MATLAB Source Codes

This is a collection of routines for use with MATLAB.

Available software includes:

  1. args, a program which shows how to count and report command line arguments;
  2. arpack, a library which computes eigenvalues and eigenvectors of large sparse matrices, accessible via the built-in EIGS command;
  3. asa005 a library which evaluates the lower tail of the noncentral Student's T distribution; this is Applied Statistics Algorithm 5;
  4. asa006 a library which computes the Cholesky factor of a positive definite symmetric matrix; this is Applied Statistics Algorithm 6;
  5. asa007 a library which computes the inverse of a positive definite symmetric matrix; this is Applied Statistics Algorithm 7;
  6. asa032 a library which evaluates the incomplete Gamma function; this is Applied Statistics Algorithm 32;
  7. asa047 a library which minimizes a scalar function of several variables using the Nelder-Mead algorithm; this is Applied Statistics Algorithm 47;
  8. asa058 a library which carries out clustering of data; this is Applied Statistics Algorithm 58;
  9. asa063 a library which evaluates the incomplete Beta function; this is Applied Statistics Algorithm 63;
  10. asa066 a library which computes the cumulative density function of the standard normal distribution; this is Applied Statistics Algorithm 66;
  11. asa076 a library which evaluates Owen's T function; this is Applied Statistics Algorithm 76;
  12. asa091, a library which computes the percentage points of the Chi-square distribution; this is Applied Statistics Algorithm 91;
  13. asa103, a library which evaluates the digamma or psi function; this is Applied Statistics Algorithm 103;
  14. asa109 a library which inverts the incomplete Beta function; this is Applied Statistics Algorithm 109;
  15. asa111 a library which evaluates the percentage points of the normal distribution; this is Applied Statistics Algorithm 111;
  16. asa113 a library which clusters data using the Banfield and Bassill transfer and swap algorithm; this is Applied Statistics Algorithm 113;
  17. asa121, a library which evaluates the trigamma function; this is Applied Statistics Algorithm 121;
  18. asa136 a library which clusters data using the Hartigan and Wong algorithm; this is Applied Statistics Algorithm 136;
  19. asa144 a library which randomly generates tables with given row and column sums; this is Applied Statistics Algorithm 144;
  20. asa147 a library which evaluates the incomplete Gamma function; this is Applied Statistics Algorithm 147;
  21. asa152, a library which evaluates point and cumulative probabilities associated with the hypergeometric distribution; this is Applied Statistics Algorithm 152;
  22. asa159, a library which computes a random table with given row and column sums; this is Applied Statistics Algorithm 159;
  23. asa172 a library which simulates the generation of a set of multi-indices by nested DO-Loops; this is Applied Statistics Algorithm 172;
  24. asa183, a library which implements the Wichman-Hill pseudorandom number generator; this is Applied Statistics Algorithm 183;
  25. asa226 a library which evaluates the noncentral incomplete Beta function; this is Applied Statistics Algorithm 226;
  26. asa239 a library which evaluates the incomplete Gamma function; this is Applied Statistics Algorithm 239;
  27. asa241, a library which computes the inverse of the normal CDF; this is Applied Statistics Algorithm 241;
  28. asa243 a library which evaluates the lower tail of the noncentral Student's T distribution; this is Applied Statistics Algorithm 243;
  29. asa245 a library which evaluates the logarithm of the Gamma function; this is Applied Statistics Algorithm 245;
  30. asa299, a library which computes the lattice points (integer coordinates) in an M-dimensional simplex; this is Applied Statistics Algorithm 299;
  31. asa310 a library which evaluates the noncentral incomplete Beta function; this is Applied Statistics Algorithm 310;
  32. beta_nc, a library which evaluates the CDF of the noncentral Beta distribution;
  33. bezier_surface, a library which reads, writes, prints and manipulates the data that defines a Bezier surface;
  34. bezier_surface_display, a program which displays a Bezier surface;
  35. birthday_remote, a program which runs a Monte Carlo simulation of the birthday paradox, and includes instructions on how to run the job, via MATLAB's BATCH facility, on a remote system such as Virginia Tech's ITHACA cluster.
  36. black_scholes, a library which implements some simple approaches to the Black-Scholes option valuation theory;
  37. blas1_c, a library which implements the Level 1 Basic Linear Algebra Subprograms, using single precision complex arithmetic;
  38. blas1_d, a library which implements the Level 1 Basic Linear Algebra Subprograms, using double precision real arithmetic;
  39. blas1_s, a library which implements the Level 1 Basic Linear Algebra Subprograms, using single precision real arithmetic;
  40. blas1_z, a library which implements the Level 1 Basic Linear Algebra Subprograms, using double precision complex arithmetic;
  41. blend, a library which carries out 1D/2D/3D blending interpolation;
  42. box_behnken, a library which computes a Box-Behnken design, that is, a set of arguments to sample the behavior of a function of multiple parameters;
  43. box_plot, a program which displays a box plot of data that consists of pairs of integers;
  44. brent a library which contains Richard Brent's routines for finding zeroes or minima of functions, without the use of derivative information.
  45. buckling_spring a program which plots solutions of the buckling spring equations.
  46. calendar_nyt, a library which shows the correspondence between dates and the New York Times volume and issue number;
  47. cavity_flow_display, a library which displays a single velocity field solution for the driven cavity;
  48. cavity_flow_movie, a library which animates the velocity solutions for the driven cavity;
  49. cc_display, a program which displays the points used in a 2D Clenshaw-Curtis quadrature rule;
  50. ccvt_box, a program which calculates a constrained CVT for points constrained to lie in a box, with some points moved to the boundary;
  51. ccvt_reflect, a program which calculates a constrained CVT for points constrained to lie in a box, with some points "pushed" towards the boundary;
  52. cg_lab_triangles, a collection of programs associated with a computer lab assignment on computational geometry and triangles;
  53. chebyshev1_rule, a program which computes and writes out a Gauss-Chebyshev type 1 quadrature rule of given order.
  54. chebyshev2_rule, a program which computes and writes out a Gauss-Chebyshev type 2 quadrature rule of given order.
