Directory  Subject  Programs  

ARITHMETIC  General 
Basis (Numerical Base Conversions) Basisop (Operations in any base between 2 and 36) Combi (Combinatory Analysis (N!, C(n,p), A(n,p)) Diophan (Diophantian equation Ax + Bx = C) Factors (Factorization of an integer number) Fraction (Simple operations on fractions) Gcd (GCD and SCM of several integer numbers) Prime (Seek if an integer number is a prime number) Primes (Write a table of prime numbers from 1 to N)  
(ARITH)  Miscellaneous 
Ndays (Number of days between two dates) Parser (Parser accepting variables with several characters) Pastri (Demo of Pascal's Triangle) Comlet (Find coincidences of letters in two given words of up to 26 letters)  
BESSEL FUNCTIONS  Real Functions 
Bessel (Calculate Bessel Coefficients) Bessel1 (Bessel Function Asymptotic Series) Besslser (Bessel Series Summation) Intbessl (Bessel Function of Integer Order) TBessi (First Kind Modified Bessel Function of Integer Order) TBessj (First Kind Bessel Function of Integer Order) TBessy (Second Kind Bessel Function of Integer Order) TBessk (Third Kind Modified Bessel Function of Integer Order) Trootj (Roots of First Kind Bessel Functions of Order N) Tzerojp (Calcullate the Kth zero of the First Derivative of Bessel Functions of Order N) Mjyzo (Zeros of Bessel Functions Jn(x),Yn(x) and their Deruvatives)  
"  Complex Functions 
Cbessj (Complex Bessel Function of the 1st Kind of integer order) Complex, Cbess0 to Cbess3 (Modules used by programs below) Tzbessi (Complex Bessel Function of the Modified 1st Kind) Tzbessj (Complex Bessel Function of the 1st Kind) Tzbessy (Complex Bessel Function of the 2nd Kind) Tzbessk (Complex Bessel Function of the 3rd Kind)  
COMPLEX  General 
Complex2,Tcomplex (Elementary Operations and Functions on Complex Numbers Complex1,Ucomplex (Complex Numbers Calculator)  
"  Complex roots 
Rootnum (Complex Root Counting Unit) Zcircle (Zero Searching algorithm) Tequa2 (2nd Degree Equation with Complex Coefficients) NEW Croot3 (3rd Degree Equation with Complex Coefficients) Tcroot4 (4th Degree Equation with Complex Coefficients) END NEW Znewton (Complex roots by Newton's Method) Tnewton (All Roots of a Complex Polynomial By Newton's Iterative Formulation) Tclague (Idem By Laguerre's Method) Fbauhube,Tbauhube (Idem By Bauhube's Method) Zmueller (Roots in Complex Domain By Mueller's Method) 

"  Complex Linear Systems & Inversion of a complex matrix 
Zmatsys (By GaussJordan Method) Lapack1, Lapack2, Tcgesv (By LU Decomposition Method  Fortran only) NEW Cdetmat(determinant only), csysmat, clu, test_clu, inv_clu, ticgt (inverse by Gauss), trslcgtc (complex linear system by Gauss), rshcgt (homogeneous complex linear system by Gauss) END NEW. 

