F08 Chapter Contents (PDF version)
F08 Chapter Introduction
NAG Library Manual

NAG Library Chapter Contents

F08 – Least Squares and Eigenvalue Problems (LAPACK)

F08 Chapter Introduction

Routine
Name
Mark of
Introduction

Purpose
F08AAF
Example Text
Example Data
21 DGELS
nagf_lapack_dgels
Solves an overdetermined or underdetermined real linear system
F08AEF
Example Text
Example Data
16 DGEQRF
nagf_lapack_dgeqrf
QR factorization of real general rectangular matrix
F08AFF
Example Text
Example Data
16 DORGQR
nagf_lapack_dorgqr
Form all or part of orthogonal Q from QR factorization determined by F08AEF (DGEQRF), F08BEF (DGEQPF) or F08BFF (DGEQP3)
F08AGF 16 DORMQR
nagf_lapack_dormqr
Apply orthogonal transformation determined by F08AEF (DGEQRF), F08BEF (DGEQPF) or F08BFF (DGEQP3)
F08AHF
Example Text
Example Data
16 DGELQF
nagf_lapack_dgelqf
LQ factorization of real general rectangular matrix
F08AJF
Example Text
Example Data
16 DORGLQ
nagf_lapack_dorglq
Form all or part of orthogonal Q from LQ factorization determined by F08AHF (DGELQF)
F08AKF 16 DORMLQ
nagf_lapack_dormlq
Apply orthogonal transformation determined by F08AHF (DGELQF)
F08ANF
Example Text
Example Data
21 ZGELS
nagf_lapack_zgels
Solves an overdetermined or underdetermined complex linear system
F08ASF
Example Text
Example Data
16 ZGEQRF
nagf_lapack_zgeqrf
QR factorization of complex general rectangular matrix
F08ATF
Example Text
Example Data
16 ZUNGQR
nagf_lapack_zungqr
Form all or part of unitary Q from QR factorization determined by F08ASF (ZGEQRF), F08BSF (ZGEQPF) or F08BTF (ZGEQP3)
F08AUF 16 ZUNMQR
nagf_lapack_zunmqr
Apply unitary transformation determined by F08ASF (ZGEQRF), F08BSF (ZGEQPF) or F08BTF (ZGEQP3)
F08AVF
Example Text
Example Data
16 ZGELQF
nagf_lapack_zgelqf
LQ factorization of complex general rectangular matrix
F08AWF
Example Text
Example Data
16 ZUNGLQ
nagf_lapack_zunglq
Form all or part of unitary Q from LQ factorization determined by F08AVF (ZGELQF)
F08AXF 16 ZUNMLQ
nagf_lapack_zunmlq
Apply unitary transformation determined by F08AVF (ZGELQF)
F08BAF
Example Text
Example Data
21 DGELSY
nagf_lapack_dgelsy
Computes the minimum-norm solution to a real linear least squares problem
F08BEF
Example Text
Example Data
16 DGEQPF
nagf_lapack_dgeqpf
QR factorization of real general rectangular matrix with column pivoting
F08BFF
Example Text
Example Data
21 DGEQP3
nagf_lapack_dgeqp3
QR factorization of real general rectangular matrix with column pivoting, using BLAS-3
F08BHF
Example Text
Example Data
21 DTZRZF
nagf_lapack_dtzrzf
Reduces a real upper trapezoidal matrix to upper triangular form
F08BKF 21 DORMRZ
nagf_lapack_dormrz
Apply orthogonal transformation determined by F08BHF (DTZRZF)
F08BNF
Example Text
Example Data
21 ZGELSY
nagf_lapack_zgelsy
Computes the minimum-norm solution to a complex linear least squares problem
F08BSF
Example Text
Example Data
16 ZGEQPF
nagf_lapack_zgeqpf
QR factorization of complex general rectangular matrix with column pivoting
F08BTF
Example Text
Example Data
21 ZGEQP3
nagf_lapack_zgeqp3
QR factorization of complex general rectangular matrix with column pivoting, using BLAS-3
F08BVF
Example Text
Example Data
21 ZTZRZF
nagf_lapack_ztzrzf
Reduces a complex upper trapezoidal matrix to upper triangular form
F08BXF 21 ZUNMRZ
nagf_lapack_zunmrz
Apply unitary transformation determined by F08BVF (ZTZRZF)
F08CEF
Example Text
Example Data
21 DGEQLF
nagf_lapack_dgeqlf
QL factorization of real general rectangular matrix
F08CFF
Example Text
Example Data
21 DORGQL
nagf_lapack_dorgql
Form all or part of orthogonal Q from QL factorization determined by F08CEF (DGEQLF)
F08CGF 21 DORMQL
nagf_lapack_dormql
Apply orthogonal transformation determined by F08CEF (DGEQLF)
F08CHF
Example Text
Example Data
21 DGERQF
nagf_lapack_dgerqf
RQ factorization of real general rectangular matrix
F08CJF
Example Text
Example Data
21 DORGRQ
