Chapter Introduction
NAG Fortran Library Contents

NAG Fortran Library

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
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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
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Example Data
21 Solves an overdetermined or underdetermined complex linear system
F08ASF
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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
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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
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
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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19 All eigenvalues and optionally all eigenvectors of real symmetric matrix, using divide-and-conquer
F08FDF
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Example Data
21 Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (divide-and-conquer)
F08FEF
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16 Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form
F08FFF
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Example Data
16 Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08FEF (DSYTRD)
F08FGF
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16 Apply orthogonal transformation determined by F08FEF (DSYTRD)
F08FNF
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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
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19 All eigenvalues and optionally all eigenvectors of complex Hermitian matrix, using divide-and-conquer
F08FRF
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21 Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (divide-and-conquer)
F08FSF
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16 Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form
F08FTF
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16 Generate unitary transformation matrix from reduction to tridiagonal form determined by F08FSF (ZHETRD)
F08FUF
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16 Apply unitary transformation matrix determined by F08FSF (ZHETRD)
F08GAF
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21 Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix (stored in packed format)
F08GBF
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21 Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (stored in packed format)
F08GCF
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19 All eigenvalues and optionally all eigenvectors of real symmetric matrix, packed storage, using divide-and-conquer
F08GEF
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16 Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage
F08GFF
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16 Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08GEF (DSPTRD)
F08GGF
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16 Apply orthogonal transformation determined by F08GEF (DSPTRD)
F08GNF
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21 Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (stored in packed format)
F08GPF
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21 Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (stored in packed format)
F08GQF
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19 All eigenvalues and optionally all eigenvectors of complex Hermitian matrix, packed storage, using divide-and-conquer
F08GSF
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16 Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage
F08GTF
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16 Generate unitary transformation matrix from reduction to tridiagonal form determined by F08GSF (ZHPTRD)
F08GUF
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16 Apply unitary transformation matrix determined by F08GSF (ZHPTRD)
F08HAF
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Example Data
21 Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
F08HBF
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Example Data
21 Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix
F08HCF
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Example Data
19 All eigenvalues and optionally all eigenvectors of real symmetric band matrix, using divide-and-conquer
F08HEF
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16 Orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form
F08HNF
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Example Data
21 Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
F08HPF
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Example Data
21 Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix
F08HQF
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19 All eigenvalues and optionally all eigenvectors of complex Hermitian band matrix, using divide-and-conquer
F08HSF
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Example Data
16 Unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form
F08JAF
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Example Data
21 Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
F08JBF
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Example Data
21 Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix
F08JCF
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Example Data
19 All eigenvalues and optionally all eigenvectors of real symmetric tridiagonal matrix, using divide-and-conquer
F08JDF
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21 Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust representations).
F08JEF
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Example Data
16 All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using implicit QL or QR
F08JFF
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16 All eigenvalues of real symmetric tridiagonal matrix, root-free variant of QL or QR
F08JGF
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16 All eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from real symmetric positive-definite matrix
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
F08JSF 16 All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using implicit QL or QR
F08JUF
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Example Data
16 All eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from complex Hermitian positive-definite matrix
F08JXF 16 Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array
F08KAF
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Example Data
21 Computes the minimum-norm solution to a real linear least-squares problem using singular value decomposition
F08KBF
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Example Data
21 Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors
F08KCF
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Example Data
21 Computes the minimum-norm solution to a real linear least-squares problem using singular value decomposition (divide-and-conquer)
F08KDF
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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
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Example Data
16 Orthogonal reduction of real general rectangular matrix to bidiagonal form
F08KFF
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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
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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
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Example Data
21 Computes the minimum-norm solution to a complex linear least-squares problem using singular value decomposition (divide-and-conquer)
F08KRF
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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
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Example Data
16 Unitary reduction of complex general rectangular matrix to bidiagonal form
F08KTF
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Example Data
16 Generate unitary transformation matrices from reduction to bidiagonal form determined by F08KSF (ZGEBRD)
F08KUF
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Example Data
16 Apply unitary transformations from reduction to bidiagonal form determined by F08KSF (ZGEBRD)
F08LEF
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Example Data
19 Reduction of real rectangular band matrix to upper bidiagonal form
F08LSF
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19 Reduction of complex rectangular band matrix to upper bidiagonal form
F08MEF
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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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21 Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix
F08NBF
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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
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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
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Example Data
21 Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix
F08NPF
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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
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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
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Example Data
21 Computes for real square nonsymmetric matrix, the eigenvalues, the real Schur form, and, optionally, the matrix of Schur vectors
F08PBF
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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
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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
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Example Data
21 Computes for complex square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors
F08PPF
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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
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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
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Example Data
16 Reorder Schur factorization of real matrix using orthogonal similarity transformation
F08QGF
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Example Data
16 Reorder Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
F08QHF
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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
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Example Data
16 Estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix
F08QTF
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Example Data
16 Reorder Schur factorization of complex matrix using unitary similarity transformation
F08QUF
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Example Data
16 Reorder Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities
F08QVF
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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
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Example Data
16 Estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix
F08SAF
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Example Data
21 Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
F08SBF
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Example Data
21 Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem
F08SCF
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Example Data
21 Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer)
F08SEF
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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
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Example Data
21 Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
F08SPF
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Example Data
21 Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem
F08SQF
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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
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Example Data
21 Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (packed storage format)
F08TBF
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Example Data
21 Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (packed storage format)
F08TCF
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Example Data
21 Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (packed storage format, 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 format)
F08TPF
Example Text
Example Data
21 Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (packed storage format)
F08TQF
Example Text
Example Data
21 Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (packed storage format, 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
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Example Data
21 Computes 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
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
F08YKF
Example Text
Example Data
20 Left and right eigenvectors of a pair of real upper quasi-triangular matrices
F08YXF
Example Text
Example Data
20 Left and right eigenvectors of a pair of complex upper triangular matrices
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
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

Chapter Introduction
NAG Fortran Library Contents

© The Numerical Algorithms Group Ltd, Oxford, UK. 2004