NAG Library Chapter Contents

F08 (lapackeig)
Least Squares and Eigenvalue Problems (LAPACK)


F08 (lapackeig) 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_lapackeig_dgels
Solves a real linear least squares problem of full rank
f08abf (dgeqrt)
Example Text
Example Data
25 dgeqrt
nagf_lapackeig_dgeqrt
Performs a QR factorization of real general rectangular matrix, with explicit blocking
f08acf (dgemqrt) 25 dgemqrt
nagf_lapackeig_dgemqrt
Applies the orthogonal transformation determined by f08abf (dgeqrt)
f08aef (dgeqrf)
Example Text
Example Data
16 dgeqrf
nagf_lapackeig_dgeqrf
Performs a QR factorization of real general rectangular matrix
f08aff (dorgqr)
Example Text
Example Data
16 dorgqr
nagf_lapackeig_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_lapackeig_dormqr
Applies an orthogonal transformation determined by f08aef (dgeqrf), f08bef (dgeqpf) or f08bff (dgeqp3)
f08ahf (dgelqf)
Example Text
Example Data
16 dgelqf
nagf_lapackeig_dgelqf
Performs a LQ factorization of real general rectangular matrix
f08ajf (dorglq)
Example Text
Example Data
16 dorglq
nagf_lapackeig_dorglq
Forms all or part of orthogonal Q from LQ factorization determined by f08ahf (dgelqf)
f08akf (dormlq) 16 dormlq
nagf_lapackeig_dormlq
Applies the orthogonal transformation determined by f08ahf (dgelqf)
f08anf (zgels)
Example Text
Example Data
21 zgels
nagf_lapackeig_zgels
Solves a complex linear least problem of full rank
f08apf (zgeqrt)
Example Text
Example Data
25 zgeqrt
nagf_lapackeig_zgeqrt
Performs a QR factorization of complex general rectangular matrix using recursive algorithm
f08aqf (zgemqrt) 25 zgemqrt
nagf_lapackeig_zgemqrt
Applies the unitary transformation determined by f08apf (zgeqrt)
f08asf (zgeqrf)
Example Text
Example Data
16 zgeqrf
nagf_lapackeig_zgeqrf
Performs a QR factorization of complex general rectangular matrix
f08atf (zungqr)
Example Text
Example Data
16 zungqr
nagf_lapackeig_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_lapackeig_zunmqr
Applies a unitary transformation determined by f08asf (zgeqrf), f08bsf (zgeqpf) or f08btf (zgeqp3)
f08avf (zgelqf)
Example Text
Example Data
16 zgelqf
nagf_lapackeig_zgelqf
Performs a LQ factorization of complex general rectangular matrix
f08awf (zunglq)
Example Text
Example Data
16 zunglq
nagf_lapackeig_zunglq
Forms all or part of unitary Q from LQ factorization determined by f08avf (zgelqf)
f08axf (zunmlq) 16 zunmlq
nagf_lapackeig_zunmlq
Applies the unitary transformation determined by f08avf (zgelqf)
f08baf (dgelsy)
Example Text
Example Data
21 dgelsy
nagf_lapackeig_dgelsy
Computes the minimum-norm solution to a real linear least squares problem
f08bbf (dtpqrt)
Example Text
Example Data
25 dtpqrt
nagf_lapackeig_dtpqrt
QR factorization of real general triangular-pentagonal matrix
f08bcf (dtpmqrt) 25 dtpmqrt
nagf_lapackeig_dtpmqrt
Applies the orthogonal transformation determined by f08bbf (dtpqrt)
f08bef (dgeqpf)
Example Text
Example Data
16 dgeqpf
nagf_lapackeig_dgeqpf
QR factorization, with column pivoting, of real general rectangular matrix
f08bff (dgeqp3)
Example Text
Example Data
22 dgeqp3
nagf_lapackeig_dgeqp3
QR factorization, with column pivoting, using BLAS-3, of real general rectangular matrix
f08bhf (dtzrzf)
Example Text
Example Data
22 dtzrzf
nagf_lapackeig_dtzrzf
Reduces a real upper trapezoidal matrix to upper triangular form
f08bkf (dormrz) 22 dormrz
nagf_lapackeig_dormrz
Applies the orthogonal transformation determined by f08bhf (dtzrzf)
f08bnf (zgelsy)
Example Text
Example Data
21 zgelsy
nagf_lapackeig_zgelsy
Computes the minimum-norm solution to a complex linear least squares problem
f08bpf (ztpqrt)
Example Text
Example Data
25 ztpqrt
nagf_lapackeig_ztpqrt
QR factorization of complex triangular-pentagonal matrix
f08bqf (ztpmqrt) 25 ztpmqrt
nagf_lapackeig_ztpmqrt
Applies the unitary transformation determined by f08bpf (ztpqrt)
f08bsf (zgeqpf)
Example Text
Example Data
16 zgeqpf
nagf_lapackeig_zgeqpf
QR factorization, with column pivoting, of complex general rectangular matrix
f08btf (zgeqp3)
Example Text
Example Data
22 zgeqp3
nagf_lapackeig_zgeqp3
QR factorization, with column pivoting, using BLAS-3, of complex general rectangular matrix
f08bvf (ztzrzf)
Example Text
Example Data
22 ztzrzf
nagf_lapackeig_ztzrzf
Reduces a complex upper trapezoidal matrix to upper triangular form
f08bxf (zunmrz) 22 zunmrz
nagf_lapackeig_zunmrz
Applies the unitary transformation determined by f08bvf (ztzrzf)
f08cef (dgeqlf)
Example Text
Example Data
22 dgeqlf
nagf_lapackeig_dgeqlf
QL factorization of real general rectangular matrix
f08cff (dorgql)
Example Text
Example Data
22 dorgql
nagf_lapackeig_dorgql
Form all or part of orthogonal Q from QL factorization determined by f08cef (dgeqlf)
f08cgf (dormql) 22 dormql
nagf_lapackeig_dormql
Applies the orthogonal transformation determined by f08cef (dgeqlf)
f08chf (dgerqf)
Example Text
Example Data
22 dgerqf
nagf_lapackeig_dgerqf
