- advection_pde, a MATLAB code which solves the advection partial differential equation (PDE) dudt + c * dudx = 0 in one spatial dimension, with a constant velocity c, and periodic boundary conditions, using the FTCS method, forward time difference, centered space difference.
- advection_pde_test
- allen_cahn_pde, a MATLAB code which sets up and solves the Allen-Cahn reaction-diffusion system of partial differential equations (PDE) in 1 space dimension and time.
- allen_cahn_pde_test
- allen_cahn_pde_etdrk4 a MATLAB code which uses the exponential time differencing (ETD) RK4 method to solve the Allen-Cahn system of stiff ordinary differential equations (ODE), by Aly-Khan Kassam, Lloyd Trefethen.
- allen_cahn_pde_etdrk4_test
- allen_cahn_pde_euler a MATLAB code which uses the Euler method to solve the Allen-Cahn PDE as a system of stiff ordinary differential equations (ODE), by Aly-Khan Kassam, Lloyd Trefethen.
- allen_cahn_pde_euler_test
- alpert_rule, a MATLAB code which sets up an Alpert quadrature rule for functions which are regular, log(x) singular, or 1/sqrt(x) singular.
- alpert_rule_test
- analemma, a MATLAB 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, based on a C program by Brian Tung.
- analemma_test
- anishchenko_ode, a MATLAB code which sets up and solves the Anishchenko ordinary differential equation (ODE), which has chaotic behavior and an attractor.
- anishchenko_ode_test
- annulus_distance, a MATLAB code which estimates the typical distance between a pair of points randomly selected inside a circular annulus.
- annulus_distance_test
- annulus_grid, a MATLAB code which computes a grid of points over the interior of a circular annulus.
- annulus_grid_test
- annulus_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of a circular annulus centered at the origin.
- annulus_integrals_test
- annulus_monte_carlo, a MATLAB 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
- annulus_rule, a MATLAB code which computes a quadrature rule for estimating integrals of a function over the interior of a circular annulus in 2D.
- annulus_rule_test
- aperiodic_tile, a MATLAB code which constructs several steps in the aperiodic tiling of the plane, using the monotile T(1,1), displaying the result graphically, by Henning Voss.
- aperiodic_tile_test
- approx_bernstein, a MATLAB code which interactively approximates a function f(x) in the interval [a,b] by constructing a Bernstein polynomial.
- approx_bernstein_test
- approx_chebyshev, a MATLAB code which interactively approximates a function f(x) in the interval [a,b] by constructing a Chebyshev polynomial interpolant that is often a good estimate of the minmax polynomial.
- approx_chebyshev_test
- approx_leastsquares, a MATLAB code which interactively approximates a function f(x) in the interval [a,b] by constructing an m-degree polynomial which minimizes the square root of the sum of the squares of the error with n sample data points.
- approx_leastsquares_test
- arclength, a MATLAB code which estimates the arclength of curves of the form (x,f(x)) or (x(t),y(t)).
- arclength_test
- arenstorf_ode, a MATLAB code which sets up and solves an ordinary differential equation (ODE) which defines a stable periodic orbit of a spacecraft around the Earth and the Moon.
- arenstorf_ode_test
- args, a function which shows how to count and report command line arguments;
- args_test
- arneodo_ode, a MATLAB code which sets up and solves the Arneodo ordinary differential equation (ODE), which has chaotic behavior and an attractor.
- arneodo_ode_test
- arpack_test, a MATLAB code which calls arpack(), which computes eigenvalues and eigenvectors of large sparse matrices, accessible via the built-in eigs() command;
- artery_pde, a MATLAB code which solves a partial differential equation (PDE) that models the displacement of arterial walls under pressure.
- artery_pde_test
- asa_2011_geometry, a MATLAB code which was used during labs, demonstrations, and lectures associated with the Geometry Algorithms portion of the class Algorithms for Science Applications II, as taught at the Scientific Computing Department, Florida State University, Spring Semester 2011.
- asa_2011_geometry_test
- asa_2011_graphs, a MATLAB code which was used during labs, demonstrations, and lectures associated with the Graph Algorithms portion of the class Algorithms for Science Applications II, as taught at the Scientific Computing Department, Florida State University, Spring Semester 2011.
- asa_2011_images, a MATLAB code which was used during labs, demonstrations, and lectures associated with the Image Algorithms portion of the class Algorithms for Science Applications II, as taught at the Scientific Computing Department, Florida State University, Spring Semester 2011.
- asa005, a MATLAB 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 MATLAB 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 MATLAB 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 MATLAB code which evaluates the incomplete Gamma function, by G Bhattacharjee. This is a version of Applied Statistics Algorithm 32.
- asa032_test
- asa047, a MATLAB 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 MATLAB 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 MATLAB 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 MATLAB 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 MATLAB 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 MATLAB 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 MATLAB 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 MATLAB 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 MATLAB code which evaluates the digamma or psi function, by Jose Bernardo. This is a version of Applied Statistics Algorithm 103.
- asa103_test
- asa109, a MATLAB 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 MATLAB 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 MATLAB 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 MATLAB code which evaluates the trigamma function, by BE Schneider. This is a version of Applied Statistics Algorithm 121.
- asa121_test
- asa136, a MATLAB code which implements a clustering algorithm, by Hartigan and Wong. This is a version of Applied Statistics Algorithm 136.
- asa136_test
- asa144, a MATLAB code which randomly generates an RxC contingency table, by James Boyett. This is a version of Applied Statistics Algorithm 144.
- asa144_test
- asa147, a MATLAB code which evaluates the incomplete Gamma function, by Chi Leung Lau. This is a version of Applied Statistics Algorithm 147.
- asa147_test
- asa152, a MATLAB 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 MATLAB code which randomly generates an RxC contingency table, by Michael Patefield; This is a version of Applied Statistics Algorithm 159.
- asa159_test
- asa172, a MATLAB 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 MATLAB code which implements a random number generator (RNG), by Wichman and Hill. This is a version of Applied Statistics Algorithm 183.
- asa183_test
- asa226, a MATLAB 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 MATLAB code which evaluates the incomplete Gamma function, by Shea. This is a version of Applied Statistics Algorithm 239.
- asa239_test
- asa241, a MATLAB 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 MATLAB 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 MATLAB 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 MATLAB 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 MATLAB 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 MATLAB 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 MATLAB 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 MATLAB code which applies the Atbash substitution cipher to a string of text.
- atbash_test
- atkinson, a MATLAB code which contains examples from the text 'Elementary Numerical Analysis', by Atkinson.
- atkinson_test
- autocatalytic_ode, a MATLAB code which sets up and solves the autocatalytic ordinary differential equation (ODE), which has chaotic behavior and an attractor.
- autocatalytic_ode_test
- axon_ode, a MATLAB code which sets up and solves the ordinary differential equations (ODE) for the Hodgkin-Huxley model of an axon.
