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MOOMBA: Modern, Object-Oriented Math(s)-Based Algorithms

Written by Daniel Prager.

Version 0.1

• SmallEiffel -0.78betax
• October 1999.
• Eiffel Forum Freeware License.

moomba-v01.zip 219 ( kilobytes) - source code
Daniel.Prager@cmis.csiro.au Daniel Prager (maintainer) mail address.

The MOOMBA project is envisaged as a place to collect together clean, correct, changeable, mathematical algorithms and applications.

It would be an Open Source project.

Objectives

• Correctness - Well-defined; safe to use
• Clarity - Not arcane, but rather informative and clear enough to encourage stimulating debate
• Practical - For fun, education, research and industry
• Wide-ranging - Lot's of useful stuff
• Alive - A project that people can get involved in

Technical

• Primary implementation language is Eiffel - modern, safe and clear
• Bindings to other languages encouraged
• Benchmarking encouraged - how does MOOMBA compare to NAG, IMSL, Mathematica etc?

Library classes (Highlights only)

• COMPLEX - complex numbers
• FOURIERIZABLE_VECTOR - fourier transforms (FFT)

Applications

• COMPLEX_TEST
• FOURIER_TEST

I have compiled these programs using the lastest SmallEiffel on Windows 98 and Windows NT. There are some problems with C-code-generation, so I recommend compilation with require_checks (or lower) if problems arise.

Status

This has been an exercise for me to learn a bit more about Eiffel, OO, and the FFT algorithm.

More ambitiously, I believe that there would be tremendous spin-offs if a library was constructed in Eiffel that implemented --- and in the process classified --- a broad selection of useful numerical algorithms/structures without significant use of external routines. I expect that such a library would complement EiffelMath nicely.

Pipe-dream ;-) Some very rudimentary classes (see above).

Requires

• Contributors
• Target applications and clusters
• Some organization

References

• Press et al, Numerical Recipes in [Pascal | C]
• Strang, Linear algebra

FOURIERIZABLE_VECTOR

A FOURIERIZABLE_VECTOR has two "forms", corresponding to -- say -- time-domain and frequency_domain.

The transform feature tells the vector to switch between these forms. This is implemented using a fast-fourier transform.

Additionally, vector operations are only permitted if they are in the same form.

Possible extensions:

1. ARRAYED_VECTOR as a non-deferred ancestor

   Instead of inheriting directly from VECTOR and ARRAY

2. REAL_FOURIERIZABLE_VECTOR as a descendant

   Use symmetry to pack a real (in the mathematical sense - not shortened DOUBLEs!) into a COMPLEX vector of half the length in one form, and presents itself as full length, but with appropriate symmetry in the other form.

   LEGENDRE_FOURIER_VECTORs, CHEBYSHEV_FOURIER_VECTORs, or even WAVELET_VECTORs etc.

3. COMPLEX

   Features standard mathematical functions (exp, sin, cos, tan etc. and inverses) extended to take complex arguments, and zealous post-conditions.

Maintainer

Daniel Prager, as at October 1999.

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