# NAG FL InterfaceF08 (Lapackeig)Least Squares and Eigenvalue Problems (LAPACK)

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F08 (Lapackeig) Chapter Introduction – A description of the Chapter and an overview of the algorithms available.

Routine
Mark of
Introduction

Purpose
f08aaf 21 dgels
nagf_lapackeig_dgels
Solves a real linear least squares problem of full rank
f08abf 25 dgeqrt
nagf_lapackeig_dgeqrt
Performs a $QR$ factorization of real general rectangular matrix, with explicit blocking
f08acf 25 dgemqrt
nagf_lapackeig_dgemqrt
Applies the orthogonal transformation determined by f08abf
f08aef 16 dgeqrf
nagf_lapackeig_dgeqrf
Performs a $QR$ factorization of real general rectangular matrix
f08aff 16 dorgqr
nagf_lapackeig_dorgqr
Forms all or part of orthogonal $Q$ from $QR$ factorization determined by f08aef, f08bef or f08bff
f08agf 16 dormqr
nagf_lapackeig_dormqr
Applies an orthogonal transformation determined by f08aef, f08bef or f08bff
f08ahf 16 dgelqf
nagf_lapackeig_dgelqf
Performs a $LQ$ factorization of real general rectangular matrix
f08ajf 16 dorglq
nagf_lapackeig_dorglq
Forms all or part of orthogonal $Q$ from $LQ$ factorization determined by f08ahf
f08akf 16 dormlq
nagf_lapackeig_dormlq
Applies the orthogonal transformation determined by f08ahf
f08anf 21 zgels
nagf_lapackeig_zgels
Solves a complex linear least problem of full rank
f08apf 25 zgeqrt
nagf_lapackeig_zgeqrt
Performs a $QR$ factorization of complex general rectangular matrix using recursive algorithm
f08aqf 25 zgemqrt
nagf_lapackeig_zgemqrt
Applies the unitary transformation determined by f08apf
f08asf 16 zgeqrf
nagf_lapackeig_zgeqrf
Performs a $QR$ factorization of complex general rectangular matrix
f08atf 16 zungqr
nagf_lapackeig_zungqr
Forms all or part of unitary $Q$ from $QR$ factorization determined by f08asf, f08bsf or f08btf
f08auf 16 zunmqr
nagf_lapackeig_zunmqr
Applies a unitary transformation determined by f08asf, f08bsf or f08btf
f08avf 16 zgelqf
nagf_lapackeig_zgelqf
Performs a $LQ$ factorization of complex general rectangular matrix
f08awf 16 zunglq
nagf_lapackeig_zunglq
Forms all or part of unitary $Q$ from $LQ$ factorization determined by f08avf
f08axf 16 zunmlq
nagf_lapackeig_zunmlq
Applies the unitary transformation determined by f08avf
f08baf 21 dgelsy
nagf_lapackeig_dgelsy
Computes the minimum-norm solution to a real linear least squares problem
f08bbf 25 dtpqrt
nagf_lapackeig_dtpqrt
$QR$ factorization of real general triangular-pentagonal matrix
f08bcf 25 dtpmqrt
nagf_lapackeig_dtpmqrt
Applies the orthogonal transformation determined by f08bbf
f08bff 22 dgeqp3
nagf_lapackeig_dgeqp3
$QR$ factorization, with column pivoting, using BLAS-3, of real general rectangular matrix
f08bhf 22 dtzrzf
nagf_lapackeig_dtzrzf
Reduces a real upper trapezoidal matrix to upper triangular form
f08bkf 22 dormrz
nagf_lapackeig_dormrz
Applies the orthogonal transformation determined by f08bhf
f08bnf 21 zgelsy
nagf_lapackeig_zgelsy
Computes the minimum-norm solution to a complex linear least squares problem
f08bpf 25 ztpqrt
nagf_lapackeig_ztpqrt
$QR$ factorization of complex triangular-pentagonal matrix
f08bqf 25 ztpmqrt
nagf_lapackeig_ztpmqrt
Applies the unitary transformation determined by f08bpf
f08btf 22 zgeqp3
nagf_lapackeig_zgeqp3
$QR$ factorization, with column pivoting, using BLAS-3, of complex general rectangular matrix
f08bvf 22 ztzrzf
nagf_lapackeig_ztzrzf
Reduces a complex upper trapezoidal matrix to upper triangular form
f08bxf 22 zunmrz
nagf_lapackeig_zunmrz
Applies the unitary transformation determined by f08bvf
f08cef 22 dgeqlf
nagf_lapackeig_dgeqlf
$QL$ factorization of real general rectangular matrix
f08cff 22 dorgql
nagf_lapackeig_dorgql
Form all or part of orthogonal $Q$ from $QL$ factorization determined by f08cef
f08cgf 22 dormql
nagf_lapackeig_dormql
Applies the orthogonal transformation determined by f08cef
f08chf 22 dgerqf
nagf_lapackeig_dgerqf
$RQ$ factorization of real general rectangular matrix
f08cjf 22 dorgrq
nagf_lapackeig_dorgrq
Form all or part of orthogonal $Q$ from $RQ$ factorization determined by f08chf
