LAPACK(3DXML) — Subroutines
Digital
Name
lapack − A library of linear algebra routines
Description
LAPACK (Linear Algebra Package) is a new library of dense linear and eigenproblem solvers that supercedes LINPACK and EISPACK, offering better performance and accuracy.
DXML includes a compiled and optimized version of LAPACK 2.0, which was released in September 1994.
LAPACK includes subroutines for solving the most common problems in numerical linear algebra:
•Solving systems of simultaneous liner equations
•Finding least squares solutions of overdetermined systems of equations
•Solving eigenvalue problems
•Solving singular value problems
The extensive functionality provided by LAPACK includes routines for the following matrix factorizations:
•LU
•Cholesky
•QR
•SVD
•Schur
•Generalized Schur
Where appropriate, these functions are provided for the following matrices:
•General
•General band
•General tridiagonal
•Symmetric
•Symmetric band
•Symmetric tridiagonal
•Symmetric, packed storage
•Symmetric positive definite
•Symmetric positive definite band
•Symmetric positive definite, tridiagonal
•Triangular
•Triangular band
•Triangular, packed storage
LAPACK extends the functionality of LINPACK and EISPACK by including equilibration, iterative refinement, error bounds, and driver routines for linear systems, routines for computing and re-ordering the Schur factorization, and condition estimation routines for eigenvalue problems. LAPACK improves on the accuracy of the standard algorithms in EISPACK by including high accuracy algorithms for finding singular values and eigenvalues of bidiagonal and tridiagonal matrices respectively that arise in SVD and symmetric eigenvalue problems.
The performance of the public-domain LAPACK routines on Alpha AXP platforms is improved through the use of the optimized BLAS subprograms.
EQUIVALENCE BETWEEN LAPACK AND LINPACK/EISPACK ROUTINES:
The LAPACK equivalence utility provides the names and parameter lists of LAPACK routines that are equivalent to the LINPACK and EISPACK routines you specify. The utility command is as follows:
/usr/share/equivalence_lapack routine_name [routine_name...]
where you replace routine_name with the LINPACK and/or EISPACK routine names. For example:
/usr/share/equivalence_lapack dgesl imtql1
return:
DGESL:
SUBROUTINE SGETRS( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
SUBROUTINE DGETRS( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO ) IMTQL1:
SUBROUTINE SSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
SUBROUTINE DSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
The LINPACK or EISPACK routine names are to the left of the colons. The equivalent LAPACK routines and calling sequences are to the right of the colons.
This utility helps you to convert LINPACK and EISPACK routine calls to equivalent LAPACK routine calls. The utility has limitations in that the argument lists of the LAPACK routines are generally different from those of the corresponding LINPACK and EISPACK routines, and the workspace requirements are often different as well.
NAMING SCHEME:
The name of each LAPACK routine is a coded specification of its function (within the very tight limits of standard Fortran 77 6-character names). All driver and computational routines have names of the form XYYZZZ, where for some driver routines the 6th character is blank.
The first letter, X, indicates the data type as follows:
S REAL
D DOUBLE PRECISION
C COMPLEX
Z COMPLEX∗16 or DOUBLE COMPLEX
The next two letters, YY, indicate the type of matrix (or of the most significant matrix). Most of these two-letter codes apply to both real and complex matrices; a few apply specifically to one or the other.
The last three letters ZZZ indicate the computation performed. For example, SGEBRD is a single precision routine that performs a bidiagonal reduction (BRD) of a real general matrix.
LIST OF ROUTINES:
LAPACK includes both computational routines that perform a distinct algorithmic task (such as performing an LU factorization) as well as driver routines that solve a complete problem (such as solving a system of linear equations). The driver routines (simple and expert) are listed first, followed by the computational routines. Auxiliary routines from LAPACK are not listed.
The Subprogram Name is the name of the manual page containing documentation on the routine.
Available SIMPLE DRIVER routines:
| Subprogram Name | Operation |
| sgesv (3lapack) | Solves a general system of linear equations |
| dgesv (3lapack) | AX=B. |
| cgesv (3lapack) | |
| zgesv (3lapack) | |
| sgbsv (3lapack) | Solves a general banded system of linear |
| dgbsv (3lapack) | equations AX=B. |
| cgbsv (3lapack) | |
| zgbsv (3lapack) | |
| sgtsv (3lapack) | Solves a general tridiagonal system of linear |
| dgtsv (3lapack) | equations AX=B. |
| cgtsv (3lapack) | |
| zgtsv (3lapack) | |
| sposv (3lapack) | Solves a symmetric/Hermitian positive definite |
| dposv (3lapack) | system of linear equations AX=B. |
| cposv (3lapack) | |
| zposv (3lapack) | |
