symmetric, packed storage: Purpose
nonsymmetric: Purpose | Purpose
real symmetric: Computational Routines for the
symmetric tridiagonal: Purpose | Purpose
symmetric, band storage: Purpose
symmetric, full storage: Purpose | Purpose
symmetric, packed storage: Purpose
usually the fastest algorithm: Purpose | Purpose

symmetric

positive definite tridiagonal matrix: Computational Routines for the
tridiagonal matrix: Computational Routines for the | Computational Routines for the

EISPACK

Preface

elementary reflectors

elimination

see also factorization or decomposition in algorithms

equality-constrained least squares

Example (from Program LA_GBSVX_EXAMPLE)

equilibration

by column

complex general

band: Purpose
dense: Purpose

complex Hermitian

positive definite, band storage: Purpose
positive definite, full storage: Purpose
positive definite, packed storage: Purpose

real general

band: Purpose
dense: Purpose

real symmetric

positive definite, band storage: Purpose
positive definite, full storage: Purpose
positive definite, packed storage: Purpose

ERINFO

Error Handling | Error Handling | Error Handling | Error Handling

errata

see release_notes

error

bounds: General Linear Systems | General Linear Systems | General Linear Systems | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Symmetric Indefinite Linear Systems | Symmetric Indefinite Linear Systems | Triangular Linear Systems | Triangular Linear Systems | Triangular Linear Systems
handling: Design of the LAPACK95 | Error Handling
routine: Error Handling

error bounds for linear systems

complex general

band: Purpose
dense: Purpose
tridiagonal: Purpose

complex Hermitian

indefinite, full storage: Purpose
indefinite, packed storage: Purpose
positive definite, band storage: Purpose
positive definite, full storage: Purpose
positive definite, packed storage: Purpose
positive definite, tridiagonal: Purpose

complex symmetric

indefinite, full storage: Purpose
indefinite, packed storage: Purpose

real general

band: Purpose
dense: Purpose
tridiagonal: Purpose

real symmetric

indefinite, full storage: Purpose
indefinite, packed storage: Purpose
positive definite, band storage: Purpose
positive definite, full storage: Purpose
positive definite, packed storage: Purpose
positive definite, tridiagonal: Purpose

ESSL

Euclidean norm

Arguments | Purpose

EXAMPLES1 (directory)

EXAMPLES2 (directory)

expert driver

description: Structure of the Documentation

f77_lapack.mod

How to call an | How to call an

f95_lapack.mod

How to call an | How to call an

factorization

see also decomposition or elimination in algorithms

Cholesky

band storage: Symmetric/Hermitian Positive Definite Linear
packed storage: Symmetric/Hermitian Positive Definite Linear
tridiagonal: Symmetric/Hermitian Positive Definite Linear

complex Hermitian

indefinite matrix: Symmetric Indefinite Linear Systems
indefinite matrix, packed storage: Symmetric Indefinite Linear Systems

complex symmetric

indefinite matrix: Symmetric Indefinite Linear Systems
indefinite matrix, packed storage: Symmetric Indefinite Linear Systems

Gauss

Purpose

generalized

Purpose

generalized RQ

Purpose

LQ

Purpose | Computational Routines for Orthogonal

LU

QL

QR

Purpose | Purpose | Arguments | Arguments | Computational Routines for Orthogonal

with column pivoting: Computational Routines for Orthogonal

real symmetric

indefinite matrix: Symmetric Indefinite Linear Systems
indefinite matrix, packed storage: Symmetric Indefinite Linear Systems

RQ

Schur

split Cholesky

FAQ

Example (from Program LA_GESVX_EXAMPLE) | Example (from Program LA_GBSVX_EXAMPLE) | Example (from Program LA_PPSVX_EXAMPLE) | Example (from Program LA_PTSVX_EXAMPLE)

Fortran standard

Preface

Fortran 77

Preface | Performance Issues | Performance Issues

Fortran 95

Preface | LAPACK95 | Performance Issues | Performance Issues

wrappers: LAPACK95

forward error

bounds: Linear Equations

Frequently Asked Questions

see FAQ

Gauss

see algorithms and factorization

Gauss-Markov

see GLM

General Gauss-Markov Linear Model Problem

see GLM

Generalized Factorization

see GRQ

Generalized Factorization

see GQR

generalized eigenproblem

Computational Routines for the | Computational Routines for the

banded, reduction: Computational Routines for the
nonsymmetric: Generalized Nonsymmetric Eigenproblems (GNEP)
packed form: Computational Routines for the

