CXML

lapack 


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.

  CXML includes a compiled and optimized version of LAPACK.

  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 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 subprogram.

  Available SIMPLE DRIVER routines:

       Subprogram Name   Operation

       sgesv             Solves a general system of linear equations
       dgesv             AX=B.
       cgesv
       zgesv

       sgbsv             Solves a general banded system of linear
       dgbsv             equations AX=B.
       cgbsv
       zgbsv

       sgtsv             Solves a general tridiagonal system of linear
       dgtsv             equations AX=B.
       cgtsv
       zgtsv

       sposv             Solves a symmetric/Hermitian positive definite
       dposv             system of linear equations AX=B.
       cposv
       zposv

       sppsv             Solves a symmetric/Hermitian positive definite
       dppsv             system of linear equations AX=B, where A is held
       cppsv             in packed storage.
       zppsv

       spbsv             Solves a symmetric/Hermitian positive definite
       dpbsv             banded system of linear equations AX=B.
       cpbsv
       zpbsv

       sptsv             Solves a symmetric/Hermitian positive definite
       dptsv             tridiagonal system of linear equations AX=B.
       cptsv
       zptsv

       ssysv             Solves a real/complex/complex symmetric/symmetric/
       dsysv             Hermitian indefinite system of linear equations
       csysv             AX=B.
       zsysv
       chesv
       zhesv

       sspsv             Solves a real/complex/complex symmetric/symmetric/
       dspsv             Hermitian indefinite system of linear equations
       cspsv             AX=B, where A is held in packed storage.
       zspsv
       chpsv
       zhpsv

       sgels             Computes the least squares solution to an over-
       dgels             determined system of linear equations, A X=B or
       cgels             A**H X=B,  or the minimum norm solution of an
       zgels             under-determined system, where A is a general
                         rectangular matrix of full rank,  using a QR
                         or LQ factorization of A.

       sgelss            Computes the minimum norm least squares solution
       dgelss            to an over- or under-determined system of linear
       cgelss            equations A X=B,  using the singular value
       zgelss            decomposition of A.

       sgglse            Solves the LSE (Constrained Linear Least Squares
       dgglse            Problem) using the GRQ (Generalized RQ)
       cgglse            factorization
       zgglse

       sggglm            Solves the GLM (Generalized Linear Regression
       dggglm            Model) using the GQR (Generalized QR)
       cggglm            factorization
       zggglm

       ssyev             Computes all eigenvalues and eigenvectors of a
       dsyev             symmetric/Hermitian matrix.
       cheev
       zheev

       ssyevd            Computes all eigenvalues and eigenvectors of a
       dsyevd            symmetric/Hermitian matrix, using a divide and
       cheevd            conquer algorithm.
       zheevd

       sspev             Computes all eigenvalues and eigenvectors of a
       dspev             symmetric/Hermitian matrix in packed storage.
       chpev
       zhpev

       sspevd            Computes all eigenvalues and eigenvectors of a
       dspevd            symmetric/Hermitian matrix in packed storage,
       chpevd            using a divide and conquer algorithm.
       zhpevd

       ssbev             Computes all eigenvalues and eigenvectors of a
       dsbev             symmetric/Hermitian band matrix.
       chbev
       zhbev

       ssbevd            Computes all eigenvalues and eigenvectors of a
       dsbevd            symmetric/Hermitian band matrix, using a divide
       chbevd            and conquer algorithm.
       zhbevd

       ssbgv             Computes all eigenvalues and eigenvectors of a
       dsbgv             symmetric/Hermitian-definite band matrix.
       chbgv
       zhbgv

       sstev             Computes all eigenvalues and eigenvectors of a
       dstev             real symmetric tridiagonal matrix.

       sstevd            Computes all eigenvalues and eigenvectors of a
       dstevd            real symmetric tridiagonal matrix, using a devide
                         and conquer algorithm.

       sgees             Computes the eigenvalues and Schur factorization
       dgees             of a general matrix, and orders the factorization
       cgees             so that selected eigenvalues are at the top left
       zgees             of the Schur form.

