Routine |
Mark of Introduction |
Purpose |
|---|---|---|
| f08aaf
Example Text Example Data |
21 | dgels nagf_lapackeig_dgels Solves a real linear least squares problem of full rank |
| f08abf
Example Text Example Data |
25 | dgeqrt nagf_lapackeig_dgeqrt Performs a factorization of real general rectangular matrix, with explicit blocking |
| f08acf | 25 | dgemqrt nagf_lapackeig_dgemqrt Applies the orthogonal transformation determined by f08abf |
| f08aef
Example Text Example Data |
16 | dgeqrf nagf_lapackeig_dgeqrf Performs a factorization of real general rectangular matrix |
| f08aff
Example Text Example Data |
16 | dorgqr nagf_lapackeig_dorgqr Forms all or part of orthogonal from factorization determined by f08aef, f08bef or f08bff |
| f08agf | 16 | dormqr nagf_lapackeig_dormqr Applies an orthogonal transformation determined by f08aef, f08bef or f08bff |
| f08ahf
Example Text Example Data |
16 | dgelqf nagf_lapackeig_dgelqf Performs a factorization of real general rectangular matrix |
| f08ajf
Example Text Example Data |
16 | dorglq nagf_lapackeig_dorglq Forms all or part of orthogonal from factorization determined by f08ahf |
| f08akf | 16 | dormlq nagf_lapackeig_dormlq Applies the orthogonal transformation determined by f08ahf |
| f08anf
Example Text Example Data |
21 | zgels nagf_lapackeig_zgels Solves a complex linear least problem of full rank |
| f08apf
Example Text Example Data |
25 | zgeqrt nagf_lapackeig_zgeqrt Performs a factorization of complex general rectangular matrix using recursive algorithm |
| f08aqf | 25 | zgemqrt nagf_lapackeig_zgemqrt Applies the unitary transformation determined by f08apf |
| f08asf
Example Text Example Data |
16 | zgeqrf nagf_lapackeig_zgeqrf Performs a factorization of complex general rectangular matrix |
| f08atf
Example Text Example Data |
16 | zungqr nagf_lapackeig_zungqr Forms all or part of unitary from factorization determined by f08asf, f08bsf or f08btf |
| f08auf | 16 | zunmqr nagf_lapackeig_zunmqr Applies a unitary transformation determined by f08asf, f08bsf or f08btf |
| f08avf
Example Text Example Data |
16 | zgelqf nagf_lapackeig_zgelqf Performs a factorization of complex general rectangular matrix |
| f08awf
Example Text Example Data |
16 | zunglq nagf_lapackeig_zunglq Forms all or part of unitary from factorization determined by f08avf |
| f08axf | 16 | zunmlq nagf_lapackeig_zunmlq Applies the unitary transformation determined by f08avf |
| f08baf
Example Text Example Data |
21 | dgelsy nagf_lapackeig_dgelsy Computes the minimum-norm solution to a real linear least squares problem |
| f08bbf
Example Text Example Data |
25 | dtpqrt nagf_lapackeig_dtpqrt factorization of real general triangular-pentagonal matrix |
| f08bcf | 25 | dtpmqrt nagf_lapackeig_dtpmqrt Applies the orthogonal transformation determined by f08bbf |
| f08bef
Example Text Example Data |
16 (Deprecated) | dgeqpf nagf_lapackeig_dgeqpf factorization, with column pivoting, of real general rectangular matrix |
| f08bff
Example Text Example Data |
22 | dgeqp3 nagf_lapackeig_dgeqp3 factorization, with column pivoting, using BLAS-3, of real general rectangular matrix |
| f08bhf
Example Text Example Data |
22 | dtzrzf nagf_lapackeig_dtzrzf Reduces a real upper trapezoidal matrix to upper triangular form |
| f08bkf | 22 | dormrz nagf_lapackeig_dormrz Applies the orthogonal transformation determined by f08bhf |
| f08bnf
Example Text Example Data |
21 | zgelsy nagf_lapackeig_zgelsy Computes the minimum-norm solution to a complex linear least squares problem |
| f08bpf
Example Text Example Data |
25 | ztpqrt nagf_lapackeig_ztpqrt factorization of complex triangular-pentagonal matrix |
| f08bqf | 25 | ztpmqrt nagf_lapackeig_ztpmqrt Applies the unitary transformation determined by f08bpf |
| f08bsf
Example Text Example Data |
16 (Deprecated) | zgeqpf nagf_lapackeig_zgeqpf factorization, with column pivoting, of complex general rectangular matrix |
| f08btf
Example Text Example Data |
22 | zgeqp3 nagf_lapackeig_zgeqp3 factorization, with column pivoting, using BLAS-3, of complex general rectangular matrix |
| f08bvf
Example Text Example Data |
22 | ztzrzf nagf_lapackeig_ztzrzf Reduces a complex upper trapezoidal matrix to upper triangular form |
| f08bxf | 22 | zunmrz nagf_lapackeig_zunmrz Applies the unitary transformation determined by f08bvf |
| f08cef
Example Text Example Data |
22 | dgeqlf nagf_lapackeig_dgeqlf factorization of real general rectangular matrix |
| f08cff
Example Text Example Data |
22 | dorgql nagf_lapackeig_dorgql Form all or part of orthogonal from factorization determined by f08cef |
