| Routine Name |
Mark of Introduction |
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 factorization of real general rectangular matrix |
| F08AFF
Example Text Example Data |
16 | DORGQR nagf_lapack_dorgqr Form all or part of orthogonal from 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 factorization of real general rectangular matrix |
| F08AJF
Example Text Example Data |
16 | DORGLQ nagf_lapack_dorglq Form all or part of orthogonal from 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 factorization of complex general rectangular matrix |
| F08ATF
Example Text Example Data |
16 | ZUNGQR nagf_lapack_zungqr Form all or part of unitary from 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 factorization of complex general rectangular matrix |
| F08AWF
Example Text Example Data |
16 | ZUNGLQ nagf_lapack_zunglq Form all or part of unitary from 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 factorization of real general rectangular matrix with column pivoting |
| F08BFF
Example Text Example Data |
21 | DGEQP3 nagf_lapack_dgeqp3 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 factorization of complex general rectangular matrix with column pivoting |
| F08BTF
Example Text Example Data |
21 | ZGEQP3 nagf_lapack_zgeqp3 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 factorization of real general rectangular matrix |
| F08CFF
Example Text Example Data |
21 | DORGQL nagf_lapack_dorgql Form all or part of orthogonal from 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 factorization of real general rectangular matrix |
| F08CJF
Example Text Example Data |
21 | DORGRQ nagf_lapack_dorgrq Form all or part of orthogonal from 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 factorization of complex general rectangular matrix |
| F08CTF
Example Text Example Data |
21 | ZUNGQL nagf_lapack_zungql Form all or part of orthogonal from 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 factorization of complex general rectangular matrix |
| F08CWF
Example Text Example Data |
21 | ZUNGRQ nagf_lapack_zungrq Form all or part of orthogonal from 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 or algorithm |
| F08JFF
Example Text Example Data |
16 | DSTERF nagf_lapack_dsterf All eigenvalues of real symmetric tridiagonal matrix, root-free variant of the or 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 or 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 , and 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 , and 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 , or , 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 , or , 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 , or , packed storage, 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 , or , packed storage, 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
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21 | DSBGVX nagf_lapack_dsbgvx Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem |
| F08UCF
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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
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19 | DSBGST nagf_lapack_dsbgst Reduction of real symmetric-definite banded generalized eigenproblem to standard form , such that has the same bandwidth as |
| F08UFF | 19 | DPBSTF nagf_lapack_dpbstf Computes a split Cholesky factorization of real symmetric positive definite band matrix |
| F08UNF
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21 | ZHBGV nagf_lapack_zhbgv Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem |
| F08UPF
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21 | ZHBGVX nagf_lapack_zhbgvx Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem |
| F08UQF
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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
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19 | ZHBGST nagf_lapack_zhbgst Reduction of complex Hermitian-definite banded generalized eigenproblem to standard form , such that has the same bandwidth as |
| F08UTF | 19 | ZPBSTF nagf_lapack_zpbstf Computes a split Cholesky factorization of complex Hermitian positive definite band matrix |
| F08VAF
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21 | DGGSVD nagf_lapack_dggsvd Computes the generalized singular value decomposition of a real matrix pair |
| F08VEF
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21 | DGGSVP nagf_lapack_dggsvp Computes orthogonal matrices as processing steps for computing the generalized singular value decomposition of a real matrix pair |
| F08VNF
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21 | ZGGSVD nagf_lapack_zggsvd Computes the generalized singular value decomposition of a complex matrix pair |
| F08VSF
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21 | ZGGSVP nagf_lapack_zggsvp Computes orthogonal matrices as processing steps for computing the generalized singular value decomposition of a complex matrix pair |
| F08WAF
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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21 | DTGSJA nagf_lapack_dtgsja Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair |
| F08YFF
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21 | DTGEXC nagf_lapack_dtgexc Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation |
| F08YGF
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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
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21 | DTGSYL nagf_lapack_dtgsyl Solves the real-valued generalized Sylvester equation |
| F08YKF
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20 | DTGEVC nagf_lapack_dtgevc Left and right eigenvectors of a pair of real upper quasi-triangular matrices |
| F08YLF
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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
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21 | ZTGSJA nagf_lapack_ztgsja Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair |
| F08YTF
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21 | ZTGEXC nagf_lapack_ztgexc Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation |
| F08YUF
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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
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21 | ZTGSYL nagf_lapack_ztgsyl Solves the complex generalized Sylvester equation |
| F08YXF
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20 | ZTGEVC nagf_lapack_ztgevc Left and right eigenvectors of a pair of complex upper triangular matrices |
| F08YYF
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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
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21 | DGGLSE nagf_lapack_dgglse Solves the real linear equality-constrained least squares (LSE) problem |
| F08ZBF
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21 | DGGGLM nagf_lapack_dggglm Solves a real general Gauss–Markov linear model (GLM) problem |
| F08ZEF
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21 | DGGQRF nagf_lapack_dggqrf Computes a generalized factorization of a real matrix pair |
| F08ZFF
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21 | DGGRQF nagf_lapack_dggrqf Computes a generalized factorization of a real matrix pair |
| F08ZNF
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21 | ZGGLSE nagf_lapack_zgglse Solves the complex linear equality-constrained least squares (LSE) problem |
| F08ZPF
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21 | ZGGGLM nagf_lapack_zggglm Solves a complex general Gauss–Markov linear model (GLM) problem |
| F08ZSF
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21 | ZGGQRF nagf_lapack_zggqrf Computes a generalized factorization of a complex matrix pair |
| F08ZTF
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21 | ZGGRQF nagf_lapack_zggrqf Computes a generalized factorization of a complex matrix pair |