nagf_lapack_dorgrq
Form all or part of orthogonal Q from RQ factorization determined by F08CHF (DGERQF)
F08CKF 21 DORMRQ
nagf_lapack_dormrq
Apply orthogonal transformation determined by F08CHF (DGERQF)
F08CSF
Example Text
Example Data
21 ZGEQLF
nagf_lapack_zgeqlf
QL factorization of complex general rectangular matrix
F08CTF
Example Text
Example Data
21 ZUNGQL
nagf_lapack_zungql
Form all or part of orthogonal Q from QL factorization determined by F08CSF (ZGEQLF)
F08CUF 21 ZUNMQL
nagf_lapack_zunmql
Apply unitary transformation determined by F08CSF (ZGEQLF)
F08CVF
Example Text
Example Data
21 ZGERQF
nagf_lapack_zgerqf
RQ factorization of complex general rectangular matrix
F08CWF
Example Text
Example Data
21 ZUNGRQ
nagf_lapack_zungrq
Form all or part of orthogonal Q from RQ factorization determined by F08CVF (ZGERQF)
F08CXF 21 ZUNMRQ
nagf_lapack_zunmrq
Apply unitary transformation determined by F08CVF (ZGERQF)
F08FAF
Example Text
Example Data
21 DSYEV
nagf_lapack_dsyev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix
F08FBF
Example Text
Example Data
21 DSYEVX
nagf_lapack_dsyevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix
F08FCF
Example Text
Example Data
19 DSYEVD
nagf_lapack_dsyevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer)
F08FDF
Example Text
Example Data
21 DSYEVR
nagf_lapack_dsyevr
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations)
F08FEF
Example Text
Example Data
16 DSYTRD
nagf_lapack_dsytrd
Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form
F08FFF
Example Text
Example Data
16 DORGTR
nagf_lapack_dorgtr
Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08FEF (DSYTRD)
F08FGF
Example Text
Example Data
16 DORMTR
nagf_lapack_dormtr
Apply orthogonal transformation determined by F08FEF (DSYTRD)
F08FLF 21 DDISNA
nagf_lapack_ddisna
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
F08FNF
Example Text
Example Data
21 ZHEEV
nagf_lapack_zheev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
F08FPF
Example Text
Example Data
21 ZHEEVX
nagf_lapack_zheevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
F08FQF
Example Text
Example Data
19 ZHEEVD
nagf_lapack_zheevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix (divide-and-conquer)
F08FRF
Example Text
Example Data
21 ZHEEVR
nagf_lapack_zheevr
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations)
F08FSF
Example Text
Example Data
16 ZHETRD
nagf_lapack_zhetrd
Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form
F08FTF
Example Text
Example Data
16 ZUNGTR
nagf_lapack_zungtr
Generate unitary transformation matrix from reduction to tridiagonal form determined by F08FSF (ZHETRD)
F08FUF
Example Text
Example Data
16 ZUNMTR
nagf_lapack_zunmtr
Apply unitary transformation matrix determined by F08FSF (ZHETRD)
F08GAF
Example Text
Example Data
21 DSPEV
nagf_lapack_dspev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
F08GBF
Example Text
Example Data
21 DSPEVX
nagf_lapack_dspevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
F08GCF
Example Text
Example Data
19 DSPEVD
nagf_lapack_dspevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix, packed storage (divide-and-conquer)
F08GEF
Example Text
Example Data
16 DSPTRD
nagf_lapack_dsptrd
Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage
F08GFF
Example Text
Example Data
16 DOPGTR
nagf_lapack_dopgtr
Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08GEF (DSPTRD)
F08GGF
Example Text
Example Data
16 DOPMTR
nagf_lapack_dopmtr
Apply orthogonal transformation determined by F08GEF (DSPTRD)
F08GNF
Example Text
Example Data
21 ZHPEV
nagf_lapack_zhpev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
F08GPF
Example Text
Example Data
21 ZHPEVX
nagf_lapack_zhpevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
F08GQF
Example Text
Example Data
19 ZHPEVD
nagf_lapack_zhpevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix, packed storage (divide-and-conquer)
