F08 (lapackeig) 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_lapackeig_dgels Solves a real linear least squares problem of full rank |
| f08abf (dgeqrt)
Example Text Example Data |
25 | dgeqrt nagf_lapackeig_dgeqrt Performs a factorization of real general rectangular matrix, with explicit blocking |
| f08acf (dgemqrt) | 25 | dgemqrt nagf_lapackeig_dgemqrt Applies the orthogonal transformation determined by f08abf (dgeqrt) |
| f08aef (dgeqrf)
Example Text Example Data |
16 | dgeqrf nagf_lapackeig_dgeqrf Performs a factorization of real general rectangular matrix |
| f08aff (dorgqr)
Example Text Example Data |
16 | dorgqr nagf_lapackeig_dorgqr Forms all or part of orthogonal from factorization determined by f08aef (dgeqrf), f08bef (dgeqpf) or f08bff (dgeqp3) |
| f08agf (dormqr) | 16 | dormqr nagf_lapackeig_dormqr Applies an orthogonal transformation determined by f08aef (dgeqrf), f08bef (dgeqpf) or f08bff (dgeqp3) |
| f08ahf (dgelqf)
Example Text Example Data |
16 | dgelqf nagf_lapackeig_dgelqf Performs a factorization of real general rectangular matrix |
| f08ajf (dorglq)
Example Text Example Data |
16 | dorglq nagf_lapackeig_dorglq Forms all or part of orthogonal from factorization determined by f08ahf (dgelqf) |
| f08akf (dormlq) | 16 | dormlq nagf_lapackeig_dormlq Applies the orthogonal transformation determined by f08ahf (dgelqf) |
| f08anf (zgels)
Example Text Example Data |
21 | zgels nagf_lapackeig_zgels Solves a complex linear least problem of full rank |
| f08apf (zgeqrt)
Example Text Example Data |
25 | zgeqrt nagf_lapackeig_zgeqrt Performs a factorization of complex general rectangular matrix using recursive algorithm |
| f08aqf (zgemqrt) | 25 | zgemqrt nagf_lapackeig_zgemqrt Applies the unitary transformation determined by f08apf (zgeqrt) |
| f08asf (zgeqrf)
Example Text Example Data |
16 | zgeqrf nagf_lapackeig_zgeqrf Performs a factorization of complex general rectangular matrix |
| f08atf (zungqr)
Example Text Example Data |
16 | zungqr nagf_lapackeig_zungqr Forms all or part of unitary from factorization determined by f08asf (zgeqrf), f08bsf (zgeqpf) or f08btf (zgeqp3) |
| f08auf (zunmqr) | 16 | zunmqr nagf_lapackeig_zunmqr Applies a unitary transformation determined by f08asf (zgeqrf), f08bsf (zgeqpf) or f08btf (zgeqp3) |
| f08avf (zgelqf)
Example Text Example Data |
16 | zgelqf nagf_lapackeig_zgelqf Performs a factorization of complex general rectangular matrix |
| f08awf (zunglq)
Example Text Example Data |
16 | zunglq nagf_lapackeig_zunglq Forms all or part of unitary from factorization determined by f08avf (zgelqf) |
| f08axf (zunmlq) | 16 | zunmlq nagf_lapackeig_zunmlq Applies the unitary transformation determined by f08avf (zgelqf) |
| f08baf (dgelsy)
Example Text Example Data |
21 | dgelsy nagf_lapackeig_dgelsy Computes the minimum-norm solution to a real linear least squares problem |
| f08bbf (dtpqrt)
Example Text Example Data |
25 | dtpqrt nagf_lapackeig_dtpqrt factorization of real general triangular-pentagonal matrix |
| f08bcf (dtpmqrt) | 25 | dtpmqrt nagf_lapackeig_dtpmqrt Applies the orthogonal transformation determined by f08bbf (dtpqrt) |
| f08bef (dgeqpf)
Example Text Example Data |
16 | dgeqpf nagf_lapackeig_dgeqpf factorization, with column pivoting, of real general rectangular matrix |
| f08bff (dgeqp3)
Example Text Example Data |
22 | dgeqp3 nagf_lapackeig_dgeqp3 factorization, with column pivoting, using BLAS-3, of real general rectangular matrix |
| f08bhf (dtzrzf)
Example Text Example Data |
22 | dtzrzf nagf_lapackeig_dtzrzf Reduces a real upper trapezoidal matrix to upper triangular form |
| f08bkf (dormrz) | 22 | dormrz nagf_lapackeig_dormrz Applies the orthogonal transformation determined by f08bhf (dtzrzf) |
| f08bnf (zgelsy)
Example Text Example Data |
21 | zgelsy nagf_lapackeig_zgelsy Computes the minimum-norm solution to a complex linear least squares problem |
