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 – a description of the Chapter and an overview of the algorithms available

Routine
Name
Mark of
Introduction

Purpose
F08AAF (DGELS)
Example Text
Example Data
21 DGELS
nagf_lapack_dgels
Solves a real linear least squares problem of full rank
F08ABF (DGEQRT)
Example Text
Example Data
25 DGEQRT
nagf_lapack_dgeqrt
Performs a QR factorization of real general rectangular matrix, with explicit blocking
F08ACF (DGEMQRT) 25 DGEMQRT
nagf_lapack_dgemqrt
Applies the orthogonal transformation determined by F08ABF (DGEQRT)
F08AEF (DGEQRF)
Example Text
Example Data
16 DGEQRF
nagf_lapack_dgeqrf
Performs a QR factorization of real general rectangular matrix
F08AFF (DORGQR)
Example Text
Example Data
16 DORGQR
nagf_lapack_dorgqr
Forms all or part of orthogonal Q from QR factorization determined by F08AEF (DGEQRF), F08BEF (DGEQPF) or F08BFF (DGEQP3)
F08AGF (DORMQR) 16 DORMQR
nagf_lapack_dormqr
Applies an orthogonal transformation determined by F08AEF (DGEQRF), F08BEF (DGEQPF) or F08BFF (DGEQP3)
F08AHF (DGELQF)
Example Text
Example Data
16 DGELQF
nagf_lapack_dgelqf
Performs a LQ factorization of real general rectangular matrix
F08AJF (DORGLQ)
Example Text
Example Data
16 DORGLQ
nagf_lapack_dorglq
Forms all or part of orthogonal Q from LQ factorization determined by F08AHF (DGELQF)
F08AKF (DORMLQ) 16 DORMLQ
nagf_lapack_dormlq
Applies the orthogonal transformation determined by F08AHF (DGELQF)
F08ANF (ZGELS)
Example Text
Example Data
21 ZGELS
nagf_lapack_zgels
Solves a complex linear least problem of full rank
F08APF (ZGEQRT)
Example Text
Example Data
25 ZGEQRT
nagf_lapack_zgeqrt
Performs a QR factorization of complex general rectangular matrix using recursive algorithm
F08AQF (ZGEMQRT) 25 ZGEMQRT
nagf_lapack_zgemqrt
Applies the unitary transformation determined by F08APF (ZGEQRT)
F08ASF (ZGEQRF)
Example Text
Example Data
16 ZGEQRF
nagf_lapack_zgeqrf
Performs a QR factorization of complex general rectangular matrix
F08ATF (ZUNGQR)
Example Text
Example Data
16 ZUNGQR
nagf_lapack_zungqr
Forms all or part of unitary Q from QR factorization determined by F08ASF (ZGEQRF), F08BSF (ZGEQPF) or F08BTF (ZGEQP3)
F08AUF (ZUNMQR) 16 ZUNMQR
nagf_lapack_zunmqr
Applies a unitary transformation determined by F08ASF (ZGEQRF), F08BSF (ZGEQPF) or F08BTF (ZGEQP3)
F08AVF (ZGELQF)
Example Text
Example Data
16 ZGELQF
nagf_lapack_zgelqf
Performs a LQ factorization of complex general rectangular matrix
F08AWF (ZUNGLQ)
Example Text
Example Data
16 ZUNGLQ
nagf_lapack_zunglq
Forms all or part of unitary Q from LQ factorization determined by F08AVF (ZGELQF)
F08AXF (ZUNMLQ) 16 ZUNMLQ
nagf_lapack_zunmlq
Applies the unitary transformation determined by F08AVF (ZGELQF)
F08BAF (DGELSY)
Example Text
Example Data
21 DGELSY
nagf_lapack_dgelsy
Computes the minimum-norm solution to a real linear least squares problem
F08BBF (DTPQRT)
Example Text
Example Data
25 DTPQRT
nagf_lapack_dtpqrt
QR factorization of real general triangular-pentagonal matrix
F08BCF (DTPMQRT) 25 DTPMQRT
nagf_lapack_dtpmqrt
Applies the orthogonal transformation determined by F08BBF (DTPQRT)
F08BEF (DGEQPF)
Example Text
Example Data
16 DGEQPF
nagf_lapack_dgeqpf
QR factorization, with column pivoting, of real general rectangular matrix
F08BFF (DGEQP3)
Example Text
Example Data
21 DGEQP3
nagf_lapack_dgeqp3
QR factorization, with column pivoting, using BLAS-3, of real general rectangular matrix
F08BHF (DTZRZF)
Example Text
Example Data
21 DTZRZF
nagf_lapack_dtzrzf
Reduces a real upper trapezoidal matrix to upper triangular form
F08BKF (DORMRZ) 21 DORMRZ
nagf_lapack_dormrz
Applies the orthogonal transformation determined by F08BHF (DTZRZF)
F08BNF (ZGELSY)
Example Text
Example Data
21 ZGELSY
nagf_lapack_zgelsy
Computes the minimum-norm solution to a complex linear least squares problem
F08BPF (ZTPQRT)
Example Text
Example Data
25 ZTPQRT
nagf_lapack_ztpqrt