       sgeev             Computes the eigenvalues and left and right
       dgeev             eigenvectors of a general matrix
       cgeev
       zgeev

       sgesvd            Computes the singular value decomposition (SVD)
       dgesvd            of a general rectangular matrix.
       cgesvd
       zgesvd

       ssygv             Computes all eigenvalues and the eigenvectors
       dsygv             of a generalized symmetric/Hermitian-definite
       chegv             generalized eigenproblem, Ax= lambda Bx,  ABx=
       zhegv             lambda x,  or BAx= lambda x.

       sspgv             Computes all eigenvalues and eigenvectors of  a
       dspgv             generalized symmetric/Hermitian-definite generalized
       chpgv             eigenproblem,  Ax = lambda Bx,  ABx= lambda x,  or
       zhpgv             BAx= lambda x, where A and B are in packed storage.

       sgegs             Computes the generalized eigenvalues, Schur form,
       dgegs             and left and/or right Schur vectors for a pair of
       cgegs             nonsymmetric matrices
       zgegs

       sgegv             Computes the generalized eigenvalues, and left
       dgegv             and/or right generalized eigenvectors for a pair of
       cgegv             nonsymmetric matrices
       zgegv

       sggsvd            Computes the Generalized Singular Value
       dggsvd            Decomposition
       cggsvd
       zggsvd

  Available EXPERT DRIVER routines:

       Subprogram Name   Operation

       sgesvx            Solves a general system of linear equations AX=B,
       dgesvx            A**T X=B or A**H X=B, and provides an estimate of
       cgesvx            the condition number and error bounds on the
       zgesvx            solution.

       sgbsvx            Solves a general banded system of linear equations
       dgbsvx            AX=B, A**T X=B or A**H X=B, and provides an
       cgbsvx            estimate of the condition number and error bounds
       zgbsvx            on the solution.

       sgtsvx            Solves a general tridiagonal system of linear
       dgtsvx            equations AX=B, A**T X=B or A**H X=B, and provides
       cgtsvx            an estimate of the condition number  and error
       zgtsvx            bounds on the solution.

       sposvx            Solves a symmetric/Hermitian positive definite
       dposvx            system of linear equations AX=B, and provides
       cposvx            an estimate of the condition number and error
       zposvx            bounds on the asolution.

       sppsvx            Solves a symmetric/Hermitian positive definite
       dppsvx            system of linear equations AX=B, where A is held
       cppsvx            in packed storage, and provides an estimate of the
       zppsvx            condition number and error bounds on the solution.

       spbsvx            Solves a symmetric/Hermitian positive definite
       dpbsvx            banded system of linear equations AX=B, and provides
       cpbsvx            an estimate of the condition number and error bounds
       zpbsvx            on the solution.

       sptsvx            Solves a symmetric/Hermitian positive definite
       dptsvx            tridiagonal system of linear equations AX=B, and
       cptsvx            provides an estimate of the condition number and
       zptsvx            error bounds on the solution.

       ssysvx            Solves a real/complex/complex symmetric/symmetric/
       dsysvx            Hermitian indefinite system  of linear equations
       csysvx            AX=B, and provides an estimate of the condition
       zsysvx            number and error bounds on the solution.
       chesvx
       zhesvx

       sspsvx            Solves a real/complex/complex symmetric/symmetric/
       dspsvx            Hermitian indefinite system of linear equations AX=B,
       cspsvx            where A is held in packed storage, and provides an
       zspsvx            estimate of the condition number and error bounds on
       chpsvx            the solution.
       zhpsvx

       sgelsx            Computes the minimum norm least squares solution
       dgelsx            to an over- or under-determined system of linear
       cgelsx            equations A X=B, using a complete orthogonal
       zgelsx            factorization of A.

