F08 (lapack) Chapter Introduction – a description of the Chapter and an overview of the algorithms available
| Routine Name |
Mark of Introduction |
Purpose |
| f08aaf (dgels)
Example Text Example Data |
21 | DGELS nagf_lapack_dgels Solves a real linear least squares 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 |
22 | DGEQP3 nagf_lapack_dgeqp3 factorization, with column pivoting, using BLAS-3, of real general rectangular matrix |
| f08bhf (dtzrzf)
Example Text Example Data |
22 | DTZRZF nagf_lapack_dtzrzf Reduces a real upper trapezoidal matrix to upper triangular form |
| f08bkf (dormrz) | 22 | 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 |
22 | ZGEQP3 nagf_lapack_zgeqp3 factorization, with column pivoting, using BLAS-3, of complex general rectangular matrix |
| f08bvf (ztzrzf)
Example Text Example Data |
22 | ZTZRZF nagf_lapack_ztzrzf Reduces a complex upper trapezoidal matrix to upper triangular form |
| f08bxf (zunmrz) | 22 | ZUNMRZ nagf_lapack_zunmrz Applies the unitary transformation determined by f08bvf (ztzrzf) |
| f08cef (dgeqlf)
Example Text Example Data |
22 | DGEQLF nagf_lapack_dgeqlf factorization of real general rectangular matrix |
| f08cff (dorgql)
Example Text Example Data |
22 | DORGQL nagf_lapack_dorgql Form all or part of orthogonal from factorization determined by f08cef (dgeqlf) |
| f08cgf (dormql) | 22 | DORMQL nagf_lapack_dormql Applies the orthogonal transformation determined by f08cef (dgeqlf) |
| f08chf (dgerqf)
Example Text Example Data |
22 | DGERQF nagf_lapack_dgerqf factorization of real general rectangular matrix |
| f08cjf (dorgrq)
Example Text Example Data |
22 | DORGRQ nagf_lapack_dorgrq Form all or part of orthogonal from factorization determined by f08chf (dgerqf) |
| f08ckf (dormrq) | 22 | DORMRQ nagf_lapack_dormrq Applies the orthogonal transformation determined by f08chf (dgerqf) |
| f08csf (zgeqlf)
Example Text Example Data |
22 | ZGEQLF nagf_lapack_zgeqlf factorization of complex general rectangular matrix |
| f08ctf (zungql)
Example Text Example Data |
22 | ZUNGQL nagf_lapack_zungql Form all or part of unitary from factorization determined by f08csf (zgeqlf) |
| f08cuf (zunmql) | 22 | ZUNMQL nagf_lapack_zunmql Applies the unitary transformation determined by f08csf (zgeqlf) |
| f08cvf (zgerqf)
Example Text Example Data |
22 | ZGERQF nagf_lapack_zgerqf factorization of complex general rectangular matrix |
| f08cwf (zungrq)
Example Text Example Data |
22 | ZUNGRQ nagf_lapack_zungrq Form all or part of unitary from factorization determined by f08cvf (zgerqf) |
| f08cxf (zunmrq) | 22 | 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) | 22 | 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 |
22 | 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 |
22 | DSTEGR nagf_lapack_dstegr Computes selected eigenvalues and, optionally, the corresponding 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 |
22 | 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 |
22 | ZSTEGR nagf_lapack_zstegr Computes selected eigenvalues and, optionally, the corresponding 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 |
22 | 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)
Example Text Example Data |
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)
Example Text Example Data |
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)
Example Text Example Data |
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 |
| f08vcf (dggsvd3)
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26.0 | DGGSVD3 nagf_lapack_dggsvd3 Computes, using BLAS-3, the generalized singular value decomposition of a real matrix pair |
| f08vef (dggsvp)
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22 | DGGSVP nagf_lapack_dggsvp Produces orthogonal matrices that simultaneously reduce the by matrix and the by matrix to upper triangular form |
| f08vgf (dggsvp3)
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26.0 | DGGSVP3 nagf_lapack_dggsvp3 Produces orthogonal matrices, using BLAS-3, 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 |
| f08vqf (zggsvd3)
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26.0 | ZGGSVD3 nagf_lapack_zggsvd3 Computes, using BLAS-3, the generalized singular value decomposition of a complex matrix pair |
| f08vsf (zggsvp)
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22 | ZGGSVP nagf_lapack_zggsvp Produces unitary matrices that simultaneously reduce the complex, by , matrix and the complex, by , matrix to upper triangular form |
| f08vuf (zggsvp3)
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26.0 | ZGGSVP3 nagf_lapack_zggsvp3 Produces unitary matrices, using BLAS-3, 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 |
| f08wcf (dggev3)
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26.0 | DGGEV3 nagf_lapack_dggev3 Computes, for a real nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors |
| f08wef (dgghrd) | 20 | DGGHRD nagf_lapack_dgghrd Performs an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form |
| f08wff (dgghd3) | 26.0 | DGGHD3 nagf_lapack_dgghd3 Performs, using BLAS-3, 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 |
| f08wqf (zggev3)
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26.0 | ZGGEV3 nagf_lapack_zggev3 Computes, for a complex nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors |
| f08wsf (zgghrd) | 20 | ZGGHRD nagf_lapack_zgghrd Performs a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form |
| f08wtf (zgghd3) | 26.0 | ZGGHD3 nagf_lapack_zgghd3 Performs, using BLAS-3, 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)
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 |
| f08xcf (dgges3)
Example Text Example Data |
26.0 | DGGES3 nagf_lapack_dgges3 Computes, for a real nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors |
| 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)
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 |
| f08xqf (zgges3)
Example Text Example Data |
26.0 | ZGGES3 nagf_lapack_zgges3 Computes, for a complex nonsymmetric matrix pair, using BLAS-3, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors |
| f08xsf (zhgeqz)
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, square, matrices |
| f08yef (dtgsja)
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22 | DTGSJA nagf_lapack_dtgsja Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair |
| f08yff (dtgexc)
Example Text Example Data |
22 | 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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22 | 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)
Example Text Example Data |
22 | 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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22 | 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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22 | ZTGSJA nagf_lapack_ztgsja Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair |
| f08ytf (ztgexc)
Example Text Example Data |
22 | ZTGEXC nagf_lapack_ztgexc Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation |
| f08yuf (ztgsen)
Example Text Example Data |
22 | 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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22 | 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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22 | 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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22 | DGGQRF nagf_lapack_dggqrf Computes a generalized factorization of a real matrix pair |
| f08zff (dggrqf)
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22 | DGGRQF nagf_lapack_dggrqf Computes a generalized factorization of a real matrix pair |
| f08znf (zgglse)
Example Text Example Data |
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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22 | ZGGQRF nagf_lapack_zggqrf Computes a generalized factorization of a complex matrix pair |
| f08ztf (zggrqf)
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22 | ZGGRQF nagf_lapack_zggrqf Computes a generalized factorization of a complex matrix pair |