RQ factorization of real general rectangular matrix
f08cjf (dorgrq)
Example Text
Example Data
22 dorgrq
nagf_lapackeig_dorgrq
Form all or part of orthogonal Q from RQ factorization determined by f08chf (dgerqf)
f08ckf (dormrq) 22 dormrq
nagf_lapackeig_dormrq
Applies the orthogonal transformation determined by f08chf (dgerqf)
f08csf (zgeqlf)
Example Text
Example Data
22 zgeqlf
nagf_lapackeig_zgeqlf
QL factorization of complex general rectangular matrix
f08ctf (zungql)
Example Text
Example Data
22 zungql
nagf_lapackeig_zungql
Form all or part of unitary Q from QL factorization determined by f08csf (zgeqlf)
f08cuf (zunmql) 22 zunmql
nagf_lapackeig_zunmql
Applies the unitary transformation determined by f08csf (zgeqlf)
f08cvf (zgerqf)
Example Text
Example Data
22 zgerqf
nagf_lapackeig_zgerqf
RQ factorization of complex general rectangular matrix
f08cwf (zungrq)
Example Text
Example Data
22 zungrq
nagf_lapackeig_zungrq
Form all or part of unitary Q from RQ factorization determined by f08cvf (zgerqf)
f08cxf (zunmrq) 22 zunmrq
nagf_lapackeig_zunmrq
Applies the unitary transformation determined by f08cvf (zgerqf)
f08faf (dsyev)
Example Text
Example Data
21 dsyev
nagf_lapackeig_dsyev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix
f08fbf (dsyevx)
Example Text
Example Data
21 dsyevx
nagf_lapackeig_dsyevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix
f08fcf (dsyevd)
Example Text
Example Data
19 dsyevd
nagf_lapackeig_dsyevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer)
f08fdf (dsyevr)
Example Text
Example Data
21 dsyevr
nagf_lapackeig_dsyevr
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations)
f08fef (dsytrd)
Example Text
Example Data
16 dsytrd
nagf_lapackeig_dsytrd
Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form
f08fff (dorgtr)
Example Text
Example Data
16 dorgtr
nagf_lapackeig_dorgtr
Generate orthogonal transformation matrix from reduction to tridiagonal form determined by f08fef (dsytrd)
f08fgf (dormtr)
Example Text
Example Data
16 dormtr
nagf_lapackeig_dormtr
Applies the orthogonal transformation determined by f08fef (dsytrd)
f08flf (ddisna) 22 ddisna
nagf_lapackeig_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_lapackeig_zheev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
f08fpf (zheevx)
Example Text
Example Data
21 zheevx
nagf_lapackeig_zheevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
f08fqf (zheevd)
Example Text
Example Data
19 zheevd
nagf_lapackeig_zheevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix (divide-and-conquer)
f08frf (zheevr)
Example Text
Example Data
21 zheevr
nagf_lapackeig_zheevr
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations)
f08fsf (zhetrd)
Example Text
Example Data
16 zhetrd
nagf_lapackeig_zhetrd
Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form
f08ftf (zungtr)
Example Text
Example Data
16 zungtr
nagf_lapackeig_zungtr
Generate unitary transformation matrix from reduction to tridiagonal form determined by f08fsf (zhetrd)
f08fuf (zunmtr)
Example Text
Example Data
16 zunmtr
nagf_lapackeig_zunmtr
Applies the unitary transformation matrix determined by f08fsf (zhetrd)
f08gaf (dspev)
Example Text
Example Data
21 dspev
nagf_lapackeig_dspev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
f08gbf (dspevx)
Example Text
Example Data
21 dspevx
nagf_lapackeig_dspevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
f08gcf (dspevd)
Example Text
Example Data
19 dspevd
nagf_lapackeig_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_lapackeig_dsptrd
Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage
f08gff (dopgtr)
Example Text
Example Data
16 dopgtr
nagf_lapackeig_dopgtr
Generate orthogonal transformation matrix from reduction to tridiagonal form determined by f08gef (dsptrd)
f08ggf (dopmtr)
Example Text
Example Data
16 dopmtr
nagf_lapackeig_dopmtr
Applies the orthogonal transformation determined by f08gef (dsptrd)
f08gnf (zhpev)
Example Text
Example Data
21 zhpev
nagf_lapackeig_zhpev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
f08gpf (zhpevx)
Example Text
Example Data
21 zhpevx
nagf_lapackeig_zhpevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
f08gqf (zhpevd)
Example Text
Example Data
19 zhpevd
nagf_lapackeig_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_lapackeig_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_lapackeig_zupgtr
Generates a unitary transformation matrix from reduction to tridiagonal form determined by f08gsf (zhptrd)
f08guf (zupmtr)
Example Text
Example Data
16 zupmtr
nagf_lapackeig_zupmtr
Applies the unitary transformation matrix determined by f08gsf (zhptrd)
f08haf (dsbev)
Example Text
Example Data
21 dsbev
nagf_lapackeig_dsbev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
f08hbf (dsbevx)
Example Text
Example Data
21 dsbevx
nagf_lapackeig_dsbevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
f08hcf (dsbevd)
Example Text
Example Data
19 dsbevd
nagf_lapackeig_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_lapackeig_dsbtrd