- axon_ode_test
- backtrack_binary_rc, a MATLAB code which carries out a backtrack search for a set of binary decisions, using reverse communication (RC).
- backtrack_binary_rc_test
- backward_euler, a MATLAB code which solves one or more ordinary differential equations (ODE) using the (implicit) backward Euler method, using fsolve() for the implicit equation.
- backward_euler_test
- backward_euler_fixed, a MATLAB code which solves one or more ordinary differential equations (ODE) using the (implicit) backward Euler method, using a fixed point iteration for the implicit equation.
- backward_euler_fixed_test
- ball_and_stick_display, a MATLAB code which demonstrates the creation of a 3D ball and stick image;
- ball_and_stick_display_test
- ball_distance, a MATLAB code which computes the expected value of the distance between a pair of points randomly selected from the interior of the unit ball in 3D.
- ball_distance_test
- ball_grid, a MATLAB code which computes a grid of points over the interior of the unit ball in 3D.
- ball_grid_test
- ball_integrals, a MATLAB 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 MATLAB 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
- ball_positive_distance, a MATLAB code which computes the expected value of the distance between a pair of points randomly selected from the interior of the unit positive ball in 3D.
- ball_positive_distance_test
- bank, a MATLAB code which computes the check digit associated with a US Bank Routing Number check digit, or reports whether a 9-digit code is actually valid.
- bank_test
- barycentric_interp_1d, a MATLAB code which defines and evaluates the barycentric Lagrange polynomial p(x) which interpolates a set of data, so that p(x(i)) = y(i). The barycentric approach means that very high degree polynomials can safely be used.
- barycentric_interp_1d_test
- bdf2, a MATLAB 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
- bellman_ford, a MATLAB 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_approximation, a MATLAB code which looks at some simple cases of approximation of a function f(x) by a Bernstein polynomial.
- bernstein_approximation_test
- bernstein_polynomial, a MATLAB code which evaluates the Bernstein polynomials;
- bernstein_polynomial_test
- besselj, a MATLAB code which evaluates Bessel J functions of noninteger order;
- besselj_test
- besselzero, a MATLAB code which computes the zeros of Bessel functions j or y, by Greg van Winckel and Jason Nicholson.
- besselzero_test
- beta_nc, a MATLAB code which evaluates the cumulative density function (CDF) of the noncentral Beta distribution;
- beta_nc_test
- bezier_surface, a MATLAB code which reads, writes, prints and manipulates the data that defines a Bezier surface;
- bezier_surface_test
- bezier_surface_display, a MATLAB code which displays a Bezier surface;
- bezier_surface_display_test
- bicg, a MATLAB code which implements the biconjugate gradient method (BICG), which estimates the solution of a large sparse nonsymmetric linear system.
- bicg_test
- biharmonic_cheby1d, a MATLAB code which uses Chebyshev methods to solve the biharmonic equation over an interval, a fourth order two point boundary value problem (BVP) in one spatial dimension.
- biharmonic_cheby1d_test
- biharmonic_exact, a MATLAB 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
- biharmonic_fd1d, a MATLAB code which applies the finite difference method to solve the biharmonic equation over an interval, a fourth order two point boundary value problem (BVP) in one spatial dimension.
- biharmonic_fd1d_test
- biharmonic_fd2d, a MATLAB code which deals with the biharmonic equation in two dimensions, whose simplest form is uxxxx + 2uxxyy + uyyyy = f.
- biharmonic_fd2d_test
- biochemical_linear_ode, a MATLAB code which sets up and solves a linear biochemical ordinary differential equation (ODE).
- biochemical_linear_ode_test
- biochemical_nonlinear_ode, a MATLAB code which sets up and solves a nonlinear biochemical ordinary differential equation (ODE).
- biochemical_nonlinear_ode_test
- bioconvection_ode, a MATLAB code which approximates solutions to a system of ordinary differential equations (ODE) which model a bioconvection problem, and which are related to the Lorenz system.
- bioconvection_ode_test
- bird_egg, a MATLAB code which evaluates some formulas for the shapes of bird eggs.
- bird_egg_test
- bisection, a MATLAB 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 MATLAB 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 MATLAB 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
- black_scholes, a MATLAB code which implements some simple approaches to the Black-Scholes option valuation theory, by Desmond Higham.
- black_scholes_test
- blend, a MATLAB code which carries out 1D/2D/3D blending interpolation;
- blend_test
- blood_pressure_ode, a MATLAB code which sets up and solves an ordinary differential equation (ODE) which models the variation in blood pressure in the human artery.
- blood_pressure_ode_test
- blowup_ode, a MATLAB code which sets up and solves an ordinary differential equation (ODE) y'=y^2. whose solution "blows up" in finite time.
- blowup_ode_test
- boat, a MATLAB code which considers the boat tiling puzzle, a smaller version of the eternity puzzle. The boat puzzle specifies a region R composed of 756 30-60-90 triangles, and a set of 21 "tiles", each consisting of 36 30-60-90 triangles, and seeks an arrangement of the tiles that exactly covers the region.
- boat_test
- boat_cplex_test a BASH code which calls cplex(), to read the LP file defining the boat tiling problem, solve the linear programming problem, and write the solution to a file.
- boat_gurobi_test a BASH code which calls gurobi(), to read the LP file defining the boat tiling problem, solve the linear programming problem, and write the solution to a file.
- boomerang, a MATLAB code which considers the boomerang tiling puzzle, a smaller version of the eternity puzzle. The puzzle specifies a region R composed of 2376 30-60-90 triangles, and a set of 66 "tiles", each consisting of 36 30-60-90 triangles, and seeks an arrangement of the tiles that exactly covers the region.
- boomerang_test
- boomerang_cplex_test a BASH code which calls cplex(), to read the LP file defining the boomerang tiling problem, solve the linear programming problem, and write the solution to a file.
- boundary_locus, a MATLAB code which uses the boundary locus method to display the region of absolute stability for a solver of ordinary differential equations (ODE).
- boundary_locus_test
- boundary_locus2, a MATLAB code which uses the boundary locus method to plot the boundary of the absolute stability region for a solver of ordinary differential equations (ODE), based on a procedure by Randall Leveque.
- boundary_locus2_test
- boundary_word_drafter, a MATLAB code which describes the outline of an object using a string of symbols that represent the sequence of steps tracing out the boundary, on a grid of drafters, or 30-60-90 triangles. The objects include tiles for the eternity, serenity and trinity puzzles, and the hat and turtle aperiodic monotiles.
- boundary_word_drafter_test
- boundary_word_equilateral, a MATLAB code which describes the outline of an object on a grid of equilateral triangles, using a string of symbols that represent the sequence of steps tracing out the boundary.
- boundary_word_equilateral_test
- boundary_word_hexagon, a MATLAB code which describes the outline of an object on a grid of hexagons, using a string of symbols that represent the sequence of steps tracing out the boundary.