generalized least squares

Generalized Singular Value Decomposition | Example 1 (from Program

Generalized Nonsymmetric Eigenvalue Problem

see GNEP

generalized Schur

decomposition: Generalized Nonsymmetric Eigenproblems (GNEP)
vectors: Generalized Nonsymmetric Eigenproblems (GNEP)

generalized singular value

Generalized Singular Value Decomposition

see GSVD

special cases: Generalized Singular Value Decomposition

generalized Sylvester equation

Generalized Symmetric Eigenvalue Problem

see GSEP

generalized upper Hessenberg form

generic

interface blocks: F77_LAPACK Generic Interface Blocks
interfaces: LAPACK95 | Design of the LAPACK95

GLM

Generalized Nonsymmetric Eigenproblems (GNEP)

problem: Purpose

GNEP

GQR

Generalized Linear Least Squares | Generalized Linear Least Squares

GRQ

Generalized Linear Least Squares | Generalized Linear Least Squares

GSEP

Generalized Symmetric Definite Eigenproblems

GSVD

Generalized Singular Value Decomposition | see Generalized Singular Value Decomposition | Computational Routines for the

Hermitian

Computational Routines for the | Computational Routines for the

eigenvalue problem: Symmetric Eigenproblems (SEP)
matrices: Matrix Storage Schemes

Hessenberg

upper

generalized form: Computational Routines for the

ILAENV

Optimal Value of the | Optimal Value of the | Code for One Version

illegal argument

Optional Arguments

inconsistent shapes

indefinite symmetric

Independent Software Vendor

see ISV

INFO

Availability and Installation of

installation

debugging hints: Installation Debugging Hints

insufficient memory

INTENT attribute

IN: Code for One Version
INOUT: Code for One Version
OUT: Code for One Version

INTERFACE statement

LA_SYEV/LA_HEEV | LA_SYEV/LA_HEEV | LA_GESV Multiple $\mathit{RHS}$ Case | LA_SYEV/LA_HEEV | LA_GESV

interfaces

generic: Design of the LAPACK95

invalid

argument: Error Handling
shape: Error Handling

invariant subspace

Nonsymmetric Eigenproblems (NEP) | Generalized Nonsymmetric Eigenproblems (GNEP) | Purpose | Purpose | Computational Routines for the

inverse of a matrix

ISV

BLAS

iterative refinement of the system

complex general

band: Purpose
dense: Purpose
tridiagonal: Purpose

complex Hermitian

indefinite, full storage: Purpose
indefinite, packed storage: Purpose
positive definite, band storage: Purpose
positive definite, full storage: Purpose
positive definite, packed storage: Purpose
positive definite, tridiagonal: Purpose

complex symmetric

indefinite, full storage: Purpose
indefinite, packed storage: Purpose

real general

band: Purpose
dense: Purpose
tridiagonal: Purpose

real symmetric

indefinite, full storage: Purpose
indefinite, packed storage: Purpose
positive definite, band storage: Purpose
positive definite, full storage: Purpose
positive definite, packed storage: Purpose
positive definite, tridiagonal: Purpose

KIND type parameter

la_auxmod.mod

How to call an

LA_BDSDC

LA_BDSQR

LA_GBBRD

LA_GBCON

LA_GBEQU

LA_GBRFS

LA_GBSV

Linear Equations | LA_GBSV

LA_GBSVX

Linear Equations | LA_GBSVX

LA_GBTRF

LA_GBTRS

LA_GEBAK

LA_GEBAL

LA_GEBRD

LA_GECON

LA_GEEQU

LA_GEES

Nonsymmetric Eigenproblems (NEP) | Singular Value Decomposition (SVD) | LA_GEES

LA_GEESX

Nonsymmetric Eigenproblems (NEP) | Singular Value Decomposition (SVD) | LA_GEESX

LA_GEEV

LA_GEEVX

Nonsymmetric Eigenproblems (NEP) | Singular Value Decomposition (SVD) | LA_GEEVX

LA_GEHRD

LA_GELQF

LA_GELS

Linear Least Squares (LLS) | Linear Least Squares (LLS) | LA_GELS

LA_GELSD

Linear Least Squares (LLS) | Linear Least Squares (LLS) | Linear Least Squares (LLS) | LA_GELSS / LA_GELSD

LA_GELSS

Linear Least Squares (LLS) | Linear Least Squares (LLS) | Linear Least Squares (LLS) | LA_GELSS / LA_GELSD

LA_GELSY

Linear Least Squares (LLS) | Linear Least Squares (LLS) | Linear Least Squares (LLS) | LA_GELSY

