# ====================================================================== # LAPACK, Version 1.0 Date: February 29, 1992 # LAPACK, Version 1.0a Date: June 30, 1992 # LAPACK, Version 1.0b Date: October 31, 1992 # LAPACK, Version 1.1 Date: March 31, 1993 # LAPACK, Version 2.0 Date: September 30, 1994 # LAPACK, Version 3.0 Date: June 30, 1999 # ====================================================================== # # ( 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: # ------------------- file lapack/lapack.tgz for LAPACK, version 3.0 , This is the COMPLETE package , (installation, testing, and timing) in tar gzip , form (4902944 bytes). All revisions included. , This cannot be retrieved via email. , Updated: June 30, 1999 file lapack/lapack-pc-df.zip for LAPACK, version 3.0 for Windows , Using Microsoft nmake and Digital Fortran compiler , Updated: August 9, 1999 file lapack/lapack-pc-wfc.zip for LAPACK, version 3.0 for Windows , Using Microsoft nmake and Watcom Fortran 77/32 compiler version 11.0 , Updated: August 3, 1999 file lapack/testing.tgz for This is a gzip tar file of the testing directory , (1533649 bytes). , This cannot be retrieved via email. file lapack/timing.tgz for This is a gzip tar file of the timing directory , (984426 bytes). , This cannot be retrieved via email. # ------------------- # Individual Routines: # ------------------- lib lapack/single for single precision real LAPACK routines prec single lib lapack/double for double precision real LAPACK routines prec double lib lapack/complex for single precision complex LAPACK routines prec complex lib lapack/complex16 for double precision complex LAPACK routines prec doublecomplex lib lapack/util for LAPACK utility routines lib lapack/testing for Subdirectory containing the testing routines for lapack. lib lapack/timing for Subdirectory containing the timing routines for lapack. # ------------------------- # Prebuilt LAPACK libraries: # ------------------------- lib lapack/archives for Subdirectory containing prebuilt LAPACK libraries , !! Updated for LAPACK, version 3.0!! # -------------- # Documentation: # -------------- file lapack/lapackqref.ps for LAPACK Quick Reference Guide to the Driver Routines , (VERSION 3.0) , !! NOT AVAILABLE YET!! (still contains version 2.0) file lapack/lawns/lawn81.ps for LAPACK Working Note 81: Quick Installation Guide for LAPACK , on Unix Systems , (25 pages) , Updated: June, 1999. (VERSION 3.0) file lapack/lawns/lawn41.ps for LAPACK Working Note 41: LAPACK Installation Guide , (149 pages) , Updated: June, 1999 (VERSION 3.0) file lapack/manpages.tgz for This is a gzip tar , file of the manual pages for the LAPACK driver and , computational routines. Also included is an , equivalence program, giving conversion equivalence , information for LINPACK and EISPACK to LAPACK. , (727193 bytes). This cannot be retrieved via email. file lapack/revisions.info for Text file explaining the changes that were made to the , LAPACK software in version 3.0. file lapack/release_notes for List of known problems, bugs, and compiler errors, as , well as ERRATA for the LAPACK Users' Guide and the , LAPACK code itself. , Last UPDATED: August 10, 1999 lib lapack/lawns for Subdirectory containing the LAPACK Working Notes , To find out what is available and retrieve a postscript copy , of these reports, send mail in the form: , send index from lapack/lawns , send lawnxx from lapack/lawns , These reports are kept only at netlib@www.netlib.org lib lapack/lawnspdf for Subdirectory containing pdf versions of the LAPACK Working Notes , To find out what is available and retrieve a postscript copy , of these reports, send mail in the form: , send index from lapack/lawnspdf , send lawnxx from lapack/lawnspdf , These reports are kept only at netlib@www.netlib.org # ----------------- # Related Projects: # ----------------- lib lapack/essl for Subdirectory containing CCI (Call Conversion Interface) for , LAPACK/ESSL. , See lawn82 for more information. # For the Fortran90 interface to LAPACK see directory lapack90 lib lapack90 for LAPACK90 is the Fortran90 interface to LAPACK. by Jerzy Wasniewski # For a c++ implementation of LAPACK see directory lapack++ lib lapack++ for LAPACK++. LAPACK extensions for high performance linear , algebra computations. This version includes support for solving , linear systems using LU, Cholesky, and QR matrix factorizations. by Roldan Pozo # For an f2c'ed conversion of LAPACK see directory clapack lib clapack for CLAPACK. An f2c'ed conversion of LAPACK. # For a distributed-memory implementation of LAPACK see directory scalapack lib scalapack for ScaLAPACK. A portable implementation of some of the core , routines in LAPACK across MPI, PVM, Intel Paragon, IBM SP, and SGI O2K. # ******************* # Questions/comments? Direct email to lapack@cs.utk.edu # ******************* # Jack Dongarra # Susan Blackford # ====================================================================== # *************** # 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. # It is highly recommended that you obtain a copy of the Second Edition of # the LAPACK Users' Guide published by SIAM in February 1995. This Users' # Guide gives a detailed description of the philosophy behind LAPACK as well # as an explanation of its usage. The LAPACK Users' Guide can be purchased # from: # SIAM # 3600 University City Science Center # Philadelphia, PA 19104-2688 # 215-382-9800, FAX 215-386-7999. # It will also be available from booksellers. # To order by email, send email to service@siam.org. The book is also # available via SIAM's World Wide Web URL at http://www.siam.org. The # ISBN number is 0-89871-345-5, and SIAM order code is OT46. The list # price for SIAM members is $22.80; the cost for nonmembers is $28.50. # # To view an HTML version of the Users' Guide please refer to the URL # # http://www.netlib.org/lapack/lug/lapack_lug.html. # 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. # ( l l l l ) # ( a -a a -a ) # 1/4 * ( p p -p -p ) # ( a -a -a a ) # ( c c -c -c ) # ( k -k -k k ) # ====================================================================== # -------------- # 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 blas # will retrieve 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. # ====================================================================== .