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

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

Function
Mark of
Introduction

Purpose
f08aac
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23 nag_lapackeig_dgels
Solves a real linear least squares problem of full rank
f08abc
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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
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7 nag_lapackeig_dgeqrf
Performs a $QR$ factorization of real general rectangular matrix
f08afc
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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
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7 nag_lapackeig_dgelqf
Performs a $LQ$ factorization of real general rectangular matrix
f08ajc
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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
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23 nag_lapackeig_zgels
Solves a complex linear least problem of full rank
f08apc
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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
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7 nag_lapackeig_zgeqrf
Performs a $QR$ factorization of complex general rectangular matrix
f08atc
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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
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7 nag_lapackeig_zgelqf
Performs a $LQ$ factorization of complex general rectangular matrix
f08awc
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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
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23 nag_lapackeig_dgelsy
Computes the minimum-norm solution to a real linear least squares problem
f08bbc
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24 nag_lapackeig_dtpqrt
$QR$ factorization of real general triangular-pentagonal matrix
f08bcc 24 nag_lapackeig_dtpmqrt
Applies the orthogonal transformation determined by f08bbc
f08bec
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7 (Deprecated) nag_lapackeig_dgeqpf
$QR$ factorization, with column pivoting, of real general rectangular matrix
f08bfc
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23 nag_lapackeig_dgeqp3
$QR$ factorization, with column pivoting, using BLAS-3, of real general rectangular matrix
f08bhc
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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
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23 nag_lapackeig_zgelsy
Computes the minimum-norm solution to a complex linear least squares problem
f08bpc
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24 nag_lapackeig_ztpqrt
$QR$ factorization of complex triangular-pentagonal matrix
f08bqc 24 nag_lapackeig_ztpmqrt
Applies the unitary transformation determined by f08bpc
f08bsc
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7 (Deprecated) nag_lapackeig_zgeqpf
$QR$ factorization, with column pivoting, of complex general rectangular matrix
f08btc
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23 nag_lapackeig_zgeqp3
$QR$ factorization, with column pivoting, using BLAS-3, of complex general rectangular matrix
f08bvc
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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
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23 nag_lapackeig_dgeqlf
$QL$ factorization of real general rectangular matrix
f08cfc
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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
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23 nag_lapackeig_dgerqf
$RQ$ factorization of real general rectangular matrix
f08cjc
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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
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23 nag_lapackeig_zgeqlf
$QL$ factorization of complex general rectangular matrix
f08ctc
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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
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23 nag_lapackeig_zgerqf
$RQ$ factorization of complex general rectangular matrix
f08cwc
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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
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23 nag_lapackeig_dsyev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix
f08fbc
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23 nag_lapackeig_dsyevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix
f08fcc
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7 nag_lapackeig_dsyevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer)
f08fdc
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23 nag_lapackeig_dsyevr
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations)
f08fec
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7 nag_lapackeig_dsytrd
Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form
f08ffc
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7 nag_lapackeig_dorgtr
Generate orthogonal transformation matrix from reduction to tridiagonal form determined by f08fec
f08fgc
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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
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23 nag_lapackeig_zheev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
f08fpc
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23 nag_lapackeig_zheevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
f08fqc
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7 nag_lapackeig_zheevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix (divide-and-conquer)
f08frc
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23 nag_lapackeig_zheevr
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations)
f08fsc
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7 nag_lapackeig_zhetrd
Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form
f08ftc
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7 nag_lapackeig_zungtr
Generate unitary transformation matrix from reduction to tridiagonal form determined by f08fsc
f08fuc
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7 nag_lapackeig_zunmtr
Applies the unitary transformation matrix determined by f08fsc
f08gac
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23 nag_lapackeig_dspev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
f08gbc
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23 nag_lapackeig_dspevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
f08gcc
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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
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7 nag_lapackeig_dsptrd
Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage
f08gfc
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7 nag_lapackeig_dopgtr
Generate orthogonal transformation matrix from reduction to tridiagonal form determined by f08gec
f08ggc
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7 nag_lapackeig_dopmtr
Applies the orthogonal transformation determined by f08gec
f08gnc
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23 nag_lapackeig_zhpev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
f08gpc
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23 nag_lapackeig_zhpevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
f08gqc
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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
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7 nag_lapackeig_zhptrd
Performs a unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage
f08gtc
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7 nag_lapackeig_zupgtr
Generates a unitary transformation matrix from reduction to tridiagonal form determined by f08gsc
f08guc
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7 nag_lapackeig_zupmtr
Applies the unitary transformation matrix determined by f08gsc
f08hac
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23 nag_lapackeig_dsbev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
f08hbc
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23 nag_lapackeig_dsbevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
f08hcc
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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
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7 nag_lapackeig_dsbtrd
Performs an orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form
f08hnc
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23 nag_lapackeig_zhbev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
f08hpc
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23 nag_lapackeig_zhbevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
f08hqc
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7 nag_lapackeig_zhbevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian band matrix (divide-and-conquer)
f08hsc
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7 nag_lapackeig_zhbtrd
