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( 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) |
( 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 )
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[LICENSE]LAPACK is written in Fortran90 and provides routines for solving systems of simultaneous linear equations, least-squares solutions of linear systems of equations, eigenvalue problems, and singular value problems. The associated matrix factorizations (LU, Cholesky, QR, SVD, Schur, generalized Schur) are also provided, as are related computations such as reordering of the Schur factorizations and estimating condition numbers. Dense and banded matrices are handled, but not general sparse matrices. In all areas, similar functionality is provided for real and complex matrices, in both single and double precision.
If you're uncertain of the LAPACK routine name to address your application's needs, check out the LAPACK Search Engine.
The original goal of the LAPACK project was to make the widely used EISPACK and LINPACK libraries run efficiently on shared-memory vector and parallel processors. On these machines, LINPACK and EISPACK are inefficient because their memory access patterns disregard the multi-layered memory hierarchies of the machines, thereby spending too much time moving data instead of doing useful floating-point operations. LAPACK addresses this problem by reorganizing the algorithms to use block matrix operations, such as matrix multiplication, in the innermost loops. These block operations can be optimized for each architecture to account for the memory hierarchy, and so provide a transportable way to achieve high efficiency on diverse modern machines. We use the term "transportable" instead of "portable" because, for fastest possible performance, LAPACK requires that highly optimized block matrix operations be already implemented on each machine.
LAPACK routines are written so that as much as possible of the computation is performed by calls to the Basic Linear Algebra Subprograms (BLAS). While LINPACK and EISPACK are based on the vector operation kernels of the Level 1 BLAS, LAPACK was designed at the outset to exploit the Level 3 BLAS -- a set of specifications for Fortran subprograms that do various types of matrix multiplication and the solution of triangular systems with multiple right-hand sides. Because of the coarse granularity of the Level 3 BLAS operations, their use promotes high efficiency on many high-performance computers, particularly if specially coded implementations are provided by the manufacturer.
Highly efficient machine-specific implementations of the BLAS are available for many modern high-performance computers. For details of known vendor- or ISV-provided BLAS, consult the BLAS FAQ. Alternatively, the user can download ATLAS to automatically generate an optimized BLAS library for the architecture. A Fortran77 reference implementation of the BLAS in available from netlib; however, its use is discouraged as it will not perform as well as a specially tuned implementation.
Acknowledgements: Since 2004, this material is based upon work supported by the National Science Foundation under Grant No. NSF-0444486 Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF). Until 2001, this material was based upon work supported by the National Science Foundation under Grant No. ASC-9313958 and DOE Grant No. DE-FG03-94ER25219. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF) or the Department of Energy (DOE).
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[LICENSE]# ====================================================================== # 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 # LAPACK, Version 3.0 (update) Date: October 31, 1999 # LAPACK, Version 3.0 (update) Date: May 31, 2000 # LAPACK, Version 3.1 Date: November 12, 2006 # LAPACK, Version 3.1.1 Date: February 26, 2007 # LAPACK, Version 3.2 Date: November 18, 2008 # LAPACK, Version 3.2.1 Date: April 17, 2009 # LAPACK, Version 3.2.2 Date: June 30, 2010 # LAPACK, Version 3.3.0 Date: Nov 14, 2010 # ====================================================================== # # ------------------- # SVN Access: # ------------------- svn co http://icl.cs.utk.edu/svn/lapack-dev/lapack/trunk # ------------------- # Available software: # ------------------- file lapack.tgz for LAPACK, version 3.3.0 , All revisions included. , Please refer to lapack-3.3.0.html file for release notes on release 3.3.0 , Updated: November 14, 2010 --> NEW: Standard C language APIs for LAPACK ( collaboration LAPACK and INTEL Math Kernel Library) file lapacke.tgz for LAPACK C INTERFACE, version 1.0.0.009 , Corresponds to Intel MKL 10.3 product , Updated: November 14, 2010 file lapack-3.2.2.tgz for LAPACK, version 3.2.2 , This is the package without html pages and manpages (installation and testing) in tar gzip form. 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