Fortran90 Codes

allocatable_array_test, a Fortran90 code which demonstrates how a main program can declare an allocatable array, which is then passed to a subroutine which allocates it, initializes it, and returns it to the calling program for further use.
analemma, a Fortran90 code 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 code by Brian Tung.
analemma_test
annulus_monte_carlo, a Fortran90 code 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
apportionment, a Fortran90 code which demonstrates some of the methods used or proposed for fairly assigning seats in the House of Representatives to each state;
apportionment_test
args, a Fortran90 code which reports the command line arguments of a Fortran90 code;
args_test
arpack, a Fortran90 code which is a numerical software library for solving large scale eigenvalue problems. The package is designed to compute a few eigenvalues and corresponding eigenvectors of large sparse or structured matrices, using the Implicitly Restarted Arnoldi Method (IRAM) or, in the case of symmetric matrices, the corresponding variant of the Lanczos algorithm. It is used by many popular numerical computing environments such as SciPy, Mathematica, GNU Octave and MATLAB to provide this functionality.
arpack_test
asa005, a Fortran90 code which evaluates the Cumulative Density Function (CDF) of the noncentral T Probability Density Function (PDF), by BE Cooper. This is a version of Applied Statistics Algorithm 5;
asa005_test
asa006, a Fortran90 code which computes the Cholesky factorization of a symmetric positive definite (SPD) matrix, by Michael Healy. This is a version of Applied Statistics Algorithm 6;
asa006_test
asa007, a Fortran90 code which computes the inverse of a symmetric positive definite (SPD) matrix, by Michael Healy. This is a version of Applied Statistics Algorithm 7.
asa007_test
asa032, a Fortran90 code which evaluates the incomplete Gamma function, by G Bhattacharjee. This is a version of Applied Statistics Algorithm 32.
asa032_test
asa047, a Fortran90 code 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 Fortran90 code 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 Fortran90 code which implements the K-means data clustering algorithm, by David Sparks. This is a version of Applied Statistics Algorithm 58.
asa058_test
asa063, a Fortran90 code 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 Fortran90 code which evaluates the Cumulative Density Function (CDF) of the normal probability distribution, by David Hill. This is a version of Applied Statistics Algorithm 66.
asa066_test
asa076, a Fortran90 code which evaluates the Owen T function, needed to compute the Cumulative Density Function (CDF) of the noncentral T distribution, by Young and Minder. This is a version of Applied Statistics Algorithm 76.
asa076_test
asa082, a Fortran90 code which computes the determinant of an orthogonal matrix; this is a version of Applied Statistics Algorithm 82, by J C Gower.
asa082_test
asa091, a Fortran90 code which evaluates the percentage points of the Chi-Squared distribution, by Best and Roberts. This is a version of Applied Statistics Algorithm 91.
asa091_test
asa103, a Fortran90 code which evaluates the digamma or psi function, by Jose Bernardo. This is a version of Applied Statistics Algorithm 103.
asa103_test
asa109, a Fortran90 code which inverts the incomplete Beta function, by Cran, Martin and Thomas. This is a version of Applied Statistics Algorithm 109.
asa109_test
asa111, a Fortran90 code which evaluates the percentage points of the normal distribution, by Beasley and Springer. This is a version of Applied Statistics Algorithm 111.
asa111_test
asa113, a Fortran90 code which implements a clustering algorithm using transfers and swaps, by Banfield and Bassill. This is a version of Applied Statistics Algorithm 113.
asa113_test
asa121, a Fortran90 code which evaluates the trigamma function, by BE Schneider. This is a version of Applied Statistics Algorithm 121.
asa121_test
asa136, a Fortran90 code which implements a clustering algorithm, by Hartigan and Wong. This is a version of Applied Statistics Algorithm 136.
asa136_test
asa144, a Fortran90 code which randomly generates an RxC contingency table, by James Boyett. This is a version of Applied Statistics Algorithm 144.
asa144_test
asa147, a Fortran90 code which evaluates the incomplete Gamma function, by Chi Leung Lau. This is a version of Applied Statistics Algorithm 147.
asa147_test
asa152, a Fortran90 code 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.
asa152_test
asa159, a Fortran90 code which randomly generates an RxC contingency table, by Michael Patefield; This is a version of Applied Statistics Algorithm 159.
asa159_test
asa172, a Fortran90 code 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.
asa172_test
asa183, a Fortran90 code which implements a random number generator (RNG), by Wichman and Hill. This is a version of Applied Statistics Algorithm 183.
asa183_test
asa189, a Fortran90 code which estimates the parameters of a beta binomial distribution based on a sample of values generated by the distribution, by D Smith; this is a version of Applied Statistics Algorithm 189;
asa189_test
asa205, a Fortran90 code which generates all the contingency tables corresponding to a given set of row and column sums. This is a version of Applied Statistics Algorithm 205.
asa205_test
asa226, a Fortran90 code which evaluates the Cumulative Density Function (CDF) of the noncentral Beta distribution, by Russell Lenth. This is a version of Applied Statistics Algorithm 226.
asa226_test
asa239, a Fortran90 code which evaluates the incomplete Gamma function, by Shea. This is a version of Applied Statistics Algorithm 239.
asa239_test
asa241, a Fortran90 code which evaluates the percentage points of the normal distribution, by Michael Wichura. This is a version of Applied Statistics Algorithm 241.
asa241_test
asa243, a Fortran90 code which evaluates the Cumulative Density Function (CDF) of the noncentral T distribution, by Russell Lenth; this is a version of Applied Statistics Algorithm 243.
asa243_test
asa245, a Fortran90 code which evaluates the logarithm of the Gamma function, by Allan Mcleod; this is a version of Applied Statistics Algorithm 245.
asa245_test
asa266, a Fortran90 code which evaluates various properties of the Dirichlet Probability Density Function (PDF); this is a version of Applied Statistics Algorithm 266;
asa266_test
asa299, a Fortran90 code which computes the lattice points in an M-dimensional simplex, by Chasalow and Brand; this is a version of Applied Statistics Algorithm 299;
asa299_test
asa310, a Fortran90 code which computes the Cumulative Density Function (CDF) of the noncentral Beta distribution, by Chattamvelli and Shanmugam; this is a version of Applied Statistics Algorithm 310.
asa310_test
asa314, a Fortran90 code 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;
asa314_test
atbash, a Fortran90 code which applies the Atbash substitution cipher to a string of text.
atbash_test
backtrack_binary_rc, a Fortran90 code which carries out a backtrack search for binary decisions, using reverse communication (RC).
backtrack_binary_rc_test
backward_euler, a Fortran90 code which solves one or more ordinary differential equations (ODE) using the (implicit) backward Euler method, using a version of fsolve() for the implicit equation.
backward_euler_test
ball_grid, a Fortran90 code which computes grid points inside a 3D ball.
ball_grid_test
ball_integrals, a Fortran90 code which returns the exact value of the integral of any monomial over the interior of the unit ball in 3D.
ball_integrals_test
ball_monte_carlo, a Fortran90 code which applies a Monte Carlo method to estimate integrals of a function over the interior of the unit ball in 3D;
ball_monte_carlo_test
band_qr, a Fortran90 code which computes the QR factorization of a banded matrix, and solves related linear systems, by Alfredo Remon, Enrique Quintana-Orti, Gregorio Quintana-Orti.
band_qr_test
barycentric_interp_1d, a Fortran90 code which defines and evaluates the barycentric Lagrange polynomial p(x) which interpolates data, so that p(x(i)) = y(i). The barycentric approach means that very high degree polynomials can safely be used.
barycentric_interp_1d_test
bdf2, a Fortran90 code which solves one or more ordinary differential equations (ODE) using the (implicit) backward difference formula of order 2 (BDF2), using fsolve() to solve the implicit equation.
bdf2_test
bdmlib, a Fortran90 code which estimates the weights in a Dirichlet mixture based on sample data;
bdmlib_test
bellman_ford, a Fortran90 code 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.
bellman_ford_test
bernstein_polynomial, a Fortran90 code which evaluates the Bernstein polynomials;
bernstein_polynomial_test
besselj, a Fortran90 code which evaluates Bessel J functions of noninteger order;
besselj_test
beta_nc, a Fortran90 code which evaluates the cumulative density function (CDF) of the noncentral Beta distribution;
beta_nc_test
bezier_surface, a Fortran90 code which reads, writes, prints and manipulates the data that defines a Bezier surface;
bezier_surface_test
biharmonic_exact, a Fortran90 code which evaluates exact solutions w(x,y) to the biharmonic equation del^2 w = 0 or wxxxx + 2 wxxyy + wyyyy = 0
biharmonic_exact_test
bins, a Fortran90 code which sorts data into order, or lumps it into bins, or selects an item of particular rank, or finds the unique elements in a list.
bins_test
bisection, a Fortran90 code which applies the bisection method to seek a root of f(x) over a change-of-sign interval a <= x <= b.
bisection_test
bisection_integer, a Fortran90 code which seeks an integer solution to the equation F(X)=0, using bisection within a user-supplied change of sign interval [A,B].
bisection_integer_test
bisection_rc, a Fortran90 code 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 (RC).
bisection_rc_test
bivar, a Fortran90 code which interpolates scattered bivariate data. This is a version of ACM TOMS algorithm 526, by Hiroshi Akima.
bivar_test
black_scholes, a Fortran90 code which implements some simple approaches to the Black-Scholes option valuation theory, creating graphics files for processing by gnuplot(), by Desmond Higham.
black_scholes_test
blend, a Fortran90 code which carries out 1D/2D/3D blending interpolation;
blend_test
box_behnken, a Fortran90 code which computes a Box-Behnken design, that is, arguments to sample the behavior of a function of multiple parameters;
box_behnken_test
brownian_motion_simulation, a Fortran90 code which simulates Brownian motion in an M-dimensional region, creating graphics files for processing by gnuplot().
brownian_motion_simulation_test
bump, a Fortran90 code which solves a 2D steady incompressible flow problem set in a channel with a small bump.
bump_test
burgers_exact, a Fortran90 code which evaluates exact solutions of the time-dependent 1D viscous Burgers equation.
burgers_exact_test
bvec, a Fortran90 code which demonstrates how signed integers can be stored as binary vectors, and arithmetic can be performed on them.
bvec_test
bvls, a Fortran90 code which applies linear least squares (LLS) methods to solve a system for which lower and upper constraints may have been placed on every variable, by Charles Lawson and Richard Hanson.
bvls_test
c_comment, a Fortran90 code which reads an ASCII text file, and writes a copy, in which C++ style comments have been replaced by equivalent C-style comments.
c_comment_test
c8lib, a Fortran90 code which implements certain elementary functions for double precision complex (C8) variables;
c8lib_test
c8poly, a Fortran90 code which operates on complex polynomials.
c8poly_test
caesar, a Fortran90 code which applies a Caesar Shift Cipher to a string of text.
caesar_test
calendar_nyt, a Fortran90 code which shows the correspondence between dates and the New York Times volume and issue number;
calendar_nyt_test
calpak, a Fortran90 code which computes various simple calendrical quantities. It can work with various calendars including Egyptian, English, French Revolutionary, Gregorian, Julian, and Julian Ephemeris Date. It can convert a date from one calendar to another. It can return the day of the week for a given date. It can convert from day-number/year to day/month/year format. It can calculate the time difference between two dates.
calpak_test
candy_count, a Fortran90 code which counts the types of candy in a rectangular container, which might be a vector, matrix, or 3D box. The candy is assumed to have C possible types, and to have been entered into the container in a cycle that begins with type 1. While the vector case is easy, it is already difficult to come up with a general formula for the MxN matrix case.
candy_count_test
cauchy_principal_value, a Fortran90 code which uses Gauss-Legendre quadrature to estimate the Cauchy Principal Value (CPV) of certain singular integrals.
cauchy_principal_value_test
ccn_rule, a Fortran90 code which defines a Clenshaw Curtis Nested (CCN) quadrature rule.
ccn_rule_test
ccs_io, a Fortran90 code which reads and writes sparse linear systems stored in the Compressed Column Storage (CCS) format.
ccs_io_test
ccs_to_st, a Fortran90 code which converts a sparse matrix from compressed column storage (CCS) to sparse triplet (ST) format.
ccs_to_st_test
cdflib, a Fortran90 code 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.
cdflib_test
cell, a Fortran90 code which defines a cell array, a generalization of an array which compactly stores and retrieves vector or matrix data of varying size, such as the rows of a triangular matrix.
cell_test
cg, a Fortran90 code 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_test
cg_rc, a Fortran90 code which implements the conjugate gradient (CG) method for solving a positive definite sparse linear system A*x=b, using reverse communication (RC).
cg_rc_test
change_dynamic, a Fortran90 code which uses dynamic programming to solve the change making problem, in which a given sum is to be formed using coins of various denominations.
change_dynamic_test
channel, a Fortran90 code which computes the time-independent flow of a viscous incompressible fluid in a 2D channel.
channel_test
chebyshev, a Fortran90 code which computes the Chebyshev interpolant/approximant to a given function over an interval.
chebyshev_test
chebyshev_interp_1d, a Fortran90 code which determines the combination of Chebyshev polynomials which interpolates data, so that p(x(i)) = y(i).
chebyshev_interp_1d_test
chebyshev_polynomial, a Fortran90 code 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_polynomial_test
chebyshev_series, a Fortran90 code which evaluates 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.
chebyshev_series_test
chrpak, a Fortran90 code which manipulates characters and strings;
chrpak_test
circle_arc_grid, a Fortran90 code which computes a grid of points over the length of a circle or circular arc in 2D.
circle_arc_grid_test
circle_integrals, a Fortran90 code which returns the exact value of the integral of any monomial over the circumference of the unit circle in 2D.
circle_integrals_test
circle_monte_carlo, a Fortran90 code which applies a Monte Carlo method to estimate the integral of a function along the circumference of the unit circle in 2D;
circle_monte_carlo_test
circle_packing, a Fortran90 code which performs a circle-packing test on the spacing for points;
circle_packing_test
circle_segment, a Fortran90 code which carries out computations associated with a circle segment, including height, angle, area, centroid, sampling, and quadrature, creating some graphics images using gnuplot().
circle_segment_test
clausen, a Fortran90 code which evaluates a Chebyshev interpolant to the Clausen function Cl2(x).
clausen_test
clenshaw_curtis_grid, a Fortran90 code which sets up a Clenshaw Curtis quadrature rule in multiple dimensions;
clenshaw_curtis_grid_test
closest_pair_brute, a Fortran90 code which uses brute force to solve a 2D version of the closest pair problem, which identifies the closest pair of points in a given collection.
closest_pair_brute_test
closest_point_brute, a Fortran90 code which uses brute force to find the nearest of a set of N points in D dimensions to a given test point. This is sometimes called a nearest neighbor calculation.
closest_point_brute_test
cluster_energy, a Fortran90 code which groups data into a given number of clusters to minimize the energy.
cluster_energy_test
cnf_io, a Fortran90 code which reads or writes DIMACS Conjunctive Normal Form (CNF) files defining satisfiability problems in terms of a boolean formula.
cnf_io_test
codepack, a Fortran90 code which determine if two graphs are isomorphic.
codepack_test
collatz_recursive, a Fortran90 code which demonstrates recursive programming by considering the simple Collatz 3n+1 problem.
collatz_recursive_test
color_digraph_adj, a Fortran90 code which carries out operations on color digraphs, a directed graph in which each node has been assigned a color. That information is stored in an adjacency matrix in which the diagonal elements record colors. Operations include counting the colors, computing in- and out-degrees, computing the in- and out-degree sequences, counting the edges, printing the adjacency matrix, generating fixed and random examples.
color_digraph_adj_test
color_graph_adj, a Fortran90 code which carries out operations on color graphs, an undirected graph in which each node has been assigned a color. That information is stored in an adjacency matrix in which the diagonal elements record colors. Operations include counting the colors, computing degrees, computing the degree sequences, counting the edges, printing the adjacency matrix, generating fixed and random examples.
color_graph_adj_test
colored_noise, a Fortran90 code which generates samples of noise obeying a 1/f^alpha power law.
colored_noise_test
colors, a Fortran90 code which converts between various formats for describing colors;
colors_test
combo, a Fortran90 code which ranks, unranks, enumerates, lists and randomly selects balanced sequences, cycles, graphs, Gray codes, subsets, partitions, permutations, restricted growth functions, Pruefer codes and trees.
