- albany_test, C++ programs which demonstrate the usage of the ALBANY program, which allows the implementation of finite element PDE solvers for a variety of fundamental research applications, including LCM (Laboratory for Computational Mechanics), QCAD (Quantum Computer Aided Design) and FELIX (Finite Element for Land Ice eXperiments).
- allocatable_array, a program which demonstrates how a C++ function can declare a pointer to an array, pass it to a function, which can then allocate it and fill it with data, and then return the allocated and initialized array to the calling function through the argument list.
- alpert_rule, a library which can set up an Alpert quadrature rule for functions which are regular, log(x) singular, or 1/sqrt(x) singular.
- anagram, a program which determines anagrams of a string, by James Cherry;
- analemma, a program which evaluates the equation of time, a formula for the difference between the uniform 24 hour day and the actual position of the sun, creating data files that can be plotted with gnuplot, based on a C program by Brian Tung.
- ann, a library which computes approximate nearest neighbors, by David Mount and Sunil Arya.
- ann_test, a program which uses ann() to approximate the nearest neighbors of a set of points stored in a file, by David Mount, Sunil Arya;
- ann_to_fig, a program which plots the search tree used by ann() while seeking the approximate nearest neighbors of a set of points, by David Mount, Sunil Arya;
- annulus_monte_carlo, a library which uses the Monte Carlo method to estimate the integral of a function over the interior of a circular annulus in 2D.
- annulus_rule, a library which computes a quadrature rule for estimating integrals of a function over the interior of a circular annulus in 2D.
- args, a program which reports the command line arguments with which it was invoked;
- asa005, a library which evaluates the lower tail of the noncentral Student's T distribution, by BE Cooper. This is a version of Applied Statistics Algorithm 5;
- asa006, a library which computes the Cholesky factor of a positive definite symmetric matrix, by Michael Healy. This is a version of Applied Statistics Algorithm 6;
- asa007, a library which computes the inverse of a positive definite symmetric matrix, by Michael Healy. This is a version of Applied Statistics Algorithm 7.
- asa032, a library which evaluates the incomplete Gamma function, by G Bhattacharjee. This is a version of Applied Statistics Algorithm 32;
- asa047, a library which minimizes a scalar function of several variables using the Nelder-Mead algorithm, by R ONeill. This is a version of Applied Statistics Algorithm 47;
- asa053, a library which produces sample matrices from the Wishart distribution, by William Smith and Ronald Hocking. This is a version of Applied Statistics Algorithm 53.
- asa058, a library which carries out K-means clustering of data, by David Sparks. This is a version of Applied Statistics Algorithm 58;
- asa063, a library which evaluates the incomplete Beta function, by KL Majumder and G Bhattacharjee. This is a version of Applied Statistics Algorithm 63;
- asa066, a library which computes the cumulative density function (CDF) of the standard normal distribution, by David Hill. This is a version of Applied Statistics Algorithm 66;
- asa076, a library which evaluates Owen's T function, by Young and Minder. This is a version of Applied Statistics Algorithm 76;
- asa091, a library which computes the percentage points of the Chi-square distribution, by Best and Roberts. This is a version of Applied Statistics Algorithm 91;
- asa103, a library which evaluates the digamma or psi function, by Jose Bernardo. This is a version of Applied Statistics Algorithm 103;
- asa109, a library which inverts the incomplete Beta function, by Cran, Martin and Thomas. This is a version of Applied Statistics Algorithm 109;
- asa111, a library which evaluates the percentage points of the normal distribution, by Beasley and Springer. This is a version of Applied Statistics Algorithm 111;
- asa113, a library which clusters data using a transfer and swap algorithm, by Banfield and Bassill. This is a version of Applied Statistics Algorithm 113;
- asa121, a library which evaluates the trigamma function, by BE Schneider. This is a version of Applied Statistics Algorithm 121;
- asa136, a library which implements a clustering algorithm, by Hartigan and Wong. This is a version of Applied Statistics Algorithm 136;
- asa144, a library which randomly generates tables with given row and column sums, by James Boyett. This is a version of Applied Statistics Algorithm 144;
- asa147, a library which evaluates the incomplete Gamma function, by Chi Leung Lau. This is a version of Applied Statistics Algorithm 147;
- asa152, a library which evaluates the probability density function (PDF) and cumulative density function (CDF) associated with the hypergeometric distribution, by Richard Lund. This is a version of Applied Statistics Algorithm 152;
- asa159, a library which computes a random table with given row and column sums, by Michael Patefield. This is a version of Applied Statistics Algorithm 159;
- asa172, a library which generates all M-dimensional indices in a given range, simulating the behavior of an arbitrary number of nested loops, by OFlaherty and MacKenzie. This is a version of Applied Statistics Algorithm 172;
- asa183, a library which implements a random number generator (RNG), by Wichman and Hill. This is a version of Applied Statistics Algorithm 183;
- asa226, a library which evaluates the noncentral incomplete Beta function, by Russell Lenth. this is a version of Applied Statistics Algorithm 226;
- asa239, a library which evaluates the incomplete Gamma function, by Shea. this is a version of Applied Statistics Algorithm 239;
- asa241, a library which computes the inverse of the normal cumulative density function (CDF), by Michael Wichura; this is a version of Applied Statistics Algorithm 241;
- asa243, a library which evaluates the lower tail of the noncentral Student's T distribution, by Russell Lenth; this is a version of Applied Statistics Algorithm 243;
- asa245, a library which evaluates the logarithm of the Gamma function, by Allan Mcleod; this is a version of Applied Statistics Algorithm 245;
- asa266, a library which evaluates various properties of the Dirichlet probability density function (PDF); this is a C version of Applied Statistics Algorithm 266;
- asa299, a library which computes the lattice points (integer coordinates) in an M-dimensional simplex, by Chasalow and Brand; this is a version of Applied Statistics Algorithm 299;
- asa310, a library which evaluates the noncentral incomplete Beta function, by Chattamvelli and Shanmugam; this is a version of Applied Statistics Algorithm 310;
- asa314, a library which computes the inverse of a matrix whose elements are subject to modulo arithmetic, by Roger Payne. This is a version of Applied Statistics Algorithm 314.
- atbash, a library which applies the Atbash substitution cipher to a string of text.
- backtrack_binary_rc, a library which carries out a backtrack search for a set of binary decisions, using reverse communication.
- ball_grid, a library which computes grid points inside a 3D ball.
- ball_integrals, a library which returns the exact value of the integral of any monomial over the interior of the unit ball in 3D.
- ball_monte_carlo, a library which applies a Monte Carlo method to estimate integrals of a function over the interior of the unit ball in 3D;
- bank, a library which computes the check digit associated with a US Bank Routing Number check digit, or reports whether a 9-digit code is actually valid.
- barycentric_interp_1d, a library which defines and evaluates the barycentric Lagrange polynomial p(x) which interpolates a set of data, so that p(x(i)) = y(i). The barycentric approach means that very high degree polynomials can safely be used.
- bellman_ford, a library which implements the Bellman-Ford algorithm for finding the shortest distance from a given node to all other nodes in a directed graph whose edges have been assigned real-valued lengths.
- bernstein_polynomial, a library which evaluates the Bernstein polynomials;
- besselj, a library which evaluates Bessel J functions of noninteger order;
- beta_nc, a library which evaluates the cumulative density function (CDF) of the noncentral Beta distribution;
- bicycle_lock, a library which simulates the process of determining the secret combination of a bicycle lock, an integer between 000 and 999.
- bins, a library which handles geometric data partially sorted into bins;
- bisection_integer, a library which seeks an integer solution to the equation F(X)=0, using bisection within a user-supplied change of sign interval [A,B].
- bisection_rc, a library which seeks a solution to the equation F(X)=0 using bisection within a user-supplied change of sign interval [A,B]. The procedure is written using reverse communication.
- bits_to_ui, a program which reads a text file of bits and writes a binary file in which groups of 32 bits have been interpreted as an unsigned integer;
- black_scholes, a library which implements some simple approaches to the Black-Scholes option valuation theory, by Desmond Higham.
- blas, a library which contains the Basic Linear Algebra Subprograms (BLAS) for level 1, 2 and 3, for single and double precision, and for real and complex arithmetic.
- blas_osx, a program which demonstrates how to access the BLAS library on a Macintosh that is running the OSX operating system.
- blas0, a library which contains auxilliary functions for the Basic Linear Algebra Subprograms (BLAS).
- blas1, a library which contains the Basic Linear Algebra Subprograms (BLAS) for level 1 (vector-vector operations), for single and double precision, and for real and complex arithmetic, by Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh.
- blas1_c, a library which constitutes the Level 1 Basic Linear Algebra Subprograms (BLAS), using single precision complex arithmetic, by Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh.
- blas1_d, a library which constitutes the Level 1 Basic Linear Algebra Subprograms (BLAS), using double precision real arithmetic, by Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh.
- blas1_s, a library which constitutes the Level 1 Basic Linear Algebra Subprograms (BLAS), using single precision real arithmetic, by Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh.
- blas1_z, a library which constitutes the Level 1 Basic Linear Algebra Subprograms (BLAS), using double precision complex arithmetic, by Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh.
- blas2_d, a library which constitutes the Level 2 Basic Linear Algebra Subprograms (BLAS), for matrix-vector operations, using double precision real arithmetic.
- blas2_s, a library which constitutes the Level 2 Basic Linear Algebra Subprograms (BLAS), for matrix-vector operations, using single precision real arithmetic.
- blas3_d, a library which constitutes the Level 3 Basic Linear Algebra Subprograms (BLAS) for matrix-matrix operations, using double precision arithmetic;
- blas3_s, a library which constitutes the Level 3 Basic Linear Algebra Subprograms (BLAS) for matrix-matrix operations, using single precision arithmetic;
- blend, a library which uses transfinite interpolation to fill in data within a square or a cube based on boundary values;
- bmp_io, a library which reads and writes graphics information stored in a Microsoft BMP file;
- bmp_to_ppma, a program which converts a Microsoft BMP file to an ASCII Portable Pixel Map (PPM) file;
- bmp_to_ppmb, a program which converts a Microsoft BMP file to a binary Portable Pixel Map (PPM) file;
- boost_test, programs which illustrate the use of some of the Boost libraries;
- box_behnken, a library which computes a Box-Behnken design, that is, a set of arguments to sample the behavior of a function of multiple parameters;
- brent, a library which contains routines for finding zeroes or minima of a scalar function of a scalar variable, without the use of derivative information, including a reverse communication option, by Richard Brent. The C++ version includes some customizations by John Denker.
- brownian_motion_simulation, a library which simulates Brownian motion in an M-dimensional region, creating graphics files for processing by gnuplot.
- burgers_solution, a library which evaluates exact solutions of the time-dependent 1D viscous Burgers equation.
- bvec, a library which demonstrates how signed integers can be stored as binary vectors, and arithmetic can be performed on them.
- c++_calls_c, programs which illustrate a C++ program calling a C function.
- c++_calls_f77, programs which illustrate a C++ program calling a FORTRAN77 subroutine.
- c++_calls_f90, programs which illustrate a C++ program calling a FORTRAN90 subroutine.
- c++_condor, programs which illustrate how a C++ program can be run in batch mode using the condor queueing system.
- c4_complex_lib, a C++ class for float complex (C4) numbers;
- c4lib, a library which implements a basic level of single precision complex (C4) arithmetic.
- c8_complex_lib, a C++ class for double precision complex (C8) numbers;
- c8lib, a library which implements certain elementary functions for double precision complex (C8) variables;
- caesar, a library which can apply a Caesar Shift Cipher to a string of text.
- calendar_rd, a program which computes the representation of a given date in a number of calendrical systems, by Edward Reingold and Nachum Dershowitz.
- calpak, a library which makes various calendar calculations;
- catalog, a program which extracts routine definition lines from a marked-up C, C++, FORTRAN77 or FORTRAN90 file;
- cauchy_principal_value, a library which uses Gauss-Legendre quadrature to estimate the Cauchy Principal Value (CPV) of certain singular integrals.
- caustic_opengl, a program which computes a caustic curve and displays it using OpenGL.
- cblas a program which illustrates the use of the CBLAS, a C translation of the FORTRAN77 Basic Linear Algebra Subprograms (BLAS) which are used by CLAPACK, the C translation of the FORTRAN77 LAPACK linear algebra library.
- cc_io a library which reads and writes sparse linear systems stored in the Compressed Column (CC) format.
- cc_to_st a library which converts a sparse matrix from compressed column (CC) to sparse triplet (ST) format.
- ccn_rule, a program which defines a nested Clenshaw Curtis quadrature rule.
- ccvt_box, a program which carries out a Centroidal Voronoi Tessellation (CVT) calculation constrained to a box region, with points projected to the boundary;
- cdflib, a library which evaluates the cumulative density function (CDF), inverse CDF, and certain other inverse functions, for distributions including beta, binomial, chi-square, noncentral chi-square, F, noncentral F, gamma, negative binomial, normal, Poisson, and students T, by Barry Brown, James Lovato, Kathy Russell.
- cell, a library which defines a cell array, a generalization of an array which can compactly store and retrieve vector or matrix data of varying size, such as the rows of a triangular matrix.
- cellular_automaton, a program which demonstrates the 1D Cellular Automaton known as rule #30.
- cg, a library which implements a simple version of the conjugate gradient (CG) method for solving a system of linear equations of the form A*x=b, suitable for situations in which the matrix A is positive definite (only real, positive eigenvalues) and symmetric.
- cg_rc, a library which implements the conjugate gradient (CG) method for solving a positive definite sparse linear system A*x=b, using reverse communication (RC).
- change_making, a library which considers the change making problem, in which a given sum is to be formed using coins of various denominations.
- chebyshev, a library which computes the Chebyshev interpolant/approximant to a given function over an interval.