Performs an orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form
f08hnf (zhbev)
Example Text
Example Data
21 zhbev
nagf_lapackeig_zhbev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
f08hpf (zhbevx)
Example Text
Example Data
21 zhbevx
nagf_lapackeig_zhbevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
f08hqf (zhbevd)
Example Text
Example Data
19 zhbevd
nagf_lapackeig_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_lapackeig_zhbtrd
Performs a unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form
f08jaf (dstev)
Example Text
Example Data
21 dstev
nagf_lapackeig_dstev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
f08jbf (dstevx)
Example Text
Example Data
21 dstevx
nagf_lapackeig_dstevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
f08jcf (dstevd)
Example Text
Example Data
19 dstevd
nagf_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_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
22 dstedc
nagf_lapackeig_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_lapackeig_dstebz
Computes selected eigenvalues of real symmetric tridiagonal matrix by bisection
f08jkf (dstein) 16 dstein
nagf_lapackeig_dstein
Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array
f08jlf (dstegr)
Example Text
Example Data
22 dstegr
nagf_lapackeig_dstegr
Computes selected eigenvalues and, optionally, the corresponding eigenvectors of a real symmetric tridiagonal matrix or a symmetric matrix reduced to this form (Relatively Robust Representations)
f08jsf (zsteqr) 16 zsteqr
nagf_lapackeig_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_lapackeig_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
22 zstedc
nagf_lapackeig_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_lapackeig_zstein
Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array
f08jyf (zstegr)
Example Text
Example Data
22 zstegr
nagf_lapackeig_zstegr
Computes selected eigenvalues and, optionally, the corresponding 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_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_dgebrd
Performs an orthogonal reduction of real general rectangular matrix to bidiagonal form
f08kff (dorgbr)
Example Text
Example Data
16 dorgbr
nagf_lapackeig_dorgbr
Generates an orthogonal transformation matrices from reduction to bidiagonal form determined by f08kef (dgebrd)
f08kgf (dormbr)
Example Text
Example Data
16 dormbr
nagf_lapackeig_dormbr
Applies the orthogonal transformations from reduction to bidiagonal form determined by f08kef (dgebrd)
f08khf (dgejsv)
Example Text
Example Data
23 dgejsv
nagf_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_zgebrd
Performs a unitary reduction of complex general rectangular matrix to bidiagonal form
f08ktf (zungbr)
Example Text
Example Data
16 zungbr
nagf_lapackeig_zungbr
Generates unitary transformation matrices from the reduction to bidiagonal form determined by f08ksf (zgebrd)
f08kuf (zunmbr)
Example Text
Example Data
16 zunmbr
nagf_lapackeig_zunmbr
Applies the unitary transformations from reduction to bidiagonal form determined by f08ksf (zgebrd)
f08lef (dgbbrd)
Example Text
Example Data
19 dgbbrd
nagf_lapackeig_dgbbrd
Performs a reduction of real rectangular band matrix to upper bidiagonal form
f08lsf (zgbbrd)
Example Text
Example Data
19 zgbbrd
nagf_lapackeig_zgbbrd
Reduction of complex rectangular band matrix to upper bidiagonal form
f08mdf (dbdsdc)
Example Text
Example Data
22 dbdsdc
nagf_lapackeig_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_lapackeig_dbdsqr
Performs an SVD of real bidiagonal matrix reduced from real general matrix
f08msf (zbdsqr) 16 zbdsqr
nagf_lapackeig_zbdsqr
Performs an SVD of real bidiagonal matrix reduced from complex general matrix
f08naf (dgeev)
Example Text
Example Data
21 dgeev
nagf_lapackeig_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_lapackeig_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_lapackeig_dgehrd
Performs an orthogonal reduction of real general matrix to upper Hessenberg form
f08nff (dorghr)
Example Text
Example Data
16 dorghr
nagf_lapackeig_dorghr
Generates an orthogonal transformation matrix from reduction to Hessenberg form determined by f08nef (dgehrd)
f08ngf (dormhr)
Example Text
Example Data
16 dormhr
nagf_lapackeig_dormhr
Applies the orthogonal transformation matrix from reduction to Hessenberg form determined by f08nef (dgehrd)
f08nhf (dgebal)
Example Text
Example Data
16 dgebal
nagf_lapackeig_dgebal
Balances a real general matrix
f08njf (dgebak) 16 dgebak
nagf_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_zgehrd
Performs a unitary reduction of complex general matrix to upper Hessenberg form
f08ntf (zunghr)
Example Text
Example Data
16 zunghr
nagf_lapackeig_zunghr
Generates a unitary transformation matrix from reduction to Hessenberg form determined by f08nsf (zgehrd)
f08nuf (zunmhr)
Example Text
Example Data
16 zunmhr
nagf_lapackeig_zunmhr
