# NAG CL 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.

Function
Mark of
Introduction

Purpose
f08aac 23 nag_lapackeig_dgels
Solves a real linear least squares problem of full rank
f08abc 24 nag_lapackeig_dgeqrt
Performs a $QR$ factorization of real general rectangular matrix, with explicit blocking
f08acc 24 nag_lapackeig_dgemqrt
Applies the orthogonal transformation determined by f08abc
f08aec 7 nag_lapackeig_dgeqrf
Performs a $QR$ factorization of real general rectangular matrix
f08afc 7 nag_lapackeig_dorgqr
Forms all or part of orthogonal $Q$ from $QR$ factorization determined by f08aec, f08bec or f08bfc
f08agc 7 nag_lapackeig_dormqr
Applies an orthogonal transformation determined by f08aec, f08bec or f08bfc
f08ahc 7 nag_lapackeig_dgelqf
Performs a $LQ$ factorization of real general rectangular matrix
f08ajc 7 nag_lapackeig_dorglq
Forms all or part of orthogonal $Q$ from $LQ$ factorization determined by f08ahc
f08akc 7 nag_lapackeig_dormlq
Applies the orthogonal transformation determined by f08ahc
f08anc 23 nag_lapackeig_zgels
Solves a complex linear least problem of full rank
f08apc 24 nag_lapackeig_zgeqrt
Performs a $QR$ factorization of complex general rectangular matrix using recursive algorithm
f08aqc 24 nag_lapackeig_zgemqrt
Applies the unitary transformation determined by f08apc
f08asc 7 nag_lapackeig_zgeqrf
Performs a $QR$ factorization of complex general rectangular matrix
f08atc 7 nag_lapackeig_zungqr
Forms all or part of unitary $Q$ from $QR$ factorization determined by f08asc, f08bsc or f08btc
f08auc 7 nag_lapackeig_zunmqr
Applies a unitary transformation determined by f08asc, f08bsc or f08btc
f08avc 7 nag_lapackeig_zgelqf
Performs a $LQ$ factorization of complex general rectangular matrix
f08awc 7 nag_lapackeig_zunglq
Forms all or part of unitary $Q$ from $LQ$ factorization determined by f08avc
f08axc 7 nag_lapackeig_zunmlq
Applies the unitary transformation determined by f08avc
f08bac 23 nag_lapackeig_dgelsy
Computes the minimum-norm solution to a real linear least squares problem
f08bbc 24 nag_lapackeig_dtpqrt
$QR$ factorization of real general triangular-pentagonal matrix
f08bcc 24 nag_lapackeig_dtpmqrt
Applies the orthogonal transformation determined by f08bbc
f08bfc 23 nag_lapackeig_dgeqp3
$QR$ factorization, with column pivoting, using BLAS-3, of real general rectangular matrix
f08bhc 23 nag_lapackeig_dtzrzf
Reduces a real upper trapezoidal matrix to upper triangular form
f08bkc 23 nag_lapackeig_dormrz
Applies the orthogonal transformation determined by f08bhc
f08bnc 23 nag_lapackeig_zgelsy
Computes the minimum-norm solution to a complex linear least squares problem
f08bpc 24 nag_lapackeig_ztpqrt
$QR$ factorization of complex triangular-pentagonal matrix
f08bqc 24 nag_lapackeig_ztpmqrt
Applies the unitary transformation determined by f08bpc
f08btc 23 nag_lapackeig_zgeqp3
$QR$ factorization, with column pivoting, using BLAS-3, of complex general rectangular matrix
f08bvc 23 nag_lapackeig_ztzrzf
Reduces a complex upper trapezoidal matrix to upper triangular form
f08bxc 23 nag_lapackeig_zunmrz
Applies the unitary transformation determined by f08bvc
f08cec 23 nag_lapackeig_dgeqlf
$QL$ factorization of real general rectangular matrix
f08cfc 23 nag_lapackeig_dorgql
Form all or part of orthogonal $Q$ from $QL$ factorization determined by f08cec
f08cgc 23 nag_lapackeig_dormql
Applies the orthogonal transformation determined by f08cec
f08chc 23 nag_lapackeig_dgerqf
$RQ$ factorization of real general rectangular matrix
f08cjc 23 nag_lapackeig_dorgrq
Form all or part of orthogonal $Q$ from $RQ$ factorization determined by f08chc
f08ckc 23 nag_lapackeig_dormrq
Applies the orthogonal transformation determined by f08chc
f08csc 23 nag_lapackeig_zgeqlf
$QL$ factorization of complex general rectangular matrix
f08ctc 23 nag_lapackeig_zungql
Form all or part of unitary $Q$ from $QL$ factorization determined by f08csc
f08cuc 23 nag_lapackeig_zunmql
Applies the unitary transformation determined by f08csc
f08cvc 23 nag_lapackeig_zgerqf
$RQ$ factorization of complex general rectangular matrix
f08cwc 23 nag_lapackeig_zungrq
Form all or part of unitary $Q$ from $RQ$ factorization determined by f08cvc
f08cxc 23 nag_lapackeig_zunmrq
Applies the unitary transformation determined by f08cvc
f08fac 23 nag_lapackeig_dsyev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix
f08fbc 23 nag_lapackeig_dsyevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix
f08fcc 7 nag_lapackeig_dsyevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer)