LA_GEQLF

LA_GEQP3

Example 2 | Computational Routines for Orthogonal

LA_GEQRF

LA_GERFS

LA_GERQF

LA_GESDD

LA_GESV

LA_GESVD

LA_GESVX

Linear Equations | LA_GESVX

LA_GETRF

LA_GETRI

LA_GETRS

LA_GGBAK

LA_GGBAL

Generalized Nonsymmetric Eigenproblems (GNEP) | Generalized Singular Value Decomposition | LA_GGES

LA_GGES

LA_GGESX

Generalized Nonsymmetric Eigenproblems (GNEP) | Generalized Singular Value Decomposition | LA_GGESX

LA_GGEV

Generalized Nonsymmetric Eigenproblems (GNEP) | Generalized Singular Value Decomposition | LA_GGEV

LA_GGEVX

Generalized Nonsymmetric Eigenproblems (GNEP) | Generalized Singular Value Decomposition | LA_GGEVX

LA_GGGLM

Generalized Linear Least Squares | Generalized Linear Least Squares | LA_GGGLM

LA_GGHRD

Generalized Singular Value Decomposition | Generalized Singular Value Decomposition | LA_GGSVD

LA_GGLSE

Generalized Linear Least Squares | LA_GGLSE

LA_GGSVD

LA_GGSVP

LA_GTCON

LA_GTRFS

LA_GTSV

Linear Equations | LA_GTSV

LA_GTSVX

Linear Equations | LA_GTSVX

LA_GTTRF

LA_GTTRS

Singular Value Decomposition (SVD) | LA_SBEV / LA_HBEV /

LA_HBEV

LA_HBEVD

Singular Value Decomposition (SVD) | LA_SBEV / LA_HBEV /

LA_HBEVX

Singular Value Decomposition (SVD) | LA_SBEVX / LA_HBEVX

LA_HBGST

Generalized Singular Value Decomposition | LA_SBGV / LA_SBGVD /

LA_HBGV

LA_HBGVD

Generalized Singular Value Decomposition | LA_SBGV / LA_SBGVD /

LA_HBGVX

Generalized Singular Value Decomposition | LA_SBGVX / LA_HBGVX

LA_HBTRD

LA_HECON

Singular Value Decomposition (SVD) | LA_SYEV / LA_HEEV /

LA_HEEV

LA_HEEVD

Singular Value Decomposition (SVD) | LA_SYEV / LA_HEEV /

LA_HEEVR

Singular Value Decomposition (SVD) | LA_SYEVR / LA_HEEVR

LA_HEEVX

Singular Value Decomposition (SVD) | LA_SYEVX / LA_HEEVX

LA_HEGST

Generalized Singular Value Decomposition | LA_SYGV /LA_SYGVD / LA_HEGV

LA_HEGV

LA_HEGVD

Generalized Singular Value Decomposition | LA_SYGV /LA_SYGVD / LA_HEGV

LA_HEGVX

Generalized Singular Value Decomposition | LA_SYGVX / LA_HEGVX

LA_HERFS

LA_HESV

Linear Equations | LA_SYSV / LA_HESV

LA_HESVX

Linear Equations | LA_SYSVX / LA_HESVX

LA_HETRD

LA_HETRF

LA_HETRI

LA_HETRS

LA_HGEQZ

LA_HPCON

Singular Value Decomposition (SVD) | LA_SPEV / LA_HPEV /

LA_HPEV

LA_HPEVD

Singular Value Decomposition (SVD) | LA_SPEV / LA_HPEV /

LA_HPEVX

Singular Value Decomposition (SVD) | LA_SPEVX / LA_HPEVX

LA_HPGST

Generalized Singular Value Decomposition | LA_SPGV / LA_SPGVD /

LA_HPGV

LA_HPGVD

Generalized Singular Value Decomposition | LA_SPGV / LA_SPGVD /

LA_HPGVX

Generalized Singular Value Decomposition | LA_SPGVX / LA_HPGVX

LA_HPRFS

LA_HPSV

Linear Equations | LA_SPSV / LA_HPSV

LA_HPSVX

Linear Equations | LA_SPSVX / LA_HPSVX

LA_HPTRD

LA_HPTRF

LA_HPTRI

LA_HPTRS

LA_HSEIN

LA_HSEQR

LA_LAMCH

LA_OPGTR

LA_OPMTR

LA_ORGBR

LA_ORGLQ

LA_ORGQL

LA_ORGQR

LA_ORGRQ

LA_ORGTR

LA_ORMBR

LA_ORMHR

LA_ORMLQ

LA_ORMQL

LA_ORMQR

LA_ORMRQ

LA_ORMRZ

LA_ORMTR

LA_PBCON

LA_PBEQU

LA_PBRFS

LA_PBSTF

LA_PBSV

Linear Equations | LA_PBSV

LA_PBSVX

Linear Equations | LA_PBSVX

LA_PBTRF

LA_PBTRS

LA_POCON

LA_POEQU

LA_PORFS

LA_POSV

Linear Equations | Optional Arguments | LA_POSV

