NAG Library Chapter Contents

f08 – Least Squares and Eigenvalue Problems (LAPACK)


f08 Chapter Introduction – a description of the Chapter and an overview of the algorithms available

Function
Name
Mark of
Introduction

Purpose
f08aac
Example Text
Example Data
23 nag_dgels
Solves a real linear least squares problem of full rank
f08abc
Example Text
Example Data
24 nag_dgeqrt
Performs a QR factorization of real general rectangular matrix, with explicit blocking
f08acc 24 nag_dgemqrt
Applies the orthogonal transformation determined by nag_dgeqrt (f08abc)
f08aec
Example Text
Example Data
7 nag_dgeqrf
Performs a QR factorization of real general rectangular matrix
f08afc
Example Text
Example Data
7 nag_dorgqr
Forms all or part of orthogonal Q from QR factorization determined by nag_dgeqrf (f08aec), nag_dgeqpf (f08bec) or nag_dgeqp3 (f08bfc)
f08agc 7 nag_dormqr
Applies an orthogonal transformation determined by nag_dgeqrf (f08aec), nag_dgeqpf (f08bec) or nag_dgeqp3 (f08bfc)
f08ahc
Example Text
Example Data
7 nag_dgelqf
Performs a LQ factorization of real general rectangular matrix
f08ajc
Example Text
Example Data
7 nag_dorglq
Forms all or part of orthogonal Q from LQ factorization determined by nag_dgelqf (f08ahc)
f08akc 7 nag_dormlq
Applies the orthogonal transformation determined by nag_dgelqf (f08ahc)
f08anc
Example Text
Example Data
23 nag_zgels
Solves a complex linear least problem of full rank
f08apc
Example Text
Example Data
24 nag_zgeqrt
Performs a QR factorization of complex general rectangular matrix using recursive algorithm
f08aqc 24 nag_zgemqrt
Applies the unitary transformation determined by nag_zgeqrt (f08apc)
f08asc
Example Text
Example Data
7 nag_zgeqrf
Performs a QR factorization of complex general rectangular matrix
f08atc
Example Text
Example Data
7 nag_zungqr
Forms all or part of unitary Q from QR factorization determined by nag_zgeqrf (f08asc), nag_zgeqpf (f08bsc) or nag_zgeqp3 (f08btc)
f08auc 7 nag_zunmqr
Applies a unitary transformation determined by nag_zgeqrf (f08asc), nag_zgeqpf (f08bsc) or nag_zgeqp3 (f08btc)
f08avc
Example Text
Example Data
7 nag_zgelqf
Performs a LQ factorization of complex general rectangular matrix
f08awc
Example Text
Example Data
7 nag_zunglq
Forms all or part of unitary Q from LQ factorization determined by nag_zgelqf (f08avc)
f08axc 7 nag_zunmlq
Applies the unitary transformation determined by nag_zgelqf (f08avc)
f08bac
Example Text
Example Data
23 nag_dgelsy
Computes the minimum-norm solution to a real linear least squares problem
f08bbc
Example Text
Example Data
24 nag_dtpqrt
QR factorization of real general triangular-pentagonal matrix
f08bcc 24 nag_dtpmqrt
Applies the orthogonal transformation determined by nag_dtpqrt (f08bbc)
f08bec
Example Text
Example Data
7 nag_dgeqpf
QR factorization, with column pivoting, of real general rectangular matrix
f08bfc
Example Text
Example Data
23 nag_dgeqp3
QR factorization, with column pivoting, using BLAS-3, of real general rectangular matrix
f08bhc
Example Text
Example Data
23 nag_dtzrzf
Reduces a real upper trapezoidal matrix to upper triangular form
f08bkc 23 nag_dormrz
Applies the orthogonal transformation determined by nag_dtzrzf (f08bhc)
f08bnc
Example Text
Example Data
23 nag_zgelsy
Computes the minimum-norm solution to a complex linear least squares problem
f08bpc
Example Text
Example Data
24 nag_ztpqrt
QR factorization of complex triangular-pentagonal matrix
f08bqc 24 nag_ztpmqrt
Applies the unitary transformation determined by nag_ztpqrt (f08bpc)
f08bsc
Example Text
Example Data
7 nag_zgeqpf
QR factorization, with column pivoting, of complex general rectangular matrix
f08btc
Example Text
Example Data
23 nag_zgeqp3
QR factorization, with column pivoting, using BLAS-3, of complex general rectangular matrix
f08bvc
Example Text
Example Data
23 nag_ztzrzf
Reduces a complex upper trapezoidal matrix to upper triangular form
f08bxc 23 nag_zunmrz
Applies the unitary transformation determined by nag_ztzrzf (f08bvc)
f08cec
Example Text
Example Data
23 nag_dgeqlf
QL factorization of real general rectangular matrix
f08cfc
Example Text
Example Data
23 nag_dorgql
Form all or part of orthogonal Q from QL factorization determined by nag_dgeqlf (f08cec)
f08cgc 23 nag_dormql
Applies the orthogonal transformation determined by nag_dgeqlf (f08cec)
f08chc
Example Text
Example Data
23 nag_dgerqf
RQ factorization of real general rectangular matrix
f08cjc
Example Text
Example Data
23 nag_dorgrq
Form all or part of orthogonal Q from RQ factorization determined by nag_dgerqf (f08chc)
f08ckc 23 nag_dormrq
Applies the orthogonal transformation determined by nag_dgerqf (f08chc)
f08csc
Example Text
Example Data
23 nag_zgeqlf
QL factorization of complex general rectangular matrix
f08ctc
Example Text
Example Data
23 nag_zungql
Form all or part of unitary Q from QL factorization determined by nag_zgeqlf (f08csc)
f08cuc 23 nag_zunmql
Applies the unitary transformation determined by nag_zgeqlf (f08csc)
f08cvc
Example Text
Example Data
23 nag_zgerqf
RQ factorization of complex general rectangular matrix
f08cwc
Example Text
Example Data
23 nag_zungrq
Form all or part of unitary Q from RQ factorization determined by nag_zgerqf (f08cvc)