- boundary_word_hexagon_test
- boundary_word_right, a MATLAB code which describes the outline of an object on a grid of isoceles right triangles, using a string of symbols that represent the sequence of steps tracing out the boundary.
- boundary_word_right_test
- boundary_word_square, a MATLAB code which describes the outline of an object on a grid of squares, using a string of symbols that represent the sequence of steps tracing out the boundary.
- boundary_word_square_test
- box_behnken, a MATLAB code which computes a Box-Behnken design, that is, a set of arguments to sample the behavior of a function of multiple parameters;
- box_behnken_test
- box_display, a MATLAB code which displays a box plot, over integer pairs of data, of a function defined by two formulas.
- box_display_test
- box_distance, a MATLAB code which estimates the distribution and expected value of the distance between two points picked uniformly at random within a 3D box.
- box_distance_test
- box_flow, a MATLAB code which solves the Navier Stokes equations (NSE), replacing the continuity equation with a pressure Poisson equation (PPE), by John Cornthwaite.
- box_flow_test
- box_games, a MATLAB code which assists in the display of game boards (checkers, cellular automatons, Conway's game of life);
- box_games_test
- box_plot, a MATLAB code which displays a box plot of data that consists of pairs of integers;
- box_plot_test
- brownian_motion_simulation, a MATLAB code which simulates Brownian motion in an M dimensional region.
- brownian_motion_simulation_test
- broyden, a MATLAB code which implements the Broyden iterative method for nonlinear equations, by Tim Kelley.
- broyden_test
- brusselator_ode, a MATLAB code which sets up and solves the Brusselator ordinary differential equation (ODE) system.
- brusselator_ode_test
- buckling_spring, a MATLAB code which plots solutions of the buckling spring equations.
- buckling_spring_test
- burgers_pde_etdrk4, a MATLAB code which uses the exponential time differencing (ETD) RK4 method to solve the Burgers PDE as a system of stiff ordinary differential equations (ODE), by Aly-Khan Kassam, Lloyd Trefethen.
- burgers_pde_etdrk4_test
- burgers_exact, a MATLAB code which evaluates exact solutions of the time-dependent 1D viscous Burgers equation.
- burgers_exact_test
- burgers_steady_viscous, a MATLAB code which solves the steady (time-independent) viscous Burgers equation using the finite difference method (FDM) applied to the conservative form of the equation, using the Newton method to solve the resulting nonlinear system.
- burgers_steady_viscous_test
- burgers_time_inviscid, a MATLAB code which solves the time-dependent inviscid Burgers equation using the finite difference method (FDM), and one of six solution methods.
- burgers_time_inviscid_test
- burgers_time_viscous, a MATLAB code which solves the time-dependent viscous Burgers equation using the finite difference method (FDM) applied to the conservative form of the equation.
- burgers_time_viscous_test
- bvec, a MATLAB code which demonstrates how signed integers can be stored as binary vectors, and arithmetic can be performed on them.
- bvec_test
- bvp_fd, a MATLAB code which demonstrates the use of the finite difference method (FDM) to solve a boundary value problem (BVP).
- bvp_fd_test
- bvp_shooting_test, a MATLAB code which demonstrates the use of the shooting method to solve a boundary value problem (BVP).
- bvp4c_test, a MATLAB code which calls bvp4c(), which solves boundary value problems (BVP) in one spatial dimension.
- bwlabel_test, a MATLAB code which calls bwlabel(), which is given a binary matrix, and organizes the 1 values into labeled clusters, using 4-way or 8-way connectivity.
- c8lib, a MATLAB code which implements certain elementary functions for complex 64 bit ("C8") variables;
- c8lib_test
- caesar, a MATLAB code which applies a Caesar Shift Cipher to a string of text.
- caesar_test
- calpak, a MATLAB 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 MATLAB 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
- capacitor_2d_test, a MATLAB code which plots data from a model of a 2D capacitor, computed by FreeFem++() and transferred using the ffmatlib() library.
- capacitor_3d_test, a MATLAB code which plots data from a model of a 3D capacitor, computed by FreeFem++() and transferred using the ffmatlib() library.
- casino_simulation, a MATLAB code which simulates a casino game that gives you 20% of your bet for heads, and only takes 17% for tails. How much will you end up winning?
- casino_simulation_test
- cauchy_method, a MATLAB code which solves one or more ordinary differential equations (ODE) using the Cauchy method.
- cauchy_method_test
- cauchy_principal_value, a MATLAB code which uses Gauss-Legendre quadrature to estimate the Cauchy Principal Value (CPV) of certain singular integrals.
- cauchy_principal_value_test
- caustic, a MATLAB code which generates an image of a caustic, by drawing n equally spaced points in a circle, and then connecting specific pairs of points using a spacing parameter m.
- caustic_test
- cavity_flow_display, a MATLAB code which displays a single velocity field solution for the driven cavity;
- cavity_flow_display_test
- cavity_flow_movie, a MATLAB code which animates the velocity solutions for the driven cavity;
- cavity_flow_movie_test
- cc_display, a MATLAB code which displays the points used in a 2D Clenshaw-Curtis quadrature rule;
- cc_display_test
- ccl_test, a MATLAB code which estimates the Lebesgue constants for sets of points in [-1,+1] computed in several ways. The program is probably of limited interest except as an example of an application of the lebesgue_constant() function.
- ccn_rule, a MATLAB code which defines a Clenshaw Curtis Nested (CCN) quadrature rule.
- ccn_rule_test
- ccs_io a MATLAB code which reads and writes sparse linear systems stored in the Compressed Column Storage (CCS) format.
- ccs_io_test
- ccs_to_st a MATLAB code which converts a sparse matrix from Compressed Column Storage (CCS) to sparse triplet (ST) format.
- ccs_to_st_test
- ccvt_reflect, a MATLAB code which calculates a Constrained Centroidal Voronoi Tessellation (CCVT) for points constrained to lie in a box, with some points pushed towards the boundary;
- ccvt_reflect_test
- cellular_automaton, a MATLAB code which prints or plots the evolution of Cellular Automaton rule #30.
- cellular_automaton_test
- cg, a MATLAB 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 symmetric positive definite (SPD).
- cg_test
- cg_lab_triangles, a collection of programs associated with a computer lab assignment on computational geometry and triangles;
- cg_lab_triangles_test
- cg_ne, a MATLAB code which implements the conjugate gradient method (CG) for the normal equations, where the matrix A is not symmetric positive definite (SPD). In this case, it is attempted to set up and solve the normal equations A'*A*x=A'*b.
- cg_ne_test
- cg_rc, a MATLAB code which implements the conjugate gradient (CG) method for solving a symmetric positive definite (SPD) sparse linear system A*x=b, using reverse communication (RC).
- cg_rc_test
- cg_squared, a MATLAB code which implements the conjugate gradient squared (CGS) method for solving a nonsymmetric sparse linear system A*x=b.
