f08 Chapter Contents (PDF version)
f08 Chapter Introduction
NAG C Library Manual

NAG Library Chapter Contents

f08 – Least Squares and Eigenvalue Problems (LAPACK)

f08 Chapter Introduction

Function
Name
Mark of
Introduction

Purpose
f08aac
Example Text
Example Data
23 nag_dgels
Solves an overdetermined or underdetermined real linear system
f08aec
Example Text
Example Data
7 nag_dgeqrf
QR factorization of real general rectangular matrix
f08afc
Example Text
Example Data
7 nag_dorgqr
Form 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
Apply orthogonal transformation determined by nag_dgeqrf (f08aec), nag_dgeqpf (f08bec) or nag_dgeqp3 (f08bfc)
f08ahc
Example Text
Example Data
7 nag_dgelqf
LQ factorization of real general rectangular matrix
f08ajc
Example Text
Example Data
7 nag_dorglq
Form all or part of orthogonal Q from LQ factorization determined by nag_dgelqf (f08ahc)
f08akc 7 nag_dormlq
Apply orthogonal transformation determined by nag_dgelqf (f08ahc)
f08anc
Example Text
Example Data
23 nag_zgels
Solves an overdetermined or underdetermined complex linear system
f08asc
Example Text
Example Data
7 nag_zgeqrf
QR factorization of complex general rectangular matrix
f08atc
Example Text
Example Data
7 nag_zungqr
Form 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
Apply unitary transformation determined by nag_zgeqrf (f08asc), nag_zgeqpf (f08bsc) or nag_zgeqp3 (f08btc)
f08avc
Example Text
Example Data
7 nag_zgelqf
LQ factorization of complex general rectangular matrix
f08awc
Example Text
Example Data
7 nag_zunglq
Form all or part of unitary Q from LQ factorization determined by nag_zgelqf (f08avc)
f08axc 7 nag_zunmlq
Apply 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
f08bec
Example Text
Example Data
7 nag_dgeqpf
QR factorization of real general rectangular matrix with column pivoting
f08bfc
Example Text
Example Data
23 nag_dgeqp3
QR factorization of real general rectangular matrix with column pivoting, using BLAS-3
f08bhc
Example Text
Example Data
23 nag_dtzrzf
Reduces a real upper trapezoidal matrix to upper triangular form
f08bkc 23 nag_dormrz
Apply 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
f08bsc
Example Text
Example Data
7 nag_zgeqpf
QR factorization of complex general rectangular matrix with column pivoting
f08btc
Example Text
Example Data
23 nag_zgeqp3
QR factorization of complex general rectangular matrix with column pivoting, using BLAS-3
f08bvc
Example Text
Example Data
23 nag_ztzrzf
Reduces a complex upper trapezoidal matrix to upper triangular form
f08bxc 23 nag_zunmrz
Apply 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
Apply 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
Apply 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 orthogonal Q from QL factorization determined by nag_zgeqlf (f08csc)
f08cuc 23 nag_zunmql
Apply 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 orthogonal Q from RQ factorization determined by nag_zgerqf (f08cvc)
f08cxc 23 nag_zunmrq
Apply 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
Apply 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
Apply 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)
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
Apply 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)
f08gsc
Example Text
Example Data
7 nag_zhptrd
Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage
f08gtc
Example Text
Example Data
7 nag_zupgtr
Generate unitary transformation matrix from reduction to tridiagonal form determined by nag_zhptrd (f08gsc)
f08guc
Example Text
Example Data
7 nag_zupmtr
Apply 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)
f08hec
Example Text
Example Data
7 nag_dsbtrd
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
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
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
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
Selected eigenvalues of real symmetric tridiagonal matrix by bisection
f08jkc 7 nag_dstein
Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array
f08jlc
Example Text
Example Data
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
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
Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array
f08jyc
Example Text
Example Data
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
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
Orthogonal reduction of real general rectangular matrix to bidiagonal form
f08kfc
Example Text
Example Data
7 nag_dorgbr
Generate orthogonal transformation matrices from reduction to bidiagonal form determined by nag_dgebrd (f08kec)
f08kgc
Example Text
Example Data
7 nag_dormbr
Apply 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
Unitary reduction of complex general rectangular matrix to bidiagonal form
f08ktc
Example Text
Example Data
7 nag_zungbr
Generate unitary transformation matrices from reduction to bidiagonal form determined by nag_zgebrd (f08ksc)
f08kuc
Example Text
Example Data
7 nag_zunmbr
Apply unitary transformations from reduction to bidiagonal form determined by nag_zgebrd (f08ksc)
f08lec
Example Text
Example Data
7 nag_dgbbrd
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
SVD of real bidiagonal matrix reduced from real general matrix
f08msc 7 nag_zbdsqr
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
Orthogonal reduction of real general matrix to upper Hessenberg form
f08nfc
Example Text
Example Data
7 nag_dorghr
Generate orthogonal transformation matrix from reduction to Hessenberg form determined by nag_dgehrd (f08nec)
f08ngc
Example Text
Example Data
7 nag_dormhr
Apply orthogonal transformation matrix from reduction to Hessenberg form determined by nag_dgehrd (f08nec)
f08nhc
Example Text
Example Data
7 nag_dgebal
Balance real general matrix
f08njc 7 nag_dgebak
Transform 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
Unitary reduction of complex general matrix to upper Hessenberg form
f08ntc
Example Text
Example Data
7 nag_zunghr
Generate unitary transformation matrix from reduction to Hessenberg form determined by nag_zgehrd (f08nsc)
f08nuc
Example Text
Example Data
7 nag_zunmhr
Apply unitary transformation matrix from reduction to Hessenberg form determined by nag_zgehrd (f08nsc)
f08nvc
Example Text
Example Data
7 nag_zgebal
Balance complex general matrix
f08nwc 7 nag_zgebak
Transform 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