| f08cgf | 22 | dormql nagf_lapackeig_dormql Applies the orthogonal transformation determined by f08cef |
| f08chf
Example Text Example Data |
22 | dgerqf nagf_lapackeig_dgerqf factorization of real general rectangular matrix |
| f08cjf
Example Text Example Data |
22 | dorgrq nagf_lapackeig_dorgrq Form all or part of orthogonal from factorization determined by f08chf |
| f08ckf | 22 | dormrq nagf_lapackeig_dormrq Applies the orthogonal transformation determined by f08chf |
| f08csf
Example Text Example Data |
22 | zgeqlf nagf_lapackeig_zgeqlf factorization of complex general rectangular matrix |
| f08ctf
Example Text Example Data |
22 | zungql nagf_lapackeig_zungql Form all or part of unitary from factorization determined by f08csf |
| f08cuf | 22 | zunmql nagf_lapackeig_zunmql Applies the unitary transformation determined by f08csf |
| f08cvf
Example Text Example Data |
22 | zgerqf nagf_lapackeig_zgerqf factorization of complex general rectangular matrix |
| f08cwf
Example Text Example Data |
22 | zungrq nagf_lapackeig_zungrq Form all or part of unitary from factorization determined by f08cvf |
| f08cxf | 22 | zunmrq nagf_lapackeig_zunmrq Applies the unitary transformation determined by f08cvf |
| f08faf
Example Text Example Data |
21 | dsyev nagf_lapackeig_dsyev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix |
| f08fbf
Example Text Example Data |
21 | dsyevx nagf_lapackeig_dsyevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix |
| f08fcf
Example Text Example Data |
19 | dsyevd nagf_lapackeig_dsyevd Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer) |
| f08fdf
Example Text Example Data |
21 | dsyevr nagf_lapackeig_dsyevr Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations) |
| f08fef
Example Text Example Data |
16 | dsytrd nagf_lapackeig_dsytrd Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form |
| f08fff
Example Text Example Data |
16 | dorgtr nagf_lapackeig_dorgtr Generate orthogonal transformation matrix from reduction to tridiagonal form determined by f08fef |
| f08fgf
Example Text Example Data |
16 | dormtr nagf_lapackeig_dormtr Applies the orthogonal transformation determined by f08fef |
| f08flf | 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
Example Text Example Data |
21 | zheev nagf_lapackeig_zheev Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix |
| f08fpf
Example Text Example Data |
21 | zheevx nagf_lapackeig_zheevx Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix |
| f08fqf
Example Text Example Data |
19 | zheevd nagf_lapackeig_zheevd Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix (divide-and-conquer) |
| f08frf
Example Text Example Data |
21 | zheevr nagf_lapackeig_zheevr Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations) |
| f08fsf
Example Text Example Data |
16 | zhetrd nagf_lapackeig_zhetrd Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form |
| f08ftf
Example Text Example Data |
16 | zungtr nagf_lapackeig_zungtr Generate unitary transformation matrix from reduction to tridiagonal form determined by f08fsf |
| f08fuf
Example Text Example Data |
16 | zunmtr nagf_lapackeig_zunmtr Applies the unitary transformation matrix determined by f08fsf |
| f08gaf
Example Text Example Data |
21 | dspev nagf_lapackeig_dspev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage |
| f08gbf
Example Text Example Data |
21 | dspevx nagf_lapackeig_dspevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage |
| f08gcf
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
Example Text Example Data |
16 | dsptrd nagf_lapackeig_dsptrd Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage |
| f08gff
Example Text Example Data |
16 | dopgtr nagf_lapackeig_dopgtr Generate orthogonal transformation matrix from reduction to tridiagonal form determined by f08gef |
| f08ggf
Example Text Example Data |
16 | dopmtr nagf_lapackeig_dopmtr Applies the orthogonal transformation determined by f08gef |
| f08gnf
Example Text Example Data |
21 | zhpev nagf_lapackeig_zhpev Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage |
| f08gpf
Example Text Example Data |
21 | zhpevx nagf_lapackeig_zhpevx Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage |
| f08gqf
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
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
Example Text Example Data |
16 | zupgtr nagf_lapackeig_zupgtr Generates a unitary transformation matrix from reduction to tridiagonal form determined by f08gsf |
| f08guf
Example Text Example Data |
16 | zupmtr nagf_lapackeig_zupmtr Applies the unitary transformation matrix determined by f08gsf |
| f08haf
Example Text Example Data |
