F08 Chapter Contents (PDF version)
F08 Chapter Introduction
NAG Library Manual

# NAG Library Chapter ContentsF08 – Least Squares and Eigenvalue Problems (LAPACK)

### F08 Chapter Introduction

 RoutineName Mark ofIntroduction Purpose F08AAF Example Text Example Data 21 DGELS nagf_lapack_dgels Solves an overdetermined or underdetermined real linear system F08AEF Example Text Example Data 16 DGEQRF nagf_lapack_dgeqrf QR factorization of real general rectangular matrix F08AFF Example Text Example Data 16 DORGQR nagf_lapack_dorgqr Form all or part of orthogonal Q from QR factorization determined by F08AEF (DGEQRF), F08BEF (DGEQPF) or F08BFF (DGEQP3) F08AGF 16 DORMQR nagf_lapack_dormqr Apply orthogonal transformation determined by F08AEF (DGEQRF), F08BEF (DGEQPF) or F08BFF (DGEQP3) F08AHF Example Text Example Data 16 DGELQF nagf_lapack_dgelqf LQ factorization of real general rectangular matrix F08AJF Example Text Example Data 16 DORGLQ nagf_lapack_dorglq Form all or part of orthogonal Q from LQ factorization determined by F08AHF (DGELQF) F08AKF 16 DORMLQ nagf_lapack_dormlq Apply orthogonal transformation determined by F08AHF (DGELQF) F08ANF Example Text Example Data 21 ZGELS nagf_lapack_zgels Solves an overdetermined or underdetermined complex linear system F08ASF Example Text Example Data 16 ZGEQRF nagf_lapack_zgeqrf QR factorization of complex general rectangular matrix F08ATF Example Text Example Data 16 ZUNGQR nagf_lapack_zungqr Form all or part of unitary Q from QR factorization determined by F08ASF (ZGEQRF), F08BSF (ZGEQPF) or F08BTF (ZGEQP3) F08AUF 16 ZUNMQR nagf_lapack_zunmqr Apply unitary transformation determined by F08ASF (ZGEQRF), F08BSF (ZGEQPF) or F08BTF (ZGEQP3) F08AVF Example Text Example Data 16 ZGELQF nagf_lapack_zgelqf LQ factorization of complex general rectangular matrix F08AWF Example Text Example Data 16 ZUNGLQ nagf_lapack_zunglq Form all or part of unitary Q from LQ factorization determined by F08AVF (ZGELQF) F08AXF 16 ZUNMLQ nagf_lapack_zunmlq Apply unitary transformation determined by F08AVF (ZGELQF) F08BAF Example Text Example Data 21 DGELSY nagf_lapack_dgelsy Computes the minimum-norm solution to a real linear least squares problem F08BEF Example Text Example Data 16 DGEQPF nagf_lapack_dgeqpf QR factorization of real general rectangular matrix with column pivoting F08BFF Example Text Example Data 21 DGEQP3 nagf_lapack_dgeqp3 QR factorization of real general rectangular matrix with column pivoting, using BLAS-3 F08BHF Example Text Example Data 21 DTZRZF nagf_lapack_dtzrzf Reduces a real upper trapezoidal matrix to upper triangular form F08BKF 21 DORMRZ nagf_lapack_dormrz Apply orthogonal transformation determined by F08BHF (DTZRZF) F08BNF Example Text Example Data 21 ZGELSY nagf_lapack_zgelsy Computes the minimum-norm solution to a complex linear least squares problem F08BSF Example Text Example Data 16 ZGEQPF nagf_lapack_zgeqpf QR factorization of complex general rectangular matrix with column pivoting F08BTF Example Text Example Data 21 ZGEQP3 nagf_lapack_zgeqp3 QR factorization of complex general rectangular matrix with column pivoting, using BLAS-3 F08BVF Example Text Example Data 21 ZTZRZF nagf_lapack_ztzrzf Reduces a complex upper trapezoidal matrix to upper triangular form F08BXF 21 ZUNMRZ nagf_lapack_zunmrz Apply unitary transformation determined by F08BVF (ZTZRZF) F08CEF Example Text Example Data 21 DGEQLF nagf_lapack_dgeqlf QL factorization of real general rectangular matrix F08CFF Example Text Example Data 21 DORGQL nagf_lapack_dorgql Form all or part of orthogonal Q from QL factorization determined by F08CEF (DGEQLF) F08CGF 21 DORMQL nagf_lapack_dormql Apply orthogonal transformation determined by F08CEF (DGEQLF) F08CHF Example Text Example Data 21 DGERQF nagf_lapack_dgerqf RQ factorization of real general rectangular matrix F08CJF Example Text Example Data 21 DORGRQ nagf_lapack_dorgrq Form all or part of orthogonal Q from RQ factorization determined by F08CHF (DGERQF) F08CKF 21 DORMRQ nagf_lapack_dormrq Apply orthogonal transformation determined by F08CHF (DGERQF) F08CSF Example Text Example Data 21 ZGEQLF nagf_lapack_zgeqlf QL factorization of complex general rectangular matrix