| Routine Name |
Mark of Introduction |
Purpose |
| F08AAF (DGELS)
Example Text Example Data |
21 | DGELS nagf_lapack_dgels Solves a real linear least problem of full rank |
| F08ABF (DGEQRT)
Example Text Example Data |
25 | DGEQRT nagf_lapack_dgeqrt Performs a factorization of real general rectangular matrix, with explicit blocking |
| F08ACF (DGEMQRT) | 25 | DGEMQRT nagf_lapack_dgemqrt Applies the orthogonal transformation determined by F08ABF (DGEQRT) |
| F08AEF (DGEQRF)
Example Text Example Data |
16 | DGEQRF nagf_lapack_dgeqrf Performs a factorization of real general rectangular matrix |
| F08AFF (DORGQR)
Example Text Example Data |
16 | DORGQR nagf_lapack_dorgqr Forms all or part of orthogonal from factorization determined by F08AEF (DGEQRF), F08BEF (DGEQPF) or F08BFF (DGEQP3) |
| F08AGF (DORMQR) | 16 | DORMQR nagf_lapack_dormqr Applies an orthogonal transformation determined by F08AEF (DGEQRF), F08BEF (DGEQPF) or F08BFF (DGEQP3) |
| F08AHF (DGELQF)
Example Text Example Data |
16 | DGELQF nagf_lapack_dgelqf Performs a factorization of real general rectangular matrix |
| F08AJF (DORGLQ)
Example Text Example Data |
16 | DORGLQ nagf_lapack_dorglq Forms all or part of orthogonal from factorization determined by F08AHF (DGELQF) |
| F08AKF (DORMLQ) | 16 | DORMLQ nagf_lapack_dormlq Applies the orthogonal transformation determined by F08AHF (DGELQF) |
| F08ANF (ZGELS)
Example Text Example Data |
21 | ZGELS nagf_lapack_zgels Solves a complex linear least problem of full rank |
| F08APF (ZGEQRT)
Example Text Example Data |
25 | ZGEQRT nagf_lapack_zgeqrt Performs a factorization of complex general rectangular matrix using recursive algorithm |
| F08AQF (ZGEMQRT) | 25 | ZGEMQRT nagf_lapack_zgemqrt Applies the unitary transformation determined by F08APF (ZGEQRT) |
| F08ASF (ZGEQRF)
Example Text Example Data |
16 | ZGEQRF nagf_lapack_zgeqrf Performs a factorization of complex general rectangular matrix |
| F08ATF (ZUNGQR)
Example Text Example Data |
16 | ZUNGQR nagf_lapack_zungqr Forms all or part of unitary from factorization determined by F08ASF (ZGEQRF), F08BSF (ZGEQPF) or F08BTF (ZGEQP3) |
| F08AUF (ZUNMQR) | 16 | ZUNMQR nagf_lapack_zunmqr Applies a unitary transformation determined by F08ASF (ZGEQRF), F08BSF (ZGEQPF) or F08BTF (ZGEQP3) |
| F08AVF (ZGELQF)
Example Text Example Data |
16 | ZGELQF nagf_lapack_zgelqf Performs a factorization of complex general rectangular matrix |
| F08AWF (ZUNGLQ)
Example Text Example Data |
16 | ZUNGLQ nagf_lapack_zunglq Forms all or part of unitary from factorization determined by F08AVF (ZGELQF) |
| F08AXF (ZUNMLQ) | 16 | ZUNMLQ nagf_lapack_zunmlq Applies the unitary transformation determined by F08AVF (ZGELQF) |
| F08BAF (DGELSY)
Example Text Example Data |
21 | DGELSY nagf_lapack_dgelsy Computes the minimum-norm solution to a real linear least squares problem |
| F08BBF (DTPQRT)
Example Text Example Data |
25 | DTPQRT nagf_lapack_dtpqrt factorization of real general triangular-pentagonal matrix |
| F08BCF (DTPMQRT) | 25 | DTPMQRT nagf_lapack_dtpmqrt Applies the orthogonal transformation determined by F08BBF (DTPQRT) |
| F08BEF (DGEQPF)
Example Text Example Data |
16 | DGEQPF nagf_lapack_dgeqpf factorization, with column pivoting, of real general rectangular matrix |
| F08BFF (DGEQP3)
Example Text Example Data |
21 | DGEQP3 nagf_lapack_dgeqp3 factorization, with column pivoting, using BLAS-3, of real general rectangular matrix |
| F08BHF (DTZRZF)
Example Text Example Data |
21 | DTZRZF nagf_lapack_dtzrzf Reduces a real upper trapezoidal matrix to upper triangular form |
| F08BKF (DORMRZ) | 21 | DORMRZ nagf_lapack_dormrz Applies the orthogonal transformation determined by F08BHF (DTZRZF) |
| F08BNF (ZGELSY)
Example Text Example Data |
21 | ZGELSY nagf_lapack_zgelsy Computes the minimum-norm solution to a complex linear least squares problem |
| F08BPF (ZTPQRT)
Example Text Example Data |
25 | ZTPQRT nagf_lapack_ztpqrt factorization of complex triangular-pentagonal matrix |
| F08BQF (ZTPMQRT) | 25 | ZTPMQRT nagf_lapack_ztpmqrt Applies the unitary transformation determined by F08BPF (ZTPQRT) |
| F08BSF (ZGEQPF)
Example Text Example Data |
16 | ZGEQPF nagf_lapack_zgeqpf factorization, with column pivoting, of complex general rectangular matrix |