21 | dsbev nagf_lapackeig_dsbev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix |
| f08hbf
Example Text Example Data |
21 | dsbevx nagf_lapackeig_dsbevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix |
| f08hcf
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
Example Text Example Data |
16 | dsbtrd nagf_lapackeig_dsbtrd Performs an orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form |
| f08hnf
Example Text Example Data |
21 | zhbev nagf_lapackeig_zhbev Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix |
| f08hpf
Example Text Example Data |
21 | zhbevx nagf_lapackeig_zhbevx Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix |
| f08hqf
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
Example Text Example Data |
16 | zhbtrd nagf_lapackeig_zhbtrd Performs a unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form |
| f08jaf
Example Text Example Data |
21 | dstev nagf_lapackeig_dstev Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix |
| f08jbf
Example Text Example Data |
21 | dstevx nagf_lapackeig_dstevx Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix |
| f08jcf
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
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
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
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
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
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 | 16 | dstebz nagf_lapackeig_dstebz Computes selected eigenvalues of real symmetric tridiagonal matrix by bisection |
| f08jkf | 16 | dstein nagf_lapackeig_dstein Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array |
| f08jlf
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 | 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
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
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 | 16 | zstein nagf_lapackeig_zstein Computes selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array |
| f08jyf
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
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
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
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
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
Example Text Example Data |
16 | dgebrd nagf_lapackeig_dgebrd Performs an orthogonal reduction of real general rectangular matrix to bidiagonal form |
| f08kff
Example Text Example Data |
16 | dorgbr nagf_lapackeig_dorgbr Generates an orthogonal transformation matrices from reduction to bidiagonal form determined by f08kef |
| f08kgf
Example Text Example Data |
16 | dormbr nagf_lapackeig_dormbr Applies the orthogonal transformations from reduction to bidiagonal form determined by f08kef |
| f08khf
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
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) |
| f08kmf
Example Text Example Data |
27 | dgesvdx nagf_lapackeig_dgesvdx Computes all or selected singular values of the singular value decomposition of a real general matrix, optionally computing the corresponding left and right singular vectors |
| f08knf
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
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
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
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
Example Text Example Data |
16 | zgebrd nagf_lapackeig_zgebrd Performs a unitary reduction of complex general rectangular matrix to bidiagonal form |
| f08ktf
Example Text Example Data |
16 | zungbr nagf_lapackeig_zungbr Generates unitary transformation matrices from the reduction to bidiagonal form determined by f08ksf |
| f08kuf
Example Text Example Data |
16 | zunmbr nagf_lapackeig_zunmbr Applies the unitary transformations from reduction to bidiagonal form determined by f08ksf |
| f08kvf
Example Text Example Data |
27 | zgejsv nagf_lapackeig_zgejsv Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (preconditioned Jacobi) |
| f08kwf
Example Text Example Data |
27 | zgesvj nagf_lapackeig_zgesvj Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors (fast Jacobi) |
| f08kzf
Example Text Example Data |
27 | zgesvdx nagf_lapackeig_zgesvdx Computes all or selected singular values of the singular value decomposition of a complex general matrix, optionally computing the corresponding left and right singular vectors |
| f08lef
Example Text Example Data |
19 | dgbbrd nagf_lapackeig_dgbbrd Performs a reduction of real rectangular band matrix to upper bidiagonal form |
| f08lsf
Example Text Example Data |
