NAG Fortran Library

F08 – Least-squares and Eigenvalue Problems (LAPACK)

F08 Chapter Introduction

Routine
Name
Mark of
Introduction

Purpose
F08AEF (SGEQRF/DGEQRF) Example Text Example Data 16 QR factorization of real general rectangular matrix
F08AFF (SORGQR/DORGQR) Example Text Example Data 16 Form all or part of orthogonal Q from QR factorization determined by F08AEF (SGEQRF/DGEQRF) or F08BEF (SGEQPF/DGEQPF)
F08AGF (SORMQR/DORMQR) 16 Apply orthogonal transformation determined by F08AEF (SGEQRF/DGEQRF) or F08BEF (SGEQPF/DGEQPF)
F08AHF (SGELQF/DGELQF) Example Text Example Data 16 LQ factorization of real general rectangular matrix
F08AJF (SORGLQ/DORGLQ) Example Text Example Data 16 Form all or part of orthogonal Q from LQ factorization determined by F08AHF (SGELQF/DGELQF)
F08AKF (SORMLQ/DORMLQ) 16 Apply orthogonal transformation determined by F08AHF (SGELQF/DGELQF)
F08ASF (CGEQRF/ZGEQRF) Example Text Example Data 16 QR factorization of complex general rectangular matrix
F08ATF (CUNGQR/ZUNGQR) Example Text Example Data 16 Form all or part of unitary Q from QR factorization determined by F08ASF (CGEQRF/ZGEQRF) or F08BSF (CGEQPF/ZGEQPF)
F08AUF (CUNMQR/ZUNMQR) 16 Apply unitary transformation determined by F08ASF (CGEQRF/ZGEQRF) or F08BSF (CGEQPF/ZGEQPF)
F08AVF (CGELQF/ZGELQF) Example Text Example Data 16 LQ factorization of complex general rectangular matrix
F08AWF (CUNGLQ/ZUNGLQ) Example Text Example Data 16 Form all or part of unitary Q from LQ factorization determined by F08AVF (CGELQF/ZGELQF)
F08AXF (CUNMLQ/ZUNMLQ) 16 Apply unitary transformation determined by F08AVF (CGELQF/ZGELQF)
F08BEF (SGEQPF/DGEQPF) Example Text Example Data 16 QR factorization of real general rectangular matrix with column pivoting
F08BSF (CGEQPF/ZGEQPF) Example Text Example Data 16 QR factorization of complex general rectangular matrix with column pivoting
F08FCF (SSYEVD/DSYEVD) Example Text Example Data 19 All eigenvalues and optionally all eigenvectors of real symmetric matrix, using divide and conquer
F08FEF (SSYTRD/DSYTRD) Example Text Example Data 16 Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form
F08FFF (SORGTR/DORGTR) Example Text Example Data 16 Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08FEF (SSYTRD/DSYTRD)
F08FGF (SORMTR/DORMTR) Example Text Example Data 16 Apply orthogonal transformation determined by F08FEF (SSYTRD/DSYTRD)
F08FQF (CHEEVD/ZHEEVD) Example Text Example Data 19 All eigenvalues and optionally all eigenvectors of complex Hermitian matrix, using divide and conquer
F08FSF (CHETRD/ZHETRD) Example Text Example Data 16 Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form
F08FTF (CUNGTR/ZUNGTR) Example Text Example Data 16 Generate unitary transformation matrix from reduction to tridiagonal form determined by F08FSF (CHETRD/ZHETRD)
F08FUF (CUNMTR/ZUNMTR) Example Text Example Data 16 Apply unitary transformation matrix determined by F08FSF (CHETRD/ZHETRD)
F08GCF (SSPEVD/DSPEVD) Example Text Example Data 19 All eigenvalues and optionally all eigenvectors of real symmetric matrix, packed storage, using divide and conquer
F08GEF (SSPTRD/DSPTRD) Example Text Example Data 16 Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage
F08GFF (SOPGTR/DOPGTR) Example Text Example Data 16 Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08GEF (SSPTRD/DSPTRD)
F08GGF (SOPMTR/DOPMTR) Example Text Example Data 16 Apply orthogonal transformation determined by F08GEF (SSPTRD/DSPTRD)
F08GQF (CHPEVD/ZHPEVD) Example Text Example Data 19 All eigenvalues and optionally all eigenvectors of complex Hermitian matrix, packed storage, using divide and conquer
F08GSF (CHPTRD/ZHPTRD) Example Text Example Data 16 Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage
F08GTF (CUPGTR/ZUPGTR) Example Text Example Data 16 Generate unitary transformation matrix from reduction to tridiagonal form determined by F08GSF (CHPTRD/ZHPTRD)
F08GUF (CUPMTR/ZUPMTR) Example Text Example Data 16 Apply unitary transformation matrix determined by F08GSF (CHPTRD/ZHPTRD)
F08HCF (SSBEVD/DSBEVD) Example Text Example Data 19 All eigenvalues and optionally all eigenvectors of real symmetric band matrix, using divide and conquer
