by Kamran Husain

IN THIS CHAPTER

• Scilab

• Pari

• Using LISP-STAT

• A Last Note

This book has dealt with many issues regarding the tools available for Linux. Now, let's look at some of the mathematics tools for Linux. Specifically, we will work with tools for doing mathe-matical and statistical applications under Linux. One such tool we will be working with is Scilab, an interactive math and graphics package. Another tool for symbolic math is Pari. For statistical operations using LISP choose LISP-STAT.

Hopefully, this chapter will give you a comfortable alternative to writing applications in languages other than FORTRAN on Linux. (The FORTRAN compiler is called f77.)

The Scilab application is developed by the Institut National de Recherche de Informatique et en Automatique (INRIA) in France. Although this application is not as formidable as MATLAB, a commercial product with more bells and whistles, Scilab is still powerful enough to provide decent graphics and solutions to math problems.

With Scilab you can do matrix multiplication, plot graphs, and so on. Using its built-in functions, Scilab enables you to write your own functions. With its toolbox, you can build your own signal-processing functions in addition to those provided by Scilab.

Added to all its features, the help file is quite voluminous. If you want to find out how to do a math problem with Scilab, you will probably find it in the docs. Added to the good documentation are sample programs to get you started.

Now that you are probably interested in Scilab, you will want to know where to get it. Scilab is free via the Internet. The primary site is ftp.inria.fr, and the directory for this is in INRIA/Projects/Meta2/Scilab. Look for the zipped file with the latest date. Each zipped file is complete in itself. Mirror sites include sunsite.unc.edu and tsx-11.mit.edu.

The file you are looking for is called scilab-2.1.1-linux.tar.gz. In its unzipped form, the file is about 17MB in size. After utarring this file, you will have a directory called scilab-2.1.1 with all related files and accessories.

After you have installed it, go to the bin subdirectory and modify the Scilab shell script file. Replace the assignment of the SCI variable with the path to the location of your Scilab files. For example, in my case I set the value to

SCI="/home/khusain/scilab-2.1.1"

The prompt for Scilab is -->. You will see responses to your commands immediately below where you type in entries.

A healthy example of how to use Scilab would probably be beneficial. Let's see how to declare values:

-->x=1.0

This sets x equal to 1.0. To declare an array, use square brackets:

-->x=[1 2 3]

x =

!  1. 2. 3. !

The documentation for the Scilab application is in the doc/intro directory where you installed Scilab. It contains a PostScript document called intro.ps which contains the user's manual titled Introduction to Scilab. Take time to read this manual carefully.

For a list of all the available functions in Scilab, you can look in the man/LaTex-doc directory for a PostScript file called Docu.ps. (Yes, the file names are cryptic!) Print this file for a handy paper list of all the available functions. All these functions are still accessible from the help buttons in the front panel.

The Pari package is useful for doing symbolic mathematical operations. Its primary features include an arbitrary precision calculator, its own programming facilities, and interfaces to C libraries.

To get Pari, use the FTP site megrez.math.u-bordeaux.fr, and from the /pub/pari/unix directory get the gplinux.tar.gz file. The binaries may not work with a later version of Linux because the binaries are built with older versions of shared libraries. If you have a newer version of Linux than the one supported by Pari, either you can edit the sources yourself or wait until the authors of Pari catch up. Sorry.

With the version of Linux on the CD-ROM at the back of this book, you need to compile your own version of Pari. The source files are in the pari-1.39.03.tar.gz file. The source tar file unpacks into three directories: src, doc, and samples. You will find the samples very useful indeed.

To compile the sources, run the Makemakefile command in the src directory. When creating this version, remove the definition of the option -DULONG_NOT_DEFINED from the CFLAGS macro in the newly created Makefile. Then type make at the prompt. Be prepared to wait a while for this package to compile.

After you have installed the source files for Pari, type gp at the console prompt. Your prompt will be a question mark (?). Start by typing simple arithmetic expressions at this prompt. You should be rewarded with answers immediately. Let's look at the following sample session:

? 4*8

%1=32

? 4/7*5/6

%2=10/21

The answer was returned to us in fractions. To get real numbers, introduce just one real number in the equation. You will then get the answer as a real number. The percent signs identify the returned line numbers.

? 4.0/7 * 5/6

%3=0.476190476190476190476190

To set the precision in number of digits, you use the ?\precision command. The maximum number of digits is 315,623, a large number for just about all users. For a modest precision of 10 digits to the right of the decimal point, use this:

?\precision=10

? 4.0/7*5/6

%4=0.476190047

You can even work with expressions, as shown in the following example:

? (x+2)*(x+3)

%5=x^2+5*x+6

You can assign values to variables to get the correct answer from evaluating an expression:

? x=3

%6=3

? eval(%5)

%7=60

This is not where the power of Pari ends, though. You can factor numbers, solve differential equations, and even factor polynomials. The FTP site for Pari contains a wealth of information and samples. See megrez.math.u-bordeaux.fr. Also, the docs directory contains samples and the manual to help you get started.

For statistical computing, consider using LISP-STAT. Written by Luke Tierney at the University of Minnesota, LISP-STAT is a very powerful, interactive, object-oriented LISP package.

The LISP-STAT package is available from ftp.stat.umn.edu in the /pub/xlispstat directory. Get the latest tar file version you can--currently, xlispstat-3-44.tar.gz. In order to build this file you need the dld library for Linux. This dld library is found in tsx-11.mit.edu in the /pub/linux/binaries/libs directory as dld-3.2.5.bin.tar.gz. Install this dld library in the /lib directory first.

At the command prompt in an Xterm, type xlispstat. You will be presented with a > prompt. Type commands at this prompt. For example, to multiply two matrices together, use the following command:

> (def a (matrix `(3 3) `(2 5 7 1 2 3 1 1 2)))

A

> (def b (matrix `(3 1) `(4 5 6)))

B

> (matmult a b)

#2A((75.0) (32.0) (21))

The variables in LISP-STAT are not case sensitive. Note the single quote (`) before the list of numbers for the matrix. If you omit the quote, the list will be evaluated and replaced with the result of the evaluation. By leaving the single quote in there, you are forcing the interpreter to leave the list in its place.

Let's try solving a simple set of linear equations using LISP-STAT. The following would be a simple example to solve:

3.8x + 7.2y = 16.5

1.3x - 0.9y = -22.1

The following script would set up and solve this linear equation problem:

> (def a (matrix `(2 2) `(3.8 7.2 1.3 -0.9)))

A

> (def b (matrix `(2 1) `(16.5 -22.1)))

B

> (matmult (inverse a) b)

#2A((-11.288732394366198) (8.249608763693271))

You can do other math operations on lists of numbers as well. See the following example for calculating the mean of a list of numbers:

> (def sm (list 1.1 2.3 4.1 5.7 2.1))

SM

> (mean SM)

3.06

There are many plotting functions available for LISP-STAT. For plotting one variable, try the function plot-function. For (x,y) pairs of numbers, use the plot-lines function. For a function of two variables, use the spin-function. For 3-D plots, use the spin-plot function.

You can get a considerable amount of information from the documents available online at the FTP site ftp.stat.ucla.edu (in directory /pub/lisp/xlisp/xlisp-stat/docs) or in the Web page at http://euler.bd.psu.edu. For more information, read the book LISP-STAT by Luke Tierney (John Wiley).