       ssyevx            Computes selected eigenvalues and eigenvectors of a
       dsyevx            symmetric/Hermitian matrix.
       cheevx
       zheevx

       sspevx            Computes selected eigenvalues and eigenvectors of a
       dspevx            symmetric/Hermitian matrix in packed storage.
       chpevx
       zhpevx

       ssbevx            Computes selected eigenvalues and eigenvectors of a
       dsbevx            symmetric/Hermitian band matrix.
       chbevx
       zhbevx

       sstevx            Computes selected eigenvalues and eigenvectors of a
       dstevx            real symmetric tridiagonal matrix.

       sgeesx            Computes the eigenvalues and Schur factorization of
       dgeesx            a general matrix, orders the factorization so that
       cgeesx            selected eigenvalues are at the top left of the
       zgeesx            Schur form, and computes reciprocal condition
                         numbers for the average of the selected eigenvalues,
                         and for the associated right invariant subspace.

       sgeevx            Computes the eigenvalues and left and right eigen-
       dgeevx            vectors of a general matrix,  with preliminary
       cgeevx            balancing of the matrix, and computes reciprocal
       zgeevx            condition numbers for the eigenvalues and right
                         eigenvectors.

  Available COMPUTATIONAL routines:

       Subprogram Name   Operation

       sbdsqr            Computes the singular value decomposition
       dbdsqr            (SVD) of a real bidiagonal matrix, using
       cbdsqr            the bidiagonal QR algorithm.
       zbdsqr

       sgbcon            Estimates the reciprocal of the condition
       dgbcon            number of a general band matrix, in either
       cgbcon            the 1-norm or the infinity-norm, using
       zgbcon            the LU factorization computed by
                         SGBTRF/CGBTRF.

       sgbequ            Computes row and column scalings to
       dgbequ            equilibrate a general band matrix and reduce
       cgbequ            its condition number.
       zgbequ

       sgbrfs            Improves the computed solution to a
       dgbrfs            general banded system of linear equations
       cgbrfs            AX=B, A**T X=B or A**H X=B, and provides
       zgbrfs            forward and backward error bounds for the
                         solution.

       sgbtrf            Computes an LU factorization of a general
       dgbtrf            band matrix, using partial pivoting with
       cgbtrf            row interchanges.
       zgbtrf

       sgbtrs            Solves a general banded system of linear
       dgbtrs            equations AX=B, A**T X=B or A**H X=B, using
       cgbtrs            the LU factorization computed by
       zgbtrs            SGBTRF/CGBTRF.

       sgebak            Transforms eigenvectors of a balanced
       dgebak            matrix to those of the original matrix
       cgebak            supplied to SGEBAL/CGEBAL.
       zgebak

       sgebal            Balances a general matrix in order to
       dgebal            improve the accuracy of computed
       cgebal            eigenvalues.
       zgebal

       sgebrd            Reduces a general rectangular matrix to
       dgebrd            real bidiagonal form by an orthogonal/
       cgebrd            unitary transformation.
       zgebrd

       sgbbrd            Reduces a general rectangular banded matrix
       dgbbrd            to real bidiagonal form by an orthogonal/
       cgbbrd            unitary transformation.
       zgbbrd

       sgecon            Estimates the reciprocal of the condition
       dgecon            number of a general matrix, in either the
       cgecon            1-norm or the infinity-norm, using the
       zgecon            LU factorization computed by SGETRF/CGETRF.

       sgeequ            Computes row and column scalings to
       dgeequ            equilibrate a general rectangular matrix
       cgeequ            and reduce its condition number.
       zgeequ

       sgehrd            Reduces a general matrix to upper
       dgehrd            Hessenberg form by an orthogonal/unitary
       cgehrd            similarity transformation.
       zgehrd

       sgelqf            Computes an LQ factorization of a general
       dgelqf            rectangular matrix.
       cgelqf
       zgelqf

       sgeqlf             Computes a QL factorization of a general
       dgeqlf            rectangular matrix.
       cgeqlf
       zgeqlf

       sgeqpf            Computes a QR factorization with column
       dgeqpf            pivoting of a general rectangular matrix.
       cgeqpf
       zgeqpf

       sgeqrf            Computes a QR factorization of a general
       dgeqrf            rectangular matrix.
       cgeqrf
       zgeqrf

       sgerfs            Improves the computed solution to a
       dgerfs            general system of linear equations AX=B,
       cgerfs            A**T X=B or A**H X=B, and provides forward
       zgerfs            and backward error bounds for the solution.