| F08BTF (ZGEQP3)
Example Text Example Data |
21 | ZGEQP3 nagf_lapack_zgeqp3 factorization, with column pivoting, using BLAS-3, of complex general rectangular matrix |
| F08BVF (ZTZRZF)
Example Text Example Data |
21 | ZTZRZF nagf_lapack_ztzrzf Reduces a complex upper trapezoidal matrix to upper triangular form |
| F08BXF (ZUNMRZ) | 21 | ZUNMRZ nagf_lapack_zunmrz Applies the unitary transformation determined by F08BVF (ZTZRZF) |
| F08CEF (DGEQLF)
Example Text Example Data |
21 | DGEQLF nagf_lapack_dgeqlf factorization of real general rectangular matrix |
| F08CFF (DORGQL)
Example Text Example Data |
21 | DORGQL nagf_lapack_dorgql Form all or part of orthogonal from factorization determined by F08CEF (DGEQLF) |
| F08CGF (DORMQL) | 21 | DORMQL nagf_lapack_dormql Applies the orthogonal transformation determined by F08CEF (DGEQLF) |
| F08CHF (DGERQF)
Example Text Example Data |
21 | DGERQF nagf_lapack_dgerqf factorization of real general rectangular matrix |
| F08CJF (DORGRQ)
Example Text Example Data |
21 | DORGRQ nagf_lapack_dorgrq Form all or part of orthogonal from factorization determined by F08CHF (DGERQF) |
| F08CKF (DORMRQ) | 21 | DORMRQ nagf_lapack_dormrq Applies the orthogonal transformation determined by F08CHF (DGERQF) |
| F08CSF (ZGEQLF)
Example Text Example Data |
21 | ZGEQLF nagf_lapack_zgeqlf factorization of complex general rectangular matrix |
| F08CTF (ZUNGQL)
Example Text Example Data |
21 | ZUNGQL nagf_lapack_zungql Form all or part of unitary from factorization determined by F08CSF (ZGEQLF) |
| F08CUF (ZUNMQL) | 21 | ZUNMQL nagf_lapack_zunmql Applies the unitary transformation determined by F08CSF (ZGEQLF) |
| F08CVF (ZGERQF)
Example Text Example Data |
21 | ZGERQF nagf_lapack_zgerqf factorization of complex general rectangular matrix |
| F08CWF (ZUNGRQ)
Example Text Example Data |
21 | ZUNGRQ nagf_lapack_zungrq Form all or part of unitary from factorization determined by F08CVF (ZGERQF) |
| F08CXF (ZUNMRQ) | 21 | ZUNMRQ nagf_lapack_zunmrq Applies the unitary transformation determined by F08CVF (ZGERQF) |
| F08FAF (DSYEV)
Example Text Example Data |
21 | DSYEV nagf_lapack_dsyev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix |
| F08FBF (DSYEVX)
Example Text Example Data |
21 | DSYEVX nagf_lapack_dsyevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix |
| F08FCF (DSYEVD)
Example Text Example Data |
19 | DSYEVD nagf_lapack_dsyevd Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer) |
| F08FDF (DSYEVR)
Example Text Example Data |
21 | DSYEVR nagf_lapack_dsyevr Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations) |
| F08FEF (DSYTRD)
Example Text Example Data |
16 | DSYTRD nagf_lapack_dsytrd Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form |
| F08FFF (DORGTR)
Example Text Example Data |
16 | DORGTR nagf_lapack_dorgtr Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08FEF (DSYTRD) |
| F08FGF (DORMTR)
Example Text Example Data |
16 | DORMTR nagf_lapack_dormtr Applies the orthogonal transformation determined by F08FEF (DSYTRD) |
| F08FLF (DDISNA) | 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 (ZHEEV)
Example Text Example Data |
21 | ZHEEV nagf_lapack_zheev Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix |
| F08FPF (ZHEEVX)
Example Text Example Data |
21 | ZHEEVX nagf_lapack_zheevx Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix |
| F08FQF (ZHEEVD)
Example Text Example Data |
19 | ZHEEVD nagf_lapack_zheevd Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix (divide-and-conquer) |
| F08FRF (ZHEEVR)
Example Text Example Data |
21 | ZHEEVR nagf_lapack_zheevr Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations) |
| F08FSF (ZHETRD)
Example Text Example Data |
16 | ZHETRD nagf_lapack_zhetrd Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form |
| F08FTF (ZUNGTR)
Example Text Example Data |
16 | ZUNGTR nagf_lapack_zungtr Generate unitary transformation matrix from reduction to tridiagonal form determined by F08FSF (ZHETRD) |
| F08FUF (ZUNMTR)
Example Text Example Data |
16 | ZUNMTR nagf_lapack_zunmtr Applies the unitary transformation matrix determined by F08FSF (ZHETRD) |
| F08GAF (DSPEV)
Example Text Example Data |
21 | DSPEV nagf_lapack_dspev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage |
| F08GBF (DSPEVX)