f08cxc 23 nag_zunmrq
Applies the unitary transformation determined by nag_zgerqf (f08cvc)
f08fac
Example Text
Example Data
23 nag_dsyev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix
f08fbc
Example Text
Example Data
23 nag_dsyevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix
f08fcc
Example Text
Example Data
7 nag_dsyevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer)
f08fdc
Example Text
Example Data
23 nag_dsyevr
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations)
f08fec
Example Text
Example Data
7 nag_dsytrd
Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form
f08ffc
Example Text
Example Data
7 nag_dorgtr
Generate orthogonal transformation matrix from reduction to tridiagonal form determined by nag_dsytrd (f08fec)
f08fgc
Example Text
Example Data
7 nag_dormtr
Applies the orthogonal transformation determined by nag_dsytrd (f08fec)
f08flc 23 nag_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
Example Text
Example Data
23 nag_zheev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
f08fpc
Example Text
Example Data
23 nag_zheevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
f08fqc
Example Text
Example Data
7 nag_zheevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix (divide-and-conquer)
f08frc
Example Text
Example Data
23 nag_zheevr
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations)
f08fsc
Example Text
Example Data
7 nag_zhetrd
Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form
f08ftc
Example Text
Example Data
7 nag_zungtr
Generate unitary transformation matrix from reduction to tridiagonal form determined by nag_zhetrd (f08fsc)
f08fuc
Example Text
Example Data
7 nag_zunmtr
Applies the unitary transformation matrix determined by nag_zhetrd (f08fsc)
f08gac
Example Text
Example Data
23 nag_dspev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
f08gbc
Example Text
Example Data
23 nag_dspevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
f08gcc
Example Text
Example Data
7 nag_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
Example Text
Example Data
7 nag_dsptrd
Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage
f08gfc
Example Text
Example Data
7 nag_dopgtr
Generate orthogonal transformation matrix from reduction to tridiagonal form determined by nag_dsptrd (f08gec)
f08ggc
Example Text
Example Data
7 nag_dopmtr
Applies the orthogonal transformation determined by nag_dsptrd (f08gec)
f08gnc
Example Text
Example Data
23 nag_zhpev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
f08gpc
Example Text
Example Data
23 nag_zhpevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
f08gqc
Example Text
Example Data
7 nag_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
Example Text
Example Data
7 nag_zhptrd
Performs a unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage
f08gtc
Example Text
Example Data
7 nag_zupgtr
Generates a unitary transformation matrix from reduction to tridiagonal form determined by nag_zhptrd (f08gsc)
f08guc
Example Text
Example Data
7 nag_zupmtr
Applies the unitary transformation matrix determined by nag_zhptrd (f08gsc)
f08hac
Example Text
Example Data
23 nag_dsbev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
f08hbc
Example Text
Example Data
23 nag_dsbevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
f08hcc
Example Text
Example Data
7 nag_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
Example Text
Example Data
7 nag_dsbtrd
Performs an orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form
f08hnc
Example Text
Example Data
23 nag_zhbev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
f08hpc
Example Text
Example Data
23 nag_zhbevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
f08hqc
Example Text
Example Data
7 nag_zhbevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian band matrix (divide-and-conquer)
f08hsc
Example Text
Example Data
7 nag_zhbtrd
Performs a unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form
f08jac
Example Text
Example Data
23 nag_dstev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
f08jbc
Example Text
Example Data
23 nag_dstevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
f08jcc
Example Text
Example Data
7 nag_dstevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer)
f08jdc
Example Text
Example Data
23 nag_dstevr
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations)
f08jec
Example Text
Example Data
7 nag_dsteqr
Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using the implicit QL or QR algorithm
f08jfc
Example Text
Example Data
7 nag_dsterf
Computes all eigenvalues of real symmetric tridiagonal matrix, root-free variant of the QL or QR algorithm
f08jgc
Example Text
Example Data
7 nag_dpteqr
Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from real symmetric positive definite matrix
f08jhc
Example Text
Example Data
23 nag_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_dstebz
Computes selected eigenvalues of real symmetric tridiagonal matrix by bisection
f08jkc 7 nag_dstein
Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array
f08jlc
Example Text
Example Data
23 nag_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_zsteqr
Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using the implicit QL or QR algorithm
