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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. alpert_rule_test 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. analemma_test 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_monte_carlo_test annulus_rule, a library which computes a quadrature rule for estimating integrals of a function over the interior of a circular annulus in 2D. annulus_rule_test args, a program which reports the command line arguments with which it was invoked; args_test 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; asa005_test 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; asa006_test 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, asa007_test asa032, a library which evaluates the incomplete Gamma function, by G Bhattacharjee; this is a version of Applied Statistics Algorithm 32; asa032_test 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; asa047_test 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. asa053_test asa058, a library which carries out K-means clustering of data, by David Sparks; this is a version of Applied Statistics Algorithm 58; asa058_test asa063, a library which evaluates the incomplete Beta function, by KL Majumder and G Bhattacharjee; this is a version of Applied Statistics Algorithm 63; asa063_test 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; asa066_test 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 multidimensional 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 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. ascii_to_mri, a program which restores MRI data to its original binary format, having been previously converted to an ASCII text file. ascii_to_mri_test atbash, a library which applies the Atbash substitution cipher to a string of text. atbash_test 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 a grid of points over the interior of the unit ball in 3D. 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. 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. 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. blas1_c, a library of the Level 1 Basic Linear Algebra Subprograms (BLAS), using single precision complex arithmetic; blas1_d, a library of the Level 1 Basic Linear Algebra Subprograms (BLAS), using double precision real arithmetic; blas1_s, a library of the Level 1 Basic Linear Algebra Subprograms (BLAS), using single precision real arithmetic; blas1_z, a library of the Level 1 Basic Linear Algebra Subprograms (BLAS), using double precision complex arithmetic; blas2_d, a library which constitutes the Level 2 Basic Linear Algebra Subprograms (BLAS), using double precision real arithmetic. blas2_s, a library which constitutes the Level 2 Basic Linear Algebra Subprograms (BLAS), 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 real arithmetic. blas3_s, a library which constitutes the Level 3 Basic Linear Algebra Subprograms (BLAS) for matrix-matrix operations, using single precision real arithmetic. blend, a library which carries out 1D/2D/3D blending interpolation; 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. 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, programs which illustrate some of the features of the C programming language. c_arrays, programs which illustrate the use of vectors, matrices and tensors. 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. c_files, programs which illustrate the use of files. c_intrinsics, a program which illustrates the use of intrinsic functions supplied by the C language. c_mistake, programs which illustrate some simple but devious programming mistakes in C. c_operators, a program which illustrates the use of the operators supplied by the C language. c_random, programs which illustrate the use of the C random number generator (RNG) functions. c4_complex_lib, a library which defines a single precision complex (C4) variable as a structure, and implements certain corresponding elementary functions. c4lib, a library which implements certain elementary functions for single precision complex (C4) variables using the C99 "float complex" datatype. c8_complex_lib, a library which defines a double precision complex (C8) variable as a structure, and implements certain corresponding elementary functions. c8lib, a library which implements certain elementary functions for double precision complex (C8) variables using the C99 standard "double complex" datatype. caesar, a library which can apply a Caesar Shift Cipher to a string of text. calpak, a library which makes various calendar calculations; cauchy_principal_value, a library which uses Gauss-Legendre quadrature to estimate the Cauchy Principal Value (CPV) of certain singular integrals. 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 one of a sequence of Clenshaw Curtis Nested (CCN) quadrature rules of any order. 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 or 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. chrpak, a library which can manipulate characters and strings; circle_arc_grid, a library 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. 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; cnoise, a library which generates samples of noise obeying a 1/f^alpha power law, by Miroslav Stoyanov. 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 library 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 statistical correlation functions. cosine_transform, a library which demonstrates some simple properties of the discrete cosine transform (DCT). csparse, a library which carries out the direct solution of sparse linear systems, by Timothy Davis. 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. cycle_brent, 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 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; 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). f77split, a program which splits a file containing multiple FORTRAN77 routines into separate files; f90split, a program which splits a file containing multiple FORTRAN90 routines into separate files; fair_dice_simulation, a program which simulates N tosses of 2 dice, making a histogram of the results. 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. fd_predator_prey, a program which solves a pair of predator prey ordinary differential equations (ODE's) using a finite difference method (FDM) approximation. 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) difference 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 implements a finite difference method (FDM), explicit in time, of 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 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_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 method (FEM) 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_pack, a library which implements various 2D finite element method (FEM) calculations; 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. 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. fftpack4, a library which implements the Fast Fourier Transform (FFT) by Paul Swarztrauber and Dick Valent, translated by Andrew Fernandes; fftw, C programs which illustrate the use of FFTW, a library of routines for the Fast Fourier Transform (FFT), by Matteo Frigo and Steven Johnson. 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. flood_opengl, a program which uses OpenGL to allow the user to select regions of an image and flood them with color, by Art Wetzel. 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. forest_fire_simulation, a program which models the occurrence of fires in a forest, and displays the status of the forest using X Windows, by Michael Creutz. freefem++_msh_io, a library which can read and write files used by the FreeFem++ finite element program to store mesh information. functions_openmp, a program which demonstrates the behavior of a few of the OpenMP library functions. gcc_intrinsics, a program which demonstrates or tests some of the intrinsic functions made available by the Gnu gcc compiler for C. gcc_quadmath, a program which illustrates the use of quadruple precision real arithmetic, as provided on some systems by the gcc compiler for C. gegenbauer_cc, a library which computes the Gegenbauer weighted integral of a function f(x) using a Clenshaw-Curtis approach. gegenbauer_polynomial, a library which evaluates the Gegenbauer polynomial and associated functions. 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, a library which allows an executing C, C++ or FORTRAN program to interact with the gnuplot graphics program, by Nicholas Devillard. 