| sppsv (3lapack) | Solves a symmetric/Hermitian positive definite |
| dppsv (3lapack) | system of linear equations AX=B, where A is held |
| cppsv (3lapack) | in packed storage. |
| zppsv (3lapack) | |
| spbsv (3lapack) | Solves a symmetric/Hermitian positive definite |
| dpbsv (3lapack) | banded system of linear equations AX=B. |
| cpbsv (3lapack) | |
| zpbsv (3lapack) | |
| sptsv (3lapack) | Solves a symmetric/Hermitian positive definite |
| dptsv (3lapack) | tridiagonal system of linear equations AX=B. |
| cptsv (3lapack) | |
| zptsv (3lapack) | |
| ssysv (3lapack) | Solves a real/complex/complex symmetric/symmetric/ |
| dsysv (3lapack) | Hermitian indefinite system of linear equations |
| csysv (3lapack) | AX=B. |
| zsysv (3lapack) | |
| chesv (3lapack) | |
| zhesv (3lapack) | |
| sspsv (3lapack) | Solves a real/complex/complex symmetric/symmetric/ |
| dspsv (3lapack) | Hermitian indefinite system of linear equations |
| cspsv (3lapack) | AX=B, where A is held in packed storage. |
| zspsv (3lapack) | |
| chpsv (3lapack) | |
| zhpsv (3lapack) | |
| sgels (3lapack) | Computes the least squares solution to an over- |
| dgels (3lapack) | determined system of linear equations, A X=B or |
| cgels (3lapack) | A∗∗H X=B, or the minimum norm solution of an |
| zgels (3lapack) | under-determined system, where A is a general |
| rectangular matrix of full rank, using a QR | |
| or LQ factorization of A. | |
| sgelss (3lapack) | Computes the minimum norm least squares solution |
| dgelss (3lapack) | to an over- or under-determined system of linear |
| cgelss (3lapack) | equations A X=B, using the singular value |
| zgelss (3lapack) | decomposition of A. |
| sgglse (3lapack) | Solves the LSE (Constrained Linear Least Squares |
| dgglse (3lapack) | Problem) using the GRQ (Generalized RQ) |
| cgglse (3lapack) | factorization |
| zgglse (3lapack) | |
| sggglm (3lapack) | Solves the GLM (Generalized Linear Regression |
| dggglm (3lapack) | Model) using the GQR (Generalized QR) |
| cggglm (3lapack) | factorization |
| zggglm (3lapack) | |
| ssyev (3lapack) | Computes all eigenvalues and eigenvectors of a |
| dsyev (3lapack) | symmetric/Hermitian matrix. |
| cheev (3lapack) | |
| zheev (3lapack) | |
| ssyevd (3lapack) | Computes all eigenvalues and eigenvectors of a |
| dsyevd (3lapack) | symmetric/Hermitian matrix, using a divide and |
| cheevd (3lapack) | conquer algorithm. |
| zheevd (3lapack) | |
| sspev (3lapack) | Computes all eigenvalues and eigenvectors of a |
| dspev (3lapack) | symmetric/Hermitian matrix in packed storage. |
| chpev (3lapack) | |
| zhpev (3lapack) | |
| sspevd (3lapack) | Computes all eigenvalues and eigenvectors of a |
| dspevd (3lapack) | symmetric/Hermitian matrix in packed storage, |
| chpevd (3lapack) | using a divide and conquer algorithm. |
| zhpevd (3lapack) | |
| ssbev (3lapack) | Computes all eigenvalues and eigenvectors of a |
| dsbev (3lapack) | symmetric/Hermitian band matrix. |
| chbev (3lapack) | |
| zhbev (3lapack) | |
| ssbevd (3lapack) | Computes all eigenvalues and eigenvectors of a |
| dsbevd (3lapack) | symmetric/Hermitian band matrix, using a divide |
| chbevd (3lapack) | and conquer algorithm. |
| zhbevd (3lapack) | |
| ssbgv (3lapack) | Computes all eigenvalues and eigenvectors of a |
| dsbgv (3lapack) | symmetric/Hermitian-definite band matrix. |
| chbgv (3lapack) | |
| zhbgv (3lapack) | |
| sstev (3lapack) | Computes all eigenvalues and eigenvectors of a |
| dstev (3lapack) | real symmetric tridiagonal matrix. |
| sstevd (3lapack) | Computes all eigenvalues and eigenvectors of a |
| dstevd (3lapack) | real symmetric tridiagonal matrix, using a devide |
| and conquer algorithm. | |
| sgees (3lapack) | Computes the eigenvalues and Schur factorization |
| dgees (3lapack) | of a general matrix, and orders the factorization |
| cgees (3lapack) | so that selected eigenvalues are at the top left |
| zgees (3lapack) | of the Schur form. |
| sgeev (3lapack) | Computes the eigenvalues and left and right |
| dgeev (3lapack) | eigenvectors of a general matrix |
| cgeev (3lapack) | |
| zgeev (3lapack) | |
| sgesvd (3lapack) | Computes the singular value decomposition (SVD) |
| dgesvd (3lapack) | of a general rectangular matrix. |
| cgesvd (3lapack) | |
| zgesvd (3lapack) | |
| ssygv (3lapack) | Computes all eigenvalues and the eigenvectors |
| dsygv (3lapack) | of a generalized symmetric/Hermitian-definite |
| chegv (3lapack) | generalized eigenproblem, Ax= lambda Bx, ABx= |
| zhegv (3lapack) | lambda x, or BAx= lambda x. |
| sspgv (3lapack) | Computes all eigenvalues and eigenvectors of a |
| dspgv (3lapack) | generalized symmetric/Hermitian-definite generalized |
| chpgv (3lapack) | eigenproblem, Ax = lambda Bx, ABx= lambda x, or |
| zhpgv (3lapack) | BAx= lambda x, where A and B are in packed storage. |
| sgegs (3lapack) | Computes the generalized eigenvalues, Schur form, |
| dgegs (3lapack) | and left and/or right Schur vectors for a pair of |
| cgegs (3lapack) | nonsymmetric matrices |
| zgegs (3lapack) | |