- cg_squared_test
- chain_letter_tree, a MATLAB code which analyzes a similarity matrix for 11 versions of a single chain letter and produces a dendrogram or tree diagram that suggests the degrees of relatedness and the evolutionary history of the letters.
- change_diophantine, a MATLAB code which sets up a Diophantine equation to solve the change making problem, which counts the number of ways a given sum can be formed using coins of various denominations.
- change_diophantine_test
- change_dynamic, a MATLAB 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
- change_greedy, a MATLAB code which uses the greedy method to seek a solution to the change making problem, which tries to match a given amount by selecting coins of various denominations.
- change_greedy_test
- change_polynomial, a MATLAB code which uses a polynomial multiplication algorithm to count the ways of making various sums using a given number of coins.
- change_polynomial_test
- chebyshev, a MATLAB code which computes the Chebyshev interpolant/approximant to a given function over an interval.
- chebyshev_test
- chebyshev_interp_1d, a MATLAB code which determines the combination of Chebyshev polynomials which interpolates a set of data, so that p(x(i)) = y(i).
- chebyshev_interp_1d_test
- chebyshev_matrix, a MATLAB code which defines the Chebyshev differentiation matrix, by Lloyd Trefethen.
- chebyshev_matrix_test
- chebyshev_polynomial, a MATLAB code which considers the Chebyshev polynomials T(i,x), U(i,x), V(i,x) and W(i,x).
- chebyshev_polynomial_test
- chebyshev_series, a MATLAB code which evaluates a Chebyshev series approximating a function f(x), while efficiently computing one, two, three or four derivatives of the series, by Manfred Zimmer.
- chebyshev_series_test
- chebyshev1_exactness, a MATLAB code which tests the polynomial exactness of Gauss-Chebyshev type 1 quadrature rules.
- chebyshev1_exactness_test
- chebyshev1_rule, a MATLAB code which computes and writes out a Gauss-Chebyshev type 1 quadrature rule of given order.
- chebyshev1_rule_test
- chebyshev2_exactness, a MATLAB code which tests the polynomial exactness of Gauss-Chebyshev type 2 quadrature rules.
- chebyshev2_exactness_test
- chebyshev2_rule, a MATLAB code which computes and writes out a Gauss-Chebyshev type 2 quadrature rule of given order.
- chebyshev2_rule_test
- chen_ode, a MATLAB code which sets up and solves the Chen system of ordinary differential equations (ODE).
- chen_ode_test
- cheney_kincaid, a MATLAB code which contains examples from the text 'Numerical Mathematics and Computing', by Cheney and Kincaid.
- cheney_kincaid_test
- chinese_remainder_theorem, a MATLAB code which demonstrates the Chinese remainder theorem, for reconstructing a number based on its remainders against a set of bases.
- chinese_remainder_theorem_test
- chirikov_iteration, a MATLAB code which applies the Chirikov map repeatedly to a given (x,y) initial condition.
- chirikov_iteration_test
- chladni_figures, a MATLAB code which creates Chladni figures of the eigenmodes of a thin vibrating plate, by Martin Gander and Felix Kwok.
- chladni_figures_test
- chrominoes, a MATLAB code which searches for tilings of a polygonal region using polyominoes, in which a coloring scheme is used to reduce the problem size and quickly eliminate certain arrangements.
- chrominoes_test
- chrpak, a MATLAB code which manipulates characters and strings;
- chrpak_test
- chuckaluck_simulation, a MATLAB code which simulates the Chuck-a-Luck gambling game.
- chuckaluck_simulation_test
- circle_arc_grid, a MATLAB code which computes grid points along a circular arc.
- circle_arc_grid_test
- circle_distance, a MATLAB code which computes the expected value of the distance between a pair of points randomly selected on the circumference of the unit circle in 2D.
- circle_distance_test
- circle_grid_display a MATLAB code which reads a matrix of integers, and draws a corresponding grid of circles filled with color.
- circle_grid_display_test
- circle_integrals, a MATLAB 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_map, a MATLAB code which illustrates how a matrix maps points on the unit circle to an ellipse.
- circle_map_test
- circle_monte_carlo, a MATLAB 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_positive_distance, a MATLAB code which estimates the mean and variance of the distance between a random pair of points on the circumference of the unit positive circle in 2D.
- circle_positive_distance_test
- circle_rule, a MATLAB code which computes quadrature rules for the unit circle in 2D, to approximate integrals of f(x,y) over the circumference of the circle of radius 1 and center (0,0).
- circle_rule_test
- circle_segment, a MATLAB code which carries out computations associated with a circle segment, including height, angle, area, centroid, sampling, and quadrature.
- circle_segment_test
- circles, a MATLAB code which draws one or more circles, while controlling the center locations, radii, colors, edge colors, and transparency, by Chad Greene.
- circles_test
- cities, a MATLAB code which works with city-to-city distance matrices;
- cities_test
- clausen, a MATLAB code which evaluates a Chebyshev interpolant to the Clausen function Cl2(x).
- clausen_test
- clenshaw_curtis_rule, a MATLAB code which implements a Clenshaw Curtis quadrature rule;
- clenshaw_curtis_rule_test
- clock_solitaire_simulation, a MATLAB code which simulates the game of clock solitaire. The deck is dealt into 13 piles of 4 cards each. Repeatedly, the top card a pile is removed, and its rank indicates the next pile to consider. Game continues until an empty pile is reached. The game is won if all piles are empty. The quantity of interest is the probability of winning.
- clock_solitaire_simulation_test
- closest_pair_brute, a MATLAB 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
- cnoise, a MATLAB code which generates samples of noise obeying a 1/f^alpha power law, by Miroslav Stoyanov.
- cnoise_test
- cobweb_plot, a MATLAB code which displays a cobweb plot illustrating the process of function iteration.
- cobweb_plot_test
- coin_simulation, a MATLAB code which looks at ways of simulating or visualizing the results of many tosses of a fair or biased coin.
- coin_simulation_test
- collatz, a MATLAB code which computes and analyzes the Collatz sequence, also known as the hailstone sequence or 3n+1 sequence;
- collatz_test
- collatz_parfor, a MATLAB code using the parfor() statement for parallel execution, to find the longest Collatz sequence in the range 1 through N.
- collatz_parfor_test
- collatz_polynomial, a MATLAB code which implements the Collatz polynomial iteration, a polynomial analog of the numerical iteration that is also known as the 3n+1 conjecture or the hailstone sequence.
- collatz_polynomial_test
- collatz_recursive, a MATLAB code which demonstrates recursive programming by considering the simple Collatz 3n+1 problem.
- collatz_recursive_test
- collocation, a MATLAB code which demonstrates the use of collocation to produce a function g(x) that satisfies the same constraints as a function f(x), but only at a discrete set of points.
- collocation_test
- colored_noise, a MATLAB code which generates samples of noise obeying a 1/f^alpha power law.