Performs a unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form
f08jac
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23 nag_lapackeig_dstev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
f08jbc
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23 nag_lapackeig_dstevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
f08jcc
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7 nag_lapackeig_dstevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer)
f08jdc
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23 nag_lapackeig_dstevr
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations)
f08jec
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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
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7 nag_lapackeig_dsterf
Computes all eigenvalues of real symmetric tridiagonal matrix, root-free variant of the $QL$ or $QR$ algorithm
f08jgc
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7 nag_lapackeig_dpteqr
Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from real symmetric positive definite matrix
f08jhc
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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
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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
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7 nag_lapackeig_zpteqr
Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from complex Hermitian positive definite matrix
f08jvc
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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
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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
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23 nag_lapackeig_dgelss
Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition
f08kbc
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23 nag_lapackeig_dgesvd
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors
f08kcc
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23 nag_lapackeig_dgelsd
Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition (divide-and-conquer)
f08kdc
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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
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7 nag_lapackeig_dgebrd
Performs an orthogonal reduction of real general rectangular matrix to bidiagonal form
f08kfc
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7 nag_lapackeig_dorgbr
Generates an orthogonal transformation matrices from reduction to bidiagonal form determined by f08kec
f08kgc
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7 nag_lapackeig_dormbr
Applies the orthogonal transformations from reduction to bidiagonal form determined by f08kec
f08khc
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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
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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
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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
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23 nag_lapackeig_zgelss
Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition
f08kpc
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23 nag_lapackeig_zgesvd
Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors
f08kqc
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23 nag_lapackeig_zgelsd
Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition (divide-and-conquer)
f08krc
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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
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7 nag_lapackeig_zgebrd
Performs a unitary reduction of complex general rectangular matrix to bidiagonal form
f08ktc
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7 nag_lapackeig_zungbr
Generates unitary transformation matrices from the reduction to bidiagonal form determined by f08ksc
f08kuc
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7 nag_lapackeig_zunmbr
Applies the unitary transformations from reduction to bidiagonal form determined by f08ksc
f08kvc
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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
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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
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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
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7 nag_lapackeig_dgbbrd
Performs a reduction of real rectangular band matrix to upper bidiagonal form
f08lsc
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7 nag_lapackeig_zgbbrd
Reduction of complex rectangular band matrix to upper bidiagonal form
f08mbc
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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
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23 nag_lapackeig_dbdsdc
Computes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divide-and-conquer)
f08mec
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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
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23 nag_lapackeig_dgeev
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix
f08nbc
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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
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7 nag_lapackeig_dgehrd
Performs an orthogonal reduction of real general matrix to upper Hessenberg form
f08nfc
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7 nag_lapackeig_dorghr
Generates an orthogonal transformation matrix from reduction to Hessenberg form determined by f08nec
f08ngc
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7 nag_lapackeig_dormhr
Applies the orthogonal transformation matrix from reduction to Hessenberg form determined by f08nec
f08nhc
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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
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23 nag_lapackeig_zgeev
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix
f08npc
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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
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7 nag_lapackeig_zgehrd
Performs a unitary reduction of complex general matrix to upper Hessenberg form
f08ntc
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7 nag_lapackeig_zunghr
Generates a unitary transformation matrix from reduction to Hessenberg form determined by f08nsc
f08nuc
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7 nag_lapackeig_zunmhr
Applies the unitary transformation matrix from reduction to Hessenberg form determined by f08nsc
f08nvc
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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
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23 nag_lapackeig_dgees
Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors
f08pbc
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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
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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
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23 nag_lapackeig_zgees
Computes for complex square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors
f08ppc
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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
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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
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7 nag_lapackeig_dtrexc
Reorders a Schur factorization of real matrix using orthogonal similarity transformation
f08qgc
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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
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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
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7 nag_lapackeig_dtrsna
Computes estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix
f08qtc
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7 nag_lapackeig_ztrexc
Reorders a Schur factorization of complex matrix using unitary similarity transformation
f08quc
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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
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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
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7 nag_lapackeig_ztrsna
Computes estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix
f08rac
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24 nag_lapackeig_dorcsd
Computes the CS decomposition of an orthogonal matrix partitioned into four real submatrices
f08rnc
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24 nag_lapackeig_zuncsd
Computes the CS decomposition of a unitary matrix partitioned into four complex submatrices
