From: TRON::"uunet!surfer.EPM.ORNL.GOV!netlibd" 13-JUN-1992 16:45:10.81
To: squire

# Caveat receptor.  Jack Dongarra - [email-masked], 
#                   Eric Grosse   - [email-masked]
#
# We would like to thank Sequent Computer Systems Inc.
# for the computer used to run netlib.
#
# We are running a new version of netlib which allows
# setting of chunk size used for reply. Try: send index
# for a list of new features.

#!/bin/sh
# to unpack, sh this message
PATH=/bin:/usr/bin
cat > index <<'CUT HERE..........'
 ========================================================================
 LAPACK, Version 1.0         Date:  February 29, 1992
 ========================================================================

             ( L   A    P    A    C    K )
             ( L  -A    P   -A    C   -K )
             ( L   A    P    A   -C   -K )
             ( L  -A    P   -A   -C    K )
             ( L   A   -P   -A    C    K )
             ( L  -A   -P    A    C   -K )

 --------------------------
 Available software/reports:
 --------------------------

lapack.tar.z  (FOR XNETLIB USERS ONLY) This is the COMPLETE package
              (installation, testing, and timing) in tar compressed
              form (6867561 bytes).
              This cannot be retrieved via email.

testing.tar.z (FOR XNETLIB USERS ONLY) This is a compressed
              tar file of the testing directory (2328102 bytes).
              This cannot be retrieved via email.

timing.tar.z (FOR XNETLIB USERS ONLY) This is a compressed
              tar file of the timing directory (991735 bytes).
              This cannot be retrieved via email.

testing     - Subdirectory containing the testing routines for lapack.

timing      - Subdirectory containing the timing routines for lapack.

lawns       - Subdirectory containing the LAPACK Working Notes
              To find out what is available send mail in the form:
                     send index from lapack/lawns

index         This index

release_notes List of known problems, bugs, and compiler errors, as
              well as ERRATA for the LAPACK Users' Guide and the
              LAPACK code itself.

 *******************
 Questions/comments?  Direct email to [email-masked]
 *******************

 Jack Dongarra
 Susan Ostrouchov

 ========================================================================

 ***************
 WHAT IS LAPACK?
 ***************

 LAPACK is a transportable library of Fortran 77 subroutines for
 solving the most common problems in numerical linear algebra: systems
 of linear equations, linear least squares problems, eigenvalue problems,
 and singular value problems. It has been designed to be efficient
 on a wide range of modern high-performance computers.
 
 LAPACK is intended to be the successor to LINPACK and EISPACK.
 It extends the functionality of these packages 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 algorithms and software have been restructured to achieve high
 efficiency on vector processors, high-performance ``superscalar''
 workstations, and shared-memory multiprocessors. 
 A comprehensive testing and timing suite is provided along with the
 LAPACK software.
 
 The LAPACK Users' Guide will be published by SIAM and will be available
 in or around May, 1992.  LAPACK Users' Guide gives an informal
 introduction to the design of the algorithms and software, summarizes
 the contents of the package, and describes the conventions used in the 
 software and documentation, and includes complete specifications for 
 calling the routines.

 The complete LAPACK package can be obtained on magnetic media from NAG 
 for a nominal handling charge.  For further details contact NAG at one
 of the following addresses:
 
 NAG Inc                       NAG Ltd              NAG GmbH
 1400 Opus Place               Wilkinson House      Schleissheimerstrasse 5
 Suite 200                     Jordan Hill Road     W-8046 Garching bei Munchen
 Downers Grove, IL 60515-5702  Oxford OX2 8DR       Germany 
 USA                           England
 Tel: +1 708 971 2337          Tel: +44 865 511245  Tel: +49 89 3207395
 Fax: +1 708 971 2706          Fax: +44 865 310139  Fax: +49 89 3207396

 LAPACK has been funded in part by NSF, DOE, and DARPA, with
 developmental support from NAG Ltd., Cray Research, and many friends
 and colleagues around the world.