Example Text Example Data |
21 | DSPEVX nagf_lapack_dspevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage |
| F08GCF (DSPEVD)
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 or Pal–Walker–Kahan variant of the or algorithm) |
| F08GEF (DSPTRD)
Example Text Example Data |
16 | DSPTRD nagf_lapack_dsptrd Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage |
| F08GFF (DOPGTR)
Example Text Example Data |
16 | DOPGTR nagf_lapack_dopgtr Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08GEF (DSPTRD) |
| F08GGF (DOPMTR)
Example Text Example Data |
16 | DOPMTR nagf_lapack_dopmtr Applies the orthogonal transformation determined by F08GEF (DSPTRD) |
| F08GNF (ZHPEV)
Example Text Example Data |
21 | ZHPEV nagf_lapack_zhpev Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage |
| F08GPF (ZHPEVX)
Example Text Example Data |
21 | ZHPEVX nagf_lapack_zhpevx Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage |
| F08GQF (ZHPEVD)
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 or Pal–Walker–Kahan variant of the or algorithm) |
| F08GSF (ZHPTRD)
Example Text Example Data |
16 | ZHPTRD nagf_lapack_zhptrd Performs a unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage |
| F08GTF (ZUPGTR)
Example Text Example Data |
16 | ZUPGTR nagf_lapack_zupgtr Generates a unitary transformation matrix from reduction to tridiagonal form determined by F08GSF (ZHPTRD) |
| F08GUF (ZUPMTR)
Example Text Example Data |
16 | ZUPMTR nagf_lapack_zupmtr Applies the unitary transformation matrix determined by F08GSF (ZHPTRD) |
| F08HAF (DSBEV)
Example Text Example Data |
21 | DSBEV nagf_lapack_dsbev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix |
| F08HBF (DSBEVX)
Example Text Example Data |
21 | DSBEVX nagf_lapack_dsbevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix |
| F08HCF (DSBEVD)
Example Text Example Data |
19 | DSBEVD nagf_lapack_dsbevd Computes all eigenvalues and, optionally, all eigenvectors of real symmetric band matrix (divide-and-conquer or Pal–Walker–Kahan variant of the or algorithm) |
| F08HEF (DSBTRD)
Example Text Example Data |
16 | DSBTRD nagf_lapack_dsbtrd Performs an orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form |
| F08HNF (ZHBEV)
Example Text Example Data |
21 | ZHBEV nagf_lapack_zhbev Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix |
| F08HPF (ZHBEVX)
Example Text Example Data |
21 | ZHBEVX nagf_lapack_zhbevx Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix |
| F08HQF (ZHBEVD)
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 (ZHBTRD)
Example Text Example Data |
16 | ZHBTRD nagf_lapack_zhbtrd Performs a unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form |
| F08JAF (DSTEV)
Example Text Example Data |
21 | DSTEV nagf_lapack_dstev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix |
| F08JBF (DSTEVX)
Example Text Example Data |
21 | DSTEVX nagf_lapack_dstevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix |
| F08JCF (DSTEVD)
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 (DSTEVR)
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 (DSTEQR)
Example Text Example Data |
16 | DSTEQR nagf_lapack_dsteqr Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using the implicit or algorithm |
| F08JFF (DSTERF)
Example Text Example Data |
16 | DSTERF nagf_lapack_dsterf Computes all eigenvalues of real symmetric tridiagonal matrix, root-free variant of the or algorithm |
| F08JGF (DPTEQR)
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 (DSTEDC)
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 (DSTEBZ) | 16 | DSTEBZ nagf_lapack_dstebz Computes selected eigenvalues of real symmetric tridiagonal matrix by bisection |
| F08JKF (DSTEIN) | 16 | DSTEIN nagf_lapack_dstein Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array |
| F08JLF (DSTEGR)
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 (ZSTEQR) | 16 | ZSTEQR nagf_lapack_zsteqr Computes all eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using the implicit or algorithm |
| F08JUF (ZPTEQR)
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 (ZSTEDC)
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 (ZSTEIN) | 16 | ZSTEIN nagf_lapack_zstein Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array |
| F08JYF (ZSTEGR)