f08ckf 22 dormrq
nagf_lapackeig_dormrq
Applies the orthogonal transformation determined by f08chf
f08csf 22 zgeqlf
nagf_lapackeig_zgeqlf
$QL$ factorization of complex general rectangular matrix
f08ctf 22 zungql
nagf_lapackeig_zungql
Form all or part of unitary $Q$ from $QL$ factorization determined by f08csf
f08cuf 22 zunmql
nagf_lapackeig_zunmql
Applies the unitary transformation determined by f08csf
f08cvf 22 zgerqf
nagf_lapackeig_zgerqf
$RQ$ factorization of complex general rectangular matrix
f08cwf 22 zungrq
nagf_lapackeig_zungrq
Form all or part of unitary $Q$ from $RQ$ factorization determined by f08cvf
f08cxf 22 zunmrq
nagf_lapackeig_zunmrq
Applies the unitary transformation determined by f08cvf
f08faf 21 dsyev
nagf_lapackeig_dsyev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix
f08fbf 21 dsyevx
nagf_lapackeig_dsyevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix
f08fcf 19 dsyevd
nagf_lapackeig_dsyevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer)
f08fdf 21 dsyevr
nagf_lapackeig_dsyevr
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations)
f08fef 16 dsytrd
nagf_lapackeig_dsytrd
Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form
f08fff 16 dorgtr
nagf_lapackeig_dorgtr
Generate orthogonal transformation matrix from reduction to tridiagonal form determined by f08fef
f08fgf 16 dormtr
nagf_lapackeig_dormtr
Applies the orthogonal transformation determined by f08fef
f08flf 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 21 zheev
nagf_lapackeig_zheev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
f08fpf 21 zheevx
nagf_lapackeig_zheevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
f08fqf 19 zheevd
nagf_lapackeig_zheevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix (divide-and-conquer)
f08frf 21 zheevr
nagf_lapackeig_zheevr
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations)
f08fsf 16 zhetrd
nagf_lapackeig_zhetrd
Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form
f08ftf 16 zungtr
nagf_lapackeig_zungtr
Generate unitary transformation matrix from reduction to tridiagonal form determined by f08fsf
f08fuf 16 zunmtr
nagf_lapackeig_zunmtr
Applies the unitary transformation matrix determined by f08fsf
f08gaf 21 dspev
nagf_lapackeig_dspev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
f08gbf 21 dspevx
nagf_lapackeig_dspevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
f08gcf 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 16 dsptrd
nagf_lapackeig_dsptrd
Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage
f08gff 16 dopgtr
nagf_lapackeig_dopgtr
Generate orthogonal transformation matrix from reduction to tridiagonal form determined by f08gef
f08ggf 16 dopmtr
nagf_lapackeig_dopmtr
Applies the orthogonal transformation determined by f08gef
f08gnf 21 zhpev
nagf_lapackeig_zhpev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
f08gpf 21 zhpevx
nagf_lapackeig_zhpevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
f08gqf 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 16 zhptrd
nagf_lapackeig_zhptrd
Performs a unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage
f08gtf 16 zupgtr
nagf_lapackeig_zupgtr
Generates a unitary transformation matrix from reduction to tridiagonal form determined by f08gsf
f08guf 16 zupmtr
nagf_lapackeig_zupmtr
Applies the unitary transformation matrix determined by f08gsf
f08haf 21 dsbev
nagf_lapackeig_dsbev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
f08hbf 21 dsbevx
nagf_lapackeig_dsbevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
f08hcf 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 16 dsbtrd
nagf_lapackeig_dsbtrd
Performs an orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form
f08hnf 21 zhbev
nagf_lapackeig_zhbev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
f08hpf 21 zhbevx
nagf_lapackeig_zhbevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
f08hqf 19 zhbevd
nagf_lapackeig_zhbevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian band matrix (divide-and-conquer)
f08hsf 16 zhbtrd