| f08bpf (ztpqrt)
Example Text Example Data |
25 | ztpqrt nagf_lapackeig_ztpqrt factorization of complex triangular-pentagonal matrix |
| f08bqf (ztpmqrt) | 25 | ztpmqrt nagf_lapackeig_ztpmqrt Applies the unitary transformation determined by f08bpf (ztpqrt) |
| f08bsf (zgeqpf)
Example Text Example Data |
16 | zgeqpf nagf_lapackeig_zgeqpf factorization, with column pivoting, of complex general rectangular matrix |
| f08btf (zgeqp3)
Example Text Example Data |
22 | zgeqp3 nagf_lapackeig_zgeqp3 factorization, with column pivoting, using BLAS-3, of complex general rectangular matrix |
| f08bvf (ztzrzf)
Example Text Example Data |
22 | ztzrzf nagf_lapackeig_ztzrzf Reduces a complex upper trapezoidal matrix to upper triangular form |
| f08bxf (zunmrz) | 22 | zunmrz nagf_lapackeig_zunmrz Applies the unitary transformation determined by f08bvf (ztzrzf) |
| f08cef (dgeqlf)
Example Text Example Data |
22 | dgeqlf nagf_lapackeig_dgeqlf factorization of real general rectangular matrix |
| f08cff (dorgql)
Example Text Example Data |
22 | dorgql nagf_lapackeig_dorgql Form all or part of orthogonal from factorization determined by f08cef (dgeqlf) |
| f08cgf (dormql) | 22 | dormql nagf_lapackeig_dormql Applies the orthogonal transformation determined by f08cef (dgeqlf) |
| f08chf (dgerqf)
Example Text Example Data |
22 | dgerqf nagf_lapackeig_dgerqf factorization of real general rectangular matrix |
| f08cjf (dorgrq)
Example Text Example Data |
22 | dorgrq nagf_lapackeig_dorgrq Form all or part of orthogonal from factorization determined by f08chf (dgerqf) |
| f08ckf (dormrq) | 22 | dormrq nagf_lapackeig_dormrq Applies the orthogonal transformation determined by f08chf (dgerqf) |
| f08csf (zgeqlf)
Example Text Example Data |
22 | zgeqlf nagf_lapackeig_zgeqlf factorization of complex general rectangular matrix |
| f08ctf (zungql)
Example Text Example Data |
22 | zungql nagf_lapackeig_zungql Form all or part of unitary from factorization determined by f08csf (zgeqlf) |
| f08cuf (zunmql) | 22 | zunmql nagf_lapackeig_zunmql Applies the unitary transformation determined by f08csf (zgeqlf) |
| f08cvf (zgerqf)
Example Text Example Data |
22 | zgerqf nagf_lapackeig_zgerqf factorization of complex general rectangular matrix |
| f08cwf (zungrq)
Example Text Example Data |
22 | zungrq nagf_lapackeig_zungrq Form all or part of unitary from factorization determined by f08cvf (zgerqf) |
| f08cxf (zunmrq) | 22 | zunmrq nagf_lapackeig_zunmrq Applies the unitary transformation determined by f08cvf (zgerqf) |
| f08faf (dsyev)
Example Text Example Data |
21 | dsyev nagf_lapackeig_dsyev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix |
| f08fbf (dsyevx)
Example Text Example Data |
21 | dsyevx nagf_lapackeig_dsyevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix |
| f08fcf (dsyevd)
Example Text Example Data |
19 | dsyevd nagf_lapackeig_dsyevd Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer) |
| f08fdf (dsyevr)
Example Text Example Data |
21 | dsyevr nagf_lapackeig_dsyevr Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations) |
| f08fef (dsytrd)
Example Text Example Data |
16 | dsytrd nagf_lapackeig_dsytrd Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form |
| f08fff (dorgtr)
Example Text Example Data |
16 | dorgtr nagf_lapackeig_dorgtr Generate orthogonal transformation matrix from reduction to tridiagonal form determined by f08fef (dsytrd) |
| f08fgf (dormtr)
Example Text Example Data |
16 | dormtr nagf_lapackeig_dormtr Applies the orthogonal transformation determined by f08fef (dsytrd) |
| f08flf (ddisna) | 22 | ddisna nagf_lapackeig_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_lapackeig_zheev Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix |
| f08fpf (zheevx)
Example Text Example Data |
21 | zheevx nagf_lapackeig_zheevx Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix |
| f08fqf (zheevd)