19 | zgbbrd nagf_lapackeig_zgbbrd Reduction of complex rectangular band matrix to upper bidiagonal form |
| f08mbf
Example Text Example Data |
27 | dbdsvdx nagf_lapackeig_dbdsvdx Computes all or selected singular values of the singular value decomposition of a real square bidiagonal matrix, optionally computing the corresponding left and right singular vectors |
| f08mdf
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
Example Text Example Data |
16 | dbdsqr nagf_lapackeig_dbdsqr Performs an SVD of real bidiagonal matrix reduced from real general matrix |
| f08msf | 16 | zbdsqr nagf_lapackeig_zbdsqr Performs an SVD of real bidiagonal matrix reduced from complex general matrix |
| f08naf
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
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
Example Text Example Data |
16 | dgehrd nagf_lapackeig_dgehrd Performs an orthogonal reduction of real general matrix to upper Hessenberg form |
| f08nff
Example Text Example Data |
16 | dorghr nagf_lapackeig_dorghr Generates an orthogonal transformation matrix from reduction to Hessenberg form determined by f08nef |
| f08ngf
Example Text Example Data |
16 | dormhr nagf_lapackeig_dormhr Applies the orthogonal transformation matrix from reduction to Hessenberg form determined by f08nef |
| f08nhf
Example Text Example Data |
16 | dgebal nagf_lapackeig_dgebal Balances a real general matrix |
| f08njf | 16 | dgebak nagf_lapackeig_dgebak Transforms eigenvectors of real balanced matrix to those of original matrix supplied to f08nhf |
| f08nnf
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
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
Example Text Example Data |
16 | zgehrd nagf_lapackeig_zgehrd Performs a unitary reduction of complex general matrix to upper Hessenberg form |
| f08ntf
Example Text Example Data |
16 | zunghr nagf_lapackeig_zunghr Generates a unitary transformation matrix from reduction to Hessenberg form determined by f08nsf |
| f08nuf
Example Text Example Data |
16 | zunmhr nagf_lapackeig_zunmhr Applies the unitary transformation matrix from reduction to Hessenberg form determined by f08nsf |
| f08nvf
Example Text Example Data |
16 | zgebal nagf_lapackeig_zgebal Balances a complex general matrix |
| f08nwf | 16 | zgebak nagf_lapackeig_zgebak Transforms eigenvectors of complex balanced matrix to those of original matrix supplied to f08nvf |
| f08paf
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
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
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 | 16 | dhsein nagf_lapackeig_dhsein Computes selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration |
| f08pnf
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
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
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 | 16 | zhsein nagf_lapackeig_zhsein Computes selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration |
| f08qff
Example Text Example Data |
16 | dtrexc nagf_lapackeig_dtrexc Reorders a Schur factorization of real matrix using orthogonal similarity transformation |
| f08qgf
Example Text Example Data |
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
Example Text Example Data |
16 | dtrsyl nagf_lapackeig_dtrsyl Solves the real Sylvester matrix equation , and are upper quasi-triangular or transposes |
| f08qkf | 16 | dtrevc nagf_lapackeig_dtrevc Computes left and right eigenvectors of real upper quasi-triangular matrix |
| f08qlf
Example Text Example Data |
16 | dtrsna nagf_lapackeig_dtrsna Computes estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix |
| f08qtf
Example Text Example Data |
16 | ztrexc nagf_lapackeig_ztrexc Reorders a Schur factorization of complex matrix using unitary similarity transformation |
| f08quf
Example Text Example Data |
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
Example Text Example Data |
16 | ztrsyl nagf_lapackeig_ztrsyl Solves the complex Sylvester matrix equation , and are upper triangular or conjugate-transposes |
| f08qxf | 16 | ztrevc nagf_lapackeig_ztrevc Computes left and right eigenvectors of complex upper triangular matrix |
| f08qyf
Example Text Example Data |
16 | ztrsna nagf_lapackeig_ztrsna Computes estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix |
| f08raf
Example Text Example Data |
25 | dorcsd nagf_lapackeig_dorcsd Computes the CS decomposition of an orthogonal matrix partitioned into four real submatrices |
| f08rnf
Example Text Example Data |
25 | zuncsd nagf_lapackeig_zuncsd Computes the CS decomposition of a unitary matrix partitioned into four complex submatrices |
| f08saf