combo_test
communicator_mpi, a Fortran90 code which creates new communicators involving a subset of initial set of MPI processes in the default communicator MPI_COMM_WORLD.
communicator_mpi_test
companion_matrix, a Fortran90 code which computes the companion matrix for a polynomial. The polynomial may be represented in the standard monomial basis, or as a sum of Chebyshev, Gegenbauer, Hermite, Laguerre, or Lagrange basis polynomials. All the roots of the polynomial can be determined as the eigenvalues of the corresponding companion matrix.
companion_matrix_test
compass_search, a Fortran90 code which seeks the minimizer of a scalar function of several variables using compass search, a direct search algorithm that does not use derivatives.
compass_search_test
complex_numbers_test, a Fortran90 code which demonstrates some simple features involved in the use of complex numbers.
components, a Fortran90 code which organizes contiguous cells into labeled clusters, for a 1D, 2D, or 3D array. This code has uses in image analysis and percolation simulation.
components_test
condition, a Fortran90 code which implements methods of computing or estimating the condition number of a matrix.
condition_test
continued_fraction, a Fortran90 code which deals with simple and generalized continued fractions.
continued_fraction_test
cordic, a Fortran90 code which computes a few special functions using the CORDIC algorithm.
cordic_test
cosine_transform, a Fortran90 code which demonstrates some simple properties of the discrete cosine transform (DCT).
cosine_transform_test
crystal_coordinates, a Fortran90 code which generates the coordinates of a set of 4 * NX * NY * NZ points in a rectangular block of NX * NY * NZ cells, with face-centered cubic (FCC) symmetry.
crystal_coordinates_test
csv_io, a Fortran90 code which reads and writes files that use the Comma Separated Value (CSV) format.
csv_io_test
cube_exactness, a Fortran90 code which computes the polynomial exactness of quadrature rules over the interior of a cube in 3D.
cube_exactness_test
cube_grid, a Fortran90 code which computes a grid of points over the interior of a cube in 3D.
cube_grid_test
cube_integrals, a Fortran90 code which returns the exact value of the integral of any monomial over the interior of the unit cube in 3D.
cube_integrals_test
cube_monte_carlo, a Fortran90 code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit cube in 3D.
cube_monte_carlo_test
cuda_loop, a Fortran90 code which shows how, in a CUDA program running on a Graphics Processing Unit (GPU), the choice of block and thread factors determines the allocation of tasks to processors.
cuda_loop_test
cvt, a Fortran90 code which computes elements of a Centroidal Voronoi Tessellation (CVT).
cvt_test
cvt_basis, a Fortran90 code which uses discrete Centroidal Voronoi Tessellation (CVT) techniques to produce a small set of basis vectors that are good cluster centers for a large set of data vectors;
cvt_basis_test
cvt_basis_flow, a Fortran90 code which extracts dominant solution modes from solutions of a flow problem governed by the Navier Stokes Equations (NSE) using Centroidal Voronoi Tessellation (CVT) methods.
cvt_box, a Fortran90 code which calculates a Centroidal Voronoi Tessellation (CVT) constrained to a box region, with points projected to the boundary;
cvt_box_test
cvtp, a Fortran90 code which creates a Centroidal Voronoi Tessellation on a Periodic region (CVTP).
cvtp_test
cvt_triangulation, a Fortran90 code which applies Centroidal Voronoi Tessellation (CVT) techniques to the test_triangulation() set;
cvt_triangulation_test
cyclic_reduction, a Fortran90 code which solves a tridiagonal linear system using cyclic reduction.
cyclic_reduction_test
diaphony, a Fortran90 code which reads a file of N points in M dimensions and computes its diaphony, a measure of point dispersion.
diaphony_test
differ, a Fortran90 code which is given function values at equally spaced locations, and the order of a derivative, and uses the finite difference method (FDM) to compute a linear combination of these function values which approximated that derivative.
differ_test
digraph_adj, a Fortran90 code which carries out operations on digraphs, a directed graph. Information is stored in an adjacency matrix. Operations include computing in- and out-degrees, computing the in- and out-degree sequences, counting the edges, printing the adjacency matrix, generating fixed and random examples.
digraph_adj_test
digraph_arc, a Fortran90 code which carries out operations on digraphs, a directed graph. Information is stored in an arc list, pairs of nodes forming edges. Operations include computing in- and out-degrees, computing the in- and out-degree sequences, counting the edges, printing the arc list, generating fixed and random examples.
digraph_arc_test
dijkstra, a Fortran90 code which implements a simple version of the Dijkstra minimum distance algorithm for graphs.
dijkstra_test
discrete_pdf_sample_2d, a Fortran90 code which demonstrates how to construct a Probability Density Function (PDF) from a table of sample data, and then to use that PDF to create new samples.
discrete_pdf_sample_2d_test
disk_grid, a Fortran90 code 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_grid_test
disk_monte_carlo, a Fortran90 code which applies a Monte Carlo method to estimate integrals of a function over the interior of the general disk in 2D;
disk_monte_carlo_test
disk01_integrals, a Fortran90 code which returns the exact value of the integral of any monomial over the interior of the unit disk in 2D.
disk01_integrals_test
disk01_monte_carlo, a Fortran90 code which applies a Monte Carlo method to estimate integrals of a function over the interior of the unit disk in 2D;
disk01_monte_carlo_test
disk01_positive_monte_carlo, a Fortran90 code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit positive disk in 2D;
disk01_positive_monte_carlo_test
distance_to_position, a Fortran90 code which estimates the positions of cities based on a city-to-city distance table.
distance_to_position_test
divdif, a Fortran90 code which creates, prints and manipulates divided difference polynomials from a table of values (x,f(x)). The code can compute the coefficients of the Newton and power sum forms of the interpolating polynomial. It can compute the derivative or antiderivate polynomial. It can compute the form of the Lagrange basis polynomials. It can compute the points and weights for Newton Cotes quadrature rules. It can compute the weights for a Lagrange interpolation scheme.
divdif_test
doomsday, a Fortran90 code 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.
doomsday_test
dqed, a Fortran90 code which solves (square) systems of nonlinear equations, or minimizes the residual in a set of nonlinear equations, using least squares, by Richard Hanson and Fred Krogh.
dqed_test
dream, a Fortran90 code 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.
dream_test
duel_simulation, a Fortran90 code which simulates N repetitions of a duel between two players, each of whom has a known firing accuracy.
duel_simulation_test
dutch, a Fortran90 code which carries out tasks in computational geometry.
dutch_test
edge, a Fortran90 code which defines some test functions in 1D, 2D and 3D for the detection of edges or discontinuities. It uses gnuplot() to display the jumps in curves and surfaces.
edge_test
eigs, a Fortran90 code which computes the eigenvalues and eigenvectors of a matrix.
eigs_test
eispack, a Fortran90 code which carries out eigenvalue computations. It includes a function to compute the singular value decomposition (SVD) of a rectangular matrix. superseded by lapack();
eispack_test
ellipse, a Fortran90 code which carries out geometric calculations for ellipses and ellipsoids, including area, distance to a point, eccentricity, perimeter, points along the perimeter, random sampling, conversion between standard and quadratic forms.
ellipse_test
ellipse_grid, a Fortran90 code which computes grid points over the interior of an ellipse in 2D.
ellipse_grid_test
ellipse_monte_carlo, a Fortran90 code which uses the Monte Carlo method to estimate the value of integrals over the interior of an ellipse in 2D.
ellipse_monte_carlo_test
ellipsoid, a Fortran90 code which carries out geometric calculations for ellipsoids, including area, random sampling, conversion between standard and quadratic forms.
ellipsoid_test
ellipsoid_grid, a Fortran90 code which computes a grid of points over the interior of an ellipsoid in 3D.
ellipsoid_grid_test
ellipsoid_monte_carlo, a Fortran90 code which uses the Monte Carlo method to estimate the value of integrals over the interior of an ellipsoid in M dimensions.
ellipsoid_monte_carlo_test
elliptic_integral, a Fortran90 code which evaluates complete elliptic integrals of first, second and third kind, using the Carlson elliptic integral functions.
elliptic_integral_test
etdrk4, a Fortran90 code which uses the ETD RK4 method to solve systems of stiff ordinary differential equations (ODE), by Aly-Khan Kassam, Lloyd Trefethen.
etdrk4_test
euler, a Fortran90 code which solves one or more ordinary differential equations (ODE) using the forward Euler method.
euler_test
exactness, a Fortran90 code 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).
exactness_test
extract, a Fortran90 code which pulls a copy of a Fortran block data, function, module, program or subroutine from a big file, and saves the copy in a little file.
extract_test
f90_combinatorics, a Fortran90 code which considers a variety of problems in combinatorics involving counting, combinations, permutations, and so on.
f90_exact, a Fortran90 code which evaluates exact solutions to a few selected examples of ordinary differential equations (ODE) and partial differential equations (PDE).
f90_monte_carlo, a Fortran90 code which uses Monte Carlo sampling to estimate areas and integrals.
f90_ode_solver, a Fortran90 code which solves one or more differential equations (ODE) using a method of a particular order, either explicit or implicit. Some methods require a nonlinear equation solver. Some methods used a fixed stepsize, while others adapt the stepsize based on an error estimate.
f90_random_test, a Fortran90 code which calls the random number generator (RNG) routines.
f90_rule, a Fortran90 code which computes a quadrature rule which estimates the integral of a function f(x), which might be defined over a one dimensional region (a line) or more complex shapes such as a circle, a triangle, a quadrilateral, a polygon, or a higher dimensional region, and which might include an associated weight function w(x).
f90_simulation, a Fortran90 code which uses simulation to study card games, contests, and other processes which have a random element. Usually, the purpose is to try to predict the average behavior of the system over many trials.
f90split, a Fortran90 code which reads a Fortran file and creates individual files for every blockdata, function, module, program, or subroutine in the file.
f90split_test
fair_dice_simulation, a Fortran90 code which simulates N games where two fair dice are thrown and summed, creating graphics files for processing by gnuplot().
fair_dice_simulation_test
fd_predator_prey, a Fortran90 code which solves a pair of predator prey ordinary differential equations (ODE) using the finite difference method (FDM), and plots the data with gnuplot().
fd_predator_prey_test
fd1d_advection_diffusion_steady, a Fortran90 code 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_diffusion_steady_test
fd1d_advection_ftcs, a Fortran90 code 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_ftcs_test
fd1d_advection_lax, a Fortran90 code 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_test
fd1d_advection_lax_wendroff, a Fortran90 code 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_advection_lax_wendroff_test
fd1d_burgers_lax, a Fortran90 code 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_lax_test
fd1d_burgers_leap, a Fortran90 code 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_burgers_leap_test
fd1d_bvp, a Fortran90 code which applies the finite difference method (FDM) to a two point boundary value problem (BVP) in one spatial dimension.
fd1d_bvp_test
fd1d_heat_explicit, a Fortran90 code which implements a finite difference method (FDM), explicit in time, of the time dependent 1D heat equation;
fd1d_heat_explicit_test
fd1d_heat_implicit, a Fortran90 code which implements a finite difference method (FDM), implicit in time, of the time dependent 1D heat equation;
fd1d_heat_implicit_test
fd1d_heat_steady, a Fortran90 code which implements a finite difference method (FDM) for the steady time-independent 1D heat equation;
fd1d_heat_steady_test
fd1d_predator_prey, a Fortran90 code which implements the finite difference method (FDM) for a predator-prey system with time and 1D spatial dependence, by Marcus Garvie.
fd1d_predator_prey_test
fd1d_wave, a Fortran90 code which applies the finite difference method (FDM) to solve the time-dependent wave equation utt = c * uxx in one spatial dimension.
fd1d_wave_test
fd2d_heat_steady, a Fortran90 code which implements a finite difference method (FDM) for the steady time-independent 2D heat equation;
fd2d_heat_steady_test
fd2d_predator_prey, a Fortran90 code which implements the finite difference method (FDM) for a 2D predator-prey system, by Marcus Garvie.
fd2d_predator_prey_test
fem_basis, a Fortran90 code which defines and evaluates basis functions associated with the finite element method (FEM) for any degree in an M-dimensional simplex: 1D interval, 2D triangle, 3D tetrahedron, and higher dimensional generalizations.)
fem_basis_test
fem_io, a Fortran90 code which reads or writes FEM files, which describe the nodes, elements, and function values associated with a finite element method (FEM) model;
fem_io_test
fem_to_gmsh, a Fortran90 code 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_gmsh_test
fem_to_medit, a Fortran90 code which reads FEM files defining the node coordinates, boundary nodes, and elements of a finite element mesh, and rewrites the data as a medit() MESH file.
fem_to_medit_test
fem_to_tec, a Fortran90 code which converts FEM models into tecplot ASCII files.
fem_to_tec_test
fem_to_triangle, a Fortran90 code 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 Jonathan Shewchuk's triangle() program
fem_to_triangle_test
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().
fem_to_xml_test
fem1d, a Fortran90 code which applies the finite element method (FEM), using piecewise linear basis functions, to a linear two point boundary value problem (BVP) in 1D;
fem1d_test
fem1d_adaptive, a Fortran90 code 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_adaptive_test
fem1d_bvp_linear, a Fortran90 code 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_linear_test
fem1d_bvp_quadratic, a Fortran90 code 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_bvp_quadratic_test
fem1d_heat_steady, a Fortran90 code which implements the finite element method (FEM) for the steady time-independent 1D heat equation;
fem1d_heat_steady_test
fem1d_lagrange, a Fortran90 code 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_lagrange_test
fem1d_nonlinear, a Fortran90 code which applies the finite element method (FEM), with piecewise linear basis functions, to a nonlinear two point boundary value problem (BVP) in 1D;
fem1d_nonlinear_test
fem1d_pack, a Fortran90 code which contains utilities for 1D finite element method (FEM) calculations.
fem1d_pack_test
fem1d_pmethod, a Fortran90 code which applies the p-method version of the finite element method (FEM) to a linear two point boundary value problem (BVP) in 1D;
fem1d_pmethod_test
fem1d_project, a Fortran90 code 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_project_test
fem1d_sample, a Fortran90 code which samples a scalar or vector finite element function of one variable, defined by FEM files, returning interpolated values at the sample points.
fem1d_sample_test
fem2d_bvp_linear, a Fortran90 code 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_linear_test
fem2d_bvp_quadratic, a Fortran90 code 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_quadratic_test
fem2d_bvp_serene, a Fortran90 code 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_bvp_serene_test
fem2d_heat, a Fortran90 code which uses the finite element method (FEM) and the backward Euler method to solve the time-dependent heat equation on an arbitrary triangulated region in 2D. The user supplies some information in some problem-dependent subroutines.
fem2d_heat_test
fem2d_heat_rectangle, a Fortran90 code which implements the finite element method (FEM) for the time dependent heat equation on a triangulated square in 2D;
fem2d_heat_rectangle_test
fem2d_pack, a Fortran90 code which implements simple 2D finite element method (FEM) calculations;
fem2d_pack_test
fem2d_poisson_rectangle, a Fortran90 code which solves the 2D Poisson equation on a rectangle, using the finite element method (FEM), and piecewise quadratic triangular elements.
fem2d_poisson_rectangle_test
fem2d_poisson_rectangle_linear, a Fortran90 code which solves the 2D Poisson equation on a rectangle, using the finite element method (FEM), and piecewise linear triangular elements.
fem2d_poisson_rectangle_linear_test
fem2d_sample, a Fortran90 code which samples at arbitray points a finite element function, defined by FEM files, three text files describing the nodes, triangles, and coefficients.
fem2d_sample_test
fem3d_pack, a Fortran90 code which contains utilities for 3D finite element method (FEM) calculations.
fem3d_pack_test
fem3d_sample, a Fortran90 code which evaluates a finite element function defined on a 3D tetrahedral mesh.
fem3d_sample_test
fftpack5, a Fortran90 code which computes Fast Fourier Transforms (FFTs), by Paul Swarztrauber and Dick Valent;
fftpack5_test
fftpack51, a Fortran90 code which computes Fast Fourier Transforms (FFTs), using real 64 bit arithmetic, by Paul Swarztrauber and Dick Valent;
fftpack51_test
fftw_test, a Fortran90 code which calls fftw(), which computes Fast Fourier Transforms (FFT), by Matteo Frigo and Steven Johnson.