Example Text Example Data |
19 | zheevd nagf_lapackeig_zheevd Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix (divide-and-conquer) |
| f08frf (zheevr)
Example Text Example Data |
21 | zheevr nagf_lapackeig_zheevr Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations) |
| f08fsf (zhetrd)
Example Text Example Data |
16 | zhetrd nagf_lapackeig_zhetrd Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form |
| f08ftf (zungtr)
Example Text Example Data |
16 | zungtr nagf_lapackeig_zungtr Generate unitary transformation matrix from reduction to tridiagonal form determined by f08fsf (zhetrd) |
| f08fuf (zunmtr)
Example Text Example Data |
16 | zunmtr nagf_lapackeig_zunmtr Applies the unitary transformation matrix determined by f08fsf (zhetrd) |
| f08gaf (dspev)
Example Text Example Data |
21 | dspev nagf_lapackeig_dspev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage |
| f08gbf (dspevx)
Example Text Example Data |
21 | dspevx nagf_lapackeig_dspevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage |
| f08gcf (dspevd)
Example Text Example Data |
19 | dspevd nagf_lapackeig_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_lapackeig_dsptrd Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage |
| f08gff (dopgtr)
Example Text Example Data |
16 | dopgtr nagf_lapackeig_dopgtr Generate orthogonal transformation matrix from reduction to tridiagonal form determined by f08gef (dsptrd) |
| f08ggf (dopmtr)
Example Text Example Data |
16 | dopmtr nagf_lapackeig_dopmtr Applies the orthogonal transformation determined by f08gef (dsptrd) |
| f08gnf (zhpev)
Example Text Example Data |
21 | zhpev nagf_lapackeig_zhpev Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage |
| f08gpf (zhpevx)
Example Text Example Data |
21 | zhpevx nagf_lapackeig_zhpevx Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage |
| f08gqf (zhpevd)
Example Text Example Data |
19 | zhpevd nagf_lapackeig_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_lapackeig_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_lapackeig_zupgtr Generates a unitary transformation matrix from reduction to tridiagonal form determined by f08gsf (zhptrd) |
| f08guf (zupmtr)
Example Text Example Data |
16 | zupmtr nagf_lapackeig_zupmtr Applies the unitary transformation matrix determined by f08gsf (zhptrd) |
| f08haf (dsbev)
Example Text Example Data |
21 | dsbev nagf_lapackeig_dsbev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix |
| f08hbf (dsbevx)
Example Text Example Data |
21 | dsbevx nagf_lapackeig_dsbevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix |
| f08hcf (dsbevd)
Example Text Example Data |
19 | dsbevd nagf_lapackeig_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_lapackeig_dsbtrd Performs an orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form |
| f08hnf (zhbev)
Example Text Example Data |
21 | zhbev nagf_lapackeig_zhbev Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix |
| f08hpf (zhbevx)
Example Text Example Data |
21 | zhbevx nagf_lapackeig_zhbevx Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix |
| f08hqf (zhbevd)
Example Text Example Data |
19 | zhbevd nagf_lapackeig_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_lapackeig_zhbtrd Performs a unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form |
| f08jaf (dstev)
Example Text Example Data |
21 | dstev nagf_lapackeig_dstev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix |
| f08jbf (dstevx)
Example Text Example Data |
21 | dstevx nagf_lapackeig_dstevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix |
| f08jcf (dstevd)
Example Text Example Data |
19 | dstevd nagf_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_dstebz Computes selected eigenvalues of real symmetric tridiagonal matrix by bisection |
| f08jkf (dstein) | 16 | dstein nagf_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_dgebrd Performs an orthogonal reduction of real general rectangular matrix to bidiagonal form |
