PasMatLib

Description

by Nikolai Shokhirev

Introduction
Why Pascal?
Library description

Basic types
Dynamic arrays
Linear algebra
Display routines
Special functions
Optimization
Signal processing
Data processing
Numerical Methods
Pascal translation of Forsythe-Malcolm-Moler FORTRAN procedures

Project status
User guide
Downloads

Introduction

There are some areas (e.g. science, engineering, education) where the development of ideas, concepts, models and methods is more time-consuming than the accompanying computations. In such areas tools like Mathematica (http://www.wolfram.com), MATLAB (http://www.mathworks.com) and Maple (http://www.maplesoft.com) are widely used.

Advantages of tools for doing symbolic and/or numeric calculations:
1. Abundance of built-in methods and features
2. Flexibility with a variety of supporting techniques
3. Scripting and programming abilities for further enhancement

Drawbacks:
1. Necessity to learn a lot of features
2. Restriction of flexibility by predefined approaches
3. Necessity to learn tool-specific programming methods or
4. Use of third party add-ins

The alternative approach is to use high-level programming languages. Note that, in such areas programming is usually only a tool. This approach has its advantages and disadvantages as well.

Advantages:
1. Relatively small number of language elements
2. Flexibility is (almost) unlimited
3. Potential high efficiency
4. Self-sufficiency

Disadvantages:
1. Necessity to write programs from scratch
2. Relatively low productivity (for non-professional programmers)

Numerous libraries and packages help to overcome the disadvantages of the programming approach.

This is an attempt to develop yet another package. I have been using it for several years.

Why Pascal?

Why not? Object Pascal is a well developed Object-oriented language with an elegant object model. Its basic subset is very compact and easy to learn. It can be mastered gradually. It is less error-prone than some other languages.

I do not accept the extreme opinions like “Real programmers do not use Pascal” or “All real code was written in FORTRAN” (although the majority of classical algorithms were really written in 50s and 60s in FORTRAN and ALGOL and later rewritten to other languages).
I also do not share a common misconception that code efficiency is determined by language. Obviously, the Quick Sort algorithm will beat the Bubble Sort with increase of dimension regardless of the used language.
There are a lot of libraries in FORTRAN, C, C++, Java, Python, etc.( I have my own collection in C++ and FORTRAN). Despite of the existing collections of the mathematical code in Pascal (see e.g. JEDI Math http://sourceforge.net/projects/jedimath/ and Numerical Method in Pascal http://www-rab.larc.nasa.gov/nmp/ ) this area needs more contributions.

Library description

Basic types

Float real and complex types, constants, conversion routines and basic complex routines; Types: TArrayType, TSliceType, IRestore, IComment, TComment.
Unit uMatTypes - Only properties and public methods are displayed

Dynamic Arrays

Light-weight dynamic arrays (see the description here).

Units	Description
uDynArrays	Dynamic float, integer, complex and Boolean arrays
uDynArrUtils	Linear algebra utilities and basic routines
uDynArrIO	I/O routines for dynamic arrays
uDynArrUtilsX	Linear algebra extra utilities (mainly for testing)

Linear Algebra

Linear algebra objects and routines.

Units	Description
uDynLinAlg	Linear algebra routines (Based on EBK&NVS Library)
uDynObjAlg	Object algebra routines

Display Routines

Display routines for vectors, matrices and plots (see the description here).

Units	Description
uGraph2D	TPlot2D and TPlotBox2D classes
fDisplay	Display Form
uSurface	TSurfase definition
fDisplayCVal	Display complex format form
fDisplayVal	Display format form
fMapBox	fMapBox form
fPlot2D	fPlot2D form
fSurface	TFormSurface class
uGrid2D	TGrid2D and TGrid2Dm classes
uMapBox	TMapBox class
uDisplay	Display utilities
uColorMap	Color map routines
uPainter	TPainterLight and TPainter classes
uPainter0	TPainter0 class

Special functions

Collection of special functions and random.

Units Description

uSpecFunc Real special functions

uIsaac High-quality pseudo-random number generator algorithm by © Bob Jenkins

uRand13 13 Dimensional Low Discrepancy Sobol Sequences

Units	Description
uSpecFunc	Real special functions
uIsaac	High-quality pseudo-random number generator algorithm by © Bob Jenkins
uRand13	13 Dimensional Low Discrepancy Sobol Sequences

Optimization

Units	Description
uLevenbergMarquardt	Levenberg-Marquardt fit and optimization, SVD fit
uOptimization	TOptim1D class
uOptimUtils	Optimization utilities: bracketing, 1D minimization
uZerion	1D function zero search

Signal processing

Fourier transform and simple filtering

Units	Description
uFourier	Fourier signal processing library
uAverage	Derivatives and average routines
uFourierDisplay	13 Dimensional Low Discrepancy Sobol Sequences

Data processing

Units	Description
uDynData	Signal and Data objects
uDynDataUtils	Data and signal processing utilities
uSpline	1D and 2D spline routines
uStatUtils	Statistical processing library

Numerical Methods

Units	Description
uIntegration	Numerical integration
uODE	Ordinary differential equations

Pascal translation of Forsythe-Malcolm-Moler FORTRAN procedures

Our Pascal translations of the original FORTRAN procedures [1, 2] were included into EBK&NVS library and later into ObjMath and PasMatLib. Inspired by the publication of the Fortran-90 translation [3], I collected the procedures (except URAND) in a separate unit uFMM ( The individual Pascal procedures are still included in several PasMatLib units). The unit uFMM is available as an independent download. The use of uFMM requires uMatTypes and uDynArrays (included in the download). The unit test also requires uDynArrUtils, uDynArrUtilsX, uDynObjAlg, uDynArrIO.

References

"Computer Methods for Mathematical Computations", by George E. Forsythe, Michael A. Malcolm, and Cleve B. Moler. Prentice-Hall, 1977.
Netlib Repository http://www.netlib.org/fmm/
Public Domain Aeronautical Software (PDAS) http://www.pdas.com/free.htm
ForToPas - FORTRAN to Pascal converter