6.24 F08 Least-squares and Eigenvalue Problems

f08 - Least-squares and Eigenvalue Problems (LAPACK)

f08 Chapter Introduction

Routine Name Mark of Introduction Purpose
f08aac 23 nag_dgels
Solves a real linear least problem of full rank
f08abc 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 7 nag_dgeqrf
Performs a QR factorization of real general rectangular matrix
f08afc 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 7 nag_dgelqf
Performs a LQ factorization of real general rectangular matrix
f08ajc 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 23 nag_zgels
Solves a complex linear least problem of full rank
f08apc 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 7 nag_zgeqrf
Performs a QR factorization of complex general rectangular matrix
f08atc 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 7 nag_zgelqf
Performs a LQ factorization of complex general rectangular matrix
f08awc 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 23 nag_dgelsy
Computes the minimum-norm solution to a real linear least squares problem
f08bbc 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 7 nag_dgeqpf
QR factorization, with column pivoting, of real general rectangular matrix
f08bfc 23 nag_dgeqp3
QR factorization, with column pivoting, using BLAS-3, of real general rectangular matrix
f08bhc 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 23 nag_zgelsy
Computes the minimum-norm solution to a complex linear least squares problem
f08bpc 24 nag_ztpqrt
QR factorization of complex triangular-pentagonal matrix
f08bqc 24 nag_ztpmqrt
Applies the unitary transformation determined by nag_ztpqrt (f08bpc)
f08bsc 7 nag_zgeqpf
QR factorization, with column pivoting, of complex general rectangular matrix
f08btc 23 nag_zgeqp3
QR factorization, with column pivoting, using BLAS-3, of complex general rectangular matrix
f08bvc 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 23 nag_dgeqlf
QL factorization of real general rectangular matrix
f08cfc 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 23 nag_dgerqf
RQ factorization of real general rectangular matrix
f08cjc 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 23 nag_zgeqlf
QL factorization of complex general rectangular matrix
f08ctc 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 23 nag_zgerqf
RQ factorization of complex general rectangular matrix
f08cwc 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 23 nag_dsyev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix
f08fbc 23 nag_dsyevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix
f08fcc 7 nag_dsyevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer)
f08fdc 23 nag_dsyevr
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations)
f08fec 7 nag_dsytrd
Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form
f08ffc 7 nag_dorgtr
Generate orthogonal transformation matrix from reduction to tridiagonal form determined by nag_dsytrd (f08fec)
f08fgc 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 23 nag_zheev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
f08fpc 23 nag_zheevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
f08fqc 7 nag_zheevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix (divide-and-conquer)
f08frc 23 nag_zheevr
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations)
f08fsc 7 nag_zhetrd
Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form
f08ftc 7 nag_zungtr
Generate unitary transformation matrix from reduction to tridiagonal form determined by nag_zhetrd (f08fsc)
f08fuc 7 nag_zunmtr
Applies the unitary transformation matrix determined by nag_zhetrd (f08fsc)
f08gac 23 nag_dspev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
f08gbc 23 nag_dspevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
f08gcc 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 7 nag_dsptrd
Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage
f08gfc 7 nag_dopgtr
Generate orthogonal transformation matrix from reduction to tridiagonal form determined by nag_dsptrd (f08gec)
f08ggc 7 nag_dopmtr
Applies the orthogonal transformation determined by nag_dsptrd (f08gec)
f08gnc 23 nag_zhpev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
f08gpc 23 nag_zhpevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
f08gqc 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 7 nag_zhptrd
Performs a unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage
f08gtc 7 nag_zupgtr
Generates a unitary transformation matrix from reduction to tridiagonal form determined by nag_zhptrd (f08gsc)
f08guc 7 nag_zupmtr
Applies the unitary transformation matrix determined by nag_zhptrd (f08gsc)
f08hac 23 nag_dsbev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
f08hbc 23 nag_dsbevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
f08hcc 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 7 nag_dsbtrd
Performs an orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form
f08hnc 23 nag_zhbev
Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
f08hpc 23 nag_zhbevx
Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
f08hqc 7 nag_zhbevd
Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian band matrix (divide-and-conquer)
f08hsc 7 nag_zhbtrd
Performs a unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form
f08jac 23 nag_dstev
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
f08jbc 23 nag_dstevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
f08jcc 7 nag_dstevd
Computes all eigenvalues and, optionally, all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer)
f08jdc 23 nag_dstevr
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations)
f08jec 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 7 nag_dsterf
Computes all eigenvalues of real symmetric tridiagonal matrix, root-free variant of the QL or QR algorithm
f08jgc 7 nag_dpteqr
Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from real symmetric positive definite matrix
f08jhc 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 23 nag_dstegr
Computes all eigenvalues and, optionally, 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 7 nag_zpteqr
Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from complex Hermitian positive definite matrix
f08jvc 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 23 nag_zstegr
Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (Relatively Robust Representations)
f08kac 23 nag_dgelss
Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition
f08kbc 23 nag_dgesvd
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors
f08kcc 23 nag_dgelsd
Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition (divide-and-conquer)
f08kdc 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 7 nag_dgebrd
Performs an orthogonal reduction of real general rectangular matrix to bidiagonal form
f08kfc 7 nag_dorgbr
Generates an orthogonal transformation matrices from reduction to bidiagonal form determined by nag_dgebrd (f08kec)
f08kgc 7 nag_dormbr
Applies the orthogonal transformations from reduction to bidiagonal form determined by nag_dgebrd (f08kec)
f08khc 23 nag_dgejsv
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (preconditioned Jacobi)
f08kjc 23 nag_dgesvj
Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (fast Jacobi)
f08knc 23 nag_zgelss
Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition
f08kpc 23 nag_zgesvd
Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors
f08kqc 23 nag_zgelsd
Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition (divide-and-conquer)
f08krc 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 7 nag_zgebrd