F08GSF
Example Text
Example Data
16 ZHPTRD
nagf_lapack_zhptrd
Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage
F08GTF
Example Text
Example Data
16 ZUPGTR
nagf_lapack_zupgtr
Generate unitary transformation matrix from reduction to tridiagonal form determined by F08GSF (ZHPTRD)
F08GUF
Example Text
Example Data
16 ZUPMTR
nagf_lapack_zupmtr
Apply unitary transformation matrix determined by F08GSF (ZHPTRD)
F08HAF
Example Text
Example Data
21 DSBEV
nagf_lapack_dsbev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
F08HBF
Example Text
Example Data
21 DSBEVX
nagf_lapack_dsbevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
F08HCF
Example Text
Example Data
19 DSBEVD
nagf_lapack_dsbevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric band matrix (divide-and-conquer)
F08HEF
Example Text
Example Data
16 DSBTRD
nagf_lapack_dsbtrd
Orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form
F08HNF
Example Text
Example Data
21 ZHBEV
nagf_lapack_zhbev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
F08HPF
Example Text
Example Data
21 ZHBEVX
nagf_lapack_zhbevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
F08HQF
Example Text
Example Data
19 ZHBEVD
nagf_lapack_zhbevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian band matrix (divide-and-conquer)
F08HSF
Example Text
Example Data
16 ZHBTRD
nagf_lapack_zhbtrd
Unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form
F08JAF
Example Text
Example Data
21 DSTEV
nagf_lapack_dstev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
F08JBF
Example Text
Example Data
21 DSTEVX
nagf_lapack_dstevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
F08JCF
Example Text
Example Data
19 DSTEVD
nagf_lapack_dstevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer)
F08JDF
Example Text
Example Data
21 DSTEVR
nagf_lapack_dstevr
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations)
F08JEF
Example Text
Example Data
16 DSTEQR
nagf_lapack_dsteqr
All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using the implicit QL or QR algorithm
F08JFF
Example Text
Example Data
16 DSTERF
nagf_lapack_dsterf
All eigenvalues of real symmetric tridiagonal matrix, root-free variant of the QL or QR algorithm
F08JGF
Example Text
Example Data
16 DPTEQR
nagf_lapack_dpteqr
Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from real symmetric positive definite matrix
F08JHF
Example Text
Example Data
21 DSTEDC
nagf_lapack_dstedc
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a matrix reduced to this form (divide-and-conquer)
F08JJF 16 DSTEBZ
nagf_lapack_dstebz
Selected eigenvalues of real symmetric tridiagonal matrix by bisection
F08JKF 16 DSTEIN
nagf_lapack_dstein
Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array
F08JLF
Example Text
Example Data
21 DSTEGR
nagf_lapack_dstegr
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a symmetric matrix reduced to this form (Relatively Robust Representations)
F08JSF 16 ZSTEQR
nagf_lapack_zsteqr
All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using the implicit QL or QR algorithm
F08JUF
Example Text
Example Data
16 ZPTEQR
nagf_lapack_zpteqr
Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from complex Hermitian positive definite matrix
F08JVF
Example Text
Example Data
21 ZSTEDC
nagf_lapack_zstedc
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (divide-and-conquer)
F08JXF 16 ZSTEIN
nagf_lapack_zstein
Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array
F08JYF
Example Text
Example Data
21 ZSTEGR
nagf_lapack_zstegr
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (Relatively Robust Representations)
F08KAF
Example Text
Example Data
21 DGELSS
nagf_lapack_dgelss
Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition
F08KBF
Example Text
Example Data
21 DGESVD
nagf_lapack_dgesvd
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors
F08KCF
Example Text