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 ========================================================================

 --------------
 About the BLAS
 --------------
 
 THE BLAS ARE NOT PROVIDED BY NETLIB WHEN LAPACK ROUTINES ARE REQUESTED.
 
 LAPACK routines are written so that as much as possible of the computation 
 is performed by calls to the Basic Linear Algebra Subprograms (BLAS).
 Highly efficient machine-specific implementations of the BLAS are
 available for many modern high-performance computers. The BLAS
 enable LAPACK routines to achieve high performance with portable software.
 
 The BLAS are not strictly speaking part of LAPACK, but Fortran 77 code
 for the BLAS is distributed with LAPACK, or can be obtained separately
 from  netlib:
 send index from cor 
 will retreive more information.  We consider the Fortran version the model 
 implementation and as such is not expected to perform as well as a specially 
 tuned implementation on most high-performance computers --- on some machines 
 it may give much worse performance ---  but it allows users to run LAPACK 
 software on machines that do not offer any other implementation of the BLAS.
 
 -------------
 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.

 ========================================================================

 Below is the list of available routines from LAPACK.  The
 routines are listed in two groups -- driver routines (simple
 and expert) and computational routines.  The driver routines are listed
 in the order in which they appear in the "LAPACK Quick Reference Guide
 to the Driver Routines".  The computational routines are listed in
 alphabetical order.  This index was compiled from Appendix A: "Index of
 Driver and Computational Routines" of the LAPACK Users' Guide.
 
 ========================================================================

 Available SIMPLE DRIVER routines:
 ---------------------------------

SGESV    Solves a general system of linear equations AX=B.
DGESV  
CGESV  
ZGESV  

SGBSV    Solves a general banded system of linear equations AX=B.
DGBSV  
CGBSV  
ZGBSV  

SGTSV    Solves a general tridiagonal system of linear equations AX=B.
DGTSV  
CGTSV  
ZGTSV  

SPOSV    Solves a symmetric/Hermitian positive definite system of linear
DPOSV    equations AX=B.
CPOSV  
ZPOSV  

SPPSV    Solves a symmetric/Hermitian positive definite system of linear
DPPSV    equations AX=B, where A is held in packed storage.
CPPSV  
ZPPSV  

SPBSV    Solves a symmetric/Hermitian positive definite banded system
DPBSV    of linear  equations AX=B.
CPBSV  
ZPBSV  

SPTSV    Solves a symmetric/Hermitian positive definite tridiagonal system
DPTSV    of linear equations AX=B.
CPTSV  
ZPTSV  

SSYSV    Solves a real symmetric/complex symmetric/complex Hermitian
DSYSV    indefinite system of linear equations AX=B.
CSYSV  
ZSYSV  
CHESV  
ZHESV  

SSPSV    Solves a real symmetric/complex symmetric/complex Hermitian
DSPSV    indefinite system of linear equations AX=B, where A is held
CSPSV    in packed storage.
ZSPSV   
CHPSV  
ZHPSV  

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

SGELSS   Computes the minimum norm least squares solution to an over-
DGELSS   or under-determined system of linear equations A X=B,  using
CGELSS   the singular value decomposition of A.
ZGELSS  

SSYEV    Computes all eigenvalues and eigenvectors of a symmetric/Hermitian
DSYEV    matrix.
CHEEV  
ZHEEV  

SSPEV    Computes all eigenvalues and eigenvectors of a symmetric/Hermitian
DSPEV    matrix in packed storage.
CHPEV  
ZHPEV  

SSBEV    Computes all eigenvalues and eigenvectors of a symmetric/Hermitian
DSBEV    band matrix.
CHBEV  
ZHBEV  

SSTEV    Computes all eigenvalues and eigenvectors of a real symmetric
DSTEV    tridiagonal matrix.