f08juc
Example Text
Example Data
7 nag_zpteqr
Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from complex Hermitian positive definite matrix
f08jvc
Example Text
Example Data
23 nag_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_zstein
Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array
f08jyc
Example Text
Example Data
23 nag_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
Example Text
Example Data
23 nag_dgelss
Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition
f08kbc
Example Text
Example Data
23 nag_dgesvd
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors
f08kcc
Example Text
Example Data
23 nag_dgelsd
Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition (divide-and-conquer)
f08kdc
Example Text
Example Data
23 nag_dgesdd
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
f08kec
Example Text
Example Data
7 nag_dgebrd
Performs an orthogonal reduction of real general rectangular matrix to bidiagonal form
f08kfc
Example Text
Example Data
7 nag_dorgbr
Generates an orthogonal transformation matrices from reduction to bidiagonal form determined by nag_dgebrd (f08kec)
f08kgc
Example Text
Example Data
7 nag_dormbr
Applies the orthogonal transformations from reduction to bidiagonal form determined by nag_dgebrd (f08kec)
f08khc
Example Text
Example Data
23 nag_dgejsv
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (preconditioned Jacobi)
f08kjc
Example Text
Example Data
23 nag_dgesvj
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (fast Jacobi)
f08knc
Example Text
Example Data
23 nag_zgelss
Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition
f08kpc
Example Text
Example Data
23 nag_zgesvd
Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors
f08kqc
Example Text
Example Data
23 nag_zgelsd
Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition (divide-and-conquer)
f08krc
Example Text
Example Data
23 nag_zgesdd
Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
f08ksc
Example Text
Example Data
7 nag_zgebrd
Performs a unitary reduction of complex general rectangular matrix to bidiagonal form
f08ktc
Example Text
Example Data
7 nag_zungbr
Generates unitary transformation matrices from the reduction to bidiagonal form determined by nag_zgebrd (f08ksc)
f08kuc
Example Text
Example Data
7 nag_zunmbr
Applies the unitary transformations from reduction to bidiagonal form determined by nag_zgebrd (f08ksc)
f08lec
Example Text
Example Data
7 nag_dgbbrd
Performs a reduction of real rectangular band matrix to upper bidiagonal form
f08lsc
Example Text
Example Data
7 nag_zgbbrd
Reduction of complex rectangular band matrix to upper bidiagonal form
f08mdc
Example Text
Example Data
23 nag_dbdsdc
Computes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divide-and-conquer)
f08mec
Example Text
Example Data
7 nag_dbdsqr
Performs an SVD of real bidiagonal matrix reduced from real general matrix
f08msc 7 nag_zbdsqr
Performs an SVD of real bidiagonal matrix reduced from complex general matrix
f08nac
Example Text
Example Data
23 nag_dgeev
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix
f08nbc
Example Text
Example Data
23 nag_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
Example Text
Example Data
7 nag_dgehrd
Performs an orthogonal reduction of real general matrix to upper Hessenberg form
f08nfc
Example Text
Example Data
7 nag_dorghr
Generates an orthogonal transformation matrix from reduction to Hessenberg form determined by nag_dgehrd (f08nec)
f08ngc
Example Text
Example Data
7 nag_dormhr
Applies the orthogonal transformation matrix from reduction to Hessenberg form determined by nag_dgehrd (f08nec)
f08nhc
Example Text
Example Data
7 nag_dgebal
Balances a real general matrix
f08njc 7 nag_dgebak
Transforms eigenvectors of real balanced matrix to those of original matrix supplied to nag_dgebal (f08nhc)
f08nnc
Example Text
Example Data
23 nag_zgeev
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix
f08npc
Example Text
Example Data
23 nag_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
Example Text
Example Data
7 nag_zgehrd
Performs a unitary reduction of complex general matrix to upper Hessenberg form
f08ntc
Example Text
Example Data
7 nag_zunghr
Generates a unitary transformation matrix from reduction to Hessenberg form determined by nag_zgehrd (f08nsc)
f08nuc
Example Text
Example Data
7 nag_zunmhr
Applies the unitary transformation matrix from reduction to Hessenberg form determined by nag_zgehrd (f08nsc)
f08nvc
Example Text
Example Data
7 nag_zgebal
Balances a complex general matrix
f08nwc 7 nag_zgebak
Transforms eigenvectors of complex balanced matrix to those of original matrix supplied to nag_zgebal (f08nvc)
f08pac
Example Text
Example Data
23 nag_dgees
Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors
f08pbc
Example Text
Example Data
23 nag_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
Example Text
Example Data
7 nag_dhseqr
Computes the eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix
f08pkc 7 nag_dhsein
Computes selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration
f08pnc
Example Text
Example Data
23 nag_zgees
Computes for complex square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors
f08ppc
Example Text
Example Data
23 nag_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
Example Text
Example Data
7 nag_zhseqr
Computes the eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix
f08pxc 7 nag_zhsein
Computes selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration
f08qfc
Example Text
Example Data
7 nag_dtrexc
Reorders a Schur factorization of real matrix using orthogonal similarity transformation
f08qgc
Example Text
Example Data
7 nag_dtrsen
Reorders a Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
f08qhc
Example Text
Example Data
7 nag_dtrsyl
Solves the real Sylvester matrix equation AX+XB=C, A and B are upper quasi-triangular or transposes
f08qkc 7 nag_dtrevc
Computes left and right eigenvectors of real upper quasi-triangular matrix
f08qlc
Example Text
Example Data
7 nag_dtrsna
Computes estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix
f08qtc
Example Text
Example Data
7 nag_ztrexc
Reorders a Schur factorization of complex matrix using unitary similarity transformation
f08quc
Example Text
Example Data
7 nag_ztrsen
Reorders a Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
f08qvc
Example Text
Example Data
7 nag_ztrsyl
Solves the complex Sylvester matrix equation AX+XB=C, A and B are upper triangular or conjugate-transposes
f08qxc 7 nag_ztrevc
Computes left and right eigenvectors of complex upper triangular matrix
f08qyc
Example Text
Example Data
7 nag_ztrsna
Computes estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix
f08rac
Example Text
Example Data
24 nag_dorcsd
Computes the CS decomposition of an orthogonal matrix partitioned into four real submatrices
f08rnc
Example Text
Example Data
24 nag_zuncsd
Computes the CS decomposition of a unitary matrix partitioned into four complex submatrices
f08sac
Example Text
Example Data
23 nag_dsygv
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
f08sbc
Example Text
Example Data
23 nag_dsygvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
f08scc
Example Text
Example Data
23 nag_dsygvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer)
f08sec
Example Text
Example Data
7 nag_dsygst
Performs a reduction to standard form of real symmetric-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, B factorized by nag_dpotrf (f07fdc)
f08snc
Example Text
Example Data
23 nag_zhegv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
f08spc
Example Text
Example Data
23 nag_zhegvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
f08sqc
Example Text
Example Data
23 nag_zhegvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer)
f08ssc
Example Text
Example Data
7 nag_zhegst
Performs a reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, B factorized by nag_zpotrf (f07frc)
f08tac
Example Text
Example Data
23 nag_dspgv
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
f08tbc
Example Text
Example Data
23 nag_dspgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
f08tcc
Example Text
Example Data
23 nag_dspgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage (divide-and-conquer)
f08tec
Example Text
Example Data
7 nag_dspgst
Performs a reduction to standard form of real symmetric-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, packed storage, B factorized by nag_dpptrf (f07gdc)
f08tnc
Example Text
Example Data
23 nag_zhpgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
f08tpc
Example Text
Example Data
23 nag_zhpgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
f08tqc
Example Text
Example Data
23 nag_zhpgvd
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage (divide-and-conquer)
f08tsc
Example Text
Example Data
7 nag_zhpgst
Performs a reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, packed storage, B factorized by nag_zpptrf (f07grc)
f08uac
Example Text
Example Data
23 nag_dsbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
f08ubc
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23 nag_dsbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
f08ucc
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23 nag_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_dsbgst
Performs a reduction of real symmetric-definite banded generalized eigenproblem Ax=λBx to standard form Cy=λy, such that C has the same bandwidth as A
f08ufc 7 nag_dpbstf
Computes a split Cholesky factorization of real symmetric positive definite band matrix A
f08unc
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23 nag_zhbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
f08upc
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23 nag_zhbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
f08uqc
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23 nag_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_zhbgst
Performs a reduction of complex Hermitian-definite banded generalized eigenproblem Ax=λBx to standard form Cy=λ y, such that C has the same bandwidth as A
f08utc 7 nag_zpbstf
Computes a split Cholesky factorization of complex Hermitian positive definite band matrix A
f08vac
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9 nag_dggsvd
Computes the generalized singular value decomposition of a real matrix pair
f08vcc