- chebyshev_interp_1d, a library which determines the combination of Chebyshev polynomials which interpolates a set of data, so that p(x(i)) = y(i).
- chebyshev_polynomial, a library which considers the Chebyshev polynomials T(i,x), U(i,x), V(i,x) and W(i,x). Functions are provided to evaluate the polynomials, determine their zeros, produce their polynomial coefficients, produce related quadrature rules, project other functions onto these polynomial bases, and integrate double and triple products of the polynomials.
- chebyshev_series, a library which can evaluate a Chebyshev series approximating a function f(x), while efficiently computing one, two or three derivatives of the series, which approximate f'(x), f''(x), and f'''(x), by Manfred Zimmer.
- chebyshev1_rule, a program which computes and writes out a Gauss-Chebyshev type 1 quadrature rule of given order.
- chebyshev2_rule, a program which computes and writes out a Gauss-Chebyshev type 2 quadrature rule of given order.
- chrpak, a library which can manipulate characters and strings;
- circle_arc_grid, a program which computes grid points along a circular arc.
- circle_integrals, a library which returns the exact value of the integral of any monomial over the circumference of the unit circle in 2D.
- circle_monte_carlo, a library which applies a Monte Carlo method to estimate the integral of a function along the circumference of the unit circle in 2D;
- circle_rule, a library which computes quadrature rules for the unit circle in 2D, that is, the circumference of the circle of radius 1 and center (0,0).
- circle_segment, a library which carries out computations associated with a circle segment, including height, angle, area, centroid, sampling, and quadrature, creating some graphics images using gnuplot.
- cities, a library which works with city-to-city distance matrices;
- clapack_test, C++ programs which illustrate the use of CLAPACK, a translation of the FORTRAN77 BLAS and LAPACK linear algebra libraries, including single and double precision, real and complex arithmetic.
- clausen, a library which evaluates a Chebyshev interpolant to the Clausen function Cl2(x).
- clenshaw_curtis_rule, a program which implements a Clenshaw Curtis quadrature rule;
- cnf_io, a library which reads or writes Conjunctive Normal Form (CNF) data files, used to store boolean formulas.
- collatz_recursive, a library which demonstrates recursive programming by considering the simple Collatz 3n+1 problem.
- colored_noise, a library which generates samples of noise obeying a 1/f^alpha power law.
- combination_lock, a program which simulates the process of determining the secret combination of a lock.
- combo, a library which includes routines for ranking, unranking, enumerating and randomly selecting balanced sequences, cycles, graphs, Gray codes, subsets, partitions, permutations, restricted growth functions, Pruefer codes and trees.
- communicator_mpi, a program which creates new communicators involving a subset of initial set of MPI processes in the default communicator MPI_COMM_WORLD.
- compass_search, a library which seeks the minimizer of a scalar function of several variables using compass search, a direct search algorithm that does not use derivatives.
- complex_numbers, a program which demonstrates some simple features involved in the use of complex numbers in C programming.
- condition, a library which implements methods of computing or estimating the condition number of a matrix.
- continued_fraction a library which implements some simple algorithms for dealing with simple and generalized continued fractions.
- cordic, a library which computes a few special functions using the CORDIC algorithm.
- correlation, a library which contains examples of statistical correlation functions.
- cosine_transform, a library which demonstrates some simple properties of the discrete cosine transform (DCT).
- cpp, programs which illustrate some features of the C++ language;
- cpp_arrays, programs which illustrate the use of vectors, matrices and tensors.
- cpp_files, programs which illustrate the use of files.
- cpp_intrinsics, a program which illustrates the use of intrinsic functions supplied by C++.
- cpp_random, programs which illustrate the use of the C++ random number generator (RNG) functions.
- cr2crlf, a program which converts carriage returns to carriage returns + linefeeds in a file;
- cr2lf, a program which converts carriage returns to linefeeds in a file;
- crc, a library which computes the cyclic redundancy checksum (CRC) as used by the PNG data format.
- crrm, a program which removes carriage returns from a file;
- cube_arbq_rule, a library which returns quadrature rules, with exactness up to total degree 15, over the interior of the symmetric cube in 3D, by Hong Xiao and Zydrunas Gimbutas.
- cube_exactness, a library which investigates the polynomial exactness of quadrature rules over the interior of a cube in 3D.
- cube_felippa_rule, a library which returns Felippa's quadratures rules for approximating integrals over the interior of a cube in 3D.
- cube_grid, a library which computes a grid of points over the interior of a cube in 3D.
- cube_integrals, a library which returns the exact value of the integral of any monomial over the interior of the unit cube in 3D.
- cube_monte_carlo, a library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit cube in 3D.
- cuda_loop, a library which shows how, in a CUDA program, the user's choice of block and thread factors determines the allocation of tasks to processors.
- cvt, a library which computes an N point CVT Centroidal Voronoi Tessellation (CVT) in M dimensions;
- cvt_dataset, a program which creates a Centroidal Voronoi Tessellation (CVT) dataset;
- cycle_brent, a library which carries out an iterated function evaluation to determine the nearest element of a cycle, and the cycle's length, using Brent's method.
- cycle_floyd, a library which carries out an iterated function evaluation, and seeks to determine the nearest element of a cycle, and the cycle's length, using Floyd's method.
- cyclic_reduction, a library which solves a tridiagonal linear system using cyclic reduction;
- decomment, a program which removes from a file every line that begins with "#" (a common convention for indicating comments);
- delaunay_tree_2d, a program which computes the Delaunay triangulation of a 2D dataset, by Olivier Devillers.
- diaphony, a program which reads a file of N points in M dimensions and computes its diaphony, a measure of point dispersion.
- differ, determines the finite difference coefficients necessary in order to combine function values at known locations to compute an approximation of given accuracy to a derivative of a given order.
- dijkstra, a library which implements a simple version of Dijkstra's minimum distance algorithm for graphs.
- dijkstra_openmp, a program which uses OpenMP to parallelize a simple example of Dijkstra's minimum distance algorithm for graphs.
- disk_grid, a library which computes grid points within the interior of a disk of user specified radius and center in 2D, using GNUPLOT to create an image of the grid.
- disk_monte_carlo, a library which applies a Monte Carlo method to estimate integrals of a function over the interior of the general disk in 2D;
- disk_rule, a library which computes quadrature rules for the general disk in 2D.
- disk01_integrals, a library which returns the exact value of the integral of any monomial over the interior of the unit disk in 2D.
- disk01_monte_carlo, a library which applies a Monte Carlo method to estimate integrals of a function over the interior of the unit disk in 2D;
- disk01_quarter_monte_carlo, a library which applies a Monte Carlo method to estimate integrals of a function over the interior of the unit quarter disk in 2D;
- disk01_rule, a library which computes quadrature rules for the unit disk in 2D, that is, the interior of the circle of radius 1 and center (0,0).
- dislin_test, C++ programs which illustrate the use of dislin, a scientific graphics package, by Helmut Michels.
- divdif, a library which uses divided differences to compute the polynomial interpolant to a given set of data.
- doomsday, a library which is given the year, month and day of a date, and uses John Conway's doomsday algorithm to determine the corresponding day of the week.
- dream, a program which implements the DREAM algorithm for accelerating Markov Chain Monte Carlo (MCMC) convergence using differential evolution, using five user functions to define the problem, by Guannan Zhang.
- duel_simulation, a program which simulates N repetitions of a duel between two players, each of whom has a known firing accuracy.
- edge, a library which defines some test functions in 1D, 2D and 3D for the detection of edges or discontinuities, and using gnuplot to display the curves or surfaces.
- eispack, a library which carries out eigenvalue computations. It includes a function to compute the singular value decomposition (SVD) of a rectangular matrix. This library was superseded by LAPACK;
- ellipse_grid, a library which computes grid points over the interior of an ellipse in 2D.
- ellipse_monte_carlo, a library which uses the Monte Carlo method to estimate the value of integrals over the interior of an ellipse in 2D.
- ellipsoid_grid, a library which computes a grid of points over the interior of an ellipsoid in 3D.
- ellipsoid_monte_carlo, a library which uses the Monte Carlo method to estimate the value of integrals over the interior of an ellipsoid in M dimensions.
- elliptic_integral, a library which evaluates complete elliptic integrals of first, second and third kind, using Carlson's elliptic integral functions.
- exactness, a library which investigates the exactness of quadrature rules that estimate the integral of a function with a density, such as 1, exp(-x) or exp(-x^2), over an interval such as [-1,+1], [0,+oo) or (-oo,+oo).
- fair_dice_simulation, a program which simulates N tosses of 2 dice, creating graphics files for processing by gnuplot.
- fastgl, a library which carries out the rapid computation of the Kth value and weight of an N point Gauss-Legendre quadrature rule, by Ignace Bogaert.
- faure, a library which computes elements of the Faure M-dimensional Quasi Mont Carlo (QMC) sequence;
- faure_dataset, a program which creates a Faure Quasi Mont Carlo (QMC) dataset;
- fd_predator_prey, a program which solves a pair of predator prey ordinary differential equations (ODE's) using the finite difference method (FDM).
- fd1d_advection_diffusion_steady, a program which applies the finite difference method (FDM) to solve the steady advection diffusion equation v*ux-k*uxx=0 in one spatial dimension, with constant velocity v and diffusivity k, writing graphics files for processing by gnuplot.
- fd1d_advection_ftcs, a program which applies the finite difference method (FDM) to solve the time-dependent advection equation ut = - c * ux in one spatial dimension, with a constant velocity, using the forward time centered space (FTCS) method, writing graphics files for processing by gnuplot.
- fd1d_advection_lax, a program which applies the finite difference method (FDM) to solve the time-dependent advection equation ut = - c * ux in one spatial dimension, with a constant velocity, using the Lax method to approximate the time derivative, writing graphics files for processing by gnuplot.
- fd1d_advection_lax_wendroff, a program which applies the finite difference method (FDM) to solve the time-dependent advection equation ut = - c * ux in one spatial dimension, with a constant velocity, using the Lax-Wendroff method to approximate the time derivative, writing graphics files for processing by gnuplot.
- fd1d_burgers_lax, a program which applies the finite difference method (FDM) and the Lax Wendroff method to solve the non-viscous time-dependent Burgers equation in one spatial dimension.
- fd1d_burgers_leap, a program which applies the finite difference method (FDM) and the leapfrog approach to solve the non-viscous time-dependent Burgers equation in one spatial dimension.
- fd1d_bvp, a program which applies the finite difference method (FDM) to a two point boundary value problem (BVP) in one spatial dimension.
- fd1d_heat_explicit, a library which uses the finite difference method (FDM), with explicit time stepping, to solve the time dependent 1D heat equation;
- fd1d_heat_implicit, a program which implements a finite difference method (FDM), implicit in time, of the time dependent 1D heat equation;
- fd1d_heat_steady, a program which implements a finite difference method (FDM) for the steady (time independent) 1D heat equation;
- fd1d_wave, a program which applies the finite difference method (FDM) to solve the time-dependent wave equation utt = c * uxx in one spatial dimension.
- fd2d_heat_steady, a program which implements a finite difference method (FDM) for the steady (time independent) 2D heat equation;
- fem_basis, a library which can define and evaluate finite element method (FEM) basis functions for any degree in an M-dimensional simplex (1D interval, 2D triangle, 3D tetrahedron, and higher dimensional generalizations.)
- fem_io, a library which reads or writes FEM files, which describe the nodes, elements, and function values associated with a finite element method (FEM) model;
- fem_to_gmsh, a program which reads a pair of FEM files defining node coordinates and elements, of a 1D, 2D or 3D mesh, namely a file of node coordinates and a file of elements defined by node indices, and creates a Gmsh mesh file.
- fem_to_medit, a program which reads a pair of FEM files defining node coordinates and elements, of a 2D mesh, namely a file of node coordinates and a file of elements defined by node indices, and creates a corresponding MEDIT mesh file.
- fem_to_mesh, a program which reads a set of FEM files defining the node coordinates, boundary nodes, and elements of a finite element mesh, and rewrites the data as a MESH file.
- fem_to_triangle, a program which reads FEM files defining a 2D mesh of triangles, namely a file of node coordinates and a file of elements defined by node indices, and creates a corresponding pair of node and element files for use by Jonathan Shewchuk's triangle program.
- fem_to_xml, reads a pair of FEM files defining node coordinates and elements, of a 1D, 2D or 3D mesh, namely a file of node coordinates and a file of elements defined by node indices, and creates a corresponding XML file for input to DOLFIN or FENICS.
- fem1d, a program which applies the finite element method (FEM), using piecewise linear basis functions, to a linear two point boundary value problem (BVP) in 1D;
- fem1d_adaptive, a program which uses an adaptive mesh when applying the finite element method (FEM), with piecewise linear basis functions, to a linear two point boundary value problem (BVP) in 1D;
- fem1d_bvp_linear, a program which applies the finite element method (FEM), with piecewise linear elements, to a two point boundary value problem (BVP) in one spatial dimension, and compares the computed and exact solutions with the L2 and seminorm errors.
- fem1d_bvp_quadratic, a program which applies the finite element method (FEM), with piecewise quadratic elements, to a two point boundary value problem (BVP) in one spatial dimension, and compares the computed and exact solutions with the L2 and seminorm errors.
- fem1d_heat_steady, a program which implements the finite element method (FEM) for the steady (time independent) 1D heat equation;
- fem1d_lagrange, a library which sets up the matrices and vectors associated with the finite element method (FEM) solution of a boundary value problem (BVP) -u''+u=f(x), using Lagrange basis polynomials.
- fem1d_nonlinear, a program which applies the finite element method (FEM), with piecewise linear basis functions, to a nonlinear two point boundary value problem (BVP) in 1D;
- fem1d_pack, a library which contains utilities for 1D finite element method (FEM) calculations.