       sgerqf            Computes an RQ factorization of a
       dgerqf            general rectangular matrix.
       cgerqf
       zgerqf

       sgetrf            Computes an LU factorization of a
       dgetrf            general matrix, using partial pivoting
       cgetrf            with row interchanges.
       zgetrf

       sgetri            Computes the inverse of a general matrix,
       dgetri            using the LU factorization computed by
       cgetri            SGETRF/CGETRF.
       zgetri

       sgetrs            Solves a general system of linear
       dgetrs            equations AX=B, A**T X=B or A**H X=B,
       cgetrs            using the LU factorization computed by
       zgetrs            SGETRF/CGETRF.

       sggbak            Forms the right or left eigenvectors
       dggbak            of the generalized eigenvalue problem
       cggbak            by backward transformation on the
       zggbak            computed eigenvectors of the balanced
                         matrix output by xGGBAL.

       sggbal            Balances a pair of general real/complex
       dggbal            matrices for the generalized eigenvalue
       cggbal            problem A x = lambda B x.
       zggbal

       sgghrd            Reduces a pair of real/complex matrices
       dgghrd            to generalized upper Hessenberg form
       cgghrd            using orthogonal/unitary similarity
       zgghrd            transformations

       sggsvp            Computes orthogonal/unitary matrices
       dggsvp            as a preprocessing step for computing
       cggsvp            the generalized singular value
       zggsvp            decomposition

       sgtcon            Estimates the reciprocal of the
       dgtcon            condition number of a general tridiagonal
       cgtcon            matrix, in either the 1-norm or the
       zgtcon            infinity-norm, using the LU factorization
                         computed by SGTTRF/CGTTRF.

       sgtrfs            Improves the computed solution to a
       dgtrfs            general tridiagonal system of linear
       cgtrfs            equations AX=B, A**T X=B or A**H X=B,
       zgtrfs            and providesforward and backward error
                         bounds for the solution.

       sgttrf            Computes an LU factorization of a general
       dgttrf            tridiagonal matrix, using partial
       cgttrf            pivoting with row interchanges.
       zgttrf

       sgttrs            Solves a general tridiagonal system of
       dgttrs            linear equations AX=B, A**T X=B or
       cgttrs            A**H X=B, using the LU factorization
       zgttrs            computed by SGTTRF/CGTTRF.

       shgeqz            Implements a single-/double-shift
       dhgeqz            version of the QZ method for finding
       chgeqz            the generalized eigenvalues of the equation
       zhgeqz            det(A - w(i) B) = 0

       shsein            Computes specified right and/or left
       dhsein            eigenvectors of an upper Hessenberg
       chsein            matrix by inverse iteration.
       zhsein

       shseqr            Computes the eigenvalues and Schur
       dhseqr            factorization of an upper Hessenberg
       chseqr            matrix, using the multishift QR algorithm.
       zhseqr

       sopgtr            Generates the orthogonal/unitary
       dopgtr            transformation matrix from a reduction
       cupgtr            to tridiagonal form determined by
       zupgtr            SSPTRD/CHPTRD.

       sopmtr            Multiplies a general matrix by the
       dopmtr            orthogonal/unitary transformation matrix
       cupmtr            from a reduction to tridiagonal form
       zupmtr            determined by SSPTRD/CHPTRD.