QR factorization of complex triangular-pentagonal matrix
F08BQF (ZTPMQRT) 25 ZTPMQRT
nagf_lapack_ztpmqrt
Applies the unitary transformation determined by F08BPF (ZTPQRT)
F08BSF (ZGEQPF)
Example Text
Example Data
16 ZGEQPF
nagf_lapack_zgeqpf
QR factorization, with column pivoting, of complex general rectangular matrix
F08BTF (ZGEQP3)
Example Text
Example Data
21 ZGEQP3
nagf_lapack_zgeqp3
QR factorization, with column pivoting, using BLAS-3, of complex general rectangular matrix
F08BVF (ZTZRZF)
Example Text
Example Data
21 ZTZRZF
nagf_lapack_ztzrzf
Reduces a complex upper trapezoidal matrix to upper triangular form
F08BXF (ZUNMRZ) 21 ZUNMRZ
nagf_lapack_zunmrz
Applies the unitary transformation determined by F08BVF (ZTZRZF)
F08CEF (DGEQLF)
Example Text
Example Data
21 DGEQLF
nagf_lapack_dgeqlf
QL factorization of real general rectangular matrix
F08CFF (DORGQL)
Example Text
Example Data
21 DORGQL
nagf_lapack_dorgql
Form all or part of orthogonal Q from QL factorization determined by F08CEF (DGEQLF)
F08CGF (DORMQL) 21 DORMQL
nagf_lapack_dormql
Applies the orthogonal transformation determined by F08CEF (DGEQLF)
F08CHF (DGERQF)
Example Text
Example Data
21 DGERQF
nagf_lapack_dgerqf
RQ factorization of real general rectangular matrix
F08CJF (DORGRQ)
Example Text
Example Data
21 DORGRQ
nagf_lapack_dorgrq
Form all or part of orthogonal Q from RQ factorization determined by F08CHF (DGERQF)
F08CKF (DORMRQ) 21 DORMRQ
nagf_lapack_dormrq
Applies the orthogonal transformation determined by F08CHF (DGERQF)
F08CSF (ZGEQLF)
Example Text
Example Data
21 ZGEQLF
nagf_lapack_zgeqlf
QL factorization of complex general rectangular matrix
F08CTF (ZUNGQL)
Example Text
Example Data
21 ZUNGQL
nagf_lapack_zungql
Form all or part of unitary Q from QL factorization determined by F08CSF (ZGEQLF)
F08CUF (ZUNMQL) 21 ZUNMQL
nagf_lapack_zunmql
Applies the unitary transformation determined by F08CSF (ZGEQLF)
F08CVF (ZGERQF)
Example Text
Example Data
21 ZGERQF
nagf_lapack_zgerqf
RQ factorization of complex general rectangular matrix
F08CWF (ZUNGRQ)
Example Text
Example Data
21 ZUNGRQ
nagf_lapack_zungrq
Form all or part of unitary Q from RQ factorization determined by F08CVF (ZGERQF)
F08CXF (ZUNMRQ) 21 ZUNMRQ
nagf_lapack_zunmrq
Applies the unitary transformation determined by F08CVF (ZGERQF)
F08FAF (DSYEV)
Example Text
Example Data
21 DSYEV
nagf_lapack_dsyev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix
F08FBF (DSYEVX)
Example Text
Example Data
21 DSYEVX
nagf_lapack_dsyevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix
F08FCF (DSYEVD)
Example Text
Example Data
19 DSYEVD
nagf_lapack_dsyevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer)
F08FDF (DSYEVR)
Example Text
Example Data
21 DSYEVR
nagf_lapack_dsyevr
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations)
F08FEF (DSYTRD)
Example Text
Example Data
16 DSYTRD
nagf_lapack_dsytrd
Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form
F08FFF (DORGTR)
Example Text
Example Data
16 DORGTR
nagf_lapack_dorgtr
Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08FEF (DSYTRD)
F08FGF (DORMTR)
Example Text
Example Data
16 DORMTR
nagf_lapack_dormtr
Applies the orthogonal transformation determined by F08FEF (DSYTRD)
F08FLF (DDISNA) 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 (ZHEEV)
Example Text
Example Data
21 ZHEEV
nagf_lapack_zheev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
F08FPF (ZHEEVX)
Example Text
Example Data
21 ZHEEVX
nagf_lapack_zheevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
F08FQF (ZHEEVD)
Example Text
Example Data
19 ZHEEVD
nagf_lapack_zheevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix (divide-and-conquer)
F08FRF (ZHEEVR)
Example Text
Example Data
21 ZHEEVR
nagf_lapack_zheevr
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations)
F08FSF (ZHETRD)
Example Text
Example Data
16 ZHETRD
nagf_lapack_zhetrd
Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form
F08FTF (ZUNGTR)
Example Text
Example Data
16 ZUNGTR
nagf_lapack_zungtr
Generate unitary transformation matrix from reduction to tridiagonal form determined by F08FSF (ZHETRD)
F08FUF (ZUNMTR)
Example Text
Example Data
16 ZUNMTR
nagf_lapack_zunmtr
Applies the unitary transformation matrix determined by F08FSF (ZHETRD)
F08GAF (DSPEV)
Example Text
Example Data
21 DSPEV
nagf_lapack_dspev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
F08GBF (DSPEVX)
Example Text
Example Data
21 DSPEVX
nagf_lapack_dspevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
F08GCF (DSPEVD)
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 or Pal–Walker–Kahan variant of the QL or QR algorithm)
F08GEF (DSPTRD)
Example Text
Example Data
16 DSPTRD
nagf_lapack_dsptrd
Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage
F08GFF (DOPGTR)
Example Text
Example Data
16 DOPGTR
nagf_lapack_dopgtr
Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08GEF (DSPTRD)
F08GGF (DOPMTR)
Example Text
Example Data
16 DOPMTR
nagf_lapack_dopmtr
Applies the orthogonal transformation determined by F08GEF (DSPTRD)
F08GNF (ZHPEV)
Example Text
Example Data
21 ZHPEV
nagf_lapack_zhpev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
F08GPF (ZHPEVX)
Example Text
Example Data
21 ZHPEVX
nagf_lapack_zhpevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
F08GQF (ZHPEVD)
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 or Pal–Walker–Kahan variant of the QL or QR algorithm)
F08GSF (ZHPTRD)
Example Text
Example Data
16 ZHPTRD
nagf_lapack_zhptrd
Performs a unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage
F08GTF (ZUPGTR)
Example Text
Example Data
16 ZUPGTR
nagf_lapack_zupgtr
Generates a unitary transformation matrix from reduction to tridiagonal form determined by F08GSF (ZHPTRD)
F08GUF (ZUPMTR)
Example Text
Example Data
16 ZUPMTR
nagf_lapack_zupmtr
Applies the unitary transformation matrix determined by F08GSF (ZHPTRD)
F08HAF (DSBEV)
Example Text
Example Data
21 DSBEV
nagf_lapack_dsbev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
F08HBF (DSBEVX)
Example Text
Example Data
21 DSBEVX
nagf_lapack_dsbevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
F08HCF (DSBEVD)
Example Text
Example Data
19 DSBEVD
nagf_lapack_dsbevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric band matrix (divide-and-conquer or Pal–Walker–Kahan variant of the QL or QR algorithm)
F08HEF (DSBTRD)
Example Text
Example Data
16 DSBTRD
nagf_lapack_dsbtrd
Performs an orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form
F08HNF (ZHBEV)
Example Text
Example Data
21 ZHBEV
nagf_lapack_zhbev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
F08HPF (ZHBEVX)
Example Text
Example Data
21 ZHBEVX
nagf_lapack_zhbevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
F08HQF (ZHBEVD)
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 (ZHBTRD)
Example Text
Example Data
16 ZHBTRD
nagf_lapack_zhbtrd
Performs a unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form
F08JAF (DSTEV)
Example Text
Example Data
21 DSTEV
nagf_lapack_dstev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
F08JBF (DSTEVX)
Example Text
Example Data
21 DSTEVX
nagf_lapack_dstevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
F08JCF (DSTEVD)
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 (DSTEVR)
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 (DSTEQR)
Example Text
Example Data
16 DSTEQR
nagf_lapack_dsteqr
Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using the implicit QL or QR algorithm
F08JFF (DSTERF)
Example Text
Example Data
16 DSTERF
nagf_lapack_dsterf
Computes all eigenvalues of real symmetric tridiagonal matrix, root-free variant of the QL or QR algorithm
F08JGF (DPTEQR)
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 (DSTEDC)
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 (DSTEBZ) 16 DSTEBZ
