SpYorick 0.1b

Table of contents

• Introduction
• Prerequisites
• Installing
• License
• The package
• The author
• Bibliography

What is it?

It is a plugin package for Yorick (>= version 1.4) that, among other interesting things, adds functions that operate both on dense and sparse matrices.

What is a sparse matrix?

Well, if you don't know what it is then this product is probably not for you. A sparse matrix is a matrix which is mostly filled with zeros. This allows us to store that matrix in a more compact form, reducing memory use and increasing computational speed in linear algebra operations.

What formats does SpYorick support?

I've been studying many different formats. I pretty like Scilab's coordinate storage, where the row index, the column index and the value are stored. It is easy to use and allows one to do most operations in a high order level (without using too much C). However it eats too much memory.

Thus, I opted form Compressed Row Storage [1] format, which is a bit more complicated but works extremely well for doing operations between matrices and vectors, and not so well for matrix <-> matrix operations.

Note: as a side note, I must say that linked list format is used when solving a linear system of equations. The reason why this format is not employed in the rest of the package is simply that Yorick lacks a good garbage collector, and is based on a sort of reference counting one, which is hard to use and --to me-- error prone.

What can SpYorick do with sparse matrices?

Currently there's only one big absence: matrix product. The supported operations that have to do with sparse matrices are:

• Creation: dense <-> sparse conversions, diagonal matrices.
• Unary operations: transposition, adjoint, complex conjugation, promotion to complex.
• Binary operations: addition, substraction, product by vector and by scalar,kronecker product.
• Iterative solvers: conjugate gradient.
• Direct solvers: gaussian elimination.

And what else does it supply?

Well, there are a lot of other interesting additions, such as:

• Small functions which are missing in Yorick: imag(), real(), etc.
• Functions for calculating norms and escalar products.
• User friendly bindings to the LAPACK library for diagonalizing matrices, either real or complex.
• User friendly bindings to the FFTW-2.0 library for performing fast in/out-of-place Fast Fourier Transforms of complex vectors.

There are a number of things that you must get in order to install SpYorick:

• Some version of Unix. I don't know how to do all this under Windows and, folks, I don't even want to!
• Yorick (>= 1.4). You need a version which is properly installed. You don't need the sources, just a working Yorick.
• LAPACK. Please install a library that has been compiled with G77. RedHat's contributed RPM/SRPM is broken so please grab Debian's sources for LAPACK together with the corresponding *.diff file and build it in your system.
• FFTW-2.0. You can get it at the FFTW home site

In principle it should be possible to build SpYorick without some of these additions: it's just a matter of tweaking MyMakefile a bit. However, I've had not time to do this in a more friendly way.

• Get and install Yorick (>= 1.4) and the other libraries.
• Unpack the SpYorick package.
• Get into the spyorick directory and configure the system by issuing:

  	  make -f MyMakefile
  	

• You are ready to work from that directory:

  	  $ cd tests
  	  $ ../spyorick
  	  Copyright (c) 1996.  The Regents of the University of California.
  	  All rights reserved.  Yorick 1.4 ready.  For help type 'help'
  	  > #include "all.i"
  	  "TESTING SPARSE CREATION (double)"
  	  "================================"
  	  "1) double"
  	  "   size = "  2  "; sparse <-> full ok!"
  	  "   size = "  4  "; sparse <-> full ok!"
  	  [... and a whole bunch of output]
  	

  or you can do a

  	  make -f MyMakefile install
  	

  that will copy the executable, plus `sparse.i', plus `cg.i' to the appropiate places in your $HOME directory.

Copyright (c) Juan Jose Garcia Ripoll.
All rights reserved.

Redistribution and use in source and binary forms, with or
without modification, are permitted provided that the following
conditions are met:

1. Redistributions of source code must retain the above copyright
   notice, this list of conditions and the following disclaimer.

2. Redistributions in binary form must reproduce the above
   copyright notice, this list of conditions and the following
   disclaimer in the documentation and/or other materials provided
   with the distribution.

3. All advertising materials mentioning features or use of this
   software must display the following acknowledgement:
	This product includes software developed by Juan Jose
	Garcia Ripoll.

4. The name of Juan Jose Garcia Ripoll may not be used to endorse
   or promote products derived from this software without
   specific prior written permission.

THIS SOFTWARE IS PROVIDED BY JUAN JOSE GARCIA RIPOLL ``AS IS''
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL HE BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE.
    

      Juan Jose Garcia Ripoll
      E.T.S.I. Industriales
      Univ. Castilla-La Mancha
      c/Camilo Jose Cela
      E-13071 Ciudad Real
      Spain
      
      job:  jjgarcia@ind-cr.uclm.es
      home: worm@arrakis.es
      www:  http://www.arrakis.es/~worm
    

[1] R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, H. Van der Vorst. "Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods", SIAM (1994). (Available at http://www.netlib.org/templates/Templates.html)