| Routine Name |
Mark of Introduction |
Purpose |
| F08AAF Example Text Example Data |
21 | Solves an overdetermined or underdetermined real linear system |
| F08AEF Example Text Example Data |
16 | QR factorization of real general rectangular matrix |
| F08AFF Example Text Example Data |
16 | Form all or part of orthogonal Q from QR factorization determined by F08AEF (DGEQRF) or F08BEF (DGEQPF) |
| F08AGF | 16 | Apply orthogonal transformation determined by F08AEF (DGEQRF) or F08BEF (DGEQPF) |
| F08AHF Example Text Example Data |
16 | LQ factorization of real general rectangular matrix |
| F08AJF Example Text Example Data |
16 | Form all or part of orthogonal Q from LQ factorization determined by F08AHF (DGELQF) |
| F08AKF | 16 | Apply orthogonal transformation determined by F08AHF (DGELQF) |
| F08ANF Example Text Example Data |
21 | Solves an overdetermined or underdetermined complex linear system |
| F08ASF Example Text Example Data |
16 | QR factorization of complex general rectangular matrix |
| F08ATF Example Text Example Data |
16 | Form all or part of unitary Q from QR factorization determined by F08ASF (ZGEQRF) or F08BSF (ZGEQPF) |
| F08AUF | 16 | Apply unitary transformation determined by F08ASF (ZGEQRF) or F08BSF (ZGEQPF) |
| F08AVF Example Text Example Data |
16 | LQ factorization of complex general rectangular matrix |
| F08AWF Example Text Example Data |
16 | Form all or part of unitary Q from LQ factorization determined by F08AVF (ZGELQF) |
| F08AXF | 16 | Apply unitary transformation determined by F08AVF (ZGELQF) |
| F08BAF Example Text Example Data |
21 | Computes the minimum-norm solution to a real linear least-squares problem |
| F08BEF Example Text Example Data |
16 | QR factorization of real general rectangular matrix with column pivoting |
| F08BFF Example Text Example Data |
21 | QR factorization of real general rectangular matrix with column pivoting, using BLAS-3 |
| F08BHF Example Text Example Data |
21 | Reduces a real upper trapezoidal matrix to upper triangular form |
| F08BKF | 21 | Apply orthogonal transformation determined by F08BHF (DTZRZF) |
| F08BNF Example Text Example Data |
21 | Computes the minimum-norm solution to a complex linear least-squares problem |
| F08BSF Example Text Example Data |
16 | QR factorization of complex general rectangular matrix with column pivoting |
| F08BTF Example Text Example Data |
21 | QR factorization of complex general rectangular matrix with column pivoting, using BLAS-3 |
| F08BVF Example Text Example Data |
21 | Reduces a complex upper trapezoidal matrix to upper triangular form |
| F08BXF | 21 | Apply unitary transformation determined by F08BVF (ZTZRZF) |
| F08CEF Example Text Example Data |
21 | QL factorization of real general rectangular matrix |
| F08CFF Example Text Example Data |
21 | Form all or part of orthogonal Q from QL factorization determined by F08CEF (DGEQLF) |
| F08CGF | 21 | Apply orthogonal transformation determined by F08CEF (DGEQLF) |
| F08CHF Example Text Example Data |
21 | RQ factorization of real general rectangular matrix |
| F08CJF Example Text Example Data |
21 | Form all or part of orthogonal Q from RQ factorization determined by F08CHF (DGERQF) |
| F08CKF | 21 | Apply orthogonal transformation determined by F08CHF (DGERQF) |
| F08CSF Example Text Example Data |
21 | QL factorization of complex general rectangular matrix |
| F08CTF Example Text Example Data |
21 | Form all or part of orthogonal Q from QL factorization determined by F08CSF (ZGEQLF) |
| F08CUF | 21 | Apply unitary transformation determined by F08CSF (ZGEQLF) |
| F08CVF Example Text Example Data |
21 | RQ factorization of complex general rectangular matrix |
| F08CWF Example Text Example Data |
21 | Form all or part of orthogonal Q from RQ factorization determined by F08CVF (ZGERQF) |
| F08CXF | 21 | Apply unitary transformation determined by F08CVF (ZGERQF) |
| F08FAF Example Text Example Data |
21 | Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix |
| F08FBF Example Text Example Data |
21 | Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix |
| F08FCF Example Text Example Data |
19 | All eigenvalues and optionally all eigenvectors of real symmetric matrix (divide-and-conquer) |
| F08FDF Example Text Example Data |
21 | Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations) |
| F08FEF Example Text Example Data |
16 | Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form |
| F08FFF Example Text Example Data |
16 | Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08FEF (DSYTRD) |
| F08FGF Example Text Example Data |
16 | Apply orthogonal transformation determined by F08FEF (DSYTRD) |
| F08FLF | 21 | 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 | Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix |
| F08FPF Example Text Example Data |
21 | Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix |
| F08FQF Example Text Example Data |
19 | All eigenvalues and optionally all eigenvectors of complex Hermitian matrix (divide-and-conquer) |
| F08FRF Example Text Example Data |
21 | Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix (Relatively Robust Representations) |
| F08FSF Example Text Example Data |
16 | Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form |
| F08FTF Example Text Example Data |
16 | Generate unitary transformation matrix from reduction to tridiagonal form determined by F08FSF (ZHETRD) |
| F08FUF Example Text Example Data |
16 | Apply unitary transformation matrix determined by F08FSF (ZHETRD) |