LA_POSVX

Linear Equations | LA_POSVX

LA_POTRF

LA_POTRI

LA_POTRS

LA_PPCON

LA_PPEQU

LA_PPRFS

LA_PPSV

Linear Equations | LA_PPSV

LA_PPSVX

Linear Equations | LA_PPSVX

LA_PPTRF

LA_PPTRI

LA_PPTRS

la_precision.mod

LA_PTCON

LA_PTEQR

LA_PTRFS

LA_PTSV

Linear Equations | LA_PTSV

LA_PTSVX

Linear Equations | LA_PTSVX

LA_PTTRF

LA_PTTRS

Singular Value Decomposition (SVD) | LA_SBEV / LA_HBEV /

LA_SBEV

LA_SBEVD

Singular Value Decomposition (SVD) | LA_SBEV / LA_HBEV /

LA_SBEVX

Singular Value Decomposition (SVD) | LA_SBEVX / LA_HBEVX

LA_SBGST

Generalized Singular Value Decomposition | LA_SBGV / LA_SBGVD /

LA_SBGV

LA_SBGVD

Generalized Singular Value Decomposition | LA_SBGV / LA_SBGVD /

LA_SBGVX

Generalized Singular Value Decomposition | LA_SBGVX / LA_HBGVX

LA_SBTRD

LA_SPCON

Singular Value Decomposition (SVD) | LA_SPEV / LA_HPEV /

LA_SPEV

LA_SPEVD

Singular Value Decomposition (SVD) | LA_SPEV / LA_HPEV /

LA_SPEVX

Singular Value Decomposition (SVD) | LA_SPEVX / LA_HPEVX

LA_SPGST

Generalized Singular Value Decomposition | LA_SPGV / LA_SPGVD /

LA_SPGV

LA_SPGVD

Generalized Singular Value Decomposition | LA_SPGV / LA_SPGVD /

LA_SPGVX

Generalized Singular Value Decomposition | LA_SPGVX / LA_HPGVX

LA_SPRFS

LA_SPSV

Linear Equations | LA_SPSV / LA_HPSV

LA_SPSVX

Linear Equations | LA_SPSVX / LA_HPSVX

LA_SPTRD

LA_SPTRF

LA_SPTRI

LA_SPTRS

LA_STEBZ

LA_STEDC

LA_STEGR

LA_STEIN

LA_STEQR

LA_STERF

Singular Value Decomposition (SVD) | LA_STEV / LA_STEVD

LA_STEV

LA_STEVD

Singular Value Decomposition (SVD) | LA_STEV / LA_STEVD

LA_STEVR

Singular Value Decomposition (SVD) | LA_STEVR

LA_STEVX

Singular Value Decomposition (SVD) | LA_STEVX

LA_SYCON

Singular Value Decomposition (SVD) | LA_SYEV / LA_HEEV /

LA_SYEV

Singular Value Decomposition (SVD) | Code for One Version | LA_SYEV / LA_HEEV /

LA_SYEVD

LA_SYEVR

Singular Value Decomposition (SVD) | LA_SYEVR / LA_HEEVR

LA_SYEVX

Singular Value Decomposition (SVD) | LA_SYEVX / LA_HEEVX

LA_SYGST

Generalized Singular Value Decomposition | LA_SYGV /LA_SYGVD / LA_HEGV

LA_SYGV

LA_SYGVD

Generalized Singular Value Decomposition | LA_SYGV /LA_SYGVD / LA_HEGV

LA_SYGVX

Generalized Singular Value Decomposition | LA_SYGVX / LA_HEGVX

LA_SYRFS

LA_SYSV

Linear Equations | LA_SYSV / LA_HESV

LA_SYSVX

Linear Equations | LA_SYSVX / LA_HESVX

LA_SYTRD

LA_SYTRF

LA_SYTRI

LA_SYTRS

LA_TBCON

LA_TBRFS

LA_TBTRS

LA_TGEVC

LA_TGEXC

LA_TGSEN

LA_TGSJA

LA_TGSNA

LA_TGSYL

LA_TPCON

LA_TPRFS

LA_TPTRI

LA_TPTRS

LA_TRCON

LA_TREVC

LA_TREXC

LA_TRRFS

LA_TRSEN

LA_TRSNA

LA_TRSYL

LA_TRTRI

LA_TRTRS

LA_TZRZF

LA_UNGBR

Computational Routines for the | Computational Routines for the

LA_UNGHR

LA_UNGLQ

LA_UNGQL

LA_UNGQR

LA_UNGRQ

LA_UNGTR

LA_UNMBR

LA_UNMHR

LA_UNMLQ

LA_UNMQL

LA_UNMQR

LA_UNMRQ

LA_UNMRZ

LA_UNMTR

LA_UPGTR

LA_UPMTR

LAPACK

Preface | Problems that LAPACK95 can | LAPACK | Performance Issues | Performance Tables

home page: LAPACK
Installation Guide: LAPACK
library: LAPACK95
package: LAPACK
test suites: LAPACK
Users' Guide: Symmetric Eigenproblems (SEP) | Symmetric Eigenproblems (SEP) | Singular Value Decomposition (SVD) | Generalized Nonsymmetric Eigenproblems (GNEP)