f08fdc 23 nag_lapackeig_dsyevr
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations)
f08fec 7 nag_lapackeig_dsytrd
Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form
f08ffc 7 nag_lapackeig_dorgtr
Generate orthogonal transformation matrix from reduction to tridiagonal form determined by f08fec
f08fgc 7 nag_lapackeig_dormtr
Applies the orthogonal transformation determined by f08fec
f08flc 23 nag_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
f08fnc 23 nag_lapackeig_zheev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
f08fpc 23 nag_lapackeig_zheevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
f08fqc 7 nag_lapackeig_zheevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix (divide-and-conquer)
f08frc 23 nag_lapackeig_zheevr
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations)
f08fsc 7 nag_lapackeig_zhetrd
Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form
f08ftc 7 nag_lapackeig_zungtr
Generate unitary transformation matrix from reduction to tridiagonal form determined by f08fsc
f08fuc 7 nag_lapackeig_zunmtr
Applies the unitary transformation matrix determined by f08fsc
f08gac 23 nag_lapackeig_dspev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
f08gbc 23 nag_lapackeig_dspevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
f08gcc 7 nag_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)
f08gec 7 nag_lapackeig_dsptrd
Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage
f08gfc 7 nag_lapackeig_dopgtr
Generate orthogonal transformation matrix from reduction to tridiagonal form determined by f08gec
f08ggc 7 nag_lapackeig_dopmtr
Applies the orthogonal transformation determined by f08gec
f08gnc 23 nag_lapackeig_zhpev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
f08gpc 23 nag_lapackeig_zhpevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
f08gqc 7 nag_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)
f08gsc 7 nag_lapackeig_zhptrd
Performs a unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage
f08gtc 7 nag_lapackeig_zupgtr
Generates a unitary transformation matrix from reduction to tridiagonal form determined by f08gsc
f08guc 7 nag_lapackeig_zupmtr
Applies the unitary transformation matrix determined by f08gsc
f08hac 23 nag_lapackeig_dsbev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
f08hbc 23 nag_lapackeig_dsbevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
f08hcc 7 nag_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)
f08hec 7 nag_lapackeig_dsbtrd
Performs an orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form
f08hnc 23 nag_lapackeig_zhbev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
f08hpc 23 nag_lapackeig_zhbevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
f08hqc 7 nag_lapackeig_zhbevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian band matrix (divide-and-conquer)
f08hsc 7 nag_lapackeig_zhbtrd
Performs a unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form
f08jac 23 nag_lapackeig_dstev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
f08jbc 23 nag_lapackeig_dstevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
f08jcc 7 nag_lapackeig_dstevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer)
f08jdc 23 nag_lapackeig_dstevr
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations)
f08jec 7 nag_lapackeig_dsteqr
Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using the implicit $QL$ or $QR$ algorithm
f08jfc 7 nag_lapackeig_dsterf
Computes all eigenvalues of real symmetric tridiagonal matrix, root-free variant of the $QL$ or $QR$ algorithm
f08jgc 7 nag_lapackeig_dpteqr
Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from real symmetric positive definite matrix
f08jhc 23 nag_lapackeig_dstedc
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a matrix reduced to this form (divide-and-conquer)
f08jjc 7 nag_lapackeig_dstebz
Computes selected eigenvalues of real symmetric tridiagonal matrix by bisection
f08jkc 7 nag_lapackeig_dstein
Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array
f08jlc 23 nag_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)
f08jsc 7 nag_lapackeig_zsteqr
Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using the implicit $QL$ or $QR$ algorithm
f08juc 7 nag_lapackeig_zpteqr
Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from complex Hermitian positive definite matrix
f08jvc 23 nag_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)
f08jxc 7 nag_lapackeig_zstein
Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array