"  Eigenvalues & Eigenvectors of a Complex Square Matrix 
Tceigen (By QR algorithm) Tcomeig (By Jacobi's Method) 

"  Complex Functions or Polynomials 
Mcgama (Calculate Function Gamma with a complex argument) Meiz (Calculate the complex exponential integral EI(z) with a complex argument) Mcpsi (Calculate the Psi Function for a complex argument) Mclpn (Calculate the Legendre Polynomials of 1st Kind for a complex argument) Mclqn (Calculate the Legendre Polynomials of 2nd Kind for a complex argument) Mclpmn (Calculate the Associated Legendre Functions of 1st Kind and their First Derivatives for a complex argument) Mclqmn (Calculate the Associated Legendre Functions of 2nd Kind and their First Derivatives for a complex argument) CHorner (Evaluate a complex Polynomial by Horner's Rule) 

DIFFERENTIAL EQUATIONS  Y'=F(X, Y) with initial condition  Eulromb (EulerRomberg Method) Adambash (AdamsBashforth Method) Teqdiff1 (RungeKutta Method of order 4) Tequdifp (Differential Equations of p variables of order 1 By RungeKutta Method of order 4) Teqdiffpc (PredictionCorrection Method) Awp, Tawp (with automatic step size control) T_dgls (Examples of 1st order ODE Systems) URkf45, Trkf45 (RungeKuttaFehlberg Method for a 1st order ODE system) Gear, Mgear (1st order Stiff ODE system By Gear's Method) Tros4 (1st order Stiff ODE system By Rosenbrock's Method) Ab_mou, Tabmou (1st order ODE system By AdamsBashfordMoulton Method) Bulirsch,Tbulirsch (1st order ODE system By BulirschStoerGragg Method) Einb_rk,Teinbrk (1st order ODE system By RungeKutta enbedding formula) Implruku,Legendre,Timplruk (1st order ODE system By Implicit RungeKuttaGauss Method) Trk4 (1st order ODE system of size N=2 By RungeKutta Method) Trk4n1 (1st order ODE system (N<=10) By By RungeKutta Method) Equdif, Tequdif (1st order ODE system (N<=10) By RungeKutta Method) with time step control 

"  ODE of order N>1 with initial conditions 
Tequdifn (Differential Equations of order N By RungeKutta Method of order 4) Stormer (Differential Equations of order 2 By Stormer's Method) Laplace,Laplace1,Laplace2 (Solve Laplace Equation  3 examples)  
"  Two Point Boundary Problems of 1st or 2nd Order 
Rwp,M_rwp (Solve a Two Point Boundary Problem of 1st Order By the Shooting Method) Limits (Solve a Two Point Boundary Problem of 2ndt Order By a Runge_Kutta Method) Tshoot (Solve a Two Point Boundary Problem of 2nd Order By the Shooting Method)  
FUNCTIONS  Polynomial Approximations 
Chebyshe,Tchebysh (Chebyshev Polynomial Approximation) Tchebint ((Chebyshev Polynomial Approximation  Integral) Tchebder ((Chebyshev Polynomial Approximation  Derivative)  
"  discrete Functions 
Dinteg (Integrate a discrete Function F(x) by the Weighting Coefficients Method) Disinteg (Program to demonstrate the discrete Simpson Integration Primitiv (discrete Primitive Subroutine) Tcheapp (Best Approximation of a discrete Real Function F(x) By STIEFELREMES's Polynomial Method TPolint (Polynomial Interpolation or Extrapolation of a discrete Function F(x) using Polynomials) TRatint (Polynomial Interpolation or Extrapolation of a discrete Function F(x) using a Quotient of Polynomials) Tseval (Cubic Spline Interpolation of a discrete Function given by N Points  
"  Integrals 
Integra (General Integration Subroutine) TGauss (Integration of a real Function F(x), F(x,y) or F(x,y,z) by Gauss Method TSimpson (Integration of a real Function F(x) by Simpson's Method Tqanc8 (Integration of a real function F(x) by Qanc8 subroutine with control of absolute and relative precisions) Tromberg (Integration of a real Function F(x) by Romberg's Method Clencurt (Integration of F(x) using the summed ClenshawCurtis formula) Sinint, Tsinintegral (calculate integrals of sin(x) and cos(x)) F_beisp (Examples used by integration programs) Kubnec,Tkubnec (Cubature over Rectangles using NewtonCotes Formula) Tk3nec (Cubature over Triangles using 3pts NewtonCotes Formula and RombergRichardson extrapolation) Kubgauss,Tk4gau (Cubature over Rectangles using Gauss Formula) Tk3gan (Cubature over Triangles using summed Gaussian Npts Formula)  
"  Interpolation 
Confract (Interpolate a Function F(x) By continuous Fractions Trigpoly (Interpolate a Function F(x) By trigonometric Polynomials Lagrange (Lagrange Interpolation of a Function F(x)) Newton (Newton Interpolation of a Function F(x))  
"  Limited Development 
Ltddev (Calculate a limited development of a real function F(x) at point x0 with step h