SGEES    Computes the eigenvalues and Schur factorization of a general
DGEES    matrix, and orders the factorization so that selected eigenvalues
CGEES    are at the top left of the Schur form.
ZGEES  

SGEEV    Computes the eigenvalues and left and right eigenvectors of
DGEEV    a general matrix.
CGEEV  
ZGEEV  

SGESVD   Computes the singular value decomposition (SVD) of a general
DGESVD   rectangular matrix.
CGESVD  
ZGESVD  

SSYGV    Computes all eigenvalues and the eigenvectors of  a generalized
DSYGV    symmetric/Hermitian-definite generalized eigenproblem,
CHEGV    Ax= lambda Bx,  ABx= lambda x,  or BAx= lambda x.
ZHEGV  

SSPGV    Computes all eigenvalues and eigenvectors of  a generalized
DSPGV    symmetric/Hermitian-definite generalized eigenproblem,  Ax= lambda
CHPGV    Bx,  ABx= lambda x,  or BAx= lambda x, where A and B are in packed
ZHPGV    storage.

 Available EXPERT DRIVER routines:
 ---------------------------------

SGESVX   Solves a general system of linear equations AX=B, A**T X=B
DGESVX   or A**H X=B, and provides an estimate of the condition number
CGESVX   and error bounds on the solution.
ZGESVX  

SGBSVX   Solves a general banded system of linear equations AX=B, A**T
DGBSVX   X=B or A**H X=B, and provides an estimate of the condition number
CGBSVX   and error bounds on the solution.
ZGBSVX  

SGTSVX   Solves a general tridiagonal system of linear equations AX=B,
DGTSVX   A**T X=B or A**H X=B, and provides an estimate of the condition
CGTSVX   number  and error bounds on the solution.
ZGTSVX  

SPOSVX   Solves a symmetric/Hermitian positive definite system of linear
DPOSVX   equations AX=B, and provides an estimate of the condition number
CPOSVX   and error bounds on the solution.
ZPOSVX  

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

SPBSVX   Solves a symmetric/Hermitian positive definite banded system
DPBSVX   of linear equations AX=B, and provides an estimate of the condition
CPBSVX   number and error bounds on the solution.
ZPBSVX  

SPTSVX   Solves a symmetric/Hermitian positive definite tridiagonal
DPTSVX   system of linear equations AX=B, and provides an estimate of
CPTSVX   the condition number and error bounds on the solution.
ZPTSVX  

SSYSVX   Solves a real symmetric/complex symmetric/complex Hermitian
DSYSVX   indefinite system  of linear equations AX=B, and provides an
CSYSVX   estimate of the condition number  and error bounds on the solution.
ZSYSVX  
CHESVX  
ZHESVX  

SSPSVX   Solves a real symmetric/complex symmetric/complex Hermitian
DSPSVX   indefinite system of linear equations AX=B, where A is held
CSPSVX   in packed storage, and provides an estimate of the condition
ZSPSVX   number and error bounds on the solution.
CHPSVX  
ZHPSVX  

SGELSX   Computes the minimum norm least squares solution to an over-
DGELSX   or under-determined system of linear equations A X=B, using a
CGELSX   complete orthogonal factorization of A.
ZGELSX  

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 real
DSTEVX   symmetric tridiagonal matrix.

SGEESX   Computes the eigenvalues and Schur factorization of a general
DGEESX   matrix, orders the factorization so that selected eigenvalues
CGEESX   are at the top left of the Schur form, and computes reciprocal
ZGEESX   condition numbers for the average of the selected eigenvalues,
         and for the associated right invariant subspace.

SGEEVX   Computes the eigenvalues and left and right eigenvectors of
DGEEVX   a general matrix,  with preliminary balancing of the matrix,
CGEEVX   and computes reciprocal condition numbers for the eigenvalues
ZGEEVX   and right eigenvectors.