LAPACK95

Preface | LAPACK95 | Performance Tables

commercial use of: Commercial Use
documentation: Structure of the Documentation
driver routines: Driver Routines
FAQ: LAPACK95
home page: LAPACK95
naming: Design of the LAPACK95
source code: LAPACK95
test suites: LAPACK95

leading diagonal blocks

least squares solution

Purpose | Purpose | Purpose | Purpose

libblas.a

How to call an | How to call an | How to call an

liblapack.a

How to call an | How to call an | How to call an | How to call an

liblapack95.a

How to call an | How to call an | How to call an

linear equations

Problems that LAPACK95 can | Linear Least Squares (LLS)

linear least squares problem

equality-constrained

Purpose

generalized

equality-constrained (LSE): Generalized Linear Least Squares
regression model (GLM): Generalized Linear Least Squares

weighted

Linear Least Squares (LLS) | Linear Least Squares (LLS)

LINPACK

Preface

LLS (Linear Least Squares)

LOGICAL FUNCTION SELECT

Example 2 (from Program

lower bidiagonal

form: Computational Routines for the
matrix: Computational Routines for the

LQ factorization

Generalized Linear Least Squares | Generalized Linear Least Squares

LSE

problem: Purpose

LU factorization

Levels of Routines | General Linear Systems | General Linear Systems | General Linear Systems

machine

constants returned by LA_LAMCH: Machine Dependent Constants (Function
dependencies (ILAENV): Incorporating Machine Dependencies

make.inc

matrices

balancing

bidiagonal

lower: Computational Routines for the
upper: Computational Routines for the

complex

unitary: Purpose | Purpose | Purpose | Purpose | Purpose | Purpose

complex general

band: Purpose | Purpose
dense: Purpose | Purpose
tridiagonal: Purpose | Purpose

complex Hermitian

Generalized Nonsymmetric Eigenproblems (GNEP)

band storage: Computational Routines for the
block diagonal $1 \times 1$ and $2 \times 2$: Purpose
block diagonal $1 \times 1$ and $2 \times 2$: Purpose
block diagonal $1 \times 1$ and $2 \times 2$: Purpose
block diagonal $1 \times 1$ and $2 \times 2$: Purpose
indefinite: Symmetric Indefinite Linear Systems
indefinite, full storage: Purpose | Purpose
indefinite, packed storage: Purpose | Purpose | Symmetric Indefinite Linear Systems
inverse: Symmetric/Hermitian Positive Definite Linear | Symmetric Indefinite Linear Systems
inverse, packed storage: Symmetric/Hermitian Positive Definite Linear | Symmetric Indefinite Linear Systems
packed storage: Computational Routines for the
positive definite: Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Symmetric Indefinite Linear Systems | Computational Routines for the
positive definite, band storage: Purpose | Purpose | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Computational Routines for the | Computational Routines for the
positive definite, full storage: Purpose | Purpose
positive definite, packed storage: Purpose | Purpose | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Symmetric Indefinite Linear Systems | Computational Routines for the
positive definite, tridiagonal: LA_PTSV | Purpose | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear

complex symmetric

block diagonal $1 \times 1$ and $2 \times 2$: Purpose
block diagonal $1 \times 1$ and $2 \times 2$: Purpose
block diagonal $1 \times 1$ and $2 \times 2$: Purpose
block diagonal $1 \times 1$ and $2 \times 2$: Purpose
indefinite: Symmetric Indefinite Linear Systems | Symmetric Indefinite Linear Systems
indefinite, full storage: Purpose | Purpose
indefinite, packed storage: Purpose | Purpose | Symmetric Indefinite Linear Systems | Symmetric Indefinite Linear Systems
inverse: Symmetric Indefinite Linear Systems
inverse, packed storage: Symmetric Indefinite Linear Systems

effective rank

Purpose

full rank

Purpose

general

inverse: General Linear Systems

orthogonal

packed storage: Computational Routines for the
product: Computational Routines for Orthogonal

pencil

permutation

quasi-triangular

upper: Computational Routines for the | Computational Routines for the

rank deficient

Purpose

real general

band: Purpose | Purpose
dense: Purpose | Purpose
tridiagonal: Purpose | Purpose

real orthogonal

real symmetric

band storage: Computational Routines for the
block diagonal $1 \times 1$ and $2 \times 2$: Purpose
block diagonal $1 \times 1$ and $2 \times 2$: Purpose
block diagonal $1 \times 1$ and $2 \times 2$: Purpose
block diagonal $1 \times 1$ and $2 \times 2$: Purpose
indefinite: Symmetric Indefinite Linear Systems | Symmetric Indefinite Linear Systems
indefinite, full storage: Purpose | Purpose
indefinite, packed storage: Purpose | Purpose | Symmetric Indefinite Linear Systems | Symmetric Indefinite Linear Systems
inverse: Symmetric/Hermitian Positive Definite Linear | Symmetric Indefinite Linear Systems
inverse, packed storage: Symmetric/Hermitian Positive Definite Linear | Symmetric Indefinite Linear Systems
packed storage: Computational Routines for the
positive definite: Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Computational Routines for the
positive definite, band storage: Purpose | Purpose | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Computational Routines for the | Computational Routines for the
positive definite, full storage: Purpose | Purpose
positive definite, packed storage: Purpose | Purpose | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Computational Routines for the
positive definite, tridiagonal: LA_PTSV | Purpose | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear | Symmetric/Hermitian Positive Definite Linear

singular value problems

complex unitary: Purpose
real orthogonal: Purpose

Sylvester equation

transformation

generalized singular value: Purpose

trapezoidal

triangular

inverse: Triangular Linear Systems
packed, inverse: Triangular Linear Systems
upper: Computational Routines for the

unit lower triangular(L)

unitary

packed storage: Computational Routines for the
product: Computational Routines for Orthogonal

upper

Hessenberg: Computational Routines for the | Computational Routines for the
trapezoidal: Computational Routines for Orthogonal
triangular (U): Purpose | Purpose | Purpose | Purpose | Purpose | Purpose | Purpose | Purpose | Purpose | Purpose | Purpose | Purpose | LA_PTSV | Purpose | Purpose | Purpose | Purpose | Purpose

matrix pairs

eigenvalues

generalized nonsymmetric: Purpose | Purpose

singular value

generalized: Purpose

megaflops

memory allocation

Mirror Repositories of netlib

minimum norm

least squares solution: Linear Least Squares (LLS) | Purpose | Purpose | Purpose
solution: Linear Least Squares (LLS) | Example 2 (from Program

mirror repositories of netlib

MODULE

F77_LAPACK: How to call an | How to call an
F95_LAPACK: How to call an | How to call an
LA_AUXMOD: How to call an
LA_PRECISION: Data Types and Precision | How to call an | How to call an

MODULE statement

naming scheme

Naming Scheme

computational routine: Naming Scheme
driver routine: Naming Scheme
LAPACK95: Design of the LAPACK95

near-singularity

NEP

netlib

Computational Routines for the | Computational Routines for the

mirror repositories: Mirror Repositories of netlib

non-negative diagonal elements

nonsymmetric eigenproblem

generalized: Generalized Nonsymmetric Eigenproblems (GNEP)

Nonsymmetric Eigenvalue Problem

see NEP

ONLY option

Code for One Version

operation counts for LAPACK

Performance Tables | Performance Tables

optimal block size

optional arguments

Linear Least Squares (LLS) | Linear Least Squares (LLS)