  55. chrpak, a library which manipulates characters and strings;
  56. cities, a library which works with city-to-city distance matrices;
  57. clenshaw_curtis_grid, a library which implements a multidimensional Clenshaw Curtis quadrature rule;
  58. clenshaw_curtis_rule, a program which implements a Clenshaw Curtis quadrature rule;
  59. collatz, a library which computes and analyzes the Collatz sequence (or "hailstone" sequence or "3n+1 sequence");
  60. collatz_parallel is a program which seeks the maximum Collatz sequence between 1 and N; it runs in parallel using MATLAB's "parfor" facility.
  61. color_remote, a program which carries out the color segmentation of an image in parallell, using MATLAB's SPMD facility; this includes instructions on how to run the job, via MATLAB's BATCH facility, on a remote system such as Virginia Tech's ITHACA cluster.
  62. contour_sequence, a program which creates images suitable for animation from a sequence of (X,Y,U(X,Y)) data files;
  63. contour_sequence3, a program which creates images suitable for animation from one pair of X, Y files, and a sequence of U(X,Y) data files;
  64. contour_sequence4, a program which creates images suitable for animation from one XY file and a sequence of U(X,Y) data files;
  65. coordinate_search, a program which implements the coordinate search algorithm for the minimization of a scalar function of several variables.
  66. cordic, a library which computes a few special functions using the CORDIC algorithm.
  67. cvt, a library which computes an N-point Centroidal Voronoi Tessellation in M dimensions;
  68. cvt_1d_nonuniform, a program which computes an N-point Centroidal Voronoi Tessellation in 1 dimension, under a nonuniform density, and plots the evolution of the locations of the generators during the iteration;
  69. cvt_dataset a program which creates a CVT dataset;
  70. cvt_demo, a program which interactively, graphically demonstrates a CVT calculation;
  71. cvt_metric, a program which computes a CVT under a spatially varying metric;
  72. cvt_movie, a program which creates an animation of the evolution of a CVT;
  73. cvt_movie2, a program which creates a CVT movie;
  74. cvt_movie3, a program which creates a CVT movie in a region of unusual shape;
  75. cvt_movie4, a program which creates a CVT movie in a square, with a density function that drives points to the corners;
  76. cvt_movie5, a program which repeats cvt_movie3, but with hexagonal grid initialization, fixed points, and boundary projection;
  77. dice_simulation a program which simulates N tosses of M dice, making a histogram of the results.
  78. direction_arrows, a program which reads coordinate data from one file, velocity data from another file, and makes an arrow plot of the direction field.
  79. direction_arrows_grid, a program which reads velocity data at "scattered" points, and makes a direction vector plot on a uniform grid of user-specified density.
  80. direction_arrows_sequence, a program which reads a fixed coordinate file, and a sequence of velocity data files and makes a sequence of velocity direction arrow plots.
  81. direction_arrows_sequence2, a program which reads a sequence of coordinate and velocity data and makes a sequence of velocity direction arrow plots.
  82. direction_arrows2, a program which reads coordinate and velocity data from a single file and makes an arrow plot of the direction field.
  83. discrete_pdf_sample a program 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.
  84. dist_plot, a program which makes contour plots of the distance function, as defined and used in Persson and Strang's distmesh code;
  85. distance_to_position a program which estimates the positions of cities based on a city-to-city distance table.
  86. distance_to_position_sphere a program which estimates the positions of cities on a sphere (such as the earth) based on a city-to-city distance table.
  87. distmesh, a library which carries out Persson and Strang's method of mesh generation;
  88. distmesh_3d, a library which constitutes the 3D subset of Persson and Strang's distmesh code;
  89. divdif, a library which constructs, evaluates and manipulates divided difference tables;
  90. dunavant, a library which defines Dunavant quadrature rules in a triangle;
  91. entrust, a library which uses trust-region methods to solve problems in scalar optimization or nonlinear least squares, by Borggaard and Cliff.
  92. faure, a library which computes the Faure M-dimensional quasirandom sequence;
  93. fd_predator_prey, a program which solves a pair of predator prey ODE's using a finite difference approximation.
  94. fd1d_bvp, a program which applies the finite difference method to a two point boundary value problem in one spatial dimension.
  95. fd1d_heat_explicit, a program which implements a finite difference solution, explicit in time, of the time dependent 1D heat equation;
  96. fd1d_heat_implicit, a program which implements a finite difference solution, implicit in time, of the time dependent 1D heat equation;
  97. fd1d_heat_steady, a program which implements a finite difference solution for the steady (time independent) 1D heat equation;
  98. fd1d_predator_prey, a program which implements a finite difference algorithm for a predator-prey system with spatial variation in 1D;
  99. fd1d_plot, a program which plots solutions from the FD1D_PREDATOR_PREY program.
  100. fd2d_predator_prey, a program which implements a finite difference algorithm for a predator-prey system with spatial variation in 2D.
  101. fdi_opt, a program which demonstrates the use of MATLAB's FMINCON constrained minimization function, taking advantage of MATLAB's Parallel Computing Toolbox for faster execution.
  102. fekete, a library which sets up one of seven Fekete rules for interpolation or quadrature in a triangle;
  103. felippa, a library which defines quadrature rules for lines, triangles, quadrilaterals, pyramids, wedges, tetrahedrons and hexahedrons.
  104. fem_50, a program which implements a Finite Element Method solver using about 50 lines of MATLAB code;
  105. fem_50_heat, a program which is a version of fem_50 for the time-dependent heat equation;
  106. fem_basis_q4_display, a program which displays any single basis function associated with an arbitrary linear quadrilateral ("Q4") mesh;
  107. fem_basis_t3_display, a program which displays any single basis function associated with an arbitrary 3-node triangle "T3" mesh;
  108. fem_basis_t4_display, a program which displays any single basis function associated with an arbitrary 4-node triangle "T4" mesh;
  109. fem_basis_t6_display, a program which displays any single basis function associated with an arbitrary 6-node triangle "T6" mesh;
  110. fem_io, a library which reads or writes FEM files, (three text files describing a finite element model);
  111. fem_to_tec, a program which reads a set of FEM files, (three text files describing a finite element model), and writes a TEC filesuitable for display by TECPLOT;
  112. fem1d, a program which applies the finite element method, using piecewise linear basis functions, to a linear two point boundary value problem in 1D;
  113. fem1d_adaptive, a program which uses an adaptive mesh when applying the finite element method, with piecewise linear basis functions, to a linear two point boundary value problem in 1D;
  114. fem1d_bvp_linear, a program which applies the finite element method, with piecewise linear elements, to a two point boundary value problem in one spatial dimension.