Performs a unitary reduction of complex general rectangular matrix to bidiagonal form
f08ktc 7 nag_zungbr
Generates unitary transformation matrices from the reduction to bidiagonal form determined by nag_zgebrd (f08ksc)
f08kuc 7 nag_zunmbr
Applies the unitary transformations from reduction to bidiagonal form determined by nag_zgebrd (f08ksc)
f08lec 7 nag_dgbbrd
Performs a reduction of real rectangular band matrix to upper bidiagonal form
f08lsc 7 nag_zgbbrd
Reduction of complex rectangular band matrix to upper bidiagonal form
f08mdc 23 nag_dbdsdc
Computes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divide-and-conquer)
f08mec 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 23 nag_dgeev
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix
f08nbc 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 7 nag_dgehrd
Performs an orthogonal reduction of real general matrix to upper Hessenberg form
f08nfc 7 nag_dorghr
Generates an orthogonal transformation matrix from reduction to Hessenberg form determined by nag_dgehrd (f08nec)
f08ngc 7 nag_dormhr
Applies the orthogonal transformation matrix from reduction to Hessenberg form determined by nag_dgehrd (f08nec)
f08nhc 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 23 nag_zgeev
Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix
f08npc 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 7 nag_zgehrd
Performs a unitary reduction of complex general matrix to upper Hessenberg form
f08ntc 7 nag_zunghr
Generates a unitary transformation matrix from reduction to Hessenberg form determined by nag_zgehrd (f08nsc)
f08nuc 7 nag_zunmhr
Applies the unitary transformation matrix from reduction to Hessenberg form determined by nag_zgehrd (f08nsc)
f08nvc 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 23 nag_dgees
Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors
f08pbc 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 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 23 nag_zgees
Computes for complex square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors
f08ppc 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 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 7 nag_dtrexc
Reorders a Schur factorization of real matrix using orthogonal similarity transformation
f08qgc 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 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 7 nag_dtrsna
Computes estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix
f08qtc 7 nag_ztrexc
Reorders a Schur factorization of complex matrix using unitary similarity transformation
f08quc 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 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 7 nag_ztrsna
Computes estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix
f08rac 24 nag_dorcsd
Computes the CS decomposition of an orthogonal matrix partitioned into four real submatrices
f08rnc 24 nag_zuncsd
Computes the CS decomposition of a unitary matrix partitioned into four complex submatrices
f08sac 23 nag_dsygv
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
f08sbc 23 nag_dsygvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
f08scc 23 nag_dsygvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer)
f08sec 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 23 nag_zhegv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
f08spc 23 nag_zhegvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
f08sqc 23 nag_zhegvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer)
f08ssc 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 23 nag_dspgv
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
f08tbc 23 nag_dspgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
f08tcc 23 nag_dspgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage (divide-and-conquer)
f08tec 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 23 nag_zhpgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
f08tpc 23 nag_zhpgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
f08tqc 23 nag_zhpgvd
Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage (divide-and-conquer)
f08tsc 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 23 nag_dsbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
f08ubc 23 nag_dsbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
f08ucc 23 nag_dsbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem (divide-and-conquer)
f08uec 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 23 nag_zhbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
f08upc 23 nag_zhbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
f08uqc 23 nag_zhbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem (divide-and-conquer)
f08usc 7 nag_zhbgst
Performs a reduction of complex Hermitian-definite banded generalized eigenproblem Ax=λBx to standard form Cy=λ</mi> <mi>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 9 nag_dggsvd
Computes the generalized singular value decomposition of a real matrix pair
f08vec 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
f08vnc 9 nag_zggsvd
Computes the generalized singular value decomposition of a complex matrix pair
f08vsc 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
f08wac 23 nag_dggev
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
f08wbc 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
f08wec 7 nag_dgghrd
Performs 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 23 nag_zggev
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
f08wpc 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
f08wsc 7 nag_zgghrd
Performs 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 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 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
f08xec 7 nag_dhgeqz
Computes eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices
f08xnc 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 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
f08xsc 7 nag_zhgeqz
Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex, square, matrices
f08yec 23 nag_dtgsja
Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair
f08yfc 23 nag_dtgexc
Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation
f08ygc 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 23 nag_dtgsyl
Solves the real-valued, generalized, quasi-trangular, Sylvester equation
f08ykc 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 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 23 nag_ztgsja
Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair
f08ytc 23 nag_ztgexc
Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation
f08yuc 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 23 nag_ztgsyl
Solves the complex generalized Sylvester equation
f08yxc 7 nag_ztgevc
Computes left and right eigenvectors of a pair of complex upper triangular matrices
f08yyc 23 nag_ztgsna
Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a complex matrix pair in generalized Schur canonical form
f08zac 9 nag_dgglse
Solves the real linear equality-constrained least squares (LSE) problem
f08zbc 9 nag_dggglm
Solves a real general Gauss-Markov linear model (GLM) problem
f08zec 23 nag_dggqrf
Computes a generalized QR factorization of a real matrix pair
f08zfc 23 nag_dggrqf
Computes a generalized RQ factorization of a real matrix pair
f08znc 9 nag_zgglse
Solves the complex linear equality-constrained least squares (LSE) problem
f08zpc 9 nag_zggglm
Solves a complex general Gauss-Markov linear model (GLM) problem
f08zsc 23 nag_zggqrf
Computes a generalized QR factorization of a complex matrix pair
f08ztc 23 nag_zggrqf
Computes a generalized RQ factorization of a complex matrix pair