OPTIONAL attribute

Design of the LAPACK95 | Code for One Version

orthogonal

matrix: Symmetric Eigenproblems (SEP)

orthonormal

basis: Nonsymmetric Eigenproblems (NEP) | Purpose | Purpose | Computational Routines for the
columns: Computational Routines for Orthogonal | Computational Routines for Orthogonal
rows: Computational Routines for Orthogonal | Computational Routines for Orthogonal

overdetermined system

packed

form

see packed storage

storage

Linear Equations | Matrix Storage Schemes

scheme: Example 1

partial pivoting

with row interchanges: General Linear Systems | General Linear Systems | General Linear Systems

pencil

see matrices

performance

pivot growth factor

Linear Equations | Example (from Program LA_GESVX_EXAMPLE)

complex general

band matrix: Purpose
dense matrix: Purpose

real general

band matrix: Purpose
dense matrix: Purpose

poor performance

Errors and Poor Performance | Errors and Poor Performance | Errors and Poor Performance

positive definite

precision

QL factorization

Example 2 | Computational Routines for Orthogonal

QR factorization

generalized (GQR): Generalized Linear Least Squares
with column pivoting: Computational Routines for Orthogonal

quasi-triangular matrix

Computational Routines for the | Computational Routines for the

quotient singular value decomposition

rank

deficient of matrix: Purpose
of argument: Design of the LAPACK95

README

reciprocal

condition number: Example (from Program LA_GESVX_EXAMPLE) | Example (from Program LA_PPSVX_EXAMPLE) | Example (from Program LA_PTSVX_EXAMPLE) | Example (from Program LA_GGESX_EXAMPLE) | Example (from Program LA_GGEVX_EXAMPLE)
condition numbers: Arguments
pivot growth factor: Example (from Program LA_GESVX_EXAMPLE)

reduction

to bidiagonal form: Computational Routines for the
to tridiagonal form: Example 1 (from Program | Computational Routines for the | Computational Routines for the | Computational Routines for the

reflectors

see elementary reflectors

regression, generalized linear

Example (from Program LA_GGLSE_EXAMPLE)

Relatively Robust Representation

see RRR

release_notes

LAPACK

reliability

see test suites

residual sum-of-squares

right

eigenvectors: Nonsymmetric Eigenproblems (NEP)
singular vectors: Example 2 (from Program

row

index

interchanges

Example 1

partial pivoting: General Linear Systems | General Linear Systems | General Linear Systems

RQ factorization

generalized (GRQ): Generalized Linear Least Squares

RRR

driver: Symmetric Eigenproblems (SEP)

scaling

Purpose

Schur

complex form

Purpose | Purpose

decomposition

see factorization | see factorization

factorization

complex: Nonsymmetric Eigenproblems (NEP)
generalized: Generalized Nonsymmetric Eigenproblems (GNEP) | Computational Routines for the | Computational Routines for the

form

generalized

complex form: Purpose | Purpose | Purpose | Purpose
left vectors: Purpose | Purpose | Purpose | Purpose
real form: Purpose | Purpose | Purpose | Purpose
right vectors: Purpose | Purpose | Purpose | Purpose
vectors: Generalized Nonsymmetric Eigenproblems (GNEP) | Purpose | Purpose | Purpose | Purpose

real form

Purpose | Purpose

vectors

selected cluster of eigenvalues

SEP

Generalized Nonsymmetric Eigenproblems (GNEP)

simple driver

Naming Scheme | Symmetric Eigenproblems (SEP) | Singular Value Decomposition (SVD)

single

shift: Computational Routines for the

singular

vectors

Singular Value Decomposition (SVD) | Purpose | Purpose | Computational Routines for the

compact form: Computational Routines for the
left: Singular Value Decomposition (SVD) | Purpose
right: Singular Value Decomposition (SVD) | Purpose | Purpose | Example 2 (from Program

singular value

Singular Value Decomposition (SVD) | Purpose | Purpose

bidiagonal factor: Computational Routines for the
decomposition: Singular Value Decomposition (SVD) | Purpose | Purpose
generalized: Generalized Singular Value Decomposition | Purpose
greatest: Arguments
problems: Problems that LAPACK95 can

singular value decomposition

Linear Least Squares (LLS)

generalized: Generalized Singular Value Decomposition | Generalized Singular Value Decomposition | Generalized Singular Value Decomposition
generalized, special cases: Generalized Singular Value Decomposition
quotient: Generalized Singular Value Decomposition

SLAMCH

LA_LAMCH Interfaces

spectral factorization

split Cholesky factorization

SRC (directory)

stability

Accuracy and Stability

standard

form

packed form: Computational Routines for the

storage

scheme

Matrix Storage Schemes

band: Example 1
packed: Example 1

subspaces

deflating: Generalized Nonsymmetric Eigenproblems (GNEP)
invariant: Generalized Nonsymmetric Eigenproblems (GNEP)