| F08GAF Example Text Example Data |
21 | Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage |
| F08GBF Example Text Example Data |
21 | Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage |
| F08GCF Example Text Example Data |
19 | All eigenvalues and optionally all eigenvectors of real symmetric matrix, packed storage (divide-and-conquer) |
| F08GEF Example Text Example Data |
16 | Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage |
| F08GFF Example Text Example Data |
16 | Generate orthogonal transformation matrix from reduction to tridiagonal form determined by F08GEF (DSPTRD) |
| F08GGF Example Text Example Data |
16 | Apply orthogonal transformation determined by F08GEF (DSPTRD) |
| F08GNF Example Text Example Data |
21 | Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage |
| F08GPF Example Text Example Data |
21 | Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix, packed storage |
| F08GQF Example Text Example Data |
19 | All eigenvalues and optionally all eigenvectors of complex Hermitian matrix, packed storage (divide-and-conquer) |
| F08GSF Example Text Example Data |
16 | Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage |
| F08GTF Example Text Example Data |
16 | Generate unitary transformation matrix from reduction to tridiagonal form determined by F08GSF (ZHPTRD) |
| F08GUF Example Text Example Data |
16 | Apply unitary transformation matrix determined by F08GSF (ZHPTRD) |
| F08HAF Example Text Example Data |
21 | Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix |
| F08HBF Example Text Example Data |
21 | Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix |
| F08HCF Example Text Example Data |
19 | All eigenvalues and optionally all eigenvectors of real symmetric band matrix (divide-and-conquer) |
| F08HEF Example Text Example Data |
16 | Orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form |
| F08HNF Example Text Example Data |
21 | Computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix |
| F08HPF Example Text Example Data |
21 | Computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix |
| F08HQF Example Text Example Data |
19 | All eigenvalues and optionally all eigenvectors of complex Hermitian band matrix (divide-and-conquer) |
| F08HSF Example Text Example Data |
16 | Unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form |
| F08JAF Example Text Example Data |
21 | Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix |
| F08JBF Example Text Example Data |
21 | Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix |
| F08JCF Example Text Example Data |
19 | All eigenvalues and optionally all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer) |
| F08JDF Example Text Example Data |
21 | Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations) |
| F08JEF 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 Example Text Example Data |
16 | All eigenvalues of real symmetric tridiagonal matrix, root-free variant of QL or QR |
| F08JGF Example Text Example Data |
16 | All eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from real symmetric positive-definite matrix |
| F08JHF Example Text Example Data |
21 | Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a matrix reduced to this form (divide-and-conquer) |
| F08JJF | 16 | Selected eigenvalues of real symmetric tridiagonal matrix by bisection |
| F08JKF | 16 | Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array |
| F08JLF Example Text Example Data |
21 | 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 | All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using implicit QL or QR |
| F08JUF Example Text Example Data |
16 | All eigenvalues and eigenvectors of real symmetric positive-definite tridiagonal matrix, reduced from complex Hermitian positive-definite matrix |
| F08JVF Example Text Example Data |
21 | 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 | Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array |
| F08JYF Example Text Example Data |
21 | 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 | Computes the minimum-norm solution to a real linear least-squares problem using singular value decomposition |
| F08KBF Example Text Example Data |
21 | Computes the singular value decomposition of a real matrix, optionally computing the left and/or right singular vectors |
| F08KCF Example Text Example Data |
21 | 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 | 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 | Orthogonal reduction of real general rectangular matrix to bidiagonal form |
| F08KFF Example Text Example Data |
16 | Generate orthogonal transformation matrices from reduction to bidiagonal form determined by F08KEF (DGEBRD) |
| F08KGF Example Text Example Data |
16 | Apply orthogonal transformations from reduction to bidiagonal form determined by F08KEF (DGEBRD) |
| F08KNF Example Text Example Data |
21 | Computes the minimum-norm solution to a complex linear least-squares problem using singular value decomposition |
| F08KPF Example Text Example Data |
21 | Computes the singular value decomposition of a complex matrix, optionally computing the left and/or right singular vectors |
| F08KQF Example Text Example Data |
21 | 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 | 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 | Unitary reduction of complex general rectangular matrix to bidiagonal form |
| F08KTF Example Text Example Data |