nagf_lapack_dstebz
Computes selected eigenvalues of real symmetric tridiagonal matrix by bisection
F08JKF (DSTEIN) 16 DSTEIN
nagf_lapack_dstein
Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array
F08JLF (DSTEGR)
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 (ZSTEQR) 16 ZSTEQR
nagf_lapack_zsteqr
Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using the implicit QL or QR algorithm
F08JUF (ZPTEQR)
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 (ZSTEDC)
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 (ZSTEIN) 16 ZSTEIN
nagf_lapack_zstein
Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array
F08JYF (ZSTEGR)
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 (DGELSS)
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 (DGESVD)
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 (DGELSD)
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 (DGESDD)
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 (DGEBRD)
Example Text
Example Data
16 DGEBRD
nagf_lapack_dgebrd
Performs an orthogonal reduction of real general rectangular matrix to bidiagonal form
F08KFF (DORGBR)
Example Text
Example Data
16 DORGBR
nagf_lapack_dorgbr
Generates an orthogonal transformation matrices from reduction to bidiagonal form determined by F08KEF (DGEBRD)
F08KGF (DORMBR)
Example Text
Example Data
16 DORMBR
nagf_lapack_dormbr
Applies the orthogonal transformations from reduction to bidiagonal form determined by F08KEF (DGEBRD)
F08KHF (DGEJSV)
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 (DGESVJ)
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 (ZGELSS)
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 (ZGESVD)
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 (ZGELSD)
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 (ZGESDD)
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 (ZGEBRD)
Example Text
Example Data
16 ZGEBRD
nagf_lapack_zgebrd
Performs a unitary reduction of complex general rectangular matrix to bidiagonal form
F08KTF (ZUNGBR)
Example Text
Example Data
16 ZUNGBR
nagf_lapack_zungbr
Generates unitary transformation matrices from the reduction to bidiagonal form determined by F08KSF (ZGEBRD)
F08KUF (ZUNMBR)
Example Text
Example Data
16 ZUNMBR
nagf_lapack_zunmbr
Applies the unitary transformations from reduction to bidiagonal form determined by F08KSF (ZGEBRD)
F08LEF (DGBBRD)
Example Text
Example Data
19 DGBBRD
nagf_lapack_dgbbrd
Performs a reduction of real rectangular band matrix to upper bidiagonal form
F08LSF (ZGBBRD)
Example Text
Example Data
19 ZGBBRD
nagf_lapack_zgbbrd
Reduction of complex rectangular band matrix to upper bidiagonal form
F08MDF (DBDSDC)
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 (DBDSQR)
Example Text
Example Data
16 DBDSQR
nagf_lapack_dbdsqr
Performs an SVD of real bidiagonal matrix reduced from real general matrix
F08MSF (ZBDSQR) 16 ZBDSQR
nagf_lapack_zbdsqr
Performs an SVD of real bidiagonal matrix reduced from complex general matrix
F08NAF (DGEEV)
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 (DGEEVX)
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 (DGEHRD)
Example Text
Example Data
16 DGEHRD
nagf_lapack_dgehrd
Performs an orthogonal reduction of real general matrix to upper Hessenberg form
F08NFF (DORGHR)
Example Text
Example Data
16 DORGHR
nagf_lapack_dorghr
Generates an orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (DGEHRD)
F08NGF (DORMHR)
Example Text
Example Data
16 DORMHR
nagf_lapack_dormhr
Applies the orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (DGEHRD)
F08NHF (DGEBAL)
Example Text
Example Data
16 DGEBAL
nagf_lapack_dgebal
Balances a real general matrix
F08NJF (DGEBAK) 16 DGEBAK
nagf_lapack_dgebak
Transforms eigenvectors of real balanced matrix to those of original matrix supplied to F08NHF (DGEBAL)
F08NNF (ZGEEV)
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 (ZGEEVX)