Applies the unitary transformation matrix from reduction to Hessenberg form determined by f08nsf (zgehrd)
f08nvf (zgebal)
Example Text
Example Data
16 zgebal
nagf_lapackeig_zgebal
Balances a complex general matrix
f08nwf (zgebak) 16 zgebak
nagf_lapackeig_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_lapackeig_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_lapackeig_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
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16 dhseqr
nagf_lapackeig_dhseqr
Computes the eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix
f08pkf (dhsein) 16 dhsein
nagf_lapackeig_dhsein
Computes selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration
f08pnf (zgees)
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21 zgees
nagf_lapackeig_zgees
Computes for complex square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors
f08ppf (zgeesx)
Example Text
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21 zgeesx
nagf_lapackeig_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
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16 zhseqr
nagf_lapackeig_zhseqr
Computes the eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix
f08pxf (zhsein) 16 zhsein
nagf_lapackeig_zhsein
Computes selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration
f08qff (dtrexc)
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16 dtrexc
nagf_lapackeig_dtrexc
Reorders a Schur factorization of real matrix using orthogonal similarity transformation
f08qgf (dtrsen)
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16 dtrsen
nagf_lapackeig_dtrsen
Reorders a Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
f08qhf (dtrsyl)
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16 dtrsyl
nagf_lapackeig_dtrsyl
Solves the real Sylvester matrix equation AX+XB=C, A and B are upper quasi-triangular or transposes
f08qkf (dtrevc) 16 dtrevc
nagf_lapackeig_dtrevc
Computes left and right eigenvectors of real upper quasi-triangular matrix
f08qlf (dtrsna)
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16 dtrsna
nagf_lapackeig_dtrsna
Computes estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix
f08qtf (ztrexc)
Example Text
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16 ztrexc
nagf_lapackeig_ztrexc
Reorders a Schur factorization of complex matrix using unitary similarity transformation
f08quf (ztrsen)
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16 ztrsen
nagf_lapackeig_ztrsen
Reorders a Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
f08qvf (ztrsyl)
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16 ztrsyl
nagf_lapackeig_ztrsyl
Solves the complex Sylvester matrix equation AX+XB=C, A and B are upper triangular or conjugate-transposes
f08qxf (ztrevc) 16 ztrevc
nagf_lapackeig_ztrevc
Computes left and right eigenvectors of complex upper triangular matrix
f08qyf (ztrsna)
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16 ztrsna
nagf_lapackeig_ztrsna
Computes estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix
f08raf (dorcsd)
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25 dorcsd
nagf_lapackeig_dorcsd
Computes the CS decomposition of an orthogonal matrix partitioned into four real submatrices
f08rnf (zuncsd)
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25 zuncsd
nagf_lapackeig_zuncsd
Computes the CS decomposition of a unitary matrix partitioned into four complex submatrices
f08saf (dsygv)
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21 dsygv
nagf_lapackeig_dsygv
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
f08sbf (dsygvx)
Example Text
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21 dsygvx
nagf_lapackeig_dsygvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
f08scf (dsygvd)
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21 dsygvd
nagf_lapackeig_dsygvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer)
f08sef (dsygst)
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16 dsygst
nagf_lapackeig_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)
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21 zhegv
nagf_lapackeig_zhegv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
f08spf (zhegvx)
Example Text
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21 zhegvx
nagf_lapackeig_zhegvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
f08sqf (zhegvd)
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21 zhegvd
nagf_lapackeig_zhegvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer)
f08ssf (zhegst)
Example Text
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16 zhegst
nagf_lapackeig_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)
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21 dspgv
nagf_lapackeig_dspgv
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
f08tbf (dspgvx)
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21 dspgvx
nagf_lapackeig_dspgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