| sgegv (3lapack) | Computes the generalized eigenvalues, and left |
| dgegv (3lapack) | and/or right generalized eigenvectors for a pair of |
| cgegv (3lapack) | nonsymmetric matrices |
| zgegv (3lapack) | |
| sggsvd (3lapack) | Computes the Generalized Singular Value |
| dggsvd (3lapack) | Decomposition |
| cggsvd (3lapack) | |
| zggsvd (3lapack) |
Available EXPERT DRIVER routines:
| Subprogram Name | Operation |
| sgesvx (3lapack) | Solves a general system of linear equations AX=B, |
| dgesvx (3lapack) | A∗∗T X=B or A∗∗H X=B, and provides an estimate of |
| cgesvx (3lapack) | the condition number and error bounds on the |
| zgesvx (3lapack) | solution. |
| sgbsvx (3lapack) | Solves a general banded system of linear equations |
| dgbsvx (3lapack) | AX=B, A∗∗T X=B or A∗∗H X=B, and provides an |
| cgbsvx (3lapack) | estimate of the condition number and error bounds |
| zgbsvx (3lapack) | on the solution. |
| sgtsvx (3lapack) | Solves a general tridiagonal system of linear |
| dgtsvx (3lapack) | equations AX=B, A∗∗T X=B or A∗∗H X=B, and provides |
| cgtsvx (3lapack) | an estimate of the condition number and error |
| zgtsvx (3lapack) | bounds on the solution. |
| sposvx (3lapack) | Solves a symmetric/Hermitian positive definite |
| dposvx (3lapack) | system of linear equations AX=B, and provides |
| cposvx (3lapack) | an estimate of the condition number and error |
| zposvx (3lapack) | bounds on the asolution. |
| sppsvx (3lapack) | Solves a symmetric/Hermitian positive definite |
| dppsvx (3lapack) | system of linear equations AX=B, where A is held |
| cppsvx (3lapack) | in packed storage, and provides an estimate of the |
| zppsvx (3lapack) | condition number and error bounds on the solution. |
| spbsvx (3lapack) | Solves a symmetric/Hermitian positive definite |
| dpbsvx (3lapack) | banded system of linear equations AX=B, and provides |
| cpbsvx (3lapack) | an estimate of the condition number and error bounds |
| zpbsvx (3lapack) | on the solution. |
| sptsvx (3lapack) | Solves a symmetric/Hermitian positive definite |
| dptsvx (3lapack) | tridiagonal system of linear equations AX=B, and |
| cptsvx (3lapack) | provides an estimate of the condition number and |
| zptsvx (3lapack) | error bounds on the solution. |
| ssysvx (3lapack) | Solves a real/complex/complex symmetric/symmetric/ |
| dsysvx (3lapack) | Hermitian indefinite system of linear equations |
| csysvx (3lapack) | AX=B, and provides an estimate of the condition |
| zsysvx (3lapack) | number and error bounds on the solution. |
| chesvx (3lapack) | |
| zhesvx (3lapack) | |
| sspsvx (3lapack) | Solves a real/complex/complex symmetric/symmetric/ |
| dspsvx (3lapack) | Hermitian indefinite system of linear equations AX=B, |
| cspsvx (3lapack) | where A is held in packed storage, and provides an |
| zspsvx (3lapack) | estimate of the condition number and error bounds on |
| chpsvx (3lapack) | the solution. |
| zhpsvx (3lapack) | |
| sgelsx (3lapack) | Computes the minimum norm least squares solution |
| dgelsx (3lapack) | to an over- or under-determined system of linear |
| cgelsx (3lapack) | equations A X=B, using a complete orthogonal |
| zgelsx (3lapack) | factorization of A. |
| ssyevx (3lapack) | Computes selected eigenvalues and eigenvectors of a |
| dsyevx (3lapack) | symmetric/Hermitian matrix. |
| cheevx (3lapack) | |
| zheevx (3lapack) | |
| sspevx (3lapack) | Computes selected eigenvalues and eigenvectors of a |
| dspevx (3lapack) | symmetric/Hermitian matrix in packed storage. |
| chpevx (3lapack) | |
| zhpevx (3lapack) | |
| ssbevx (3lapack) | Computes selected eigenvalues and eigenvectors of a |
| dsbevx (3lapack) | symmetric/Hermitian band matrix. |
| chbevx (3lapack) | |
| zhbevx (3lapack) | |
| sstevx (3lapack) | Computes selected eigenvalues and eigenvectors of a |
| dstevx (3lapack) | real symmetric tridiagonal matrix. |
| sgeesx (3lapack) | Computes the eigenvalues and Schur factorization of |
| dgeesx (3lapack) | a general matrix, orders the factorization so that |
| cgeesx (3lapack) | selected eigenvalues are at the top left of the |
| zgeesx (3lapack) | Schur form, and computes reciprocal condition |
| numbers for the average of the selected eigenvalues, | |
| and for the associated right invariant subspace. | |
| sgeevx (3lapack) | Computes the eigenvalues and left and right eigen- |
| dgeevx (3lapack) | vectors of a general matrix, with preliminary |
| cgeevx (3lapack) | balancing of the matrix, and computes reciprocal |
| zgeevx (3lapack) | condition numbers for the eigenvalues and right |
| eigenvectors. |
Available COMPUTATIONAL routines:
| Subprogram Name | Operation |
| sbdsqr (3lapack) | Computes the singular value decomposition |
| dbdsqr (3lapack) | (SVD) of a real bidiagonal matrix, using |
| cbdsqr (3lapack) | the bidiagonal QR algorithm. |
| zbdsqr (3lapack) | |
| sgbcon (3lapack) | Estimates the reciprocal of the condition |
| dgbcon (3lapack) | number of a general band matrix, in either |
| cgbcon (3lapack) | the 1-norm or the infinity-norm, using |