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, optionally, computes reciprocal condition numbers for selected 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
Selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration
f08qfc
Example Text
Example Data
7 nag_dtrexc
Reorder Schur factorization of real matrix using orthogonal similarity transformation
f08qgc
Example Text
Example Data
7 nag_dtrsen
Reorder 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
Solve real Sylvester matrix equation AX+XB=C, A and B are upper quasi-triangular or transposes
f08qkc 7 nag_dtrevc
Left and right eigenvectors of real upper quasi-triangular matrix
f08qlc
Example Text
Example Data
7 nag_dtrsna
Estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix
f08qtc
Example Text
Example Data
7 nag_ztrexc
Reorder Schur factorization of complex matrix using unitary similarity transformation
f08quc
Example Text
Example Data
7 nag_ztrsen
Reorder 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
Solve complex Sylvester matrix equation AX+XB=C, A and B are upper triangular or conjugate-transposes
f08qxc 7 nag_ztrevc
Left and right eigenvectors of complex upper triangular matrix
f08qyc
Example Text
Example Data
7 nag_ztrsna
Estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix
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
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
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
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
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
Example Text
Example Data
23 nag_dsbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
f08ucc
Example Text
Example Data
23 nag_dsbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem (divide-and-conquer)
f08uec
Example Text
Example Data
7 nag_dsbgst
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
Example Text
Example Data
23 nag_zhbgv
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
f08upc
Example Text
Example Data
23 nag_zhbgvx
Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
f08uqc
Example Text
Example Data
23 nag_zhbgvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem (divide-and-conquer)
f08usc
Example Text
Example Data
7 nag_zhbgst
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
Example Text
Example Data
9 nag_dggsvd
Computes the generalized singular value decomposition of a real matrix pair
f08vec
Example Text
Example Data
23 nag_dggsvp
Computes orthogonal matrices as processing steps for computing the generalized singular value decomposition of a real matrix pair
f08vnc
Example Text
Example Data
9 nag_zggsvd
Computes the generalized singular value decomposition of a complex matrix pair
f08vsc
Example Text
Example Data
23 nag_zggsvp
Computes orthogonal matrices as processing steps for computing the generalized singular value decomposition of a complex matrix pair
f08wac
Example Text
Example Data
23 nag_dggev
Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
f08wbc
Example Text
Example Data
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
Orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
f08whc 7 nag_dggbal
Balance a pair of real general matrices
f08wjc 7 nag_dggbak
Transform eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to nag_dggbal (f08whc)
f08wnc
Example Text
Example Data
23 nag_zggev
Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
f08wpc
Example Text
Example Data
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
Unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
f08wvc 7 nag_zggbal
Balance a pair of complex general matrices
f08wwc 7 nag_zggbak
Transform eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to nag_zggbal (f08wvc)
f08xac
Example Text
Example Data
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
Example Text
Example Data
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
Example Text
Example Data
7 nag_dhgeqz
Eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices
f08xnc
Example Text
Example Data
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
Example Text
Example Data
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
Example Text
Example Data
7 nag_zhgeqz
Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex general matrices
f08yec
Example Text
Example Data
23 nag_dtgsja
Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair
f08yfc
Example Text
Example Data
23 nag_dtgexc
Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation
f08ygc
Example Text
Example Data
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
Example Text
Example Data
23 nag_dtgsyl
Solves the real-valued generalized Sylvester equation
f08ykc
Example Text
Example Data
7 nag_dtgevc
Left and right eigenvectors of a pair of real upper quasi-triangular matrices
f08ylc
Example Text
Example Data
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
Example Text
Example Data
23 nag_ztgsja
Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair
f08ytc
Example Text
Example Data
23 nag_ztgexc
Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation
f08yuc
Example Text
Example Data
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
Example Text
Example Data
23 nag_ztgsyl
Solves the complex generalized Sylvester equation
f08yxc
Example Text
Example Data
7 nag_ztgevc
Left and right eigenvectors of a pair of complex upper triangular matrices
f08yyc
Example Text
Example Data
23 nag_ztgsna
Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a complex matrix pair in generalized Schur canonical form
f08zac
Example Text
Example Data
9 nag_dgglse
Solves the real linear equality-constrained least squares (LSE) problem
f08zbc
Example Text
Example Data
9 nag_dggglm
Solves a real general Gauss–Markov linear model (GLM) problem
f08zec
Example Text
Example Data
23 nag_dggqrf
Computes a generalized QR factorization of a real matrix pair
f08zfc
Example Text
Example Data
23 nag_dggrqf
Computes a generalized RQ factorization of a real matrix pair
f08znc
Example Text
Example Data
9 nag_zgglse
Solves the complex linear equality-constrained least squares (LSE) problem
f08zpc
Example Text
Example Data
9 nag_zggglm
Solves a complex general Gauss–Markov linear model (GLM) problem
f08zsc
Example Text
Example Data
23 nag_zggqrf
Computes a generalized QR factorization of a complex matrix pair
f08ztc
Example Text
Example Data
23 nag_zggrqf
Computes a generalized RQ factorization of a complex matrix pair

f08 Chapter Contents (PDF version)
f08 Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012