f08tcf (dspgvd)
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21 dspgvd
nagf_lapackeig_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
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16 dspgst
nagf_lapackeig_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)
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21 zhpgv
nagf_lapackeig_zhpgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
f08tpf (zhpgvx)
Example Text
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21 zhpgvx
nagf_lapackeig_zhpgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
f08tqf (zhpgvd)
Example Text
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21 zhpgvd
nagf_lapackeig_zhpgvd
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage (divide-and-conquer)
f08tsf (zhpgst)
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16 zhpgst
nagf_lapackeig_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)
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21 dsbgv
nagf_lapackeig_dsbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
f08ubf (dsbgvx)
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21 dsbgvx
nagf_lapackeig_dsbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
f08ucf (dsbgvd)
Example Text
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21 dsbgvd
nagf_lapackeig_dsbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem (divide-and-conquer)
f08uef (dsbgst)
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19 dsbgst
nagf_lapackeig_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_lapackeig_dpbstf
Computes a split Cholesky factorization of real symmetric positive definite band matrix A
f08unf (zhbgv)
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21 zhbgv
nagf_lapackeig_zhbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
f08upf (zhbgvx)
Example Text
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21 zhbgvx
nagf_lapackeig_zhbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
f08uqf (zhbgvd)
Example Text
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21 zhbgvd
nagf_lapackeig_zhbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem (divide-and-conquer)
f08usf (zhbgst)
Example Text
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19 zhbgst
nagf_lapackeig_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_lapackeig_zpbstf
Computes a split Cholesky factorization of complex Hermitian positive definite band matrix A
f08vaf (dggsvd)
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21 dggsvd
nagf_lapackeig_dggsvd
Computes the generalized singular value decomposition of a real matrix pair
f08vcf (dggsvd3)
Example Text
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26.0 dggsvd3
nagf_lapackeig_dggsvd3
Computes, using BLAS-3, the generalized singular value decomposition of a real matrix pair
f08vef (dggsvp)
Example Text
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22 dggsvp
nagf_lapackeig_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
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26.0 dggsvp3
nagf_lapackeig_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)
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21 zggsvd
nagf_lapackeig_zggsvd
Computes the generalized singular value decomposition of a complex matrix pair
f08vqf (zggsvd3)
Example Text
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26.0 zggsvd3
nagf_lapackeig_zggsvd3
Computes, using BLAS-3, the generalized singular value decomposition of a complex matrix pair
f08vsf (zggsvp)
Example Text
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22 zggsvp
nagf_lapackeig_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
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26.0 zggsvp3
nagf_lapackeig_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
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21 dggev
nagf_lapackeig_dggev
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
f08wbf (dggevx)
Example Text
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21 dggevx
nagf_lapackeig_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
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26.0 dggev3
nagf_lapackeig_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_lapackeig_dgghrd
Performs an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
f08wff (dgghd3) 26.0 dgghd3
nagf_lapackeig_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_lapackeig_dggbal
Balances a pair of real, square, matrices
f08wjf (dggbak) 20 dggbak
nagf_lapackeig_dggbak
Transforms eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to f08whf (dggbal)
f08wnf (zggev)
Example Text
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21 zggev
nagf_lapackeig_zggev
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
f08wpf (zggevx)
Example Text
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21 zggevx
nagf_lapackeig_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