       sorgbr            Generates the orthogonal/unitary
       dorgbr            transformation matrices from a reduction
       cungbr            to bidiagonal form determined by SGEBRD/CGEBRD.
       zungbr

       sorghr            Generates the orthogonal/unitary
       dorghr            transformation matrix from a reduction
       cunghr            to Hessenberg form determined by SGEHRD/CGEHRD.
       zunghr

       sorglq            Generates all or part of the orthogonal/
       dorglq            unitary matrix Q from an LQ factorization
       cunglq            determined by SGELQF/CGELQF.
       zunglq

       sorgql            Generates all or part of the orthogonal/
       dorgql            unitary matrix Q from a QL factorization
       cungql            determined by SGEQLF/CGEQLF.
       zungql

       sorgqr            Generates all or part of the orthogonal/
       dorgqr            unitary matrix Q from a QR factorization
       cungqr            determined by SGEQRF/CGEQRF.
       zungqr

       sorgrq            Generates all or part of the
       dorgrq            orthogonal/unitary matrix Q from an RQ
       cungrq            factorization determined by SGERQF/CGERQF.
       zungrq

       sorgtr            Generates the orthogonal/unitary
       dorgtr            transformation matrix from a reduction
       cungtr            to tridiagonal form determined by
       zungtr            SSYTRD/CHETRD.

       sormbr            Multiplies a general matrix by one of
       dormbr            the orthogonal/unitary transformation
       cunmbr            matrices from a reduction to bidiagonal form
       zunmbr            determined by SGEBRD/CGEBRD.

       sormhr            Multiplies a general matrix by the
       dormhr            orthogonal/unitary transformation matrix
       cunmhr            from a reduction to Hessenberg form
       zunmhr            determined by SGEHRD/CGEHRD.

       sormlq            Multiplies a general matrix by the
       dormlq            orthogonal/unitary matrix from an LQ
       cunmlq            factorization determined by SGELQF/CGELQF.
       zunmlq

       sormql            Multiplies a general matrix by the
       dormql            orthogonal/unitary matrix from a QL
       cunmql            factorization determined by SGEQLF/CGEQLF.
       zunmql

       sormqr            Multiplies a general matrix by the
       dormqr            orthogonal/unitary matrix from a QR
       cunmqr            factorization determined by SGEQRF/CGEQRF.
       zunmqr

       sormrq            Multiplies a general matrix by the
       dormrq            orthogonal/unitary matrix from an RQ
       cunmrq            factorization determined by SGERQF/CGERQF.
       zunmrq

       sormtr            Multiplies a general matrix by the
       dormtr            orthogonal/unitary transformation matrix
       cunmtr            from a reduction to tridiagonal form
       zunmtr            determined by SSYTRD/CHETRD.

       spbcon            Estimates the reciprocal of the condition
       dpbcon            number of a symmetric/Hermitian positive
       cpbcon            definite band matrix, using the Cholesky
       zpbcon             factorization computed by SPBTRF/CPBTRF.

       spbequ            Computes row and column scalings to
       dpbequ            equilibrate a symmetric/Hermitian positive
       cpbequ            definite band matrix and reduce its condition
       zpbequ            number.

       spbrfs            Improves the computed solution to a
       dpbrfs            symmetric/Hermitian positive definite banded
       cpbrfs            system of linear equations AX=B, and provides
       zpbrfs            forward and backward error bounds for the
                         solution.

       spbtrf            Computes the Cholesky factorization of a
       dpbtrf            symmetric/Hermitian positive definite band
       cpbtrf            matrix.
       zpbtrf

       spbtrs            Solves a symmetric/Hermitian positive
       dpbtrs            definite banded system of linear equations
       cpbtrs            AX=B, using the Cholesky factorization
       zpbtrs            computed by SPBTRF/CPBTRF.

       spocon            Estimates the reciprocal of the condition
       dpocon            number of a symmetric/Hermitian positive
       cpocon            definite matrix, using the Cholesky
       zpocon            factorization computed by SPOTRF/CPOTRF.

       spoequ            Computes row and column scalings to equilibrate
       dpoequ            a symmetric/Hermitian positive definite matrix
       cpoequ            and reduce its condition number.
       zpoequ

       sporfs            Improves the computed solution to a
       dporfs            symmetric/Hermitian positive definite system
       cporfs            of linear equations AX=B, and provides forward
       zporfs            and backward error bounds for the solution.