F08CTF Example Text Example Data 21 ZUNGQL nagf_lapack_zungql Form all or part of orthogonal Q from QL factorization determined by F08CSF (ZGEQLF) F08CUF 21 ZUNMQL nagf_lapack_zunmql Apply unitary transformation determined by F08CSF (ZGEQLF) F08CVF Example Text Example Data 21 ZGERQF nagf_lapack_zgerqf RQ factorization of complex general rectangular matrix F08CWF Example Text Example Data 21 ZUNGRQ nagf_lapack_zungrq Form all or part of orthogonal Q from RQ factorization determined by F08CVF (ZGERQF) F08CXF 21 ZUNMRQ nagf_lapack_zunmrq Apply unitary transformation determined by F08CVF (ZGERQF) F08FAF Example Text Example Data 21 DSYEV nagf_lapack_dsyev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix F08FBF Example Text Example Data 21 DSYEVX nagf_lapack_dsyevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix F08FCF Example Text Example Data 19 DSYEVD nagf_lapack_dsyevd Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer) F08FDF Example Text Example Data 21 DSYEVR nagf_lapack_dsyevr Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations) F08FEF Example Text Example Data 16 DSYTRD nagf_lapack_dsytrd Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form F08FFF Example Text Example Data 16 DORGTR nagf_lapack_dorgtr Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08FEF (DSYTRD) F08FGF Example Text Example Data 16 DORMTR nagf_lapack_dormtr Apply orthogonal transformation determined by F08FEF (DSYTRD) F08FLF 21 DDISNA nagf_lapack_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 F08FNF Example Text Example Data 21 ZHEEV nagf_lapack_zheev Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix F08FPF Example Text Example Data 21 ZHEEVX nagf_lapack_zheevx Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix F08FQF Example Text Example Data 19 ZHEEVD nagf_lapack_zheevd Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix (divide-and-conquer) F08FRF Example Text Example Data 21 ZHEEVR nagf_lapack_zheevr Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations) F08FSF Example Text Example Data 16 ZHETRD nagf_lapack_zhetrd Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form F08FTF Example Text Example Data 16 ZUNGTR nagf_lapack_zungtr Generate unitary transformation matrix from reduction to tridiagonal form determined by F08FSF (ZHETRD) F08FUF Example Text Example Data 16 ZUNMTR nagf_lapack_zunmtr Apply unitary transformation matrix determined by F08FSF (ZHETRD) F08GAF Example Text Example Data 21 DSPEV nagf_lapack_dspev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage F08GBF Example Text Example Data 21 DSPEVX nagf_lapack_dspevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage F08GCF Example Text Example Data 19 DSPEVD nagf_lapack_dspevd Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix, packed storage (divide-and-conquer) F08GEF Example Text Example Data 16 DSPTRD nagf_lapack_dsptrd Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage F08GFF Example Text Example Data 16 DOPGTR nagf_lapack_dopgtr Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08GEF (DSPTRD) F08GGF Example Text Example Data 16 DOPMTR nagf_lapack_dopmtr Apply orthogonal transformation determined by F08GEF (DSPTRD) F08GNF Example Text Example Data 21 ZHPEV nagf_lapack_zhpev Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage F08GPF Example Text Example Data 21 ZHPEVX nagf_lapack_zhpevx Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage F08GQF Example Text Example Data 19 ZHPEVD nagf_lapack_zhpevd Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix, packed storage (divide-and-conquer) F08GSF Example Text Example Data 16 ZHPTRD nagf_lapack_zhptrd Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage F08GTF Example Text Example Data 16 ZUPGTR nagf_lapack_zupgtr Generate unitary transformation matrix from reduction to tridiagonal form determined by F08GSF (ZHPTRD) F08GUF Example Text Example Data 16 ZUPMTR nagf_lapack_zupmtr Apply unitary transformation matrix determined by F08GSF (ZHPTRD) F08HAF Example Text Example Data 21 DSBEV nagf_lapack_dsbev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix F08HBF Example Text Example Data 21 DSBEVX nagf_lapack_dsbevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix F08HCF Example Text Example Data 19 DSBEVD nagf_lapack_dsbevd Computes all eigenvalues and, optionally, all eigenvectors of real symmetric band matrix (divide-and-conquer) F08HEF Example Text Example Data 16 DSBTRD nagf_lapack_dsbtrd Orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form F08HNF Example Text Example Data 21 ZHBEV nagf_lapack_zhbev Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix F08HPF Example Text Example Data 21 ZHBEVX nagf_lapack_zhbevx Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix F08HQF Example Text Example Data 19 ZHBEVD nagf_lapack_zhbevd Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian band matrix (divide-and-conquer) F08HSF Example Text Example Data 16 ZHBTRD nagf_lapack_zhbtrd Unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form F08JAF Example Text Example Data 21 DSTEV nagf_lapack_dstev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix F08JBF Example Text Example Data 21 DSTEVX nagf_lapack_dstevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix F08JCF Example Text Example Data 19 DSTEVD nagf_lapack_dstevd Computes all eigenvalues and, optionally, all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer) F08JDF Example Text Example Data 21 DSTEVR nagf_lapack_dstevr Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations) F08JEF Example Text Example Data 16 DSTEQR nagf_lapack_dsteqr All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using the implicit QL or QR algorithm F08JFF Example Text Example Data 16 DSTERF nagf_lapack_dsterf All eigenvalues of real symmetric tridiagonal matrix, root-free variant of the QL or QR algorithm F08JGF Example Text Example Data 16 DPTEQR nagf_lapack_dpteqr Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from real symmetric positive definite matrix F08JHF Example Text Example Data 21 DSTEDC nagf_lapack_dstedc Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a matrix reduced to this form (divide-and-conquer) F08JJF 16 DSTEBZ nagf_lapack_dstebz Selected eigenvalues of real symmetric tridiagonal matrix by bisection F08JKF 16 DSTEIN nagf_lapack_dstein Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array F08JLF Example Text Example Data 21 DSTEGR nagf_lapack_dstegr 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 ZSTEQR nagf_lapack_zsteqr All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using the implicit QL or QR algorithm F08JUF Example Text Example Data 16 ZPTEQR nagf_lapack_zpteqr Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from complex Hermitian positive definite matrix F08JVF Example Text Example Data 21 ZSTEDC nagf_lapack_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) F08JXF 16 ZSTEIN nagf_lapack_zstein Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array F08JYF Example Text Example Data 21 ZSTEGR nagf_lapack_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) F08KAF Example Text Example Data 21 DGELSS nagf_lapack_dgelss Computes the minimum-norm solution to a real linear least squares problem using singular value decomposition F08KBF Example Text Example Data 21 DGESVD nagf_lapack_dgesvd Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors F08KCF Example Text Example Data 21 DGELSD nagf_lapack_dgelsd 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 DGESDD nagf_lapack_dgesdd 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 DGEBRD nagf_lapack_dgebrd Orthogonal reduction of real general rectangular matrix to bidiagonal form F08KFF Example Text Example Data 16 DORGBR nagf_lapack_dorgbr Generate orthogonal transformation matrices from reduction to bidiagonal form determined by F08KEF (DGEBRD) F08KGF Example Text Example Data 16 DORMBR nagf_lapack_dormbr Apply orthogonal transformations from reduction to bidiagonal form determined by F08KEF (DGEBRD) F08KHF Example Text Example Data 23 DGEJSV nagf_lapack_dgejsv Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (preconditioned Jacobi) F08KJF Example Text Example Data 23 DGESVJ nagf_lapack_dgesvj Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors (fast Jacobi) F08KNF Example Text Example Data 21 ZGELSS nagf_lapack_zgelss Computes the minimum-norm solution to a