| Routine Name |
Mark of Introduction |
Purpose |
| F08AAF
Example Text Example Data |
21 | DGELS Solves an overdetermined or underdetermined real linear system |
| F08AEF
Example Text Example Data |
16 | DGEQRF |
| F08AFF
Example Text Example Data |
16 | DORGQR Form all or part of orthogonal |
| F08AGF | 16 | DORMQR Apply orthogonal transformation determined by F08AEF (DGEQRF) or F08BEF (DGEQPF) |
| F08AHF
Example Text Example Data |
16 | DGELQF |
| F08AJF
Example Text Example Data |
16 | DORGLQ Form all or part of orthogonal |
| F08AKF | 16 | DORMLQ Apply orthogonal transformation determined by F08AHF (DGELQF) |
| F08ANF
Example Text Example Data |
21 | ZGELS Solves an overdetermined or underdetermined complex linear system |
| F08ASF
Example Text Example Data |
16 | ZGEQRF |
| F08ATF
Example Text Example Data |
16 | ZUNGQR Form all or part of unitary |
| F08AUF | 16 | ZUNMQR Apply unitary transformation determined by F08ASF (ZGEQRF) or F08BSF (ZGEQPF) |
| F08AVF
Example Text Example Data |
16 | ZGELQF |
| F08AWF
Example Text Example Data |
16 | ZUNGLQ Form all or part of unitary |
| F08AXF | 16 | ZUNMLQ Apply unitary transformation determined by F08AVF (ZGELQF) |
| F08BAF
Example Text Example Data |
21 | DGELSY Computes the minimum-norm solution to a real linear least-squares problem |
| F08BEF
Example Text Example Data |
16 | DGEQPF |
| F08BFF
Example Text Example Data |
21 | DGEQP3 |
| F08BHF
Example Text Example Data |
21 | DTZRZF Reduces a real upper trapezoidal matrix to upper triangular form |
| F08BKF | 21 | DORMRZ Apply orthogonal transformation determined by F08BHF (DTZRZF) |
| F08BNF
Example Text Example Data |
21 | ZGELSY Computes the minimum-norm solution to a complex linear least-squares problem |
| F08BSF
Example Text Example Data |
16 | ZGEQPF |
| F08BTF
Example Text Example Data |
21 | ZGEQP3 |
| F08BVF
Example Text Example Data |
21 | ZTZRZF Reduces a complex upper trapezoidal matrix to upper triangular form |
| F08BXF | 21 | ZUNMRZ Apply unitary transformation determined by F08BVF (ZTZRZF) |
| F08CEF
Example Text Example Data |
21 | DGEQLF |
| F08CFF
Example Text Example Data |
21 | DORGQL Form all or part of orthogonal |
| F08CGF | 21 | DORMQL Apply orthogonal transformation determined by F08CEF (DGEQLF) |
| F08CHF
Example Text Example Data |
21 | DGERQF |
| F08CJF
Example Text Example Data |
21 | DORGRQ Form all or part of orthogonal |
| F08CKF | 21 | DORMRQ Apply orthogonal transformation determined by F08CHF (DGERQF) |
| F08CSF
Example Text Example Data |
21 | ZGEQLF |
| F08CTF
Example Text Example Data |
21 | ZUNGQL Form all or part of orthogonal |
| F08CUF | 21 | ZUNMQL Apply unitary transformation determined by F08CSF (ZGEQLF) |
| F08CVF
Example Text Example Data |
21 | ZGERQF |
| F08CWF
Example Text Example Data |
21 | ZUNGRQ Form all or part of orthogonal |
| F08CXF | 21 | ZUNMRQ Apply unitary transformation determined by F08CVF (ZGERQF) |
| F08FAF
Example Text Example Data |
21 | DSYEV Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix |
| F08FBF
Example Text Example Data |
21 | DSYEVX Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix |
| F08FCF
Example Text Example Data |
19 | DSYEVD Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer) |
| F08FDF
Example Text Example Data |
21 | DSYEVR Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations) |
| F08FEF
Example Text Example Data |
16 | DSYTRD Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form |
| F08FFF
Example Text Example Data |
16 | DORGTR Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08FEF (DSYTRD) |
| F08FGF
Example Text Example Data |
16 | DORMTR Apply orthogonal transformation determined by F08FEF (DSYTRD) |
| F08FLF | 21 | 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 Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix |
| F08FPF
Example Text Example Data |
21 | ZHEEVX Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix |
| F08FQF
Example Text Example Data |
19 | ZHEEVD Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix (divide-and-conquer) |
| F08FRF
Example Text Example Data |
21 | ZHEEVR Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations) |
| F08FSF
Example Text Example Data |
16 | ZHETRD Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form |
| F08FTF
Example Text Example Data |
16 | ZUNGTR Generate unitary transformation matrix from reduction to tridiagonal form determined by F08FSF (ZHETRD) |
| F08FUF
Example Text Example Data |
16 | ZUNMTR Apply unitary transformation matrix determined by F08FSF (ZHETRD) |
| F08GAF
Example Text Example Data |
21 | DSPEV Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage |
| F08GBF
Example Text Example Data |
21 | DSPEVX Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage |
| F08GCF
Example Text Example Data |
19 | DSPEVD Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix, packed storage (divide-and-conquer) |
| F08GEF
Example Text Example Data |
16 | DSPTRD Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage |
| F08GFF
Example Text Example Data |
16 | DOPGTR Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08GEF (DSPTRD) |
| F08GGF
Example Text Example Data |
16 | DOPMTR Apply orthogonal transformation determined by F08GEF (DSPTRD) |