| f08kff (dorgbr)
Example Text Example Data |
16 | dorgbr nagf_lapackeig_dorgbr Generates an orthogonal transformation matrices from reduction to bidiagonal form determined by f08kef (dgebrd) |
| f08kgf (dormbr)
Example Text Example Data |
16 | dormbr nagf_lapackeig_dormbr Applies the orthogonal transformations from reduction to bidiagonal form determined by f08kef (dgebrd) |
| f08khf (dgejsv)
Example Text Example Data |
23 | dgejsv nagf_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_zgebrd Performs a unitary reduction of complex general rectangular matrix to bidiagonal form |
| f08ktf (zungbr)
Example Text Example Data |
16 | zungbr nagf_lapackeig_zungbr Generates unitary transformation matrices from the reduction to bidiagonal form determined by f08ksf (zgebrd) |
| f08kuf (zunmbr)
Example Text Example Data |
16 | zunmbr nagf_lapackeig_zunmbr Applies the unitary transformations from reduction to bidiagonal form determined by f08ksf (zgebrd) |
| f08lef (dgbbrd)
Example Text Example Data |
19 | dgbbrd nagf_lapackeig_dgbbrd Performs a reduction of real rectangular band matrix to upper bidiagonal form |
| f08lsf (zgbbrd)
Example Text Example Data |
19 | zgbbrd nagf_lapackeig_zgbbrd Reduction of complex rectangular band matrix to upper bidiagonal form |
| f08mdf (dbdsdc)
Example Text Example Data |
22 | dbdsdc nagf_lapackeig_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_lapackeig_dbdsqr Performs an SVD of real bidiagonal matrix reduced from real general matrix |
| f08msf (zbdsqr) | 16 | zbdsqr nagf_lapackeig_zbdsqr Performs an SVD of real bidiagonal matrix reduced from complex general matrix |
| f08naf (dgeev)
Example Text Example Data |
21 | dgeev nagf_lapackeig_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_lapackeig_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_lapackeig_dgehrd Performs an orthogonal reduction of real general matrix to upper Hessenberg form |
| f08nff (dorghr)
Example Text Example Data |
16 | dorghr nagf_lapackeig_dorghr Generates an orthogonal transformation matrix from reduction to Hessenberg form determined by f08nef (dgehrd) |
| f08ngf (dormhr)
Example Text Example Data |
16 | dormhr nagf_lapackeig_dormhr Applies the orthogonal transformation matrix from reduction to Hessenberg form determined by f08nef (dgehrd) |
| f08nhf (dgebal)
Example Text Example Data |
16 | dgebal nagf_lapackeig_dgebal Balances a real general matrix |
| f08njf (dgebak) | 16 | dgebak nagf_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_zgehrd Performs a unitary reduction of complex general matrix to upper Hessenberg form |
| f08ntf (zunghr)
Example Text Example Data |
16 | zunghr nagf_lapackeig_zunghr Generates a unitary transformation matrix from reduction to Hessenberg form determined by f08nsf (zgehrd) |
| f08nuf (zunmhr)
Example Text Example Data |
16 | zunmhr nagf_lapackeig_zunmhr Applies the unitary transformation matrix from reduction to Hessenberg form determined by f08nsf (zgehrd) |
| f08nvf (zgebal)
Example Text Example Data |
16 | zgebal nagf_lapackeig_zgebal Balances a complex general matrix |
| f08nwf (zgebak) | 16 | zgebak nagf_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_dhseqr Computes the eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix |
| f08pkf (dhsein) | 16 | dhsein nagf_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_zhseqr Computes the eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix |
| f08pxf (zhsein) | 16 | zhsein nagf_lapackeig_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_lapackeig_dtrexc Reorders a Schur factorization of real matrix using orthogonal similarity transformation |
| f08qgf (dtrsen)
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16 | dtrsen nagf_lapackeig_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_lapackeig_dtrsyl Solves the real Sylvester matrix equation , and are upper quasi-triangular or transposes |