  115. fem1d_function_10_display is a program which reads a prefix defining three finite element data files, reads the data, samples the finite element function, and displays a plot.
  116. fem1d_nonlinear, a program which applies the finite element method, with piecewise linear basis functions, to a nonlinear two point boundary value problem in 1D;
  117. fem1d_pmethod, a program which applies the p-method version of the finite element method to a linear two point boundary value problem in 1D;
  118. fem1d_project is a program which projects data into a finite element space, including the least squares approximation of data, or the projection of a finite element solution from one mesh to another.
  119. fem1d_sample, a program which samples a scalar or vector finite element function of one variable, defined by FEM files, returning interpolated values at the sample points.
  120. fem2d_heat, a program which applies the finite element method for the time-dependent heat equation on a triangulated square in 2D;
  121. fem2d_pack, a library which performs simple 2D finite element computations;
  122. fem2d_poisson, a program which solves the 2D Poissone equation on a rectangle, using the finite element method, and piecewise quadratic triangular elements.
  123. fem2d_poisson_linear is a program which solves the 2D Poisson equation on a rectangle, using the finite element method, and piecewise linear triangular elements.
  124. fem2d_project is a program which projects a function F(X,Y), given as data, into a given finite element space of piecewise linear triangular elements.
  125. fem2d_project_function is a program which projects a function F(X,Y), given as a formula, into a given finite element space of piecewise linear triangular elements.
  126. fem2d_sample, a program which samples a finite element function, defined by FEM files, (three text files describing the nodes, triangles, and coefficients); at arbitrary points.
  127. fem3d_pack is a library which contains utilities for 3D finite element calculations.
  128. fem3d_project is a program which projects a function F(X,Y,Z), given as a data, into a given finite element space of piecewise linear tetrahedral elements.
  129. fem3d_sample is a program library which evaluates a finite element function defined on a 3D tetrahedral mesh.
  130. ffh_sparse, a program which applies the finite element method to the heat equations on an arbitrary triangulated region in 2D. This is a special version of FREE_FEM_HEAT that uses MATLAB's sparse matrix features;
  131. ffns_sparse, a program which applies the finite element method to the steady incompressible Navier Stokes equations on an arbitrary triangulated region in 2D. This is a special version of FREE_FEM_NAVIER_STOKES that uses MATLAB's sparse matrix features;
  132. ffp_sparse, a program which applies the finite element method to the Poisson equations on an arbitrary triangulated region in 2D. This is a special version of FREE_FEM_POISSON that uses MATLAB's sparse matrix features;
  133. ffs_sparse, a program which is a finite element code for the steady incompressible Stokes equations on an arbitrary triangulated region in 2D. This is a special version of FREE_FEM_STOKES that uses MATLAB's sparse matrix features;
  134. fft_serial is a program which computes a Fast Fourier Transform, and is intended as a starting point for implementing an OpenMP parallel version.
  135. filum, a library which handles files and filenames;
  136. floyd is a library which implements Floyd's algorithm for finding the shortest distance between pairs of nodes on a directed graph.
  137. floyd_parallel is a program which attempts to run a parallel implementation of Floyd's algorithm for finding the shortest distance between pairs of nodes on a directed graph.
  138. free_fem_heat, a program which applies the finite element method to the time dependent heat equation on an arbitrary triangulated region in 2D;
  139. free_fem_navier_stokes, a program which applies the finite element method to the steady incompressible Navier Stokes equations on an arbitrary triangulated region in 2D;
  140. free_fem_poisson, a program which applies the finite element method to Poisson's equation on an arbitrary triangulated region in 2D;
  141. free_fem_stokes, a program which applies the finite element method for the steady incompressible Stokes equations on an arbitrary triangulated region in 2D;
  142. gamblers_ruin_simulation, a program which simulates the game of gambler's ruin.
  143. gegenbauer_rule, a program which computes and writes out a Gauss-Gegenbauer quadrature rule of given order.
  144. gen_hermite_rule, a program which computes and writes out a generalized Gauss-Hermite quadrature rule of given order and parameter value ALPHA.
  145. gen_laguerre_rule, a program which computes and writes out a generalized Gauss-Laguerre quadrature rule of given order and parameter value ALPHA.
  146. geometry, a library which performs 2D/3D geometric calculations;
  147. geompack, a library which computes the Delaunay triangulation for a set of points in 2D;
  148. gl_display, a program which displays the points used in a 2D Gauss-Legendre quadrature rule;
  149. gm_rules, a library which defines Grundmann-Moeller quadratures rules for an M-dimensional simplex.
  150. grf_display, a program which reads a GRF file defining a mathematical graph and displays it in the MATLAB graphics window.
  151. grf_io, a library which reads or writes a GRF file;
  152. grid, a library which computes N random points on a uniform M dimensional grid;
  153. grid_dataset, a program which creates a grid dataset;
  154. halton, a library which calculates the Halton M-dimensional quasirandom sequence;
  155. halton_dataset, a program which creates N elements of an M dimensional Halton sequence and write them to a file.
  156. hammersley, a library which computes the Hammersley M-dimensional quasirandom sequence;
  157. hammersley_dataset, a program which creates N elements of an M dimensional Hammersley sequence and write them to a file.
  158. hb_io, a library which reads and writes files in the Harwell Boeing sparse matrix format;
  159. hb_to_mm, a program which converts a sparse matrix stored in a Harwell Boeing file to Matrix Market format;
  160. hb_to_msm, a program which converts a sparse matrix stored in a Harwell Boeing file to MATLAB sparse matrix format;
  161. hb_to_st a program which reads a sparse matrix in a Harwell-Boeing file and writes an equivalent Sparse Triplet file.
  162. hcell_flow_display, a program which plots the physical data, pressures or velocities, from a run of the HCELL program;
  163. hello, a program which prints out "Hello, world!".
  164. hermite_phys_product, a library which writes out a table of the integrals of products of pairs of Hermite (physicist) polynomials with a linear or exponential weight.
  165. hermite_prob_product, a library which writes out a table of the integrals of products of pairs of Hermite (probabilist) polynomials with a linear or exponential weight.
  166. hermite_rule, a program which computes and writes out a Gauss-Hermite quadrature rule of given order.
  167. hex_grid, a library which generates a hexagonal grid of points in the unit square or an arbitrary rectangle;
  168. hex_grid_angle, a library which defines a hexagonal grid of points in the unit square, with an arbitrary center, angle, and spacing.