 Available COMPUTATIONAL routines:
 ---------------------------------

SBDSQR   Computes the singular value decomposition (SVD) of a real bidiagonal
DBDSQR   matrix, using the bidiagonal QR algorithm.
CBDSQR  
ZBDSQR  

SGBCON   Estimates the reciprocal of the condition number of a general
DGBCON   band matrix,  in either the 1-norm or the infinity-norm, using
CGBCON   the LU factorization computed by SGBTRF/CGBTRF.
ZGBCON  

SGBEQU   Computes row and column scalings to equilibrate a general band
DGBEQU   matrix  and reduce its condition number.
CGBEQU  
ZGBEQU  

SGBRFS   Improves the computed solution to a general banded system of
DGBRFS   linear equations AX=B, A**T X=B or A**H X=B, and provides forward
CGBRFS   and backward error bounds for the solution.
ZGBRFS  

SGBTRF   Computes an LU factorization of a general band matrix, using
DGBTRF   partial pivoting with row interchanges.
CGBTRF  
ZGBTRF  

SGBTRS   Solves a general banded system of linear equations AX=B,
DGBTRS   A**T X=B or A**H X=B, using the LU factorization computed
CGBTRS   by SGBTRF/CGBTRF.
ZGBTRS  

SGEBAK   Transforms eigenvectors of a balanced matrix to those of the
DGEBAK   original matrix supplied to SGEBAL/CGEBAL.
CGEBAK  
ZGEBAK  

SGEBAL   Balances a general matrix in order to improve the accuracy
DGEBAL   of computed eigenvalues.
CGEBAL  
ZGEBAL  

SGEBRD   Reduces a general rectangular matrix to real bidiagonal form
DGEBRD   by an orthogonal/unitary transformation.
CGEBRD  
ZGEBRD  

SGECON   Estimates the reciprocal of the condition number of a general
DGECON   matrix, in either the 1-norm or the infinity-norm, using the
CGECON   LU factorization computed by SGETRF/CGETRF.
ZGECON  

SGEEQU   Computes row and column scalings to equilibrate a general
DGEEQU   rectangular matrix and reduce its condition number.
CGEEQU  
ZGEEQU  

SGEHRD   Reduces a general matrix to upper Hessenberg form by an
DGEHRD   orthogonal/unitary similarity transformation.
CGEHRD  
ZGEHRD  

SGELQF   Computes an LQ factorization of a general rectangular matrix.
DGELQF  
CGELQF  
ZGELQF  

SGEQLF   Computes a QL factorization of a general rectangular matrix.
DGEQLF  
CGEQLF  
ZGEQLF  

SGEQPF   Computes a QR factorization with column pivoting of a general
DGEQPF   rectangular matrix.
CGEQPF  
ZGEQPF  

SGEQRF   Computes a QR factorization of a general rectangular matrix.
DGEQRF  
CGEQRF  
ZGEQRF  

SGERFS   Improves the computed solution to a general system of linear
DGERFS   equations AX=B, A**T X=B or A**H X=B, and provides forward and
CGERFS   backward error bounds for the solution.
ZGERFS  

SGERQF   Computes an RQ factorization of a general rectangular matrix.
DGERQF  
CGERQF  
ZGERQF  

SGETRF   Computes an LU factorization of a general matrix, using partial
DGETRF   pivoting with row interchanges.
CGETRF  
ZGETRF  

SGETRI   Computes the inverse of a general matrix, using the LU factorization
DGETRI   computed by SGETRF/CGETRF.
CGETRI  
ZGETRI  

SGETRS   Solves a general system of linear equations AX=B, A**T X=B
DGETRS   or A**H X=B, using the LU factorization computed by SGETRF/CGETRF.
CGETRS  
ZGETRS  

SGTCON   Estimates the reciprocal of the condition number of a general
DGTCON   tridiagonal matrix, in either the 1-norm or the infinity-norm,
CGTCON   using the LU factorization computed by SGTTRF/CGTTRF.
ZGTCON  