Example Text Example Data |
21 | dsygv nagf_lapackeig_dsygv Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem |
| f08sbf
Example Text Example Data |
21 | dsygvx nagf_lapackeig_dsygvx Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem |
| f08scf
Example Text Example Data |
21 | dsygvd nagf_lapackeig_dsygvd Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer) |
| f08sef
Example Text Example Data |
16 | dsygst nagf_lapackeig_dsygst Performs a reduction to standard form of real symmetric-definite generalized eigenproblem , or , factorized by f07fdf |
| f08snf
Example Text Example Data |
21 | zhegv nagf_lapackeig_zhegv Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem |
| f08spf
Example Text Example Data |
21 | zhegvx nagf_lapackeig_zhegvx Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem |
| f08sqf
Example Text Example Data |
21 | zhegvd nagf_lapackeig_zhegvd Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer) |
| f08ssf
Example Text Example Data |
16 | zhegst nagf_lapackeig_zhegst Performs a reduction to standard form of complex Hermitian-definite generalized eigenproblem , or , factorized by f07frf |
| f08taf
Example Text Example Data |
21 | dspgv nagf_lapackeig_dspgv Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage |
| f08tbf
Example Text Example Data |
21 | dspgvx nagf_lapackeig_dspgvx Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage |
| f08tcf
Example Text Example Data |
21 | dspgvd nagf_lapackeig_dspgvd Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage (divide-and-conquer) |
| f08tef
Example Text Example Data |
16 | dspgst nagf_lapackeig_dspgst Performs a reduction to standard form of real symmetric-definite generalized eigenproblem , or , packed storage, factorized by f07gdf |
| f08tnf
Example Text Example Data |
21 | zhpgv nagf_lapackeig_zhpgv Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage |
| f08tpf
Example Text Example Data |
21 | zhpgvx nagf_lapackeig_zhpgvx Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage |
| f08tqf
Example Text Example Data |
21 | zhpgvd nagf_lapackeig_zhpgvd Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage (divide-and-conquer) |
| f08tsf
Example Text Example Data |
16 | zhpgst nagf_lapackeig_zhpgst Performs a reduction to standard form of complex Hermitian-definite generalized eigenproblem , or , packed storage, factorized by f07grf |
| f08uaf
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
Example Text Example Data |
21 | dsbgvx nagf_lapackeig_dsbgvx Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem |
| f08ucf
Example Text Example Data |
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
Example Text Example Data |
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 | 19 | dpbstf nagf_lapackeig_dpbstf Computes a split Cholesky factorization of real symmetric positive definite band matrix |
| f08unf
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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
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
Example Text Example Data |
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
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 | 19 | zpbstf nagf_lapackeig_zpbstf Computes a split Cholesky factorization of complex Hermitian positive definite band matrix |
| f08vaf
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21 (Deprecated) | dggsvd nagf_lapackeig_dggsvd Computes the generalized singular value decomposition of a real matrix pair |
| f08vcf
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26 | dggsvd3 nagf_lapackeig_dggsvd3 Computes, using BLAS-3, the generalized singular value decomposition of a real matrix pair |
| f08vef
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22 (Deprecated) | dggsvp nagf_lapackeig_dggsvp Produces orthogonal matrices that simultaneously reduce the by matrix and the by matrix to upper triangular form |
| f08vgf
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26 | 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
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21 (Deprecated) | zggsvd nagf_lapackeig_zggsvd Computes the generalized singular value decomposition of a complex matrix pair |
| f08vqf
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26 | zggsvd3 nagf_lapackeig_zggsvd3 Computes, using BLAS-3, the generalized singular value decomposition of a complex matrix pair |
| f08vsf
Example Text Example Data |
22 (Deprecated) | zggsvp nagf_lapackeig_zggsvp Produces unitary matrices that simultaneously reduce the complex, by , matrix and the complex, by , matrix to upper triangular form |
| f08vuf
Example Text Example Data |