nagf_lapackeig_zhbtrd
Performs a unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form
f08jaf 21 dstev
nagf_lapackeig_dstev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
f08jbf 21 dstevx
nagf_lapackeig_dstevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
f08jcf 19 dstevd
nagf_lapackeig_dstevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer)
f08jdf 21 dstevr
nagf_lapackeig_dstevr
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations)
f08jef 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 16 dsterf
nagf_lapackeig_dsterf
Computes all eigenvalues of real symmetric tridiagonal matrix, root-free variant of the $QL$ or $QR$ algorithm
f08jgf 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 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 16 dstebz
nagf_lapackeig_dstebz
Computes selected eigenvalues of real symmetric tridiagonal matrix by bisection
f08jkf 16 dstein
nagf_lapackeig_dstein
Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array
f08jlf 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 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 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 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 16 zstein
nagf_lapackeig_zstein
Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array
f08jyf 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 21 dgelss
nagf_lapackeig_dgelss
Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition
f08kbf 21 dgesvd
nagf_lapackeig_dgesvd
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors
f08kcf 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 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 16 dgebrd
nagf_lapackeig_dgebrd
Performs an orthogonal reduction of real general rectangular matrix to bidiagonal form
f08kff 16 dorgbr
nagf_lapackeig_dorgbr
Generates an orthogonal transformation matrices from reduction to bidiagonal form determined by f08kef
f08kgf 16 dormbr
nagf_lapackeig_dormbr
Applies the orthogonal transformations from reduction to bidiagonal form determined by f08kef
f08khf 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 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)
f08kmf 27 dgesvdx
nagf_lapackeig_dgesvdx
Computes all or selected singular values of the singular value decomposition of a real general matrix, optionally computing the corresponding left and right singular vectors
f08knf 21 zgelss
nagf_lapackeig_zgelss
Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition
f08kpf 21 zgesvd
nagf_lapackeig_zgesvd
Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors
f08kqf 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 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 16 zgebrd
nagf_lapackeig_zgebrd
Performs a unitary reduction of complex general rectangular matrix to bidiagonal form
f08ktf 16 zungbr
nagf_lapackeig_zungbr
Generates unitary transformation matrices from the reduction to bidiagonal form determined by f08ksf
f08kuf 16 zunmbr
nagf_lapackeig_zunmbr
Applies the unitary transformations from reduction to bidiagonal form determined by f08ksf
f08kvf 27 zgejsv
nagf_lapackeig_zgejsv
Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (preconditioned Jacobi)
f08kwf 27 zgesvj
nagf_lapackeig_zgesvj
Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (fast Jacobi)
f08kzf 27 zgesvdx
nagf_lapackeig_zgesvdx
Computes all or selected singular values of the singular value decomposition of a complex general matrix, optionally computing the corresponding left and right singular vectors
f08lef 19 dgbbrd
nagf_lapackeig_dgbbrd
Performs a reduction of real rectangular band matrix to upper bidiagonal form
f08lsf 19 zgbbrd
nagf_lapackeig_zgbbrd
Reduction of complex rectangular band matrix to upper bidiagonal form
f08mbf 27 dbdsvdx
nagf_lapackeig_dbdsvdx
Computes all or selected singular values of the singular value decomposition of a real square bidiagonal matrix, optionally computing the corresponding left and right singular vectors
f08mdf 22 dbdsdc
nagf_lapackeig_dbdsdc
Computes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divide-and-conquer)