| F08GNF
Example Text Example Data |
21 | ZHPEV Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage |
| F08GPF
Example Text Example Data |
21 | ZHPEVX Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage |
| F08GQF
Example Text Example Data |
19 | ZHPEVD Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian matrix, packed storage (divide-and-conquer) |
| F08GSF
Example Text Example Data |
16 | ZHPTRD Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage |
| F08GTF
Example Text Example Data |
16 | ZUPGTR Generate unitary transformation matrix from reduction to tridiagonal form determined by F08GSF (ZHPTRD) |
| F08GUF
Example Text Example Data |
16 | ZUPMTR Apply unitary transformation matrix determined by F08GSF (ZHPTRD) |
| F08HAF
Example Text Example Data |
21 | DSBEV Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix |
| F08HBF
Example Text Example Data |
21 | DSBEVX Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix |
| F08HCF
Example Text Example Data |
19 | DSBEVD Computes all eigenvalues and, optionally, all eigenvectors of real symmetric band matrix (divide-and-conquer) |
| F08HEF
Example Text Example Data |
16 | DSBTRD Orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form |
| F08HNF
Example Text Example Data |
21 | ZHBEV Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix |
| F08HPF
Example Text Example Data |
21 | ZHBEVX Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix |
| F08HQF
Example Text Example Data |
19 | ZHBEVD Computes all eigenvalues and, optionally, all eigenvectors of complex Hermitian band matrix (divide-and-conquer) |
| F08HSF
Example Text Example Data |
16 | ZHBTRD Unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form |
| F08JAF
Example Text Example Data |
21 | DSTEV Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix |
| F08JBF
Example Text Example Data |
21 | DSTEVX Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix |
| F08JCF
Example Text Example Data |
19 | DSTEVD Computes all eigenvalues and, optionally, all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer) |
| F08JDF
Example Text Example Data |
21 | DSTEVR Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations) |
| F08JEF
Example Text Example Data |
16 | DSTEQR All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using the implicit |
| F08JFF
Example Text Example Data |
16 | DSTERF All eigenvalues of real symmetric tridiagonal matrix, root-free variant of the |
| F08JGF
Example Text Example Data |
16 | DPTEQR Computes all eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from real symmetric positive-definite matrix |
| F08JHF
Example Text Example Data |
21 | DSTEDC 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 Selected eigenvalues of real symmetric tridiagonal matrix by bisection |
| F08JKF | 16 | DSTEIN Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array |
| F08JLF
Example Text Example Data |
21 | DSTEGR Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a symmetric matrix reduced to this form (Relatively Robust Representations) |
| F08JSF | 16 | ZSTEQR All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using the implicit |
| F08JUF
Example Text Example Data |
16 | ZPTEQR Computes all eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from complex Hermitian positive-definite matrix |
| F08JVF
Example Text Example Data |
21 | ZSTEDC 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 Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array |
| F08JYF
Example Text Example Data |
21 | ZSTEGR Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (Relatively Robust Representations) |
| F08KAF
Example Text Example Data |
21 | DGELSS Computes the minimum-norm solution to a real linear least-squares problem using singular value decomposition |
| F08KBF
Example Text Example Data |
21 | 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 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 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 Orthogonal reduction of real general rectangular matrix to bidiagonal form |
| F08KFF
Example Text Example Data |
16 | DORGBR Generate orthogonal transformation matrices from reduction to bidiagonal form determined by F08KEF (DGEBRD) |
| F08KGF
Example Text Example Data |
16 | DORMBR Apply orthogonal transformations from reduction to bidiagonal form determined by F08KEF (DGEBRD) |
| F08KNF
Example Text Example Data |
21 | ZGELSS Computes the minimum-norm solution to a complex linear least-squares problem using singular value decomposition |
| F08KPF
Example Text Example Data |
21 | 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 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 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 Unitary reduction of complex general rectangular matrix to bidiagonal form |
| F08KTF
Example Text Example Data |
16 | ZUNGBR Generate unitary transformation matrices from reduction to bidiagonal form determined by F08KSF (ZGEBRD) |
| F08KUF
Example Text Example Data |
16 | ZUNMBR Apply unitary transformations from reduction to bidiagonal form determined by F08KSF (ZGEBRD) |
| F08LEF
Example Text Example Data |