complex linear least squares problem using singular value decomposition F08KPF Example Text Example Data 21 ZGESVD nagf_lapack_zgesvd Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors F08KQF Example Text Example Data 21 ZGELSD nagf_lapack_zgelsd 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 ZGESDD nagf_lapack_zgesdd 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 ZGEBRD nagf_lapack_zgebrd Unitary reduction of complex general rectangular matrix to bidiagonal form F08KTF Example Text Example Data 16 ZUNGBR nagf_lapack_zungbr Generate unitary transformation matrices from reduction to bidiagonal form determined by F08KSF (ZGEBRD) F08KUF Example Text Example Data 16 ZUNMBR nagf_lapack_zunmbr Apply unitary transformations from reduction to bidiagonal form determined by F08KSF (ZGEBRD) F08LEF Example Text Example Data 19 DGBBRD nagf_lapack_dgbbrd Reduction of real rectangular band matrix to upper bidiagonal form F08LSF Example Text Example Data 19 ZGBBRD nagf_lapack_zgbbrd Reduction of complex rectangular band matrix to upper bidiagonal form F08MDF Example Text Example Data 21 DBDSDC nagf_lapack_dbdsdc Computes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divide-and-conquer) F08MEF Example Text Example Data 16 DBDSQR nagf_lapack_dbdsqr SVD of real bidiagonal matrix reduced from real general matrix F08MSF 16 ZBDSQR nagf_lapack_zbdsqr SVD of real bidiagonal matrix reduced from complex general matrix F08NAF Example Text Example Data 21 DGEEV nagf_lapack_dgeev Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix F08NBF Example Text Example Data 21 DGEEVX nagf_lapack_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 F08NEF Example Text Example Data 16 DGEHRD nagf_lapack_dgehrd Orthogonal reduction of real general matrix to upper Hessenberg form F08NFF Example Text Example Data 16 DORGHR nagf_lapack_dorghr Generate orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (DGEHRD) F08NGF Example Text Example Data 16 DORMHR nagf_lapack_dormhr Apply orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (DGEHRD) F08NHF Example Text Example Data 16 DGEBAL nagf_lapack_dgebal Balance real general matrix F08NJF 16 DGEBAK nagf_lapack_dgebak Transform eigenvectors of real balanced matrix to those of original matrix supplied to F08NHF (DGEBAL) F08NNF Example Text Example Data 21 ZGEEV nagf_lapack_zgeev Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix F08NPF Example Text Example Data 21 ZGEEVX nagf_lapack_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 F08NSF Example Text Example Data 16 ZGEHRD nagf_lapack_zgehrd Unitary reduction of complex general matrix to upper Hessenberg form F08NTF Example Text Example Data 16 ZUNGHR nagf_lapack_zunghr Generate unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (ZGEHRD) F08NUF Example Text Example Data 16 ZUNMHR nagf_lapack_zunmhr Apply unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (ZGEHRD) F08NVF Example Text Example Data 16 ZGEBAL nagf_lapack_zgebal Balance complex general matrix F08NWF 16 ZGEBAK nagf_lapack_zgebak Transform eigenvectors of complex balanced matrix to those of original matrix supplied to F08NVF (ZGEBAL) F08PAF Example Text Example Data 21 DGEES nagf_lapack_dgees 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 DGEESX nagf_lapack_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 F08PEF Example Text Example Data 16 DHSEQR nagf_lapack_dhseqr Computes the eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix F08PKF 16 DHSEIN nagf_lapack_dhsein Selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration F08PNF Example Text Example Data 21 ZGEES nagf_lapack_zgees Computes for complex square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors F08PPF Example Text Example Data 21 ZGEESX nagf_lapack_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 F08PSF Example Text Example Data 16 ZHSEQR nagf_lapack_zhseqr Computes the eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix F08PXF 16 ZHSEIN nagf_lapack_zhsein Selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration F08QFF Example Text Example Data 16 DTREXC nagf_lapack_dtrexc Reorder Schur factorization of real matrix using orthogonal similarity transformation