up to order 5 Ltddev1 (Calculate a limited development of a real function F(x)*G(x) at point x=0 with step h up to order 25 knowing the limited developments of F(x) and G(x) Ltddev2 (Calculate a limited development of a real function F(x)/G(x) at point x=0 with step h up to order 25 knowing the limited developments of F(x) and G(x) Ltddev3 (Calculate a limited development of a real function F(x) o G(x) at point x=0 with step h up to order 25 knowing the limited developments of F(x) and G(x)  
"  Find a Minimum 
Mnbrack (Bracketing a minimum of a real Function F(x)) Golden (Seek a Minimum of a real Function F(x) By Golden Section Search) Brent (Seek a Minimum of a real Function F(x) By Brent's Method) Tamobea (Multidimensional Minimization of a Function F(X), where X is a NDIMdimensional Vector By the Downhill Simplex Method of Nelder & Mead) Tpowell (Minimization of a Function FUNC of N Variables By Powell's Method)  
"  Find a Maximum 
Steepda (Multidimensional Steepest Descent Method without partial Derivatives) Steepds (Multidimensional Steepest Descent Method with partial Derivatives)  
"  Special Functions 
MBernoa (compute Bernoulli numbers Bn using subroutine BERNOA) MEulera (compute Euler numbers Bn using subroutine EULERA) Mmtu0 (Calculate Mathieu Functions and their first Derivatives Arcsin (Calculate Arcsinus(x)) Hermite (Calculate Hermite Coefficients) Hyper (Calculate hyperbolic Functions) Invhyper (Calculate inverse hyperbolic Functions) Cliptic (Evaluate elliptic Integrals of 1st and 2nd Kinds)  
GEOMETRY  Conicals 
Arcircle (Calculate the 4 parameters of an arc of circle knowing
two of them) Conical (Reduction of conicals of equation ax²+2bxy+cy²+2dx+2ey+f=0) Conical1 (Seek the equation of a conical passing through five points)  
"  Miscellaneous 
Planets (Position of planets  ascent and declination) Surface (Calculate the internal surface of a polygon defined by n points) Triangle (Given three side or angle elements of a triangle out of six, this program will determine the missing elements and calculate the surface)  
GRAPHICS  with units Gr2d or Graph2d 
Several examples of graphic applications are given in C++; TurboPascal or
Visual Basic either with manual scales (unit Gr2d) or with automatic scales
(unit Graph2d) See corresponding directories.  
LEAST SQUARES APPROXIMATION  discrete Functions 
Approx (Least Squares Approximation of a discrete real Function F(x)) Approx1 (Least Squares Approximation of a discrete real Function F(x) with orthogonal polynomials)  
"  Onedimensional 
Lstsqr (Program to demonstrate onedimensional operation of the multinonlinear
regression) Lsqply (Program to demonstrate least squares polynomial fitting Lstsqr1 (Linear least squares demonstration program) Lstsqr2 (Least squares of order 1 or 2 demonstration program) Parafit(Parametric least squares fit) Chisqa (Program to demonstrate the Chisquare Statistics)  
"  Multidimensional 
Mltnlreg (Program to demonstrate multidimensional operation of the multinonlinear
regression) Regiter (Program to demonstrate multidimensional operation of the multinonlinear regression with iterative error reduction) Tsmplx (Multidimensional curve fitting by the Simplex Method)  
LINEAR PROGRAMMING  General 
Simplex (Program to demonstrate the Simplex Method) Tsimplex (Program to demonstrate the Simplex Method with three types of constraints) Appoint (Program to demonstrate the Appointment Method) Dantzig (Program to demonstrate the Dantzig's Model) Tpert (Time P.E.R.T. Model) Transpor (Program to demonstrate the Transport Method) Tanneal (The Salesman's Problem using the simulated annealing Method)  
MATRICES  Utilities  Basis_r, Vmblock (C++)  
"  Linear Systems 
Sysmat (GaussJordan), Tdlittl (Direct Factorization), Tlinear (Triangularization) Fseidel, Tseidel (Gauss Seidel iterative method), Dpme (Partial pivoting algorithm and reduced storage), Lu, Test_lu (LU decomposition), Nsbslv (LU for a banded system), Fband, Fbando, tband (banded systems with or without using pivots), Cg, Cgtst1 (Conjugate Gradient for symmetric systems), Tsparse (CG method for sparse symmetric systems), Syslin, Tsymsol (Gauss method for symmetric systems), Fcholy, Tcholy (Cholesky Method for symmetric positive definite systems), Tridiag (for tridiagonal linear systems), Tsvbksb (Singular Value Decomposition Method),Tvander (Solve a Vandermonde system), Toeplitz (Solve a Toeplitz system).  