  169. hex_grid_dataset, a program which creates a hexagonal grid of points in a rectangle, and write them to a file, using the hex_grid library.
  170. histogram_display, a program which makes a bar plot of a set of data stored as columns in a file; the first column is the X values, and all the other columns are Y values to be shown as a stack of bars;
  171. hot_pipe, a program which demonstrates fem_50_heat to solve a particular heat equation problem;
  172. hot_point, a program which demonstrates fem_50_heat to solve a particular heat equation problem;
  173. ihs, a library which generates the Improved Distributed Hypercube Sampling M-dimensional quasirandom sequence;
  174. ihs_dataset, a program which creates an IHS dataset and writes it to a file;
  175. inout_flow_display, a library which displays a single velocity field solution for the INOUT flow;
  176. inout_flow_movie, a library which creates an animation of the velocity solutions for the INOUT cell;
  177. int_exactness, a program which tests the polynomial exactness of quadrature rules for a finite interval;
  178. int_exactness_chebyshev1, a program which tests the polynomial exactness of Gauss-Chebyshev type 1 quadrature rules.
  179. int_exactness_chebyshev2, a program which tests the polynomial exactness of Gauss-Chebyshev type 2 quadrature rules.
  180. int_exactness_gegenbauer, a program which tests the polynomial exactness of Gauss-Gegenbauer quadrature rules.
  181. int_exactness_gen_hermite, a program which tests the polynomial exactness of generalized Gauss-Hermite quadrature rules.
  182. int_exactness_gen_laguerre, a program which tests the polynomial exactness of generalized Gauss-Laguerre quadrature rules.
  183. int_exactness_hermite, a program which tests the polynomial exactness of Gauss-Hermite quadrature rules.
  184. int_exactness_jacobi, a program which tests the polynomial exactness of Gauss-Jacobi quadrature rules.
  185. int_exactness_laguerre, a program which tests the polynomial exactness of Gauss-Laguerre quadrature rules.
  186. int_exactness_legendre, a program which tests the polynomial exactness of Gauss-Legendre quadrature rules.
  187. jacobi_rule, a program which computes and writes out a Gauss-Jacobi quadrature rule of given order.
  188. jtb_codist, a program which demonstrates how the linear system associated with a finite element problem can be treated as a codistributed array whose entries are assigned to different MATLAB workers, so that the matrix is assembled in parallel.
  189. keast, a library which defines Keast quadrature rules in a tetrahedron;
  190. kelley, a library which implements iterative methods for linear and nonlinear equations, by Tim Kelley;
  191. kmeans, a library which handles the K-Means problem;
  192. knapsack_remote, a program which runs in parallel, seeking solutions of the knapsack problem, and includes instructions on how to run the job, via MATLAB's BATCH facility, on a remote system such as Virginia Tech's ITHACA cluster.
  193. laguerre_product, a library which writes out a table of the integrals of products of pairs of Laguerre polynomials with a linear or exponential weight.
  194. laguerre_rule, a program which computes and writes out a Gauss-Laguerre quadrature rule of given order.
  195. latin_center, a library which computes N points in an M-dimensional Latin Center square;
  196. latin_edge, a library which returns N points in an M-dimensional Latin Edge square;
  197. latin_random, a library which returns N points in an M-dimensional Latin Random square;
  198. latinize, a program which adjusts N points in M dimensions to form a Latin hypercube;
  199. lattice, a library which returns lattice rules for multiple integration;
  200. lcvt, a library which makes a sort of Latinized CVT (centroidal Voronoi tessellation);
  201. lcvt_dataset, a program which creates a Latinized CVT dataset;
  202. legendre_product, a library which writes out a table of the integrals of products of pairs of Legendre polynomials with a linear or exponential weight.
  203. legendre_rule, a program which writes out a Gauss-Legendre quadrature rule of given order.
  204. legendre_rule_fast, a program which uses a fast (order N) algorithm to compute a Gauss-Legendre quadrature rule of given order.
  205. lemke, a library which implements Lemke's algorithm for the linear complementarity problem, by Paul Fackler and Mario Miranda.
  206. levels, a library which makes a contour plot, choosing the contour levels using random sampling.
  207. linear_solve_distributed is a program which solves a linear system A*x=b using MATLAB's spmd facility, so that the matrix A is "distributed" across multiple MATLAB workers.
  208. linpack_bench, a program which is the LINPACK benchmark;
  209. linpack_bench_backslash, a program which is the LINPACK benchmark, using MATLAB's builtin "backslash" operator;
  210. linpack_c, a library which constitutes a linear algebra library for single precision complex arithmetic;
  211. linpack_d, a library which constitutes a linear algebra library for double precision real arithmetic;
  212. linpack_s, a library which constitutes a linear algebra library; for single precision real arithmetic;
  213. linplus, a library which factors/solves/multiplies matrices in a variety of formats;
  214. lorenz_simulation, a program which computes and displays solutions of the Lorenz equations for various initial conditions.
  215. lyrics_remote, a program which runs in parallel, using three workers which cooperate "systolically", that is, as through they were on an assembly line. The output from worker 1 is passed to worker 2 for further processing, and so on. This includes instructions on how to run the job, via MATLAB's BATCH facility, on a remote system such as Virginia Tech's ITHACA cluster.
  216. machar, a library which dynamically computes the value of various machine characteristic constants;
  217. machine, a library which returns tabulated values of the constants associated with computer arithmetic
  218. matlab, examples which illustrate the use of MATLAB scripts and M-files;
  219. matlab_commandline, examples which illustrate how MATLAB can be run from the UNIX command line, that is, not with the usual MATLAB command window.
  220. matlab_c, examples which illustrate how C functions can be written, compiled, and called from MATLAB using the MEX facility;
  221. matlab_f77, examples which illustrate how FORTRAN77 functions can be written, compiled, and called from MATLAB using MATLAB's mex facility;
  222. matlab_movies, examples which illustrate making movies using MATLAB;
  223. matlab_os, examples which illustrate how the system command can be used to allow MATLAB to issue commands to the computer operating system (UNIX or DOS);
  224. matlab_parallel, examples which illustrate "local" parallel programming on a single computer with MATLAB's Parallel Computing Toolbox.
  225. md is a program which carries out a molecular dynamics simulation, and is intended as a starting point for implementing a parallel version.