f08jyc 23 nag_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)
f08kac 23 nag_lapackeig_dgelss
Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition
f08kbc 23 nag_lapackeig_dgesvd
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors
f08kcc 23 nag_lapackeig_dgelsd
Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition (divide-and-conquer)
f08kdc 23 nag_lapackeig_dgesdd
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
f08kec 7 nag_lapackeig_dgebrd
Performs an orthogonal reduction of real general rectangular matrix to bidiagonal form
f08kfc 7 nag_lapackeig_dorgbr
Generates an orthogonal transformation matrices from reduction to bidiagonal form determined by f08kec
f08kgc 7 nag_lapackeig_dormbr
Applies the orthogonal transformations from reduction to bidiagonal form determined by f08kec
f08khc 23 nag_lapackeig_dgejsv
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (preconditioned Jacobi)
f08kjc 23 nag_lapackeig_dgesvj
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (fast Jacobi)
f08kmc 27 nag_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
f08knc 23 nag_lapackeig_zgelss
Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition
f08kpc 23 nag_lapackeig_zgesvd
Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors
f08kqc 23 nag_lapackeig_zgelsd
Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition (divide-and-conquer)
f08krc 23 nag_lapackeig_zgesdd
Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
f08ksc 7 nag_lapackeig_zgebrd
Performs a unitary reduction of complex general rectangular matrix to bidiagonal form
f08ktc 7 nag_lapackeig_zungbr
Generates unitary transformation matrices from the reduction to bidiagonal form determined by f08ksc
f08kuc 7 nag_lapackeig_zunmbr
Applies the unitary transformations from reduction to bidiagonal form determined by f08ksc
f08kvc 27 nag_lapackeig_zgejsv
Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (preconditioned Jacobi)
f08kwc 27 nag_lapackeig_zgesvj
Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (fast Jacobi)
f08kzc 27 nag_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
f08lec 7 nag_lapackeig_dgbbrd
Performs a reduction of real rectangular band matrix to upper bidiagonal form
f08lsc 7 nag_lapackeig_zgbbrd
Reduction of complex rectangular band matrix to upper bidiagonal form
f08mbc 27 nag_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
f08mdc 23 nag_lapackeig_dbdsdc
Computes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divide-and-conquer)
f08mec 7 nag_lapackeig_dbdsqr
Performs an SVD of real bidiagonal matrix reduced from real general matrix
f08msc 7 nag_lapackeig_zbdsqr
Performs an SVD of real bidiagonal matrix reduced from complex general matrix
f08nac 23 nag_lapackeig_dgeev
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix
f08nbc 23 nag_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
f08nec 7 nag_lapackeig_dgehrd
Performs an orthogonal reduction of real general matrix to upper Hessenberg form
f08nfc 7 nag_lapackeig_dorghr
Generates an orthogonal transformation matrix from reduction to Hessenberg form determined by f08nec
f08ngc 7 nag_lapackeig_dormhr
Applies the orthogonal transformation matrix from reduction to Hessenberg form determined by f08nec
f08nhc 7 nag_lapackeig_dgebal
Balances a real general matrix
f08njc 7 nag_lapackeig_dgebak
Transforms eigenvectors of real balanced matrix to those of original matrix supplied to f08nhc
f08nnc 23 nag_lapackeig_zgeev
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix
f08npc 23 nag_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
f08nsc 7 nag_lapackeig_zgehrd
Performs a unitary reduction of complex general matrix to upper Hessenberg form
f08ntc 7 nag_lapackeig_zunghr
Generates a unitary transformation matrix from reduction to Hessenberg form determined by f08nsc
f08nuc 7 nag_lapackeig_zunmhr
Applies the unitary transformation matrix from reduction to Hessenberg form determined by f08nsc
f08nvc 7 nag_lapackeig_zgebal
Balances a complex general matrix
f08nwc 7 nag_lapackeig_zgebak
Transforms eigenvectors of complex balanced matrix to those of original matrix supplied to f08nvc
f08pac 23 nag_lapackeig_dgees
Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors
f08pbc 23 nag_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
f08pec 7 nag_lapackeig_dhseqr
Computes the eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix
f08pkc 7 nag_lapackeig_dhsein
Computes selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration
f08pnc 23 nag_lapackeig_zgees
Computes for complex square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors
f08ppc 23 nag_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
f08psc 7 nag_lapackeig_zhseqr
Computes the eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix
f08pxc 7 nag_lapackeig_zhsein
Computes selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration
f08qfc 7 nag_lapackeig_dtrexc
Reorders a Schur factorization of real matrix using orthogonal similarity transformation
f08qgc 7 nag_lapackeig_dtrsen
Reorders a Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
f08qhc 7 nag_lapackeig_dtrsyl
Solves the real Sylvester matrix equation $AX+XB=C$, $A$ and $B$ are upper quasi-triangular or transposes
f08qkc 7 nag_lapackeig_dtrevc
Computes left and right eigenvectors of real upper quasi-triangular matrix
f08qlc 7 nag_lapackeig_dtrsna
Computes estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix
f08qtc 7 nag_lapackeig_ztrexc
Reorders a Schur factorization of complex matrix using unitary similarity transformation
f08quc 7 nag_lapackeig_ztrsen
Reorders a Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
f08qvc 7 nag_lapackeig_ztrsyl
Solves the complex Sylvester matrix equation $AX+XB=C$, $A$ and $B$ are upper triangular or conjugate-transposes
f08qxc 7 nag_lapackeig_ztrevc
Computes left and right eigenvectors of complex upper triangular matrix
f08qyc 7 nag_lapackeig_ztrsna
Computes estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix
f08rac 24 nag_lapackeig_dorcsd
Computes the CS decomposition of an orthogonal matrix partitioned into four real submatrices
f08rnc 24 nag_lapackeig_zuncsd
Computes the CS decomposition of a unitary matrix partitioned into four complex submatrices
f08sac 23 nag_lapackeig_dsygv
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
f08sbc 23 nag_lapackeig_dsygvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
f08scc 23 nag_lapackeig_dsygvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer)
f08sec 7 nag_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 f07fdc
f08snc 23 nag_lapackeig_zhegv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
f08spc 23 nag_lapackeig_zhegvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
f08sqc 23 nag_lapackeig_zhegvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer)
f08ssc 7 nag_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 f07frc
f08tac 23 nag_lapackeig_dspgv
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
f08tbc 23 nag_lapackeig_dspgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
f08tcc 23 nag_lapackeig_dspgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage (divide-and-conquer)
f08tec 7 nag_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 f07gdc
f08tnc 23 nag_lapackeig_zhpgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
f08tpc 23 nag_lapackeig_zhpgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
f08tqc 23 nag_lapackeig_zhpgvd
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage (divide-and-conquer)
f08tsc 7 nag_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 f07grc
f08uac 23 nag_lapackeig_dsbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
f08ubc 23 nag_lapackeig_dsbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
f08ucc 23 nag_lapackeig_dsbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem (divide-and-conquer)
f08uec 7 nag_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 $A$
f08ufc 7 nag_lapackeig_dpbstf
Computes a split Cholesky factorization of real symmetric positive definite band matrix $A$
f08unc 23 nag_lapackeig_zhbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
f08upc 23 nag_lapackeig_zhbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
f08uqc 23 nag_lapackeig_zhbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem (divide-and-conquer)
f08usc 7 nag_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 $A$
f08utc 7 nag_lapackeig_zpbstf
Computes a split Cholesky factorization of complex Hermitian positive definite band matrix $A$
f08vcc 26 nag_lapackeig_dggsvd3
Computes, using BLAS-3, the generalized singular value decomposition of a real matrix pair
f08vgc 26 nag_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
f08vqc 26 nag_lapackeig_zggsvd3
Computes, using BLAS-3, the generalized singular value decomposition of a complex matrix pair
f08vuc 26 nag_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
f08wbc 23 nag_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
f08wcc 26 nag_lapackeig_dggev3