Example Data
21 DGELSD
nagf_lapack_dgelsd
Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition (divide-and-conquer)
F08KDF
Example Text
Example Data
21 DGESDD
nagf_lapack_dgesdd
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
F08KEF
Example Text
Example Data
16 DGEBRD
nagf_lapack_dgebrd
Orthogonal reduction of real general rectangular matrix to bidiagonal form
F08KFF
Example Text
Example Data
16 DORGBR
nagf_lapack_dorgbr
Generate orthogonal transformation matrices from reduction to bidiagonal form determined by F08KEF (DGEBRD)
F08KGF
Example Text
Example Data
16 DORMBR
nagf_lapack_dormbr
Apply orthogonal transformations from reduction to bidiagonal form determined by F08KEF (DGEBRD)
F08KHF
Example Text
Example Data
23 DGEJSV
nagf_lapack_dgejsv
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (preconditioned Jacobi)
F08KJF
Example Text
Example Data
23 DGESVJ
nagf_lapack_dgesvj
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (fast Jacobi)
F08KNF
Example Text
Example Data
21 ZGELSS
nagf_lapack_zgelss
Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition
F08KPF
Example Text
Example Data
21 ZGESVD
nagf_lapack_zgesvd
Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors
F08KQF
Example Text
Example Data
21 ZGELSD
nagf_lapack_zgelsd
Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition (divide-and-conquer)
F08KRF
Example Text
Example Data
21 ZGESDD
nagf_lapack_zgesdd
Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
F08KSF
Example Text
Example Data
16 ZGEBRD
nagf_lapack_zgebrd
Unitary reduction of complex general rectangular matrix to bidiagonal form
F08KTF
Example Text
Example Data
16 ZUNGBR
nagf_lapack_zungbr
Generate unitary transformation matrices from reduction to bidiagonal form determined by F08KSF (ZGEBRD)
F08KUF
Example Text
Example Data
16 ZUNMBR
nagf_lapack_zunmbr
Apply unitary transformations from reduction to bidiagonal form determined by F08KSF (ZGEBRD)
F08LEF
Example Text
Example Data
19 DGBBRD
nagf_lapack_dgbbrd
Reduction of real rectangular band matrix to upper bidiagonal form
F08LSF
Example Text
Example Data
19 ZGBBRD
nagf_lapack_zgbbrd
Reduction of complex rectangular band matrix to upper bidiagonal form
F08MDF
Example Text
Example Data
21 DBDSDC
nagf_lapack_dbdsdc
Computes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divide-and-conquer)
F08MEF
Example Text
Example Data
16 DBDSQR
nagf_lapack_dbdsqr
SVD of real bidiagonal matrix reduced from real general matrix
F08MSF 16 ZBDSQR
nagf_lapack_zbdsqr
SVD of real bidiagonal matrix reduced from complex general matrix
F08NAF
Example Text
Example Data
21 DGEEV
nagf_lapack_dgeev
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix
F08NBF
Example Text
Example Data
21 DGEEVX
nagf_lapack_dgeevx
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
F08NEF
Example Text
Example Data
16 DGEHRD
nagf_lapack_dgehrd
Orthogonal reduction of real general matrix to upper Hessenberg form
F08NFF
Example Text
Example Data
16 DORGHR
nagf_lapack_dorghr
Generate orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (DGEHRD)
F08NGF
Example Text
Example Data
16 DORMHR
nagf_lapack_dormhr
Apply orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (DGEHRD)
F08NHF
Example Text
Example Data
16 DGEBAL
nagf_lapack_dgebal
Balance real general matrix
F08NJF 16 DGEBAK
nagf_lapack_dgebak
Transform eigenvectors of real balanced matrix to those of original matrix supplied to F08NHF (DGEBAL)
F08NNF
Example Text
Example Data
21 ZGEEV
nagf_lapack_zgeev
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix
F08NPF
Example Text
Example Data
21 ZGEEVX
nagf_lapack_zgeevx
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
F08NSF
Example Text
Example Data
16 ZGEHRD
nagf_lapack_zgehrd
Unitary reduction of complex general matrix to upper Hessenberg form
F08NTF
Example Text
Example Data
16 ZUNGHR
nagf_lapack_zunghr