"  Matrix Inversion 
Sysmat (GaussJordan Method) Choles (Inversion By Cholesky Method) Inv_Lu (Inversion By LU Decomposition) 

"  Matrix Determinant 
Deter (By Gauss Method), Deter1 (By LU Decomosition) Deter2 (Recursive By Kramer's rule)  
"  Matrix Characteristic Polynomial 
UComplex1 (Module used by program Carpol1 below) Carpol (Real Square Tridiagonal Matrix) Carpol1 (Complex Square Matrix) Carpol2 (Real Square Matrix) Carpol3 (Real Square Symmetric Matrix)  
"  Matrix Eigenvalues/Eigenvectors 
Tpwm (Greatest Eigenvalue By the Power Method) Tpwimgt (Smallest Eigenvalue By the Power Method) Ujacobi (Jacobi's Method Module) TUjacobi (Eigenvalues é Eigenvectors of a Real Simmetric Square Matrix By Jacobi's Method)) Elprotd (for a Real Tridiagonal Square Matrix) Ttql2 (for a Symmetric Tridiagonal Square Matrix By QL Method) Ttred2 (for a Symmetric Square Matrix By Householder reduction and QL Method) Test_hqr (Eigenvalues of a general square matrix by HQR algorithm Feigen (Module foe HQR Method) Test1_hqr (Eigenvalues and Eigenvectors of a general square matrix by HQR algorithm Tephj (for a Square Hermitian matrix by Jacobi's Method)  
MECHANICS  Massspring Systems 
Circuit (Use RungrKutta Method to solve a LCR circuit or equivalent damped Massspring
System Problem) 1dof01 (Response of a 1 dof Massspring System with damping to a sinisoidal input force) 1dof02 (Response of a 1 dof Massspring System with viscous damping to a periodic input force) Modes (Frequencies and Modes of Massspring Systems without damping by Transfer Method) Ndof01 (Response of a N dof Massspring system with damping to a sinusoidal input force by Transfer Matrices Method) Ndof02 (Frequencies and Eigenmodes, Masses and modal Stiffness of a Massspring undampled System) Nfod03 (Response of a N dof Massspring System with damping to a sinisoidal input force by direct Method) Ndof04 (Step by Step Solution of a N dof Massspring System with damping by the WilsonTheta Method)  
"  Beam 
Beam (Calculate Beam Deflection for four different Support/loading Systems) Beam1 (Resonance Frequencies of a bending Beam, modal Mass and Stiffness, Deformation Modes and maximum Strain)  
"  Composite Material 
Compos01 (Calculate the stresses in a unidirectional layer of a composite material,
knowing deformations exx, eyy, gxy, and angle theta of fibers in x direction) Compos02 (Calculate the matrix linking the stresses to deformations in a laminated material made of N unidirectional composite layers) Compos03 (Calculate the deformations and stresses in a laminated material made of N unidirectional composite layers, knowing the resulting imposed efforts)  
"  Miscellaneous 
Pendulum (Calculate angular Motion of an elemntary Mass Pendulum) Ef3d  C++ and Pascal only (Small finite Elements Demonstration Program)  
POLYNOMIALS  Simple Polynomials P(x) 
Polynoms (Elementary operations on polynomials P(x)) Evalpol (Program to demonstrate the Evaluation of a polynomial) Thorner (Evaluate a Polynomial and its Derivatives by Horner's Method) Divpol1 (Division of two polynomials by increasing powers) Divpol (Euclidian division of two polynomials P(x)/Q(x)) Gcdpol (GCD and SCM of two polynomials) Combipol (Linear combination of two polynomials a.P(x) + b.Q(x)) Multpol (Multiplication of two polynomials P(x)*Q(x)) Derivpol (Nth derivative of a polynomial P(x)) Substpol (Substitution of two polynomials P(Q(x)) )  
"  Polynomial Fractions P(x)/Q(x) 
Polfract (Elementary operations on polynomial fractions F(x) = P(x)/Q(x) ) Evalfract (Program to demonstrate the Evaluation of a polynomial fraction) Invfract (Inversion of a polynomial fraction) Combifra (Linear combination of two polynomial fractions a.F1(x) + b.F2(x)) Multfrac (Multiplication of two polynomial fractions F1(x)*F2(x)) Derivfra (Nth derivative of a polynomial fraction P(x)/Q(x) ) Simpelem (Simple elements of a polynomial fraction) Substfra (Substitution of two polynomial fractions F1(F2(x)) )  
"  Utility 
Algebra (Symbolic Parser for Polynomials (only C++ and Pascal) )  
ROOTS  Polynomials 
Bairstow (Find two complex roots of a polynomial) Bairsto1 (Find all real and complex roots of a polynomial) Bernou (Find all real roots of a polynomial) Lin (Find two complex roots of a polynomial) Root4 (Real or complex roots of polynomials of degree 2, 3 and 4) Roottest (Root testing program for polynomials) Rsyndiv (Synthetic division of polynomials)  
"  Real continuous functions F(x) 