  226. md_parallel is a program which carries out a molecular dynamics simulation; it runs in parallel using MATLAB's "parfor" facility.
  227. md_remote, a program which carries out a molecular dynamics simulation; it runs in parallel using MATLAB's "parfor" facility, and includes instructions on how to run the job, via MATLAB's BATCH facility, on a remote system such as Virginia Tech's ITHACA cluster.
  228. memory_test, a program which tests the memory available on the computer by declaring and using big vectors.
  229. mesh_bandwidth, a program which returns the geometric bandwidth associated with a mesh of elements of any order and in a space of arbitrary dimension.
  230. mesh_display, a program which reads a 2D mesh of elements of any uniform order and displays a plot of the elements and nodes, with optional numbering.
  231. mgmres, a library which applies the restarted GMRES algorithm to a sparse linear system;
  232. mm_io, a library which reads and writes a Matrix Market Sparse Matrix File;
  233. mm_to_hb, a program which reads a Matrix Market sparse matrix file and creates a corresponding HB Harwell Boeing sparse matrix file.
  234. mm_to_msm, a program which reads a Matrix Market sparse matrix file and creates a corresponding MATLAB sparse matrix data structure.
  235. mm_to_st, a program which reads a Matrix Market sparse matrix file and writes a corresponding ST Sparse Triplet file.
  236. msm_to_hb, a program which writes a MATLAB sparse matrix to a Harwell Boeing file;
  237. msm_to_mm, a program which writes a MATLAB sparse matrix to a Matrix Market file;
  238. msm_to_st, a program which writes a MATLAB sparse matrix to a ST Sparse Triplet file;
  239. mxv, a program which compares the performance of (DO I, DO J) loops and (DO J, DO I ) loops for computing the product of an MxN matrix A and an N vector X.
  240. nast2d_contour, a program which reads a data file from NAST2D_F90 and creates a contour plot;
  241. nast2d_streak_display, a program which reads a streakline data file from NAST2D_F90 and displays an image of one time frame;
  242. nast2d_streak_movie, a program which reads a streakline data file from NAST2D_F90 and creates a movie;
  243. ncc_tetrahedron, a library which defines Newton-Cotes closed quadrature rules in a tetrahedron;
  244. ncc_triangle, a library which defines Newton-Cotes closed quadrature rules in a triangle;
  245. nco_tetrahedron, a library which defines Newton-Cotes open quadrature rules in a tetrahedron;
  246. nco_triangle, a library which defines Newton-Cotes open quadrature rules in a triangle;
  247. neighbors_to_metis_graph, a program which reads a file describing the neighbor structure of a tet mesh, and writes a METIS GRAPH file suitable for input to one of the family of programs based on METIS.
  248. nelder_mead, a program which implements the Nelder-Mead algorithm for the minimization of a scalar function of several variables.
  249. nested_sequence_display, a program which displays a set of nested sequences.
  250. netlab, a library which provides tools for simulation with neural networks.
  251. niederreiter2, a library which computes the Niederreiter M-dimensional quasirandom sequence, base 2;
  252. nint_exactness, a program which demonstrates how to test the polynomial exactness of a multidimensional quadrature rule defined over a finite rectangular product region.
  253. nint_exactness_mixed a program which measures the polynomial exactness of a multidimensional quadrature rule based on a mixture of 1D quadrature rule factors.
  254. nint_exactness_pyramid is a program which investigates the polynomial exactness of a quadrature rule for the pyramid.
  255. nint_exactness_tet, a program which tests the polynomial exactness of a quadrature rule for the tetrahedron;
  256. nint_exactness_tri, a program which tests the polynomial exactness of a quadrature rule for the triangle;
  257. nintlib, a library which carries out approximate integration (quadrature) in multiple dimensions;
  258. normal, a library which generates uniform pseudorandom numbers;
  259. ns3d_fem a program which sets up and solves a finite element formulation of the steady incompressible 3D Navier Stokes equations on a user-defined geometry.
  260. obj_display, a program which displays an OBJ 3D graphics file;
  261. obj_io, a library which reads and writes the data in an in an OBJ 3D graphics file;
  262. obj_to_tri_surface, a program which reads an OBJ file, and extracts the surface mesh data as a TRI_SURFACE dataset.
  263. oned, a library which contains functions useful for 1D finite element calculations.
  264. optimal_control_1d, a program which seeks the optimal control function for a one dimensional system which is represented using the finite element formulation;
  265. owens a library which evaluates Owen's T function;
  266. patterson_rule, a program which looks up and writes out a Gauss-Patterson quadrature rule of given order.
  267. pbma_io, a library which reads or writes an ASCII PBM; (Portable Bit Map) image file;
  268. pce_legendre, a program which assembles the system matrix associated with a polynomal chaos expansion of a 2D stochastic PDE, using Legendre polynomials;
  269. pgma_io, a library which reads or writes an ASCII PGM; (Portable Gray Map) image file;
  270. piecewise_linear_product_integral is a library which calculates the exact value of the integral of the product of two piecewise linear functions F(X) and G(X).
  271. ply_io, a library which reads or writes a PLY file.
  272. ply_to_tri_surface, a program which reads a PLY file, and extracts the surface mesh data as a TRI_SURFACE dataset.
  273. points_01_plot, a program which reads an ASCII file containing points in the unit square, and makes an Encapsulated PostScript image;
  274. polking programs, DFIELD5 and PPLANE5, for direction fields and phase planes of differential equations;
  275. polpak a library which evaluates recursively defined polynomials and other special functions;
  276. polygonal_surface_display a program which displays a surface in 3D described as a set of polygons;
  277. power_method a library which carries out the power method for finding a dominant eigenvalue and its eigenvector.
  278. ppma_io a library which reads or writes an ASCII PPM; (Portable Pixel Map) image file;
  279. prime_number is a program which counts the number of primes between 1 and N.
  280. prime_number_parallel is a program which counts the number of primes between 1 and N; it runs in parallel using MATLAB's "parfor" facility.
  281. prime_number_spmd is a program which counts the number of primes between 1 and N; running in parallel using MATLAB's "SPMD" feature.
  282. prob a library which evaluates and samples various probability density functions;
  283. product_factor, a program which creates a multidimensional quadrature rule from a product of distinct 1d quadrature rules;
  284. product_rule a program which creates a multidimensional quadrature rule from a product of identical 1d quadrature rules;
  285. profile a directory of programs which illustrate the use of the MATLAB profile utlity, which monitors the execution of a series of MATLAB commands, and then produces a performance profile report afterwards.