- fem1d_pmethod, a program which applies the p-method version of the finite element method (FEM) to a linear two point boundary value problem (BVP) in 1D;
- fem1d_project, a program which projects data into a finite element space, including the least squares approximation of data, or the projection of a finite element solution from one mesh to another.
- fem1d_sample, a program which samples a scalar or vector finite element function of one variable, defined by FEM files, returning interpolated values at the sample points.
- fem2d_bvp_linear, a program which applies the finite element method (FEM), with piecewise linear elements, to a 2D boundary value problem (BVP) in a rectangle, and compares the computed and exact solutions with the L2 and seminorm errors.
- fem2d_bvp_quadratic, a program which applies the finite element method (FEM), with piecewise quadratic elements, to a 2D boundary value problem (BVP) in a rectangle, and compares the computed and exact solutions with the L2 and seminorm errors.
- fem2d_bvp_serene, a program which applies the finite element method (FEM), with serendipity elements, to a 2D boundary value problem (BVP) in a rectangle, and compares the computed and exact solutions with the L2 and seminorm errors.
- fem2d_heat, a program which applies the finite element method (FEM) to solve the time-dependent heat equation in an arbitrary triangulated region in 2D;
- fem2d_heat_rectangle, a program which applies the finite element method (FEM) to solve the time dependent heat equation on a square in 2D;
- fem2d_heat_square, a library which defines the geometry of a square region, as well as boundary and initial conditions for a given heat problem, and is called by fem2d_heat as part of a solution procedure.
- fem2d_mesh_display_opengl, a program which reads a pair of FEM files defining node coordinates and elements, of a 2D mesh, and displays it using OpenGL.
- fem2d_pack, a library which implements various 2D finite element method (FEM) calculations;
- fem2d_poisson, a program which applies the finite element method (FEM) to solve Poisson's equation in an arbitrary triangulated region in 2D;
- fem2d_poisson_cg, a program which solves Poisson's equation on a triangulated region, using the finite element method (FEM), sparse storage, and a conjugate gradient solver.
- fem2d_poisson_cg_baffle, a library which defines the geometry of a channel with 13 hexagonal baffles, as well as boundary conditions for a given Poisson problem, and is called by fem2d_poisson_cg as part of a solution procedure.
- fem2d_poisson_cg_ell, a library which defines the geometry of an L-shaped region, as well as boundary conditions for a given Poisson problem, and is called by fem2d_poisson_cg as part of a solution procedure.
- fem2d_poisson_cg_lake, a library which defines the geometry of a lake-shaped region, as well as boundary conditions for a given Poisson problem, and is called by fem2d_poisson_cg as part of a solution procedure.
- fem2d_poisson_ell, a library which defines the geometry of an L-shaped region, as well as boundary conditions for a given Poisson problem, and is called by fem2d_poisson as part of a solution procedure.
- fem2d_poisson_lake, a library which defines the geometry of a lake-shaped region, as well as boundary conditions for a given Poisson problem, and is called by fem2d_poisson as part of a solution procedure.
- fem2d_poisson_rectangle, a program which solves the 2D Poisson equation on a rectangle, using the finite element method (FEM), and piecewise quadratic triangular elements.
- fem2d_poisson_rectangle_linear, a program which solves the 2D Poisson equation on a rectangle, using the finite element method (FEM), and piecewise linear triangular elements.
- fem2d_poisson_sparse, a program which uses the finite element method to solve Poisson's equation on an arbitrary triangulated region in 2D; (This is a version of fem2d_poisson which replaces the banded storage and direct solver by a sparse storage format and an iterative solver.)
- fem2d_poisson_sparse_baffle, a library which defines the geometry of a rectangular channel with 13 baffles, as well as boundary conditions for a given Poisson problem, and is called by fem2d_poisson_sparse as part of a solution procedure.
- fem2d_poisson_sparse_ell, a library which defines the geometry of an L-shaped region, as well as boundary conditions for a given Poisson problem, and is called by fem2d_poisson_sparse as part of a solution procedure.
- fem2d_poisson_sparse_lake, a library which defines the geometry of a lake-shaped region, as well as boundary conditions for a given Poisson problem, and is called by fem2d_poisson_sparse as part of a solution procedure.
- fem2d_project, a program which projects a function f(x,y), given as data, into a given finite element space of piecewise linear triangular elements.
- fem2d_project_function, a program which projects a function f(x,y), given as a formula, into a given finite element space of piecewise linear triangular elements.
- fem2d_sample, a program which samples a finite element function, defined by FEM files, (three text files describing the nodes, triangles, and coefficients); at arbitrary points.
- fem3d_pack, a library which contains utilities for 3D finite element method (FEM) calculations.
- fem3d_project, a program which projects a function f(x,y,z), given as a data, into a given space of piecewise linear tetrahedrons associated with the finite element method (FEM).
- fem3d_sample, a program library which evaluates a finite element function defined on a 3D tetrahedral mesh.
- fern_opengl, a program which uses OpenGL to display the Barnsley fractal fern.
- feynman_kac_1d, a program which demonstrates the use of the Feynman-Kac algorithm to solve Poisson's equation in a 1D interval by averaging stochastic paths to the boundary.
- feynman_kac_2d, a program which demonstrates the use of the Feynman-Kac algorithm to solve Poisson's equation in a 2D ellipse by averaging stochastic paths to the boundary.
- feynman_kac_3d, a program which demonstrates the use of the Feynman-Kac algorithm to solve Poisson's equation in a 3D ellipsoid by averaging stochastic paths to the boundary.
- fft_openmp, a program which demonstrates the computation of a Fast Fourier Transform (FFT) in parallel, using OpenMP.
- fft_serial, a program which computes a Fast Fourier Transform (FFT), and is intended as a starting point for implementing an OpenMP parallel version.
- file_name_sequence, a program which demonstrates ways to generate a sequence of filenames, which can be useful when generating a sequence of still snapshots to be animated later.
- files_multiple, a program which demonstrates how a program can open multiple output files at one time, and write data to any one specific file it chooses.
- filon, a library which can approximate integrals in which the integrand includes an oscillatory factor of sin(k*x) or cos(k*x).
- filum, a library which performs various operations with files;
- fire_serial, a program which simulates a forest fire over a rectangular array of trees, starting at a single random location. It is intended as a starting point for the development of a parallel version.
- floyd, a library which implements Floyd's algorithm for finding the shortest distance between pairs of nodes on a directed graph.
- fn, a library which evaluates elementary and special functions using Chebyshev polynomials; functions include Airy, Bessel I, J, K and Y, beta, confluent hypergeometric, error, gamma, log gamma, Pochhammer, Spence; integrals include hyperbolic cosine, cosine, Dawson, exponential, logarithmic, hyperbolic sine, sine; by Wayne Fullerton.
- freefem++_msh_io, a library which can read and write files used by the FreeFem++ finite element program to store mesh information.
- g++_intrinsics, a program which tests or demonstrates some of the intrinsic functions provided by the Gnu G++ compiler for C++.
- g++_quadmath, a program which illustrates the use of quadruple precision real arithmetic, as provided on some systems by the Gnu g++ compiler for C++.
- gegenbauer_cc, a library which computes the Gegenbauer weighted integral of a function f(x) using a Clenshaw-Curtis approach.
- gegenbauer_exactness, a program which tests the polynomial exactness of Gauss-Gegenbauer quadrature rules.
- gegenbauer_polynomial, a library which evaluates the Gegenbauer polynomial and associated functions.
- gegenbauer_rule, a program which computes and writes out a Gauss-Gegenbauer quadrature rule of given order.
- gen_hermite_rule, a program which computes and writes out a generalized Gauss-Hermite quadrature rule of given order and parameter value.
- gen_hermite_rule_ss, a program which computes and writes out a generalized Gauss-Hermite quadrature rule of given order and parameter value, using a Stroud and Secrest algorithm.
- gen_laguerre_rule, a program which computes and writes out a generalized Gauss-Laguerre quadrature rule of given order and parameter value.
- gen_laguerre_rule, a program which computes and writes out a generalized Gauss-Laguerre quadrature rule of given order and parameter value, using a Stroud and Secrest algorithm.
- geometry, a library which performs geometric calculations in 2, 3 and M dimensional space, including the computation of angles, areas, containment, distances, intersections, lengths, and volumes.
- gmsh_io, a library which can read or write some of the files created by the Gmsh program for 1D, 2D or 3D meshes used by the finite element method (FEM).
- gmsh_to_fem, a program which reads a mesh data file created by the GMSH program and writes a pair of node and element files that correspond to the FEM format.
- gnuplot_i_examples, programs which demonstrate the use of the gnuplot_i library for interactive runtime gnuplot graphics.
- gnuplot_test, C++ programs which illustrate how a program can write data and command files so that gnuplot can create plots of the program results.
- gprof, programs which illustrate the use of the gprof program performance monitor;
- graphics_examples, programs which illustrate how various kinds of data can be displayed and analyzed graphically.
- grf_display_opengl, a program which reads a GRF file defining a mathematical graph and displays it in the OpenGL graphics window.
- grf_io, a library which reads or writes a GRF file;
- grid, a library which randomly selects N distinct points from a uniform grid in the unit hypercube in M-dimensional space.
- grid_to_bmp, a program which reads a text file of data on a rectangular grid and creates a BMP file containing a color image of the data.
- gsl_test, C++ programs which illustrate the use of the Gnu Scientific Library (GSL);
- haar, a library which computes the Haar transform of data.
- halton, a library which computes elements of a Halton Quasi Monte Carlo (QMC) sequence, using a simple interface.
- halton_advanced, a library which calculates the Halton M dimensional Quasi Mont Carlo (QMC) sequence, using an advanced interface with many input quantities.
- halton_dataset, a program which creates a Halton Quasi Mont Carlo (QMC) sequence;
- hammersley, a library which computes elements of a Hammersley Quasi Monte Carlo (QMC) sequence, using a simple interface.
- hammersley_advanced, a library which computes a Hammersley M-dimensional Quasi Mont Carlo (QMC) sequence using an advanced interface with many input options;
- hammersley_dataset, a program which creates a Hammersley Quasi Mont Carlo (QMC) sequence;
- hankel_cholesky, a library which computes the upper Cholesky factor R of a nonnegative definite symmetric H matrix so that H = R' * R.
- hankel_pds, a library which can compute a lower triangular matrix L which is the Cholesky factor of a positive definite (symmetric) Hankel matrix H, that is, H = L * L'.
- hb_io, a library which reads and writes matrices in the Harwell Boeing (HB) sparse matrix format;
- hb_io_new, a library which reads and writes matrices in the Harwell Boeing (HB) sparse matrix format, modified and improved by Reinhard Resch.
- hdf5_test, programs which demonstrate the use of the HDF5 library and file format.
- heat_mpi, a program which demonstrates the use of the Message Passing Interface (MPI), by solving the 1D time dependent heat equation.
- heated_plate, a program which solves the steady state heat equation in a 2D rectangular region, and is intended as a starting point for implementing an OpenMP parallel version.
- heated_plate_openmp, a program which solves the steady (time independent) heat equation in a 2D rectangular region, using OpenMP to run in parallel.
- hello, a program which prints out "Hello, world!".
- hello_mpi, a program which prints out "Hello, world!" using the Message Passing Interface (MPI) for parallel programming.
- hello_openmp, a program which prints out "Hello, world!" within the OpenMP parallel programming environment.
- hermite, a library which computes the Hermite interpolant, a polynomial that matches function values and derivatives.
- hermite_cubic, a library which can compute the value, derivatives or integral of a Hermite cubic polynomial, or manipulate an interpolating function made up of piecewise Hermite cubic polynomials.
- hermite_exactness, a program which tests the polynomial exactness of Gauss-Hermite quadrature rules for approximating the integral of a function with density exp(-x^2) over the interval (-oo,+oo).
- hermite_polynomial, a library which evaluates the physicist's Hermite polynomial, the probabilist's Hermite polynomial, the Hermite function, and related functions.
- hermite_product_polynomial, a library which defines Hermite product polynomials, creating a multivariate polynomial as the product of univariate Hermite polynomials.
- hermite_rule, a program which computes and writes out a Gauss-Hermite quadrature rule for approximating the integral of a function with density exp(-x^2) over the interval (-oo,+oo).
- hermite_rule_ss, a program which computes and writes out a Gauss-Hermite quadrature rule to estimate the integral of a function with density exp(-x^2) over the interval (-oo,+oo), using a Stroud and Secrest algorithm.
- hermite_test_int, a library which defines test integrands for Hermite integrals with density exp(-x^2) over the interval (-oo,+oo).
- hexdump, a program which produces a hexadecimal dump of a file;
- high_card_simulation, a program which simulates a situation in which you see the cards in a deck one by one, and must select the one you think is the highest and stop; the program uses gnuplot to create a graph of the results.
- hilbert_curve, a library which computes the sequence of discrete Hilbert curves whose limit is a space-filling curve.
- histogram_data_2d_sample, a program which demonstrates how to construct a Probability Density Function (PDF) from sample data over a 2D domain, and then to use that PDF to create new samples.
- htmlindex, a program which creates a skeleton HTML page for a marked-up C, C++ or FORTRAN file;
- hyperball_integrals, a library which returns the exact value of the integral of any monomial over the interior of the unit hyperball in M dimensions.
- hyperball_monte_carlo, a library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit ball in M dimensions;
- hyperball_volume_monte_carlo, a program which applies a Monte Carlo procedure to estimate the volume of the unit ball in M dimensions;
- hypercube_exactness, a program which tests the polynomial exactness of a quadrature rule over the interior of the unit hypercube in M dimensions.
- hypercube_grid, a library which computes a grid of points over the interior of a hypercube in M dimensions.
- hypercube_integrals, a library which returns the exact value of the integral of any monomial over the interior of the unit hypercube in M dimensions.
- hypercube_monte_carlo, a library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit hypercube in M dimensions.