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26.0 nag_dggsvd3
Computes, using BLAS-3, the generalized singular value decomposition of a real matrix pair
f08vec
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23 nag_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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26.0 nag_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 nag_zggsvd
Computes the generalized singular value decomposition of a complex matrix pair
f08vqc
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26.0 nag_zggsvd3
Computes, using BLAS-3, the generalized singular value decomposition of a complex matrix pair
f08vsc
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23 nag_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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26.0 nag_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 nag_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_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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26.0 nag_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 nag_dgghrd
Performs an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
f08wfc 26.0 nag_dgghd3
Performs, using BLAS-3, an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
f08whc 7 nag_dggbal
Balances a pair of real, square, matrices
f08wjc 7 nag_dggbak
Transforms eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to nag_dggbal (f08whc)
f08wnc
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23 nag_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_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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26.0 nag_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 nag_zgghrd
Performs a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
f08wtc 26.0 nag_zgghd3
Performs, using BLAS-3, a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
f08wvc 7 nag_zggbal
Balances a pair of complex, square, matrices
f08wwc 7 nag_zggbak
Transforms eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to nag_zggbal (f08wvc)
f08xac
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23 nag_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_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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26.0 nag_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_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 nag_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_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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26.0 nag_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_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_dtgsja
Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair
f08yfc
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23 nag_dtgexc
Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation
f08ygc
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23 nag_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_dtgsyl
Solves the real-valued, generalized, quasi-trangular, Sylvester equation
f08ykc
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7 nag_dtgevc
Computes right and left generalized eigenvectors of the matrix pair A,B which is assumed to be in generalized upper Schur form
f08ylc
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23 nag_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_ztgsja
Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair
f08ytc
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23 nag_ztgexc
Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation
f08yuc
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23 nag_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_ztgsyl
Solves the complex generalized Sylvester equation
f08yxc
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7 nag_ztgevc
Computes left and right eigenvectors of a pair of complex upper triangular matrices
f08yyc
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23 nag_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_dgglse
Solves the real linear equality-constrained least squares (LSE) problem
f08zbc
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9 nag_dggglm
Solves a real general Gauss–Markov linear model (GLM) problem
f08zec
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23 nag_dggqrf
Computes a generalized QR factorization of a real matrix pair
f08zfc
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23 nag_dggrqf
Computes a generalized RQ factorization of a real matrix pair
f08znc
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9 nag_zgglse
Solves the complex linear equality-constrained least squares (LSE) problem
f08zpc
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9 nag_zggglm
Solves a complex general Gauss–Markov linear model (GLM) problem
f08zsc
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23 nag_zggqrf
Computes a generalized QR factorization of a complex matrix pair
f08ztc
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23 nag_zggrqf
Computes a generalized RQ factorization of a complex matrix pair
© The Numerical Algorithms Group Ltd, Oxford, UK. 2017