file_name_sequence, a Fortran90 code which demonstrates ways to generate a sequence of filenames, which can be useful when generating a sequence of still snapshots to be animated later.
file_name_sequence_test
files_multiple, a Fortran90 code which demonstrates how a program can open multiple output files at one time, and write data to any one specific file it chooses.
filon_rule, a Fortran90 code which uses Filon's method to approximate integrals which include an oscillatory factor of sin(k*x) or cos(k*x).
filon_rule_test
filum, a Fortran90 code which performs various operations on files;
filum_test
fisher_exact, a Fortran90 code which returns an exact solution of the Kolmogorov Petrovsky Piskonov Fisher partial differential equation (PDE) ut=uxx+u*(1-u).
fisher_exact_test
fixcon, a Fortran90 code which converts the line continuation scheme used in a Fortran77 file to that used in Fortran90 files.
fixcon_test
flame_exact, a Fortran90 code which returns the exact solution of an ordinary differential equation (ODE) which models the growth of a ball of flame in a combustion process. The exact solution is defined in terms of the Lambert W function.
flame_exact_test
floyd, a Fortran90 code which implements the Floyd algorithm for finding the shortest distance between pairs of nodes on a directed graph.
floyd_test
football_dynamic, a Fortran90 code which uses dynamic programming to count the ways of achieving a given score in football.
football_dynamic_test
football_rank, a Fortran90 code which is given a set of game scores, and produces a ranking of college football teams.
football_rank_test
freefem_msh_io, a Fortran90 code which reads and writes files used by FreeFem++ to store mesh information for the finite element method (FEM).
freefem_msh_io_test
fsolve, a Fortran90 code which solves systems of nonlinear equations, inspired by the fsolve() function in minpack(), with special interfaces fsolve_bdf2(), fsolve_be() and fsolve_tr() for handling systems associated with implicit ODE solvers of type bdf2, backward Euler, midpoint, or trapezoidal.
fsolve_test
gauss_seidel, a Fortran90 code which implements the Gauss-Seidel iteration for linear systems.
gauss_seidel_test
gdb_test, a Fortran90 code which uses the GNU debugger;
gegenbauer_cc, a Fortran90 code which computes the Gegenbauer weighted integral of a function f(x) using a Clenshaw-Curtis approach.
gegenbauer_cc_test
gegenbauer_exactness, a Fortran90 code which tests the polynomial exactness of Gauss-Gegenbauer quadrature rules.
gegenbauer_exactness_test
gegenbauer_polynomial, a Fortran90 code which evaluates the Gegenbauer polynomial and associated functions.
gegenbauer_polynomial_test
gegenbauer_rule, a Fortran90 code which computes and writes out a Gauss-Gegenbauer quadrature rule of given order.
gegenbauer_rule_test
gen_hermite_exactness, a Fortran90 code which tests the polynomial exactness of generalized Gauss-Hermite quadrature rules.
gen_hermite_exactness_test
gen_hermite_rule, a Fortran90 code which computes and writes out a generalized Gauss-Hermite quadrature rule of given order and parameter value.
gen_hermite_rule_test
gen_laguerre_exactness, a Fortran90 code which tests the polynomial exactness of generalized Gauss-Laguerre quadrature rules.
gen_laguerre_exactness_test
gen_laguerre_rule, a Fortran90 code which computes and writes out a generalized Gauss-Laguerre quadrature rule of given order and parameter value.
gen_laguerre_rule_test
gene_cluster, a Fortran90 code which clusters sets of genetic expression data;
gene_cluster_test
geometry, a Fortran90 code which performs geometric calculations in 2, 3 and M dimensional space, including the computation of angles, areas, containment, distances, intersections, lengths, and volumes.
geometry_test
geompack, a Fortran90 code which computes Delaunay triangulations, Voronoi diagrams, and other information, by Barry Joe.
geompack_test
gfortran_quadmath_test, a Fortran90 code which illustrates the use of quadruple real precision arithmetic with the Gnu Fortran compiler.
gl_fast_rule, a Fortran90 code which carries out the rapid computation of the Kth value and weight of an N point Gauss-Legendre quadrature rule, by Ignace Bogaert.
gl_fast_rule_test
glomin, a Fortran90 code which finds a global minumum of a scalar function of a scalar variable, without the use of derivative information, by Richard Brent.
glomin_test
gmsh_io, a Fortran90 code which reads or writes some of the files created by gmsh() for 1D, 2D or 3D meshes used by the finite element method (FEM).
gmsh_io_test
gmsh_to_fem, a Fortran90 code which reads a mesh data file created by gmsh() and writes a pair of node and element files that correspond to the FEM format.
gmsh_to_fem_test
gprof_test, a Fortran90 code which uses the gprof() profiling tool.
graph_adj, a Fortran90 code which carries out operations on abstract graphs, with undirected edges, represented by an adjacency matrix. Operations include breadth-first search, the computation of a minimum spanning tree, an Euler or Hamilton circuit, blocks, chromatic polynomial, or transitive closure.
graph_adj_test
graph_arc, a Fortran90 code which carries out operations on graphs. Information is stored in an arc list, pairs of nodes forming edges. Operations include the chromatic polynomial, computing degrees, computing the degree sequence, counting the edges, determining edge and node connectivity, Euler circuits, spanning trees, shortest path, printing the arc list, generating fixed and random examples.
graph_arc_test
graph_dist, a Fortran90 code which carries out operations on abstract graphs, defined by undirected edges with an associated distance matrix.
graph_dist_test
graph_paper, a Fortran90 code which makes PostScript (PS) graph paper;
graph_paper_test
graph_theory, a Fortran90 code which carries out operations on abstract graphs, such as a breadth-first-search, the computation of a minimum spanning tree, an Euler or Hamilton circuit, blocks, chromatic polynomial, or transitive closure. Objects include undirected and directed graphs, weighted graphs, and trees.
graph_theory_test
graphics_dislin_test, a Fortran90 code which graphically displays various kinds of data, using the dislin() graphics library.
graphics_gnuplot_test, a Fortran90 code which graphically displays various kinds of data, using the gnuplot() graphics program.
grf_io, a Fortran90 code which reads or writes a grf file which represents a mathematical graph;
grf_io_test
grf_to_eps, a Fortran90 code which converts a GRF file to Encapsulated PostScript (EPS) format;
grf_to_eps_test
grf_to_xyl, a Fortran90 code which converts information describing the adjacency and embedding of an abstract graph from GRF to XYL format.
grf_to_xyl_test
haar_transform, a Fortran90 code which computes the Haar transform of 1d or 2d data.
haar_transform_test
halton, a Fortran90 code which computes elements of a Halton Quasi Monte Carlo (QMC) sequence, using a simple interface.
halton_test
hammersley, a Fortran90 code which computes elements of a Hammersley Quasi Monte Carlo (QMC) sequence, using a simple interface.
hammersley_test
hankel_cholesky, a Fortran90 code which computes the upper Cholesky factor R of a symmetric positive definite (SPD) Hankel matrix H so that H = R' * R.
hankel_cholesky_test
hankel_spd, a Fortran90 code which computes a lower triangular matrix L that is the Cholesky factor of a symmetric positive definite (SPD) Hankel matrix H, that is, H = L * L'.
hankel_spd_test
hb_io, a Fortran90 code which reads and writes sparse linear systems stored in the Harwell Boeing (HB) format for sparse matrices.
hb_io_test
hb_to_st, a Fortran90 code which converts a sparse matrix from Harwell Boeing (HB) format to Sparse Triplet (ST) format.
hb_to_st_test
heat_mpi, a Fortran90 code which solves the 1D time dependent heat equation in parallel, using the Message Passing Interface (MPI).
heat_mpi_test
heated_plate, a Fortran90 code which solves the steady (time independent) heat equation in a 2D rectangular region, and is intended as a starting point for implementing a parallel version.
heated_plate_test
heated_plate_openmp, a Fortran90 code which solves the steady (time independent) heat equation in a 2D rectangular region, using OpenMP to run in parallel.
heated_plate_openmp_test
hello, a Fortran90 code which prints out "Hello, world!".
hello_test
hello_mpi, a Fortran90 code which prints 'Hello, world!' using the Message Passing Interface (MPI) for parallel execution.
hello_mpi_test
hello_openmp, a Fortran90 code which prints 'Hello, world!', using OpenMP for parallel execution.
hello_openmp_test
helmholtz_openmp, a Fortran90 code which solves the discretized Helmholtz equation in 2D using the OpenMP application program interface for carrying out parallel computations in a shared memory environment.
helmholtz_openmp_test
hermite_cubic, a Fortran90 code which computes the value, derivatives or integral of a Hermite cubic polynomial, or manipulate an interpolating function made up of piecewise Hermite cubic polynomials.
hermite_cubic_test
hermite_exactness, a Fortran90 code which tests the monomial exactness of quadrature rules for estimating Hermite-type integrals of a function f(x) with density rho(x)=exp(-x^2) over the interval (-oo,+oo).
hermite_exactness_test
hermite_integrands, a Fortran90 code which defines test integrands for Hermite integrals with density exp(-x^2) over the interval (-oo,+oo).
hermite_integrands_test
hermite_interpolant, a Fortran90 code which computes the Hermite interpolant, a polynomial that matches function values and derivatives.
hermite_interpolant_test
hermite_polynomial, a Fortran90 code which evaluates the physicist's Hermite polynomial, the probabilist's Hermite polynomial, the Hermite function, and related functions.
hermite_polynomial_test
hermite_product_polynomial, a Fortran90 code which defines Hermite product polynomials, creating a multivariate polynomial as the product of univariate Hermite polynomials.
hermite_product_polynomial_test
hex_grid, a Fortran90 code which computes points on a hexagonal grid.
hex_grid_test
hex_grid_angle, a Fortran90 code which produces a hexagonal grid of points in the unit square or an arbitrary box, allowing the user to specify an arbitrary center, angle, and grid density.
hex_grid_angle_test
hexahedron_jaskowiec_rule, a Fortran90 code which returns a symmetric Jaskowiec quadrature rule for the hexahedron, with exactness up to total degree 21.
hexahedron_jaskowiec_rule_test
hexahedron_witherden_rule, a Fortran90 code which returns a symmetric Witherden quadrature rule for the hexahedron, with exactness up to total degree 11.
hexahedron_witherden_rule_test
high_card_simulation, a Fortran90 code 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; using gnuplot() for graphics.
high_card_simulation_test
hilbert_curve, a Fortran90 code which computes the sequence of discrete Hilbert curves whose limit is a space-filling curve.
hilbert_curve_test
humps, a Fortran90 code which evaluates the humps function, its first and second derivatives, and its antiderivative.
humps_test
hyper_2f1, a Fortran90 code which evaluates the hypergeometric functions 2F1(a,b,c;x) for real or complex parameters a, b, c, and argument x, by N. Michel and M. Stoitsov.
hyper_2f1_test
hyperball_integrals, a Fortran90 code which returns the exact value of the integral of any monomial over the interior of the unit hyperball in M dimensions.
hyperball_integrals_test
hyperball_monte_carlo, a Fortran90 code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit ball in M dimensions;
hyperball_monte_carlo_test
hypercube_exactness, a Fortran90 code which tests the polynomial exactness of a quadrature rule over the interior of the unit hypercube in M dimensions.
hypercube_exactness_test
hypercube_grid, a Fortran90 code which computes a grid of points over the interior of a hypercube in M dimensions.
hypercube_grid_test
hypercube_integrals, a Fortran90 code which returns the exact value of the integral of any monomial over the interior of the unit hypercube in M dimensions.
hypercube_integrals_test
hypercube_monte_carlo, a Fortran90 code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit hypercube in M dimensions.
hypercube_monte_carlo_test
hypergeometric, a Fortran90 code which evaluates the generalized hypergeometric functions pFq, for integer p and q, for complex arguments of large magnitude, by Warren Perger, Atul Bhalla, and Mark Nardin.
hypergeometric_test
hypersphere, a Fortran90 code 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.
hypersphere_test
hypersphere_integrals, a Fortran90 code which returns the exact value of the integral of any monomial over the surface of the unit hypersphere in M dimensions.
hypersphere_integrals_test
hypersphere_monte_carlo, a Fortran90 code which applies a Monte Carlo method to estimate the integral of a function on the surface of the unit sphere in M dimensions;
hypersphere_monte_carlo_test
i4lib, a Fortran90 code which contains utilities which use single precision integer (I4) arithmetic.
i4lib_test
interp, a Fortran90 code which parameterizies and interpolates data;
interp_test
intlib, a Fortran90 code which carries out approximate integration (quadrature) in one dimension;
intlib_test
is_prime, a Fortran90 code which implements various versions of the sieve of Eratosthenes to determine whether a given integer is prime.
is_prime_test
ising_2d_simulation, a Fortran90 code which carries out a Monte Carlo simulation of an Ising model, a 2D array of positive and negative charges, each of which is likely to flip to be in agreement with neighbors, using gnuplot() to make images of the initial and final configurations.
ising_2d_simulation_test
ising_3d_simulation, a Fortran90 code which carries out a Monte Carlo simulation of an Ising model, a 3D array of positive and negative charges, each of which is likely to flip to be in agreement with neighbors.
ising_3d_simulation_test
jacobi, a Fortran90 code which implements the Jacobi method for the iterative solution of linear systems.
jacobi_test
jacobi_eigenvalue, a Fortran90 code which implements the Jacobi iteration for the determination of the eigenvalues and eigenvectors of a real symmetric matrix.
jacobi_eigenvalue_test
jacobi_exactness, a Fortran90 code which tests the monomial exactness of quadrature rules for integrals that include a Jacobi weight.
jacobi_exactness_test
jacobi_openmp, a Fortran90 code which uses OpenMP to parallelize a Jacobi iteration for solving A*x=b.
jacobi_openmp_test
jacobi_polynomial, a Fortran90 code which evaluates the Jacobi polynomial and associated functions.
jacobi_polynomial_test
jacobi_rule, a Fortran90 code which computes and print a Gauss-Jacobi quadrature rule.
jacobi_rule_test
kdv_exact, a Fortran90 code which evaluates exact solutions of the Korteweg-deVries (KdV) partial differential equation (PDE).
kdv_exact_test
kdv_ift, a FORTRAN90 code which uses the IFT method to solve the Korteweg-DeVries equation, by Aly-Khan Kassam, Lloyd Trefethen.
kdv_ift_test
ketel_one, a Fortran90 code which finds all words formed from the letters in "ketel one vodka";
ketel_one_test
kmeans, a Fortran90 code which handles the K-Means problem, which organizes N points in M dimensions into K clusters;
kmeans_test
knapsack_01_brute, a Fortran90 code which uses brute force to solve small versions of the 0/1 knapsack problem, in which a knapsack of limited weight capacity is to be packed as full as possible, selecting items from a set of varying weights;
knapsack_01_brute_test
knapsack_rational, a Fortran90 code which solves the rational knapsack problem, in which a knapsack of limited weight capacity is filled with profitable items. This variation of the 0/1 knapsack problem allows a fractional part of an item to be included in the knapsack. The result is an upper bound on the maximum possible profit for the 0/1 knapsack problem.
knapsack_rational_test
knapsack_values, a Fortran90 code which returns some simple examples of the knapsack problem, in which N items are available, each with given value V and weight W. A thief's knapsack can carry no more than K pounds. The thief seeks a selection S of items to carry in the knapsack of maximum total value.
knapsack_values_test
kronrod_rule, a Fortran90 code which computes a Gauss and Gauss-Kronrod pair of quadrature rules of arbitrary order, by Robert Piessens, Maria Branders.
kronrod_rule_test
lagrange_approx_1d, a Fortran90 code which evaluates the Lagrange polynomial p(x) of degree m which approximates n data points (x(i),y(i)).
lagrange_approx_1d_test
lagrange_interp_1d, a Fortran90 code which evaluates the Lagrange polynomial p(x) which interpolates data depending on a 1D argument, so that p(x(i)) = y(i).
lagrange_interp_1d_test
lagrange_interp_2d, a Fortran90 code which evaluates the Lagrange polynomial p(x,y) which interpolates 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_2d_test
lagrange_interp_nd, a Fortran90 code which evaluates the Lagrange polynomial p(x) which interpolates data depending on a multidimensional argument that was evaluated on a product grid, so that p(x(i)) = z(i).