| zgbcon (3lapack) | the LU factorization computed by |
| SGBTRF/CGBTRF. | |
| sgbequ (3lapack) | Computes row and column scalings to |
| dgbequ (3lapack) | equilibrate a general band matrix and reduce |
| cgbequ (3lapack) | its condition number. |
| zgbequ (3lapack) | |
| sgbrfs (3lapack) | Improves the computed solution to a |
| dgbrfs (3lapack) | general banded system of linear equations |
| cgbrfs (3lapack) | AX=B, A∗∗T X=B or A∗∗H X=B, and provides |
| zgbrfs (3lapack) | forward and backward error bounds for the |
| solution. | |
| sgbtrf (3lapack) | Computes an LU factorization of a general |
| dgbtrf (3lapack) | band matrix, using partial pivoting with |
| cgbtrf (3lapack) | row interchanges. |
| zgbtrf (3lapack) | |
| sgbtrs (3lapack) | Solves a general banded system of linear |
| dgbtrs (3lapack) | equations AX=B, A∗∗T X=B or A∗∗H X=B, using |
| cgbtrs (3lapack) | the LU factorization computed by |
| zgbtrs (3lapack) | SGBTRF/CGBTRF. |
| sgebak (3lapack) | Transforms eigenvectors of a balanced |
| dgebak (3lapack) | matrix to those of the original matrix |
| cgebak (3lapack) | supplied to SGEBAL/CGEBAL. |
| zgebak (3lapack) | |
| sgebal (3lapack) | Balances a general matrix in order to |
| dgebal (3lapack) | improve the accuracy of computed |
| cgebal (3lapack) | eigenvalues. |
| zgebal (3lapack) | |
| sgebrd (3lapack) | Reduces a general rectangular matrix to |
| dgebrd (3lapack) | real bidiagonal form by an orthogonal/ |
| cgebrd (3lapack) | unitary transformation. |
| zgebrd (3lapack) | |
| sgbbrd (3lapack) | Reduces a general rectangular banded matrix |
| dgbbrd (3lapack) | to real bidiagonal form by an orthogonal/ |
| cgbbrd (3lapack) | unitary transformation. |
| zgbbrd (3lapack) | |
| sgecon (3lapack) | Estimates the reciprocal of the condition |
| dgecon (3lapack) | number of a general matrix, in either the |
| cgecon (3lapack) | 1-norm or the infinity-norm, using the |
| zgecon (3lapack) | LU factorization computed by SGETRF/CGETRF. |
| sgeequ (3lapack) | Computes row and column scalings to |
| dgeequ (3lapack) | equilibrate a general rectangular matrix |
| cgeequ (3lapack) | and reduce its condition number. |
| zgeequ (3lapack) | |
| sgehrd (3lapack) | Reduces a general matrix to upper |
| dgehrd (3lapack) | Hessenberg form by an orthogonal/unitary |
| cgehrd (3lapack) | similarity transformation. |
| zgehrd (3lapack) | |
| sgelqf (3lapack) | Computes an LQ factorization of a general |
| dgelqf (3lapack) | rectangular matrix. |
| cgelqf (3lapack) | |
| zgelqf (3lapack) | |
| sgeqlf (3lapack) | Computes a QL factorization of a general |
| dgeqlf (3lapack) | rectangular matrix. |
| cgeqlf (3lapack) | |
| zgeqlf (3lapack) | |
| sgeqpf (3lapack) | Computes a QR factorization with column |
| dgeqpf (3lapack) | pivoting of a general rectangular matrix. |
| cgeqpf (3lapack) | |
| zgeqpf (3lapack) | |
| sgeqrf (3lapack) | Computes a QR factorization of a general |
| dgeqrf (3lapack) | rectangular matrix. |
| cgeqrf (3lapack) | |
| zgeqrf (3lapack) | |
| sgerfs (3lapack) | Improves the computed solution to a |
| dgerfs (3lapack) | general system of linear equations AX=B, |
| cgerfs (3lapack) | A∗∗T X=B or A∗∗H X=B, and provides forward |
| zgerfs (3lapack) | and backward error bounds for the solution. |
| sgerqf (3lapack) | Computes an RQ factorization of a |
| dgerqf (3lapack) | general rectangular matrix. |
| cgerqf (3lapack) | |
| zgerqf (3lapack) | |
| sgetrf (3lapack) | Computes an LU factorization of a |
| dgetrf (3lapack) | general matrix, using partial pivoting |
| cgetrf (3lapack) | with row interchanges. |
| zgetrf (3lapack) | |
| sgetri (3lapack) | Computes the inverse of a general matrix, |
| dgetri (3lapack) | using the LU factorization computed by |
| cgetri (3lapack) | SGETRF/CGETRF. |
| zgetri (3lapack) | |
| sgetrs (3lapack) | Solves a general system of linear |
| dgetrs (3lapack) | equations AX=B, A∗∗T X=B or A∗∗H X=B, |
| cgetrs (3lapack) | using the LU factorization computed by |
| zgetrs (3lapack) | SGETRF/CGETRF. |
| sggbak (3lapack) | Forms the right or left eigenvectors |
| dggbak (3lapack) | of the generalized eigenvalue problem |
| cggbak (3lapack) | by backward transformation on the |
| zggbak (3lapack) | computed eigenvectors of the balanced |
| matrix output by xGGBAL. | |
| sggbal (3lapack) | Balances a pair of general real/complex |
| dggbal (3lapack) | matrices for the generalized eigenvalue |
| cggbal (3lapack) | problem A x = lambda B x. |
| zggbal (3lapack) | |
| sgghrd (3lapack) | Reduces a pair of real/complex matrices |
| dgghrd (3lapack) | to generalized upper Hessenberg form |
| cgghrd (3lapack) | using orthogonal/unitary similarity |
| zgghrd (3lapack) | transformations |
| sggsvp (3lapack) | Computes orthogonal/unitary matrices |
| dggsvp (3lapack) | as a preprocessing step for computing |
| cggsvp (3lapack) | the generalized singular value |
| zggsvp (3lapack) | decomposition |
| sgtcon (3lapack) | Estimates the reciprocal of the |
| dgtcon (3lapack) | condition number of a general tridiagonal |
