|
Routine Name |
Mark of Introduction |
Purpose |
| F08AEF (SGEQRF/DGEQRF) Example Text Example Data | 16 | QR factorization of real general rectangular matrix |
| F08AFF (SORGQR/DORGQR) Example Text Example Data | 16 | Form all or part of orthogonal Q from QR factorization determined by F08AEF (SGEQRF/DGEQRF) or F08BEF (SGEQPF/DGEQPF) |
| F08AGF (SORMQR/DORMQR) | 16 | Apply orthogonal transformation determined by F08AEF (SGEQRF/DGEQRF) or F08BEF (SGEQPF/DGEQPF) |
| F08AHF (SGELQF/DGELQF) Example Text Example Data | 16 | LQ factorization of real general rectangular matrix |
| F08AJF (SORGLQ/DORGLQ) Example Text Example Data | 16 | Form all or part of orthogonal Q from LQ factorization determined by F08AHF (SGELQF/DGELQF) |
| F08AKF (SORMLQ/DORMLQ) | 16 | Apply orthogonal transformation determined by F08AHF (SGELQF/DGELQF) |
| F08ASF (CGEQRF/ZGEQRF) Example Text Example Data | 16 | QR factorization of complex general rectangular matrix |
| F08ATF (CUNGQR/ZUNGQR) Example Text Example Data | 16 | Form all or part of unitary Q from QR factorization determined by F08ASF (CGEQRF/ZGEQRF) or F08BSF (CGEQPF/ZGEQPF) |
| F08AUF (CUNMQR/ZUNMQR) | 16 | Apply unitary transformation determined by F08ASF (CGEQRF/ZGEQRF) or F08BSF (CGEQPF/ZGEQPF) |
| F08AVF (CGELQF/ZGELQF) Example Text Example Data | 16 | LQ factorization of complex general rectangular matrix |
| F08AWF (CUNGLQ/ZUNGLQ) Example Text Example Data | 16 | Form all or part of unitary Q from LQ factorization determined by F08AVF (CGELQF/ZGELQF) |
| F08AXF (CUNMLQ/ZUNMLQ) | 16 | Apply unitary transformation determined by F08AVF (CGELQF/ZGELQF) |
| F08BEF (SGEQPF/DGEQPF) Example Text Example Data | 16 | QR factorization of real general rectangular matrix with column pivoting |
| F08BSF (CGEQPF/ZGEQPF) Example Text Example Data | 16 | QR factorization of complex general rectangular matrix with column pivoting |
| F08FCF (SSYEVD/DSYEVD) Example Text Example Data | 19 | All eigenvalues and optionally all eigenvectors of real symmetric matrix, using divide and conquer |
| F08FEF (SSYTRD/DSYTRD) Example Text Example Data | 16 | Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form |
| F08FFF (SORGTR/DORGTR) Example Text Example Data | 16 | Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08FEF (SSYTRD/DSYTRD) |
| F08FGF (SORMTR/DORMTR) Example Text Example Data | 16 | Apply orthogonal transformation determined by F08FEF (SSYTRD/DSYTRD) |
| F08FQF (CHEEVD/ZHEEVD) Example Text Example Data | 19 | All eigenvalues and optionally all eigenvectors of complex Hermitian matrix, using divide and conquer |
| F08FSF (CHETRD/ZHETRD) Example Text Example Data | 16 | Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form |
| F08FTF (CUNGTR/ZUNGTR) Example Text Example Data | 16 | Generate unitary transformation matrix from reduction to tridiagonal form determined by F08FSF (CHETRD/ZHETRD) |
| F08FUF (CUNMTR/ZUNMTR) Example Text Example Data | 16 | Apply unitary transformation matrix determined by F08FSF (CHETRD/ZHETRD) |
| F08GCF (SSPEVD/DSPEVD) Example Text Example Data | 19 | All eigenvalues and optionally all eigenvectors of real symmetric matrix, packed storage, using divide and conquer |
| F08GEF (SSPTRD/DSPTRD) Example Text Example Data | 16 | Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage |
| F08GFF (SOPGTR/DOPGTR) Example Text Example Data | 16 | Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08GEF (SSPTRD/DSPTRD) |
| F08GGF (SOPMTR/DOPMTR) Example Text Example Data | 16 | Apply orthogonal transformation determined by F08GEF (SSPTRD/DSPTRD) |
| F08GQF (CHPEVD/ZHPEVD) Example Text Example Data | 19 | All eigenvalues and optionally all eigenvectors of complex Hermitian matrix, packed storage, using divide and conquer |
| F08GSF (CHPTRD/ZHPTRD) Example Text Example Data | 16 | Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage |
| F08GTF (CUPGTR/ZUPGTR) Example Text Example Data | 16 | Generate unitary transformation matrix from reduction to tridiagonal form determined by F08GSF (CHPTRD/ZHPTRD) |
| F08GUF (CUPMTR/ZUPMTR) Example Text Example Data | 16 | Apply unitary transformation matrix determined by F08GSF (CHPTRD/ZHPTRD) |
| F08HCF (SSBEVD/DSBEVD) Example Text Example Data | 19 | All eigenvalues and optionally all eigenvectors of real symmetric band matrix, using divide and conquer |
| F08HEF (SSBTRD/DSBTRD) Example Text Example Data | 16 | Orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form |