Generate unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (ZGEHRD)
F08NUF
Example Text
Example Data
16 ZUNMHR
nagf_lapack_zunmhr
Apply unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (ZGEHRD)
F08NVF
Example Text
Example Data
16 ZGEBAL
nagf_lapack_zgebal
Balance complex general matrix
F08NWF 16 ZGEBAK
nagf_lapack_zgebak
Transform eigenvectors of complex balanced matrix to those of original matrix supplied to F08NVF (ZGEBAL)
F08PAF
Example Text
Example Data
21 DGEES
nagf_lapack_dgees
Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors
F08PBF
Example Text
Example Data
21 DGEESX
nagf_lapack_dgeesx
Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
F08PEF
Example Text
Example Data
16 DHSEQR
nagf_lapack_dhseqr
Computes the eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix
F08PKF 16 DHSEIN
nagf_lapack_dhsein
Selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration
F08PNF
Example Text
Example Data
21 ZGEES
nagf_lapack_zgees
Computes for complex square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors
F08PPF
Example Text
Example Data
21 ZGEESX
nagf_lapack_zgeesx
Computes for real square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
F08PSF
Example Text
Example Data
16 ZHSEQR
nagf_lapack_zhseqr
Computes the eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix
F08PXF 16 ZHSEIN
nagf_lapack_zhsein
Selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration
F08QFF
Example Text
Example Data
16 DTREXC
nagf_lapack_dtrexc
Reorder Schur factorization of real matrix using orthogonal similarity transformation
F08QGF
Example Text
Example Data
16 DTRSEN
nagf_lapack_dtrsen
Reorder Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
F08QHF
Example Text
Example Data
16 DTRSYL
nagf_lapack_dtrsyl
Solve real Sylvester matrix equation AX + XB = C, A and B are upper quasi-triangular or transposes
F08QKF 16 DTREVC
nagf_lapack_dtrevc
Left and right eigenvectors of real upper quasi-triangular matrix
F08QLF
Example Text
Example Data
16 DTRSNA
nagf_lapack_dtrsna
Estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix
F08QTF
Example Text
Example Data
16 ZTREXC
nagf_lapack_ztrexc
Reorder Schur factorization of complex matrix using unitary similarity transformation
F08QUF
Example Text
Example Data
16 ZTRSEN
nagf_lapack_ztrsen
Reorder Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
F08QVF
Example Text
Example Data
16 ZTRSYL
nagf_lapack_ztrsyl
Solve complex Sylvester matrix equation AX + XB = C, A and B are upper triangular or conjugate-transposes
F08QXF 16 ZTREVC
nagf_lapack_ztrevc
Left and right eigenvectors of complex upper triangular matrix
F08QYF
Example Text
Example Data
16 ZTRSNA
nagf_lapack_ztrsna
Estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix
F08SAF
Example Text
Example Data
21 DSYGV
nagf_lapack_dsygv
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
F08SBF
Example Text
Example Data
21 DSYGVX
nagf_lapack_dsygvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
F08SCF
Example Text
Example Data
21 DSYGVD
nagf_lapack_dsygvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer)
F08SEF
Example Text
Example Data
16 DSYGST
nagf_lapack_dsygst
Reduction to standard form of real symmetric-definite generalized eigenproblem Ax = λBx, ABx = λx or BAx = λx, B factorized by F07FDF (DPOTRF)
F08SNF
Example Text
Example Data
21 ZHEGV
nagf_lapack_zhegv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
F08SPF
Example Text
Example Data
21 ZHEGVX
nagf_lapack_zhegvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
F08SQF
Example Text
Example Data
21 ZHEGVD
nagf_lapack_zhegvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer)
F08SSF
Example Text
Example Data
16 ZHEGST
nagf_lapack_zhegst
Reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax = λBx, ABx = λx or BAx = λx, B factorized by F07FRF (ZPOTRF)
F08TAF
Example Text
Example Data
21 DSPGV
nagf_lapack_dspgv