SUNPERF

support

Support | Support

SVD

see singular value decomposition | Computational Routines for the | Computational Routines for the

Sylvester

equation: Computational Routines for the
matrix equation: Computational Routines for the

symmetric

Problems that LAPACK95 can

eigenproblems (SEP): Symmetric Eigenproblems (SEP)
matrices: Matrix Storage Schemes

Symmetric Eigenvalue Problem

see SEP

system of linear equations

backward error

General Linear Systems | General Linear Systems | General Linear Systems | Symmetric/Hermitian Positive Definite Linear | Symmetric Indefinite Linear Systems

band storage: Symmetric/Hermitian Positive Definite Linear
packed storage: Symmetric/Hermitian Positive Definite Linear | Symmetric Indefinite Linear Systems
triangular band: Triangular Linear Systems
triangular matrix: Triangular Linear Systems
triangular packed: Triangular Linear Systems
tridiagonal: Symmetric/Hermitian Positive Definite Linear

condition number

General Linear Systems | General Linear Systems | Symmetric/Hermitian Positive Definite Linear

equilibration

band storage: Symmetric/Hermitian Positive Definite Linear
packed storage: Symmetric/Hermitian Positive Definite Linear

error bounds

General Linear Systems | General Linear Systems | General Linear Systems | Symmetric/Hermitian Positive Definite Linear | Symmetric Indefinite Linear Systems

band storage: Symmetric/Hermitian Positive Definite Linear
packed storage: Symmetric/Hermitian Positive Definite Linear | Symmetric Indefinite Linear Systems
triangular band: Triangular Linear Systems
triangular matrix: Triangular Linear Systems
triangular packed: Triangular Linear Systems
tridiagonal: Symmetric/Hermitian Positive Definite Linear

scaling

General Linear Systems | General Linear Systems | Symmetric/Hermitian Positive Definite Linear

band storage: Symmetric/Hermitian Positive Definite Linear
packed storage: Symmetric/Hermitian Positive Definite Linear

solution

General Linear Systems | General Linear Systems | General Linear Systems | Symmetric/Hermitian Positive Definite Linear

band storage: Symmetric/Hermitian Positive Definite Linear
packed storage: Symmetric/Hermitian Positive Definite Linear
symmetric indefinite: Symmetric Indefinite Linear Systems
symmetric indefinite, packed storage: Symmetric Indefinite Linear Systems
triangular band: Triangular Linear Systems
triangular matrix: Triangular Linear Systems
triangular packed: Triangular Linear Systems
tridiagonal: Symmetric/Hermitian Positive Definite Linear

test suites

LAPACK95 | LAPACK | Errors and Poor Performance

TESTING (directory)

TIMING (directory)

Computational Routines for the | Computational Routines for the

transformation

backward

equivalence

orthogonal: Computational Routines for the | Computational Routines for the
unitary: Computational Routines for the | Computational Routines for the

orthogonal

similarity

orthogonal: Computational Routines for the
orthogonal, band storage: Computational Routines for the
orthogonal, packed storage: Computational Routines for the
unitary: Computational Routines for the
unitary, band storage: Computational Routines for the
unitary, packed storage: Computational Routines for the

unitary

trapezoidal matrices

Performance and Troubleshooting

triangular

factor

Cholesky: Example 2 (from Program | Example 1 (from Program | Example 2 (from Program

matrices

Matrix Storage Schemes

tridiagonal

form: Levels of Routines
matrices: Matrix Storage Schemes

troubleshooting

underdetermined system

Linear Least Squares (LLS) | Linear Least Squares (LLS)

unitary

matrix: Symmetric Eigenproblems (SEP) | Example 1 (from Program

upper

bidiagonal

form: Computational Routines for the | Computational Routines for the
matrix: Computational Routines for the

Hessenberg matrix

Computational Routines for the | Computational Routines for the

trapezoidal matrix

Data Types and Precision | Data Types and Precision

triangular

form: Computational Routines for Orthogonal
matrices: Computational Routines for the

USE

F77_LAPACK

How to call an | Code for One Version

F95_LAPACK

How to call an

LA_AUXMOD

How to call an | Code for One Version

LA_PRECISION

How to call an | Code for One Version

DP: Data Types and Precision
SP: Data Types and Precision

USE statement

vendor supplied BLAS

BLAS

weighted linear least squares

Purpose

working precision (WP)

Example 2

zero-sized array