16 | Generate unitary transformation matrices from reduction to bidiagonal form determined by F08KSF (ZGEBRD) |
| F08KUF Example Text Example Data |
16 | Apply unitary transformations from reduction to bidiagonal form determined by F08KSF (ZGEBRD) |
| F08LEF Example Text Example Data |
19 | Reduction of real rectangular band matrix to upper bidiagonal form |
| F08LSF Example Text Example Data |
19 | Reduction of complex rectangular band matrix to upper bidiagonal form |
| F08MDF Example Text Example Data |
21 | Computes the singular value decomposition of a real bidiagonal matrix, optionally computing the singular vectors (divide-and-conquer) |
| F08MEF Example Text Example Data |
16 | SVD of real bidiagonal matrix reduced from real general matrix |
| F08MSF | 16 | SVD of real bidiagonal matrix reduced from complex general matrix |
| F08NAF Example Text Example Data |
21 | Computes all eigenvalues and, optionally, left and/or right eigenvectors of a real nonsymmetric matrix |
| F08NBF Example Text Example Data |
21 | 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 | Orthogonal reduction of real general matrix to upper Hessenberg form |
| F08NFF Example Text Example Data |
16 | Generate orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (DGEHRD) |
| F08NGF Example Text Example Data |
16 | Apply orthogonal transformation matrix from reduction to Hessenberg form determined by F08NEF (DGEHRD) |
| F08NHF Example Text Example Data |
16 | Balance real general matrix |
| F08NJF | 16 | Transform eigenvectors of real balanced matrix to those of original matrix supplied to F08NHF (DGEBAL) |
| F08NNF Example Text Example Data |
21 | Computes all eigenvalues and, optionally, left and/or right eigenvectors of a complex nonsymmetric matrix |
| F08NPF Example Text Example Data |
21 | 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 | Unitary reduction of complex general matrix to upper Hessenberg form |
| F08NTF Example Text Example Data |
16 | Generate unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (ZGEHRD) |
| F08NUF Example Text Example Data |
16 | Apply unitary transformation matrix from reduction to Hessenberg form determined by F08NSF (ZGEHRD) |
| F08NVF Example Text Example Data |
16 | Balance complex general matrix |
| F08NWF | 16 | Transform eigenvectors of complex balanced matrix to those of original matrix supplied to F08NVF (ZGEBAL) |
| F08PAF Example Text Example Data |
21 | 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 | 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 | Eigenvalues and Schur factorization of real upper Hessenberg matrix reduced from real general matrix |
| F08PKF | 16 | Selected right and/or left eigenvectors of real upper Hessenberg matrix by inverse iteration |
| F08PNF Example Text Example Data |
21 | Computes for complex square nonsymmetric matrix, the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors |
| F08PPF Example Text Example Data |
21 | 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 | Eigenvalues and Schur factorization of complex upper Hessenberg matrix reduced from complex general matrix |
| F08PXF | 16 | Selected right and/or left eigenvectors of complex upper Hessenberg matrix by inverse iteration |
| F08QFF Example Text Example Data |
16 | Reorder Schur factorization of real matrix using orthogonal similarity transformation |
| F08QGF 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 Example Text Example Data |
16 | Solve real Sylvester matrix equation AX+XB=C, A and B are upper quasi-triangular or transposes |
| F08QKF | 16 | Left and right eigenvectors of real upper quasi-triangular matrix |
| F08QLF Example Text Example Data |
16 | Estimates of sensitivities of selected eigenvalues and eigenvectors of real upper quasi-triangular matrix |
| F08QTF Example Text Example Data |
16 | Reorder Schur factorization of complex matrix using unitary similarity transformation |
| F08QUF 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 Example Text Example Data |
16 | Solve complex Sylvester matrix equation AX+XB=C, A and B are upper triangular or conjugate-transposes |
| F08QXF | 16 | Left and right eigenvectors of complex upper triangular matrix |
| F08QYF Example Text Example Data |
16 | Estimates of sensitivities of selected eigenvalues and eigenvectors of complex upper triangular matrix |
| F08SAF Example Text Example Data |
21 | Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem |
| F08SBF Example Text Example Data |
21 | Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem |
| F08SCF Example Text Example Data |
21 | Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem (divide-and-conquer) |
| F08SEF Example Text Example Data |
16 | Reduction to standard form of real symmetric-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, B factorized by F07FDF (DPOTRF) |
| F08SNF Example Text Example Data |
21 | Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem |
| F08SPF Example Text Example Data |
21 | Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem |
| F08SQF Example Text Example Data |
21 | Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem (divide-and-conquer) |
| F08SSF Example Text Example Data |
16 | Reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, B factorized by F07FRF (ZPOTRF) |
| F08TAF Example Text Example Data |
21 | Computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage |
| F08TBF Example Text Example Data |
21 | Computes selected eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, packed storage |