lagrange_interp_nd_test
lagrange_nd, a Fortran90 code which implements several multivariate Lagrange interpolation schemes developed by Tomas Sauer.
lagrange_nd_test
laguerre_exactness, a Fortran90 code which tests the monomial exactness of Gauss-Laguerre quadrature rules for estimating the integral of a function f(x) with density rho(x)=exp(-x) over the interval [0,+oo).
laguerre_exactness_test
laguerre_integrands, a Fortran90 code which implements test problems for Gauss-Laguerre quadrature rules for estimating the integral of a function with density exp(-x) over the interval [0,+oo).
laguerre_integrands_test
laguerre_polynomial, a Fortran90 code which evaluates the Laguerre polynomial, the generalized Laguerre polynomials, and the Laguerre function.
laguerre_polynomial_test
laguerre_rule, a Fortran90 code which computes and print a Gauss-Laguerre quadrature rule for estimating the integral of a function with density exp(-x) over the interval [0,+oo).
laguerre_rule_test
lambert_w, a Fortran90 code which evaluates Lambert's W function.
lambert_w_test
lapack_test, a Fortran90 code which calls lapack(), which is a standard linear algebra package for solving linear systems, computing matrix factorizations, and solving eigenvalue problems. A precompiled copy of the lapack() library is often available on most scientific computing systems.
lapack_d, a Fortran90 code which is the double precision real version of the lapack() linear algebra code.
lapack_d_test
laplacian_matrix, a Fortran90 code which carries out computations related to the discrete Laplacian operator, including full or sparse evaluation, evaluation for unequally spaced data sampling points, application to data samples, solution of associated linear systems, eigenvalues and eigenvectors, and extension to 2D and 3D geometry.
laplacian_matrix_test
latin_center, a Fortran90 code which computes N points in an M dimensional Latin Center square;
latin_center_test
latin_cover, a Fortran90 code which produces N Latin squares which cover an NxN square, or NxN Latin cubes which cover an NxNxN cube.
latin_cover_test
latin_edge, a Fortran90 code which returns N points in an M dimensional Latin Edge square;
latin_edge_test
latin_random, a Fortran90 code which returns N points in an M dimensional Latin Random square;
latin_random_test
latinize, a Fortran90 code which adjusts N points in M dimensions to form a Latin hypercube;
latinize_test
lattice_rule, a Fortran90 code which approximates M-dimensional integrals using lattice rules.
lattice_rule_test
lau_np, a Fortran90 code which implements heuristic algorithms for various NP-hard combinatorial problems, including the integer linear programming problem, the K-center problem, the K-median problem, the 0-1 knapsack problem, the multiple knapsack problem, the graph matching problem, the graph partitioning problem, the minimal Steiner tree problem, and the traveling salesman problem;
lau_np_test
laupack, a Fortran90 code which computes properties of mathematical graphs, including Euler circuits, Hamiltonian circuits, cliques, strongly connected components, minimal spanning tree, chromatic number, shortest paths, maximal flow, and planarity.
laupack_test
lcvt, a Fortran90 code which computes a Latinized Centroidal Voronoi Tessellation (CVT).
lcvt_test
lebesgue, a Fortran90 code which is given 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, and which uses gnuplot() to make plots of the Lebesgue function.
lebesgue_test
legendre_exactness, a Fortran90 code which tests the monomial exactness of quadrature rules for estimating Legendre-type integrals of a function f(x) with density rho(x)=1 over the interval [-1,+1].
legendre_exactness_test
legendre_fast_rule, a Fortran90 code which uses a fast algorithm to compute a Gauss-Legendre quadrature rule for estimating the integral of a function with density rho(x)=1 over the interval [-1,+1].
legendre_fast_rule_test
legendre_polynomial, a Fortran90 code which evaluates the Legendre polynomial and associated functions.
legendre_polynomial_test
legendre_product_polynomial, a Fortran90 code which defines Legendre product polynomials, creating a multivariate polynomial as the product of univariate Legendre polynomials.
legendre_product_polynomial_test
legendre_rule, a Fortran90 code which computes Gauss-Legendre quadrature rules for estimating the integral of a function with density rho(x)=1 over the interval [-1,+1].
legendre_rule_test
legendre_shifted_polynomial, a Fortran90 code which evaluates the shifted Legendre polynomial, with domain [0,1].
legendre_shifted_polynomial_test
levenshtein_distance, a Fortran90 code which returns the Levenshtein distance between two strings.
levenshtein_distance_test
levenshtein_matrix, a Fortran90 code which returns the Levenshtein distance matrix defined by two strings.
levenshtein_matrix_test
line_cvt_lloyd, a Fortran90 code which applies the Lloyd iteration repeatedly to N points, to compute a Centroidal Voronoi Tessellation (CVT) over the interior of a line segment in 1D.
line_cvt_lloyd_test
line_fekete_rule, a Fortran90 code which estimates the location of N Fekete points, for polynomial interpolation or quadrature, over the interior of a line segment in 1D.
line_fekete_rule_test
line_felippa_rule, a Fortran90 code which returns a Felippa quadrature rule over the interior of a line segment in 1D.
line_felippa_rule_test
line_grid, a Fortran90 code which computes a grid of points over the interior of a line segment in 1D.
line_grid_test
line_integrals, a Fortran90 code which returns the exact value of the integral of any monomial over the length of the unit line in 1D.
line_integrals_test
line_monte_carlo, a Fortran90 code which applies a Monte Carlo method to estimate the integral of a function over the length of the unit line in 1D.
line_monte_carlo_test
line_ncc_rule, a Fortran90 code which computes a Newton Cotes Closed (NCC) quadrature rule, using equally spaced points, over the interior of a line segment in 1D.
line_ncc_rule_test
line_nco_rule, a Fortran90 code which computes a Newton Cotes Open (NCO) quadrature rule, using equally spaced points, over the interior of a line segment in 1D.
line_nco_rule_test
linear_algebra, Fortran90 codes which carry out various linear algebra operations for matrices stored in a variety of formats.
linpack_bench, a Fortran90 code which carries out the LINPACK Benchmark.
linpack_bench_test
linpack_d, a Fortran90 code which factors and solves linear systems using double precision arithmetic, by Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart. The matrix and vector data is assumed to be real.
linpack_d_test
linpack_z, a Fortran90 code which factors and solves linear systems using double precision arithmetic, by Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart. The matrix and vector data is assumed to be complex.
linpack_z_test
llsq, a Fortran90 code 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 N data points.
llsq_test
lobatto_polynomial, a Fortran90 code which evaluates Lobatto polynomials, similar to Legendre polynomials except that they are zero at both endpoints.
lobatto_polynomial_test
local_min, a Fortran90 code which finds a local minimum of a scalar function of a scalar variable, without the use of derivative information, by Richard Brent.
local_min_test
local_min_rc, a Fortran90 code 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.
local_min_rc_test
log_normal, a Fortran90 code which returns quantities related to the log normal Probability Distribution Function (PDF).
log_normal_test
log_normal_truncated_ab, a Fortran90 code which returns quantities related to the log normal Probability Distribution Function (PDF) truncated to the interval [A,B].
log_normal_truncated_ab_test
logistic_exact, a Fortran90 code which evaluates an exact solution of the logistic equation, an ordinary differential equation (ODE) which models population growth in the face of a limited carrying capacity.
logistic_exact_test
lorenz_ode, a Fortran90 code which approximates solutions to the Lorenz system of ordinary differential equations (ODE), creating output files that can be displayed by gnuplot().
lorenz_ode_test
machar, a Fortran90 code which dynamically computes the values of various machine characteristic constants by William Cody;
machar_test
machine, a Fortran90 code which returns tabulated values of the constants associated with computer arithmetic;
machine_test
mandelbrot, a Fortran90 code which generates an ASCII Portable Pixel Map (PPM) image of the Mandelbrot fractal set;
mandelbrot_test
mandelbrot_openmp, a Fortran90 code which generates an ASCII Portable Pixel Map (PPM) image of the Mandelbrot fractal set, using OpenMP for parallel execution.
mandelbrot_openmp_test
matman, a Fortran90 code which allows a user to interactively define and manipulate matrices using integer, real, or rational arithmetic, and to perform various operations in linear algebra or linear programming modes.
matman_test
matmul, a Fortran90 code which benchmarks matrix multiplication.
matmul_test
matrix_chain_brute, a Fortran90 code which finds the cost of the most efficient ordering to use when multiplying a sequence of matrices, using brute force.
matrix_chain_brute_test
matrix_chain_dynamic, a Fortran90 code which finds the cost of the most efficient ordering to use when multiplying a sequence of matrices, using dynamic programming.
matrix_chain_dynamic_test
matrix_exponential, a Fortran90 code which demonstrates some simple approaches to the problem of computing the exponential of a matrix;
matrix_exponential_test
maze, a Fortran90 code which carries out operations on a maze, including the diameter, a random example, or a path that solves the maze.
maze_test
md, a Fortran90 code which carries out a molecular dynamics simulation, intended as a starting point for implementing a parallel version.
md_test
md_openmp, a Fortran90 code which carries out a molecular dynamics simulation, using OpenMP for parallel execution.
md_openmp_test
medit_mesh_io, a Fortran90 code which reads or writes medit() MESH files defining a finite element mesh.
medit_mesh_io_test
medit_to_fem, a Fortran90 code which reads a medit() MESH file and rewrites the information as an FEM file.
medit_to_fem_test
mgmres, a Fortran90 code which applies the restarted Generalized Minimum Residual (GMRES) algorithm to solve a sparse linear system, using Compressed Row Storage (CRS) or sparse triplet (ST) format, by Lili Ju.
mgmres_test
mgs, a Fortran90 code which is an obscure legacy code, which the student is encouraged to study, understand, and document. This example is due to Diane O'Leary.
mgs_test
middle_square, a Fortran90 code which implements the middle square algorithm for generating random integers. This is a very early method, attributed to von Neumann, which actually is deeply flawed, with short cycles.
middle_square_test
midpoint, a Fortran90 code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method, with a version of fsolve() handling the associated nonlinear equation, and using a fixed time step.
midpoint_test
midpoint_adaptive, a Fortran90 code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method, with fsolve() solving the implicit equation, and an adaptive time step. Plots of the solution and timestep history are created using gnuplot().
midpoint_adaptive_test
midpoint_explicit, a Fortran90 code which solves one or more ordinary differential equations (ODE) using the (explicit) midpoint method, also called the modified Euler method.
midpoint_explicit_test
midpoint_fixed, a Fortran90 code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method, using a fixed point iteration for the nonlinear equation.
midpoint_fixed_test
minpack, a Fortran90 code which solves systems of nonlinear equations, or the least squares minimization of the residual of linear or nonlinear equations, by Jorge More, Danny Sorenson, Burton Garbow, Kenneth Hillstrom.
minpack_test
mm_io, a Fortran90 code which reads and writes sparse linear systems stored in the Matrix Market (MM) format.
mm_io_test
monomial, a Fortran90 code 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_test
monomial_value, a Fortran90 code which evaluates a monomial in M dimensions.
monomial_value_test
multitask_mpi, a Fortran90 code which demonstrates how to multitask, that is, to execute several unrelated and distinct tasks simultaneously, using the message passing interface (MPI) for parallel execution.
multitask_mpi_test
multitask_openmp, a Fortran90 code which demonstrates how to multitask, that is, to execute several unrelated and distinct tasks simultaneously, using OpenMP for parallel execution.
multitask_openmp_test
mxm_openmp, a Fortran90 code which computes a dense matrix product C=A*B, using OpenMP for parallel execution.
mxm_openmp_test
naca, a Fortran90 code which takes the parameters of certain NACA airfoils and returns the coordinates of a sequence of points that outline the wing shape. The data is displayed with the gnuplot() graphics program.
naca_test
nas, a Fortran90 code which runs the NASA kernel benchmark.
nas_test
navier_stokes_2d_exact, a Fortran90 code which evaluates an exact solution to the incompressible time-dependent Navier-Stokes equations (NSE) over an arbitrary domain in 2D.
navier_stokes_2d_exact_test
navier_stokes_3d_exact, a Fortran90 code which evaluates an exact solution to the incompressible time-dependent Navier-Stokes equations (NSE) over an arbitrary domain in 3D.
navier_stokes_3d_exact_test
nearest_interp_1d, a Fortran90 code which interpolates data using a piecewise constant interpolant defined by the nearest neighbor criterion, creating graphics files for processing by gnuplot().
nearest_interp_1d_test
neighbors_to_metis_graph, a Fortran90 code which reads a file describing the neighbor structure of a mesh of triangles or tetrahedrons, and writes a metis_graph() file suitable for input to one of the family of programs based on metis();
neighbors_to_metis_graph_test
newton_interp_1d, a Fortran90 code which finds a polynomial interpolant to data using Newton divided differences.
newton_interp_1d_test
newton_rc, a Fortran90 code which solves a system of nonlinear equations by Newton's method, using reverse communication (RC).
newton_rc_test
niederreiter2, a Fortran90 code which computes elements of a Niederreiter Quasi Monte Carlo (QMC) sequence using base 2.
niederreiter2_test
nint_exactness_mixed, a Fortran90 code which measures the exactness of an M-dimensional quadrature rule based on a mixture of 1D quadrature rule factors.
nint_exactness_mixed_test
nintlib, a Fortran90 code which implements approximate integration or quadrature in M dimensions;
nintlib_test
nms, a Fortran90 code which includes a wide variety of numerical software, including solvers for linear systems of equations, interpolation of data, numerical quadrature, linear least squares (LLS) data fitting, the solution of nonlinear equations, ordinary differential equations (ODE), optimization and nonlinear least squares (NLS), simulation and random numbers, trigonometric approximation and Fast Fourier Transforms (FFT).
nms_test
normal, a Fortran90 code which implements a random number generator (RNG) for normally distributed values;
normal_test
normal_dataset, a Fortran90 code which creates a multivariate normal random dataset and writes it to a file.
normal_dataset_test
obj_io, a Fortran90 code which reads and writes the 3D graphics information in an Alias OBJ file;
obj_io_test
ode, a Fortran90 code which solves a system of ordinary differential equations (ODE), by Shampine and Gordon;
ode_test
openmp_test, a Fortran90 code which uses OpenMP, which is an application program interface for carrying out parallel computations in a shared memory environment.
optimize_test, a Fortran90 code which looks at the use of automatic optimization by the compiler to make the executable code run faster.
ornstein_uhlenbeck, a Fortran90 code which approximates solutions of the Ornstein-Uhlenbeck stochastic ordinary differential equation (SDE) using the Euler method and the Euler-Maruyama method, and creating graphics files for processing by gnuplot().
ornstein_uhlenbeck_test
owen, a Fortran90 code which evaluates the Owen T function.
owen_test
padua, a Fortran90 code 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.
padua_test
partition_brute, a Fortran90 code which uses a brute force algorithm to seek solutions of the partition problem, splitting a set of integers into two subsets with equal sum.
partition_brute_test
patterson_rule, a Fortran90 code 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.
patterson_rule_test
pbma_io , a Fortran90 code which reads or writes graphics files that use the ASCII Portable Bit Map (PBM) format.

pbma_io_test

pce_burgers, a Fortran90 code 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_burgers_test
pce_ode_hermite, a Fortran90 code 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.
pce_ode_hermite_test
pdb_to_xyz, a Fortran90 code which reads a Protein Data Bank (PDB) file, and, for each ATOM record in the file, extracts the atomic spatial coordinates and writes them to an XYZ file.
pdb_to_xyz_test
pdflib, a Fortran90 code which evaluates Probability Density Functions (PDF) and produces random samples from them, including beta, binomial, chi, exponential, gamma, inverse chi, inverse gamma, multinomial, normal, scaled inverse chi, and uniform.
pdflib_test
pentominoes, a Fortran90 code which forms or plots any of the 12 members of the pentomino family, shapes formed from 5 adjacent squares.
pentominoes_test
persistence, a Fortran90 code which demonstrates how to initialize, get, or set data stored within a function, using static/persistent/saved/local memory.
persistence_test
pgma_io , a Fortran90 code which reads or writes graphics files that use the ASCII Portable Gray Map (PGM) format.