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26.0 zggev3
nagf_lapackeig_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_lapackeig_zgghrd
Performs a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
f08wtf (zgghd3) 26.0 zgghd3
nagf_lapackeig_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_lapackeig_zggbal
Balances a pair of complex, square, matrices
f08wwf (zggbak) 20 zggbak
nagf_lapackeig_zggbak
Transforms eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to f08wvf (zggbal)
f08xaf (dgges)
Example Text
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21 dgges
nagf_lapackeig_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
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21 dggesx
nagf_lapackeig_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
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26.0 dgges3
nagf_lapackeig_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)
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20 dhgeqz
nagf_lapackeig_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
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21 zgges
nagf_lapackeig_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
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21 zggesx
nagf_lapackeig_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
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26.0 zgges3
nagf_lapackeig_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
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20 zhgeqz
nagf_lapackeig_zhgeqz
Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex, square, matrices
f08yef (dtgsja)
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22 dtgsja
nagf_lapackeig_dtgsja
Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair
f08yff (dtgexc)
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22 dtgexc
nagf_lapackeig_dtgexc
Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation
f08ygf (dtgsen)
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22 dtgsen
nagf_lapackeig_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)
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22 dtgsyl
nagf_lapackeig_dtgsyl
Solves the real-valued, generalized, quasi-trangular, Sylvester equation
f08ykf (dtgevc)
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20 dtgevc
nagf_lapackeig_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)
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22 dtgsna
nagf_lapackeig_dtgsna
Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a real matrix pair in generalized real Schur canonical form
f08ysf (ztgsja)
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22 ztgsja
nagf_lapackeig_ztgsja
Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair
f08ytf (ztgexc)
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22 ztgexc
nagf_lapackeig_ztgexc
Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation
f08yuf (ztgsen)
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22 ztgsen
nagf_lapackeig_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)
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22 ztgsyl
nagf_lapackeig_ztgsyl
Solves the complex generalized Sylvester equation
f08yxf (ztgevc)
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20 ztgevc
nagf_lapackeig_ztgevc
Computes left and right eigenvectors of a pair of complex upper triangular matrices
f08yyf (ztgsna)
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22 ztgsna
nagf_lapackeig_ztgsna
Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a complex matrix pair in generalized Schur canonical form
f08zaf (dgglse)
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21 dgglse
nagf_lapackeig_dgglse
Solves the real linear equality-constrained least squares (LSE) problem
f08zbf (dggglm)
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21 dggglm
nagf_lapackeig_dggglm
Solves a real general Gauss–Markov linear model (GLM) problem
f08zef (dggqrf)
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22 dggqrf
nagf_lapackeig_dggqrf
Computes a generalized QR factorization of a real matrix pair
f08zff (dggrqf)
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22 dggrqf
nagf_lapackeig_dggrqf
Computes a generalized RQ factorization of a real matrix pair
f08znf (zgglse)
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21 zgglse
nagf_lapackeig_zgglse
Solves the complex linear equality-constrained least squares (LSE) problem
f08zpf (zggglm)
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21 zggglm
nagf_lapackeig_zggglm
Solves a complex general Gauss–Markov linear model (GLM) problem
f08zsf (zggqrf)
Example Text
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22 zggqrf
nagf_lapackeig_zggqrf
Computes a generalized QR factorization of a complex matrix pair
f08ztf (zggrqf)
Example Text
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22 zggrqf
nagf_lapackeig_zggrqf
Computes a generalized RQ factorization of a complex matrix pair