| cgtcon (3lapack) | matrix, in either the 1-norm or the |
| zgtcon (3lapack) | infinity-norm, using the LU factorization |
| computed by SGTTRF/CGTTRF. | |
| sgtrfs (3lapack) | Improves the computed solution to a |
| dgtrfs (3lapack) | general tridiagonal system of linear |
| cgtrfs (3lapack) | equations AX=B, A∗∗T X=B or A∗∗H X=B, |
| zgtrfs (3lapack) | and providesforward and backward error |
| bounds for the solution. | |
| sgttrf (3lapack) | Computes an LU factorization of a general |
| dgttrf (3lapack) | tridiagonal matrix, using partial |
| cgttrf (3lapack) | pivoting with row interchanges. |
| zgttrf (3lapack) | |
| sgttrs (3lapack) | Solves a general tridiagonal system of |
| dgttrs (3lapack) | linear equations AX=B, A∗∗T X=B or |
| cgttrs (3lapack) | A∗∗H X=B, using the LU factorization |
| zgttrs (3lapack) | computed by SGTTRF/CGTTRF. |
| shgeqz (3lapack) | Implements a single-/double-shift |
| dhgeqz (3lapack) | version of the QZ method for finding |
| chgeqz (3lapack) | the generalized eigenvalues of the equation |
| zhgeqz (3lapack) | det(A - w(i) B) = 0 |
| shsein (3lapack) | Computes specified right and/or left |
| dhsein (3lapack) | eigenvectors of an upper Hessenberg |
| chsein (3lapack) | matrix by inverse iteration. |
| zhsein (3lapack) | |
| shseqr (3lapack) | Computes the eigenvalues and Schur |
| dhseqr (3lapack) | factorization of an upper Hessenberg |
| chseqr (3lapack) | matrix, using the multishift QR algorithm. |
| zhseqr (3lapack) | |
| sopgtr (3lapack) | Generates the orthogonal/unitary |
| dopgtr (3lapack) | transformation matrix from a reduction |
| cupgtr (3lapack) | to tridiagonal form determined by |
| zupgtr (3lapack) | SSPTRD/CHPTRD. |
| sopmtr (3lapack) | Multiplies a general matrix by the |
| dopmtr (3lapack) | orthogonal/unitary transformation matrix |
| cupmtr (3lapack) | from a reduction to tridiagonal form |
| zupmtr (3lapack) | determined by SSPTRD/CHPTRD. |
| sorgbr (3lapack) | Generates the orthogonal/unitary |
| dorgbr (3lapack) | transformation matrices from a reduction |
| cungbr (3lapack) | to bidiagonal form determined by SGEBRD/CGEBRD. |
| zungbr (3lapack) | |
| sorghr (3lapack) | Generates the orthogonal/unitary |
| dorghr (3lapack) | transformation matrix from a reduction |
| cunghr (3lapack) | to Hessenberg form determined by SGEHRD/CGEHRD. |
| zunghr (3lapack) | |
| sorglq (3lapack) | Generates all or part of the orthogonal/ |
| dorglq (3lapack) | unitary matrix Q from an LQ factorization |
| cunglq (3lapack) | determined by SGELQF/CGELQF. |
| zunglq (3lapack) | |
| sorgql (3lapack) | Generates all or part of the orthogonal/ |
| dorgql (3lapack) | unitary matrix Q from a QL factorization |
| cungql (3lapack) | determined by SGEQLF/CGEQLF. |
| zungql (3lapack) | |
| sorgqr (3lapack) | Generates all or part of the orthogonal/ |
| dorgqr (3lapack) | unitary matrix Q from a QR factorization |
| cungqr (3lapack) | determined by SGEQRF/CGEQRF. |
| zungqr (3lapack) | |
| sorgrq (3lapack) | Generates all or part of the |
| dorgrq (3lapack) | orthogonal/unitary matrix Q from an RQ |
| cungrq (3lapack) | factorization determined by SGERQF/CGERQF. |
| zungrq (3lapack) | |
| sorgtr (3lapack) | Generates the orthogonal/unitary |
| dorgtr (3lapack) | transformation matrix from a reduction |
| cungtr (3lapack) | to tridiagonal form determined by |
| zungtr (3lapack) | SSYTRD/CHETRD. |
| sormbr (3lapack) | Multiplies a general matrix by one of |
| dormbr (3lapack) | the orthogonal/unitary transformation |
| cunmbr (3lapack) | matrices from a reduction to bidiagonal form |
| zunmbr (3lapack) | determined by SGEBRD/CGEBRD. |
| sormhr (3lapack) | Multiplies a general matrix by the |
| dormhr (3lapack) | orthogonal/unitary transformation matrix |
| cunmhr (3lapack) | from a reduction to Hessenberg form |
| zunmhr (3lapack) | determined by SGEHRD/CGEHRD. |
| sormlq (3lapack) | Multiplies a general matrix by the |
| dormlq (3lapack) | orthogonal/unitary matrix from an LQ |
| cunmlq (3lapack) | factorization determined by SGELQF/CGELQF. |
| zunmlq (3lapack) | |
| sormql (3lapack) | Multiplies a general matrix by the |
| dormql (3lapack) | orthogonal/unitary matrix from a QL |
| cunmql (3lapack) | factorization determined by SGEQLF/CGEQLF. |
| zunmql (3lapack) | |
| sormqr (3lapack) | Multiplies a general matrix by the |
| dormqr (3lapack) | orthogonal/unitary matrix from a QR |
| cunmqr (3lapack) | factorization determined by SGEQRF/CGEQRF. |
| zunmqr (3lapack) | |
| sormrq (3lapack) | Multiplies a general matrix by the |
| dormrq (3lapack) | orthogonal/unitary matrix from an RQ |
| cunmrq (3lapack) | factorization determined by SGERQF/CGERQF. |
| zunmrq (3lapack) | |
| sormtr (3lapack) | Multiplies a general matrix by the |
| dormtr (3lapack) | orthogonal/unitary transformation matrix |
| cunmtr (3lapack) | from a reduction to tridiagonal form |
| zunmtr (3lapack) | determined by SSYTRD/CHETRD. |
| spbcon (3lapack) | Estimates the reciprocal of the condition |