- colored_noise_test
- combo, a MATLAB 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
- companion_matrix, a MATLAB 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 MATLAB 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 MATLAB code which demonstrates some of the features of using complex numbers.
- components, a MATLAB 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 MATLAB code which implements methods of computing or estimating the condition number of a matrix.
- condition_test
- conservation_ode, a MATLAB code which monitors the conservation of a quantity that should be constant, during the solution of an ordinary differential equation (ODE).
- conservation_ode_test
- conte_deboor, a MATLAB code which contains examples from the text 'Elementary Numerical Analysis' by Conte and deBoor.
- conte_deboor_test
- continuation, a MATLAB code which implements the continuation method for a simple 2D problem, involving finding a point on the unit circle, and then finding a sequence of nearby points that trace out the full curve, using only the information available in the implicit definition of the curve from the function f(x,y)=x^2+y^2-1.
- continuation_test
- continued_fraction a MATLAB code which implements some simple algorithms for dealing with simple and generalized continued fractions.
- continued_fraction_test
- contour_gradient, a MATLAB code which displays contours and gradient vectors for a function f(x,y).
- contour_gradient_test
- contour_gradient_3d, a MATLAB code which displays contours and gradient vectors for a function f(x,y) in a 3D display.
- contour_gradient_3d_test
- contour_sequence4, a MATLAB code which creates images suitable for animation from one XY file and a sequence of u(x,y) data files;
- contour_sequence4_test
- control_bio, a MATLAB code which optimizes a given cost functional of a biological model using optimal control, based on work by Suzanne Lenhart and John Workman.
- control_bio_test
- convective_rolls_test, a MATLAB code which plots data describing the convective rolling behavior of a fluid being heated from below, as computed by FreeFem++() and transferred using the ffmatlib() library.
- convective_rolls_movie_test, a MATLAB code which animates data describing the convective rolling behavior of a fluid being heated from below, as computed by FreeFem++() and transferred using the ffmatlib() library.
- convhull_test, a MATLAB code which demonstrates the use of the built-in function convhull() for the computation of the convex hull of a set of 2D points.
- coordinate_search, a MATLAB code which seeks the minimizer of a scalar function of several variables, by Jeff Borggaard.
- coordinate_search_test
- cordic, a MATLAB code which computes a few special functions using the CORDIC algorithm.
- cordic_test
- correlation, a MATLAB code which contains statistical correlation functions.
- correlation_test
- cosine_transform, a MATLAB code which demonstrates some simple properties of the discrete cosine transform (DCT).
- cosine_transform_test
- counterfeit_detection, a MATLAB code which considers problems in which one or more counterfeit coins are to be identified by the fact that they do not have the standard weight.
- counterfeit_detection_test
- cplex_solution_read, a MATLAB code which extracts solution data from a cplex() result file.
- cplex_solution_read_test
- cpr, a MATLAB code which implements the Chebyshev Proxy Rootfinder (CPR) to locate all the real zeros of a smooth real function f(x) within an interval [a,b], by John Boyd.
- cpr_test
- craps_simulation, a MATLAB code which simulates the gambling game of craps, in which a player rolls two dice. On the first roll, the player wins immediately if a 7 or 11 is rolled, and loses immediately if a 2, 3 or 12 is rolled. Otherwise, the sum of the dice on this first roll is called the point. The player now continues to roll the dice, winning if the point is rolled again, and losing if a 7 is rolled.
- craps_simulation_test
- crs_io, a MATLAB code which reads and writes sparse linear systems stored in the Compressed Row Storage (CRS) format.
- crs_io_test
- cube_arbq_rule, a MATLAB code which returns quadrature rules, with exactness up to total degree 15, over the interior of the symmetric cube in 3D, by Hong Xiao and Zydrunas Gimbutas.
- cube_arbq_rule_test
- cube_distance, a MATLAB code which computes the expected value of the distance between a pair of points randomly selected in the interior of the unit cube in 3D.
- cube_distance_test
- cube_exactness, a MATLAB code which investigates the polynomial exactness of quadrature rules over the interior of a cube in 3D.
- cube_exactness_test
- cube_felippa_rule, a MATLAB code which returns a Felippa quadrature rule for approximating integrals over the interior of a cube in 3D.
- cube_felippa_rule_test
- cube_grid, a MATLAB code which computes a grid of points over the interior of a cube in 3D.
- cube_grid_test
- cube_integrals, a MATLAB 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 MATLAB 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
- cube_surface_distance, a MATLAB code which estimates the expected value of the distance between a pair of points randomly selected on the surface of the unit cube.
- cube_surface_distance_test
- cuda_loop, a MATLAB 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 MATLAB code which computes an N-point Centroidal Voronoi Tessellation (CVT) in M dimensions;
- cvt_test
- cvt_1_movie, a MATLAB code which creates a movie of the evolution of a Centroidal Voronoi Tessellation (CVT) in the unit square;
- cvt_1_movie_test
- cvt_2_movie, a MATLAB code which animates the generation of a Centroidal Voronoi Tessellation (CVT) in the unit square, which includes a random "rebirth" at every iteration.
- cvt_2_movie_test
- cvt_3_movie, a MATLAB code which animates the generation of a Centroidal Voronoi Tessellation (CVT) for the "holey pie" region.
- cvt_3_movie_test
- cvt_4_movie, a MATLAB code which creates a Centroidal Voronoi Tessellation (CVT) movie in the unit square, with a density function that drives points to the corners;
- cvt_4_movie_test
- cvt_1d_lloyd, a MATLAB code which computes an N-point Centroidal Voronoi Tessellation (CVT) within the interval [0,1], under a uniform density, using the Lloyd method to compute the Voronoi regions exactly.
- cvt_1d_lloyd_test
- cvt_1d_lumping, a MATLAB code which allows the user to carry out a lumped version of the Lloyd iterative algorithm for a centroidal Voronoi Tessellation (CVT() in the interval [-1,+1], and is applied to investigate a relationship between a CVT and the Chebyshev Zero nodes.
- cvt_1d_lumping_test
- cvt_1d_nonuniform, a MATLAB code which computes an N-point Centroidal Voronoi Tessellation (CVT) in 1 dimension, under a nonuniform density, and plots the evolution of the locations of the generators during the iteration;
- cvt_1d_nonuniform_test
- cvt_1d_sampling, a MATLAB code which computes an N-point Centroidal Voronoi Tessellation (CVT) within the interval [0,1], under a uniform density, using sampling to estimate the Voronoi regions.
- cvt_1d_sampling_test
- cvt_2d_lumping, a MATLAB code which computes an N-point Centroidal Voronoi Tessellation (CVT) within the unit square [-1,1]^2, under a Chebyshev density, using weighted sampling (lumping) to estimate the Voronoi regions.
- cvt_2d_lumping_test
- cvt_2d_sampling, a MATLAB code which computes an N-point Centroidal Voronoi Tessellation (CVT) within the unit square [0,1]x[0,1], under a uniform density, using sampling to estimate the Voronoi regions.