SGTRFS   Improves the computed solution to a general tridiagonal system
DGTRFS   of linear equations AX=B, A**T X=B or A**H X=B, and provides
CGTRFS   forward and backward error bounds for the solution.
ZGTRFS  

SGTTRF   Computes an LU factorization of a general tridiagonal matrix,
DGTTRF   using partial pivoting with row interchanges.
CGTTRF  
ZGTTRF  

SGTTRS   Solves a general tridiagonal system of linear equations AX=B,
DGTTRS   A**T X=B or A**H X=B, using the LU factorization computed by
CGTTRS   SGTTRF/CGTTRF.
ZGTTRS  

SHSEIN   Computes specified right and/or left eigenvectors of an upper
DHSEIN   Hessenberg matrix by inverse iteration.
CHSEIN  
ZHSEIN  

SHSEQR   Computes the eigenvalues and Schur factorization of an upper
DHSEQR   Hessenberg matrix, using the multishift QR algorithm.
CHSEQR  
ZHSEQR  

SOPGTR   Generates the orthogonal/unitary transformation matrix from
DOPGTR   a reduction to tridiagonal form determined by SSPTRD/CHPTRD.
CUPGTR  
ZUPGTR  

SOPMTR   Multiplies a general matrix by the orthogonal/unitary
DOPMTR   transformation matrix from a reduction to tridiagonal form
CUPMTR   determined by SSPTRD/CHPTRD.
ZUPMTR  

SORGBR   Generates the orthogonal/unitary transformation matrices from
DORGBR   a reduction to bidiagonal form determined by SGEBRD/CGEBRD.
CUNGBR  
ZUNGBR  

SORGHR   Generates the orthogonal/unitary transformation matrix from
DORGHR   a reduction to Hessenberg form determined by SGEHRD/CGEHRD.
CUNGHR  
ZUNGHR  

SORGLQ   Generates all or part of the orthogonal/unitary matrix Q from
DORGLQ   an LQ factorization determined by SGELQF/CGELQF.
CUNGLQ  
ZUNGLQ  

SORGQL   Generates all or part of the orthogonal/unitary matrix Q from
DORGQL   a QL factorization determined by SGEQLF/CGEQLF.
CUNGQL  
ZUNGQL  

SORGQR   Generates all or part of the orthogonal/unitary matrix Q from
DORGQR   a QR factorization determined by SGEQRF/CGEQRF.
CUNGQR  
ZUNGQR  

SORGRQ   Generates all or part of the orthogonal/unitary matrix Q from
DORGRQ   an RQ factorization determined by SGERQF/CGERQF.
CUNGRQ  
ZUNGRQ  

SORGTR   Generates the orthogonal/unitary transformation matrix from
DORGTR   a reduction to tridiagonal form determined by SSYTRD/CHETRD.
CUNGTR  
ZUNGTR  

SORMBR   Multiplies a general matrix by one of the orthogonal/unitary
DORMBR   transformation  matrices from a reduction to bidiagonal form
CUNMBR   determined by SGEBRD/CGEBRD.
ZUNMBR  

SORMHR   Multiplies a general matrix by the orthogonal/unitary transformation
DORMHR   matrix from a reduction to Hessenberg form determined by SGEHRD/CGEHRD.
CUNMHR  
ZUNMHR  

SORMLQ   Multiplies a general matrix by the orthogonal/unitary matrix
DORMLQ   from an LQ factorization determined by SGELQF/CGELQF.
CUNMLQ  
ZUNMLQ  

SORMQL   Multiplies a general matrix by the orthogonal/unitary matrix
DORMQL   from a QL factorization determined by SGEQLF/CGEQLF.
CUNMQL  
ZUNMQL  

SORMQR   Multiplies a general matrix by the orthogonal/unitary matrix
DORMQR   from a QR factorization determined by SGEQRF/CGEQRF.
CUNMQR  
ZUNMQR  

SORMRQ   Multiplies a general matrix by the orthogonal/unitary matrix
DORMRQ   from an RQ factorization determined by SGERQF/CGERQF.
CUNMRQ  
ZUNMRQ  