       spotrf            Computes the Cholesky factorization of a
       dpotrf            symmetric/Hermitian positive definite matrix.
       cpotrf
       zpotrf

       spotri            Computes the inverse of a symmetric/Hermitian
       dpotri            positive definite matrix, using the Cholesky
       cpotri            factorization computed by SPOTRF/CPOTRF.
       zpotri

       spotrs            Solves a symmetric/Hermitian positive definite
       dpotrs            system of linear equations AX=B, using the
       cpotrs            Cholesky factorization computed by SPOTRF/CPOTRF.
       zpotrs

       sppcon            Estimates the reciprocal of the condition
       dppcon            number of a symmetric/Hermitian positive
       cppcon            definite matrix in packed storage, using the
       zppcon            Cholesky factorization computed by SPPTRF/CPPTRF.

       sppequ            computes row and column scalings to
       dppequ            equilibrate a symmetric/hermitian positive
       cppequ            definite matrix in packed storage and reduce
       zppequ            its condition number.

       spprfs            Improves the computed solution to a symmetric/
       dpprfs            Hermitian positive definite system of linear
       cpprfs            equations AX=B, where A is held in packed storage,
       zpprfs            and provides forward and backward error bounds
                         for the solution.

       spptrf            Computes the Cholesky factorization of a
       dpptrf            symmetric/Hermitian positive definite matrix
       cpptrf            in packed storage.
       zpptrf

       spbstf            Computes the Cholesky factorization of a
       dpbstf            symmetric/Hermitian positive definite matrix
       cpbstf            in banded storage.
       zpbstf

       spptri            Computes the inverse of a symmetric/
       dpptri            Hermitian positive definite matrix in packed
       cpptri            storage, using the Cholesky factorization computed
       zpptri            by SPPTRF/CPPTRF.

       spptrs            Solves a symmetric/Hermitian positive definite
       dpptrs            system of linear equations AX=B, where A is held
       cpptrs            in packed storage, using the Cholesky factorization
       zpptrs            computed by SPPTRF/CPPTRF.

       sptcon            Computes the reciprocal of the condition
       dptcon            number of a symmetric/Hermitian positive
       cptcon            definite tridiagonal matrix, using the LDL**H
       zptcon            factorization computed by SPTTRF/CPTTRF.

       spteqr            Computes all eigenvalues and eigenvectors
       dpteqr            of a real symmetric positive definite
       cpteqr            tridiagonal matrix, by computing the SVD of
       zpteqr            its bidiagonal Cholesky factor.

       sptrfs            Improves the computed solution to a
       dptrfs            symmetric/Hermitian positive definite
       cptrfs            tridiagonal system of linear equations AX=B,
       zptrfs            and provides forward and backward error
                         bounds for the solution.

       spttrf            Computes the LDL**H factorization of a
       dpttrf            symmetric/Hermitian positive definite
       cpttrf            tridiagonal matrix.
       zpttrf

       spttrs            Solves a symmetric/Hermitian positive definite
       dpttrs             tridiagonal system of linear equations, using
       cpttrs            the LDL**H factorization computed by SPTTRF/CPTTRF.
       zpttrs

       ssbtrd            Reduces a symmetric/Hermitian band matrix to
       dsbtrd            real symmetric tridiagonal form by an orthogonal/
       chbtrd            unitary similarity transformation.
       zhbtrd

       sspcon            Estimates the reciprocal of the condition
       dspcon            number of a real/complex/complex symmetric/
       cspcon            symmetric/Hermitian indefinite matrix in packed
       zspcon            storage, using the factorization computed by
       chpcon            SSPTRF/CSPTRF/CHPTRF.
       zhpcon

       sspgst            Reduces a symmetric/Hermitian-definite
       dspgst            generalized eigenproblem Ax= lambda Bx,
       chpgst            ABx= lambda x,  or BAx= lambda x, to standard
       zhpgst            form,  where A and B are held in packed storage,
                         and B has been factorized by SPPTRF/CPPTRF.

