Chapter Introduction (pdf version)
NAG Library Manual

F08 – Least-squares and Eigenvalue Problems (LAPACK)

F08 Chapter Introduction
Routine
Name
Mark of
Introduction

Purpose
F08AAF
Example Text
Example Data
21 Solves an overdetermined or underdetermined real linear system
F08AEF
Example Text
Example Data
16 QR factorization of real general rectangular matrix
F08AFF
Example Text
Example Data
16 Form all or part of orthogonal Q from QR factorization determined by F08AEF (DGEQRF) or F08BEF (DGEQPF)
F08AGF 16 Apply orthogonal transformation determined by F08AEF (DGEQRF) or F08BEF (DGEQPF)
F08AHF
Example Text
Example Data
16 LQ factorization of real general rectangular matrix
F08AJF
Example Text
Example Data
16 Form all or part of orthogonal Q from LQ factorization determined by F08AHF (DGELQF)
F08AKF 16 Apply orthogonal transformation determined by F08AHF (DGELQF)
F08ANF
Example Text
Example Data
21 Solves an overdetermined or underdetermined complex linear system
F08ASF
Example Text
Example Data
16 QR factorization of complex general rectangular matrix
F08ATF
Example Text
Example Data
16 Form all or part of unitary Q from QR factorization determined by F08ASF (ZGEQRF) or F08BSF (ZGEQPF)
F08AUF 16 Apply unitary transformation determined by F08ASF (ZGEQRF) or F08BSF (ZGEQPF)
F08AVF
Example Text
Example Data
16 LQ factorization of complex general rectangular matrix
F08AWF
Example Text
Example Data
16 Form all or part of unitary Q from LQ factorization determined by F08AVF (ZGELQF)
F08AXF 16 Apply unitary transformation determined by F08AVF (ZGELQF)
F08BAF
Example Text
Example Data
21 Computes the minimum-norm solution to a real linear least-squares problem
F08BEF
Example Text
Example Data
16 QR factorization of real general rectangular matrix with column pivoting
F08BFF
Example Text
Example Data
21 QR factorization of real general rectangular matrix with column pivoting, using BLAS-3
F08BHF
Example Text
Example Data
21 Reduces a real upper trapezoidal matrix to upper triangular form
F08BKF 21 Apply orthogonal transformation determined by F08BHF (DTZRZF)
F08BNF
Example Text
Example Data
21 Computes the minimum-norm solution to a complex linear least-squares problem
F08BSF
Example Text
Example Data
16 QR factorization of complex general rectangular matrix with column pivoting
F08BTF
Example Text
Example Data
21 QR factorization of complex general rectangular matrix with column pivoting, using BLAS-3
F08BVF
Example Text
Example Data
21 Reduces a complex upper trapezoidal matrix to upper triangular form
F08BXF 21 Apply unitary transformation determined by F08BVF (ZTZRZF)
F08CEF
Example Text
Example Data
21 QL factorization of real general rectangular matrix
F08CFF
Example Text
Example Data
21 Form all or part of orthogonal Q from QL factorization determined by F08CEF (DGEQLF)
F08CGF 21 Apply orthogonal transformation determined by F08CEF (DGEQLF)
F08CHF
Example Text
Example Data
21 RQ factorization of real general rectangular matrix
F08CJF
Example Text
Example Data
21 Form all or part of orthogonal Q from RQ factorization determined by F08CHF (DGERQF)
F08CKF 21 Apply orthogonal transformation determined by F08CHF (DGERQF)
F08CSF
Example Text
Example Data
21 QL factorization of complex general rectangular matrix
F08CTF
Example Text
Example Data
21 Form all or part of orthogonal Q from QL factorization determined by F08CSF (ZGEQLF)
F08CUF 21 Apply unitary transformation determined by F08CSF (ZGEQLF)
F08CVF
Example Text
Example Data
21 RQ factorization of complex general rectangular matrix
F08CWF
Example Text
Example Data
21 Form all or part of orthogonal Q from RQ factorization determined by F08CVF (ZGERQF)
F08CXF 21 Apply unitary transformation determined by F08CVF (ZGERQF)
F08FAF
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Example Data
21 Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix
F08FBF
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Example Data
21 Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix
F08FCF
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Example Data
19 All eigenvalues and optionally all eigenvectors of real symmetric matrix (divide-and-conquer)
F08FDF
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Example Data
21 Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations)
F08FEF
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Example Data
16 Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form
F08FFF
Example Text
Example Data
16 Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08FEF (DSYTRD)
F08FGF
Example Text
Example Data
16 Apply orthogonal transformation determined by F08FEF (DSYTRD)
F08FLF 21 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
F08FNF
Example Text
Example Data
21 Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
F08FPF
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Example Data
21 Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix
F08FQF
Example Text
Example Data
19 All eigenvalues and optionally all eigenvectors of complex Hermitian matrix (divide-and-conquer)
F08FRF
Example Text
Example Data
21 Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations)
F08FSF
Example Text
Example Data
16 Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form
F08FTF
Example Text
Example Data
16 Generate unitary transformation matrix from reduction to tridiagonal form determined by F08FSF (ZHETRD)
F08FUF
Example Text
Example Data
16 Apply unitary transformation matrix determined by F08FSF (ZHETRD)