- hypersphere_integrals, a library which returns the exact value of the integral of any monomial over the surface of the unit hypersphere in M dimensions.
- hypersphere_monte_carlo, a library which applies a Monte Carlo method to estimate the integral of a function on the surface of the unit sphere in M dimensions;
- hypersphere_properties, a library which carries out various operations for an M dimensional hypersphere, including converting between Cartesian and spherical coordinates, stereographic projection, sampling the surface of the sphere, and computing the surface area and volume.
- i2_binary_to_ascii, a program which converts a file of short int (I2) data from binary to ASCII format.
- i4lib, a library which contains many utility routines, using single precision integer (I4) arithmetic.
- i8lib, a library which contains many utility routines, using double precision integer (I8) arithmetic.
- ice_io, a library which can read or write an ICE dataset, which defines a 3D grid, using the NETCDF file format.
- ice_to_mesh, a program which reads a NETCDF file containing an ICE dataset and rewrites the information as a MESH file.
- ihs, a library which computes elements of the Improved Hypercube Sampling (IHS) M-dimensional Quasi Mont Carlo (QMC) sequence;
- ihs_dataset, a program which creates an Improved Hypercube Sampling (IHS) dataset;
- image_components, a library which seeks the connected nonzero or nonblack components of an image or integer array.
- image_denoise, a library which applies simple filtering operations to a noisy image.
- image_edge, a library which demonstrates a simple procedure for edge detection in images.
- index, a library which converts a M-dimensional vector index to a one-dimensional vector index; it can handle zero and one based indexing schemes, as well as column major and row major conventions.
- int_exactness, a program which tests the polynomial exactness of a 1D quadrature rule for a finite interval;
- int_exactness_chebyshev1, a program which tests the polynomial exactness of Gauss-Chebyshev type 1 quadrature rules.
- int_exactness_chebyshev2, a program which tests the polynomial exactness of Gauss-Chebyshev type 2 quadrature rules.
- int_exactness_gen_hermite, a program which tests the polynomial exactness of generalized Gauss-Hermite quadrature rules.
- int_exactness_gen_laguerre, a program which tests the polynomial exactness of generalized Gauss-Laguerre quadrature rules.
- interp, a library which can be used for parameterizing and interpolating data;
- isbn, a library which can determine the check digit for an International Standard Book Number or report whether a given ISBN is valid.
- ising_2d_simulation, a program which simulates the evolution of a 2D array of positive and negative charges, each of which is likely to flip to be in agreement with neighbors, using gnuplot to display the initial and final configurations.
- ivcon, a program which converts between various 3D graphic file formats;
- jacobi, a program which implements the Jacobi iteration for linear systems.
- jacobi_eigenvalue, a library which implements the Jacobi iteration for the iterative determination of the eigenvalues and eigenvectors of a real symmetric matrix.
- jacobi_exactness, a program which tests the polynomial exactness of rules for integrals with a Jacobi weight function.
- jacobi_openmp, a program which illustrates the use of the OpenMP application program interface to parallelize a Jacobi iteration solving A*x=b.
- jacobi_polynomial, a library which evaluates the Jacobi polynomial and associated functions.
- jacobi_rule, a program which computes and writes out a Gauss-Jacobi quadrature rule of given order.
- jacobi_rule_ss, a program which computes and writes out a Gauss-Jacobi quadrature rule of given order, using a Stroud and Secrest algorithm.
- kmeans, a library which handles the K-Means problem, which organizes a set of N points in M dimensions into K clusters;
- knapsack_01, a library which uses brute force to solve small versions of the 0/1 knapsack problem;
- kronrod, a library which can compute a Gauss and Gauss-Kronrod pair of quadrature rules of arbitrary order, by Robert Piessens, Maria Branders.
- l4lib, a library which contains many utility routines, using one byte logical (L4) variables.
- lagrange_approx_1d, a library which defines and evaluates the Lagrange polynomial p(x) of degree m which approximates a set of nd data points (x(i),y(i)).
- lagrange_interp_1d, a library which defines and evaluates the Lagrange polynomial p(x) which interpolates a set of data depending on a 1D argument, so that p(x(i)) = y(i).
- lagrange_interp_2d, a library which defines and evaluates the Lagrange polynomial p(x,y) which interpolates a set of data depending on a 2D argument that was evaluated on a product grid, so that p(x(i),y(j)) = z(i,j).
- lagrange_interp_nd, a library which defines and evaluates the Lagrange polynomial p(x) which interpolates a set of data depending on a M-dimensional argument that was evaluated on a product grid, so that p(x(i)) = z(i).
- lagrange_nd, a library which implements several multivariate Lagrange interpolation schemes developed by Tomas Sauer.
- laguerre_exactness, a program which tests the polynomial exactness of Gauss-Laguerre quadrature rules for integrating functions with density exp(-x) over [0,+oo).
- laguerre_polynomial, a library which evaluates the Laguerre polynomial, the generalized Laguerre polynomials, and the Laguerre function.
- laguerre_rule, a program which computes and writes out a Gauss-Laguerre quadrature rule for approximating the integral of a function with density exp(-x) over the interval [0,+oo).
- laguerre_rule_ss, a program which computes a Gauss-Laguerre quadrature rule of given order, and writes it to a file, using a Stroud and Secrest algorithm.
- laguerre_test_int, a library which implements test problems for for Gauss-Laguerre type quadrature rules for approximating the integral of a function with density exp(-x) over the interval [0,+oo).
- latin_center, a library which computes Latin Center Squares of N points in M dimensions;
- latin_center_dataset, a program which creates a Latin Center Hypercube dataset;
- latin_cover, a library which produces N Latin squares which cover an NxN square, or NxN Latin cubes which cover an NxNxN cube.
- latin_edge, a library which computes Latin Edge Squares of N points in M dimensions;
- latin_edge_dataset, a program which creates a Latin Edge Hypercube dataset;
- latin_random, a library which computes Latin Random Squares of N points in M dimensions;
- latin_random_dataset, a program which creates a Latin Random Hypercube dataset;
- latinize, a library which adjusts N points in M dimensions to form a Latin Hypercube;
- lattice_rule, a library which returns lattice rules for M-dimensional integration;
- lcvt, a library which creates a Latinized Centroidal Voronoi Tessellation (CVT);
- lcvt_dataset, a program which creates a Latinized Centroidal Voronoi Tessellation (CVT);
- lebesgue, a library which is given a set of nodes in 1D, and plots the Lebesgue function, and estimates the Lebesgue constant, which measures the maximum magnitude of the potential error of Lagrange polynomial interpolation.
- legendre_exactness, a program which tests the monomial exactness of quadrature rules for the Legendre problem of integrating a function with density 1 over the interval [-1,+1].
- legendre_polynomial, a library which evaluates the Legendre polynomial and associated functions.
- legendre_product_polynomial, a library which defines Legendre product polynomials, creating a multivariate polynomial as the product of univariate Legendre polynomials.
- legendre_rule, a program which writes out a Gauss-Legendre quadrature rule of given order.
- legendre_rule_fast, a program which uses a fast (order N) algorithm to compute a Gauss-Legendre quadrature rule of given order.
- legendre_shifted_polynomial, a library which evaluates the shifted Legendre polynomial, with the domain [0,1].
- levenshtein, a library which returns the Levenshtein distance between two strings.
- lf2cr, a program which converts linefeeds to carriage returns in a file;
- lf2crlf, a program which converts linefeeds to carriage return + linefeeds in a file;
- lfrm, a program which removes all linefeed characters from a file;
- life_opengl, a program which uses OpenGL to display the evolution of John Conway's Game of Life.
- life_serial, a program which computes a few steps of the evolution of John Conway's Game of Life, intended as a starting point for implementing a parallel version.
- lights_out_opengl, a program which sets up a Lights Out game and allows the user to solve it, using the OpenGL graphics window.
- line_cvt_lloyd, a library which applies Lloyd's iteration repeatedly to a set of N points, to compute a Centroidal Voronoi Tessellation (CVT) over the interior of a line segment in 1D.
- line_fekete_rule, a library which estimates the location of N Fekete points, for polynomial interpolation or quadrature, over the interior of a line segment in 1D.
- line_felippa_rule, a library which returns Felippa's quadratures rules for approximating integrals over the interior of a line segment in 1D.
- line_grid, a library which computes a grid of points over the interior of a line segment in 1D.
- line_integrals, a library which returns the exact value of the integral of any monomial over the length of the unit line in 1D.
- line_monte_carlo, a library which applies a Monte Carlo method to estimate the integral of a function over the length of the unit line in 1D.
- line_ncc_rule, a library which computes a Newton Cotes (Closed) quadrature rule, using equally spaced points, over the interior of a line segment in 1D.
- line_nco_rule, a library which computes a Newton Cotes Open (NCO) quadrature rule, using equally spaced points, over the interior of a line segment in 1D.
- linpack, a library which solves linear systems for a variety of matrix storage schemes, real or complex arithmetic, and single or double precision, by Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart.
- linpack_bench_d, a program which is a version of the double precision real LINPACK benchmark program;
- linpack_bench, a program which is a version of the single precision real LINPACK benchmark program;
- linpack_c, a library which factors matrices in a variety of formats, and solving the associated linear systems, using single precision complex arithmetic; it includes a function for the singular value decomposition (SVD) of a rectangular matrix, by Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart.
- linpack_d, a library which factors matrices in a variety of formats, and solving the associated linear systems, using double precision real arithmetic; it includes a function for the singular value decomposition (SVD) of a rectangular matrix, by Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart.
- linpack_s, a library which factors matrices in a variety of formats, and solving the associated linear systems, using single precision real arithmetic; it includes a function for the singular value decomposition (SVD) of a rectangular matrix, by Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart.
- linpack_z, a library which factors matrices in a variety of formats, and solving the associated linear systems, using double precision complex arithmetic; it includes a function for the singular value decomposition (SVD) of a rectangular matrix, by Jack Dongarra, Cleve Moler, Jim Bunch, Pete Stewart.
- lissajous_opengl, a program which computes a Lissajous curve and displays it using OpenGL.
- llsq, a library which solves the simple linear least squares (LLS) problem of finding the formula of a straight line y=a*x+b which minimizes the root-mean-square error to a set of N data points.
- lobatto_polynomial, a library which evaluates Lobatto polynomials similar to Legendre polynomials except that they are 0 at both endpoints.
- local_min_rc, a library which finds a local minimum of a scalar function of a scalar variable, without the use of derivative information, using reverse communication (RC), by Richard Brent.
- log_normal, a library which returns quantities related to the log normal Probability Distribution Function (PDF).
- log_normal_truncated_ab, a library which returns quantities related to the log normal Probability Distribution Function (PDF) truncated to the interval [A,B].
- lorenz_ode, a program which approximates solutions to the Lorenz system, creating output files that can be displayed by gnuplot.
- luhn, a library which can compute the Luhn check digit for a string, or verify a string, as used for error detection in credit card numbers.
- machar, a library which dynamically computes the values of various machine constants, by William Cody;
- machine, a library which returns tabulated values of the constants associated with computer arithmetic.
- makefiles, programs which illustrate the use of makefiles for maintaining a software project;
- mandelbrot, a program which generates an ASCII Portable Pixel Map (PPM) image of the Mandelbrot set;
- mandelbrot_openmp, a program which generates an ASCII Portable Pixel Map (PPM) image of the Mandelbrot fractal set, using OpenMP for parallel execution;
- mandelbrot_ppm, a program which generates a binary Portable Pixel Map (PPM) image of the Mandelbrot set, by Eric Weeks.
- mario, a program which creates a sort of "needlepoint" image of Mario, as an array of colored squares.
- matrix_exponential, a library which demonstrates some simple approaches to the problem of computing the exponential of a matrix.
- md, a program which carries out a molecular dynamics simulation, and is intended as a starting point for implementing an OpenMP parallel version.
- md_openmp, a program which carries out a molecular dynamics simulation in parallel using OpenMP.
- medit_io, a library which can read or write files used by the MEDIT program, which can be used to define the a mesh associated with the finite element method (FEM) in 2D or 3D, using triangles, quadrilaterals, tetrahedrons or hexahedrons.
- medit_to_fem, a program which reads a mesh file created by the MEDIT program and writes a corresponding pair of node and element files that correspond to the FEM format.
- memory_test, a program which tests the memory available on the computer by declaring and using big vectors.
- mesh_bandwidth, a program which returns the geometric bandwidth associated with a mesh of elements of any order and in a space of M dimensions.
- mesh_display_opengl, a program which reads the name of two data files defining a polygonal mesh, reads the data, and displays the mesh using OPENGL.
- mesh_io, a library which reads or writes MESH files defining a finite element mesh.
- mesh_to_ice, a program which reads a MESH file containing an ICE dataset and rewrites the information as a NETCDF file.
- metis_test, C++ programs which test the metis library, which can partition unstructured graphs or meshes, and compute fill-reducing reorderings of sparse matrices.
- mgmres, a library which applies the restarted Generalized Minimum Residual (GMRES) algorithm to solve a sparse linear system, using compressed row (CR) or sparse triplet (ST) format, by Lili Ju.
- mgs, a library which is an example of legacy code, which the student is encouraged to study, understand, and document. This example is due to Diane O'Leary.
- minesweeper, a program which is a text-based implementation of the Minesweeper game, by Detelina Stoyanova.
- minpack, a library which solves linear least squares (LLS) and nonlinear least squares (NLS) problems.
- mixed, programs which illustrate mixed language programming in which the main program is written in C++;
- monomial, a library which enumerates, lists, ranks, unranks and randomizes multivariate monomials in a space of M dimensions, with total degree less than N, equal to N, or lying within a given range.
- monomial_value, a library which evaluates a monomial in M dimensions.
- monte_carlo_rule, a program which generates a dataset of N random M-dimensional points, regards it as a quadrature rule for the unit hypercube, and writes out three files of information.