  286. puzzles, executable programs which solve simple puzzles;
  287. pyramid_rule, is a program which computes a quadrature rule for a pyramid.
  288. quad_mesh, a library which handles meshes of quadrilaterals over a 2D region;
  289. quad_mesh_rcm, a program which computes the reverse Cuthill-McKee (RCM) reordering for nodes in a mesh of 4-node quadrilaterals.
  290. quad_spmd is a program which estimates an integral using quadrature; running in parallel using MATLAB's "SPMD" feature.
  291. quad_surface_display, a program which plots piecewise bilinear data associated with a QUAD_SURFACE, that is, a 3D surface defined by a quadrilateral mesh;
  292. quadrature_test a program which reads the definition of a multidimensional quadrature rule from three files, applies the rule to a number of test integrals, and prints the results.
  293. quadrature_test_2d a program which reads the definition of a 2D quadrature rule from three files, applies the rule to a number of test integrals, and prints the results.
  294. quadrule a library which defines quadrature rules for approximating an integral;
  295. quadrule_fast a library which rapidly defines certain quadrature rules for approximating an integral;
  296. quality a library which measures the dispersion of pointsets in M dimensions;
  297. random_data, a library which generates sample points for various probability density functions, geometries, and dimensions;
  298. random_walk_1d_simulation, a program which simulates a random walk in a 1-dimensional region.
  299. random_walk_2d_simulation, a program which simulates a random walk in a 2-dimensional region.
  300. random_walk_3d_simulation, a program which simulates a random walk in a 3-dimensional region.
  301. rcm, a library which applies the reverse Cuthill McKee algorithm for reordering the nodes of a graph, and reducing the bandwidth of a corresponding sparse matrix;
  302. region_sample, a program which returns sample points from a region;
  303. sandia_rules, a library which produces a standard 1D Gauss quadrature rule of Chebyshev, Gegenbauer, generalized Hermite, generalized Laguerre, Hermite, Jacobi, Laguerre, and Legendre types.
  304. sandia_sparse, a library which can produce a multidimensional 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.
  305. satisfiability is a program which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfiability problem.
  306. satisfiability_parallel is a program which carries out a circuit satisfiability search; it runs in parallel using MATLAB's "parfor" facility.
  307. sde, a library which illustrates the properties of stochastic differential equations, and common algorithms for their analysis, by Desmond Higham;
  308. sequence_streak_display, a program which displays a "streak plot" of a numeric sequence;
  309. sgmga, a library which creates sparse grids based on a mixture of 1D quadrature rules, allowing anisotropic weights for each dimension.
  310. sir_simulation is a program which simulates the spread of a disease through a hospital room of M by N beds, using the SIR (Susceptible/Infected/Recovered) model.
  311. sobol, a library which generates elements of the Sobol M-dimensional quasirandom sequence;
  312. sparse, a directory of example programs which illustrate the use of MATLAB's SPARSE matrix utilities;
  313. sparse_grid_cc, a library which creates sparse grids based on Clenshaw-Curtis rules.
  314. sparse_grid_cc_dataset, a program which creates sparse grids based on Clenshaw-Curtis rules.
  315. sparse_grid_closed, a library which creates sparse grids based on closed rules (Clenshaw-Curtis, Newton-Cotes-Closed).
  316. sparse_grid_closed_dataset, a program which creates of a sparse grid dataset based on closed rules (Clenshaw-Curtis, Newton-Cotes-Closed).
  317. sparse_grid_composite, a library which creates sparse grids based on 1D composite rules (currently only of order 1).
  318. sparse_grid_display, a program which reads a file of points on a sparse grid, displays the grid and save the image in a PNG file;
  319. sparse_grid_gl, a library which creates sparse grids based on Gauss-Legendre rules.
  320. sparse_grid_gl_dataset, a program which creates a sparse grid dataset based on Gauss-Legendre rules.
  321. sparse_grid_hermite, a library which creates sparse grids based on Gauss-Hermite rules.
  322. sparse_grid_hermite_dataset, a program which creates a sparse grid dataset based on Gauss-Hermite rules.
  323. sparse_grid_laguerre, a library which creates sparse grids based on Gauss-Laguerre rules.
  324. sparse_grid_laguerre_dataset, a program which creates a sparse grid dataset based on Gauss-Laguerrre rules.
  325. sparse_grid_mixed, a library which creates sparse grids based a mixture of 1D factor rules.
  326. sparse_grid_open, a library which creates sparse grids based on open rules (Fejer 2, Gauss-Patterson, Newton-Cotes-Open).
  327. sparse_grid_open_dataset, a program which creates a sparse grid dataset based on open rules (Fejer 2, Gauss-Patterson, Newton-Cotes-Open).
  328. sparse_grids_display, a program which reads two files of sparse grids, displaying the first with hollow blue dots, the second with solid red dots.
  329. spinterp, a library which carries out piecewise multilinear hierarchical sparse grid interpolation, quadrature and optimization, by Andreas Klimke;
    an earlier version of this software is ACM TOMS Algorithm 847.
  330. spline, a library which interpolates and approximates via splines;
  331. st_io a library which reads and writes sparse linear systems stored in the ST "sparse triplet" Sparse Matrix format.
  332. st_to_hb, a program which converts a sparse matrix file from ST format to HB format (Harwell Boeing format);
  333. st_to_mm, a program which converts a sparse matrix file from ST format to MM format (Matrix Market format);
  334. st_to_msm, a program which reads an ST sparse triplet file and creates a corresponding MATLAB Sparse Matrix.
  335. stla_display, a program which displays an STLA file (ASCII stereolithography 3D graphics file);
  336. stla_io, a library which reads and writes an STLA file (ASCII stereolithography 3D graphics file);
  337. stla_to_tri_surface, a program which reads a STLA file, and extracts the surface mesh data as a TRI_SURFACE dataset.
  338. stla_to_tri_surface_fast, a program which is a faster version of stla_to_tri_surface.