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
F08TBF
Example Text
Example Data
21 DSPGVX
nagf_lapack_dspgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
F08TCF
Example Text
Example Data
21 DSPGVD
nagf_lapack_dspgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage (divide-and-conquer)
F08TEF
Example Text
Example Data
16 DSPGST
nagf_lapack_dspgst
Reduction to standard form of real symmetric-definite generalized eigenproblem Ax = λBx, ABx = λx or BAx = λx, packed storage, B factorized by F07GDF (DPPTRF)
F08TNF
Example Text
Example Data
21 ZHPGV
nagf_lapack_zhpgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
F08TPF
Example Text
Example Data
21 ZHPGVX
nagf_lapack_zhpgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
F08TQF
Example Text
Example Data
21 ZHPGVD
nagf_lapack_zhpgvd
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage (divide-and-conquer)
F08TSF
Example Text
Example Data
16 ZHPGST
nagf_lapack_zhpgst
Reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax = λBx, ABx = λx or BAx = λx, packed storage, B factorized by F07GRF (ZPPTRF)
F08UAF
Example Text
Example Data
21 DSBGV
nagf_lapack_dsbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
F08UBF
Example Text
Example Data
21 DSBGVX
nagf_lapack_dsbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
F08UCF
Example Text
Example Data
21 DSBGVD
nagf_lapack_dsbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem (divide-and-conquer)
F08UEF
Example Text
Example Data
19 DSBGST
nagf_lapack_dsbgst
Reduction of real symmetric-definite banded generalized eigenproblem Ax = λBx to standard form Cy = λy, such that C has the same bandwidth as A
F08UFF 19 DPBSTF
nagf_lapack_dpbstf
Computes a split Cholesky factorization of real symmetric positive definite band matrix A
F08UNF
Example Text
Example Data
21 ZHBGV
nagf_lapack_zhbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
F08UPF
Example Text
Example Data
21 ZHBGVX
nagf_lapack_zhbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
F08UQF
Example Text
Example Data
21 ZHBGVD
nagf_lapack_zhbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem (divide-and-conquer)
F08USF
Example Text
Example Data
19 ZHBGST
nagf_lapack_zhbgst
Reduction of complex Hermitian-definite banded generalized eigenproblem Ax = λBx to standard form Cy = λ y, such that C has the same bandwidth as A
F08UTF 19 ZPBSTF
nagf_lapack_zpbstf
Computes a split Cholesky factorization of complex Hermitian positive definite band matrix A
F08VAF
Example Text
Example Data
21 DGGSVD
nagf_lapack_dggsvd
Computes the generalized singular value decomposition of a real matrix pair
F08VEF
Example Text
Example Data
21 DGGSVP
nagf_lapack_dggsvp
Computes orthogonal matrices as processing steps for computing the generalized singular value decomposition of a real matrix pair
F08VNF
Example Text
Example Data
21 ZGGSVD
nagf_lapack_zggsvd
Computes the generalized singular value decomposition of a complex matrix pair
F08VSF
Example Text
Example Data
21 ZGGSVP
nagf_lapack_zggsvp
Computes orthogonal matrices as processing steps for computing the generalized singular value decomposition of a complex matrix pair
F08WAF
Example Text
Example Data
21 DGGEV
nagf_lapack_dggev
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
F08WBF
Example Text
Example Data
21 DGGEVX
nagf_lapack_dggevx
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
F08WEF 20 DGGHRD
nagf_lapack_dgghrd
Orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
F08WHF 20 DGGBAL
nagf_lapack_dggbal
Balance a pair of real general matrices
F08WJF 20 DGGBAK
nagf_lapack_dggbak
Transform eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to F08WHF (DGGBAL)
F08WNF
Example Text
Example Data
21 ZGGEV
nagf_lapack_zggev
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
F08WPF
Example Text
Example Data
21 ZGGEVX
nagf_lapack_zggevx
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors
F08WSF 20 ZGGHRD
nagf_lapack_zgghrd
Unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
F08WVF 20 ZGGBAL
nagf_lapack_zggbal
Balance a pair of complex general matrices
F08WWF 20 ZGGBAK
nagf_lapack_zggbak
Transform eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to F08WVF (ZGGBAL)
F08XAF
Example Text
Example Data
21 DGGES
nagf_lapack_dgges
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors
F08XBF
Example Text
Example Data
21 DGGESX
nagf_lapack_dggesx
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
F08XEF
Example Text
Example Data
20 DHGEQZ
nagf_lapack_dhgeqz
Eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices
F08XNF
Example Text
Example Data
21 ZGGES
nagf_lapack_zgges
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors
F08XPF
Example Text
Example Data
21 ZGGESX
nagf_lapack_zggesx
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues
F08XSF
Example Text
Example Data
20 ZHGEQZ
nagf_lapack_zhgeqz
Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex general matrices
F08YEF
Example Text
Example Data
21 DTGSJA
nagf_lapack_dtgsja
Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair
F08YFF
Example Text
Example Data
21 DTGEXC
nagf_lapack_dtgexc
Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation
F08YGF
Example Text
Example Data
21 DTGSEN
nagf_lapack_dtgsen
Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces
F08YHF
Example Text
Example Data
21 DTGSYL
nagf_lapack_dtgsyl
Solves the real-valued generalized Sylvester equation
F08YKF
Example Text
Example Data
20 DTGEVC
nagf_lapack_dtgevc
Left and right eigenvectors of a pair of real upper quasi-triangular matrices
F08YLF
Example Text
Example Data
21 DTGSNA
nagf_lapack_dtgsna
Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a real matrix pair in generalized real Schur canonical form
F08YSF
Example Text
Example Data
21 ZTGSJA
nagf_lapack_ztgsja
Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair
F08YTF
Example Text
Example Data
21 ZTGEXC
nagf_lapack_ztgexc
Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation
F08YUF
Example Text
Example Data
21 ZTGSEN
nagf_lapack_ztgsen
Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation, computes the generalized eigenvalues of the reordered pair and, optionally, computes the estimates of reciprocal condition numbers for eigenvalues and eigenspaces
F08YVF
Example Text
Example Data
21 ZTGSYL
nagf_lapack_ztgsyl
Solves the complex generalized Sylvester equation
F08YXF
Example Text
Example Data
20 ZTGEVC
nagf_lapack_ztgevc
Left and right eigenvectors of a pair of complex upper triangular matrices
F08YYF
Example Text
Example Data
21 ZTGSNA
nagf_lapack_ztgsna
Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a complex matrix pair in generalized Schur canonical form
F08ZAF
Example Text
Example Data
21 DGGLSE
nagf_lapack_dgglse
Solves the real linear equality-constrained least squares (LSE) problem
F08ZBF
Example Text
Example Data
21 DGGGLM
nagf_lapack_dggglm
Solves a real general Gauss–Markov linear model (GLM) problem
F08ZEF
Example Text
Example Data
21 DGGQRF
nagf_lapack_dggqrf
Computes a generalized QR factorization of a real matrix pair
F08ZFF
Example Text
Example Data
21 DGGRQF
nagf_lapack_dggrqf
Computes a generalized RQ factorization of a real matrix pair
F08ZNF
Example Text
Example Data
21 ZGGLSE
nagf_lapack_zgglse
Solves the complex linear equality-constrained least squares (LSE) problem
F08ZPF
Example Text
Example Data
21 ZGGGLM
nagf_lapack_zggglm
Solves a complex general Gauss–Markov linear model (GLM) problem
F08ZSF
Example Text
Example Data
21 ZGGQRF
nagf_lapack_zggqrf
Computes a generalized QR factorization of a complex matrix pair
F08ZTF
Example Text
Example Data
21 ZGGRQF
nagf_lapack_zggrqf
Computes a generalized RQ factorization of a complex matrix pair

F08 Chapter Contents (PDF version)
F08 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2011