f08sac
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23 nag_lapackeig_dsygv
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
f08sbc
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23 nag_lapackeig_dsygvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
f08scc
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23 nag_lapackeig_dsygvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer)
f08sec
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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
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23 nag_lapackeig_zhegv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
f08spc
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23 nag_lapackeig_zhegvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
f08sqc
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23 nag_lapackeig_zhegvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer)
f08ssc
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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
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23 nag_lapackeig_dspgv
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
f08tbc
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23 nag_lapackeig_dspgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
f08tcc
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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
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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
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23 nag_lapackeig_zhpgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
f08tpc
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23 nag_lapackeig_zhpgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
f08tqc
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23 nag_lapackeig_zhpgvd
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage (divide-and-conquer)
f08tsc
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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
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23 nag_lapackeig_dsbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
f08ubc
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23 nag_lapackeig_dsbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
f08ucc
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23 nag_lapackeig_dsbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem (divide-and-conquer)
f08uec
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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
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23 nag_lapackeig_zhbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
f08upc
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23 nag_lapackeig_zhbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
f08uqc
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23 nag_lapackeig_zhbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem (divide-and-conquer)
f08usc
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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 $A$
f08vac
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9 (Deprecated) nag_lapackeig_dggsvd
Computes the generalized singular value decomposition of a real matrix pair
f08vcc
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26 nag_lapackeig_dggsvd3
Computes, using BLAS-3, the generalized singular value decomposition of a real matrix pair
f08vec
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23 (Deprecated) nag_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
f08vgc
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26 nag_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
f08vnc
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9 (Deprecated) nag_lapackeig_zggsvd
Computes the generalized singular value decomposition of a complex matrix pair
f08vqc
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26 nag_lapackeig_zggsvd3
Computes, using BLAS-3, the generalized singular value decomposition of a complex matrix pair
f08vsc
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23 (Deprecated) nag_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
f08vuc
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26 nag_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
f08wac
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23 (Deprecated) nag_lapackeig_dggev
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
f08wbc
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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
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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
f08wec 7 (Deprecated) nag_lapackeig_dgghrd
Performs an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
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
f08wnc
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23 (Deprecated) nag_lapackeig_zggev
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
f08wpc
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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
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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
f08wsc 7 (Deprecated) nag_lapackeig_zgghrd
Performs a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
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
f08xac
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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
f08xbc
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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
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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
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7 nag_lapackeig_dhgeqz
Computes eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices
f08xnc
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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
f08xpc
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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
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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
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7 nag_lapackeig_zhgeqz
Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex, square, matrices
f08yec
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23 nag_lapackeig_dtgsja
Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair
f08yfc
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23 nag_lapackeig_dtgexc
Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation
f08ygc
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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
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23 nag_lapackeig_dtgsyl
Solves the real-valued, generalized, quasi-trangular, Sylvester equation
f08ykc
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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
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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
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23 nag_lapackeig_ztgsja
Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair
f08ytc
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23 nag_lapackeig_ztgexc
Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation
f08yuc
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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
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23 nag_lapackeig_ztgsyl
Solves the complex generalized Sylvester equation
f08yxc
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7 nag_lapackeig_ztgevc
Computes left and right eigenvectors of a pair of complex upper triangular matrices
f08yyc
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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
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9 nag_lapackeig_dgglse
Solves the real linear equality-constrained least squares (LSE) problem
f08zbc
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9 nag_lapackeig_dggglm
Solves a real general Gauss–Markov linear model (GLM) problem
f08zec
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23 nag_lapackeig_dggqrf
Computes a generalized $QR$ factorization of a real matrix pair
f08zfc
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23 nag_lapackeig_dggrqf
Computes a generalized $RQ$ factorization of a real matrix pair
f08znc
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9 nag_lapackeig_zgglse
Solves the complex linear equality-constrained least squares (LSE) problem
f08zpc
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9 nag_lapackeig_zggglm
Solves a complex general Gauss–Markov linear model (GLM) problem
f08zsc
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23 nag_lapackeig_zggqrf
Computes a generalized $QR$ factorization of a complex matrix pair
f08ztc
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23 nag_lapackeig_zggrqf
Computes a generalized $RQ$ factorization of a complex matrix pair