- cvt_2d_sampling_test
- cvt_3d_lumping, a MATLAB code which computes an N-point Centroidal Voronoi Tessellation (CVT) within the unit cube [-1,1]^3, under a Chebyshev density, using weighted sampling (lumping) to estimate the Voronoi regions.
- cvt_3d_lumping_test
- cvt_3d_sampling, a MATLAB code which computes an N-point Centroidal Voronoi Tessellation (CVT) within the unit cube [0,1]^3, under a uniform density, using sampling to estimate the Voronoi regions.
- cvt_3d_sampling_test
- cvt_basic, a MATLAB code which calculates a Centroidal Voronoi Tessellation (CVT) in a square with uniform density. It is intended as an introduction to the cvt_square_uniform() code.
- cvt_basic_test
- cvt_circle_nonuniform, a MATLAB code which demonstrates the computation of a centroidal Voronoi Tessellation (CVT) over a circular region, using a nonuniform density.
- cvt_circle_nonuniform_test
- cvt_circle_uniform, a MATLAB code which computes a centroidal Voronoi Tessellation (CVT) over a circular region, using a uniform density.
- cvt_circle_uniform_test
- cvt_corn, a MATLAB code which studies a 2D model of the growth of a corn kernel, by treating the surface and interior biological cells as points to be organized by a Centroidal Voronoi Tessellation (CVT) with a nonuniform density; during a sequence of growth steps, new biological cells are randomly added to the surface and interior.
- cvt_corn_test
- cvt_corn_movie, a MATLAB code which makes a movie in which the growth of a corn kernel is simulated using a Centroidal Voronoi Tessellation (CVT).
- cvt_corn_movie_test
- cvt_ellipse_uniform, a MATLAB code which iteratively calculates a Centroidal Voronoi Tessellation (CVT) over an ellipse, with a uniform density.
- cvt_ellipse_uniform_test
- cvt_square_nonuniform, a MATLAB code which iteratively calculates a Centroidal Voronoi Tessellation (CVT) over a square, with a nonuniform density.
- cvt_square_nonuniform_test
- cvt_square_pdf_discrete, a MATLAB code which iteratively calculates a Centroidal Voronoi Tessellation (CVT) over a square, with a density determined from a discrete PDF.
- cvt_square_pdf_discrete_test
- cvt_square_uniform, a MATLAB code which iteratively calculates a Centroidal Voronoi Tessellation (CVT) over a square, with a uniform density.
- cvt_square_uniform_test
- cvt_triangle_uniform, a MATLAB code which iteratively calculates a Centroidal Voronoi Tessellation (CVT) over a triangle, with a uniform density.
- cvt_triangle_uniform_test
- cvtm_1d, a MATLAB code which estimates a mirror-periodic centroidal Voronoi Tessellation (CVTM) in the periodic interval [0,1], using a version of the Lloyd iteration.
- cvtm_1d_test
- cvtp, a MATLAB code which creates a periodic Centroidal Voronoi Tessellation (CVTP).
- cvtp_test
- cvtp_1d, a MATLAB code which estimates a periodic centroidal Voronoi Tessellation (CVTP) in the periodic interval [0,1], using a version of the Lloyd iteration.
- cvtp_1d_test
- cycle_brent, a MATLAB code which carries out an iterated function evaluation, and seeks to determine the nearest element of a cycle, and the cycle length, using the Brent method.
- cycle_brent_test
- cycle_floyd, a MATLAB code which carries out an iterated function evaluation, and seeks to determine the nearest element of a cycle, and the cycle length, using the Floyd method.
- cycle_floyd_test
- cyclic_reduction, a MATLAB code which solves a tridiagonal linear system using cyclic reduction;
- cyclic_reduction_test
- delaunay_test, a MATLAB code which calls the built-in delaunay() function, which computes the Delaunay triangulation of a set of points.
- delsq, a MATLAB code which is given a grid G, and returns a corresponding sparse matrix D that defines the Laplacian operator on G. MATLAB includes a built-in version of this function.
- delsq_test
- dfield9, a MATLAB code which allows a user to interactively specify the right hand side of an ordinary differential equation (ODE). The program then displays the corresponding direction field. If the user clicks on any point in the image as an initial condition, the program displays the corresponding solution curve. The original version of this code was by John Polking.
- dg1d_advection, a MATLAB code which uses the Discontinuous Galerkin Method (DG) to approximate a solution of the advection equation. The original version of the code was written by Jan Hesthaven and Tim Warburton.
- dg1d_advection_test
- dg1d_burgers, a MATLAB code which uses the Discontinuous Galerkin Method (DG) to approximate a solution of the unsteady 1D Burgers equation. The original version of the code was written by Jan Hesthaven and Tim Warburton.
- dg1d_burgers_test
- dg1d_heat, a MATLAB code which uses the Discontinuous Galerkin Method (DG) to approximate a solution of the unsteady 1D heat equation. The original version of the code was written by Jan Hesthaven and Tim Warburton.
- dg1d_heat_test
- dg1d_maxwell, a MATLAB code which uses the Discontinuous Galerkin Method (DG) to approximate a solution of the Maxwell equations. The original version of the code was written by Jan Hesthaven and Tim Warburton.
- dg1d_maxwell_test
- dg1d_poisson, a MATLAB code which applies the discontinuous Galerkin method (DG) to a 1D version of the Poisson equation; the original version of the code was written by Beatrice Riviere.
- dg1d_poisson_test
- diaphony, a MATLAB code which reads a file of N points in M dimensions and computes its diaphony, a measure of point dispersion.
- diaphony_test
- dice_simulation, a MATLAB code which simulates N tosses of M dice, making a histogram of the resulting sums.
- dice_simulation_test
- dictionary_code, a MATLAB code which demonstates how a text file can be compressed and decompressed using a dictionary code.
- dictionary_code_test
- diff_test, a MATLAB code which calls diff(), which computes differences in a vector of data, which can be scaled to estimate derivatives of equally spaced data.
- diff_center, a MATLAB code which interactively uses centered differences to estimate the derivative of a function f(x), using a stepsize h.
- diff_center_test
- diff_forward, a MATLAB code which interactively uses forward differences to estimate the derivative of a function f(x), using a stepsize h.
- diff_forward_test
- diff2_center, a MATLAB code which interactively uses centered differences to estimate the second derivative of a function f(x), using a stepsize h.
- diff2_center_test
- differ, a MATLAB code which determines the finite difference method (FDM) coefficients to combine function values at known locations to compute an approximation of given accuracy to a derivative of a given order.
- differ_test
- diffusion_pde, a MATLAB code which solves the diffusion partial differential equation (PDE) dudt - mu * d2udx2 = 0 in one spatial dimension, with a constant diffusion coefficient mu, and periodic boundary conditions, using the forward time, centered space (FTCS) difference method.