F08GAF
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Example Data
21 Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
F08GBF
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Example Data
21 Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage
F08GCF
Example Text
Example Data
19 All eigenvalues and optionally all eigenvectors of real symmetric matrix, packed storage (divide-and-conquer)
F08GEF
Example Text
Example Data
16 Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage
F08GFF
Example Text
Example Data
16 Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08GEF (DSPTRD)
F08GGF
Example Text
Example Data
16 Apply orthogonal transformation determined by F08GEF (DSPTRD)
F08GNF
Example Text
Example Data
21 Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
F08GPF
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Example Data
21 Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage
F08GQF
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Example Data
19 All eigenvalues and optionally all eigenvectors of complex Hermitian matrix, packed storage (divide-and-conquer)
F08GSF
Example Text
Example Data
16 Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage
F08GTF
Example Text
Example Data
16 Generate unitary transformation matrix from reduction to tridiagonal form determined by F08GSF (ZHPTRD)
F08GUF
Example Text
Example Data
16 Apply unitary transformation matrix determined by F08GSF (ZHPTRD)
F08HAF
Example Text
Example Data
21 Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
F08HBF
Example Text
Example Data
21 Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
F08HCF
Example Text
Example Data
19 All eigenvalues and optionally all eigenvectors of real symmetric band matrix (divide-and-conquer)
F08HEF
Example Text
Example Data
16 Orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form
F08HNF
Example Text
Example Data
21 Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
F08HPF
Example Text
Example Data
21 Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
F08HQF
Example Text
Example Data
19 All eigenvalues and optionally all eigenvectors of complex Hermitian band matrix (divide-and-conquer)
F08HSF
Example Text
Example Data
16 Unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form
F08JAF
Example Text
Example Data
21 Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
F08JBF
Example Text
Example Data
21 Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
F08JCF
Example Text
Example Data
19 All eigenvalues and optionally all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer)
F08JDF
Example Text
Example Data
21 Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations)
F08JEF
Example Text
Example Data
16 All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using implicit QL or QR
F08JFF
Example Text
Example Data
16 All eigenvalues of real symmetric tridiagonal matrix, root-free variant of QL or QR
F08JGF
Example Text
Example Data
16 All eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from real symmetric positive-definite matrix
F08JHF
Example Text
Example Data
21 Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a matrix reduced to this form (divide-and-conquer)
F08JJF 16 Selected eigenvalues of real symmetric tridiagonal matrix by bisection
F08JKF 16 Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array
F08JLF
Example Text
Example Data
21 Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a symmetric matrix reduced to this form (Relatively Robust Representations)
F08JSF 16 All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using implicit QL or QR
F08JUF
Example Text
Example Data
16 All eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from complex Hermitian positive-definite matrix
F08JVF
Example Text
Example Data
21 Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (divide-and-conquer)
F08JXF 16 Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array
F08JYF
Example Text
Example Data
21 Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (Relatively Robust Representations)
F08KAF
Example Text
Example Data
21 Computes the minimum-norm solution to a real linear least-squares problem using singular value decomposition
F08KBF
Example Text
Example Data
21 Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors
F08KCF
Example Text
Example Data
21 Computes the minimum-norm solution to a real linear least-squares problem using singular value decomposition (divide-and-conquer)
F08KDF
Example Text
Example Data
21 Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
F08KEF
Example Text
Example Data
16 Orthogonal reduction of real general rectangular matrix to bidiagonal form
F08KFF
Example Text
Example Data
16 Generate orthogonal transformation matrices from reduction to bidiagonal form determined by F08KEF (DGEBRD)
F08KGF
Example Text
Example Data
16 Apply orthogonal transformations from reduction to bidiagonal form determined by F08KEF (DGEBRD)
F08KNF
Example Text
Example Data
21 Computes the minimum-norm solution to a complex linear least-squares problem using singular value decomposition
F08KPF
Example Text
Example Data
21 Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors
F08KQF
Example Text
Example Data
21 Computes the minimum-norm solution to a complex linear least-squares problem using singular value decomposition (divide-and-conquer)
F08KRF
Example Text
Example Data
21 Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (divide-and-conquer)
F08KSF
Example Text