f08mef 16 dbdsqr
nagf_lapackeig_dbdsqr
Performs an SVD of real bidiagonal matrix reduced from real general matrix
f08msf 16 zbdsqr
nagf_lapackeig_zbdsqr
Performs an SVD of real bidiagonal matrix reduced from complex general matrix
f08naf 21 dgeev
nagf_lapackeig_dgeev
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix
f08nbf 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 16 dgehrd
nagf_lapackeig_dgehrd
Performs an orthogonal reduction of real general matrix to upper Hessenberg form
f08nff 16 dorghr
nagf_lapackeig_dorghr
Generates an orthogonal transformation matrix from reduction to Hessenberg form determined by f08nef
f08ngf 16 dormhr
nagf_lapackeig_dormhr
Applies the orthogonal transformation matrix from reduction to Hessenberg form determined by f08nef
f08nhf 16 dgebal
nagf_lapackeig_dgebal
Balances a real general matrix
f08njf 16 dgebak
nagf_lapackeig_dgebak
Transforms eigenvectors of real balanced matrix to those of original matrix supplied to f08nhf
f08nnf 21 zgeev
nagf_lapackeig_zgeev
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix
f08npf 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 16 zgehrd
nagf_lapackeig_zgehrd
Performs a unitary reduction of complex general matrix to upper Hessenberg form
f08ntf 16 zunghr
nagf_lapackeig_zunghr
Generates a unitary transformation matrix from reduction to Hessenberg form determined by f08nsf
f08nuf 16 zunmhr
nagf_lapackeig_zunmhr
Applies the unitary transformation matrix from reduction to Hessenberg form determined by f08nsf
f08nvf 16 zgebal
nagf_lapackeig_zgebal
Balances a complex general matrix
f08nwf 16 zgebak
nagf_lapackeig_zgebak
Transforms eigenvectors of complex balanced matrix to those of original matrix supplied to f08nvf
f08paf 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 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 16 dhseqr
nagf_lapackeig_dhseqr
Computes the eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix
f08pkf 16 dhsein
nagf_lapackeig_dhsein
Computes selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration
f08pnf 21 zgees
nagf_lapackeig_zgees
Computes for complex square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors
f08ppf 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 16 zhseqr
nagf_lapackeig_zhseqr
Computes the eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix
f08pxf 16 zhsein
nagf_lapackeig_zhsein
Computes selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration
f08qff 16 dtrexc
nagf_lapackeig_dtrexc
Reorders a Schur factorization of real matrix using orthogonal similarity transformation
f08qgf 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 16 dtrsyl
nagf_lapackeig_dtrsyl
Solves the real Sylvester matrix equation $AX+XB=C$, $A$ and $B$ are upper quasi-triangular or transposes
f08qkf 16 dtrevc
nagf_lapackeig_dtrevc
Computes left and right eigenvectors of real upper quasi-triangular matrix
f08qlf 16 dtrsna
nagf_lapackeig_dtrsna
Computes estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix
f08qtf 16 ztrexc
nagf_lapackeig_ztrexc
Reorders a Schur factorization of complex matrix using unitary similarity transformation
f08quf 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 16 ztrsyl
nagf_lapackeig_ztrsyl
Solves the complex Sylvester matrix equation $AX+XB=C$, $A$ and $B$ are upper triangular or conjugate-transposes
f08qxf 16 ztrevc
nagf_lapackeig_ztrevc
Computes left and right eigenvectors of complex upper triangular matrix
f08qyf 16 ztrsna
nagf_lapackeig_ztrsna
Computes estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix
f08raf 25 dorcsd
nagf_lapackeig_dorcsd
Computes the CS decomposition of an orthogonal matrix partitioned into four real submatrices
f08rnf 25 zuncsd
nagf_lapackeig_zuncsd
Computes the CS decomposition of a unitary matrix partitioned into four complex submatrices
f08saf 21 dsygv
nagf_lapackeig_dsygv
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
f08sbf 21 dsygvx
nagf_lapackeig_dsygvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
f08scf 21 dsygvd