       ssbgst            Reduces a symmetric/Hermitian-definite
       dsbgst            generalized eigenproblem Ax= lambda Bx,
       chbgst            ABx= lambda x,  or BAx= lambda x, to standard
       zhbgst            form,  where A and B are held in banded storage,
                         and B has been factorized by SPBSTF/CPBSTF.

       ssprfs            Improves the computed solution to a real/
       dsprfs            complex/complex symmetric/symmetric/Hermitian
       csprfs            indefinite system of linear equations AX=B,
       zsprfs            where A is held in packed storage, and provides
       chprfs            forward and backward error bounds for the solution.
       zhprfs

       ssptrd            Reduces a symmetric/Hermitian matrix in packed
       dsptrd            storage to real symmetric tridiagonal form by
       chptrd            an orthogonal/unitary similarity transformation.
       zhptrd

       ssbtrd            Reduces a symmetric/Hermitian matrix in banded
       dsbtrd            storage to real symmetric tridiagonal form by
       chbtrd            an orthogonal/unitary similarity transformation.
       zhbtrd

       ssptrf            Computes the factorization of a real/complex/
       dsptrf            complex symmetric/symmetric/Hermitian-indefinite
       csptrf            matrix in packed storage, using the diagonal
       zsptrf            pivoting method.
       chptrf
       zhptrf

       ssptri            Computes the inverse of a real symmetric/
       dsptri            complex symmetric/complex Hermitian indefinite
       csptri            matrix in packed storage, using the factorization
       zsptri            computed by SSPTRF/CSPTRF/CHPTRF.
       chptri
       zhptri

       ssptrs            Solves a real/complex/complex symmetric/
       dsptrs            symmetric/Hermitian indefinite system of linear
       csptrs            equations AX=B, where A is held in packed
       zsptrs            storage, using the factorization computed
       chptrs            by SSPTRF/CSPTRF/CHPTRF.
       zhptrs

       sstebz            Computes selected eigenvalues of a real symmetric
       dstebz            tridiagonal matrix by bisection.

       sstein            Computes selected eigenvectors of a real
       dstein            symmetric tridiagonal matrix by inverse iteration.
       cstein
       zstein

       ssteqr            Computes all eigenvalues and eigenvectors of
       dsteqr            a real symmetric tridiagonal matrix, using
       csteqr            the implicit QL or QR algorithm.
       zsteqr

       ssterf            Computes all eigenvalues of a real symmetric
       dsterf            tridiagonal matrix, using a root-free variant
                         of the QL or QR algorithm.

       ssycon            Estimates the reciprocal of the condition number
       dsycon            of a real/complex/complex symmetric/symmetric/
       csycon            Hermitian indefinite matrix, using the factor-
       zsycon            ization computed by SSYTRF/CSYTRF/CHETRF.
       checon
       zhecon

       ssygst            Reduces a symmetric/Hermitian-definite generalized
       dsygst            eigenproblem Ax= lambda Bx,  ABx= lambda x,  or
       chegst            BAx= lambda x, to standard form, where B has been
       zhegst            factorized by SPOTRF/CPOTRF.

       ssyrfs            Improves the computed solution to a real/complex/
       dsyrfs            complexsymmetric/symmetric/Hermitian indefinite
       csyrfs            system of linear equations AX=B, and provides
       zsyrfs            forward and backward error bounds for the
       cherfs            solution.
       zherfs

       ssytrd            Reduces a symmetric/Hermitian matrix to real
       dsytrd            symmetric tridiagonal form by an orthogonal/
       chetrd            unitary similarity transformation.
       zhetrd

       ssytrf            Computes the factorization of a real symmetric/
       dsytrf            complex symmetric/complex Hermitian-indefinite
       csytrf            matrix, using the diagonal pivoting method.
       zsytrf
       chetrf
       zhetrf