- mpas_draw, a program which reads information from a netcdf file written by mpas(), containing the grid information and computed solution values, some of which may be time dependent, or organized in vertical atmospheric levels, and then displays graphic images of data using OpenGL.
- mpas_grid_display_opengl, programs which read information from an MPAS Grid file, stored in netcdf format, and display the main (mainly hexagonal) mesh or the dual triangulation, using OpenGL.
- mpi, programs which illustrate the use of the MPI Message Passing Interface library, for parallel programming;
- mpi_stubs, a library which may be used if a parallel program is to be compiled, loaded and run in a serial machine;
- multigrid_poisson_1d, a library which applies the multigrid method to a discretized version of the 1D Poisson equation.
- multitask_mpi, a program which demonstrates how to multitask, that is, to execute several unrelated and distinct tasks simultaneously, using MPI for parallel execution.
- multitask_openmp, a program which demonstrates how to multitask, that is, to execute several unrelated and distinct tasks simultaneously, using OpenMP for parallel execution.
- mxm, a program which sets up a matrix multiplication problem A=B*C of arbitrary size, and compares the time required for IJK, IKJ, JIK, JKI, KIJ and KJI orderings of the loops.
- mxm_openmp, a program which computes a dense matrix product C=A*B, using OpenMP for parallel execution.
- mxm_serial, a program which sets up a matrix multiplication problem A=B*C, intended as a starting point for implementing a parallel version.
- my_calendar, a program which checks a calendar file and prints lines containing the current date;
- naca, a library which can take the parameters of certain NACA airfoils and return the coordinates of a sequence of points that outline the wing shape. The points can be plotted with gnuplot.
- nas, a program which runs the NASA kernel benchmark.
- navier_stokes_2d_exact, a library which evaluates an exact solution to the incompressible time-dependent Navier-Stokes equations over an arbitrary domain in 2D.
- navier_stokes_3d_exact, a library which evaluates an exact solution to the incompressible time-dependent Navier-Stokes equations over an arbitrary domain in 3D.
- nearest_interp_1d, a library which interpolates a set of data using a piecewise constant interpolant defined by the nearest neighbor criterion, creating graphics files for processing by gnuplot.
- neighbors_to_metis_graph, a program which reads a file describing the neighbor structure of a triangulation or tet mesh, and writes a metis graph file suitable for input to one of the family of programs based on metis;
- netcdf_mpas a library which reads MPAS grid files, stored using the NETCDF format.
- netcdf_test, C++ programs which read and write netcdf files.
- newton_interp_1d, a library which finds a polynomial interpolant to data using Newton divided differences.
- niederreiter, a library which computes elements of the Niederreiter Quasi Mont Carlo (QMC) M-dimensional sequence [arbitrary base];
- niederreiter2, a library which computes elements of the Niederreiter M-dimensional Quasi Mont Carlo (QMC) sequence using base 2;
- niederreiter2_dataset, a program which creates a Niederreiter Quasi Mont Carlo (QMC) dataset with base 2;
- nint_exactness_mixed, a program which measures the polynomial exactness of an M-dimensional quadrature rule based on a mixture of 1D quadrature rule factors.
- nintlib, a library which implements approximate integration (quadrature) in M dimensions;
- normal, a library which implements a random number generator (RNG) for normally distributed values.
- normal_dataset, a program which creates a multivariate normal random dataset;
- obj_io, a library which reads and writes the data in an OBJ 3D graphics file;
- ode, a library which solves a system of ordinary differential equations, by Shampine and Gordon;
- opengl, programs which illustrate the use of the OpenGL graphics library;
- openmp, programs which illustrate the use of the OpenMP interface for parallel programming shared memory system;
- openmp_stubs, a library which is a dummy implementation of the OpenMP routines, and can be used to compile, load, and run a program using OpenMP on a system which does not have OpenMP installed.
- optimize, a program which looks at the use of automatic optimization by the compiler to make the executable code run faster.
- ornstein_uhlenbeck, a library which approximates solutions of the Ornstein-Uhlenbeck stochastic ordinary differential equation (SODE) using the Euler method, the Euler-Maruyama method, and the Milstein method, and creating graphics files for processing by gnuplot.
- owens, a library which evaluates Owen's T function;
- padua, a library which returns the coordinates of the 2D Padua points, as well as interpolation weights or quadrature weights, and images of the points in gnuplot graphics files.
- partition_problem, a library which seeks solutions of the partition problem, splitting a set of integers into two subsets with equal sum.
- patterson_rule, a program which returns the points and weights of a 1D Gauss-Patterson quadrature rule of order 1, 3, 7, 15, 31, 63, 127, 255 or 511.
- pbma_io, a library which reads or writes an ASCII Portable Bit Map (PBM) graphics file;
- pbma_to_pbmb, a program which converts an ASCII Portable Bit Map (PBM) file to a binary PBM file;
- pbmb_io, a library which reads or writes a binary Portable Bit Map (PBM) graphics file;
- pbmb_to_pbma, a program which converts a binary Portable Bit Map (PBM) file to an ASCII PBM file;
- pce_burgers, a program which defines and solves the time-dependent viscous Burgers equation, with uncertain viscosity, using a polynomial chaos expansion in terms of Hermite polynomials, by Gianluca Iaccarino.
- pce_ode_hermite, a program which sets up a simple scalar ordinary differential equation (ODE) for exponential decay with an uncertain decay rate, using a polynomial chaos expansion in terms of Hermite polynomials.
- pdflib, a library which evaluates Probability Density Functions (PDF's) and produces random samples from them, including beta, binomial, chi, exponential, gamma, inverse chi, inverse gamma, multinomial, normal, scaled inverse chi, and uniform.
- pentominoes, a library which provides some utilities for manipulating pentominoes.
- pgma_io, a library which reads or writes an ASCII Portable Gray Map (PGM) 2D graphics file;
- pgma_to_pgmb, a program which converts an ASCII Portable Gray Map (PGM) file to a binary PGM file;
- pgmb_io, a library which reads or writes a binary Portable Gray Map (PGM) 2D graphics file;
- pgmb_to_pgma, a program which converts a binary Portable Gray Map (PGM) file to an ASCII PGM file;
- piecewise_linear_product_integral, a library which calculates the exact value of the integral of the product of two piecewise linear functions f(x) and g(x).
- pink_noise, a library which computes a pink noise signal obeying a 1/f power law.
- point_merge, a library which considers N points in M dimensional space, and counts or indexes the unique or tolerably unique items.
- poisson_openmp, a program which computes an approximate solution to the Poisson equation in a rectangle, using the Jacobi iteration to solve the linear system, and OpenMP to carry out the Jacobi iteration in parallel.
- poisson_serial, a program which computes an approximate solution to the Poisson equation in a rectangle, and is intended as the starting point for the creation of a parallel version.
- poisson_simulation, a library which simulates a Poisson process in which events randomly occur with an average waiting time of Lambda, creating graphics files for processing by gnuplot.
- polpak, a library which evaluates a variety of mathematical functions, including Chebyshev, Gegenbauer, Hermite, Jacobi, Laguerre, Legendre polynomials, and the Collatz sequence.
- polygon_grid, a library which generates a grid of points over the interior of a polygon in 2D.
- polygon_integrals, a library which returns the exact value of the integral of any monomial over the interior of a polygon in 2D.
- polygon_monte_carlo, a library which applies a Monte Carlo method to estimate the integral of a function over the interior of a polygon in 2D.
- polygon_properties, a library which computes properties of an arbitrary polygon in the plane, defined by a sequence of vertices, including interior angles, area, centroid, containment of a point, convexity, diameter, distance to a point, inradius, lattice area, nearest point in set, outradius, uniform sampling.
- polygon_triangulate, a library which triangulates a possibly nonconvex polygon in 2D, and which can use gnuplot to display the external edges and internal diagonals of the triangulation.
- polygonal_surface_display_opengl, a program which displays a surface in 3D described as a set of polygons using OpenGL;
- polynomial, a library which adds, multiplies, differentiates, evaluates and prints multivariate polynomials in a space of M dimensions.
- polyomino_condense, a program which cleans up a matrix that represents a polyomino by setting all nonzero entries to 1, and removing initial and final rows and columns of zeros.
- polyomino_embed, a library which is given matrices defining a region R and a polyomino P, and determines the number of possible embeddings of the polyomino into the region, and the translations necessary to achieve them.
- polyomino_enumerate, a library which enumerates chiral, fixed and free polyominoes of moderate order.
- polyomino_index, a library which is given a matrix defining a polyomino P, and determines a correspondingly shaped matrix which contains an index for each nonzero entry in P.
- polyomino_lp_write, a program which writes an LP file describing a (binary) integer programming problem related to the tiling of a region R by copies of polyomino shapes, with possible reflections and rotations.
- polyomino_transform, a program which transforms the matrix representing a polyomino by reflection and rotation.
- power_method, a library which carries out the power method for finding a dominant eigenvalue and its eigenvector.
- power_rule, a program which constructs a power rule, that is, a product quadrature rule from identical 1D factor rules.
- ppma_io, a library which reads or writes an ASCII Portable Pixel Map (PPM) graphics file;
- ppma_to_bmp, a program which converts an ASCII Portable Pixel Map (PPM) graphics file to a Microsoft BMP file;
- ppma_to_ppmb, a program which converts an ASCII Portable Pixel Map (PPM) graphics file to binary PPM format;
- ppmb_io, a library which reads or writes a binary Portable Pixel Map (PPM) 2D pixel map graphics file;
- ppmb_to_bmp, a program which converts a binary Portable Pixel Map (PPM) file to a Microsoft BMP file;
- ppmb_to_ppma, a program which converts a binary Portable Pixel Map (PPM) file to ASCII PPM format;
- praxis, a library which minimizes a scalar function of several variables, without requiring derivative information, by Richard Brent.
- prime_mpi, a program which counts the number of primes between 1 and N, using MPI for parallel execution.
- prime_openmp, a program which counts the number of primes between 1 and N, using OpenMP for parallel execution.
- prime_serial, a program which counts the number of primes between 1 and N, and is intended as a starting point for a parallel version.
- prob, a library which evaluates, samples, inverts, and characterizes a number of Probability Density Functions (PDF's) and Cumulative Density Functions (CDF's), including anglit, arcsin, benford, birthday, bernoulli, beta_binomial, beta, binomial, bradford, burr, cardiod, cauchy, chi, chi squared, circular, cosine, deranged, dipole, dirichlet mixture, discrete, empirical, english sentence and word length, error, exponential, extreme values, f, fisk, folded normal, frechet, gamma, generalized logistic, geometric, gompertz, gumbel, half normal, hypergeometric, inverse gaussian, laplace, levy, logistic, log normal, log series, log uniform, lorentz, maxwell, multinomial, nakagami, negative binomial, normal, pareto, planck, poisson, power, quasigeometric, rayleigh, reciprocal, runs, sech, semicircular, student t, triangle, uniform, von mises, weibull, zipf.
- product_rule, a program which creates an M-dimensional quadrature rule from a product of distinct 1d quadrature rules;
- pthreads_test, programs which test pthreads, the posix thread library, to carry out parallel program execution.
- pwl_approx_1d, a library which approximates a set of data using a piecewise linear function.
- pwl_interp_1d, a library which interpolates a set of data using a piecewise linear function, creating graphics files for processing by gnuplot.
- pwl_interp_2d, a library which evaluates a piecewise linear interpolant to data defined on a regular 2D grid.
- pwl_interp_2d_scattered, a library which evaluates a piecewise linear interpolant to data which is available at an irregularly arranged set of points.
- pyramid_exactness, a program which investigates the polynomial exactness of a quadrature rule over the interior of the unit pyramid in 3D.
- pyramid_felippa_rule, a library which returns Felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3D.
- pyramid_grid, a library which computes a grid of points over the interior of the unit pyramid in 3D;
- pyramid_integrals, a library which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3D.
- pyramid_monte_carlo, a library which applies a Monte Carlo method to estimate integrals of a function over the interior of the unit pyramid in 3D;
- pyramid_rule, a program which computes a quadrature rule for a pyramid.
- qr_solve, a library which computes the linear least squares (LLS) solution of a system A*x=b.
- quad_mesh, a library which handles meshes of quadrilaterals over a 2D region;
- quad_mesh_rcm, a program which computes the Reverse Cuthill-McKee (RCM) reordering for nodes in a mesh of 4-node quadrilaterals.
- quad_mpi, a program which applies a quadrature rule to estimate an integral, working in parallel by using MPI;
- quad_openmp, a program which applies a quadrature rule to estimate an integral over a 1D interval, using OpenMP for parallel execution;
- quad_serial, a program which applies a quadrature rule to estimate an integral, intended as a starting point for parallelization exercises.
- quad2d_openmp, a program which applies a product quadrature rule to estimate an integral over a 2D rectangle, using OpenMP for parallel execution;
- quad2d_serial, a program which applies a product quadrature rule to estimate an integral over a 2D rectangle, intended as a starting point for parallelization exercises.
- quadrature_golub_welsch, a library which computes the points and weights of a Gaussian quadrature rule using the Golub-Welsch procedure.
- quadrature_least_squares, a library which computes weights for sub-interpolatory quadrature rules, that is, it estimates integrals by integrating a polynomial that approximates the function data in a least squares sense.
- quadrature_test, a program which reads the definition of an M-dimensional quadrature rule from three files, applies the rule to a number of test integrals, and prints the results.
- quadrature_test_2d, a program which reads the definition of a 2D quadrature rule from three files, applies the rule to a number of test integrals, and prints the results.
- quadrature_weights_vandermonde, a library which computes the weights of a quadrature rule using the Vandermonde matrix, assuming that the points have been specified.
- quadrature_weights_vandermonde_2d, a library which computes the weights of a 2D quadrature rule using the Vandermonde matrix, assuming that the points have been specified.