nagf_lapackeig_dsygvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer)
f08sef 16 dsygst
nagf_lapackeig_dsygst
Performs a reduction to standard form of real symmetric-definite generalized eigenproblem $Ax=\lambda Bx$, $ABx=\lambda x$ or $BAx=\lambda x$, $B$ factorized by f07fdf
f08snf 21 zhegv
nagf_lapackeig_zhegv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
f08spf 21 zhegvx
nagf_lapackeig_zhegvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
f08sqf 21 zhegvd
nagf_lapackeig_zhegvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer)
f08ssf 16 zhegst
nagf_lapackeig_zhegst
Performs a reduction to standard form of complex Hermitian-definite generalized eigenproblem $Ax=\lambda Bx$, $ABx=\lambda x$ or $BAx=\lambda x$, $B$ factorized by f07frf
f08taf 21 dspgv
nagf_lapackeig_dspgv
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
f08tbf 21 dspgvx
nagf_lapackeig_dspgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
f08tcf 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 16 dspgst
nagf_lapackeig_dspgst
Performs a reduction to standard form of real symmetric-definite generalized eigenproblem $Ax=\lambda Bx$, $ABx=\lambda x$ or $BAx=\lambda x$, packed storage, $B$ factorized by f07gdf
f08tnf 21 zhpgv
nagf_lapackeig_zhpgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
f08tpf 21 zhpgvx
nagf_lapackeig_zhpgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
f08tqf 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 16 zhpgst
nagf_lapackeig_zhpgst
Performs a reduction to standard form of complex Hermitian-definite generalized eigenproblem $Ax=\lambda Bx$, $ABx=\lambda x$ or $BAx=\lambda x$, packed storage, $B$ factorized by f07grf
f08uaf 21 dsbgv
nagf_lapackeig_dsbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
f08ubf 21 dsbgvx
nagf_lapackeig_dsbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
f08ucf 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 19 dsbgst
nagf_lapackeig_dsbgst
Performs a reduction of real symmetric-definite banded generalized eigenproblem $Ax=\lambda Bx$ to standard form $Cy=\lambda y$, such that $C$ has the same bandwidth as $A$
f08uff 19 dpbstf
nagf_lapackeig_dpbstf
Computes a split Cholesky factorization of real symmetric positive definite band matrix $A$
f08unf 21 zhbgv
nagf_lapackeig_zhbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
f08upf 21 zhbgvx
nagf_lapackeig_zhbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
f08uqf 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 19 zhbgst
nagf_lapackeig_zhbgst
Performs a reduction of complex Hermitian-definite banded generalized eigenproblem $Ax=\lambda Bx$ to standard form $Cy=\lambda y$, such that $C$ has the same bandwidth as $A$
f08utf 19 zpbstf
nagf_lapackeig_zpbstf
Computes a split Cholesky factorization of complex Hermitian positive definite band matrix $A$
f08vcf 26 dggsvd3
nagf_lapackeig_dggsvd3
Computes, using BLAS-3, the generalized singular value decomposition of a real matrix pair
f08vgf 26 dggsvp3
nagf_lapackeig_dggsvp3
Produces orthogonal matrices, using BLAS-3, that simultaneously reduce the $m×n$ matrix $A$ and the $p×n$ matrix $B$ to upper triangular form
f08vqf 26 zggsvd3
nagf_lapackeig_zggsvd3
Computes, using BLAS-3, the generalized singular value decomposition of a complex matrix pair
f08vuf 26 zggsvp3
nagf_lapackeig_zggsvp3
Produces unitary matrices, using BLAS-3, that simultaneously reduce the complex, $m×n$, matrix $A$ and the complex, $p×n$, matrix $B$ to upper triangular form
f08wbf 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 26 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
f08wff 26 dgghd3
nagf_lapackeig_dgghd3
Performs, using BLAS-3, an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
f08whf 20 dggbal
nagf_lapackeig_dggbal
Balances a pair of real, square, matrices
f08wjf 20 dggbak
nagf_lapackeig_dggbak
Transforms eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to f08whf
f08wpf 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 26 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
f08wtf 26 zgghd3
nagf_lapackeig_zgghd3