- diffusion_pde_test
- digital_dice, a MATLAB code which carries out the probability simulations described in "Digital Dice", by Paul Nahin;
- digital_dice_test
- dijkstra, a MATLAB code which implements a simple version of the Dijkstra minimum distance algorithm for graphs.
- dijkstra_test
- diophantine, a MATLAB code which finds one solution of a Diophantine equation in any number of variables.
- diophantine_test
- diophantine_nd, a MATLAB code which is given a Diophantine equation in N variables, and returns all nonnegative solutions, or all strictly positive solutions.
- diophantine_nd_doc
- diophantine_nd_test
- discrete_pdf_sample_2d, a MATLAB 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_distance, a MATLAB code which computes the expected value of the distance between a pair of points randomly selected from the interior of the unit disk in 2D.
- disk_distance_test
- disk_grid, a MATLAB 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_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of a disk of radius R centered at the origin.
- disk_integrals_test
- disk_monte_carlo, a MATLAB code which applies a Monte Carlo method to estimate integrals of a function over the interior of a disk of radius R centered at the origin.
- disk_monte_carlo_test
- disk_positive_distance, a MATLAB code which computes the expected value of the distance between a pair of points randomly selected from the interior of the unit positive disk in 2D.
- disk_positive_distance_test
- disk_rule, a MATLAB code which computes quadrature rules for the general disk in 2D.
- disk_rule_test
- disk01_integrals, a MATLAB 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_integrands, a MATLAB code which defines several test integrals over the unit disk, making it possible to check the accuracy of quadrature rules.
- disk01_integrands_test
- disk01_monte_carlo, a MATLAB 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_rule, a MATLAB code which computes quadrature rules for the unit disk in 2D.
- disk01_rule_test
- disk01_positive_monte_carlo, a MATLAB 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
- disk01_positive_rule, a MATLAB code which computes quadrature rules for the unit positive disk in 2D.
- disk01_positive_rule_test
- dist_plot, a MATLAB code which makes contour plots of the distance function, as defined and used in Persson and Strang's distmesh() code;
- dist_plot_test
- distance_to_position, a MATLAB code which estimates the positions of cities which minimizes the discrepancy with a city-to-city distance table.
- distance_to_position_test
- distance_to_position_sphere, a MATLAB code which estimates the positions of cities on a sphere (such as the earth) based on a city-to-city distance table.
- distance_to_position_sphere_test
- distmesh, a MATLAB code which carries out a method of mesh generation; by Per-Olof Persson and Gilbert Strang.
- distmesh_test
- distmesh_3d, a MATLAB code which carries out a method of mesh generation in 3D, by Per-Olof Persson and Gilbert Strang.
- distmesh_3d_test
- divdif, a MATLAB code which uses divided differences to compute the polynomial interpolant to a given set of data.
- divdif_test
- doomsday, a MATLAB 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
- dosage_ode, a MATLAB code which sets up and solves a system of ordinary differential equations (ODE) to simulate the blood levels of a medicinal drug that should stay between medicinal and toxic limits.
- dosage_ode_test
- dot_l2, a MATLAB code which interactively estimates the L2 dot product of two functions: dot_l2(f(x),g(x))_= integral ( a <= x <= b ) f(x) g(x) dx
- dot_l2_test
- double_c_data, a MATLAB code which generates, plots and writes out 2D data that forms two interlocking "C" shapes.
- double_c_data_test
- double_well_ode, a MATLAB code which sets up and solves an ordinary differential equation (ODE) which models the motion of a particle in a double well potential.
- double_well_ode_test
- dream, a MATLAB 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 MATLAB code which simulates N repetitions of a duel between two players, each of whom has a known firing accuracy.
- duel_simulation_test
- dueling_idiots, a MATLAB code which carries out the probability simulations described in "Dueling Idiots", by Paul Nahin;
- dueling_idiots_test
- duffing_ode, a MATLAB code which sets up and solves a second-order ordinary differential equation (ODE) whose solution can exhibit chaotic behavior.
- duffing_ode_test
- e_spigot, a MATLAB code which produces any number of digits of the decimal expansion of e.
- e_spigot_test
- earth_sphere, a MATLAB code which displays a 3D image of the earth, including oceans, continents, and topography, by Clay Thompson and Will Campbell.
- earth_sphere_test
- edge, a MATLAB code which defines some test functions in 1D, 2D and 3D for the detection of edges or discontinuities.
- edge_test
- eigenfaces, a MATLAB code which applies principal component analysis (PCA) to a set of images.
- eigenfaces_test
- eigs_test, a MATLAB code which calls eigs(), which is a built-in system function which computes the eigenvalues and eigenvectors of a matrix.
- elfun, a MATLAB code which evaluates elliptic integrals, include Bulirsch's integrals cel(), cel1(), cel2(), cel3(), Carlson integrals rc(), rd(), rf(), rg(), rj(), and Jacobi functions cn(), dn(), sn(), by Milan Batista.
- elfun_test
- ellipse, a MATLAB 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_distance, a MATLAB code which computes the expected value of the distance between a pair of points randomly selected on the circumference of the ellipse (x/a)^2+(y/b)^2=1 in 2D.
- ellipse_distance_test
- ellipse_grid, a MATLAB code which computes a grid of points over the interior of an ellipse in 2D.
- ellipse_grid_test
- ellipse_monte_carlo, a MATLAB 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 MATLAB code which carries out geometric calculations for ellipsoids, including area, random sampling, and volume.
- ellipsoid_test
- ellipsoid_grid, a MATLAB code which computes a grid of points over the interior of an ellipsoid in 3D.
- ellipsoid_grid_test
- ellipsoid_monte_carlo, a MATLAB 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 MATLAB code which evaluates complete elliptic integrals of first, second and third kind, using the Carlson elliptic integral functions.
- elliptic_integral_test
- epicycloid, a MATLAB code which computes, plots and tabulates an epicycloid curve.
- epicycloid_test
- equidistribution, investigates equidistribution properties relating to density functions and point sets.
- equidistribution_test
- eros, a MATLAB code which implements elementary row operations (EROs) for the interactive solution of a system of linear equations.
- eros_test
- errors, a MATLAB code which illustrates the failure of numerical algorithms;
- errors_test
- eternity, a MATLAB code which considers the eternity puzzle, an irregular dodecagon that is to be tiled by 209 pieces, each formed by 12 contiguous 30-60-90 triangles, known as polydrafters.
- eternity_test
- eternity_hexity, a MATLAB code which evaluates and manipulates a six-fold parity quantity associated with grids and tiles used in the Eternity puzzle.
- eternity_hexity_test
- eternity_tile, a MATLAB code which considers the individual tiles of the eternity puzzle, 209 distinct pieces, each formed by 36 contiguous 30-60-90 triangles, known as polydrafters, as well as tiles for the serenity and trinity puzzles, and the hat and turtle aperiodic monotile.