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 (ZGEHRD)
Example Text
Example Data
16 ZGEHRD
nagf_lapack_zgehrd
Performs a unitary reduction of complex general matrix to upper Hessenberg form
F08NTF (ZUNGHR)
Example Text
Example Data
16 ZUNGHR
nagf_lapack_zunghr
Generates a unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (ZGEHRD)
F08NUF (ZUNMHR)
Example Text
Example Data
16 ZUNMHR
nagf_lapack_zunmhr
Applies the unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (ZGEHRD)
F08NVF (ZGEBAL)
Example Text
Example Data
16 ZGEBAL
nagf_lapack_zgebal
Balances a complex general matrix
F08NWF (ZGEBAK) 16 ZGEBAK
nagf_lapack_zgebak
Transforms eigenvectors of complex balanced matrix to those of original matrix supplied to F08NVF (ZGEBAL)
F08PAF (DGEES)
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 (DGEESX)
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 (DHSEQR)
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 (DHSEIN) 16 DHSEIN
nagf_lapack_dhsein
Computes selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration
F08PNF (ZGEES)
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 (ZGEESX)
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 computes a reciprocal condition number for the average of the selected eigenvalues and for the right invariant subspace corresponding to these eigenvalues
F08PSF (ZHSEQR)
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 (ZHSEIN) 16 ZHSEIN
nagf_lapack_zhsein
Computes selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration
F08QFF (DTREXC)
Example Text
Example Data
16 DTREXC
nagf_lapack_dtrexc
Reorders a Schur factorization of real matrix using orthogonal similarity transformation
F08QGF (DTRSEN)
Example Text
Example Data
16 DTRSEN
nagf_lapack_dtrsen
Reorders a Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
F08QHF (DTRSYL)
Example Text
Example Data
16 DTRSYL
nagf_lapack_dtrsyl
Solves the real Sylvester matrix equation AX+XB=C, A and B are upper quasi-triangular or transposes
F08QKF (DTREVC) 16 DTREVC
nagf_lapack_dtrevc
Computes left and right eigenvectors of real upper quasi-triangular matrix
F08QLF (DTRSNA)
Example Text
Example Data
16 DTRSNA
nagf_lapack_dtrsna
Computes estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix
F08QTF (ZTREXC)
Example Text
Example Data
16 ZTREXC
nagf_lapack_ztrexc
Reorders a Schur factorization of complex matrix using unitary similarity transformation
F08QUF (ZTRSEN)
Example Text
Example Data
16 ZTRSEN
nagf_lapack_ztrsen
Reorders a Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
F08QVF (ZTRSYL)
Example Text
Example Data
16 ZTRSYL
nagf_lapack_ztrsyl
Solves the complex Sylvester matrix equation AX+XB=C, A and B are upper triangular or conjugate-transposes
F08QXF (ZTREVC) 16 ZTREVC
nagf_lapack_ztrevc
Computes left and right eigenvectors of complex upper triangular matrix
F08QYF (ZTRSNA)
Example Text
Example Data
16 ZTRSNA
nagf_lapack_ztrsna
Computes estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix
F08RAF (DORCSD)
Example Text
Example Data
25 DORCSD
nagf_lapack_dorcsd
Computes the CS decomposition of an orthogonal matrix partitioned into four real submatrices
F08RNF (ZUNCSD)
Example Text
Example Data
25 ZUNCSD
nagf_lapack_zuncsd
Computes the CS decomposition of a unitary matrix partitioned into four complex submatrices
F08SAF (DSYGV)
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 (DSYGVX)
Example Text
Example Data
21 DSYGVX
nagf_lapack_dsygvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
F08SCF (DSYGVD)
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 (DSYGST)
Example Text
Example Data
16 DSYGST
nagf_lapack_dsygst
Performs a reduction to standard form of real symmetric-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, B factorized by F07FDF (DPOTRF)
F08SNF (ZHEGV)
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 (ZHEGVX)
Example Text
Example Data