| f08qkf (dtrevc) | 16 | dtrevc nagf_lapackeig_dtrevc Computes left and right eigenvectors of real upper quasi-triangular matrix |
| f08qlf (dtrsna)
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16 | dtrsna nagf_lapackeig_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_lapackeig_ztrexc Reorders a Schur factorization of complex matrix using unitary similarity transformation |
| f08quf (ztrsen)
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16 | ztrsen nagf_lapackeig_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_lapackeig_ztrsyl Solves the complex Sylvester matrix equation , and are upper triangular or conjugate-transposes |
| f08qxf (ztrevc) | 16 | ztrevc nagf_lapackeig_ztrevc Computes left and right eigenvectors of complex upper triangular matrix |
| f08qyf (ztrsna)
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16 | ztrsna nagf_lapackeig_ztrsna Computes estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix |
| f08raf (dorcsd)
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25 | dorcsd nagf_lapackeig_dorcsd Computes the CS decomposition of an orthogonal matrix partitioned into four real submatrices |
| f08rnf (zuncsd)
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25 | zuncsd nagf_lapackeig_zuncsd Computes the CS decomposition of a unitary matrix partitioned into four complex submatrices |
| f08saf (dsygv)
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21 | dsygv nagf_lapackeig_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_lapackeig_dsygvx Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem |
| f08scf (dsygvd)
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21 | dsygvd nagf_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_zhegvx Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem |
| f08sqf (zhegvd)
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21 | zhegvd nagf_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_zhpgst Performs a reduction to standard form of complex Hermitian-definite generalized eigenproblem , or , packed storage, factorized by f07grf (zpptrf) |
| f08uaf (dsbgv)
Example Text Example Data |
21 | dsbgv nagf_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_dpbstf Computes a split Cholesky factorization of real symmetric positive definite band matrix |
| f08unf (zhbgv)
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21 | zhbgv nagf_lapackeig_zhbgv Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem |
| f08upf (zhbgvx)
Example Text Example Data |
21 | zhbgvx nagf_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_zpbstf Computes a split Cholesky factorization of complex Hermitian positive definite band matrix |
| f08vaf (dggsvd)
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21 | dggsvd nagf_lapackeig_dggsvd Computes the generalized singular value decomposition of a real matrix pair |
| f08vcf (dggsvd3)
Example Text Example Data |
26.0 | dggsvd3 nagf_lapackeig_dggsvd3 Computes, using BLAS-3, the generalized singular value decomposition of a real matrix pair |
| f08vef (dggsvp)
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22 | dggsvp nagf_lapackeig_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_lapackeig_dggsvp3 Produces orthogonal matrices, using BLAS-3, that simultaneously reduce the by matrix and the by matrix to upper triangular form |
| f08vnf (zggsvd)
Example Text Example Data |
21 | zggsvd nagf_lapackeig_zggsvd Computes the generalized singular value decomposition of a complex matrix pair |
| f08vqf (zggsvd3)
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26.0 | zggsvd3 nagf_lapackeig_zggsvd3 Computes, using BLAS-3, the generalized singular value decomposition of a complex matrix pair |
| f08vsf (zggsvp)