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 (DGELSS)
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 (DGESVD)
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 (DGELSD)
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 (DGESDD)
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 (DGEBRD)
Example Text Example Data |
16 | DGEBRD nagf_lapack_dgebrd Performs an orthogonal reduction of real general rectangular matrix to bidiagonal form |
| F08KFF (DORGBR)
Example Text Example Data |
16 | DORGBR nagf_lapack_dorgbr Generates an orthogonal transformation matrices from reduction to bidiagonal form determined by F08KEF (DGEBRD) |
| F08KGF (DORMBR)
Example Text Example Data |
16 | DORMBR nagf_lapack_dormbr Applies the orthogonal transformations from reduction to bidiagonal form determined by F08KEF (DGEBRD) |
| F08KHF (DGEJSV)
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 (DGESVJ)
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 (ZGELSS)
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 (ZGESVD)
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 (ZGELSD)
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 (ZGESDD)
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 (ZGEBRD)
Example Text Example Data |
16 | ZGEBRD nagf_lapack_zgebrd Performs a unitary reduction of complex general rectangular matrix to bidiagonal form |
| F08KTF (ZUNGBR)
Example Text Example Data |
16 | ZUNGBR nagf_lapack_zungbr Generates unitary transformation matrices from the reduction to bidiagonal form determined by F08KSF (ZGEBRD) |
| F08KUF (ZUNMBR)
Example Text Example Data |
16 | ZUNMBR nagf_lapack_zunmbr Applies the unitary transformations from reduction to bidiagonal form determined by F08KSF (ZGEBRD) |
| F08LEF (DGBBRD)
Example Text Example Data |
19 | DGBBRD nagf_lapack_dgbbrd Performs a reduction of real rectangular band matrix to upper bidiagonal form |
| F08LSF (ZGBBRD)
Example Text Example Data |
19 | ZGBBRD nagf_lapack_zgbbrd Reduction of complex rectangular band matrix to upper bidiagonal form |
| F08MDF (DBDSDC)
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 (DBDSQR)
Example Text Example Data |
16 | DBDSQR nagf_lapack_dbdsqr Performs an SVD of real bidiagonal matrix reduced from real general matrix |
| F08MSF (ZBDSQR) | 16 | ZBDSQR nagf_lapack_zbdsqr Performs an SVD of real bidiagonal matrix reduced from complex general matrix |
| F08NAF (DGEEV)
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 (DGEEVX)
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 (DGEHRD)
Example Text Example Data |
16 | DGEHRD nagf_lapack_dgehrd Performs an orthogonal reduction of real general matrix to upper Hessenberg form |
| F08NFF (DORGHR)
Example Text Example Data |
16 | DORGHR nagf_lapack_dorghr Generates an orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (DGEHRD) |
| F08NGF (DORMHR)
Example Text Example Data |
16 | DORMHR nagf_lapack_dormhr Applies the orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (DGEHRD) |
| F08NHF (DGEBAL)
Example Text Example Data |
16 | DGEBAL nagf_lapack_dgebal Balances a real general matrix |
| F08NJF (DGEBAK) | 16 | DGEBAK nagf_lapack_dgebak Transforms eigenvectors of real balanced matrix to those of original matrix supplied to F08NHF (DGEBAL) |
| F08NNF (ZGEEV)
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 (ZGEEVX)
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 (ZGEHRD)
Example Text Example Data |
16 | ZGEHRD nagf_lapack_zgehrd Performs a unitary reduction of complex general matrix to upper Hessenberg form |
| F08NTF (ZUNGHR)
Example Text Example Data |
16 | ZUNGHR nagf_lapack_zunghr Generates a unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (ZGEHRD) |
| F08NUF (ZUNMHR)
Example Text Example Data |
16 | ZUNMHR nagf_lapack_zunmhr Applies the unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (ZGEHRD) |
| F08NVF (ZGEBAL)
Example Text Example Data |
16 | ZGEBAL nagf_lapack_zgebal Balances a complex general matrix |
| F08NWF (ZGEBAK) | 16 | ZGEBAK nagf_lapack_zgebak Transforms eigenvectors of complex balanced matrix to those of original matrix supplied to F08NVF (ZGEBAL) |
| F08PAF (DGEES)
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 (DGEESX)
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 (DHSEQR)