21 ZHEGVX
nagf_lapack_zhegvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
F08SQF (ZHEGVD)
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 (ZHEGST)
Example Text
Example Data
16 ZHEGST
nagf_lapack_zhegst
Performs a reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, B factorized by F07FRF (ZPOTRF)
F08TAF (DSPGV)
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 (DSPGVX)
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 (DSPGVD)
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 (DSPGST)
Example Text
Example Data
16 DSPGST
nagf_lapack_dspgst
Performs a 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 (ZHPGV)
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 (ZHPGVX)
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 (ZHPGVD)
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 (ZHPGST)
Example Text
Example Data
16 ZHPGST
nagf_lapack_zhpgst
Performs a 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 (DSBGV)
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 (DSBGVX)
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 (DSBGVD)
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 (DSBGST)
Example Text
Example Data
19 DSBGST
nagf_lapack_dsbgst
Performs a 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 (DPBSTF) 19 DPBSTF
nagf_lapack_dpbstf
Computes a split Cholesky factorization of real symmetric positive definite band matrix A
F08UNF (ZHBGV)
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 (ZHBGVX)
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 (ZHBGVD)
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 (ZHBGST)
Example Text
Example Data
19 ZHBGST
nagf_lapack_zhbgst
Performs a 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 (ZPBSTF) 19 ZPBSTF
nagf_lapack_zpbstf
Computes a split Cholesky factorization of complex Hermitian positive definite band matrix A
F08VAF (DGGSVD)
Example Text
Example Data
21 DGGSVD
nagf_lapack_dggsvd
Computes the generalized singular value decomposition of a real matrix pair
F08VCF (DGGSVD3)
Example Text
Example Data
26 DGGSVD3
nagf_lapack_dggsvd3
Computes, using BLAS-3, the generalized singular value decomposition of a real matrix pair
F08VEF (DGGSVP)
Example Text
Example Data
21 DGGSVP
nagf_lapack_dggsvp
Produces orthogonal matrices that simultaneously reduce the m by n matrix A and the p by n matrix B to upper triangular form
F08VGF (DGGSVP3)
Example Text
Example Data
26 DGGSVP3
nagf_lapack_dggsvp3
Produces orthogonal matrices, using BLAS-3, that simultaneously reduce the m by n matrix A and the p by n matrix B to upper triangular form
F08VNF (ZGGSVD)
Example Text
Example Data
21 ZGGSVD
nagf_lapack_zggsvd
Computes the generalized singular value decomposition of a complex matrix pair
F08VQF (ZGGSVD3)
Example Text
Example Data
26 ZGGSVD3
nagf_lapack_zggsvd3
Computes, using BLAS-3, the generalized singular value decomposition of a complex matrix pair
F08VSF (ZGGSVP)
Example Text
Example Data
21 ZGGSVP
nagf_lapack_zggsvp
Produces unitary matrices that simultaneously reduce the complex, m by n, matrix A and the complex, p by n, matrix B to upper triangular form
F08VUF (ZGGSVP3)
Example Text
Example Data
26 ZGGSVP3
nagf_lapack_zggsvp3
Produces unitary matrices, using BLAS-3, that simultaneously reduce the complex, m by n, matrix A and the complex, p by n, matrix B to upper triangular form
F08WAF (DGGEV)
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 (DGGEVX)
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
F08WCF (DGGEV3)
Example Text
Example Data
26 DGGEV3
nagf_lapack_dggev3
Computes, for a real nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
F08WEF (DGGHRD) 20 DGGHRD
nagf_lapack_dgghrd
Performs an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
F08WFF (DGGHD3) 26 DGGHD3
nagf_lapack_dgghd3
Performs, using BLAS-3, an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
F08WHF (DGGBAL) 20 DGGBAL