F08QGF Example Text Example Data 16 DTRSEN nagf_lapack_dtrsen 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 DTRSYL nagf_lapack_dtrsyl Solve real Sylvester matrix equation AX + XB = C, A and B are upper quasi-triangular or transposes F08QKF 16 DTREVC nagf_lapack_dtrevc Left and right eigenvectors of real upper quasi-triangular matrix F08QLF Example Text Example Data 16 DTRSNA nagf_lapack_dtrsna Estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix F08QTF Example Text Example Data 16 ZTREXC nagf_lapack_ztrexc Reorder Schur factorization of complex matrix using unitary similarity transformation F08QUF Example Text Example Data 16 ZTRSEN nagf_lapack_ztrsen 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 ZTRSYL nagf_lapack_ztrsyl Solve complex Sylvester matrix equation AX + XB = C, A and B are upper triangular or conjugate-transposes F08QXF 16 ZTREVC nagf_lapack_ztrevc Left and right eigenvectors of complex upper triangular matrix F08QYF Example Text Example Data 16 ZTRSNA nagf_lapack_ztrsna Estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix F08SAF Example Text Example Data 21 DSYGV nagf_lapack_dsygv Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem F08SBF Example Text Example Data 21 DSYGVX nagf_lapack_dsygvx Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem F08SCF Example Text Example Data 21 DSYGVD nagf_lapack_dsygvd Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer) F08SEF Example Text Example Data 16 DSYGST nagf_lapack_dsygst 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 ZHEGV nagf_lapack_zhegv Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem F08SPF Example Text Example Data 21 ZHEGVX nagf_lapack_zhegvx Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem F08SQF Example Text Example Data 21 ZHEGVD nagf_lapack_zhegvd Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer) F08SSF Example Text Example Data 16 ZHEGST nagf_lapack_zhegst 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 DSPGV nagf_lapack_dspgv Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage F08TBF Example Text Example Data 21 DSPGVX nagf_lapack_dspgvx Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage F08TCF Example Text Example Data 21 DSPGVD nagf_lapack_dspgvd 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 DSPGST nagf_lapack_dspgst 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 ZHPGV nagf_lapack_zhpgv Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage F08TPF Example Text Example Data 21 ZHPGVX nagf_lapack_zhpgvx Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage F08TQF Example Text Example Data 21 ZHPGVD nagf_lapack_zhpgvd 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 ZHPGST nagf_lapack_zhpgst 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 DSBGV nagf_lapack_dsbgv Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem F08UBF Example Text Example Data 21 DSBGVX nagf_lapack_dsbgvx Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem F08UCF Example Text Example Data 21 DSBGVD nagf_lapack_dsbgvd 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 DSBGST nagf_lapack_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 F08UFF 19 DPBSTF nagf_lapack_dpbstf Computes a split Cholesky factorization of real symmetric positive definite band matrix A F08UNF Example Text Example Data 21 ZHBGV nagf_lapack_zhbgv Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem F08UPF Example Text Example Data 21 ZHBGVX nagf_lapack_zhbgvx Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem F08UQF Example Text Example Data 21 ZHBGVD nagf_lapack_zhbgvd 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 ZHBGST nagf_lapack_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 F08UTF 19 ZPBSTF nagf_lapack_zpbstf Computes a split Cholesky factorization of complex Hermitian positive definite band matrix A F08VAF Example Text Example Data 21 DGGSVD nagf_lapack_dggsvd Computes the generalized singular value decomposition of a real matrix pair F08VEF Example Text Example Data 21 DGGSVP nagf_lapack_dggsvp Computes orthogonal matrices as processing steps for computing the generalized singular value decomposition of a real matrix pair F08VNF Example Text Example