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 (DHSEIN) | 16 | DHSEIN nagf_lapack_dhsein Computes selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration |
| F08PNF (ZGEES)
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 (ZGEESX)
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 computes a reciprocal condition number for the average of the selected eigenvalues and for the right invariant subspace corresponding to these eigenvalues |
| F08PSF (ZHSEQR)
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 (ZHSEIN) | 16 | ZHSEIN nagf_lapack_zhsein Computes selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration |
| F08QFF (DTREXC)
Example Text Example Data |
16 | DTREXC nagf_lapack_dtrexc Reorders a Schur factorization of real matrix using orthogonal similarity transformation |
| F08QGF (DTRSEN)
Example Text Example Data |
16 | DTRSEN nagf_lapack_dtrsen Reorders a Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities |
| F08QHF (DTRSYL)
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16 | DTRSYL nagf_lapack_dtrsyl Solves the real Sylvester matrix equation , and are upper quasi-triangular or transposes |
| F08QKF (DTREVC) | 16 | DTREVC nagf_lapack_dtrevc Computes left and right eigenvectors of real upper quasi-triangular matrix |
| F08QLF (DTRSNA)
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16 | DTRSNA nagf_lapack_dtrsna Computes estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix |
| F08QTF (ZTREXC)
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16 | ZTREXC nagf_lapack_ztrexc Reorders a Schur factorization of complex matrix using unitary similarity transformation |
| F08QUF (ZTRSEN)
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16 | ZTRSEN nagf_lapack_ztrsen Reorders a Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities |
| F08QVF (ZTRSYL)
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16 | ZTRSYL nagf_lapack_ztrsyl Solves the complex Sylvester matrix equation , and are upper triangular or conjugate-transposes |
| F08QXF (ZTREVC) | 16 | ZTREVC nagf_lapack_ztrevc Computes left and right eigenvectors of complex upper triangular matrix |
| F08QYF (ZTRSNA)
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16 | ZTRSNA nagf_lapack_ztrsna Computes estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix |
| F08RAF (DORCSD)
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25 | DORCSD nagf_lapack_dorcsd Computes the CS decomposition of an orthogonal matrix partitioned into four real submatrices |
| F08RNF (ZUNCSD)
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25 | ZUNCSD nagf_lapack_zuncsd Computes the CS decomposition of a unitary matrix partitioned into four complex submatrices |
| F08SAF (DSYGV)
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21 | DSYGV nagf_lapack_dsygv Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem |
| F08SBF (DSYGVX)
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21 | DSYGVX nagf_lapack_dsygvx Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem |
| F08SCF (DSYGVD)
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21 | DSYGVD nagf_lapack_dsygvd Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer) |
| F08SEF (DSYGST)
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16 | DSYGST nagf_lapack_dsygst Performs a reduction to standard form of real symmetric-definite generalized eigenproblem , or , factorized by F07FDF (DPOTRF) |
| F08SNF (ZHEGV)
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21 | ZHEGV nagf_lapack_zhegv Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem |
| F08SPF (ZHEGVX)
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21 | ZHEGVX nagf_lapack_zhegvx Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem |
| F08SQF (ZHEGVD)
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21 | ZHEGVD nagf_lapack_zhegvd Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer) |
| F08SSF (ZHEGST)
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16 | ZHEGST nagf_lapack_zhegst Performs a reduction to standard form of complex Hermitian-definite generalized eigenproblem , or , factorized by F07FRF (ZPOTRF) |
| F08TAF (DSPGV)
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21 | DSPGV nagf_lapack_dspgv Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage |
| F08TBF (DSPGVX)
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21 | DSPGVX nagf_lapack_dspgvx Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage |
| F08TCF (DSPGVD)
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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 (DSPGST)
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16 | DSPGST nagf_lapack_dspgst Performs a reduction to standard form of real symmetric-definite generalized eigenproblem , or , packed storage, factorized by F07GDF (DPPTRF) |
| F08TNF (ZHPGV)
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21 | ZHPGV nagf_lapack_zhpgv Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage |
| F08TPF (ZHPGVX)
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21 | ZHPGVX nagf_lapack_zhpgvx Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage |
| F08TQF (ZHPGVD)
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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 (ZHPGST)
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16 | ZHPGST nagf_lapack_zhpgst Performs a reduction to standard form of complex Hermitian-definite generalized eigenproblem , or , packed storage, factorized by F07GRF (ZPPTRF) |
| F08UAF (DSBGV)
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21 | DSBGV nagf_lapack_dsbgv Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem |
| F08UBF (DSBGVX)
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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 (DSBGVD)
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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 (DSBGST)
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19 | DSBGST nagf_lapack_dsbgst Performs a reduction of real symmetric-definite banded generalized eigenproblem to standard form , such that has the same bandwidth as |
| F08UFF (DPBSTF) | 19 | DPBSTF nagf_lapack_dpbstf Computes a split Cholesky factorization of real symmetric positive definite band matrix |
| F08UNF (ZHBGV)
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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 (ZHBGVX)
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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 (ZHBGVD)
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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 (ZHBGST)
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19 | ZHBGST nagf_lapack_zhbgst Performs a reduction of complex Hermitian-definite banded generalized eigenproblem to standard form , such that has the same bandwidth as |
| F08UTF (ZPBSTF) | 19 | ZPBSTF nagf_lapack_zpbstf Computes a split Cholesky factorization of complex Hermitian positive definite band matrix |
| F08VAF (DGGSVD)
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21 | DGGSVD nagf_lapack_dggsvd Computes the generalized singular value decomposition of a real matrix pair |
| F08VEF (DGGSVP)
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21 | DGGSVP nagf_lapack_dggsvp Produces orthogonal matrices that simultaneously reduce the by matrix and the by matrix to upper triangular form |
| F08VNF (ZGGSVD)
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21 | ZGGSVD nagf_lapack_zggsvd Computes the generalized singular value decomposition of a complex matrix pair |
| F08VSF (ZGGSVP)
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21 | ZGGSVP nagf_lapack_zggsvp Produces unitary matrices that simultaneously reduce the complex , by , matrix and the complex, by , matrix to upper triangular form |
| F08WAF (DGGEV)
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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 (DGGEVX)
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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 (DGGHRD) | 20 | DGGHRD nagf_lapack_dgghrd Performs an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form |
| F08WHF (DGGBAL) | 20 | DGGBAL nagf_lapack_dggbal Balances a pair of real, square, matrices |
| F08WJF (DGGBAK) | 20 | DGGBAK nagf_lapack_dggbak Transforms eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to F08WHF (DGGBAL) |
| F08WNF (ZGGEV)
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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 (ZGGEVX)
