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# SUMMARY Last modified 09/08/2013 How to find a program source: Example: Matrices - Linear Systems - Solve by LU Decomposition with program Test_lu 1. Choose a language (Basic, C++, Fortran 90 or Pascal) 2. Return to previous page and Press C++ for example 3. Press Matrices 4. Press Test_lu (to get source test_lu_cpp.txt)

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 Gauss-Jordan 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 (Euler-Romberg Method)
Teqdiff1 (Runge-Kutta Method of order 4)
Tequdifp (Differential Equations of p variables of order 1 By Runge-Kutta Method of order 4)
Teqdiffpc (Prediction-Correction Method)
Awp, Tawp (with automatic step size control)
T_dgls (Examples of 1st order ODE Systems)
URkf45, Trkf45 (Runge-Kutta-Fehlberg 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 Adams-Bashford-Moulton Method)
Bulirsch,Tbulirsch (1st order ODE system By Bulirsch-Stoer-Gragg Method)
Einb_rk,Teinbrk (1st order ODE system By Runge-Kutta enbedding formula)
Implruku,Legendre,Timplruk (1st order ODE system By Implicit Runge-Kutta-Gauss Method)
Trk4 (1st order ODE system of size N=2 By Runge-Kutta Method)
Trk4n1 (1st order ODE system (N<=10) By By Runge-Kutta Method)
Equdif, Tequdif (1st order ODE system (N<=10) By Runge-Kutta Method) with time step control
" ODE of order N>1 with initial conditions Tequdifn (Differential Equations of order N By Runge-Kutta 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 STIEFEL-REMES'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 Clenshaw-Curtis formula)
Sinint, Tsinintegral (calculate integrals of sin(x) and cos(x))
F_beisp (Examples used by integration programs)
Kubnec,Tkubnec (Cubature over Rectangles using Newton-Cotes Formula)
Tk3nec (Cubature over Triangles using 3-pts Newton-Cotes Formula and Romberg-Richardson extrapolation)
Kubgauss,Tk4gau (Cubature over Rectangles using Gauss Formula)
Tk3gan (Cubature over Triangles using summed Gaussian N-pts 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 NDIM-dimensional 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 (Multi-dimensional Steepest Descent Method without partial Derivatives)
Steepds (Multi-dimensional 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 ax�+2bxy+cy�+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++; Turbo-Pascal 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)
" One-dimensional Lstsqr (Program to demonstrate one-dimensional operation of the multi-nonlinear 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 Chi-square Statistics)
" Multi-dimensional Mltnlreg (Program to demonstrate multi-dimensional operation of the multi-nonlinear regression)
Regiter (Program to demonstrate multi-dimensional operation of the multi-nonlinear regression with iterative error reduction)
Tsmplx (Multi-dimensional 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 (Gauss-Jordan), 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 (Gauss-Jordan 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 � 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 Mass-spring Systems Circuit (Use Rungr-Kutta Method to solve a LCR circuit or equivalent damped Mass-spring System Problem)
1dof01 (Response of a 1 dof Mass-spring System with damping to a sinisoidal input force)
1dof02 (Response of a 1 dof Mass-spring System with viscous damping to a periodic input force)
Modes (Frequencies and Modes of Mass-spring Systems without damping by Transfer Method)
Ndof01 (Response of a N dof Mass-spring system with damping to a sinusoidal input force by Transfer Matrices Method)
Ndof02 (Frequencies and Eigenmodes, Masses and modal Stiffness of a Mass-spring undampled System)
Nfod03 (Response of a N dof Mass-spring System with damping to a sinisoidal input force by direct Method)
Ndof04 (Step by Step Solution of a N dof Mass-spring System with damping by the Wilson-Theta Method)
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 Aitken-Steffenson 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)
" Non-Linear Systems Nlinsyst (Solve a non-linear system of two variables)
Brown,Brownts1 (Non-linear system of equations by Brown's method)
Unnes, Tnnes, Utils (Resolution of a Set of non-linear Equations)
Lm, Tlm (Non-linear 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 Chi-sq (Chi-square cumulative Distribution)
Chi-sqr (This program takes a given degree of freedom, m and value, x, and calculates the chi-square 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 low-band 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 Savitzky-Golay 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 In-place 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 T-Probability Law)
Normal (Normal and Inverse Normal Probability Functions)
Chi2 (Chi2 and inverse Chi2 Functions)
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