Computes, for a real nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
f08wfc 26 nag_lapackeig_dgghd3
Performs, using BLAS-3, an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
f08whc 7 nag_lapackeig_dggbal
Balances a pair of real, square, matrices
f08wjc 7 nag_lapackeig_dggbak
Transforms eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to f08whc
f08wpc 23 nag_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
f08wqc 26 nag_lapackeig_zggev3
Computes, for a complex nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
f08wtc 26 nag_lapackeig_zgghd3
Performs, using BLAS-3, a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
f08wvc 7 nag_lapackeig_zggbal
Balances a pair of complex, square, matrices
f08wwc 7 nag_lapackeig_zggbak
Transforms eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to f08wvc
f08xbc 23 nag_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
f08xcc 26 nag_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
f08xec 7 nag_lapackeig_dhgeqz
Computes eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices
f08xpc 23 nag_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
f08xqc 26 nag_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
f08xsc 7 nag_lapackeig_zhgeqz
Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex, square, matrices
f08yec 23 nag_lapackeig_dtgsja
Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair
f08yfc 23 nag_lapackeig_dtgexc
Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation
f08ygc 23 nag_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
f08yhc 23 nag_lapackeig_dtgsyl
Solves the real-valued, generalized, quasi-trangular, Sylvester equation
f08ykc 7 nag_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
f08ylc 23 nag_lapackeig_dtgsna
Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a real matrix pair in generalized real Schur canonical form
f08ysc 23 nag_lapackeig_ztgsja
Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair
f08ytc 23 nag_lapackeig_ztgexc
Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation
f08yuc 23 nag_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
f08yvc 23 nag_lapackeig_ztgsyl
Solves the complex generalized Sylvester equation
f08yxc 7 nag_lapackeig_ztgevc
Computes left and right eigenvectors of a pair of complex upper triangular matrices
f08yyc 23 nag_lapackeig_ztgsna
Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a complex matrix pair in generalized Schur canonical form
f08zac 9 nag_lapackeig_dgglse
Solves the real linear equality-constrained least squares (LSE) problem
f08zbc 9 nag_lapackeig_dggglm
Solves a real general Gauss–Markov linear model (GLM) problem
f08zec 23 nag_lapackeig_dggqrf
Computes a generalized $QR$ factorization of a real matrix pair
f08zfc 23 nag_lapackeig_dggrqf
Computes a generalized $RQ$ factorization of a real matrix pair
f08znc 9 nag_lapackeig_zgglse
Solves the complex linear equality-constrained least squares (LSE) problem
f08zpc 9 nag_lapackeig_zggglm
Solves a complex general Gauss–Markov linear model (GLM) problem
f08zsc 23 nag_lapackeig_zggqrf
Computes a generalized $QR$ factorization of a complex matrix pair
f08ztc 23 nag_lapackeig_zggrqf
Computes a generalized $RQ$ factorization of a complex matrix pair
f08bec 7
(Deprecated)
nag_lapackeig_dgeqpf
$QR$ factorization, with column pivoting, of real general rectangular matrix
f08bsc 7
(Deprecated)
nag_lapackeig_zgeqpf
$QR$ factorization, with column pivoting, of complex general rectangular matrix
f08vac 9
(Deprecated)
nag_lapackeig_dggsvd
Computes the generalized singular value decomposition of a real matrix pair
f08vec 23
(Deprecated)
nag_lapackeig_dggsvp
Produces orthogonal matrices that simultaneously reduce the $m×n$ matrix $A$ and the $p×n$ matrix $B$ to upper triangular form
f08vnc 9
(Deprecated)
nag_lapackeig_zggsvd
Computes the generalized singular value decomposition of a complex matrix pair
f08vsc 23
(Deprecated)
nag_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
f08wac 23
(Deprecated)
nag_lapackeig_dggev
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
f08wec 7
(Deprecated)
nag_lapackeig_dgghrd
Performs an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
f08wnc 23
(Deprecated)
nag_lapackeig_zggev
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
f08wsc 7
(Deprecated)
nag_lapackeig_zgghrd
Performs a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
f08xac 23
(Deprecated)
nag_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
f08xnc 23
(Deprecated)
nag_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