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22 | zggsvp nagf_lapackeig_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_lapackeig_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_lapackeig_dggev Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors |
| f08wbf (dggevx)
Example Text Example Data |
21 | dggevx nagf_lapackeig_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)
Example Text Example Data |
26.0 | dggev3 nagf_lapackeig_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_lapackeig_dgghrd Performs an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form |
| f08wff (dgghd3) | 26.0 | dgghd3 nagf_lapackeig_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_lapackeig_dggbal Balances a pair of real, square, matrices |
| f08wjf (dggbak) | 20 | dggbak nagf_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_zgghrd Performs a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form |
| f08wtf (zgghd3) | 26.0 | zgghd3 nagf_lapackeig_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_lapackeig_zggbal Balances a pair of complex, square, matrices |
| f08wwf (zggbak) | 20 | zggbak nagf_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_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)
Example Text Example Data |
20 | dhgeqz nagf_lapackeig_dhgeqz Computes eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices |
| f08xnf (zgges)
Example Text Example Data |
21 | zgges nagf_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_zhgeqz Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex, square, matrices |
| f08yef (dtgsja)
Example Text Example Data |
22 | dtgsja nagf_lapackeig_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_lapackeig_dtgexc Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation |
| f08ygf (dtgsen)
Example Text Example Data |
22 | dtgsen nagf_lapackeig_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_lapackeig_dtgsyl Solves the real-valued, generalized, quasi-trangular, Sylvester equation |
| f08ykf (dtgevc)
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20 | dtgevc nagf_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_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_lapackeig_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)
Example Text Example Data |
22 | ztgsyl nagf_lapackeig_ztgsyl Solves the complex generalized Sylvester equation |
| f08yxf (ztgevc)
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20 | ztgevc nagf_lapackeig_ztgevc Computes left and right eigenvectors of a pair of complex upper triangular matrices |
| f08yyf (ztgsna)
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22 | ztgsna nagf_lapackeig_ztgsna Estimates reciprocal condition numbers for specified eigenvalues and/or eigenvectors of a complex matrix pair in generalized Schur canonical form |
| f08zaf (dgglse)
Example Text Example Data |
21 | dgglse nagf_lapackeig_dgglse Solves the real linear equality-constrained least squares (LSE) problem |
| f08zbf (dggglm)
Example Text Example Data |
21 | dggglm nagf_lapackeig_dggglm Solves a real general Gauss–Markov linear model (GLM) problem |
| f08zef (dggqrf)
Example Text Example Data |
22 | dggqrf nagf_lapackeig_dggqrf Computes a generalized factorization of a real matrix pair |
| f08zff (dggrqf)
Example Text Example Data |
22 | dggrqf nagf_lapackeig_dggrqf Computes a generalized factorization of a real matrix pair |
| f08znf (zgglse)
Example Text Example Data |
21 | zgglse nagf_lapackeig_zgglse Solves the complex linear equality-constrained least squares (LSE) problem |
| f08zpf (zggglm)
Example Text Example Data |
21 | zggglm nagf_lapackeig_zggglm Solves a complex general Gauss–Markov linear model (GLM) problem |
| f08zsf (zggqrf)
Example Text Example Data |
22 | zggqrf nagf_lapackeig_zggqrf Computes a generalized factorization of a complex matrix pair |
| f08ztf (zggrqf)
Example Text Example Data |
22 | zggrqf nagf_lapackeig_zggrqf Computes a generalized factorization of a complex matrix pair |