Example Data
16 Unitary reduction of complex general rectangular matrix to bidiagonal form
F08KTF
Example Text
Example Data
16 Generate unitary transformation matrices from reduction to bidiagonal form determined by F08KSF (ZGEBRD)
F08KUF
Example Text
Example Data
16 Apply unitary transformations from reduction to bidiagonal form determined by F08KSF (ZGEBRD)
F08LEF
Example Text
Example Data
19 Reduction of real rectangular band matrix to upper bidiagonal form
F08LSF
Example Text
Example Data
19 Reduction of complex rectangular band matrix to upper bidiagonal form
F08MDF
Example Text
Example Data
21 Computes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divide-and-conquer)
F08MEF
Example Text
Example Data
16 SVD of real bidiagonal matrix reduced from real general matrix
F08MSF 16 SVD of real bidiagonal matrix reduced from complex general matrix
F08NAF
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Example Data
21 Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix
F08NBF
Example Text
Example Data
21 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
F08NEF
Example Text
Example Data
16 Orthogonal reduction of real general matrix to upper Hessenberg form
F08NFF
Example Text
Example Data
16 Generate orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (DGEHRD)
F08NGF
Example Text
Example Data
16 Apply orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (DGEHRD)
F08NHF
Example Text
Example Data
16 Balance real general matrix
F08NJF 16 Transform eigenvectors of real balanced matrix to those of original matrix supplied to F08NHF (DGEBAL)
F08NNF
Example Text
Example Data
21 Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix
F08NPF
Example Text
Example Data
21 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
F08NSF
Example Text
Example Data
16 Unitary reduction of complex general matrix to upper Hessenberg form
F08NTF
Example Text
Example Data
16 Generate unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (ZGEHRD)
F08NUF
Example Text
Example Data
16 Apply unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (ZGEHRD)
F08NVF
Example Text
Example Data
16 Balance complex general matrix
F08NWF 16 Transform eigenvectors of complex balanced matrix to those of original matrix supplied to F08NVF (ZGEBAL)
F08PAF
Example Text
Example Data
21 Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors
F08PBF
Example Text
Example Data
21 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
F08PEF
Example Text
Example Data
16 Eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix
F08PKF 16 Selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration
F08PNF
Example Text
Example Data
21 Computes for complex square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors
F08PPF
Example Text
Example Data
21 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
F08PSF
Example Text
Example Data
16 Eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix
F08PXF 16 Selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration
F08QFF
Example Text
Example Data
16 Reorder Schur factorization of real matrix using orthogonal similarity transformation
F08QGF
Example Text
Example Data
16 Reorder Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
F08QHF
Example Text
Example Data
16 Solve real Sylvester matrix equation AX+XB=C, A and B are upper quasi-triangular or transposes
F08QKF 16 Left and right eigenvectors of real upper quasi-triangular matrix
F08QLF
Example Text
Example Data
16 Estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix
F08QTF
Example Text
Example Data
16 Reorder Schur factorization of complex matrix using unitary similarity transformation
F08QUF
Example Text
Example Data
16 Reorder Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
F08QVF
Example Text
Example Data
16 Solve complex Sylvester matrix equation AX+XB=C, A and B are upper triangular or conjugate-transposes
F08QXF 16 Left and right eigenvectors of complex upper triangular matrix
F08QYF
Example Text
Example Data
16 Estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix
F08SAF
Example Text
Example Data
21 Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
F08SBF
Example Text
Example Data
21 Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
F08SCF
Example Text
Example Data
21 Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer)
F08SEF
Example Text
Example Data
16 Reduction to standard form of real symmetric-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, B factorized by F07FDF (DPOTRF)
F08SNF
Example Text
Example Data
21 Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
F08SPF
Example Text
Example Data
21 Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
F08SQF
Example Text
Example Data
21 Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer)
F08SSF
Example Text
Example Data
16 Reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, B factorized by F07FRF (ZPOTRF)
F08TAF
Example Text
Example Data
21 Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
F08TBF
Example Text
Example Data
21 Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage
F08TCF
Example Text
Example Data
21 Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage (divide-and-conquer)
F08TEF
Example Text
Example Data
16 Reduction to standard form of real symmetric-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, packed storage, B factorized by F07GDF (DPPTRF)
F08TNF
Example Text
Example Data
21 Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
F08TPF
Example Text