- quadrule, a library which defines quadrature rules for approximating integrals;
- quality, a library which computes quality of distribution measures for pointsets in M dimensions;
- quaternions, a library which carries out some simple arithmetic operations for quaternions.
- r4lib, a library which contains many utility routines, using single precision real (R4) arithmetic.
- r83, a library which contains linear algebra routines for R83 matrices (real, 64 bit, tridiagonal 3xN format).
- r83_np, a library which contains linear algebra routines for R83_NP matrices (real, 64 bit, tridiagonal 3xN format, nonpivoting factorization).
- r83p, a library which contains linear algebra routines for R83P matrices (real, 64 bit, tridiagonal periodic format).
- r83s, a library which contains linear algebra routines for R83S matrices (real, 64 bit, tridiagonal scalar format).
- r83t, a library which contains linear algebra routines for R83t matrices (real, 64 bit, tridiagonal Mx3 format).
- r83v, a library which contains linear algebra routines for R83V matrices (real, 64 bit, tridiagonal three vector format).
- r85, a library which contains linear algebra routines for R85 matrices (real, 64 bit, pentadiagonal format).
- r8bb, a library which contains linear algebra routines for R8BB matrices (real, 64 bit, border banded format).
- r8blt, a library which contains linear algebra routines for R8BLT matrices (real, 64 bit, band lower triangular format).
- r8bto, a library which contains linear algebra routines for R8BTO matrices (real, 64 bit, block Toeplitz format).
- r8but, a library which contains linear algebra routines for R8BUT matrices (real, 64 bit, band upper triangular format).
- r8cb, a library which contains linear algebra routines for R8CB matrices (real, 64 bit, Compressed Band format).
- r8cbb, a library which contains linear algebra routines for R8CBB matrices (real, 64 bit, Compressed Border Banded format).
- r8cc, a library which contains linear algebra routines for R8CC matrices (real, 64 bit, Compressed Column (Colptr,Row,Value) format).
- r8ci, a library which contains linear algebra routines for R8CI matrices (real, 64 bit, circulant format).
- r8col, a library which contains utility routines for R8COL's, that is, double precision real MxN arrays, considered as N column vectors, each of length M. The data may be thought of as a matrix of multiple columns, and many operations will be carried out columnwise.
- r8gb, a library which contains linear algebra routines for R8GB matrices (real, 64 bit, General Banded format).
- r8gd, a library which contains linear algebra routines for R8GD matrices (real, 64 bit, general diagonal format).
- r8ge, a library which contains linear algebra routines for R8GE matrices (real, 64 bit, General format).
- r8ge_np, a library which contains nonpivoting linear algebra routines for R8GE_NP matrices (real, 64 bit, General nonpivoting format).
- r8lib, a library which contains many utility routines, using double precision real (R8) arithmetic.
- r8lt, a library which contains linear algebra routines for R8LT matrices (real, 64 bit, lower triangular format).
- r8ltt, a library which contains linear algebra routines for R8LTT matrices (real, 64 bit, lower triangular Toeplitz format).
- r8ncf, a library which contains linear algebra routines for R8NCF matrices (real, 64 bit, nonsymmetric coordinate format).
- r8pbl, a library which contains linear algebra routines for R8PBL matrices (real, 64 bit, positive definite symmetric band lower format).
- r8pbu, a library which contains linear algebra routines for R8PBU matrices (real, 64 bit, positive definite symmetric band upper format).
- r8po, a library which contains linear algebra routines for R8PO matrices (real, 64 bit, positive definite symmetric format).
- r8poly, a library which contains a number of utilities for polynomials with R8 coefficients, that is, using double precision or 64 bit real arithmetic.
- r8pp, a library which contains linear algebra routines for R8PP matrices (real, 64 bit, positive definite symmetric packed format).
- r8ri, a library which contains linear algebra routines for R8RI matrices (real, 64 bit, row-indexed format).
- r8row, a library which contains utility routines for R8ROW's, that is, double precision real MxN arrays, considered as M row vectors, each of length N. The data may be thought of as a matrix of multiple rows, and many operations will be carried out rowwise.
- r8s3, a library which contains linear algebra routines for R8S3 matrices (real, 64 bit, SLAP triad (I,J,AIJ) format).
- r8sd, a library which contains linear algebra routines for R8SD matrices (real, 64 bit, symmetric diagonal format).
- r8sm, a library which contains linear algebra routines for R8SM (Sherman-Morrison) matrices (real, 64 bit, A-u*v' format).
- r8sp, a library which contains linear algebra routines for R8SP matrices (real, 64 bit, SLAP triad (I,J,AIJ) format).
- r8sr, a library which carries out linear algebra operations for R8SR matrices (real, 64 bit, diagonal + compressed row offdiagonal format).
- r8ss, a library which carries out linear algebra operations for R8SS matrices (real, 64 bit, symmetric skyline format).
- r8sto, a library which contains linear algebra routines for R8STO matrices (real, 64 bit, symmetric Toeplitz N format).
- r8to, a library which contains linear algebra routines for R8TO matrices (real, 64 bit, Toeplitz 2*N-1 format).
- r8ut, a library which contains linear algebra routines for R8UT matrices (real, 64 bit, upper triangular format).
- r8utt, a library which contains linear algebra routines for R8UTT matrices (real, 64 bit, upper triangular Toeplitz format).
- r8vm, a library which contains linear algebra routines for R8VM matrices (real, 64 bit, Vandermonde format).
- rand48, a program which demonstrates the use of the RAND48 family of random number generators (RNG's) available in the C/C++ standard library.
- randlc, a library which implements a random number generator (RNG) used by the NAS Benchmark programs.
- random_data, a library which uses a random number generator (RNG) to sample points distribute according to various probability density functions (PDF's), for various spatial dimensions, and geometries, including the M-dimensional cube, ellipsoid, simplex and sphere.
- random_mpi, a program which demonstrates one way to generate the same sequence of random numbers for both sequential execution and parallel execution under MPI.
- random_openmp, a program which illustrates how a parallel program using OpenMP can generate multiple distinct streams of random numbers.
- random_sorted, a library which generates vectors of random values which are already sorted.
- ranlib, a library which produces random samples from Probability Density Functions (PDF's), including Beta, Chi-square Exponential, F, Gamma, Multivariate normal, Noncentral chi-square, Noncentral F, Univariate normal, random permutations, Real uniform, Binomial, Negative Binomial, Multinomial, Poisson and Integer uniform, by Barry Brown and James Lovato.
- rbf_interp_1d, a library which defines and evaluates radial basis function (RBF) interpolants to 1D data.
- rbf_interp_2d, a library which defines and evaluates radial basis function (RBF) interpolants to 2D data.
- rbf_interp_nd, a library which defines and evaluates radial basis function (RBF) interpolants to M-dimensional data.
- rcm, a library which applies the Reverse Cuthill McKee (RCM) algorithm for reordering the nodes of a graph, and reducing the bandwidth of a corresponding sparse matrix;
- reactor simulation, a program which is a simple Monte Carlo simulation of the shielding effect of a slab of a certain thickness in front of a neutron source. This program was provided as an example with the book "Numerical Methods and Software."
- recomment, a program which converts C style comments to C++ style;
- reword, a program which makes a copy of a file in which every line has the same number of words;
- ring_mpi, a program which uses the MPI parallel programming environment, and measures the time necessary to copy a set of data around a ring of processes.
- rk4, a library which applies the fourth order Runge-Kutta (RK) algorithm to estimate the solution of an ordinary differential equation (ODE) at the next time step.
- rkf45, a library which applies the Runge-Kutta-Fehlberg (RKF) algorithm to solve a system of ordinary differential equations (ODEs);
- rnglib, a library which implements a random number generator (RNG) with splitting facilities, allowing multiple independent streams to be computed, by L'Ecuyer and Cote.
- root_rc, a library which seeks a solution of a scalar nonlinear equation f(x)=0, using reverse communication (RC), by Gaston Gonnet.
- roots_rc, a library which seeks solutions of a system of nonlinear equations, using reverse communication (RC), by Gaston Gonnet.
- rot13, a program which makes a copy of a file which has been encoded using the ROT13 coding and a ROT5 coding for digits.
- rotating_cube_display_opengl, a program which displays a rotating color cube in 3D, using OpenGL;
- row_echelon_integer, a library which carries out the exact computation of the integer row echelon form (IREF) and integer reduced row echelon form (IRREF) of an integer matrix.
- sandia_cubature, a library which implements quadrature rules for certain M-dimensional regions and weight functions.
- sandia_rules, a library which can produce a standard 1D Gauss quadrature rule of Chebyshev, Gegenbauer, generalized Hermite, generalized Laguerre, Hermite, Jacobi, Laguerre, and Legendre types.
- sandia_rules2, a library which contains a very small selection of functions which serve as an interface between sandia_sgmg or sandia_sgmga and sandia_rules.
- sandia_sgmg, a library which creates sparse grids based a mixture of 1D factor rules, and which experiments with the idea of using linear growth rate for the 1D quadrature rules. This is a version of sparse_grid_mixed_growth that uses a different procedure for supplying the parameters needed to evaluate certain quadrature rules.
- sandia_sgmga, a library which creates sparse grids based on a mixture of 1D quadrature rules, allowing anisotropic weights for each dimension. This is a version of sgmga that uses a different procedure for supplying the parameters needed to evaluate certain quadrature rules.
- sandia_sgmgg, a library which explores a generalized construction method for sparse grids.
- sandia_sparse, a library which can produce an M-dimensional sparse grid, based on a variety of 1D quadrature rules; only isotropic grids are generated, that is, the same rule is used in each dimension, and the same maximum order is used in each dimension.
- satisfy, a program which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfy problem.
- satisfy_mpi, a program which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfy problem, using MPI to perform the calculation in parallel.
- satisfy_openmp, a program which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfy problem, using OpenMP for parallel execution.
- schedule_openmp, a program which demonstrates the default, static, and dynamic methods of scheduling loop iterations in OpenMP to avoid work imbalance.
- screenshot_opengl, a program which shows how a program using the OpenGL graphics library can save a screenshot of the graphics being displayed.
- scvt_mpi, a program which determines a Centroidal Voronoi Tessellation (CVT) on a spherical surface, using triangle for triangulation, and the boost mpi and serialization libraries, by Doug Jacobsen;
- sde, a library which illustrates properties of stochastic ordinary differential equations (SODE's), and common algorithms for their analysis, including the Euler method, the Euler-Maruyama method, and the Milstein method, making graphics files for processing and display by gnuplot, by Desmond Higham;
- search_mpi, a program which searches integers between A and B for a solution J such that F(J)=C, carried out in parallel using MPI.
- search_serial, a program which searches the integers from A to B for a value J such that F(J) = C. this version of the program is intended as a starting point for a parallel approach.
- set_theory, a library which demonstrates various set theoretic operations using several models of a set.
- sftpack, a library which implements the slow Fourier transform, intended as a teaching tool and comparison with the Fast Fourier Transform (FFT).
- sgefa_openmp, a program which compares a standard linear algebra solver against a revised version which can be run in parallel with OpenMP.
- sgmg, a library which creates sparse grids based a mixture of 1D factor rules, and which experiments with the idea of using linear growth rate for the 1D quadrature rules.
- sgmga, a library which creates sparse grids based on a mixture of 1D quadrature rule families, allowing user specified growth rates for each family, allowing anisotropic weights for each dimension.
- shallow_water_1d, a program which simulates the evolution of a 1D fluid governed by the time-dependent shallow water equations.
- shepard_interp_1d, a library which defines and evaluates Shepard interpolants to 1D data, based on inverse distance weighting.
- shepard_interp_2d, a library which defines and evaluates Shepard interpolants to 2D data, based on inverse distance weighting.
- shepard_interp_nd, a library which defines and evaluates Shepard interpolants to M-dimensional data, based on inverse distance weighting.
- simple_ga, a program which is a simple example of a genetic algorithm, by Dennis Cormier and Sita Raghavan.
- simplex_coordinates, a library which computes the Cartesian coordinates of the vertices of a regular simplex in M dimensions.
- simplex_gm_rule, a library which defines Grundmann-Moeller quadrature rules over the interior of a triangle in 2D, a tetrahedron in 3D, or over the interior of the simplex in M dimensions.
- simplex_grid, a library which generates a regular grid of points over the interior of an arbitrary simplex in M dimensions.
- simplex_integrals, a library which returns the exact value of the integral of any monomial over the interior of the unit simplex in M dimensions.
- simplex_monte_carlo, a library which uses the Monte Carlo method to estimate an integral over the interior of the unit simplex in M dimensions.
- sine_transform, a library which demonstrates some simple properties of the discrete sine transform.
- snakes_and_ladders, programs which simulate and investigate a one-player version of the game of Snakes and Ladders.
- sobol, a library which computes elements of the Sobol M-dimensional Quasi Mont Carlo (QMC) sequence, extended to a maximal spatial dimension of 1111, by Bennett Fox.
- sobol_dataset, a program which creates a Sobol Quasi Mont Carlo (QMC) dataset;
- solve, a library which implements a linear solver which makes it easy to create doubly-dimensioned arrays and solve associated linear systems.
- sor, a library which implements a simple version of the Successive Over-Relaxation (SOR) method for the iterative solution of a linear system of equations.
- sort_rc, a library which can sort a list of any kind of objects, using reverse communication (RC).
- sparse_count, a library which for the analysis and creation of sparse grids in which a single family of 1D quadrature rules is used for all spatial dimensions, with a variety of growth rules.
- sparse_display, a library which can read information defining a matrix of numbers and display the sparsity pattern or location of the nonzero elements using gnuplot. This operation is already available in the built-in MATLAB "spy" command.
- sparse_grid_cc, a library which creates sparse grids based on Clenshaw-Curtis rules.