| F08HQF (CHBEVD/ZHBEVD) Example Text Example Data | 19 | All eigenvalues and optionally all eigenvectors of complex Hermitian band matrix, using divide and conquer |
| F08HSF (CHBTRD/ZHBTRD) Example Text Example Data | 16 | Unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form |
| F08JCF (SSTEVD/DSTEVD) Example Text Example Data | 19 | All eigenvalues and optionally all eigenvectors of real symmetric tridiagonal matrix, using divide and conquer |
| F08JEF (SSTEQR/DSTEQR) Example Text Example Data | 16 | All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using implicit QL or QR |
| F08JFF (SSTERF/DSTERF) Example Text Example Data | 16 | All eigenvalues of real symmetric tridiagonal matrix, root-free variant of QL or QR |
| F08JGF (SPTEQR/DPTEQR) Example Text Example Data | 16 | All eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from real symmetric positive-definite matrix |
| F08JJF (SSTEBZ/DSTEBZ) | 16 | Selected eigenvalues of real symmetric tridiagonal matrix by bisection |
| F08JKF (SSTEIN/DSTEIN) | 16 | Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array |
| F08JSF (CSTEQR/ZSTEQR) | 16 | All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using implicit QL or QR |
| F08JUF (CPTEQR/ZPTEQR) Example Text Example Data | 16 | All eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from complex Hermitian positive-definite matrix |
| F08JXF (CSTEIN/ZSTEIN) | 16 | Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array |
| F08KEF (SGEBRD/DGEBRD) Example Text Example Data | 16 | Orthogonal reduction of real general rectangular matrix to bidiagonal form |
| F08KFF (SORGBR/DORGBR) Example Text Example Data | 16 | Generate orthogonal transformation matrices from reduction to bidiagonal form determined by F08KEF (SGEBRD/DGEBRD) |
| F08KGF (SORMBR/DORMBR) Example Text Example Data | 16 | Apply orthogonal transformations from reduction to bidiagonal form determined by F08KEF (SGEBRD/DGEBRD) |
| F08KSF (CGEBRD/ZGEBRD) Example Text Example Data | 16 | Unitary reduction of complex general rectangular matrix to bidiagonal form |
| F08KTF (CUNGBR/ZUNGBR) Example Text Example Data | 16 | Generate unitary transformation matrices from reduction to bidiagonal form determined by F08KSF (CGEBRD/ZGEBRD) |
| F08KUF (CUNMBR/ZUNMBR) Example Text Example Data | 16 | Apply unitary transformations from reduction to bidiagonal form determined by F08KSF (CGEBRD/ZGEBRD) |
| F08LEF (SGBBRD/DGBBRD) Example Text Example Data | 19 | Reduction of real rectangular band matrix to upper bidiagonal form |
| F08LSF (CGBBRD/ZGBBRD) Example Text Example Data | 19 | Reduction of complex rectangular band matrix to upper bidiagonal form |
| F08MEF (SBDSQR/DBDSQR) Example Text Example Data | 16 | SVD of real bidiagonal matrix reduced from real general matrix |
| F08MSF (CBDSQR/ZBDSQR) | 16 | SVD of real bidiagonal matrix reduced from complex general matrix |
| F08NEF (SGEHRD/DGEHRD) Example Text Example Data | 16 | Orthogonal reduction of real general matrix to upper Hessenberg form |
| F08NFF (SORGHR/DORGHR) Example Text Example Data | 16 | Generate orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (SGEHRD/DGEHRD) |
| F08NGF (SORMHR/DORMHR) Example Text Example Data | 16 | Apply orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (SGEHRD/DGEHRD) |
| F08NHF (SGEBAL/DGEBAL) Example Text Example Data | 16 | Balance real general matrix |
| F08NJF (SGEBAK/DGEBAK) | 16 | Transform eigenvectors of real balanced matrix to those of original matrix supplied to F08NHF (SGEBAL/DGEBAL) |
| F08NSF (CGEHRD/ZGEHRD) Example Text Example Data | 16 | Unitary reduction of complex general matrix to upper Hessenberg form |
| F08NTF (CUNGHR/ZUNGHR) Example Text Example Data | 16 | Generate unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (CGEHRD/ZGEHRD) |
| F08NUF (CUNMHR/ZUNMHR) Example Text Example Data | 16 | Apply unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (CGEHRD/ZGEHRD) |
| F08NVF (CGEBAL/ZGEBAL) Example Text Example Data | 16 | Balance complex general matrix |
| F08NWF (CGEBAK/ZGEBAK) | 16 | Transform eigenvectors of complex balanced matrix to those of original matrix supplied to F08NVF (CGEBAL/ZGEBAL) |
| F08PEF (SHSEQR/DHSEQR) Example Text Example Data | 16 | Eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix |
| F08PKF (SHSEIN/DHSEIN) | 16 | Selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration |
| F08PSF (CHSEQR/ZHSEQR) Example Text Example Data | 16 | Eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix |
| F08PXF (CHSEIN/ZHSEIN) | 16 | Selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration |
| F08QFF (STREXC/DTREXC) Example Text Example Data | 16 | Reorder Schur factorization of real matrix using orthogonal similarity transformation |
| F08QGF (STRSEN/DTRSEN) Example Text Example Data | 16 | Reorder Schur factorization of real matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities |
| F08QHF (STRSYL/DTRSYL) Example Text Example Data | 16 | Solve real Sylvester matrix equation AX + XB = C, A and B are upper quasi-triangular or transposes |
| F08QKF (STREVC/DTREVC) | 16 | Left and right eigenvectors of real upper quasi-triangular matrix |
| F08QLF (STRSNA/DTRSNA) Example Text Example Data | 16 | Estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix |
| F08QTF (CTREXC/ZTREXC) Example Text Example Data | 16 | Reorder Schur factorization of complex matrix using unitary similarity transformation |
| F08QUF (CTRSEN/ZTRSEN) Example Text Example Data | 16 | Reorder Schur factorization of complex matrix, form orthonormal basis of right invariant subspace for selected eigenvalues, with estimates of sensitivities |
| F08QVF (CTRSYL/ZTRSYL) Example Text Example Data | 16 | Solve complex Sylvester matrix equation AX + XB = C, A and B are upper triangular or conjugate-transposes |
| F08QXF (CTREVC/ZTREVC) | 16 | Left and right eigenvectors of complex upper triangular matrix |
| F08QYF (CTRSNA/ZTRSNA) Example Text Example Data | 16 | Estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix |
| F08SEF (SSYGST/DSYGST) Example Text Example Data | 16 | Reduction to standard form of real symmetric-definite generalized eigenproblem Ax = λ Bx, ABx = λ x or BAx = λ x, B factorized by F07FDF (SPOTRF/DPOTRF) |
| F08SSF (CHEGST/ZHEGST) Example Text Example Data | 16 | Reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax = λ Bx, ABx = λ x or BAx = λ x, B factorized by F07FRF (CPOTRF/ZPOTRF) |
| F08TEF (SSPGST/DSPGST) Example Text Example Data | 16 | Reduction to standard form of real symmetric-definite generalized eigenproblem Ax=λ Bx, ABx = λ x or BAx = λ x, packed storage, B factorized by F07GDF (SPPTRF/DPPTRF) |
| F08TSF (CHPGST/ZHPGST) Example Text Example Data | 16 | Reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax=λ Bx, ABx = λ x or BAx = λ x, packed storage, B factorized by F07GRF (CPPTRF/ZPPTRF) |
| F08UEF (SSBGST/DSBGST) Example Text Example Data | 19 | Reduction of real symmetric-definite banded generalized eigenproblem Ax = λ Bx to standard form Cy = λ y, such that C has the same bandwidth as A |
| F08UFF (SPBSTF/DPBSTF) | 19 | Computes a split Cholesky factorization of real symmetric positive-definite band matrix A |
| F08USF (CHBGST/ZHBGST) Example Text Example Data | 19 | Reduction of complex Hermitian-definite banded generalized eigenproblem Ax = λ Bx to standard form Cy = λ y, such that C has the same bandwidth as A |
| F08UTF (CPBSTF/ZPBSTF) | 19 | Computes a split Cholesky factorization of complex Hermitian positive-definite band matrix A |
| F08WEF (SGGHRD/DGGHRD) | 20 | Orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form |
| F08WHF (SGGBAL/DGGBAL) | 20 | Balance a pair of real general matrices |
| F08WJF (SGGBAK/DGGBAK) | 20 | Transform eigenvectors of a pair of real balanced matrices to those of original matrix pair supplied to F08WHF (SGGBAL/DGGBAL) |
| F08WSF (CGGHRD/ZGGHRD) | 20 | Unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form |
| F08WVF (CGGBAL/ZGGBAL) | 20 | Balance a pair of complex general matrices |
| F08WWF (CGGBAK/ZGGBAK) | 20 | Transform eigenvectors of a pair of complex balanced matrices to those of original matrix pair supplied to F08WVF (CGGBAL/ZGGBAL) |
| F08XEF (SHGEQZ/DHGEQZ) Example Text Example Data | 20 | Eigenvalues and generalized Schur factorization of real generalized upper Hessenberg form reduced from a pair of real general matrices |
| F08XSF (CHGEQZ/ZHGEQZ) Example Text Example Data | 20 | Eigenvalues and generalized Schur factorization of complex generalized upper Hessenberg form reduced from a pair of complex general matrices |
| F08YKF (STGEVC/DTGEVC) Example Text Example Data | 20 | Left and right eigenvectors of a pair of real upper quasi-triangular matrices |
| F08YXF (CTGEVC/ZTGEVC) Example Text Example Data | 20 | Left and right eigenvectors of a pair of complex upper triangular matrices |