nagf_lapack_dggbal
Balances a pair of real, square, matrices
F08WJF (DGGBAK) 20 DGGBAK
nagf_lapack_dggbak
Transforms eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to F08WHF (DGGBAL)
F08WNF (ZGGEV)
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 (ZGGEVX)
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
F08WQF (ZGGEV3)
Example Text
Example Data
26 ZGGEV3
nagf_lapack_zggev3
Computes, for a complex nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
F08WSF (ZGGHRD) 20 ZGGHRD
nagf_lapack_zgghrd
Performs a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
F08WTF (ZGGHD3) 26 ZGGHD3
nagf_lapack_zgghd3
Performs, using BLAS-3, a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
F08WVF (ZGGBAL) 20 ZGGBAL
nagf_lapack_zggbal
Balances a pair of complex, square, matrices
F08WWF (ZGGBAK) 20 ZGGBAK
nagf_lapack_zggbak
Transforms eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to F08WVF (ZGGBAL)
F08XAF (DGGES)
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 (DGGESX)
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
F08XCF (DGGES3)
Example Text
Example Data
26 DGGES3
nagf_lapack_dgges3
Computes, for a real nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors
F08XEF (DHGEQZ)
Example Text
Example Data
20 DHGEQZ
nagf_lapack_dhgeqz
Computes eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices
F08XNF (ZGGES)
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 (ZGGESX)
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
F08XQF (ZGGES3)
Example Text
Example Data
26 ZGGES3
nagf_lapack_zgges3
Computes, for a complex nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors
F08XSF (ZHGEQZ)
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, square, matrices
F08YEF (DTGSJA)
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 (DTGEXC)
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 (DTGSEN)
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 (DTGSYL)
Example Text
Example Data
21 DTGSYL
nagf_lapack_dtgsyl
Solves the real-valued, generalized, quasi-trangular, Sylvester equation
F08YKF (DTGEVC)
Example Text
Example Data
20 DTGEVC
nagf_lapack_dtgevc
Computes right and left generalized eigenvectors of the matrix pair A,B which is assumed to be in generalized upper Schur form
F08YLF (DTGSNA)
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 (ZTGSJA)
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 (ZTGEXC)
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 (ZTGSEN)
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 (ZTGSYL)
Example Text
Example Data
21 ZTGSYL
nagf_lapack_ztgsyl
Solves the complex generalized Sylvester equation
F08YXF (ZTGEVC)
Example Text
Example Data
20 ZTGEVC
nagf_lapack_ztgevc
Computes left and right eigenvectors of a pair of complex upper triangular matrices
F08YYF (ZTGSNA)
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 (DGGLSE)
Example Text
Example Data
21 DGGLSE
nagf_lapack_dgglse
Solves the real linear equality-constrained least squares (LSE) problem
F08ZBF (DGGGLM)
Example Text
Example Data
21 DGGGLM
nagf_lapack_dggglm
Solves a real general Gauss–Markov linear model (GLM) problem
F08ZEF (DGGQRF)
Example Text
Example Data
21 DGGQRF
nagf_lapack_dggqrf
Computes a generalized QR factorization of a real matrix pair
F08ZFF (DGGRQF)
Example Text
Example Data
21 DGGRQF
nagf_lapack_dggrqf
Computes a generalized RQ factorization of a real matrix pair
F08ZNF (ZGGLSE)
Example Text
Example Data
21 ZGGLSE
nagf_lapack_zgglse
Solves the complex linear equality-constrained least squares (LSE) problem
F08ZPF (ZGGGLM)
Example Text
Example Data
21 ZGGGLM
nagf_lapack_zggglm
Solves a complex general Gauss–Markov linear model (GLM) problem
F08ZSF (ZGGQRF)
Example Text
Example Data
21 ZGGQRF
nagf_lapack_zggqrf
Computes a generalized QR factorization of a complex matrix pair
F08ZTF (ZGGRQF)
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. 2016