- sparse_grid_cc_dataset, a program which creates a sparse grid dataset based on Clenshaw-Curtis rules.
- sparse_grid_gl, a library which creates sparse grids based on Gauss-Legendre rules.
- sparse_grid_gl_dataset, a program which creates a sparse grid dataset based on Gauss-Legendre rules.
- sparse_grid_hermite, a library which creates sparse grids based on Gauss-Hermite rules.
- sparse_grid_hermite_dataset, a program which creates a sparse grid dataset based on Gauss-Hermite rules.
- sparse_grid_hw, a library which creates sparse grids based on Gauss-Legendre, Gauss-Hermite, Gauss-Patterson, or a nested variation of Gauss-Hermite rules, by Florian Heiss and Viktor Winschel.
- sparse_grid_laguerre, a library which creates sparse grids based on Gauss-Laguerre rules.
- sparse_grid_laguerre_dataset, a program which creates a sparse grid dataset based on Gauss-Laguerrre rules.
- sparse_grid_mixed, a library which creates sparse grids based on a mixture of 1D factor rules.
- sparse_grid_mixed_dataset, a program which creates a sparse grid dataset based on a mixture of 1D rules.
- sparse_grid_open, a library which creates sparse grids based on open rules (Fejer 2, Gauss-Patterson, Newton-Cotes-Open).
- sparse_grid_open_dataset, a program which creates a sparse grid dataset based on open rules (Fejer 2, Gauss-Patterson, Newton-Cotes-Open).
- sparse_interp_nd, a library which can be used to define a sparse interpolant to a function f(x) of a M-dimensional argument.
- sphere_exactness, a program which tests the polynomial exactness of a quadrature rule over the surface of the unit sphere in 3D;
- sphere_fibonacci_grid, a library which uses a Fibonacci spiral to create a grid of points on the surface of the unit sphere in 3D.
- sphere_grid, a library which provides a number of ways of generating grids of points, or of points and lines, or of points and lines and faces, over the surface of the unit sphere in 3D.
- sphere_integrals, a library which returns the exact value of the integral of any monomial over the surface of the unit sphere in 3D.
- sphere_lebedev_rule, a library which computes Lebedev quadrature rules for the surface of the unit sphere in 3D;
- sphere_llq_grid, a library which uses longitudes and latitudes to create grids of points, lines, and quadrilaterals on the surface of the unit sphere in 3D.
- sphere_llt_grid, a library which uses longitudes and latitudes to create grids of points, lines, and triangles on the surface of the unit sphere in 3D.
- sphere_monte_carlo, a library which applies a Monte Carlo method to estimate the integral of a function over the surface of the unit sphere in 3D;
- sphere_quad, a library which uses triangulation to approximate an integral over the surface of the unit sphere in 3D;
- sphere_stereograph, a library which computes the stereographic mapping between points on the plane Z=1 and the surface of the unit sphere in 3D.
- sphere_triangle_monte_carlo, a library which used the Monte Carlo method to estimate the integral of a function defined in a triangle on the surface of the unit sphere in 3D.
- sphere_triangle_quad, a library which uses quadrature to estimate the integral of a function in a spherical triangle on the surface of the unit sphere in 3D.
- sphere_voronoi_display_opengl, a program which displays a sphere and randomly selected generator points, and then gradually colors in points closest to each generator on the surface of the unit sphere in 3D .
- sphere_xyz_display_opengl, a program which reads XYZ information defining points in 3D that lie (presumably) on the surface of the unit sphere in 3D, and displays an image of the sphere and the points, using OpenGL;
- spiral_data, a library which computes a velocity vector field that satisfies the continuity equation, writing the data to a file that can be plotted by gnuplot.
- spline, a library which interpolates or approximates data by piecewise polynomial functions;
- spring_ode, a program which shows how line printer graphics can be used to make a crude illustration of a solution of the ordinary differential equation (ODE) that describes the motion of a weight attached to a spring.
- spring_ode2, a program which shows how gnuplot graphics can be used to illustrate a solution of the ordinary differential equation (ODE) that describes the motion of a weight attached to a spring.
- square_arbq_rule, a library which returns quadrature rules, with exactness up to total degree 20, over the interior of the symmetric square in 2D, by Hong Xiao and Zydrunas Gimbutas.
- square_exactness, a library which investigates the polynomial exactness of quadrature rules for f(x,y) over the interior of a square in 2D.
- square_felippa_rule, a library which returns Felippa's quadratures rules for approximating integrals over the interior of a square in 2D.
- square_grid, a library which computes a grid of points over the interior of a square in 2D.
- square_integrals, a library which returns the exact value of the integral of any monomial over the interior of the unit square in 2D.
- square_minimal_rule, a library which returns "almost minimal" quadrature rules, with exactness up to total degree 55, over the interior of the symmetric square in 2D, by Mattia Festa and Alvise Sommariva.
- square_monte_carlo, a library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit square in 2D.
- square_symq_rule, a library which returns symmetric quadrature rules, with exactness up to total degree 20, over the interior of the symmetric square in 2D, by Hong Xiao and Zydrunas Gimbutas.
- st_io, a library which reads and writes sparse linear systems stored in the Sparse Triplet (ST) format.
- st_to_cc, a library which converts sparse matrix data from Sparse Triplet (ST) format to Compressed Column (CC) format;
- star_discrepancy, a program which computes bounds on the star discrepancy of a set of N points in M dimensions, stored as a table file, by Eric Thiemard.
- stla_io, a library which reads and writes ASCII stereolithography (STL) 3d graphics files;
- stochastic_diffusion, functions which implement several versions of a stochastic diffusivity coefficient.
- stochastic_heat2d, a program which implements a finite difference method (FDM) for the steady (time independent) 2D heat equation, with a stochastic heat diffusivity coefficient.
- stochastic_rk, a library which applies a Runge-Kutta (RK) scheme to a stochastic ordinary differential equation (SODE).
- stokes_2d_exact, a library which evaluates exact solutions to the incompressible steady Stokes equations over the unit square in 2D.
- string_simulation, a program which simulates the behavior of a vibrating string by solving the corresponding initial boundary value problem (IBVP), creating files that can be displayed by gnuplot.
- stroud, a library which defines quadrature rules for a variety of M-dimensional regions, including the interior of the square, cube and hypercube, the pyramid, cone and ellipse, the hexagon, the M-dimensional octahedron, the circle, sphere and hypersphere, the triangle, tetrahedron and simplex, and the surface of the circle, sphere and hypersphere.
- subpak, a library which contains many utility routines;
- subset, a library which enumerates, generates, randomizes, ranks and unranks combinatorial objects including combinations, compositions, Gray codes, index sets, partitions, permutations, polynomials, subsets, and Young tables. Backtracking routines are included to solve some combinatorial problems.
- subset_sum, a program which seeks solutions of the subset sum problem.
- subset_sum_serial, a program which seeks solutions of the subset sum problem, intended as a starting point for a parallel computing approach.
- superlu_openmp, programs which illustrate how to use the SUPERLU library with the OpenMP parallel programming interface, which applies a fast direct solution method to solve sparse linear systems, by James Demmel, John Gilbert, and Xiaoye Li.
- superlu_test, C++ programs which illustrate how a CPP program can call the SUPERLU library (which is written in C), which applies a fast direct solution method to solve sparse linear systems, by James Demmel, John Gilbert, and Xiaoye Li.
- svd_basis, a program which applies the singular value decomposition (SVD) to a set of vectors, to extract the dominant modes;
- svd_demo, a program which demonstrates the calculation of the singular value decomposition (SVD) and some of its properties;
- svd_snowfall, a program which reads a file containing historical snowfall data and analyzes the data with the Singular Value Decomposition (SVD), displaying the results using gnuplot.
- svd_truncated, a program which demonstrates the computation of the reduced or truncated Singular Value Decomposition (SVD) that is useful for cases when one dimension of the matrix is much smaller than the other.
- table_delaunay, a program which computes the Delaunay triangulation of a set of points stored as a table file;
- table_io, a library which reads and writes a simple dataset stored as a table file;
- table_latinize, a program which reads a dataset of N points in M dimensions from a table file, adjusts data to form a Latin Hypercube;
- table_quality, a program which reads a dataset of N points in the M-dimensional unit hypercube from a table file, and analyzes the quality of dispersion;
- table_voronoi, a program which reads a set of 2D points from a table file, and prints information about the Voronoi diagram;
- task_division, a library which implements a simple procedure for smoothly dividing T tasks among P processors; such a method can be useful in MPI and other parallel environments, particularly when T is not an exact multiple of P, and when the processors can be indexed starting from 0 or from 1.
- test_approx, a library which implements test problems for approximation, provided as a set of (x,y) data.
- test_eigen, a library which implements test matrices for eigenvalue analysis.
- test_int, a library which implements test problems for approximate integration in one dimension.
- test_int_2d, a library which implements test problems for approximate integration in two dimensions.
- test_interp, a library which defines test problems for interpolation, provided as a set of (x,y) data.
- test_interp_1d, a library which defines test problems for interpolation of data y(x), which depends on a 1D argument.
- test_interp_2d, a library which defines test problems for interpolation of data z(x,y), depending on a 2D argument.
- test_interp_nd, a library which defines test problems for interpolation of data z(x), depending on an M-dimensional argument.
- test_lls, a library which implements linear least squares (LLS) test problems of the form A*x=b.
- test_mat, a library which defines test matrices for which some of the determinant, eigenvalues, inverse, null vectors, P*L*U factorization or linear system solution are already known, including the Vandermonde and Wathen matrix.
- test_matrix_exponential, a library which defines a set of test cases for computing the matrix exponential.
- test_min, a library which implements test problems for minimization of a scalar function of a scalar variable.
- test_nearest, a library which tests the time complexity of various procedures for solving the nearest neighbor problem.
- test_nint, a library which implements test problems for approximate integration (quadrature) in M dimensions.
- test_opt_con, a library which defines test problems for the minimization of a scalar function of several variables, with the search constrained to lie within a specified hyper-rectangle.
- test_optimization, a library which implements test problems for optimization of a scalar function of several variables, as described by Molga and Smutnicki.
- test_values, a library which returns a small set of values for a variety of mathematical functions, suitable for a rough test of accuracy for algorithms;
- test_zero, a library which implements test problems for the solution of a single nonlinear equation in one variable.
- testpack, a program which demonstrates the use of a set of test integrand functions chosen by Alan Genz.
- tet_mesh, a library which works with tetrahedral meshes in 3D;
- tet_mesh_boundary, a program which reads information defining a tetrahedral mesh of points in 3D, and determines the triangular faces that form the boundary of the mesh; it writes files containing the nodes and elements defining this tri_surface data.
- tet_mesh_display_opengl, a program which reads two files describing a tetrahedral mesh in 3D and displays it using OpenGL.
- tet_mesh_l2q, a program which reads information about a 4-node (linear) tet mesh and creates data defining a corresponding 10-node (quadratic) tet mesh;
- tet_mesh_q2l, a program which reads information about a 10-node (quadratic) tet mesh and creates data defining a corresponding 4-node (linear) tet mesh;
- tet_mesh_quad, a program which estimates the integral of a function over a region defined by a tetrahedral mesh.
- tet_mesh_quality, a program which reads a node coordinate file and a tetrahedron file and returns quality measures for the tetrahedronal mesh;
- tet_mesh_rcm, a program which computes the Reverse Cuthill McKee (RCM) reordering for the nodes of a tet_mesh that uses 4-node or 10-node tetrahedrons;
- tet_mesh_refine, a program which refines a tet mesh;
- tet_mesh_tet_neighbors, a program which reads information about a tet mesh and writes out a list of the tetrahedrons that are adjacent to a given tetrahedron;
- tet_mesh_volumes, a program which computes the volume of each tetrahedron in a tet mesh;
- tetrahedron_arbq_rule, a library which returns quadrature rules, with exactness up to total degree 15, over the interior of a tetrahedron in 3D, by Hong Xiao and Zydrunas Gimbutas.
- tetrahedron_exactness, a program which tests the polynomial exactness of a quadrature rule over the interior of a tetrahedron in 3D.
- tetrahedron_felippa_rule, a library which returns Felippa's quadratures rules for approximating integrals over the interior of a tetrahedron in 3D.
- tetrahedron_grid, a library which computes a grid of points over the interior of a tetrahedron in 3D.
- tetrahedron_integrals, a library which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3D.
- tetrahedron_keast_rule, a library which defines ten quadrature rules, of degree of exactness 0 through 8, over the interior of the tetrahedron in 3D.
- tetrahedron_monte_carlo, a library which uses the Monte Carlo method to estimate an integral over the interior of a general tetrahedron in 3D.
- tetrahedron_ncc_rule, a library which defines Newton-Cotes closed (NCC) quadrature rules over the interior of a tetrahedron in 3D.
- tetrahedron_nco_rule, a library which defines Newton-Cotes open (NCO) quadrature rules over the interior of a tetrahedron in 3D.
- tetrahedron_properties, a program which computes properties including the centroid, circumsphere, dihedral angles, edge lengths, face angles, face areas, insphere, quality, solid angles, and volume of a tetrahedron in 3D.
- tetrahedron01_monte_carlo, a library which uses the Monte Carlo method to estimate an integral over the interior of the unit tetrahedron in 3D.
- three_body_simulation, a program which simulates the behavior of three planets, constrained to lie in a plane, and moving under the influence of gravity, by Walter Gander and Jiri Hrebicek.
- tiler_3d, a library which blends a pattern repeatedly into a region in 3D;
- timer, programs which measure the CPU time used by a portion of a user's program;
- timestamp, a library which prints the current YMDHMS date as a timestamp, and other timekeeping operations;
- toeplitz_cholesky, a library which computes the Cholesky factorization of a nonnegative definite symmetric Toeplitz matrix.
- toms097, a library which computes the distance between all pairs of nodes in a directed graph with weighted edges, using Floyd's algorithm. This is a version of ACM TOMS algorithm 97.