26 | 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
Example Text Example Data |
21 (Deprecated) | dggev nagf_lapackeig_dggev Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors |
| f08wbf
Example Text Example Data |
21 | dggevx nagf_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
Example Text Example Data |
26 | 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 | 20 (Deprecated) | dgghrd nagf_lapackeig_dgghrd Performs an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form |
| f08wff | 26 | dgghd3 nagf_lapackeig_dgghd3 Performs, using BLAS-3, an orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form |
| f08whf | 20 | dggbal nagf_lapackeig_dggbal Balances a pair of real, square, matrices |
| f08wjf | 20 | dggbak nagf_lapackeig_dggbak Transforms eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to f08whf |
| f08wnf
Example Text Example Data |
21 (Deprecated) | zggev nagf_lapackeig_zggev Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors |
| f08wpf
Example Text Example Data |
21 | zggevx nagf_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
Example Text Example Data |
26 | 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 | 20 (Deprecated) | zgghrd nagf_lapackeig_zgghrd Performs a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form |
| f08wtf | 26 | zgghd3 nagf_lapackeig_zgghd3 Performs, using BLAS-3, a unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form |
| f08wvf | 20 | zggbal nagf_lapackeig_zggbal Balances a pair of complex, square, matrices |
| f08wwf | 20 | zggbak nagf_lapackeig_zggbak Transforms eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to f08wvf |
| f08xaf
Example Text Example Data |
21 (Deprecated) | 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
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
Example Text Example Data |
26 | 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
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
Example Text Example Data |
21 (Deprecated) | 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
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
Example Text Example Data |
26 | 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
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
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
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22 | dtgexc nagf_lapackeig_dtgexc Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation |
| f08ygf
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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
Example Text Example Data |
22 | dtgsyl nagf_lapackeig_dtgsyl Solves the real-valued, generalized, quasi-trangular, Sylvester equation |
| f08ykf
Example Text Example Data |
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
Example Text Example Data |
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
Example Text Example Data |
22 | ztgsja nagf_lapackeig_ztgsja Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair |
| f08ytf
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
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
Example Text Example Data |
22 | ztgsyl nagf_lapackeig_ztgsyl Solves the complex generalized Sylvester equation |
| f08yxf
Example Text Example Data |
20 | ztgevc nagf_lapackeig_ztgevc Computes left and right eigenvectors of a pair of complex upper triangular matrices |
| f08yyf
Example Text Example Data |
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
Example Text Example Data |
21 | dgglse nagf_lapackeig_dgglse Solves the real linear equality-constrained least squares (LSE) problem |
| f08zbf
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21 | dggglm nagf_lapackeig_dggglm Solves a real general Gauss–Markov linear model (GLM) problem |
| f08zef
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22 | dggqrf nagf_lapackeig_dggqrf Computes a generalized factorization of a real matrix pair |
| f08zff
Example Text Example Data |
22 | dggrqf nagf_lapackeig_dggrqf Computes a generalized factorization of a real matrix pair |
| f08znf
Example Text Example Data |
21 | zgglse nagf_lapackeig_zgglse Solves the complex linear equality-constrained least squares (LSE) problem |
| f08zpf
Example Text Example Data |
21 | zggglm nagf_lapackeig_zggglm Solves a complex general Gauss–Markov linear model (GLM) problem |
| f08zsf
Example Text Example Data |
22 | zggqrf nagf_lapackeig_zggqrf Computes a generalized factorization of a complex matrix pair |
| f08ztf
Example Text Example Data |
22 | zggrqf nagf_lapackeig_zggrqf Computes a generalized factorization of a complex matrix pair |