pgma_io_test

pink_noise, a Fortran90 code which computes a pink noise signal obeying a 1/f power law.
pink_noise_test
plot_points, a Fortran90 code which makes an Encapsulated PostScript (EPS) plot of points in 2D.
plot_points_test
plot_to_ps, a Fortran90 code which reads simple text commands and creates a PostScript (PS) image;
plot_to_ps_test
poisson_1d, a Fortran code which solves a discretized version of the Poisson equation -uxx = f(x) on the interval a ≤ x ≤ b, with Dirichlet boundary conditions u(a) = ua, u(b) = ub. The linear system is solved using Gauss-Seidel iteration.
poisson_1d_test
poisson_1d_multigrid, a Fortran90 code which applies the multigrid method to a discretized version of the 1D Poisson equation.
poisson_1d_multigrid_test
poisson_2d, a Fortran90 code which solves the Poisson equation in a rectangle, using finite differences and Jacobi iteration.
poisson_2d_test
poisson_openmp, a Fortran90 code 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_openmp_test
poisson_simulation, a Fortran90 code which simulates a Poisson process in which events randomly occur with an average waiting time of Lambda, creating output for graphics by gnuplot().
poisson_simulation_test
polpak, a Fortran90 code which evaluates a variety of mathematical functions, polynomials, and sequences, including Bell, Benford, Bernoulli, Bernstein, Cardan, Catalan, Charlier, Chebyshev, Collatz, Delannoy, Euler, Fibonacci, Gegenbauer, Gudermannian, Harmonic, Hermite, Hofstadter, Hypergeometric 2F1, Jacobi, Krawtchouk, Laguerre, Lambert, Legendre, Lerch, Meixner, Mertens, Moebius, Motzkin, Phi, Stirling Number, Tau, Tribonacci, Zernike.
polpak_test
polygon, a Fortran90 code 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, counter clockwise ordering, diameter, distance to a point, inradius, lattice area, nearest point in set, outradius, uniform sampling, and triangulation.
polygon_test
polygon_grid, a Fortran90 code which generates a grid of points over the interior of a polygon in 2D.
polygon_grid_test
polygon_integrals, a Fortran90 code which returns the exact value of the integral of any monomial over the interior of a polygon in 2D.
polygon_integrals_test
polygon_monte_carlo, a Fortran90 code which applies a Monte Carlo method to estimate the integral of a function over the interior of a polygon in 2D.
polygon_monte_carlo_test
polygon_triangulate, a Fortran90 code which triangulates a possibly nonconvex polygon in 2D, and which uses gnuplot() to display the external edges and internal diagonals of the triangulation.
polygon_triangulate_test
polynomial, a Fortran90 code which adds, multiplies, differentiates, evaluates and prints multivariate polynomials in a space of M dimensions.
polynomial_test
polynomial_conversion, a Fortran90 code which converts representations of a polynomial between monomial, Bernstein, Chebyshev, Gegenbauer, Hermite, Laguerre and Legendre forms.
polynomial_conversion_test
polynomial_root_bound, a Fortran90 code which computes the Cauchy bound on the magnitude of all roots of a polynomial with complex coefficients.
polynomial_root_bound_test
polynomials, a Fortran90 code which defines multivariate polynomials over rectangular domains, for which certain information is to be determined, such as the maximum and minimum values.
polynomials_test
polyominoes, a Fortran90 code which manipulates polyominoes and tilings.
polyominoes_test
porous_medium_exact, a Fortran90 code which returns an exact solution of the porous medium equation (PME), dudt=Del^2(u^m), a partial differential equation (PDE) related to the diffusion equation, based on the Barenblatt solution.
porous_medium_exact_test
power_method, a Fortran90 code which carries out the power method for finding a dominant eigenvalue and its eigenvector.
power_method_test
power_rule, a Fortran90 code which constructs a power rule, that is, a product quadrature rule from identical 1D factor rules.
power_rule_test
ppma_io , a Fortran90 code which reads or writes graphics files that use the ASCII Portable Pixel Map (PPM) format.

ppma_io_test

pppack, a Fortran90 code which computes piecewise polynomial functions, including cubic splines, by Carl deBoor.
pppack_test
praxis, a Fortran90 code which minimizes a scalar function of several variables, without requiring derivative information, by Richard Brent.
praxis_test
predator_prey_ode, a Fortran90 code which solves a time-dependent predator-prey system of ordinary differential equations (ODE).
predator_prey_ode_test
prime, a Fortran90 code which counts the number of primes between 1 and N, and is intended as a starting point for a parallel version.
prime_test
prime_mpi, a Fortran90 code which counts primes between 1 and N, using Message Passing Interface (MPI) for parallel execution.
prime_mpi_test
prime_openmp, a Fortran90 code which counts primes between 1 and N, using OpenMP for parallel execution.
prime_openmp_test
prime_pi, a Fortran90 code which evaluates Pi(n), the number of primes less than or equal to an integer n.
prime_pi_test
prism_jaskowiec_rule, a Fortran90 code which returns symmetric quadrature rules, with exactness up to total degree 20, over the interior of a prism with triangular base, by Jan Jaskowiec, Natarajan Sukumar.
prism_jaskowiec_rule_test
prism_witherden_rule, a Fortran90 code which returns a symmetric Witherden quadrature rule for a prism with triangular base, with exactness up to total degree 10.
prism_witherden_rule_test
prob, a Fortran90 code which evaluates, samples, inverts, and characterizes Probability Density Functions (PDF) and Cumulative Density Functions (CDF), 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.
prob_test
product_rule, a Fortran90 code which constructs a product quadrature rule from distinct 1D factor rules.
product_rule_test
ps_gg_align, a Fortran90 code which implements global string alignment algorithms which work in linear space, and compute both the optimal score and the optimal alignment. Gaps in the alignment are assigned an affine gap penalty. The algorithms are due to Chao.
ps_gg_align_test
ps_lg_align, a Fortran90 code which implements local string alignment algorithms which work in linear space, and compute both the optimal score and the optimal alignment. Gaps in the alignment are assigned an affine gap penalty. The algorithms are due to Chao.
ps_qg_align, a Fortran90 code which implements quasi-global string alignment algorithms which work in linear space, and compute both the optimal score and the optimal alignment. Gaps in the alignment are assigned an affine gap penalty. The algorithms are due to Chao.
ps_write, a Fortran90 code which creates PostScript (PS) graphics files.
ps_write_test
puzzles, a Fortran90 code which was used to solve various puzzles.
pwl_approx_1d, a Fortran90 code which approximates data using a piecewise linear function.
pwl_approx_1d_test
pwl_interp_1d, a Fortran90 code which interpolates data using a piecewise linear function.
pwl_interp_1d_test
pwl_interp_2d, a Fortran90 code which evaluates a piecewise linear interpolant to data defined on a regular 2D grid.
pwl_interp_2d_test
pwl_interp_2d_scattered, a Fortran90 code which evaluates a piecewise linear interpolant to data which is available at an irregularly arranged set of points.
pwl_interp_2d_scattered_test
pwl_product_integral, a Fortran90 code which calculates the exact value of the integral of the product of two piecewise linear functions f(x) and g(x).
pwl_product_integral_test
pyramid_exactness, a Fortran90 code which computes the monomial exactness of a quadrature rule over the interior of a pyramid in 3D.
pyramid_exactness_test
pyramid_felippa_rule, a Fortran90 code which returns a Felippa quadrature rule for approximating integrals over the interior of a pyramid in 3D.
pyramid_felippa_rule_test
pyramid_grid, a Fortran90 code which computes a grid of points over the interior of the unit pyramid in 3D;
pyramid_grid_test
pyramid_integrals, a Fortran90 code which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3D.
pyramid_integrals_test
pyramid_jaskowiec_rule, a Fortran90 code which returns quadrature rules, with exactness up to total degree 20, over the interior of a pyramid in 3D, by Jan Jaskowiec, Natarajan Sukumar.
pyramid_jaskowiec_rule_test
pyramid_monte_carlo, a Fortran90 code which applies a Monte Carlo method to estimate integrals of a function over the interior of the unit pyramid in 3D;
pyramid_monte_carlo_test
pyramid_rule, a Fortran90 code which computes a conical product quadrature rule over the interior of the unit pyramid in 3D;
pyramid_rule_test
pyramid_witherden_rule, a Fortran90 code which returns a Witherden quadrature rule, with exactness up to total degree 10, over the interior of a pyramid.
pyramid_witherden_rule_test
qr_solve, a Fortran90 code which computes the linear least squares (LLS) solution of a system A*x=b.
qr_solve_test
quad_mpi, a Fortran90 code which approximates an integral using a quadrature rule, and carries out the computation in parallel using the Message Passing Interface (MPI).
quad_mpi_test
quad_openmp, a Fortran90 code which applies a quadrature rule to estimate an integral over a 1D interval, using OpenMP for parallel execution.
quad_openmp_test
quad_rule, a Fortran90 code which implements rules for approximate integration (quadrature) in one dimension;
quad_rule_test
quad_serial, a Fortran90 code which approximates an integral using a quadrature rule, and is intended as a starting point for parallelization exercises.
quad_serial_test
quad2d, a Fortran90 code which estimates an integral over a 2D rectangle using quadrature, intended as the starting point for program optimization or parallelization.
quad2d_test
quadmom, a Fortran90 code which computes a Gaussian quadrature rule for a weight function rho(x) based on the Golub-Welsch procedure that only requires knowledge of the moments of rho(x).
quadmom_test
quadpack, a Fortran90 code which estimates integrals using numerical quadrature, by Piessens, deDoncker-Kapenga, Ueberhuber, and Kahaner.
quadpack_test
quadrature_golub_welsch, a Fortran90 code which computes the points and weights of a Gaussian quadrature rule using the Golub-Welsch procedure, assuming that the points have been specified.
quadrature_golub_welsch_test
quadrature_least_squares, a Fortran90 code 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_least_squares_test
quadrature_weights_vandermonde, a Fortran90 code which computes the weights of a quadrature rule using the Vandermonde matrix, assuming that the points have been specified.
quadrature_weights_vandermonde_test
quadrature_weights_vandermonde_2d, a Fortran90 code which computes the weights of a 2D quadrature rule using the Vandermonde matrix, assuming that the points have been specified.
quadrature_weights_vandermonde_2d_test
quadrilateral_mesh, a Fortran90 code which handles meshes of quadrilaterals over a 2D region;
quadrilateral_mesh_test
quadrilateral_mesh_rcm, a Fortran90 code which computes the Reverse Cuthill McKee (RCM) reordering for nodes in a mesh of 4-node quadrilaterals.
quadrilateral_mesh_rcm_test
quadrilateral_witherden_rule, a Fortran90 code which returns a symmetric Witherden quadrature rule for the quadrilateral, with exactness up to total degree 21.
quadrilateral_witherden_rule_test
quality, a Fortran90 code which computes quality of distribution measures for pointsets in M dimensions;
quality_test
quaternions, a Fortran90 code which carries out some simple arithmetic operations for quaternions.
quaternions_test
quotes, a Fortran90 code which prints a random quote from a file;
quotes_test
r83, a Fortran90 code which contains linear algebra routines for r83 matrices (real, 64 bit, tridiagonal 3xN format).
r83_test
r83_np, a Fortran90 code which contains linear algebra routines for r83_np matrices (real, 64 bit, tridiagonal 3xN format, nonpivoting factorization).
r83_np_test
r83p, a Fortran90 code which contains linear algebra routines for r83p matrices (real, 64 bit, tridiagonal periodic format).
r83p_test
r83s, a Fortran90 code which contains linear algebra routines for r83s matrices (real, 64 bit, tridiagonal scalar format).
r83s_test
r83t, a Fortran90 code which contains linear algebra routines for r83t matrices (real, 64 bit, tridiagonal Mx3 format).
r83t_test
r83v, a Fortran90 code which contains linear algebra routines for r83v matrices (real, 64 bit, tridiagonal three vector format).
r83v_test
r85, a Fortran90 code which contains linear algebra routines for r85 matrices (real, 64 bit, pentadiagonal format).
r85_test
r8bb, a Fortran90 code which contains linear algebra routines for r8bb matrices (real, 64 bit, border banded format).
r8bb_test
r8blt, a Fortran90 code which contains linear algebra routines for r8blt matrices (real, 64 bit, band lower triangular format).
r8blt_test
r8bto, a Fortran90 code which contains linear algebra routines for r8bto matrices (real, 64 bit, block Toeplitz format).
r8bto_test
r8but, a Fortran90 code which contains linear algebra routines for r8but matrices (real, 64 bit, band upper triangular format).
r8but_test
r8cb, a Fortran90 code which contains linear algebra routines for r8cb matrices (real, 64 bit, Compressed Band format).
r8cb_test
r8cbb, a Fortran90 code which contains linear algebra routines for r8cbb matrices (real, 64 bit, Compressed Border Banded format).
r8cbb_test
r8ccs, a Fortran90 code which contains linear algebra routines for r8ccs matrices (real, 64 bit, Compressed Column Storage (Colptr,Row,Value) format).
r8ccs_test
r8ci, a Fortran90 code which contains linear algebra routines for r8ci matrices (real, 64 bit, circulant format).
r8ci_test
r8col, a Fortran90 code which contains utility routines for an R8COL, that is, a double precision real MxN array, 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.
r8col_test
r8gb, a Fortran90 code which contains linear algebra routines for r8gb matrices (real, 64 bit, General Banded format).
r8gb_test
r8gd, a Fortran90 code which contains linear algebra routines for r8gd matrices (real, 64 bit, general diagonal format).
r8gd_test
r8ge, a Fortran90 code which contains linear algebra routines for R8GE matrices (real, 64 bit, General format).
r8ge_test
r8lib, a Fortran90 code which contains many utility routines, using double precision real (R8) arithmetic.
r8lib_test
r8lt, a Fortran90 code which contains linear algebra routines for R8LT matrices (real, 64 bit, Lower Triangular).
r8lt_test
r8ltt, a Fortran90 code which contains linear algebra routines for r8ltt matrices (real, 64 bit, lower triangular Toeplitz format).
r8ltt_test
r8ncf, a Fortran90 code which contains linear algebra routines for r8ncf matrices (real, 64 bit, nonsymmetric coordinate format).
r8ncf_test
r8pbl, a Fortran90 code which contains linear algebra routines for r8pbl matrices (real, 64 bit, symmetric positive definite (SPD) band lower format).
r8pbl_test
r8pbu, a Fortran90 code which contains linear algebra routines for r8pbu matrices (real, 64 bit, symmetric positive definite (SPD) band upper format).
r8pbu_test
r8po, a Fortran90 code which contains linear algebra routines for r8po matrices (real, 64 bit, symmetric positive definite (SPD) format).
r8po_test
r8poly, a Fortran90 code which operates on real polynomials, including evaluation, differentiation, integration, multiplication, synthetic division, shifting the base, computing a power, taking the norm. It also defines Chebyshev, Lagrange and Legendre polynomials.
r8poly_test
r8pp, a Fortran90 code which contains linear algebra routines for r8pp matrices (real, 64 bit, symmetric positive definite (SPD) packed format).
r8pp_test
r8ri, a Fortran90 code which contains linear algebra routines for r8ri matrices (real, 64 bit, row indexed format).
r8ri_test
r8row, a Fortran90 code which contains utilities for an R8ROW, that is, a double precision real MxN array, 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.
r8row_test
r8sd, a Fortran90 code which contains linear algebra routines for r8sd matrices (real, 64 bit, symmetric diagonal format).
r8sd_test
r8sm, a Fortran90 code which contains linear algebra routines for r8sm matrices (real, 64 bit, Sherman-Morrison A-u*v' format).
r8sm_test
r8sr, a Fortran90 code which carries out linear algebra operations for r8sr matrices (real, 64 bit, diagonal + compressed row offdiagonal format).
r8sr_test
r8ss, a Fortran90 code which carries out linear algebra operations for r8ss matrices (real, 64 bit, symmetric skyline format).
r8ss_test
r8st, a Fortran90 code which contains linear algebra routines for R8ST matrices (real, 64 bit, Sparse Triplet).
r8st_test
r8sto, a Fortran90 code which contains linear algebra routines for r8sto matrices (real, 64 bit, symmetric Toeplitz N format).