- toms112, a library which determines whether a point is contained in a polygon, by Moshe Shimrat. This is a version of ACM TOMS algorithm 112.
- toms178, a library which seeks the minimizer of a scalar function of several variables using the Hooke-Jeeves method, by Arthur Kaupe. This is a version of ACM TOMS algorithm 178.
- toms179, a library which calculates the incomplete Beta ratio, by Oliver Ludwig. This is a version of ACM TOMS algorithm 179.
- toms291, a library which approximates the logarithm of the Gamma function; this is a version of ACM TOMS algorithm 291.
- toms443, a library which evaluates Lambert's W function. This is a version of ACM TOMS algorithm 443.
- toms446, a library which manipulates Chebyshev series for interpolation and approximation. This is a version of ACM TOMS algorithm 446, by Roger Broucke.
- toms462, a library which evaluates the upper right tail of the bivariate normal distribution; that is, the probability that normal variables X and Y with correlation R will satisfy H <= X and K <= Y. This is a version of ACM TOMS algorithm 462.
- toms515, a library which can select subsets of size K from a set of size N, This is a version of ACM TOMS Algorithm 515, by Bill Buckles, Matthew Lybanon.
- toms577, a library which evaluates Carlson's elliptic integral functions RC, RD, RF and RJ. This is a version of ACM TOMS algorithm 577.
- toms655, a library which computes the weights for interpolatory quadrature rule; this library is commonly called IQPACK, by Sylvan Elhay and Jaroslav Kautsky. This is a version of ACM TOMS algorithm 655.
- toms743, a library which evaluates Lambert's W function. This is a version of ACM TOMS algorithm 743, by Barry, Barry and Culligan-Hensley.
- toms886, a library which defines the Padua points for interpolation in a 2D region, including the rectangle, triangle, and ellipse, by Marco Caliari, Stefano de Marchi, Marco Vianello. This is a version of ACM TOMS algorithm 886.
- toms917, a library which evaluates the Wright Omega function, by Piers Lawrence, Robert Corless, David Jeffrey. This is a version of ACM TOMS algorithm 917.
- treepack, a library which carries out computations on trees, a simple kind of graph that is minimally connected.
- tri_surface_display_opengl, a program which displays a 3D triangulated surface or TRI_SURFACE using OpenGL;
- tri_surface_io, a library which reads and writes the 3D graphics information in a tri_surface file;
- triangle_analyze, a program which reads a triangle defined in a file, and uses the triangle_properties() library to compute angles, area, centroid, circumcircle, edge lengths, incircle, orientation, orthocenter, and quality.
- triangle_dunavant_rule, a library which defines Dunavant quadrature rules over the interior of a triangle in 2D.
- triangle_exactness, a program which tests the polynomial exactness of a quadrature rule over the interior of a triangle in 2D.
- triangle_fekete_rule, a library which sets up one of seven Fekete rules for interpolation or quadrature over the interior of a triangle in 2D.
- triangle_felippa_rule, a library which returns Felippa's quadratures rules for approximating integrals over the interior of a triangle in 2D.
- triangle_grid, a library which computes a grid of points over the interior of a triangle in 2D.
- triangle_histogram, a program which computes histograms of data over the interior of the unit triangle in 2D.
- triangle_integrals, a library which returns the exact value of the integral of any polynomial over the interior of an arbitrary triangle in 2D.
- triangle_interpolate, a library which shows how vertex data can be interpolated at any point in the interior of a triangle.
- triangle_io, a library which can read or write some of the files created by Jonathan Shewchuk's triangle program.
- triangle_lyness_rule, a library which returns Lyness-Jespersen quadrature rules over the interior of a triangle in 2D;
- triangle_monte_carlo, a library which uses the Monte Carlo method to estimate an integral over the interior of a general triangle in 2D.
- triangle_ncc_rule, a library which defines Newton-Cotes closed (NCC) quadrature rules over the interior of a triangle in 2D.
- triangle_nco_rule, a library which defines Newton-Cotes open (NCO) quadrature rules over the interior of a triangle in 2D.
- triangle_properties, a program which computes properties, including angles, area, centroid, circumcircle, edge lengths, incircle, orientation, orthocenter, and quality, of a triangle in 2D.
- triangle_svg, a library which uses Scalable Vector Graphics (SVG) to plot a triangle and any number of points, to illustrate quadrature rules and sampling techniques.
- triangle_symq_rule, a library which returns efficient symmetric quadrature rules, with exactness up to total degree 50, over the interior of a triangle in 2D, by Hong Xiao and Zydrunas Gimbutas.
- triangle_to_fem, a program which reads the NODE and ELE files created by the triangle program to describe a triangular mesh, and writes a corresponding pair of node and element files in the 2D FEM format.
- triangle_to_medit, a program which reads the NODE and ELE files created by the triangle() program to describe a triangular mesh, and writes a corresponding MESH file for input to medit().
- triangle_to_xml, a program which reads the NODE and ELE files created by triangle() to describe a triangular mesh in 2D, and writes out a corresponding XML mesh file for use by DOLFIN or FENICS.
- triangle_wandzura_rule, a library which returns quadrature rules of exactness 5, 10, 15, 20, 25 and 30 over the interior of the triangle in 2D.
- triangle01_integrals, a library which returns the integral of any monomial over the interior of the unit triangle in 2D.
- triangle01_monte_carlo, a library which uses the Monte Carlo method to estimate an integral over the interior of the unit triangle in 2D.
- triangulation, a library which computes the triangulation of a set of points in the plane, and performs various operations using a triangulation, including searching a Delaunay triangulation to find which triangle contains a given point.
- triangulation_boundary_nodes, a program which reads data defining a triangulation, determines which nodes lie on the boundary, and writes their coordinates to a file;
- triangulation_corner, a program which modifies triangulations in which one or more triangles have more than one boundary edge.
- triangulation_delaunay_discrepancy, a program which measures the amount by which a triangulation fails the local Delaunay test;
- triangulation_display_opengl, a program which reads two files describing a triangulation and displays it using OpenGL.
- triangulation_histogram, a program which computes histograms of data over a triangulation.
- triangulation_l2q, a program which reads information about a 3-node (linear) triangulation and creates data defining a corresponding 6-node (quadratic) triangulation;
- triangulation_mask, a program which reads a triangulation and calls a user-supplied routine to consider each triangle for deletion;
- triangulation_node_to_element, a program which reads files describing a set of nodes, their triangulation, and the value of one or more quantities at each node, and outputs a file that averages the quantities for each element. This operation in effect creates an "order1" finite element model of the data.
- triangulation_orient, a program which ensures that the triangles in an order 3 or order 6 triangulation have positive orientation;
- triangulation_plot, a program which plots the nodes and elements of a triangulation as a PostScript (PS) file;
- triangulation_q2l, a program which reads information about a 6-node triangulation and creates data defining a corresponding 3-node triangulation;
- triangulation_quad, a program which reads information about a triangulation and the value of a function at the nodes and estimates the integral of the function over the triangulated region.
- triangulation_quality, a program which reads information about a triangulation and computes various quality measures;
- triangulation_rcm, a program which computes the Reverse Cuthill McKee (RCM) reordering for the nodes of a triangulation that uses 3-node or 6-node triangles;
- triangulation_refine, a program which refines a triangulation;
- triangulation_svg, a program which creates an SVG image of a triangulation, which can be displayed by a web browser.
- triangulation_t3_to_t4, a program which reads information about a 3-node triangulation and creates data defining a corresponding 4-node triangulation (vertices + centroid);
- triangulation_triangle_neighbors, a program which reads data defining a triangulation, finds the three neighbor triangles for each triangle, and writes them to a file;
- truncated_normal, a library which works with the truncated normal distribution over [A,B], or [A,+oo) or (-oo,B], returning the probability density function (PDF), the cumulative density function (CDF), the inverse CDF, the mean, the variance, and sample values.
- truncated_normal_rule, a program which computes a quadrature rule for a normal probability density function (PDF), sometimes called a Gaussian distribution, that has been truncated to [A,+oo), (-oo,B] or [A,B].
- tsg, programs which demonstrate the use of the TasmanianSparseGrid (TSG) package, which implements routines for working with sparse grids, to efficiently estimate integrals or compute interpolants of scalar functions of multidimensional arguments, by Miroslav Stoyanov.
- tsp_brute, a program which reads a file of city-to-city distances and solves a (small!) traveling salesperson problem, using brute force.
- ubvec, a library which demonstrates how nonnegative integers can be stored as unsigned binary vectors, and arithmetic can be performed on them.
- umfpack_test, C++ programs which call umfpack to solve a sparse linear system.
- uncontrol, a program which removes control characters from a file;
- unicycle, a library which considers permutations containing a single cycle, sometimes called cyclic permutations.
- uniform, a library which implements uniform random number generators (RNG's) for a variety of arithmetic types.
- uniform_dataset, a program which creates a file of uniform pseudorandom values;
- upc, is a library which computes the check digit of a uniform product code (UPC), or reports whether a full 12-digit UPC is actually valid.
- valgrind_test, programs which illustrate the use of the VALGRIND suite of programs which includes a memory leak detector.
- van_der_corput, a library which evaluates the van der Corput 1-dimensional Quasi Mont Carlo (QMC) sequence, using a simple interface.
- van_der_corput_advanced, a library which computes elements of the van der Corput 1-dimensional Quasi Mont Carlo (QMC) sequence, allowing more sophisticated input and control.
- van_der_corput_dataset, a program which creates a file of Quasi Mont Carlo (QMC) van der Corput values;
- vandermonde, a library which implements the Bjork-Pereyra algorithm for accurate solution of linear systems involving the Vandermonde matrix.
- vandermonde_approx_1d, a library which finds a polynomial approximant to data y(x) of a 1D argument by setting up and solving an overdetermined linear system for the polynomial coefficients involving the Vandermonde matrix.
- vandermonde_approx_2d, a library which finds a polynomial approximant p(x,y) to data z(x,y) of a 2D argument by setting up and solving an overdetermined linear system for the polynomial coefficients involving the Vandermonde matrix.
- vandermonde_interp_1d, a library which finds a polynomial interpolant to data y(x) of a 1D argument by setting up and solving a linear system for the polynomial coefficients involving the Vandermonde matrix, creating graphics files for processing by gnuplot.
- vandermonde_interp_2d, a library which finds a polynomial interpolant to data z(x,y) of a 2D argument by setting up and solving a linear system for the polynomial coefficients involving the Vandermonde matrix.
- walker_sample, a library which efficiently samples a discrete probability vector using Walker sampling.
- walsh, a library which implements versions of the Walsh and Haar transforms.
- wathen, a library which compares storage schemes (full, banded, sparse triplet ) and solution strategies: Linpack full, Linpack banded, conjugate gradient (CG), for linear systems involving the Wathen matrix, which can arise when solving a problem using the finite element method (FEM).
- wave_mpi, a program which uses finite differences and the Message Passing Interface (MPI) to estimate a solution to the wave equation.
- wavelet, a library which does some simple wavelet calculations;
- wedge_exactness, a program which investigates the polynomial exactness of a quadrature rule over the interior of the unit wedge in 3D.
- wedge_felippa_rule, a library which returns quadrature rules for approximating integrals over the interior of the unit wedge in 3D.
- wedge_grid, a library which computes a grid of points over the interior of the unit wedge in 3D.
- wedge_integrals, a library which returns the exact value of the integral of any monomial over the interior of the unit wedge in 3D.
- wedge_monte_carlo, a library which uses the Monte Carlo method to estimate an integral over the interior of the unit wedge in 3D.
- weekday, a library which determines the day of the week corresponding to a given date, such as 14 October 1066, Julian calendar, ... which was a Saturday.
- width, a program which returns the length and location of the longest line in a text file;
- wishart, a library which produces sample matrices from the Wishart or Bartlett distributions, useful for sampling random covariance matrices.
- wrap, a program which wraps a file so that no line is longer than 80 characters;
- wrap2, a program which wraps a text file so that no line is longer than a given maximum; the wrapping may be done slightly earlier than at the maximum, in order to avoid breaking words;
- wtime, a library which returns a reading of the wall clock time in seconds.
- x_window_test, C++ programs which test the X Window system.
- xy_display_opengl, a program which reads XY information defining points in 2D and displays an image using OpenGL;
- xy_io, a library which reads and writes XY, XYL and XYF files defining points, lines, and faces in 2D.
- xyf_display_opengl, a program which reads XYF information defining points and faces in 2D and displays an image using OpenGL;
- xyl_display_opengl, a program which reads XYL information defining points and lines in 2D and displays an image using OpenGL;
- xyz_display_opengl, a program which reads XYZ information defining points in 3D and displays an image using OpenGL;
- xyz_io, a library which reads and writes XYZ, XYZL and XYZF files defining points, lines and faces in 3D.
- xyzf_display_opengl, a program which reads XYZF information defining points and faces in 3D and displays an image using OpenGL;
- xyzl_display_opengl, a program which reads XYZL information defining points and lines in 3D and displays an image using OpenGL;
- zero_rc, a library which seeks a solution of a scalar nonlinear equation f(x)=0, using reverse communication (RC), by Richard Brent.
- ziggurat, a library which samples the uniform, normal or exponential distributions, using the ziggurat method, by Marsaglia and Tsang.
- ziggurat_inline, a library which samples the uniform, normal or exponential distributions, using the ziggurat method, by Marsaglia and Tsang. In this original version, each random number generator (RNG) is implemented inline, for increased speed.
- ziggurat_openmp, a program which demonstrates how the ziggurat library can be used as a random number generator (RNG) in an OpenMP parallel program.

petsc_test, C++ programs which illustrate the use of PETSC, a suite of data structures and routines for the scalable parallel solution of scientific applications modeled by partial differential equations.

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