SORMTR   Multiplies a general matrix by the orthogonal/unitary
DORMTR   transformation matrix from a reduction to tridiagonal form
CUNMTR   determined by SSYTRD/CHETRD.
ZUNMTR  

SPBCON   Estimates the reciprocal of the condition number of a
DPBCON   symmetric/Hermitian positive definite band matrix, using the
CPBCON   Cholesky factorization computed by SPBTRF/CPBTRF.
ZPBCON  

SPBEQU   Computes row and column scalings to equilibrate a symmetric/Hermitian
DPBEQU   positive definite band matrix and reduce its condition number.
CPBEQU  
ZPBEQU  

SPBRFS   Improves the computed solution to a symmetric/Hermitian positive
DPBRFS   definite banded system of linear equations AX=B, and provides
CPBRFS   forward and backward error bounds for the solution.
ZPBRFS  

SPBTRF   Computes the Cholesky factorization of a symmetric/Hermitian
DPBTRF   positive definite band matrix.
CPBTRF  
ZPBTRF  

SPBTRS   Solves a symmetric/Hermitian positive definite banded system
DPBTRS   of linear equations AX=B, using the Cholesky factorization
CPBTRS   computed by SPBTRF/CPBTRF.
ZPBTRS  

SPOCON   Estimates the reciprocal of the condition number of a
DPOCON   symmetric/Hermitian positive definite matrix, using the
CPOCON   Cholesky factorization computed by SPOTRF/CPOTRF.
ZPOCON   by SPOTRF/CPOTRF.

SPOEQU   Computes row and column scalings to equilibrate a symmetric/Hermitian
DPOEQU   positive definite matrix and reduce its condition number.
CPOEQU  
ZPOEQU  

SPORFS   Improves the computed solution to a symmetric/Hermitian positive
DPORFS   definite system of linear equations AX=B, and provides forward
CPORFS   and backward error bounds for the solution.
ZPORFS  

SPOTRF   Computes the Cholesky factorization of a symmetric/Hermitian
DPOTRF   positive definite matrix.
CPOTRF  
ZPOTRF  

SPOTRI   Computes the inverse of a symmetric/Hermitian positive definite
DPOTRI   matrix, using the Cholesky factorization computed by SPOTRF/CPOTRF.
CPOTRI  
ZPOTRI  

SPOTRS   Solves a symmetric/Hermitian positive definite system of linear
DPOTRS   equations AX=B, using the Cholesky factorization computed by
CPOTRS   SPOTRF/CPOTRF.
ZPOTRS  

SPPCON   Estimates the reciprocal of the condition number of a
DPPCON   symmetric/Hermitian positive definite matrix in packed storage,
CPPCON   using the Cholesky factorization computed by SPPTRF/CPPTRF.
ZPPCON  

SPPEQU   Computes row and column scalings to equilibrate a symmetric/Hermitian
DPPEQU   positive definite matrix in packed storage and reduce its condition
CPPEQU   number.
ZPPEQU  

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

SPPTRF   Computes the Cholesky factorization of a symmetric/Hermitian
DPPTRF   positive definite matrix in packed storage.
CPPTRF  
ZPPTRF  

SPPTRI   Computes the inverse of  a symmetric/Hermitian positive definite
DPPTRI   matrix in packed storage, using the Cholesky factorization computed
CPPTRI   by SPPTRF/CPPTRF.
ZPPTRI  

SPPTRS   Solves a symmetric/Hermitian positive definite system of linear
DPPTRS   equations AX=B, where A is held in packed storage, using the
CPPTRS   Cholesky factorization computed by SPPTRF/CPPTRF.
ZPPTRS  

SPTCON   Computes the reciprocal of the condition number of a
DPTCON   symmetric/Hermitian positive definite tridiagonal matrix,
CPTCON   using the LDL**H factorization computed by SPTTRF/CPTTRF.
ZPTCON  