F08HEF (SSBTRD/DSBTRD) Example Text Example Data 16 Orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form
F08HQF (CHBEVD/ZHBEVD) Example Text Example Data 19 All eigenvalues and optionally all eigenvectors of complex Hermitian band matrix, using divide and conquer
F08HSF (CHBTRD/ZHBTRD) Example Text Example Data 16 Unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form
F08JCF (SSTEVD/DSTEVD) Example Text Example Data 19 All eigenvalues and optionally all eigenvectors of real symmetric tridiagonal matrix, using divide and conquer
F08JEF (SSTEQR/DSTEQR) Example Text Example Data 16 All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using implicit QL or QR
F08JFF (SSTERF/DSTERF) Example Text Example Data 16 All eigenvalues of real symmetric tridiagonal matrix, root-free variant of QL or QR
F08JGF (SPTEQR/DPTEQR) Example Text Example Data 16 All eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from real symmetric positive-definite matrix
F08JJF (SSTEBZ/DSTEBZ) 16 Selected eigenvalues of real symmetric tridiagonal matrix by bisection
F08JKF (SSTEIN/DSTEIN) 16 Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array
F08JSF (CSTEQR/ZSTEQR) 16 All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using implicit QL or QR
F08JUF (CPTEQR/ZPTEQR) Example Text Example Data 16 All eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from complex Hermitian positive-definite matrix
F08JXF (CSTEIN/ZSTEIN) 16 Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array
F08KEF (SGEBRD/DGEBRD) Example Text Example Data 16 Orthogonal reduction of real general rectangular matrix to bidiagonal form
F08KFF (SORGBR/DORGBR) Example Text Example Data 16 Generate orthogonal transformation matrices from reduction to bidiagonal form determined by F08KEF (SGEBRD/DGEBRD)
F08KGF (SORMBR/DORMBR) Example Text Example Data 16 Apply orthogonal transformations from reduction to bidiagonal form determined by F08KEF (SGEBRD/DGEBRD)
F08KSF (CGEBRD/ZGEBRD) Example Text Example Data 16 Unitary reduction of complex general rectangular matrix to bidiagonal form
F08KTF (CUNGBR/ZUNGBR) Example Text Example Data 16 Generate unitary transformation matrices from reduction to bidiagonal form determined by F08KSF (CGEBRD/ZGEBRD)
F08KUF (CUNMBR/ZUNMBR) Example Text Example Data 16 Apply unitary transformations from reduction to bidiagonal form determined by F08KSF (CGEBRD/ZGEBRD)
F08LEF (SGBBRD/DGBBRD) Example Text Example Data 19 Reduction of real rectangular band matrix to upper bidiagonal form
F08LSF (CGBBRD/ZGBBRD) Example Text Example Data 19 Reduction of complex rectangular band matrix to upper bidiagonal form
F08MEF (SBDSQR/DBDSQR) Example Text Example Data 16 SVD of real bidiagonal matrix reduced from real general matrix
F08MSF (CBDSQR/ZBDSQR) 16 SVD of real bidiagonal matrix reduced from complex general matrix
F08NEF (SGEHRD/DGEHRD) Example Text Example Data 16 Orthogonal reduction of real general matrix to upper Hessenberg form
F08NFF (SORGHR/DORGHR) Example Text Example Data 16 Generate orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (SGEHRD/DGEHRD)
F08NGF (SORMHR/DORMHR) Example Text Example Data 16 Apply orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (SGEHRD/DGEHRD)
F08NHF (SGEBAL/DGEBAL) Example Text Example Data 16 Balance real general matrix
F08NJF (SGEBAK/DGEBAK) 16 Transform eigenvectors of real balanced matrix to those of original matrix supplied to F08NHF (SGEBAL/DGEBAL)
F08NSF (CGEHRD/ZGEHRD) Example Text Example Data 16 Unitary reduction of complex general matrix to upper Hessenberg form
F08NTF (CUNGHR/ZUNGHR) Example Text Example Data 16 Generate unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (CGEHRD/ZGEHRD)
F08NUF (CUNMHR/ZUNMHR) Example Text Example Data 16 Apply unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (CGEHRD/ZGEHRD)
F08NVF (CGEBAL/ZGEBAL) Example Text Example Data 16 Balance complex general matrix
F08NWF (CGEBAK/ZGEBAK) 16 Transform eigenvectors of complex balanced matrix to those of original matrix supplied to F08NVF (CGEBAL/ZGEBAL)