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. grid, a library which randomly selects N distinct points from a uniform grid in the unit hypercube in M-dimensional space. 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. hammersley, a library which computes elements of a Hammersley Quasi Monte Carlo (QMC) sequence, using a simple interface. 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 files in the Harwell Boeing (HB) sparse matrix format; hdf5, functions 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 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 interpolant 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_test_int, a library which defines test integrands for Hermite integrals with density exp(-x^2) over the interval (-oo,+oo). 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. 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. 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 C program which reads a NETCDF file containing an ICE dataset and rewrites the information as a MESH file. 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_denoise_openmp, a library which applies simple filtering operations to a noisy image, carrying out the operation in parallel using OpenMP. image_edge, a library which demonstrates a simple procedure for edge detection in images. index, a library which converts a multidimensional 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. interp, a library which can be used for parameterizing and interpolating data; is_serial, a program which is a serial version of the NAS Parallel Benchmark Integer Sort (IS). 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 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. jacobi, a program which implements the Jacobi iteration for the iterative solution of 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_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. julia_openmp, a program which produces an image of a Julia set, using OpenMP to carry out the computation in parallel. julia_set, a program which generates a TGA or TARGA graphics file of a Julia set. 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. ladders, a program which seeks to transform one five letter word into another, by changing one letter at a time, using only legitimate English words. This puzzle was invented by Lewis Carroll, who called it "Doublets", but it is also known as "Word Ladders" or "Word Golf". The program is by Donald Knuth. 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 multidimensional argument that was evaluated on a product grid, so that p(x(i)) = z(i). 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_test_int, a library which implements test problems for approximate integration over a semi-infinite interval, often carried out using Gauss-Laguerre quadrature. laplace_mpi, a program which solves Laplace's equation on a rectangle, using the Message Passing Interface (MPI) for parallel execution. laplacian, a library which carries out computations related to the discrete Laplacian operator, including full or sparse evaluation, evaluation for unequally spaced data sampling points, application to a set of data samples, solution of associated linear systems, eigenvalues and eigenvectors, and extension to 2D and 3D geometry. latin_cover, a library which produces N Latin squares which cover an NxN square, or NxN Latin cubes which cover an NxNxN cube. 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; 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 to integrate a function with density 1 over the interval [-1,+1]. legendre_rule_fast, a program which uses a fast (order N) algorithm to compute a Gauss-Legendre quadrature rule of given order to integrate a function with density 1 over the interval [-1,+1]. 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. life_opengl, a program which uses OpenGL to display the evolution of John Conway's Game of Life, by Simon Green. 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) (NCC) 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. The original version of this library is by Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart. linpack_bench, a program which is a version of the LINPACK benchmark program; 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 to compute the singular value decomposition (SVD) of a rectangular matrix. The original version of this library is by Jack Dongarra, Jim Bunch, Cleve Moler, 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 to compute the singular value decomposition (SVD) of a rectangular matrix. The original version of this library is by Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart. 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 of ordinary differential equations (ODEs), 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 characteristic 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_ascii, a program which generates an ASCII text image of the Mandelbrot set, using just two lines of C code. 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. matmul, a program which carries out a matrix multiplication benchmark; matrix_exponential, a library which demonstrates some simple approaches to the problem of computing the exponential of a matrix. matt_message, a program which simulates the operation of a satellite warning system which communicates by a series of formatted messages indicating the location and type of various threats. md, a program which carries out a molecular dynamics (MD) simulation, and is intended as a starting point for implementing an OpenMP parallel version. md_openmp, a program which carries out a molecular dynamics (MD) 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_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 call metis to 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. mixed, programs which illustrate the use of mixed language programming in which the main routine is written in C; mm_io, a library which reads and writes a Matrix Market (MM) Sparse Matrix File; 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. mpi, programs which illustrate the use of the Message Passing Interface (MPI) 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. mri_to_ascii, a program which converts the binary data in a Magnetic Resonance Imaging (MRI) file to ASCII text. mri_to_pgm, a program which converts the binary data in a Magnetic Resonance Imaging (MRI) file to a sequence of Portable Gray Map (PGM) image files. 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. 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 (NSE) 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 (NSE) 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. 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. nintlib, a library which implements approximate integration (quadrature) in M dimensions; normal, a library which implements random number generators (RNG's) for normally distributed values. nsasm, a library which computes the jacobian matrix associated with a finite element method (FEM) approximation of the incompressible steady Navier-Stokes equations (NSE) in 2D, and to store these as a sparse matrix, by Per-Olof Persson. obj_to_ply, a program which converts a 3D graphics file from OBJ format to PLY format format, by Greg Turk. ode, a library which solves a system of ordinary differential equations (ODEs), by Shampine and Gordon; ode_moshier, a library which implements the Adams-Bashforth-Moulton and Runge-Kutta (RK) methods of solving systems of ordinary differential equations (ODE's), by Steven Moshier. 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. partial_digest, a library which solves the partial digest problem; 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) bit map graphics file; pbmb_io, a library which reads or writes a binary Portable Bit Map (PBM) graphics file; pbmlib, a library which reads or writes graphics files in the Portable Bit Map (PBM) format; pce_burgers, a program which solves a version of 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. pcl_read, a program which reads a PCL file and extracts the numeric data; 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. peri1d, a program which sets up and solves a 1D time-dependent peridynamics problem, by Miroslav Stoyanov; peri2d, a program which sets up and solves a 2D time-dependent peridynamics problem, by Miroslav Stoyanov; 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. 2b1af7f3a8