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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 (ZGGHRD) | 20 | ZGGHRD nagf_lapack_zgghrd Performs a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form |
| F08WVF (ZGGBAL) | 20 | ZGGBAL nagf_lapack_zggbal Balances a pair of complex, square, matrices |
| F08WWF (ZGGBAK) | 20 | ZGGBAK nagf_lapack_zggbak Transforms eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to F08WVF (ZGGBAL) |
| F08XAF (DGGES)
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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 (DGGESX)
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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 (DHGEQZ)
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20 | DHGEQZ nagf_lapack_dhgeqz Computes eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices |
| F08XNF (ZGGES)
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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 (ZGGESX)
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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 (ZHGEQZ)
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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, square, matrices |
| F08YEF (DTGSJA)
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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 (DTGEXC)
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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 (DTGSEN)
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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 (DTGSYL)
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21 | DTGSYL nagf_lapack_dtgsyl Solves the real-valued, generalized, quasi-trangular, Sylvester equation |
| F08YKF (DTGEVC)
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20 | DTGEVC nagf_lapack_dtgevc Computes right and left generalized eigenvectors of the matrix pair ) which is assumed to be in generalized upper Schur form |
| F08YLF (DTGSNA)
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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 (ZTGSJA)
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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 (ZTGEXC)
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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 (ZTGSEN)
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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 (ZTGSYL)
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21 | ZTGSYL nagf_lapack_ztgsyl Solves the complex generalized Sylvester equation |
| F08YXF (ZTGEVC)
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20 | ZTGEVC nagf_lapack_ztgevc Computes left and right eigenvectors of a pair of complex upper triangular matrices |
| F08YYF (ZTGSNA)
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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 (DGGLSE)
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21 | DGGLSE nagf_lapack_dgglse Solves the real linear equality-constrained least squares (LSE) problem |
| F08ZBF (DGGGLM)
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21 | DGGGLM nagf_lapack_dggglm Solves a real general Gauss–Markov linear model (GLM) problem |
| F08ZEF (DGGQRF)
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21 | DGGQRF nagf_lapack_dggqrf Computes a generalized factorization of a real matrix pair |
| F08ZFF (DGGRQF)
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21 | DGGRQF nagf_lapack_dggrqf Computes a generalized factorization of a real matrix pair |
| F08ZNF (ZGGLSE)
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21 | ZGGLSE nagf_lapack_zgglse Solves the complex linear equality-constrained least squares (LSE) problem |
| F08ZPF (ZGGGLM)
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21 | ZGGGLM nagf_lapack_zggglm Solves a complex general Gauss–Markov linear model (GLM) problem |
| F08ZSF (ZGGQRF)
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21 | ZGGQRF nagf_lapack_zggqrf Computes a generalized factorization of a complex matrix pair |
| F08ZTF (ZGGRQF)
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21 | ZGGRQF nagf_lapack_zggrqf Computes a generalized factorization of a complex matrix pair |