Performs, using BLAS-3, a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
f08wvf 20 zggbal
nagf_lapackeig_zggbal
Balances a pair of complex, square, matrices
f08wwf 20 zggbak
nagf_lapackeig_zggbak
Transforms eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to f08wvf
f08xbf 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 26 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 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
f08xpf 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 26 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 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 22 dtgsja
nagf_lapackeig_dtgsja
Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair
f08yff 22 dtgexc
nagf_lapackeig_dtgexc
Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation
f08ygf 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 22 dtgsyl
nagf_lapackeig_dtgsyl
Solves the real-valued, generalized, quasi-trangular, Sylvester equation
f08ykf 20 dtgevc
nagf_lapackeig_dtgevc
Computes right and left generalized eigenvectors of the matrix pair $\left(A,B\right)$ which is assumed to be in generalized upper Schur form
f08ylf 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 22 ztgsja
nagf_lapackeig_ztgsja
Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair
f08ytf 22 ztgexc
nagf_lapackeig_ztgexc
Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation
f08yuf 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 22 ztgsyl
nagf_lapackeig_ztgsyl
Solves the complex generalized Sylvester equation
f08yxf 20 ztgevc
nagf_lapackeig_ztgevc
Computes left and right eigenvectors of a pair of complex upper triangular matrices
f08yyf 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 21 dgglse
nagf_lapackeig_dgglse
Solves the real linear equality-constrained least squares (LSE) problem
f08zbf 21 dggglm
nagf_lapackeig_dggglm
Solves a real general Gauss–Markov linear model (GLM) problem
f08zef 22 dggqrf
nagf_lapackeig_dggqrf
Computes a generalized $QR$ factorization of a real matrix pair
f08zff 22 dggrqf
nagf_lapackeig_dggrqf
Computes a generalized $RQ$ factorization of a real matrix pair
f08znf 21 zgglse
nagf_lapackeig_zgglse
Solves the complex linear equality-constrained least squares (LSE) problem
f08zpf 21 zggglm
nagf_lapackeig_zggglm
Solves a complex general Gauss–Markov linear model (GLM) problem
f08zsf 22 zggqrf
nagf_lapackeig_zggqrf
Computes a generalized $QR$ factorization of a complex matrix pair
f08ztf 22 zggrqf
nagf_lapackeig_zggrqf
Computes a generalized $RQ$ factorization of a complex matrix pair
f08bef 16
(Deprecated)
dgeqpf
nagf_lapackeig_dgeqpf
$QR$ factorization, with column pivoting, of real general rectangular matrix
f08bsf 16
(Deprecated)
zgeqpf
nagf_lapackeig_zgeqpf
$QR$ factorization, with column pivoting, of complex general rectangular matrix
f08vaf 21
(Deprecated)
dggsvd
nagf_lapackeig_dggsvd
Computes the generalized singular value decomposition of a real matrix pair
f08vef 22
(Deprecated)
dggsvp
nagf_lapackeig_dggsvp
Produces orthogonal matrices that simultaneously reduce the $m×n$ matrix $A$ and the $p×n$ matrix $B$ to upper triangular form
f08vnf 21
(Deprecated)
zggsvd
nagf_lapackeig_zggsvd
Computes the generalized singular value decomposition of a complex matrix pair
f08vsf 22
(Deprecated)
zggsvp
nagf_lapackeig_zggsvp
Produces unitary matrices that simultaneously reduce the complex, $m×n$, matrix $A$ and the complex, $p×n$, matrix $B$ to upper triangular form
f08waf 21
(Deprecated)
dggev
nagf_lapackeig_dggev
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
f08wef 20
(Deprecated)
dgghrd
nagf_lapackeig_dgghrd
Performs an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
f08wnf 21
(Deprecated)
zggev
nagf_lapackeig_zggev
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
f08wsf 20
(Deprecated)
zgghrd
nagf_lapackeig_zgghrd
Performs a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
f08xaf 21
(Deprecated)
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
f08xnf 21
(Deprecated)
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