  339. stroud, a library which implements numerical integration over M-dimensional regions, including spheres, toruses and other shapes;
  340. subpak, a library which includes many utility routines;
  341. subset, a library which ranks, unranks, and generates random subsets, combinations, permutations, and so on;
  342. sudoku, a library which handles Sudoku puzzles;
  343. sum_million, a program which sums the integers from 1 to 1,000,000, as a demonstration of how to rate a computer's speed;
  344. svd_basis, a program which applies the singular value decomposition to a collection of data vectors, extracting dominant modes;
  345. svd_demo, a program which demonstrates the calculation of the singular value decomposition and some of its properties;
  346. table_delaunay, a program which reads a TABLE file of N points in 2 dimensions and writes out the Delaunay triangulation;
  347. table_io, a library which reads and writes a simple TABLE file;
  348. table_latinize, a program which reads a TABLE file of N points in M dimensions, adjusts to form a Latin hypercube;
  349. table_merge, a program which reads a TABLE file of N points in M dimensions, removes duplicates or points that are closer than some tolerance, and writes the reduced set of points to a file.
  350. table_quality, a program which reads a TABLE file of N points in M dimensions, in the unit hypercube, and returns estimates of the quality of the point dispersion;
  351. table_read, a program which reads a TABLE file containing comment lines beginning with '#', and a matrix of data, one row per line;
  352. tanh_quad, a library which sets up the tanh quadrature rule;
  353. tanh_sinh_rule, a program which computes and writes out a tanh-sinh quadrature rule of given order.
  354. tcell_flow_display, a library which displays a single velocity field solution for the T cell;
  355. tcell_flow_movie, a library which creates an animation of the velocity solutions for the T cell;
  356. tcell_rom, a program which solves a reduced order model of a finite element solution of the Navier Stokes equations in a "T-Cell" flow region;
  357. tec_io, a library which reads or writes a TEC file containing finite element information;
  358. tec_to_fem, a program which reads a TEC file suitable for display by TECPLOT, extracts the information, and writes a corresponding set of FEM files, three text files describing the finite element model;
  359. templates, a library which carries out the iterative solution of linear systems;
  360. test_con, a library which implements test problems for numerical continuation.
  361. test_int_2d, a library which implements test problems for approximate integration (quadrature) in two dimensions.
  362. test_int_hermite, a library which implements test problems for approximate integration over an infinite interval.
  363. test_int_laguerre, a library which implements test problems for approximate integration over a semi-infinite interval.
  364. test_mat a library which defines a set of test matrices.
  365. test_matrix, a library which defines a set of test matrices and utilities, by Nick Higham;
  366. test_min, a library which implements test problems for minimization of a scalar function of a scalar variable.
  367. test_nint, a library which implements test problems for approximate integration (quadrature) in multiple dimensions.
  368. test_ode, a library which defines some sample ODE's for testing initial value problem solvers;
  369. test_tri_int, a library which implements test functions for integration over a triangle in 2 dimensions.
  370. test_triangulation, a library which defines test problems for triangulation;
  371. test_values, a library which returns selected values of some special functions;
  372. test_zero, a library which defines some functions f(x) suitable for testing software that solves f(x)=0;
  373. testpack a library which defines a set of test integrand functions by Alan Genz.
  374. tet_mesh a library which works with tetrahedral meshes in 3D;
  375. tet_mesh_display, a program which reads data defining a (small) tet mesh, displays a wireframe image of the nodes and edges;
  376. tet_mesh_l2q, a program which reads information about a 4-node (linear) tet mesh and creates data defining a corresponding 10-node (quadratic) tet mesh;
  377. tet_mesh_q2l, a program which reads information about a 10-node (quadratic) tet mesh and creates data defining a corresponding 4-node (linear) tet mesh;
  378. tet_mesh_quality, a program which computes various quality measures for a tet mesh of a set of nodes in 3D;
  379. tet_mesh_rcm, a program which computes the reverse Cuthill-McKee reordering for the nodes of a tet mesh that uses 4-node or 10-node tetrahedrons;
  380. tet_mesh_refine, a program which refines a tet mesh;
  381. tet_mesh_tet_neighbors, a program which reads information about a tet mesh and writes out a list of the tetrahedrons that are adjacent to a given tetrahedron;
  382. tet_mesh_volumes is a program which computes the volume of each tetrahedron in a tet mesh;
  383. tetrahedron_monte_carlo, a program which uses the Monte Carlo method to estimate an integral over a tetrahedron.
  384. tetrahedron_properties, a program which prints out the properties of a tetrahedron whose vertex coordinates are read from a file;
  385. threed, a library which contains functions useful for 3D finite element calculations.
  386. threed_to_tecplot, a program which accepts computational data from a 3D finite element fluid flow program and writes it to a PLT file for postprocessing by TECPLOT.
  387. threed_to_vtk, a program which accepts computational data from a 3D finite element fluid flow program and writes it to a VTK "legacy" file for postprocessing by PARAVIEW.
  388. threed_to_vtu, a program which accepts computational data from a 3D finite element fluid flow program and writes it to a VTK unstructured grid file for postprocessing by PARAVIEW.
  389. threed_to_vu, a program which accepts computational data from a 3D finite element fluid flow program and writes it to a file for postprocessing by VU.
  390. timer, examples which illustrate how to time a piece of code;
  391. timestamp, a library which prints the current YMDHMS date as a timestamp;
  392. timing_parallel is a directory of programs which illustrate how to time a parallel MATLAB program.
  393. toms178 a library which seeks the minimizer of a scalar function of several variables using the Hooke-Jeeves method;
    this is a MATLAB version of ACM TOMS algorithm 178.
  394. toms179 a library which calculates the incomplete Beta ratio;
    this is a MATLAB version of ACM TOMS algorithm 179.
  395. toms291 a library which approximates the logarithm of the Gamma function;
    this is a MATLAB version of ACM TOMS algorithm 291.
  396. toms847, a library which carries out piecewise multilinear hierarchical sparse grid interpolation, commonly known as SPINTERP, by Andreas Klimke;
    this is ACM TOMS Algorithm 847.
  397. toms866 a library which contains the Incompressible Flow Iterative Solution Software (IFISS);
    this is ACM TOMS algorithm 866.
  398. traffic_simulation, a program which simulates the cars waiting to get through a traffic light.
  399. tri_surface_display, a program which displays a triangulated surface;
  400. tri_surface_io, a library which reads and writes the 3D graphics information in a TRI_SURFACE file;
  401. tri_surface_to_obj, a program which reads a TRI_SURFACE dataset and extracts the surface mesh data as an OBJ file.