F08PEF (SHSEQR/DHSEQR) Example Text Example Data 16 Eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix
F08PKF (SHSEIN/DHSEIN) 16 Selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration
F08PSF (CHSEQR/ZHSEQR) Example Text Example Data 16 Eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix
F08PXF (CHSEIN/ZHSEIN) 16 Selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration
F08QFF (STREXC/DTREXC) Example Text Example Data 16 Reorder Schur factorization of real matrix using orthogonal similarity transformation
F08QGF (STRSEN/DTRSEN) Example Text Example Data 16 Reorder Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
F08QHF (STRSYL/DTRSYL) Example Text Example Data 16 Solve real Sylvester matrix equation AX + XB = C, A and B are upper quasi-triangular or transposes
F08QKF (STREVC/DTREVC) 16 Left and right eigenvectors of real upper quasi-triangular matrix
F08QLF (STRSNA/DTRSNA) Example Text Example Data 16 Estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix
F08QTF (CTREXC/ZTREXC) Example Text Example Data 16 Reorder Schur factorization of complex matrix using unitary similarity transformation
F08QUF (CTRSEN/ZTRSEN) Example Text Example Data 16 Reorder Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
F08QVF (CTRSYL/ZTRSYL) Example Text Example Data 16 Solve complex Sylvester matrix equation AX + XB = C, A and B are upper triangular or conjugate-transposes
F08QXF (CTREVC/ZTREVC) 16 Left and right eigenvectors of complex upper triangular matrix
F08QYF (CTRSNA/ZTRSNA) Example Text Example Data 16 Estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix
F08SEF (SSYGST/DSYGST) Example Text Example Data 16 Reduction to standard form of real symmetric-definite generalized eigenproblem Ax = λ Bx, ABx = λ x or BAx = λ x, B factorized by F07FDF (SPOTRF/DPOTRF)
F08SSF (CHEGST/ZHEGST) Example Text Example Data 16 Reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax = λ Bx, ABx = λ x or BAx = λ x, B factorized by F07FRF (CPOTRF/ZPOTRF)
F08TEF (SSPGST/DSPGST) Example Text Example Data 16 Reduction to standard form of real symmetric-definite generalized eigenproblem Ax=λ Bx, ABx = λ x or BAx = λ x, packed storage, B factorized by F07GDF (SPPTRF/DPPTRF)
F08TSF (CHPGST/ZHPGST) Example Text Example Data 16 Reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax=λ Bx, ABx = λ x or BAx = λ x, packed storage, B factorized by F07GRF (CPPTRF/ZPPTRF)
F08UEF (SSBGST/DSBGST) Example Text Example Data 19 Reduction of real symmetric-definite banded generalized eigenproblem Ax = λ Bx to standard form Cy = λ y, such that C has the same bandwidth as A
F08UFF (SPBSTF/DPBSTF) 19 Computes a split Cholesky factorization of real symmetric positive-definite band matrix A
F08USF (CHBGST/ZHBGST) Example Text Example Data 19 Reduction of complex Hermitian-definite banded generalized eigenproblem Ax = λ Bx to standard form Cy = λ y, such that C has the same bandwidth as A
F08UTF (CPBSTF/ZPBSTF) 19 Computes a split Cholesky factorization of complex Hermitian positive-definite band matrix A
F08WEF (SGGHRD/DGGHRD) 20 Orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
F08WHF (SGGBAL/DGGBAL) 20 Balance a pair of real general matrices
F08WJF (SGGBAK/DGGBAK) 20 Transform eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to F08WHF (SGGBAL/DGGBAL)
F08WSF (CGGHRD/ZGGHRD) 20 Unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
F08WVF (CGGBAL/ZGGBAL) 20 Balance a pair of complex general matrices
F08WWF (CGGBAK/ZGGBAK) 20 Transform eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to F08WVF (CGGBAL/ZGGBAL)
F08XEF (SHGEQZ/DHGEQZ) Example Text Example Data 20 Eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices
F08XSF (CHGEQZ/ZHGEQZ) Example Text Example Data 20 Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex general matrices
F08YKF (STGEVC/DTGEVC) Example Text Example Data 20 Left and right eigenvectors of a pair of real upper quasi-triangular matrices
F08YXF (CTGEVC/ZTGEVC) Example Text Example Data 20 Left and right eigenvectors of a pair of complex upper triangular matrices

Table of Contents
© The Numerical Algorithms Group Ltd, Oxford UK. 2002