SPTEQR   Computes all eigenvalues and eigenvectors of a real symmetric
DPTEQR   positive definite tridiagonal matrix, by computing the SVD of
CPTEQR   its bidiagonal Cholesky factor.
ZPTEQR  

SPTRFS   Improves the computed solution to a symmetric/Hermitian positive
DPTRFS   definite tridiagonal system of linear equations AX=B, and provides
CPTRFS   forward and backward error bounds for the solution.
ZPTRFS  

SPTTRF   Computes the LDL**H factorization of a symmetric/Hermitian
DPTTRF   positive definite tridiagonal matrix.
CPTTRF  
ZPTTRF  

SPTTRS   Solves a symmetric/Hermitian positive definite tridiagonal
DPTTRS   system of linear equations, using the LDL**H factorization
CPTTRS   computed by SPTTRF/CPTTRF.
ZPTTRS  

SSBTRD   Reduces a symmetric/Hermitian band matrix to real symmetric
DSBTRD   tridiagonal form by an orthogonal/unitary similarity transformation.
CHBTRD  
ZHBTRD  

SSPCON   Estimates the reciprocal of the condition number of a real
DSPCON   symmetric/complex symmetric/complex Hermitian indefinite
CSPCON   matrix in packed storage, using the factorization computed
ZSPCON   by SSPTRF/CSPTRF/CHPTRF.
CHPCON  
ZHPCON  

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

SSPRFS   Improves the computed solution to  a real symmetric/complex
DSPRFS   symmetric/complex Hermitian indefinite system of linear equations
CSPRFS   AX=B, where A is held in packed storage, and provides forward
ZSPRFS   and backward error bounds for the solution.
CHPRFS  
ZHPRFS  

SSPTRD   Reduces a symmetric/Hermitian matrix in packed storage to real
DSPTRD   symmetric tridiagonal form by an orthogonal/unitary similarity
CHPTRD   transformation.
ZHPTRD  

SSPTRF   Computes the factorization of a real symmetric/complex
DSPTRF   symmetric/complex Hermitian-indefinite matrix in packed storage,
CSPTRF   using the diagonal pivoting method.
ZSPTRF  
CHPTRF  
ZHPTRF  

SSPTRI   Computes the inverse of a real symmetric/complex symmetric/complex
DSPTRI   Hermitian indefinite matrix in packed storage, using the factorization
CSPTRI   computed by SSPTRF/CSPTRF/CHPTRF.
ZSPTRI  
CHPTRI  
ZHPTRI  

SSPTRS   Solves a real symmetric/complex symmetric/complex Hermitian
DSPTRS   indefinite system of linear equations AX=B, where A is held
CSPTRS   in packed storage, using the factorization computed
ZSPTRS   by SSPTRF/CSPTRF/CHPTRF.
CHPTRS  
ZHPTRS  

SSTEBZ   Computes selected eigenvalues of a real symmetric tridiagonal
DSTEBZ   matrix by bisection.

SSTEIN   Computes selected eigenvectors of a real symmetric tridiagonal
DSTEIN   matrix by inverse iteration.
CSTEIN  
ZSTEIN  

SSTEQR   Computes all eigenvalues and eigenvectors of a real symmetric
DSTEQR   tridiagonal matrix, using the implicit QL or QR algorithm.
CSTEQR  
ZSTEQR  

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

SSYCON   Estimates the reciprocal of the condition number of a real
DSYCON   symmetric/complex symmetric/complex Hermitian indefinite matrix,
CSYCON   using the factorization computed by SSYTRF/CSYTRF/CHETRF.
ZSYCON  
CHECON  
ZHECON  

SSYGST   Reduces a symmetric/Hermitian-definite generalized eigenproblem
DSYGST   Ax= lambda Bx,  ABx= lambda x,  or BAx= lambda x, to standard
CHEGST   form, where B has been factorized by SPOTRF/CPOTRF.
ZHEGST  