r8sto_test
r8to, a C code which contains linear algebra routines for r8to matrices (real, 64 bit, Toeplitz 2*N-1 format).
r8to_test
r8ut, a Fortran90 code which contains linear algebra routines for r8ut matrices (real, 64 bit, Upper Triangular).
r8ut_test
r8utp, a Fortran90 code which carries out linear algebra operations on r8utp matrices, real 64 bit, Upper Triangular Packed format.
r8utp_test
r8utt, a Fortran90 code which contains linear algebra routines for r8utt matrices (real, 64 bit, upper triangular Toeplitz format).
r8utt_test
r8vm, a Fortran90 code which contains linear algebra routines for r8vm matrices (real, 64 bit, Vandermonde format).
r8vm_test
randlc, a Fortran90 code which implements a random number generator (RNG) used by the nas() benchmarks.
randlc_test
random_data, a Fortran90 code which uses a random number generator (RNG) to sample points distributed according to various probability density functions (PDF), spatial dimensions, and geometries, including the M-dimensional cube, ellipsoid, simplex and sphere.
random_data_test
random_mpi, a Fortran90 code which generates the same sequence of values from a random number generator (RNG) for both sequential execution and parallel execution under the Message Passing Interface (MPI).
random_mpi_test
random_openmp, a Fortran90 code which generates multiple distinct streams of random numbers using OpenMP for parallel execution.
random_openmp_test
random_sorted, a Fortran90 code which uses a random number generator (RNG) to create a vector of random values which are already sorted.
random_sorted_test
ranlib, a Fortran90 code which is a library of random number generators which produces random samples from Probability Density Functions (PDF), 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.
ranlib_test
ranmap, a Fortran90 code which creates PostScript (PS) images of iterated affine mappings, including the Barnsley fractal fern and the Levy dragon.
ranmap_test
rbf_interp_1d, a Fortran90 code which defines and evaluates radial basis function (RBF) interpolants to 1D data.
rbf_interp_1d_test
rbf_interp_2d, a Fortran90 code which defines and evaluates radial basis function (RBF) interpolants to 2D data.
rbf_interp_2d_test
rbf_interp_nd, a Fortran90 code which defines and evaluates radial basis function (RBF) interpolants to multidimensional data.
rbf_interp_nd_test
rcm, a Fortran90 code which applies the Reverse Cuthill McKee (RCM) algorithm for reordering the nodes of a graph, and reducing the bandwidth of a corresponding sparse matrix;
rcm_test
reactor_simulation, a Fortran90 code 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 was provided as an example with the book 'Numerical Methods and Software'.
reactor_simulation_test
reformat, a Fortran90 code which makes a copy of a file with a given number of words per line.
reformat_test
region, a Fortran90 code which reads 3D magnetic resonance imaging (MRI) voxel data, and groups the voxels into connected regions, called components or segments;
region_test
ring_mpi, a Fortran90 code which uses the Message Passing Interface (MPI), and measures the time necessary to copy data around a ring of processes.
ring_mpi_test
rk1, a Fortran90 code which solves one or more ordinary differential equations (ODE) using an explicit Runge-Kutta method of order 1, usually known as Euler's explicit method.
rk1_test
rk1_implicit, a Fortran90 code which solves one or more ordinary differential equations (ODE) using the Runge-Kutta order 1 implicit method, using fsolve() to solve the implicit equation, and using a fixed time step. rk1_implicit() is commonly called the backward Euler method.
rk1_implicit_test
rk2, a Fortran90 code which solves one or more ordinary differential equations (ODE) using an explicit Runge-Kutta method of order 2, also known as Heun's method, the modified Euler method, or the explicit midpoint method.
rk2_test
rk2_implicit, a Fortran90 code which solves one or more ordinary differential equations (ODE) using the Runge-Kutta order 2 implicit method, using fsolve() to solve the implicit equation, and using a fixed time step. rk2_implicit() is also known as the implicit midpoint method.
rk2_implicit_test
rk4, a Fortran90 code which applies the fourth order Runge-Kutta (RK) algorithm to estimate the solution of an ordinary differential equation (ODE).
rk4_test
rkf45, a Fortran90 code which applies a Runge-Kutta-Fehlberg (RKF) solver to a system of ordinary differential equations (ODE);
rkf45_test
rnglib, a Fortran90 code which implements a random number generator (RNG) with splitting facilities, allowing multiple independent streams to be computed, by L'Ecuyer and Cote.
rnglib_test
root_rc, a Fortran90 code which seeks a solution of a scalar nonlinear equation f(x) = 0, or a system of nonlinear equations, using reverse communication (RC), by Gaston Gonnet.
root_rc_test
roots_rc, a Fortran90 code which seeks a solution of a system of nonlinear equations f(x) = 0, using reverse communication (RC), by Gaston Gonnet.
roots_rc_test
row_echelon_integer, a Fortran90 code which carries out the exact computation of the integer row echelon form (IREF) and integer reduced row echelon form (IRREF) of an integer matrix.
row_echelon_integer_test
sandia_cubature, a Fortran90 code which computes M-dimensional quadrature rules for certain regions and weight functions.
sandia_cubature_test
sandia_cvt, a Fortran90 code which positions a given number of points in an arbitrary region, using probabilistic Centroidal Voronoi Tessellation (CVT) techniques to achieve good coverage and separation; developed for Sandia National Laboratory;
sandia_cvt_test
sandia_rules, a Fortran90 code which produces 1D quadrature rules of Chebyshev, Clenshaw Curtis, Fejer 2, Gegenbauer, generalized Hermite, generalized Laguerre, Hermite, Jacobi, Laguerre, legendre and Patterson types.
sandia_rules_test
sandia_sgmgg, a Fortran90 code which explores a generalized construction method for sparse grids.
sandia_sgmgg_test
sandia_sparse, a Fortran90 code which produces a 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.
sandia_sparse_test
satisfy_brute, a Fortran90 code which uses brute force to find all assignments of values to a set of logical variables which make a complicated logical statement true.
satisfy_brute_test
satisfy_mpi, a Fortran90 code which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfiability problem, using the Message Passing Interface (MPI) to work in parallel.
satisfy_mpi_test
satisfy_openmp, a Fortran90 code which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfiability problem, using OpenMP for parallel execution.
satisfy_openmp_test
schedule_openmp, a Fortran90 code which demonstrates the default, static, and dynamic methods of scheduling loop iterations in OpenMP to avoid work imbalance.
schedule_openmp_test
sde, a Fortran90 code which illustrates properties of stochastic ordinary differential equations (SODE), 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;
sde_test
search_mpi, a Fortran90 code which searches integers between A and B for a value J such that F(J) = C, using MPI for parallel execution.
search_mpi_test
set_theory, a Fortran90 code which demonstrates various set theoretic operations using several models of a set.
set_theory_test
sftpack, a Fortran90 code which implements the slow Fourier transform, intended as a teaching tool and comparison with the Fast Fourier Transform (FFT).
sftpack_test
sgmga, a Fortran90 code which creates sparse grids based on a mixture of 1D quadrature rules, allowing anisotropic weights for each dimension.
sgmga_test
shallow_water_1d, a Fortran90 code which simulates the evolution of a 1D fluid governed by the time-dependent shallow water equations.
shallow_water_1d_test
shepard_interp_1d, a Fortran90 code which defines and evaluates Shepard interpolants to 1D data, based on inverse distance weighting.
shepard_interp_1d_test
shepard_interp_2d, a Fortran90 code which defines and evaluates Shepard interpolants to 2D data, based on inverse distance weighting.
shepard_interp_2d_test
shepard_interp_nd, a Fortran90 code which defines and evaluates Shepard interpolants to multidimensional data, based on inverse distance weighting.
shepard_interp_nd_test
sigmoid_derivative, a Fortran90 code which evaluates derivatives of any order for the sigmoid function s(x)=1/(1+exp(-x)). The test code creates graphics images using gnuplot().
sigmoid_derivative_test
simplex_coordinates, a Fortran90 code which computes the Cartesian coordinates of the vertices of a regular simplex in M dimensions.
simplex_coordinates_test
simplex_gm_rule, a Fortran90 code which defines Grundmann-Moeller quadrature rules over the interior of a triangle in 2D, a tetrahedron in 3D, or a simplex in M dimensions.
simplex_gm_rule_test
simplex_grid, a Fortran90 code which generates a regular grid of points over the interior of an arbitrary simplex in M dimensions.
simplex_grid_test
simplex_integrals, a Fortran90 code which returns the exact value of the integral of any monomial over the interior of the unit simplex in M dimensions.
simplex_integrals_test
simplex_monte_carlo, a Fortran90 code which uses the Monte Carlo method to estimate an integral over the interior of the unit simplex in M dimensions.
simplex_monte_carlo_test
sine_gordon_exact, a Fortran90 code which returns an exact solution of the Sine-Gordon equation, a partial differential equation (PDE) of the form uxy=sin(u).
sine_gordon_exact_test
sine_transform, a Fortran90 code which demonstrates some simple properties of the discrete sine transform (DST).
sine_transform_test
slap, a Fortran90 code which forms the Sparse Linear Algebra Package (SLAP), for the iterative solution of sparse linear systems, by Anne Greenbaum and Mark Seager.
slap_test
slap_io, a Fortran90 code which reads and writes sparse matrix files in the SLAP format;
slap_io_test
slatec, a FORTRAN90 code which collects standard numerical libraries, including blas(), bvsup(), dassl(), depac(), drive(), eispack(), fftpack(), fishpack(), fnlib(), linpack(), machine(), minpack(), mp(), pchip(), pppack(), quadpack(), slap(), sos(), splp(), and xerror().
slatec_test
snakes_and_ladders, a Fortran90 code which provides tools for the study of the game of Snakes and Ladders.
snakes_and_ladders_test
sncndn, a Fortran90 code which evaluates the Jacobi elliptic functions sn(u,m), cn(u,m), and dn(u,m).
sncndn_test
sobol, a Fortran90 code which computes elements of a Sobol Quasi Monte Carlo (QMC) sequence, by Bennett Fox.
sobol_test
solve, a Fortran90 code which demonstrates how Gauss elimination can be used to solve a linear system A*x=b.
solve_test
sort_rc, a Fortran90 code which sorts a list of any kind of objects, using reverse communication (RC).
sort_rc_test
spaeth, a Fortran90 code which analyzes data by grouping it into clusters.
spaeth_test
spaeth2, a Fortran90 code which analyzes data by grouping it into clusters.
spaeth2_test
sparse_count, a Fortran90 code which analyzes sparse grids in which a single family of 1D quadrature rules is used for all spatial dimensions, with a variety of growth rules.
sparse_count_test
sparse_display, a Fortran90 code which reads information defining a matrix of numbers and display the sparsity pattern or location of the nonzero elements using gnuplot(). This operation is similar to the MATLAB spy() command.
sparse_display_test
sparse_grid_cc, a Fortran90 code which creates sparse grids based on Clenshaw-Curtis rules.
sparse_grid_cc_test
sparse_grid_gl, a Fortran90 code which creates sparse grids based on Gauss-legendre rules.
sparse_grid_gl_test
sparse_grid_hermite, a Fortran90 code which creates sparse grids based on Gauss-Hermite rules.
sparse_grid_hermite_test
sparse_grid_hw, a Fortran90 code 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_hw_test
sparse_grid_laguerre, a Fortran90 code which creates sparse grids based on Gauss-Laguerre rules.
sparse_grid_laguerre_test
sparse_grid_mixed, a Fortran90 code which creates a sparse grid dataset based on a mixed set of 1D factor rules.
sparse_grid_mixed_test
sparse_interp_nd, a Fortran90 code which defines a sparse interpolant to a function f(x) of a multidimensional argument.
sparse_interp_nd_test
sparsekit, a Fortran90 code which implements operations on sparse matrices, including conversion between various formats, by Yousef Saad.
sparsekit_test
specfun, a Fortran90 code which computes special functions, including Bessel I, J, K and Y functions, and the Dawson, E1, EI, Erf, Gamma, log Gamma, Psi/Digamma functions, by William Cody and Laura Stoltz;
specfun_test
special_functions, a Fortran90 code which evaluates special functions, including Airy, Associated Legendre, Bernoulli Numbers, Bessel, Beta, Complete Elliptic Integral, Cosine Integral, Elliptic Integral, Error, Euler Numbers, Exponential Integral, Fresnel Integral, Gamma, Hankel, Hermite polynomials, Hypergeometric 2F1, Incomplete Beta, Incomplete Gamma, Jacobian Elliptic, Kelvin, Kummer Confluent Hypergeometric, Laguerre polynomials, Lambda, Legendre functions, Legendre polynomials, Mathieu, Modified Spherical Bessel, Parabolic Cylinder, Psi, Riccati-Bessel, Sine Integral, Spheroidal Angular, Spheroidal Wave, Struve, Tricomi Confluent Hypergeometric, Whittaker, by Shanjie Zhang, Jianming Jin;
special_functions_test
sphere_cubed_grid, a Fortran90 code which uses the projection of a cube to create grids of points, lines, and quadrilaterals on the surface of the unit sphere in 3D.
sphere_cubed_grid_test
sphere_cvt, a Fortran90 code which uses a Centroidal Voronoi Tessellation (CVT) to generate a mesh of well-separated points on the surface of the unit sphere in 3D.
sphere_cvt_test
sphere_delaunay, a Fortran90 code which reads a file containing the coordinates of points on the surface of the unit sphere in 3D, computes the Delaunay triangulation, and outputs a PostScript (PS) file of the image;
sphere_delaunay_test
sphere_design_rule, a Fortran90 code which returns point sets on the surface of the unit sphere in 3D, known as designs, which estimate integrals.
sphere_design_rule_test
sphere_exactness, a Fortran90 code which tests the monomial exactness of a quadrature rule over the surface of the unit sphere in 3D.
sphere_exactness_test
sphere_fibonacci_grid, a Fortran90 code which uses a Fibonacci spiral to create a grid of points on the surface of the unit sphere in 3D.
sphere_fibonacci_grid_test
sphere_grid, a Fortran90 code which generates grids of points, or of points and lines, or of points and lines and faces, on the surface of the unit sphere in 3D.
sphere_grid_test
sphere_integrals, a Fortran90 code which returns the exact value of the integral of any monomial over the surface of the unit sphere in 3D.
sphere_integrals_test
sphere_lebedev_rule, a Fortran90 code which computes Lebedev quadrature rules on the surface of the unit sphere in 3D.
sphere_lebedev_rule_test
sphere_llq_grid, a Fortran90 code which uses longitudes and latitudes to create grids of points, lines, and quadrilaterals on the surface of the unit sphere in 3D.
sphere_llq_grid_test
sphere_llt_grid, a Fortran90 code which uses longitudes and latitudes to create grids of points, lines, and triangles on the surface of the unit sphere in 3D.
sphere_llt_grid_test
sphere_monte_carlo, a Fortran90 code which applies a Monte Carlo method to estimate the integral of a function on the surface of the unit sphere in 3D;
sphere_monte_carlo_test
sphere_quad, a Fortran90 code which uses triangulation to approximate an integral on the surface of the unit sphere in 3D;
sphere_quad_test
sphere_stereograph, a Fortran90 code which computes the stereographic mapping between points on the surface of the unit sphere in 3D and points on the plane Z = 1; a generalized mapping is also available.
sphere_stereograph_test
sphere_triangle_monte_carlo, a Fortran90 code which applies a Monte Carlo method to estimate the integral of a function over a spherical triangle on the surface of the unit sphere in 3D;
sphere_triangle_monte_carlo_test
sphere_triangle_quad, a Fortran90 code which uses quadrature to estimate the integral of a function over a spherical triangle on the surface of the unit sphere in 3D.
sphere_triangle_quad_test
sphere_voronoi, a Fortran90 code which reads a file containing the coordinates of points on the surface of the unit sphere in 3D, computes the Voronoi diagram, and outputs a PostScript (PS) file of the image;
sphere_voronoi_test
spiral_exact, a Fortran90 code which computes a 2D velocity vector field that is an exact solution of the continuity equation.
spiral_exact_test
spline, a Fortran90 code which interpolates and approximates via splines;
spline_test
square_arbq_rule, a Fortran90 code 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_arbq_rule_test
square_exactness, a Fortran90 code which computes the polynomial exactness of quadrature rules for f(x,y) over the interior of a quadrilateral in 2D.