| dpbcon (3lapack) | number of a symmetric/Hermitian positive |
| cpbcon (3lapack) | definite band matrix, using the Cholesky |
| zpbcon (3lapack) | factorization computed by SPBTRF/CPBTRF. |
| spbequ (3lapack) | Computes row and column scalings to |
| dpbequ (3lapack) | equilibrate a symmetric/Hermitian positive |
| cpbequ (3lapack) | definite band matrix and reduce its condition |
| zpbequ (3lapack) | number. |
| spbrfs (3lapack) | Improves the computed solution to a |
| dpbrfs (3lapack) | symmetric/Hermitian positive definite banded |
| cpbrfs (3lapack) | system of linear equations AX=B, and provides |
| zpbrfs (3lapack) | forward and backward error bounds for the |
| solution. | |
| spbtrf (3lapack) | Computes the Cholesky factorization of a |
| dpbtrf (3lapack) | symmetric/Hermitian positive definite band |
| cpbtrf (3lapack) | matrix. |
| zpbtrf (3lapack) | |
| spbtrs (3lapack) | Solves a symmetric/Hermitian positive |
| dpbtrs (3lapack) | definite banded system of linear equations |
| cpbtrs (3lapack) | AX=B, using the Cholesky factorization |
| zpbtrs (3lapack) | computed by SPBTRF/CPBTRF. |
| spocon (3lapack) | Estimates the reciprocal of the condition |
| dpocon (3lapack) | number of a symmetric/Hermitian positive |
| cpocon (3lapack) | definite matrix, using the Cholesky |
| zpocon (3lapack) | factorization computed by SPOTRF/CPOTRF. |
| spoequ (3lapack) | Computes row and column scalings to equilibrate |
| dpoequ (3lapack) | a symmetric/Hermitian positive definite matrix |
| cpoequ (3lapack) | and reduce its condition number. |
| zpoequ (3lapack) | |
| sporfs (3lapack) | Improves the computed solution to a |
| dporfs (3lapack) | symmetric/Hermitian positive definite system |
| cporfs (3lapack) | of linear equations AX=B, and provides forward |
| zporfs (3lapack) | and backward error bounds for the solution. |
| spotrf (3lapack) | Computes the Cholesky factorization of a |
| dpotrf (3lapack) | symmetric/Hermitian positive definite matrix. |
| cpotrf (3lapack) | |
| zpotrf (3lapack) | |
| spotri (3lapack) | Computes the inverse of a symmetric/Hermitian |
| dpotri (3lapack) | positive definite matrix, using the Cholesky |
| cpotri (3lapack) | factorization computed by SPOTRF/CPOTRF. |
| zpotri (3lapack) | |
| spotrs (3lapack) | Solves a symmetric/Hermitian positive definite |
| dpotrs (3lapack) | system of linear equations AX=B, using the |
| cpotrs (3lapack) | Cholesky factorization computed by SPOTRF/CPOTRF. |
| zpotrs (3lapack) | |
| sppcon (3lapack) | Estimates the reciprocal of the condition |
| dppcon (3lapack) | number of a symmetric/Hermitian positive |
| cppcon (3lapack) | definite matrix in packed storage, using the |
| zppcon (3lapack) | Cholesky factorization computed by SPPTRF/CPPTRF. |
| sppequ (3lapack) | computes row and column scalings to |
| dppequ (3lapack) | equilibrate a symmetric/hermitian positive |
| cppequ (3lapack) | definite matrix in packed storage and reduce |
| zppequ (3lapack) | its condition number. |
| spprfs (3lapack) | Improves the computed solution to a symmetric/ |
| dpprfs (3lapack) | Hermitian positive definite system of linear |
| cpprfs (3lapack) | equations AX=B, where A is held in packed storage, |
| zpprfs (3lapack) | and provides forward and backward error bounds |
| for the solution. | |
| spptrf (3lapack) | Computes the Cholesky factorization of a |
| dpptrf (3lapack) | symmetric/Hermitian positive definite matrix |
| cpptrf (3lapack) | in packed storage. |
| zpptrf (3lapack) | |
| spbstf (3lapack) | Computes the Cholesky factorization of a |
| dpbstf (3lapack) | symmetric/Hermitian positive definite matrix |
| cpbstf (3lapack) | in banded storage. |
| zpbstf (3lapack) | |
| spptri (3lapack) | Computes the inverse of a symmetric/ |
| dpptri (3lapack) | Hermitian positive definite matrix in packed |
| cpptri (3lapack) | storage, using the Cholesky factorization computed |
| zpptri (3lapack) | by SPPTRF/CPPTRF. |
| spptrs (3lapack) | Solves a symmetric/Hermitian positive definite |
| dpptrs (3lapack) | system of linear equations AX=B, where A is held |
| cpptrs (3lapack) | in packed storage, using the Cholesky factorization |
| zpptrs (3lapack) | computed by SPPTRF/CPPTRF. |
| sptcon (3lapack) | Computes the reciprocal of the condition |
| dptcon (3lapack) | number of a symmetric/Hermitian positive |
| cptcon (3lapack) | definite tridiagonal matrix, using the LDL∗∗H |
| zptcon (3lapack) | factorization computed by SPTTRF/CPTTRF. |
| spteqr (3lapack) | Computes all eigenvalues and eigenvectors |
| dpteqr (3lapack) | of a real symmetric positive definite |
| cpteqr (3lapack) | tridiagonal matrix, by computing the SVD of |
| zpteqr (3lapack) | its bidiagonal Cholesky factor. |
| sptrfs (3lapack) | Improves the computed solution to a |
| dptrfs (3lapack) | symmetric/Hermitian positive definite |
| cptrfs (3lapack) | tridiagonal system of linear equations AX=B, |
| zptrfs (3lapack) | and provides forward and backward error |
| bounds for the solution. | |
| spttrf (3lapack) | Computes the LDL∗∗H factorization of a |
