******************************************************************************
*                                                                            *
*                                 TPMATH2.ZIP                                *
*                                                                            *
*                       MATHEMATICAL LIBRARY IN PASCAL                       *
*                           PART 2 : DEMO PROGRAMS                           *
*                           Last updated : May 2000                          *
*                                                                            *
******************************************************************************


                            AUTHOR : Dr Jean DEBORD

               Laboratoire de Pharmacologie, Faculte de Medecine
               2 Rue du Docteur Marcland, 87025 Limoges (France)
                               debord@unilim.fr
                            JDebord@compuserve.com
               

******************************************************************************
 This library is distributed as freeware. You may use it any way you like, as
 long as you don't charge money for it, remove the copyright notices, or hold
 anyone liable for its results.
******************************************************************************



CONTENTS
========

Main directory
--------------

  TPMATH2.TXT  : This file

Subdirectory FMATH
------------------

  SPEED.PAS    : Test of assembler routines for 387+ coprocessors
  TESTFUNC.PAS : Test of elementary functions
  SPECFUNC.PAS : Test of special functions
  GRAFUNC.PAS  : Graph of a function
  TESTCOMP.PAS : Test of complex numbers and functions

  SPECFUNC.DAT : Data for testing special functions

Subdirectory MATRICES
---------------------

  CHOLESK.PAS  : Cholesky factorization of a positive definite matrix
  DETINV.PAS   : Determinant and inverse of a square matrix
  SYSEQ.PAS    : System of linear equations (Gauss-Jordan elimination)
  SYSEQLU.PAS  : System of linear equations (LU decomposition)
  SYSEQSVD.PAS : System of linear equations (Singular value decomposition)
  SYSEQ_QR.PAS : System of linear equations (QR decomposition)
  SYSEQC.PAS   : System of linear equations with complex coefficients
  EIGENSYM.PAS : Eigenvalues and eigenvectors of a symmetric matrix
  EIGENVAL.PAS : Eigenvalues of a general square matrix
  EIGENVEC.PAS : Real eigenvalue and eigenvector of a general square matrix

  MATRIX1.DAT  : Data for determinant, inverse and eigenvalues
  MATRIX2.DAT  : Data for systems of equations
  MATRIX3.DAT  : Data for systems of equations with complex coefficients
  MATRIX4.DAT  : Data for Cholesky factorization

Subdirectory OPTIM
------------------

  HESSIAN.PAS  : Gradient and Hessian of a function of several variables
  MIN1.PAS     : Minimization of a function of one variable
  MINFUNC.PAS  : Minimization of a function of several variables

  MINALGO*.INC : Minimization algorithms for MINFUNC.PAS
  MINFUNC*.INC : Example functions for MINFUNC.PAS

Subdirectory FOURIER
--------------------

  TESTFFT.PAS  : Test of Fast Fourier Transform
                 (modified from Don Cross, with permission)

Subdirectory RANDOM
-------------------

  RANTEST.PAS  : Test of random number generator
  RANGAUS.PAS  : Gaussian random numbers
  RANMUL.PAS   : Random vector from a multinormal distribution
  RANMULL.PAS  : Random vector from a multi-lognormal distribution
  TESTMCMC.PAS : Simulation by Markov Chain Monte Carlo (normal distrib.)
  TESTMC2.PAS  : Simulation by Markov Chain Monte Carlo (lognormal distrib.)

  RANMUL.DAT   : Data for multinormal distribution
  RANMULL.DAT  : Data for multi-lognormal distribution

Subdirectory REG
----------------

  REGPOLY.PAS  : Linear and polynomial regressions
  REGMULT.PAS  : Multiple linear regression
  REGEXPO.PAS  : Nonlinear regression : sum of exponentials
  REGFRAC.PAS  : Nonlinear regression : rational fraction
  CORREL.PAS   : Variance-covariance and correlation matrix
  TESTPCA.PAS  : Principal component analysis

  REG*.INC     : Routines used by the regression programs

  LINE.DAT     : Data for linear regression
  POLYNOM.DAT  : Data for polynomial regression
  INHIB.DAT    : Data for multiple linear regression (from ref. 2)
  ORAL1.DAT    : Data for nonlinear regression (sum of exponentials)
  ORAL2.DAT    : Data for nonlinear regression (sum of exponentials)
  IV2.DAT      : Data for nonlinear regression (sum of exponentials)
  ENZYME.DAT   : Data for nonlinear regression (rational fraction)
  PCA.DAT      : Data for principal component analysis


SYSTEM REQUIREMENTS
===================

- PC or compatible

- Math coprocessor recommended

- Pascal compiler: Turbo Pascal 5.0+ (DOS)
                   Free Pascal (FPC) 0.99.14+ (DOS / Linux)

Note: The plotting library (unit PLOT.PAS in TPMATH1.ZIP) is not yet fully
compatible with FPC / Linux. Hence, the programs which use graphics cannot
be compiled under Linux.


INSTALLATION
============

- Extract the archive in a given directory. Be sure to preserve the
  subdirectory structure of the archive (if you use PKUNZIP, be sure to
  use the -d option to create subdirectories, i.e. pkunzip -d tpmath2.zip)

- The units and include files contained in TPMATH1.ZIP must be installed
  in directories accessible to the compiler.

The use of the programs is explained in the comment part of each file.


REFERENCES
==========

(1) D. CROSS
    Fast Fourier Transforms
    http://www.intersrv.com/~dcross/fft.html

(2) J. DEBORD, P. N'DIAYE, J. C. BOLLINGER et al
	Cholinesterase inhibition by derivatives of 2-amino-4,6-dimethylpyridine
	J. Enzyme Inhib., 1997, 12, 13-26

(3) J. D. GAYRARD
	MATHLIB2.ZIP on Compuserve's BPASCAL forum
	Also available at the Delphi Super Page:
	http://wcarchive.cdrom.com/pub/delphi_www/
	in the Delphi 1.0 Freeware section.

(4) R. GOMENI & C. GOMENI
	Automod : A polyalgorithm for an integrated analysis of 
	linear pharmacokinetic models.
	Comput. Biol. Med., 1979, 9, 39-48

(5) D. W. MARQUARDT
	An algorithm for least squares estimation of nonlinear parameters.
	J. Soc. Indust. Appl. Math., 1963, 11, 431-441

(6) A. R. MILLER
	Basic Programs for Scientists and Engineers.
	Sybex, 1981

(7) J. A. NELDER & R. MEAD
	A simplex method for function minimization.
	Comput. J., 1964, 7, 308-313

(8) W. H. PRESS, S. A. TEUKOLSKY, W. T. VETTERLING & B. P. FLANNERY
	Numerical Recipes. The Art of Scientific Computing.
	Cambridge University Press, 2nd edition 1992

(9) Turbo Pascal Numerical Methods Toolbox.
	Borland International, 1986