| F08TCF Example Text Example Data |
21 | 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 | Reduction to standard form of real symmetric-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, packed storage, B factorized by F07GDF (DPPTRF) |
| F08TNF Example Text Example Data |
21 | Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage |
| F08TPF Example Text Example Data |
21 | Computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, packed storage |
| F08TQF Example Text Example Data |
21 | 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 | Reduction to standard form of complex Hermitian-definite generalized eigenproblem Ax=λBx, ABx=λx or BAx=λx, packed storage, B factorized by F07GRF (ZPPTRF) |
| F08UAF Example Text Example Data |
21 | Computes all the eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem |
| F08UBF Example Text Example Data |
21 | Computes selected eigenvalues, and optionally, the eigenvectors of a real banded generalized symmetric-definite eigenproblem |
| F08UCF Example Text Example Data |
21 | 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 | Reduction of real symmetric-definite banded generalized eigenproblem Ax=λBx to standard form Cy=λy, such that C has the same bandwidth as A |
| F08UFF | 19 | Computes a split Cholesky factorization of real symmetric positive-definite band matrix A |
| F08UNF Example Text Example Data |
21 | Computes all the eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem |
| F08UPF Example Text Example Data |
21 | Computes selected eigenvalues, and optionally, the eigenvectors of a complex banded generalized Hermitian-definite eigenproblem |
| F08UQF Example Text Example Data |
21 | 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 | Reduction of complex Hermitian-definite banded generalized eigenproblem Ax=λBx to standard form Cy=λ y, such that C has the same bandwidth as A |
| F08UTF | 19 | Computes a split Cholesky factorization of complex Hermitian positive-definite band matrix A |
| F08VAF Example Text Example Data |
21 | Computes the generalized singular value decomposition of a real matrix pair |
| F08VEF Example Text Example Data |
21 | Computes orthogonal matrices as processing steps for computing the generalized singular value decomposition of a real matrix pair |
| F08VNF Example Text Example Data |
21 | Computes the generalized singular value decomposition of a complex matrix pair |
| F08VSF Example Text Example Data |
21 | Computes orthogonal matrices as processing steps for computing the generalized singular value decomposition of a complex matrix pair |
| F08WAF Example Text Example Data |
21 | 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 | 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 | Orthogonal reduction of a pair of real general matrices to generalized upper Hessenberg form |
| F08WHF | 20 | Balance a pair of real general matrices |
| F08WJF | 20 | 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 | 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 | 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 | Unitary reduction of a pair of complex general matrices to generalized upper Hessenberg form |
| F08WVF | 20 | Balance a pair of complex general matrices |
| F08WWF | 20 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | Computes the generalized singular value decomposition of a real upper triangular (or trapezoidal) matrix pair |
| F08YFF Example Text Example Data |
21 | Reorders the generalized real Schur decomposition of a real matrix pair using an orthogonal equivalence transformation |
| F08YGF Example Text Example Data |
21 | 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 | Solves the real-valued generalized Sylvester equation |
| F08YKF Example Text Example Data |
20 | Left and right eigenvectors of a pair of real upper quasi-triangular matrices |
| F08YLF Example Text Example Data |
21 | 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 | Computes the generalized singular value decomposition of a complex upper triangular (or trapezoidal) matrix pair |
| F08YTF Example Text Example Data |
21 | Reorders the generalized Schur decomposition of a complex matrix pair using an unitary equivalence transformation |
| F08YUF Example Text Example Data |
21 | 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 | Solves the complex generalized Sylvester equation |
| F08YXF Example Text Example Data |
20 | Left and right eigenvectors of a pair of complex upper triangular matrices |
| F08YYF Example Text Example Data |
21 | 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 | Solves the real linear equality-constrained least-squares (LSE) problem |
| F08ZBF Example Text Example Data |
21 | Solves a real general Gauss–Markov linear model (GLM) problem |
| F08ZEF Example Text Example Data |
21 | Computes a generalized QR factorization of a real matrix pair |
| F08ZFF Example Text Example Data |
21 | Computes a generalized RQ factorization of a real matrix pair |
| F08ZNF Example Text Example Data |
21 | Solves the complex linear equality-constrained least-squares (LSE) problem |
| F08ZPF Example Text Example Data |
21 | Solves a complex general Gauss–Markov linear model (GLM) problem |
| F08ZSF Example Text Example Data |
21 | Computes a generalized QR factorization of a complex matrix pair |
| F08ZTF Example Text Example Data |
21 | Computes a generalized RQ factorization of a complex matrix pair |