19 | DGBBRD Reduction of real rectangular band matrix to upper bidiagonal form |
| F08LSF
Example Text Example Data |
19 | ZGBBRD Reduction of complex rectangular band matrix to upper bidiagonal form |
| F08MDF
Example Text Example Data |
21 | 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 SVD of real bidiagonal matrix reduced from real general matrix |
| F08MSF | 16 | ZBDSQR SVD of real bidiagonal matrix reduced from complex general matrix |
| F08NAF
Example Text Example Data |
21 | DGEEV Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix |
| F08NBF
Example Text Example Data |
21 | 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 Orthogonal reduction of real general matrix to upper Hessenberg form |
| F08NFF
Example Text Example Data |
16 | DORGHR Generate orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (DGEHRD) |
| F08NGF
Example Text Example Data |
16 | DORMHR Apply orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (DGEHRD) |
| F08NHF
Example Text Example Data |
16 | DGEBAL Balance real general matrix |
| F08NJF | 16 | DGEBAK Transform eigenvectors of real balanced matrix to those of original matrix supplied to F08NHF (DGEBAL) |
| F08NNF
Example Text Example Data |
21 | ZGEEV Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix |
| F08NPF
Example Text Example Data |
21 | 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 Unitary reduction of complex general matrix to upper Hessenberg form |
| F08NTF
Example Text Example Data |
16 | ZUNGHR Generate unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (ZGEHRD) |
| F08NUF
Example Text Example Data |
16 | ZUNMHR Apply unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (ZGEHRD) |
| F08NVF
Example Text Example Data |
16 | ZGEBAL Balance complex general matrix |
| F08NWF | 16 | ZGEBAK Transform eigenvectors of complex balanced matrix to those of original matrix supplied to F08NVF (ZGEBAL) |
| F08PAF
Example Text Example Data |
21 | 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 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 Computes the eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix |
| F08PKF | 16 | DHSEIN Selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration |
| F08PNF
Example Text Example Data |
21 | 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 Computes for real square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues |
| F08PSF
Example Text Example Data |
16 | ZHSEQR Computes the eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix |
| F08PXF | 16 | ZHSEIN Selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration |
| F08QFF
Example Text Example Data |
16 | DTREXC Reorder Schur factorization of real matrix using orthogonal similarity transformation |
| F08QGF
Example Text Example Data |
16 | DTRSEN Reorder Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities |
| F08QHF
Example Text Example Data |
16 | DTRSYL Solve real Sylvester matrix equation |
| F08QKF | 16 | DTREVC Left and right eigenvectors of real upper quasi-triangular matrix |
| F08QLF
Example Text Example Data |
16 | DTRSNA Estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix |
| F08QTF
Example Text Example Data |
16 | ZTREXC Reorder Schur factorization of complex matrix using unitary similarity transformation |
| F08QUF
Example Text Example Data |
16 | ZTRSEN Reorder Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities |
| F08QVF
Example Text Example Data |
16 | ZTRSYL Solve complex Sylvester matrix equation |
| F08QXF | 16 | ZTREVC Left and right eigenvectors of complex upper triangular matrix |
| F08QYF
Example Text Example Data |
16 | ZTRSNA Estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix |
| F08SAF
Example Text Example Data |
21 | DSYGV Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem |
| F08SBF
Example Text Example Data |
21 | DSYGVX Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem |
| F08SCF
Example Text Example Data |
21 | 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 Reduction to standard form of real symmetric-definite generalized eigenproblem |
| F08SNF
Example Text Example Data |
21 | ZHEGV Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem |
| F08SPF
Example Text Example Data |
21 | ZHEGVX Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem |
| F08SQF
Example Text Example Data |
21 | 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 Reduction to standard form of complex Hermitian-definite generalized eigenproblem |
| F08TAF
Example Text Example Data |
21 | 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 Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage |
| F08TCF
Example Text Example Data |
21 | 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 Reduction to standard form of real symmetric-definite generalized eigenproblem |
| F08TNF
Example Text Example Data |
21 | 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 Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage |
| F08TQF
Example Text Example Data |
21 | 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 Reduction to standard form of complex Hermitian-definite generalized eigenproblem |
| F08UAF
Example Text Example Data |
21 | DSBGV Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem |
| F08UBF