square_exactness_test
square_felippa_rule, a Fortran90 code which returns a Felippa quadrature rule over the interior of a square in 2D.
square_felippa_rule_test
square_grid, a Fortran90 code which computes a grid of points over the interior of a square in 2D.
square_grid_test
square_hex_grid, a Fortran90 code which computes a hexagonal grid of points over the interior of a square in 2D.
square_hex_grid_test
square_integrals, a Fortran90 code which returns the exact value of the integral of any monomial over the interior of the unit square or symmetric unit square in 2D.
square_integrals_test
square_minimal_rule, a Fortran90 code 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_minimal_rule_test
square_monte_carlo, a Fortran90 code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit square in 2D.
square_monte_carlo_test
square_symq_rule, a Fortran90 code 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.
square_symq_rule_test
ss_gd_align, a Fortran90 code which implements some of the linear space alignment algorithms described in the reference by Chao.
ss_gd_align_test
ss_gg_align, a Fortran90 code which implements the sequence/sequence global gap alignment, one of the string matching algorithms described in the reference by Chao.
ss_gg_align_test
ss_lg_align, a Fortran90 code which implements the sequence/sequence local alignment, one of the string matching algorithms described by Chao.
ss_lg_align_test
ss_qg_align, a Fortran90 code which implements the sequence/sequence global gap alignment, one of the string matching algorithms described by Chao.
ss_qg_align_test
st_io, a Fortran90 code which reads and writes sparse linear systems stored in the Sparse Triplet (ST) format.
st_io_test
st_to_ccs, a Fortran90 code which converts sparse matrix data from Sparse Triplet (ST) format to Compressed Column Storage (CCS) format;
st_to_ccs_test
st_to_hb, a Fortran90 code which converts a sparse matrix file from Sparse Triplet (ST) format to Harwell Boeing (HB) format;
st_to_hb_test
starpac, a Fortran90 code which performs statistical data analysis. It includes functions for nonlinear least squares regression, time series analysis in both time and frequency domains), line printer graphics, basic statistical analysis, and linear least squares regression, by Janet Donaldson.
starpac_test
steam, a Fortran90 code which computes steam table properties including pressure and density, based on a National Bureau of Standards (NBS) package;
steam_test
steam_interact, a Fortran90 code which allows the user to interactively query the steam table functions from the National Bureau of Standards (NBS).
steam_interact_test
stiff_ode, a Fortran90 code which considers an ordinary differential equation (ODE) which is an example of a stiff ODE.
stiff_ode_test
stla_io, a Fortran90 code which reads and writes the 3D graphics information in an ASCII stereolithography (STL) file;
stla_io_test
stochastic_diffusion, a Fortran90 code which implements several versions of a stochastic diffusivity coefficient, using gnuplot() to create graphic images of sample realizations of the diffusivity field.
stochastic_diffusion_test
stochastic_heat2d, a Fortran90 code which implements a finite difference method (FDM) for the steady 2D heat equation, with a stochastic heat diffusivity coefficient.
stochastic_heat2d_test
stochastic_rk, a Fortran90 code which applies a Runge-Kutta (RK) scheme to a stochastic ordinary differential equation (SDE).
stochastic_rk_test
stokes_2d_exact, a Fortran90 code which evaluates exact solutions to the incompressible steady Stokes equations over the unit square in 2D.
stokes_2d_exact_test
string_pde, a Fortran90 code which sets up and solves the partial differential equations (PDE) describing a vibrating string, creating files that can be displayed by gnuplot().
string_pde_test
stripack, a Fortran90 code which computes the Delaunay triangulation or Voronoi diagram of points on a unit sphere, by Robert Renka.
stripack_test
stripack_bench, a Fortran90 code which times the execution of stripack()'s Delaunay triangulation procedure over the surface of a sphere, for a random set of N nodes.
stripack_bench_test
stripack_delaunay, a Fortran90 code which reads points on the unit sphere, calls stripack() to compute the Delaunay triangulation, and writes it to a file.
stripack_delaunay_test
stripack_voronoi, a Fortran90 code which reads points on the unit sphere, computes the Voronoi diagram, and writes it to a file.
stripack_voronoi_test
stroud_rule, a Fortran90 code 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.
stroud_rule_test
subpak, a Fortran90 code which includes a number of utility routines.
subpak_test
subset, a Fortran90 code 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_test
subset_sum, a Fortran90 code which seeks solutions of the subset sum problem, in which it is desired to find a subset of integers which has a given sum.
subset_sum_test
subset_sum_backtrack, a Fortran90 code which uses backtracking to find solutions of the subset sum problem, in which it is desired to find a subset of integers which has a given sum.
subset_sum_backtrack_test
subset_sum_brute, a Fortran90 code which uses brute force to find solutions of the subset sum problem, in which it is desired to find a subset of integers which has a given sum.
subset_sum_brute_test
subset_sum_swap, a Fortran90 code which uses swapping to try to improve an initial estimated solution of the subset sum problem, which seeks a subset of a set of integers which has a given sum. Even when an exact solution exists, this approach often only finds an approximate solution.
subset_sum_swap_test
svd_basis, a Fortran90 code which applies the singular value decomposition (SVD) to a collection of data vectors, extracting dominant modes;
svd_basis_test
svd_basis_weight, a Fortran90 code which applies the singular value decomposition (SVD) to a collection of weighted data vectors, extracting dominant modes;
svd_basis_weight_test
svd_snowfall, a Fortran90 code which reads a file containing historical snowfall data and analyzes the data with the Singular Value Decomposition (SVD), displaying the results using gnuplot().
svd_snowfall_test
svd_test, a Fortran90 code which demonstrates the Singular Value Decomposition (SVD).
svd_truncated, a Fortran90 code 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.
svd_truncated_test
table_columns, a Fortran90 code which reads a table file of N points in M dimensions and creates a new file by copying various columns, with repetition and shuffling;
table_columns_test
table_io, a Fortran90 code which reads and writes data as a table file.
table_io_test
table_quality, a Fortran90 code which reads a table file of N points in M dimensions and computes the uniformity of the placement of the points;
table_quality_test
table_top, a Fortran90 code which displays patterns in a set of N points in M dimensions.
table_top_test
tec_io, a Fortran90 code which reads or writes a tecplot() ASCII TEC file containing a model associated with the finite element method (FEM).
tec_io_test
tec_to_fem, a Fortran90 code which converts a tecplot ASCII file into an FEM model.
tec_to_fem_test
test_approx, a Fortran90 code which implements test problems for approximation, provided as (x,y) data.
test_approx_test
test_con, a Fortran90 code which defines tests for the continuation problem, which considers a function F(X) with N-dimensional argument X and N-1 dimensional result. In general, this defines an implicit one-dimensional curve of solutions X(LAMBDA). A continuation code starts from a single point on this curve and tries to compute a sequence of solutions that form a path.
test_con_test
test_eigen, a Fortran90 code which implements test matrices for eigenvalue analysis.
test_eigen_test
test_int, a Fortran90 code which implements test problems for approximate integration in one dimension.
test_int_test
test_int_2d, a Fortran90 code which implements test problems for approximate integration in two dimensions.
test_int_2d_test
test_interp, a Fortran90 code which defines test problems for interpolation, provided as (x,y(x)) data.
test_interp_test
test_interp_1d, a Fortran90 code which defines test problems for interpolation of data y(x), which depends on a 1D argument.
test_interp_1d_test
test_interp_2d, a Fortran90 code which defines test problems for interpolation of data z(x,y), depending on a 2D argument.
test_interp_2d_test
test_interp_nd, a Fortran90 code which defines test problems for interpolation of data z(x), depending on an M-dimensional argument.
test_interp_nd_test
test_lls, a Fortran90 code which implements linear least squares (LLS) test problems of the form A*x=b.
test_lls_test
test_matrix, a Fortran90 code which defines test matrices for which the condition number, determinant, eigenvalues, eigenvectors, inverse, null vectors, P*L*U factorization or linear system solution are known. Examples include the Fibonacci, Hilbert, Redheffer, Vandermonde, Wathen and Wilkinson matrices.
test_matrix_test
test_matrix_exponential, a Fortran90 code which defines test cases for computing the matrix exponential.
test_matrix_exponential_test
test_mesh, a Fortran90 code which implements some sample 2D meshes.
test_mesh_test
test_min, a Fortran90 code which implements test problems for minimization of a scalar function of a scalar variable.
test_min_test
test_nearest, a Fortran90 code which tests the time complexity of various procedures for solving the nearest neighbor problem.
test_nearest_test
test_nint, a Fortran90 code which implements test problems for approximate integration (quadrature) in M dimensions.
test_nint_test
test_nls, a Fortran90 code which implements nonlinear least squares (NLS) test problems.
test_nls_test
test_nonlin, a Fortran90 code which implements test problems for the solution of systems of nonlinear equations.
test_nonlin_test
test_ode, a FORTRAN90 code which defines a set of test initial value problems for ordinary differential equations (ODE).
test_ode_test
test_opt, a Fortran90 code which implements test problems for optimization of a scalar function of several variables.
test_opt_test
test_opt_con, a Fortran90 code 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_opt_con_test
test_optimization, a Fortran90 code which implements test problems for optimization of a scalar function of several variables, as described by Molga and Smutnicki.
test_optimization_test
test_partial_digest, a Fortran90 code which generates cases of the partial digest problem.
test_partial_digest_test
test_tet_mesh, a Fortran90 code which implements test problems for tetrahedralization or meshing of arbitrary regions in 3 dimensions.
test_tet_mesh_test
test_triangulation, a Fortran90 code which implements test problems for triangularization or meshing of arbitrary regions in 2 dimensions.
test_triangulation_test
test_values, a Fortran90 code which supplies test values of various mathematical functions, including Abramowitz, AGM, Airy, Bell, Bernoulli, Bessel, Beta, Binomial, Bivariate Normal, Catalan, Cauchy, Chebyshev, Chi Square, Clausen, Clebsch Gordan, Collatz, Cosine integral, Dawson, Debye, Dedekind, dilogarithm, Dixon elliptic functions, Exponential integral, Elliptic, Error, Euler, Exponential integral, F probability, Fresnel, Frobenius, Gamma, Gegenbauer, Goodwin, Gudermannian, Harmonic, Hermite, Hypergeometric 1F1, Hypergeometric 2F1, inverse trigonometic, Jacobi Elliptic functions sn(), cn(), dn(), the Julian Ephemeris Date, Kelvin, Knapsack, Laguerre, Lambert W, Laplace, Legendre, Lerch, Lobachevsky, Lobatto, Logarithmic integral, Log normal, McNugget numbers, Mersenne primes, Mertens, Mittag-Leffler, Moebius, Multinomial, Negative binomial, Nine J, Normal, Omega, Owen, Partition, Phi, Pi, Poisson, Polylogarithm, Polynomial Resultant, Polyomino, Prime, Psi, Rayleigh, Hyperbolic Sine integral, Sigma, Sine Power integral, Sine integral, Six J, Sphere area, Sphere volume, Spherical harmonic, Stirling, Stromgen, Struve, Student, Subfactorial, Student probability, Three J, Transport, Trigamma, Truncated normal, van der Corput, von Mises, Weibull, Wright Omega, Zeta.
test_values_test
test_zero, a Fortran90 code which implements test problems for the solution of a single nonlinear equation in one variable.
test_zero_test
tester, a BASH script which runs the test codes.
tet_mesh, a Fortran90 code which carries out various tasks associated with tetrahedral meshes in 3D;
tet_mesh_test
tet_mesh_boundary, a Fortran90 code which determines the triangular mesh that bounds a tet mesh.
tet_mesh_boundary_test
tet_mesh_quad, a Fortran90 code which estimates the integral of a function over a region defined by a tetrahedral mesh.
tet_mesh_quad_test
tet_mesh_quality, a Fortran90 code which reads information about a tet mesh of points in 3D and computes various quality measures;
tet_mesh_quality_test
tet_mesh_to_gmsh, a Fortran90 code which writes a tetrahedral mesh to a gmsh() file.
tet_mesh_to_gmsh_test
tet_mesh_to_xml, a Fortran90 code which writes a tetrahedral mesh to an XML file.
tet_mesh_to_xml_test
tetrahedron, a Fortran90 code 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.
tetrahedron_test
tetrahedron_arbq_rule, a Fortran90 code 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_arbq_rule_test
tetrahedron_exactness, a Fortran90 code which computes the monomial exactness of a quadrature rule over the interior of a tetrahedron in 3D.
tetrahedron_exactness_test
tetrahedron_felippa_rule, a Fortran90 code which returns a Felippa quadrature rule for approximating integrals over the interior of a tetrahedron in 3D.
tetrahedron_felippa_rule_test
tetrahedron_grid, a Fortran90 code which computes a grid of points over the interior of a tetrahedron in 3D.
tetrahedron_grid_test
tetrahedron_integrals, a Fortran90 code which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3D.
tetrahedron_integrals_test
tetrahedron_jaskowiec_rule, a Fortran90 code which returns quadrature rules, with exactness up to total degree 20, over the interior of a tetrahedron in 3D, by Jan Jaskowiec, Natarajan Sukumar.
tetrahedron_jaskowiec_rule_test
tetrahedron_keast_rule, a Fortran90 code which returns a Keast quadrature rule, with exactness between 0 and 8, over the interior of a tetrahedron in 3D.
tetrahedron_keast_rule_test
tetrahedron_monte_carlo, a Fortran90 code which uses the Monte Carlo method to estimate an integral over the interior of a general tetrahedron in 3D.
tetrahedron_monte_carlo_test
tetrahedron_ncc_rule, a Fortran90 code which defines Newton-Cotes Closed (NCC) quadrature rules over the interior of a tetrahedron in 3D.
tetrahedron_ncc_rule_test
tetrahedron_nco_rule, a Fortran90 code which defines Newton-Cotes Open (NCO) quadrature rules over the interior of a tetrahedron in 3D.
tetrahedron_nco_rule_test
tetrahedron_witherden_rule, a Fortran90 code which returns a symmetric Witherden quadrature rule for the tetrahedron, with exactness up to total degree 10.
tetrahedron_witherden_rule_test
tetrahedron01_monte_carlo, a Fortran90 code which uses the Monte Carlo method to estimate an integral over the interior of the unit tetrahedron in 3D.
tetrahedron01_monte_carlo_test
three_body_ode, a Fortran90 code 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.
three_body_ode_test
tiler_2d, a Fortran90 code which demonstrates how to graphically "tile" a 2D box with a repeated pattern, using transfinite interpolation.
tiler_2d_test
tiler_3d, a Fortran90 code which demonstrates how to graphically "tile" a 3D box with a repeated pattern, using transfinite interpolation.
tiler_3d_test
timer_test, a Fortran90 code which tests various timing functions.
timestamp, a Fortran90 code which prints the current YMDHMS date as a timestamp.
timestamp_test
toeplitz, a Fortran90 code solves a variety of Toeplitz and circulant linear systems.
toeplitz_test
toeplitz_cholesky, a Fortran90 code which computes the Cholesky factorization of a nonnegative definite symmetric Toeplitz matrix.
toeplitz_cholesky_test
toms097, a Fortran90 code which computes the distance between all pairs of nodes in a directed graph with weighted edges, using the Floyd algorithm.
toms097_test
toms112, a Fortran90 code which determines whether a point is contained in a polygon, by Moshe Shimrat. This is a version of ACM TOMS algorithm 112.
toms112_test
toms178, a Fortran90 code which optimizes a scalar functional of multiple variables using the Hooke-Jeeves method, by Arthur Kaupe. This is a version of ACM TOMS algorithm 178.
toms178_test
toms179, a Fortran90 code which evaluates the modified Beta function, by Oliver Ludwig. This is a version of ACM TOMS algorithm 179.
toms179_test
toms243, a Fortran90 code which evaluates the logarithm of a complex value, by David Collens. This is a version of ACM TOMS algorithm 243.
toms243_test
toms291, a Fortran90 code which evaluates the logarithm of the Gamma function, by Malcolm Pike and David Hill. This is a version of ACM TOMS algorithm 291.
toms291_test

toms419

toms419_test
toms443, a Fortran90 code which evaluates the Lambert W function, by Fritsch, Shafer and Crowley. This is a version of ACM TOMS algorithm 443.