Example Data
21 Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage
F08TQF
Example Text
Example Data
21 Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage (divide-and-conquer)
F08TSF
Example Text
Example Data
16 Reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, packed storage, B factorized by F07GRF (ZPPTRF)
F08UAF
Example Text
Example Data
21 Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
F08UBF
Example Text
Example Data
21 Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem
F08UCF
Example Text
Example Data
21 Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem (divide-and-conquer)
F08UEF
Example Text
Example Data
19 Reduction of real symmetric-definite banded generalized eigenproblem Ax=λBx to standard form Cy=λy, such that C has the same bandwidth as A
F08UFF 19 Computes a split Cholesky factorization of real symmetric positive-definite band matrix A
F08UNF
Example Text
Example Data
21 Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
F08UPF
Example Text
Example Data
21 Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem
F08UQF
Example Text
Example Data
21 Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem (divide-and-conquer)
F08USF
Example Text
Example Data
19 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
F08UTF 19 Computes a split Cholesky factorization of complex Hermitian positive-definite band matrix A
F08VAF
Example Text
Example Data
21 Computes the generalized singular value decomposition of a real matrix pair
F08VEF
Example Text
Example Data
21 Computes orthogonal matrices as processing steps for computing the generalized singular value decomposition of a real matrix pair
F08VNF
Example Text
Example Data
21 Computes the generalized singular value decomposition of a complex matrix pair
F08VSF
Example Text
Example Data
21 Computes orthogonal matrices as processing steps for computing the generalized singular value decomposition of a complex matrix pair
F08WAF
Example Text
Example Data
21 Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
F08WBF
Example Text
Example Data
21 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
F08WEF 20 Orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form
F08WHF 20 Balance a pair of real general matrices
F08WJF 20 Transform eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to F08WHF (DGGBAL)
F08WNF
Example Text
Example Data
21 Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors
F08WPF
Example Text
Example Data
21 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
F08WSF 20 Unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form
F08WVF 20 Balance a pair of complex general matrices
F08WWF 20 Transform eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to F08WVF (ZGGBAL)
F08XAF
Example Text
Example Data
21 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
F08XBF
Example Text
Example Data
21 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
F08XEF
Example Text
Example Data
20 Eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices
F08XNF
Example Text
Example Data
21 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
F08XPF
Example Text
Example Data
21 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
F08XSF
Example Text
Example Data
20 Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex general matrices
F08YEF
Example Text
Example Data
21 Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair
F08YFF
Example Text
Example Data
21 Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation
F08YGF
Example Text
Example Data
21 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
F08YHF
Example Text
Example Data
21 Solves the real-valued generalized Sylvester equation
F08YKF
Example Text
Example Data
20 Left and right eigenvectors of a pair of real upper quasi-triangular matrices
F08YLF
Example Text
Example Data
21 Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a real matrix pair in generalized real Schur canonical form
F08YSF
Example Text
Example Data
21 Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair
F08YTF
Example Text
Example Data
21 Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation
F08YUF
Example Text
Example Data
21 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
F08YVF
Example Text
Example Data
21 Solves the complex generalized Sylvester equation
F08YXF
Example Text
Example Data
20 Left and right eigenvectors of a pair of complex upper triangular matrices
F08YYF
Example Text
Example Data
21 Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a complex matrix pair in generalized Schur canonical form
F08ZAF
Example Text
Example Data
21 Solves the real linear equality-constrained least-squares (LSE) problem
F08ZBF
Example Text
Example Data
21 Solves a real general Gauss–Markov linear model (GLM) problem
F08ZEF
Example Text
Example Data
21 Computes a generalized QR factorization of a real matrix pair
F08ZFF
Example Text
Example Data
21 Computes a generalized RQ factorization of a real matrix pair
F08ZNF
Example Text
Example Data
21 Solves the complex linear equality-constrained least-squares (LSE) problem
F08ZPF
Example Text
Example Data
21 Solves a complex general Gauss–Markov linear model (GLM) problem
F08ZSF
Example Text
Example Data
21 Computes a generalized QR factorization of a complex matrix pair
F08ZTF
Example Text
Example Data
21 Computes a generalized RQ factorization of a complex matrix pair

Chapter Introduction (pdf version)
NAG Library Manual

The Numerical Algorithms Group Ltd, Oxford, UK. 2006