Aitken (Find a real root of a real function F(x) by Aitken acceleration method) Bisect (Find a real root of a real function F(x) by bisection method) Tquart (Find a real root of a real function F(x) by bisection and quartile methods) Mueller (Find a real root of a real function F(x) by Mueller's method) Newto1 (Find a real root of a real function F(x) by Newton's method) Nextroot (Find another real root of a real function F(x)) Regula (Find a real root of a real function F(x) by the modified false position method) Secant (Find a real root of a real function F(x) by the secant method) Steffen (Find a real root of a real function F(x) by the AitkenSteffenson iteration method) Zbrent (Find a real root of a real function F(x) by Brent's method) Fpegasus,Tpegasus ((Find a real root of a real function F(x) by the Pegasus method) Fzeroin,Tzeroin ((Find a real root of a real function F(x) by the Zeroin method)  
"  NonLinear Systems 
Nlinsyst (Solve a nonlinear system of two variables) Brown,Brownts1 (Nonlinear system of equations by Brown's method) Unnes, Tnnes, Utils (Resolution of a Set of nonlinear Equations) Lm, Tlm (Nonlinear system of equations by Least Squares)  
SERIES APPROXIMATION  Miscellaneous 
Asymerf (Asymptotic series expansion of the integral of 2 exp(X*X)/(X*sqrt(PI)),
the normalized error function) Chebecon (Program to demonstrate Chebyshev Economization) Chebyser (Chebyshev series coefficients Evaluation) Cmplxser (Complex Series Evaluation) Horner (Program to demonstrate Horner's Rule) Invnorm (This program calculates an approximation to the integral of the normal distribution function from x to infinity) Recipro (Program to demonstrate the Series Inversion of a Polynomial) Reverse (Program to demonstrate the Series Reversion of a Polynomial)  
"  Special Functions 
Chisq (Chisquare cumulative Distribution) Chisqr (This program takes a given degree of freedom, m and value, x, and calculates the chisquare density distribution function value, y) LogN! (Demonstration of the Series approximation subroutine for LN(X!)  
SIGNAL PROCESSING  Fourier Analysis 
Tfft (Program to demonstrate Fast Fourier Transform) Fourier (Calculate the Fourier harmonic #n of a periodic discrete function F(x) defined by ndata points) Disfour (Calculate the Fourier coefficients of a periodic discrete function using module Fourier) Analfour (Calculate the Fourier coefficients of a periodic function F(x) using module Fourier)  
(SIGNAL)  Filtering 
Tfilters (Program to demonstrate Butterworth lowband numerical filter)  
"  Shock Spectrum 
Tshocksp (Program to demonstrate the calculation of an acceleration
shock spectrum)  
"  Deconvolution 
Deconv (Program to demonstrate the deconvolution of a discrete speed)  
"  Smoothing 
Smooth (Smoothing an array of N ordinates Y(i) with ascending order abcissas) Tsavgol (Smoothing an array of N ordinates Y(i) with ascending order abcissas using SavitzkyGolay filter coefficients)  
SORTING  Utilities 
Sort1 (Program to demonstrate the straight Insertion Method) Sort2 (Program to demonstrate the Shell Method) Sort3 (Program to demonstrate the Heapsort Method) Tqcksrt (Program to demonstrate the Quicksort Method) NEW Bubble (Program to demonstrate the Bubble Method) Merge (Program to demonstrate the Merge Method) Mssort (Program to demonstrate the Inplace Merge Method) Fsearch, Search (Program to demonstrate Searching Functions for Lists of Names)  
STATISTICS  General 
Distri (Program to demonstrate Statistical Distributions) Fdistri (Calculate the F distribution for f, nu1, nu2 given) Fstat (Statistical functions for one or two variables) Moment (Calculate the means and moments of a statistical variable) Tmoment (Calculate the the statistical moments of a distribution: Mean, variance, Skewness...) Tmdian (Median Value of an Array using Heapsort) Tmdian1 (Median Value of an Array without Sorting) Momnts (Calculate the mean and first three moments of a set of data) Simlp (Simple linear regression minimizing the Sum of Absolute Deviation)  
(STAT)  Special Functions 
Gamma (Program to demonstrate the Gamma Function) Ibeta (Calculate the incomplete Beta Function Ix(a,b))  
"  Standard Laws 
Tnormal (Calculate the standardized Normal Law probabilities mean=0, standard deviation=1 for 37 < X < 37) Student (Calculate Student TProbability Law) Normal (Normal and Inverse Normal Probability Functions) Chi2 (Chi2 and inverse Chi2 Functions) 