| dpttrf (3lapack) | symmetric/Hermitian positive definite |
| cpttrf (3lapack) | tridiagonal matrix. |
| zpttrf (3lapack) | |
| spttrs (3lapack) | Solves a symmetric/Hermitian positive definite |
| dpttrs (3lapack) | tridiagonal system of linear equations, using |
| cpttrs (3lapack) | the LDL∗∗H factorization computed by SPTTRF/CPTTRF. |
| zpttrs (3lapack) | |
| ssbtrd (3lapack) | Reduces a symmetric/Hermitian band matrix to |
| dsbtrd (3lapack) | real symmetric tridiagonal form by an orthogonal/ |
| chbtrd (3lapack) | unitary similarity transformation. |
| zhbtrd (3lapack) | |
| sspcon (3lapack) | Estimates the reciprocal of the condition |
| dspcon (3lapack) | number of a real/complex/complex symmetric/ |
| cspcon (3lapack) | symmetric/Hermitian indefinite matrix in packed |
| zspcon (3lapack) | storage, using the factorization computed by |
| chpcon (3lapack) | SSPTRF/CSPTRF/CHPTRF. |
| zhpcon (3lapack) | |
| sspgst (3lapack) | Reduces a symmetric/Hermitian-definite |
| dspgst (3lapack) | generalized eigenproblem Ax= lambda Bx, |
| chpgst (3lapack) | ABx= lambda x, or BAx= lambda x, to standard |
| zhpgst (3lapack) | form, where A and B are held in packed storage, |
| and B has been factorized by SPPTRF/CPPTRF. | |
| ssbgst (3lapack) | Reduces a symmetric/Hermitian-definite |
| dsbgst (3lapack) | generalized eigenproblem Ax= lambda Bx, |
| chbgst (3lapack) | ABx= lambda x, or BAx= lambda x, to standard |
| zhbgst (3lapack) | form, where A and B are held in banded storage, |
| and B has been factorized by SPBSTF/CPBSTF. | |
| ssprfs (3lapack) | Improves the computed solution to a real/ |
| dsprfs (3lapack) | complex/complex symmetric/symmetric/Hermitian |
| csprfs (3lapack) | indefinite system of linear equations AX=B, |
| zsprfs (3lapack) | where A is held in packed storage, and provides |
| chprfs (3lapack) | forward and backward error bounds for the solution. |
| zhprfs (3lapack) | |
| ssptrd (3lapack) | Reduces a symmetric/Hermitian matrix in packed |
| dsptrd (3lapack) | storage to real symmetric tridiagonal form by |
| chptrd (3lapack) | an orthogonal/unitary similarity transformation. |
| zhptrd (3lapack) | |
| ssbtrd (3lapack) | Reduces a symmetric/Hermitian matrix in banded |
| dsbtrd (3lapack) | storage to real symmetric tridiagonal form by |
| chbtrd (3lapack) | an orthogonal/unitary similarity transformation. |
| zhbtrd (3lapack) | |
| ssptrf (3lapack) | Computes the factorization of a real/complex/ |
| dsptrf (3lapack) | complex symmetric/symmetric/Hermitian-indefinite |
| csptrf (3lapack) | matrix in packed storage, using the diagonal |
| zsptrf (3lapack) | pivoting method. |
| chptrf (3lapack) | |
| zhptrf (3lapack) | |
| ssptri (3lapack) | Computes the inverse of a real symmetric/ |
| dsptri (3lapack) | complex symmetric/complex Hermitian indefinite |
| csptri (3lapack) | matrix in packed storage, using the factorization |
| zsptri (3lapack) | computed by SSPTRF/CSPTRF/CHPTRF. |
| chptri (3lapack) | |
| zhptri (3lapack) | |
| ssptrs (3lapack) | Solves a real/complex/complex symmetric/ |
| dsptrs (3lapack) | symmetric/Hermitian indefinite system of linear |
| csptrs (3lapack) | equations AX=B, where A is held in packed |
| zsptrs (3lapack) | storage, using the factorization computed |
| chptrs (3lapack) | by SSPTRF/CSPTRF/CHPTRF. |
| zhptrs (3lapack) | |
| sstebz (3lapack) | Computes selected eigenvalues of a real symmetric |
| dstebz (3lapack) | tridiagonal matrix by bisection. |
| sstein (3lapack) | Computes selected eigenvectors of a real |
| dstein (3lapack) | symmetric tridiagonal matrix by inverse iteration. |
| cstein (3lapack) | |
| zstein (3lapack) | |
| ssteqr (3lapack) | Computes all eigenvalues and eigenvectors of |
| dsteqr (3lapack) | a real symmetric tridiagonal matrix, using |
| csteqr (3lapack) | the implicit QL or QR algorithm. |
| zsteqr (3lapack) | |
| ssterf (3lapack) | Computes all eigenvalues of a real symmetric |
| dsterf (3lapack) | tridiagonal matrix, using a root-free variant |
| of the QL or QR algorithm. | |
| ssycon (3lapack) | Estimates the reciprocal of the condition number |
| dsycon (3lapack) | of a real/complex/complex symmetric/symmetric/ |
| csycon (3lapack) | Hermitian indefinite matrix, using the factor- |
| zsycon (3lapack) | ization computed by SSYTRF/CSYTRF/CHETRF. |
| checon (3lapack) | |
| zhecon (3lapack) | |
| ssygst (3lapack) | Reduces a symmetric/Hermitian-definite generalized |
| dsygst (3lapack) | eigenproblem Ax= lambda Bx, ABx= lambda x, or |
| chegst (3lapack) | BAx= lambda x, to standard form, where B has been |
| zhegst (3lapack) | factorized by SPOTRF/CPOTRF. |
| ssyrfs (3lapack) | Improves the computed solution to a real/complex/ |
| dsyrfs (3lapack) | complexsymmetric/symmetric/Hermitian indefinite |
| csyrfs (3lapack) | system of linear equations AX=B, and provides |
| zsyrfs (3lapack) | forward and backward error bounds for the |
| cherfs (3lapack) | solution. |
| zherfs (3lapack) | |
| ssytrd (3lapack) | Reduces a symmetric/Hermitian matrix to real |