Example Text Example Data |
21 | DSBGVX Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem |
| F08UCF
Example Text Example Data |
21 | 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 Reduction of real symmetric-definite banded generalized eigenproblem |
| F08UFF | 19 | DPBSTF Computes a split Cholesky factorization of real symmetric positive-definite band matrix |
| F08UNF
Example Text Example Data |
21 | ZHBGV Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem |
| F08UPF
Example Text Example Data |
21 | ZHBGVX Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem |
| F08UQF
Example Text Example Data |
21 | 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 Reduction of complex Hermitian-definite banded generalized eigenproblem |
| F08UTF | 19 | ZPBSTF Computes a split Cholesky factorization of complex Hermitian positive-definite band matrix |
| F08VAF
Example Text Example Data |
21 | DGGSVD Computes the generalized singular value decomposition of a real matrix pair |
| F08VEF
Example Text Example Data |
21 | DGGSVP Computes orthogonal matrices as processing steps for computing the generalized singular value decomposition of a real matrix pair |
| F08VNF
Example Text Example Data |
21 | ZGGSVD Computes the generalized singular value decomposition of a complex matrix pair |
| F08VSF
Example Text Example Data |
21 | ZGGSVP Computes orthogonal matrices as processing steps for computing the generalized singular value decomposition of a complex matrix pair |
| F08WAF
Example Text Example Data |
21 | 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 Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors |
| F08WEF | 20 | DGGHRD Orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form |
| F08WHF | 20 | DGGBAL Balance a pair of real general matrices |
| F08WJF | 20 | DGGBAK Transform eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to F08WHF (DGGBAL) |
| F08WNF
Example Text Example Data |
21 | 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 Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors; also, optionally, the balancing transformation, the reciprocal condition numbers for the eigenvalues and for the right eigenvectors |
| F08WSF | 20 | ZGGHRD Unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form |
| F08WVF | 20 | ZGGBAL Balance a pair of complex general matrices |
| F08WWF | 20 | ZGGBAK Transform eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to F08WVF (ZGGBAL) |
| F08XAF
Example Text Example Data |
21 | 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 Computes, for a real nonsymmetric matrix pair, the generalized eigenvalues, the generalized real Schur form and, optionally, the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues |
| F08XEF
Example Text Example Data |
20 | DHGEQZ 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 | 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 Computes, for a complex nonsymmetric matrix pair, the generalized eigenvalues, the generalized complex Schur form and, optionally, the left and/or right matrices of Schur vectors; also, optionally, computes reciprocal condition numbers for selected eigenvalues |
| F08XSF
Example Text Example Data |
20 | ZHGEQZ Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex general matrices |
| F08YEF
Example Text Example Data |
21 | DTGSJA Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair |
| F08YFF
Example Text Example Data |
21 | DTGEXC Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation |
| F08YGF
Example Text Example Data |
21 | 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 |
21 | DTGSYL Solves the real-valued generalized Sylvester equation |
| F08YKF
Example Text Example Data |
20 | DTGEVC Left and right eigenvectors of a pair of real upper quasi-triangular matrices |
| F08YLF
Example Text Example Data |
21 | 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 |
21 | ZTGSJA Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair |
| F08YTF
Example Text Example Data |
21 | ZTGEXC Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation |
| F08YUF
Example Text Example Data |
21 | 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 |
21 | ZTGSYL Solves the complex generalized Sylvester equation |
| F08YXF
Example Text Example Data |
20 | ZTGEVC Left and right eigenvectors of a pair of complex upper triangular matrices |
| F08YYF
Example Text Example Data |
21 | 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 Solves the real linear equality-constrained least-squares (LSE) problem |
| F08ZBF
Example Text Example Data |
21 | DGGGLM Solves a real general Gauss–Markov linear model (GLM) problem |
| F08ZEF
Example Text Example Data |
21 | DGGQRF Computes a generalized |
| F08ZFF
Example Text Example Data |
21 | DGGRQF Computes a generalized |
| F08ZNF
Example Text Example Data |
21 | ZGGLSE Solves the complex linear equality-constrained least-squares (LSE) problem |
| F08ZPF
Example Text Example Data |
21 | ZGGGLM Solves a complex general Gauss–Markov linear model (GLM) problem |
| F08ZSF
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21 | ZGGQRF Computes a generalized |
| F08ZTF
Example Text Example Data |
21 | ZGGRQF Computes a generalized |