A small numerical analysis library in Common Lisp

Gene Michael Stover

created Saturday, 2007 January 6
updated Monday, 2007 January 22

Copyright © 2007 Gene Michael Stover. All rights reserved. Permission to copy, store, & view this document unmodified & in its entirety is granted.

Contents

• 1 What is this?
• 2 License
• 3 Examples of use
• 4 Obtaining
• 5 How to use it
• A. Other File Formats
• Bibliography

1 What is this?

fixme: As of 2007 January 6, this is unfinished. In fact, it's just started. It's an experimental work in progress.

This is a small library to approximate perform some ``numerical analysis'' calculations, which include:

• interpolating polynomials over one variable &
• approximating numerical solutions to linear systems.

This library is small & provides a few specific features which I needed for a special case¹. It is probably most useful if you have an application in which you need only a few types of numerical analysis operations & your data sets aren't large. For more demanding numerical analysis needs, look at the ``mathematics'' entry at CL$^{iki}$ the common lisp wiki.

2 License

The library is licensed according to the Gnu Lesser General Public License. [2] The text of that agreement is at http://www.gnu.org/licenses/licenses.html#LGPL.

This documentation (which are are reading now) is not covered by an open source license. See the copyright notice at the top of this document.

3 Examples of use

Most (all?) of the algorithms in the library are from Numerical Analysis by Burden & Faires. [1]

4 Obtaining

• matrix.lisp
• numerical-analysis.lisp
• loadall.lisp
• my Lisp unit test framework [3]

5 How to use it

1. Download the source file from http://cybertiggyr.com/gene/big/bigo.lisp.
2. You might want loadall.lisp.²

3. Youw will need test.lisp from My Lisp Unit Test Framework [3].

4. Load test.lisp into your Lisp. Then load bigo.lisp into your Lisp. loadall.lisp does this.
5. Obtain your performance measurements. They must be in the form of a list of two-list elements. Each two-list element consists of a FIRST which is the size of the input & a SECOND which is the cost. The cost can be number of times some function was called, the amount of wall-time required for your function to run, the amount of memory it used, or whatever else you want to measure. Let's assume that you bound your measurements to a global variable called *MEASUREMENT*.

6. (in-package "COM.CYBERTIGGYR.BIGO")

7. (bigo *measurement*)

8. The string you get in return will be he Big-O cost for the function you measured. The string is formatted for L^ATEX.

A. Other File Formats

• This document is available in multi-file HTML format at
  http://cybertiggyr.com/gene/linear/.
• This document is available in Pointless Document Format (PDF) at
  http://cybertiggyr.com/gene/linear/linear.pdf.

Bibliography

1

Richard L. Burden - J. Douglass Faires.
Numerical Analysis.
PWS-KENT Publishing Company, fourth edition, 1989.
ISBN 0-53491-585-X.

2

Free Software Foundation.
Lesser general public license.
world wide web.
http://www.gnu.org/licenses/licenses.html#LGPL.

3

Gene Michael Stover.
My lisp unit test framework.
cybertiggyr.com/gene, June 2005.
http://cybertiggyr.com/gene/lut/.