toms443_test
toms446, a Fortran90 code which manipulates Chebyshev series for interpolation and approximation; this is a version of ACM TOMS algorithm 446, by Roger Broucke.
toms446_test
toms453, a Fortran90 code which determines the abscissas and weights for a Gaussian quadrature formula for the Bromwich integral; this is a version of ACM TOMS algorithm 453.
toms453_test
toms462, a Fortran90 code which evaluates the upper right tail of the bivariate normal Probability Density Function (PDF); 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.
toms462_test
toms493, a Fortran90 code which seeks the roots of a real polynomial, commonly called rpoly(); this is a version of ACM TOMS algorithm 493, by Michael Jenkins.
toms493_test
toms515, a Fortran90 code which selects subsets of size K from a set of size N. This is a version of ACM TOMS Algorithm 515, by Bill Buckles, Matthew Lybanon.
toms515_test
toms526, a Fortran90 code which interpolates scattered bivariate data. This is a version of ACM TOMS algorithm 526, by Hiroshi Akima;
toms526_test
toms577, a Fortran90 code which evaluates the Carlson elliptic integral functions RC, RD, RF and RJ. This is a version of ACM TOMS algorithm 577;
toms577_test
toms611, a Fortran90 code which seeks the minimizer of a scalar functional of multiple variables. This is a version of ACM TOMS algorithm 611, by David Gay.
toms611_test
toms647, a Fortran90 code which evaluates Faure, Halton and Sobol Quasi Monte Carlo (QMC) sequences. This is a version of ACM TOMS algorithm 647.
toms647_test
toms655, a Fortran90 code which computes the weights for interpolatory quadrature rules; this is commonly called IQPACK, by Sylvan Elhay and Jaroslav Kautsky. This is a version of ACM TOMS algorithm 655.
toms655_test
toms659, a Fortran90 code which computes elements of the Sobol Quasi Monte Carlo (QMC) sequence; this is a version of ACM TOMS algorithm 659.
toms659_test
toms660, a Fortran90 code which takes scattered 2D data and produces an interpolating function F(X,Y). This is a version of ACM TOMS algorithm 660, called qshep2d, by Robert Renka.
toms660_test
toms661, a Fortran90 code which takes scattered 3D data and produces an interpolating function F(X,Y,Z). This is a version of ACM TOMS algorithm 661, called qshep3d, by Robert Renka.
toms661_test
toms672, a Fortran90 code which generates an interpolatory quadrature rule of highest possible order, given preassigned abscissas. This can be used to generate Gauss-Kronrod and Gauss-Patterson quadrature rules. This is commonly called EXTEND. This is a version of ACM TOMS algorithm 672.
toms672_test
toms708, a Fortran90 code which computes the incomplete Beta function ratio Ix(a,b).
toms708_test
toms715, a Fortran90 code which evaluates special functions, including the Bessel I, J, K, and Y functions of order 0, of order 1, and of any real order, the Dawson integral, the error function, exponential integrals, the gamma function, the normal distribution function, the psi function. This is a version of ACM TOMS algorithm 715.
toms715_test
toms726, a Fortran90 code which computes recursion coefficients for orthogonal polynomials, and the abscissa and weights for related quadrature rules. by Walter Gautschi. This is commonly called ORTHPOL. This is a version of ACM TOMS algorithm 726.
toms726_test
toms738, a Fortran90 code which evaluates the Niederreiter Quasi Monte Carlo (QMC) sequence; this is a version of ACM TOMS algorithm 738;
toms738_test
toms743, a Fortran90 code which evaluates the Lambert W function. This is a version of ACM TOMS algorithm 743, by Barry, Barry and Culligan-Hensley.
toms743_test
toms757, a Fortran90 code which evaluates uncommon special functions, by Allan Mcleod; this is a version of ACM TOMS algorithm 757;
toms757_test
toms792, a Fortran90 code which tests functions that interpolate scattered data in the plane; by Robert Renka; this is a version of ACM TOMS algorithm 792.
toms792_test
toms886, a Fortran90 code 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.
toms886_test
trapezoidal, a Fortran90 code which solves one or more ordinary differential equations (ODE) using the (implicit) trapezoidal method, and a version of fsolve() to handle the nonlinear equation.
trapezoidal_test
treepack, a Fortran90 code which defines, analyzes, and manipulates trees, a simple kind of graph with no circuits. Special cases include rooted and binary trees. Representations include adjacency, arc, Pruefer code, and parent. Operations include center, diameter, eccentricity, enumeration, generation one at a time, random selection, traversal.
treepack_test
tri_surface_io, a Fortran90 code which reads and writes the 3D graphics information in a tri_surface file;
tri_surface_io_test
triangle, a Fortran90 code which computes properties, including angles, area, centroid, circumcircle, edge lengths, incircle, orientation, orthocenter, and quality, of a triangle in 2D.
triangle_test
triangle_analyze, a Fortran90 code which reads a triangle defined in a file, and computes angles, area, centroid, circumcircle, edge lengths, incircle, orientation, orthocenter, and quality.
triangle_analyze_test
triangle_dunavant_rule, a Fortran90 code which defines Dunavant rules for quadrature over the interior of a triangle in 2D.
triangle_dunavant_rule_test
triangle_exactness, a Fortran90 code which computes the monomial exactness quadrature rule over the interior of a triangle in 2D.
triangle_exactness_test
triangle_fekete_rule, a Fortran90 code which defines a Fekete rule for interpolation or quadrature over the interior of a triangle in 2D.
triangle_fekete_rule_test
triangle_felippa_rule, a Fortran90 code which returns a Felippa quadrature rule for approximating integrals over the interior of a triangle in 2D.
triangle_felippa_rule_test
triangle_grid, a Fortran90 code which computes a grid of points over the interior of a triangle in 2D.
triangle_grid_test
triangle_histogram, a Fortran90 code which computes histograms of data over the interior of the unit triangle in 2D.
triangle_histogram_test
triangle_integrals, a Fortran90 code which returns the exact value of the integral of any polynomial over the interior of an arbitrary triangle in 2D.
triangle_integrals_test
triangle_interpolate, a Fortran90 code which shows how vertex data can be interpolated at any point in the interior of a triangle.
triangle_interpolate_test
triangle_io, a Fortran90 code which reads or writes some of the files created by Jonathan Shewchuk's triangle() program.
triangle_io_test
triangle_lyness_rule, a Fortran90 code which returns a Lyness-Jespersen quadrature rule over the interior of a triangle in 2D.
triangle_lyness_rule_test
triangle_monte_carlo, a Fortran90 code which uses the Monte Carlo method to estimate an integral over the interior of a general triangle in 2D.
triangle_monte_carlo_test
triangle_ncc_rule, a Fortran90 code which defines Newton-Cotes Closed (NCC) quadrature rules over the interior of a triangle in 2D.
triangle_ncc_rule_test
triangle_nco_rule, a Fortran90 code which defines Newton-Cotes Open (NCO) quadrature rules over the interior of a triangle in 2D.
triangle_nco_rule_test
triangle_svg, a Fortran90 code which uses Scalable Vector Graphics (SVG) to plot a triangle and any number of points, to illustrate quadrature rules and sampling techniques.
triangle_svg_test
triangle_symq_rule, a Fortran90 code which returns efficient symmetric quadrature rules, with exactness up to total degree 50, over the interior of an arbitrary triangle in 2D, by Hong Xiao and Zydrunas Gimbutas.
triangle_symq_rule_test
triangle_to_fem, a Fortran90 code which reads the NODE and ELE files created by Jonathan Shewchuk's triangle() program to describe a triangular mesh, and writes a corresponding pair of node and element files in the 2D FEM format.
triangle_to_fem_test
triangle_to_medit, a Fortran90 code which reads the NODE and ELE files created by Jonathan Shewchuk's triangle() program to describe a triangular mesh, and writes a corresponding medit() MESH file.
triangle_to_medit_test
triangle_to_xml, a Fortran90 code which reads the NODE and ELE files created by Jonathan Shewchuk's triangle() program to describe a triangular mesh in 2D, and writes out a corresponding XML mesh file for use by dolfin() or fenics().
triangle_to_xml_test
triangle_twb_rule, a Fortran90 code which generates the points and weights of quadrature rules over the interior of a triangle in 2D, determined by Taylor, Wingate, and Bos.
triangle_twb_rule_test
triangle_wandzura_rule, a Fortran90 code which returns Wandzura quadrature rules of exactness 5, 10, 15, 20, 25 or 30 over the interior of the triangle in 2D.
triangle_wandzura_rule_test
triangle_witherden_rule, a Fortran90 code which returns a symmetric Witherden quadrature rule for the triangle, with exactness up to total degree 20.
triangle_witherden_rule_test
triangle01_integrals, a Fortran90 code which returns the integral of any monomial over the interior of the unit triangle in 2D.
triangle01_integrals_test
triangle01_monte_carlo, a Fortran90 code which uses the Monte Carlo method to estimate an integral over the interior of the unit triangle in 2D.
triangle01_monte_carlo_test
triangulation, a Fortran90 code which computes the triangulation 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_test
triangulation_l2q, a Fortran90 code which reads information about a 3-node (linear) triangulation and creates data defining a corresponding 6-node (quadratic) triangulation;
triangulation_l2q_test
triangulation_mask, a Fortran90 code which reads a triangulation and calls a user-supplied routine to consider each triangle for deletion;
triangulation_orient, a Fortran90 code which ensures that the triangles in an order 3 or order 6 triangulation have positive orientation;
triangulation_orient_test
triangulation_plot, a Fortran90 code which plots the nodes and elements of a triangulation as a PostScript (PS) file;
triangulation_plot_test
triangulation_q2l, a Fortran90 code which reads information about a 6-node triangulation and creates data defining a corresponding 3-node triangulation;
triangulation_q2l_test
triangulation_quad, a Fortran90 code 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_quad_test
triangulation_quality, a Fortran90 code which reads information about a triangulation and computes various quality measures;
triangulation_quality_test
triangulation_rcm, a Fortran90 code which reads files describing a triangulation of nodes in 2D, and applies the Reverse Cuthill McKee (RCM) algorithm to produce a renumbering of the triangulation with a reduced bandwidth.
triangulation_rcm_test
triangulation_svg, a Fortran90 code which creates an SVG image of a triangulation, which can be displayed by a web browser.
triangulation_svg_test
triangulation_t3_to_t4, a Fortran90 code which reads information about a 3-node triangulation and creates data defining a corresponding 4-node triangulation (vertices + centroid);
triangulation_t3_to_t4_test
triangulation_triangle_neighbors, a Fortran90 code which reads data defining a triangulation, determines the neighboring triangles of each triangle, and writes that information to a file.
triangulation_triangle_neighbors_test
truncated_normal, a Fortran90 code 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_test
truncated_normal_rule, a Fortran90 code which computes a quadrature rule for a normal probability density function (PDF), also called a Gaussian distribution, that has been truncated to [A,+oo), (-oo,B] or [A,B].
truncated_normal_rule_test
tsp_brute, a Fortran90 code which reads a file of city-to-city distances and solves a (small!) traveling salesperson problem (TSP), using brute force.
tsp_brute_test
tsp_lau, a Fortran90 code which implements a heuristic algorithm for the solution of the traveling salesperson problem (TSP).
tsp_lau_test
ubvec, a Fortran90 code which demonstrates how unsigned binary vectors, strings of 0 and 1, represent nonnegative integers or subsets or other mathematical objects, for which various arithmetic and logical operations can be defined.
ubvec_test
unicycle, a Fortran90 code which considers permutations containing a single cycle, sometimes called cyclic permutations.
unicycle_test
uniform, a Fortran90 code which implements random number generators (RNG) for a variety of arithmetic types.
uniform_test
van_der_corput, a Fortran90 code which computes elements of a 1D van der Corput Quasi Monte Carlo (QMC) sequence using a simple interface.
van_der_corput_test
vandermonde, a Fortran90 code which implements the Bjork-Pereyra algorithm for accurate solution of linear systems involving the Vandermonde matrix.
vandermonde_test
vandermonde_approx_1d, a Fortran90 code 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_1d_test
vandermonde_approx_2d, a Fortran90 code 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_approx_2d_test
vandermonde_interp_1d, a Fortran90 code 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_1d_test
vandermonde_interp_2d, a Fortran90 code 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.
vandermonde_interp_2d_test
vtk_io, a Fortran90 code which reads and writes some simple forms of VTK files.
vtk_io_test
walker_sample, a Fortran90 code which efficiently samples a discrete probability vector using Walker sampling.
walker_sample_test
walsh_transform, a Fortran90 code which implements the Walsh data transform.
walsh_transform_test
wathen_matrix, a Fortran90 code which compares storage schemes (full, banded, sparse triplet ) and solution strategies (Linpack full, Linpack banded, conjugate gradient) for linear systems involving the Wathen matrix, which can arise when solving a problem using the finite element method (FEM).
wathen_matrix_test
wave_mpi, a Fortran90 code which uses the finite difference method (FDM) to estimate a solution to the wave equation, using the Message Passing Interface (MPI) for parallel execution.
wave_mpi_test
wavelet, a Fortran90 code which does some simple calculations with wavelet transforms;
wavelet_test
wedge_exactness, a Fortran90 code which investigates the polynomial exactness of a quadrature rule over the interior of the unit wedge in 3D.
wedge_exactness_test
wedge_felippa_rule, a Fortran90 code which returns a Felippa quadrature rule for approximating integrals over the interior of the unit wedge in 3D.
wedge_felippa_rule_test
wedge_grid, a Fortran90 code which computes a grid of points over the interior of the unit wedge in 3D.
wedge_grid_test
wedge_integrals, a Fortran90 code which returns the exact value of the integral of any monomial over the interior of the unit wedge in 3D.
wedge_integrals_test
wedge_monte_carlo, a Fortran90 code which uses the Monte Carlo method to estimate an integral over the interior of the unit wedge in 3D.
wedge_monte_carlo_test
weekday, a Fortran90 code which determines the day of the week corresponding to a given date, such as 14 October 1066, Julian calendar, which was a Saturday.
weekday_test
wishart_matrix, a Fortran90 code which produces sample matrices from the Wishart or Bartlett distributions, useful for sampling random covariance matrices.
wishart_matrix_test
wordsnake, a Fortran90 code which tries to find a good solution to the "Wordsnake Puzzle", in which a list of words is reordered, trying to maximize the overlap of successive words.
wordsnake_test
wtime, a Fortran90 code which returns a reading of the wall clock time in seconds.
wtime_test
xerror, a Fortran90 code which reports and handles errors detected during execution.
xerror_test
xy_io, a Fortran90 code which reads and writes simple graphics files in the XY, XYL and XYF formats.
xy_io_test
xyz_io, a Fortran90 code which reads and writes simple graphics files in the XYZ, XYZL and XYZF formats.
xyz_io_test
xyz_to_pdb, a Fortran90 code which reads an XYZ file containing a list of spatial coordinates, and writes a Protein Data Bank (PDB) file containing ATOM records with the given coordinates.
xyz_to_pdb_test
zero_brent, a Fortran90 code which seeks a solution of a scalar nonlinear equation f(x)=0, by Richard Brent.
zero_brent_test
zero_chandrupatla, a Fortran90 code which finds a zero of a scalar function of a scalar variable, starting from a change of sign interval, using the Chandrupatla method, which can converge faster than bisection, regula falsi, or Brent's method, by Tirupathi Chandrapatla.
zero_chandrupatla_test
zero_itp, a Fortran90 code which finds a zero of a scalar function of a scalar variable, starting from a change of sign interval, using the Interpolate/Truncate/Project (ITP) method, which has faster convergence than the bisection method.
zero_itp_test
zero_laguerre, a Fortran90 code which uses Laguerre's method to find the zero of a function. The method needs first and second derivative information. The method almost always works when the function is a polynomial.
zero_laguerre_test
zero_muller, a Fortran90 code which seeks a root of a nonlinear equation using the Muller method, with complex arithmetic.
zero_muller_test
zero_rc, a Fortran90 code which seeks a solution of a scalar nonlinear equation f(x)=0, using reverse communication (RC), by Richard Brent.
zero_rc_test
zoomin, a Fortran90 code which implements many procedures for finding the zero of a scalar nonlinear function.
zoomin_test

Last revised on 13 November 2024.