Data 21 ZGGSVD nagf_lapack_zggsvd Computes the generalized singular value decomposition of a complex matrix pair F08VSF Example Text Example Data 21 ZGGSVP nagf_lapack_zggsvp Computes orthogonal matrices as processing steps for computing the generalized singular value decomposition of a complex matrix pair F08WAF Example Text Example Data 21 DGGEV nagf_lapack_dggev 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 DGGEVX nagf_lapack_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 F08WEF 20 DGGHRD nagf_lapack_dgghrd Orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form F08WHF 20 DGGBAL nagf_lapack_dggbal Balance a pair of real general matrices F08WJF 20 DGGBAK nagf_lapack_dggbak 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 ZGGEV nagf_lapack_zggev 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 ZGGEVX nagf_lapack_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 F08WSF 20 ZGGHRD nagf_lapack_zgghrd Unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form F08WVF 20 ZGGBAL nagf_lapack_zggbal Balance a pair of complex general matrices F08WWF 20 ZGGBAK nagf_lapack_zggbak 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 DGGES nagf_lapack_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 F08XBF Example Text Example Data 21 DGGESX nagf_lapack_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 F08XEF Example Text Example Data 20 DHGEQZ nagf_lapack_dhgeqz 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 ZGGES nagf_lapack_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 F08XPF Example Text Example Data 21 ZGGESX nagf_lapack_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 F08XSF Example Text Example Data 20 ZHGEQZ nagf_lapack_zhgeqz 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 DTGSJA nagf_lapack_dtgsja Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair F08YFF Example Text Example Data 21 DTGEXC nagf_lapack_dtgexc Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation F08YGF Example Text Example Data 21 DTGSEN nagf_lapack_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 F08YHF Example Text Example Data 21 DTGSYL nagf_lapack_dtgsyl Solves the real-valued generalized Sylvester equation F08YKF Example Text Example Data 20 DTGEVC nagf_lapack_dtgevc Left and right eigenvectors of a pair of real upper quasi-triangular matrices F08YLF Example Text Example Data 21 DTGSNA nagf_lapack_dtgsna 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 ZTGSJA nagf_lapack_ztgsja Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair F08YTF Example Text Example Data 21 ZTGEXC nagf_lapack_ztgexc Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation F08YUF Example Text Example Data 21 ZTGSEN nagf_lapack_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 F08YVF Example Text Example Data 21 ZTGSYL nagf_lapack_ztgsyl Solves the complex generalized Sylvester equation F08YXF Example Text Example Data 20 ZTGEVC nagf_lapack_ztgevc Left and right eigenvectors of a pair of complex upper triangular matrices F08YYF Example Text Example Data 21 ZTGSNA nagf_lapack_ztgsna 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 DGGLSE nagf_lapack_dgglse Solves the real linear equality-constrained least squares (LSE) problem F08ZBF Example Text Example Data 21 DGGGLM nagf_lapack_dggglm Solves a real general Gauss–Markov linear model (GLM) problem F08ZEF Example Text Example Data 21 DGGQRF nagf_lapack_dggqrf Computes a generalized QR factorization of a real matrix pair F08ZFF Example Text Example Data 21 DGGRQF nagf_lapack_dggrqf Computes a generalized RQ factorization of a real matrix pair F08ZNF Example Text Example Data 21 ZGGLSE nagf_lapack_zgglse Solves the complex linear equality-constrained least squares (LSE) problem F08ZPF Example Text Example Data 21 ZGGGLM nagf_lapack_zggglm Solves a complex general Gauss–Markov linear model (GLM) problem F08ZSF Example Text Example Data 21 ZGGQRF nagf_lapack_zggqrf Computes a generalized QR factorization of a complex matrix pair F08ZTF Example Text Example Data 21 ZGGRQF nagf_lapack_zggrqf Computes a generalized RQ factorization of a complex matrix pair

F08 Chapter Contents (PDF version)
F08 Chapter Introduction
NAG Library Manual