SSYRFS   Improves the computed solution to  a real symmetric/complex
DSYRFS   symmetric/complex Hermitian indefinite system of linear equations
CSYRFS   AX=B, and provides forward and backward error bounds for the
ZSYRFS   solution.
CHERFS  
ZHERFS  

SSYTRD   Reduces a symmetric/Hermitian matrix to real symmetric tridiagonal
DSYTRD   form by an orthogonal/unitary similarity transformation.
CHETRD  
ZHETRD  

SSYTRF   Computes the factorization of a real symmetric/complex
DSYTRF   symmetric/complex Hermitian-indefinite matrix, using the
CSYTRF   diagonal pivoting method.
ZSYTRF  
CHETRF  
ZHETRF  

SSYTRI   Computes the inverse of a real symmetric/complex symmetric/complex
DSYTRI   Hermitian indefinite matrix, using the factorization computed
CSYTRI   by SSYTRF/CSYTRF/CHETRF.
ZSYTRI  
CHETRI  
ZHETRI  

SSYTRS   Solves a real symmetric/complex symmetric/complex Hermitian
DSYTRS   indefinite system of linear equations AX=B, using the factorization
CSYTRS   computed by SSPTRF/CSPTRF/CHPTRF.
ZSYTRS  
CHETRS  
ZHETRS  

STBCON   Estimates the reciprocal of the condition number of a triangular
DTBCON   band matrix, in either the 1-norm or the infinity-norm.
CTBCON  
ZTBCON  

STBRFS   Provides forward and backward error bounds for the solution
DTBRFS   of a triangular banded system of linear equations AX=B,
CTBRFS   A**T X=B or A**H X=B.
ZTBRFS  

STBTRS   Solves a triangular banded system of linear equations AX=B,
DTBTRS   A**T X=B or A**H X=B.
CTBTRS  
ZTBTRS  

STPCON   Estimates the reciprocal of the condition number of a triangular
DTPCON   matrix in packed storage, in either the 1-norm or the infinity-norm.
CTPCON  
ZTPCON  

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

STPTRI   Computes the inverse of a triangular matrix in packed storage.
DTPTRI  
CTPTRI  
ZTPTRI  

STPTRS   Solves a triangular system of linear equations AX=B,
DTPTRS   A**T X=B or A**H X=B, where A is held in packed storage.
CTPTRS  
ZTPTRS  

STRCON   Estimates the reciprocal of the condition number of a triangular
DTRCON   matrix, in either the 1-norm or the infinity-norm.
CTRCON  
ZTRCON  

STREVC   Computes left and right eigenvectors of an upper
DTREVC   quasi-triangular/triangular matrix.
CTREVC  
ZTREVC  

STREXC   Reorders the Schur factorization of a matrix by a unitary
DTREXC   similarity transformation.
CTREXC  
ZTREXC  

STRRFS   Provides forward and backward error bounds for the solution
DTRRFS   of a triangular system of linear equations A X=B, A**T X=B or
CTRRFS   A**H X=B.
ZTRRFS  

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

STRSNA   Estimates the reciprocal condition numbers (sensitivities)
DTRSNA   of selected eigenvalues and eigenvectors of an upper
CTRSNA   quasi-triangular/triangular matrix.
ZTRSNA  

STRSYL   Solves the Sylvester matrix equation A X +/- X B=C where A
DTRSYL   and B are upper quasi-triangular/triangular, and may be transposed.
CTRSYL  
ZTRSYL  

STRTRI   Computes the inverse of a triangular matrix.
DTRTRI  
CTRTRI  
ZTRTRI  

STRTRS   Solves a triangular system of linear equations AX=B,
DTRTRS   A**T X=B or A**H X=B.
CTRTRS  
ZTRTRS  

STZRQF   Computes an RQ factorization of an upper trapezoidal matrix.
DTZRQF  
CTZRQF  
ZTZRQF  
CUT HERE..........