       ssytri            Computes the inverse of a real/complex/complex
       dsytri            symmetric/symmetric/Hermitian indefinite matrix,
       csytri            using the factorization computed by SSYTRF/CSYTRF/
       zsytri            CHETRF.
       chetri
       zhetri

       ssytrs            Solves a real/complex/complex symmetric/
       dsytrs            symmetric/Hermitian indefinite system of
       csytrs            linear equations AX=B, using the factorization
       zsytrs            computed by SSPTRF/CSPTRF/CHPTRF.
       chetrs
       zhetrs

       stbcon            Estimates the reciprocal of the condition
       dtbcon            number of a triangular band matrix, in either
       ctbcon            the 1-norm or the infinity-norm.
       ztbcon

       stbrfs            Provides forward and backward error bounds
       dtbrfs            for the solution of a triangular banded system
       ctbrfs            of linear equations AX=B, A**T X=B or A**H X=B.
       ztbrfs

       stbtrs            Solves a triangular banded system of linear
       dtbtrs            equations AX=B, A**T X=B or A**H X=B.
       ctbtrs
       ztbtrs

       stgevc            Computes selected left and/or right
       dtgevc            generalized eigenvectors of a pair of
       ctgevc            real/complex upper triangular matrices.
       ztgevc

       stgsja            Computes the generalized singular value
       dtgsja            decomposition of two real/complex upper
       ctgsja            "triangular (or trapezoidal)" matrices as
       ztgsja            output by xGGSVP.

       stpcon            Estimates the reciprocal of the condition
       dtpcon            number of a triangular matrix in packed
       ctpcon            storage, in either the 1-norm or the infinity-
       ztpcon            norm.

       stprfs            Provides forward and backward error bounds
       dtprfs            for the solution of a triangular system of
       ctprfs            linear equations AX=B, A**T X=B or A**H X=B,
       ztprfs            where A is held in packed storage.

       stptri            Computes the inverse of a triangular matrix
       dtptri            in packed storage.
       ctptri
       ztptri

       stptrs            Solves a triangular system of linear equations
       dtptrs            AX=B, A**T X=B or A**H X=B, where A is held in
       ctptrs            packed storage.
       ztptrs

       strcon            Estimates the reciprocal of the condition
       dtrcon            number of a triangular matrix, in either the
       ctrcon            1-norm or the infinity-norm.
       ztrcon

       strevc            Computes left and right eigenvectors of an
       dtrevc            upper quasi-triangular/triangular matrix.
       ctrevc
       ztrevc

       strexc            Reorders the Schur factorization of a matrix
       dtrexc            by a unitary similarity transformation.
       ctrexc
       ztrexc

       strrfs            Provides forward and backward error bounds
       dtrrfs            for the solution of a triangular system of
       ctrrfs            linear equations A X=B, A**T X=B or
       ztrrfs            A**H X=B.

       strsen            Reorders the Schur factorization of a matrix
       dtrsen            in order to find an orthonormal basis of a right
       ctrsen            invariant subspace corresponding to selected
       ztrsen            eigenvalues, and returns reciprocal condition
                         numbers (sensitivities) of the average of the
                         cluster of eigenvalues and of the invariant
                         subspace.

       strsna            Estimates the reciprocal condition numbers
       dtrsna            (sensitivities) of selected eigenvalues and
       ctrsna            eigenvectors of an upper quasi-triangular/
       ztrsna            triangular matrix.

       strsyl            Solves the Sylvester matrix equation
       dtrsyl            A X +/- X B=C where A and B are upper quasi-
       ctrsyl            triangular/triangular, and may be transposed.
       ztrsyl

       strtri             Computes the inverse of a triangular matrix.
       dtrtri
       ctrtri
       ztrtri

       strtrs            Solves a triangular system of linear equations
       dtrtrs            AX=B, A**T X=B or A**H X=B.
       ctrtrs
       ztrtrs

       stzrqf            Computes an RQ factorization of an upper
       dtzrqf            trapezoidal matrix.
       ctzrqf
       ztzrqf

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