| dsytrd (3lapack) | symmetric tridiagonal form by an orthogonal/ |
| chetrd (3lapack) | unitary similarity transformation. |
| zhetrd (3lapack) | |
| ssytrf (3lapack) | Computes the factorization of a real symmetric/ |
| dsytrf (3lapack) | complex symmetric/complex Hermitian-indefinite |
| csytrf (3lapack) | matrix, using the diagonal pivoting method. |
| zsytrf (3lapack) | |
| chetrf (3lapack) | |
| zhetrf (3lapack) | |
| ssytri (3lapack) | Computes the inverse of a real/complex/complex |
| dsytri (3lapack) | symmetric/symmetric/Hermitian indefinite matrix, |
| csytri (3lapack) | using the factorization computed by SSYTRF/CSYTRF/ |
| zsytri (3lapack) | CHETRF. |
| chetri (3lapack) | |
| zhetri (3lapack) | |
| ssytrs (3lapack) | Solves a real/complex/complex symmetric/ |
| dsytrs (3lapack) | symmetric/Hermitian indefinite system of |
| csytrs (3lapack) | linear equations AX=B, using the factorization |
| zsytrs (3lapack) | computed by SSPTRF/CSPTRF/CHPTRF. |
| chetrs (3lapack) | |
| zhetrs (3lapack) | |
| stbcon (3lapack) | Estimates the reciprocal of the condition |
| dtbcon (3lapack) | number of a triangular band matrix, in either |
| ctbcon (3lapack) | the 1-norm or the infinity-norm. |
| ztbcon (3lapack) | |
| stbrfs (3lapack) | Provides forward and backward error bounds |
| dtbrfs (3lapack) | for the solution of a triangular banded system |
| ctbrfs (3lapack) | of linear equations AX=B, A∗∗T X=B or A∗∗H X=B. |
| ztbrfs (3lapack) | |
| stbtrs (3lapack) | Solves a triangular banded system of linear |
| dtbtrs (3lapack) | equations AX=B, A∗∗T X=B or A∗∗H X=B. |
| ctbtrs (3lapack) | |
| ztbtrs (3lapack) | |
| stgevc (3lapack) | Computes selected left and/or right |
| dtgevc (3lapack) | generalized eigenvectors of a pair of |
| ctgevc (3lapack) | real/complex upper triangular matrices. |
| ztgevc (3lapack) | |
| stgsja (3lapack) | Computes the generalized singular value |
| dtgsja (3lapack) | decomposition of two real/complex upper |
| ctgsja (3lapack) | "triangular (or trapezoidal)" matrices as |
| ztgsja (3lapack) | output by xGGSVP. |
| stpcon (3lapack) | Estimates the reciprocal of the condition |
| dtpcon (3lapack) | number of a triangular matrix in packed |
| ctpcon (3lapack) | storage, in either the 1-norm or the infinity- |
| ztpcon (3lapack) | norm. |
| stprfs (3lapack) | Provides forward and backward error bounds |
| dtprfs (3lapack) | for the solution of a triangular system of |
| ctprfs (3lapack) | linear equations AX=B, A∗∗T X=B or A∗∗H X=B, |
| ztprfs (3lapack) | where A is held in packed storage. |
| stptri (3lapack) | Computes the inverse of a triangular matrix |
| dtptri (3lapack) | in packed storage. |
| ctptri (3lapack) | |
| ztptri (3lapack) | |
| stptrs (3lapack) | Solves a triangular system of linear equations |
| dtptrs (3lapack) | AX=B, A∗∗T X=B or A∗∗H X=B, where A is held in |
| ctptrs (3lapack) | packed storage. |
| ztptrs (3lapack) | |
| strcon (3lapack) | Estimates the reciprocal of the condition |
| dtrcon (3lapack) | number of a triangular matrix, in either the |
| ctrcon (3lapack) | 1-norm or the infinity-norm. |
| ztrcon (3lapack) | |
| strevc (3lapack) | Computes left and right eigenvectors of an |
| dtrevc (3lapack) | upper quasi-triangular/triangular matrix. |
| ctrevc (3lapack) | |
| ztrevc (3lapack) | |
| strexc (3lapack) | Reorders the Schur factorization of a matrix |
| dtrexc (3lapack) | by a unitary similarity transformation. |
| ctrexc (3lapack) | |
| ztrexc (3lapack) | |
| strrfs (3lapack) | Provides forward and backward error bounds |
| dtrrfs (3lapack) | for the solution of a triangular system of |
| ctrrfs (3lapack) | linear equations A X=B, A∗∗T X=B or |
| ztrrfs (3lapack) | A∗∗H X=B. |
| strsen (3lapack) | Reorders the Schur factorization of a matrix |
| dtrsen (3lapack) | in order to find an orthonormal basis of a right |
| ctrsen (3lapack) | invariant subspace corresponding to selected |
| ztrsen (3lapack) | eigenvalues, and returns reciprocal condition |
| numbers (sensitivities) of the average of the | |
| cluster of eigenvalues and of the invariant | |
| subspace. | |
| strsna (3lapack) | Estimates the reciprocal condition numbers |
| dtrsna (3lapack) | (sensitivities) of selected eigenvalues and |
| ctrsna (3lapack) | eigenvectors of an upper quasi-triangular/ |
| ztrsna (3lapack) | triangular matrix. |
| strsyl (3lapack) | Solves the Sylvester matrix equation |
| dtrsyl (3lapack) | A X +/- X B=C where A and B are upper quasi- |
| ctrsyl (3lapack) | triangular/triangular, and may be transposed. |
| ztrsyl (3lapack) | |
| strtri (3lapack) | Computes the inverse of a triangular matrix. |
| dtrtri (3lapack) | |
| ctrtri (3lapack) | |
| ztrtri (3lapack) | |
| strtrs (3lapack) | Solves a triangular system of linear equations |
| dtrtrs (3lapack) | AX=B, A∗∗T X=B or A∗∗H X=B. |
| ctrtrs (3lapack) | |
| ztrtrs (3lapack) | |
| stzrqf (3lapack) | Computes an RQ factorization of an upper |
| dtzrqf (3lapack) | trapezoidal matrix. |
| ctzrqf (3lapack) | |
| ztzrqf (3lapack) |