  402. tri_surface_to_ply, a program which converts a TRI_SURFACE dataset to a dataset suitable for storage as a PLY file.
  403. tri_surface_to_stla, a program which reads a TRI_SURFACE dataset and extracts the surface mesh data as an ASCII STL file.
  404. triangle_histogram, a program which computes histograms of data on the unit triangle.
  405. triangle_monte_carlo, a program which uses the Monte Carlo method to estimate an integral over a triangle.
  406. triangle_properties, a program which computes properties of a triangle whose vertex coordinates are read from a file.
  407. triangulation, a library which computes the triangulation of a set of points in the plane, and to perform various operations using a triangulation;
  408. triangulation_boundary_nodes, a program which reads data defining a triangulation, determines which nodes lie on the boundary, and writes their coordinates to a file;
  409. triangulation_corner, a program which modifies triangulations in which one or more triangles have more than one boundary edge.
  410. triangulation_delaunay_discrepancy is a program which measures the amount by which a triangulation fails the local Delaunay test;
  411. triangulation_display, a program which displays the nodes and elements of a triangulation on the MATLAB graphics screen;
  412. triangulation_histogram, a program which computes histograms of data over a triangulation.
  413. triangulation_l2q, a program which reads information about a 3-node (linear) triangulation and creates data defining a corresponding 6-node (quadratic) triangulation;
  414. triangulation_mask, a program which reads a triangulation and calls a user-supplied routine to consider each triangle for deletion;
  415. triangulation_order1_display, a program which plots piecewise constant data associated with a triangulation;
  416. triangulation_order3_contour, a program which plots color contours of a scalar quantity evaluated at the nodes of a 3-node triangle triangulation.
  417. triangulation_order6_contour, a program which plots color contours of a scalar quantity evaluated at the nodes of a 6-node triangle triangulation.
  418. triangulation_orient, a program which ensures that the triangles in an order 3 or order 6 triangulation have positive orientation;
  419. triangulation_plot, a program which plots the nodes and elements of a triangulation as a PostScript file;
  420. triangulation_q2l, a program which reads information about a 6-node triangulation and creates data defining a corresponding 3-node triangulation;
  421. triangulation_quad, a program which reads information about a triangulation and the value of a function at the nodes and estimates the integral of the function over the triangulated region.
  422. triangulation_quality, a program which reads information about a triangulation and computes various quality measures;
  423. triangulation_rcm, a program which computes the reverse Cuthill-McKee reordering for the nodes of a triangulation that uses 3-node or 6-node triangles;
  424. triangulation_refine, a program which refines a triangulation;
  425. triangulation_t3_to_t4, a program which reads information about a 3-node T3 triangulation and creates data defining a corresponding 4-node T4 triangulation;
  426. triangulation_triangle_neighbors, a program which reads data defining a triangulation, finds the three neighbor triangles for each triangle, and writes them to a file;
  427. tumor, a program which demonstrates a model of tumor growth;
  428. twod, a library which contains functions useful for 2D finite element calculations.
  429. twod_to_vtk, a program which accepts computational data from a 2D finite element fluid flow program and writes it to a VTK "legacy" file for postprocessing by PARAVIEW.
  430. twod_to_vtu, a program which accepts computational data from a 2D finite element fluid flow program and writes it to a VTK unstructured grid file for postprocessing by PARAVIEW.
  431. uniform, a library which computes N elements of a uniform pseudorandom sequence;
  432. uniform_dataset, a program which creates N elements of an M dimensional uniform pseudorandom sequence and writes them to a file.
  433. van_der_corput, a library which computes elements of the van der Corput 1-dimensional quasirandom sequence;
  434. van_der_corput_dataset, a program which creates N elements of a van der Corput sequence and writes them to a file.
  435. vector_magnitude_grid, a program which reads vector data at "scattered" points, computes an interpolatory function, evaluates it on a uniform grid of user-specified density, and produces a contour plot of the vector magnitude.
  436. vector_stream_grid, a program which reads vector data at "scattered" points, computes an interpolatory function, evaluates it on a uniform grid of user-specified density, and produces a streamline plot.
  437. velocity_arrows, a program which reads coordinate data and velocity data from two files and makes an arrow plot of the velocity field.
  438. velocity_arrows_grid, a program which reads node and velocity data, stored in two files, at "scattered" points, and makes a velocity vector plot on a uniform grid of user-specified density.
  439. velocity_arrows_grid_sequence2, a program which reads a single XYUV file of nodes and velocities, interpolates the data onto a smooth grid, plots the data and writes it to a PNG file, and then repeats the process for the next file.
  440. velocity_arrows_grid2, a program which reads node and velocity data, stored in one file, at "scattered" points, and makes a velocity vector plot on a uniform grid of user-specified density.
  441. velocity_arrows_sequence, a program which reads a fixed coordinate data file, and a sequence of velocity data files, and makes a sequence of velocity arrow plots.
  442. velocity_arrows_sequence2, a program which reads a single XYUV file of nodes and velocities, plots the data and writes it to a PNG file, and then repeats the process for the next file.
  443. velocity_arrows2, a program which reads coordinate and velocity data from a single file and makes an arrow plot of the velocity field.
  444. voronoi_mountains, a program which makes a "mountain plot" of a Voronoi diagram, that is, a surface plot of the distance from each point to its nearest Voronoi generator.
  445. wandzura, a library which returns one of 6 Wandzura rules for quadrature in a triangle;
  446. xy_display a program which reads a XY file containing the coordinates of points in 2D, and displays an image in the MATLAB graphics window;
  447. xy_io, a library which reads and writes XY files.
  448. xyf_display is a program which reads XYF information defining points and faces in 2D, and displays an image in the MATLAB graphics window.
  449. xyl_display is a program which reads XYL information defining points and lines in 2D, and displays an image in the MATLAB graphics window.
  450. xyz_display is a program which reads XYZ information defining points in 3D, and displays an image in the MATLAB graphics window.
  451. xyz_io, a library which reads and writes XYZ files.
  452. xyzf_display is a program which reads XYZF information defining points and faces in 3D, and displays an image in the MATLAB graphics window.
  453. xyzl_display is a program which reads XYZL information defining points and lines in 3D, and displays an image in the MATLAB graphics window.
  454. ziggurat, a library which samples the uniform, normal or exponential distributions, using the ziggurat method.

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Last revised on 07 November 2009.