- eternity_tile_test
- euclid, a MATLAB code which investigates various versions of Euclid's algorithm for computing the greatest common divisor (GCD) of two integers.
- euclid_test
- euler, a MATLAB code which solves one or more ordinary differential equations (ODE) using the forward Euler method.
- euler_test
- exactness, a MATLAB 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
- exm, a MATLAB code which contains scripts and data discussed in the electronic textbook "Experiments with Matlab", by Cleve Moler, including easter, Fast Fourier Transforms, Fibonacci numbers, the fractal fern, the game of Life, magic matrices, the Mandelbrot set, Morse code, Music, Ordinary Differential Equations, the page rank algorithm, planetary orbits, predator prey equations, the shallow water equations, Sudoku puzzles.
- exm_test
- exp_ode, a MATLAB code which sets up and solves an ordinary differential equation (ODE) whose solution is an exponential function.
- exp_ode_test
- faces_average, a MATLAB code which averages several images of the same face;
- faces_average_test
- fair_dice_simulation, a MATLAB code which simulates N tosses of 2 dice, making a histogram of the resulting sums.
- fair_dice_simulation_test
- faure, a MATLAB code which computes the Faure M dimensional Quasi Mont Carlo (QMC) sequence;
- faure_test
- fd_predator_prey, a MATLAB code which solves a time-dependent predator prey system using the finite difference method (FDM).
- fd_predator_prey_test
- fd1d_advection_diffusion_steady, a MATLAB 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.
- fd1d_advection_diffusion_steady_test
- fd1d_advection_ftcs, a MATLAB 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) difference scheme.
- fd1d_advection_ftcs_test
- fd1d_advection_lax, a MATLAB 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.
- fd1d_advection_lax_test
- fd1d_advection_lax_wendroff, a MATLAB 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.
- fd1d_advection_lax_wendroff_test
- fd1d_burgers_lax, a MATLAB 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 MATLAB 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 MATLAB code which applies the finite difference method (FDM) to a two point boundary value problem (BVP) in one spatial dimension.
- fd1d_bvp_test
- fd1d_display, a MATLAB code which reads a pair of files defining a 1D finite difference method (FDM) of a function, and plots the data.
- fd1d_display_test
- fd1d_heat_explicit, a MATLAB code which implements a finite difference method (FDM), explicit in time, to solve the time dependent 1D heat equation;
- fd1d_heat_explicit_test
- fd1d_heat_implicit, a MATLAB code which implements a finite difference method (FDM), implicit in time, to solve the time dependent 1D heat equation;
- fd1d_heat_implicit_test
- fd1d_heat_steady, a MATLAB code which implements a finite difference method (FDM) for the steady (time independent) 1D heat equation;
- fd1d_heat_steady_test
- fd1d_poisson, a MATLAB code which solves a Poisson equation over a user-specified discretized interval, with given functions f(x) (right hand side) and g(x) (Dirichlet boundary conditions), using the Finite Difference Method (FDM).
- fd1d_poisson_test
- fd1d_predator_prey, a MATLAB 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_predator_prey_plot, a MATLAB code which plots solutions of the predator prey differential equations, by Marcus Garvie.
- fd1d_predator_prey_plot_test
- fd1d_wave, a MATLAB 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_convergence_test, a MATLAB code which calls fd2d_poisson(), which repeatedly solves a Poisson equation on a sequence of finer meshes, so that the relationship between mesh size H and error norm E can be explored.
- fd2d_heat_steady, a MATLAB code which implements a finite difference method (FDM) for the steady (time independent) 2D heat equation;
- fd2d_heat_steady_test
- fd2d_poisson, a MATLAB code which solves a Poisson equation over a user-specified discretized rectangle, with given functions f(x,y) (right hand side) and g(x,y) (Dirichlet boundary conditions), using the Finite Difference Method (FDM).
- fd2d_poisson_test
- fd2d_predator_prey, a MATLAB code which implements a finite difference method (FDM) for a time and 2D space dependent predator-prey system, by Marcus Garvie.
- fd2d_predator_prey_test
- fd3d_poisson, a MATLAB code which solves a Poisson equation over a user-specified discretized 3d block, with given functions f(x,y,z) (right hand side) and g(x,y,z) (Dirichlet boundary conditions), using the Finite Difference Method (FDM).
- fd3d_poisson_test
- fem_basis, a MATLAB code which defines and evaluates finite element method (FEM) basis functions for any degree in an M dimensional simplex (1D interval, 2D triangle, 3D tetrahedron, and higher dimensional generalizations.)
- fem_basis_test
- fem_basis_q4_display, a MATLAB code which displays any single finite element method (FEM) basis function associated with an arbitrary linear quadrilateral Q4 mesh;
- fem_basis_q4_display_test
- fem_basis_t3_display, a MATLAB code which displays a basis function for the finite element method (FEM) associated with an arbitrary 3-node triangle T3 mesh;
- fem_basis_t3_display_test
- fem_basis_t4_display, a MATLAB code which displays a basis function for the finite element method (FEM) associated with an arbitrary 4-node triangle T4 mesh;
- fem_basis_t4_display_test
- fem_basis_t6_display, a MATLAB code which displays a basis function for the finite element method (FEM) associated with an arbitrary 6-node triangle T6 mesh;
- fem_basis_t6_display_test
- fem_io, a MATLAB 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_neumann, a MATLAB code which sets up a time-dependent reaction-diffusion equation in 1D, with Neumann boundary conditions, discretized using the finite element method (FEM).
- fem_neumann_test
- fem_to_gmsh, a MATLAB 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 MATLAB code which reads a set of FEM files defining the node coordinates, boundary nodes, and elements of a finite element mesh, and rewrites the data as a medit() MESH file.
- fem_to_medit_test
- fem_to_tec, a MATLAB code which converts FEM models into tecplot() ASCII files.
- fem_to_tec_test
- fem_to_triangle, a MATLAB 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 use by Jonathan Shewchuk's triangle() program.
- fem_to_triangle_test
- fem_to_xml, a MATLAB 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 corresponding XML file for input to dolfin() or fenics().
- fem_to_xml_test
- fem1d, a MATLAB 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 MATLAB 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_approximate, a MATLAB code which uses a given finite element method (FEM) mesh and piecewise linear (PWL) basis functions to approximate a set of data points, while controlling the variation in the derivative.
- fem1d_approximate_test
- fem1d_bvp_linear, a MATLAB code which applies the finite element method (FEM), with piecewise linear (PWL) 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 MATLAB code which applies the finite element method (FEM), with piecewise quadratic (PWQ) 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_display, a MATLAB code which reads three files defining a 1D arbitrary degree basis function associated with the finite element method (FEM), and displays a plot.
- fem1d_display_test
- fem1d_function_10_display, a MATLAB code which reads three files defining a 1D piecewise linear finite element method (FEM) function and displays a plot.
- fem1d_display_function_10_test
- fem1d_heat_explicit, a MATLAB code which uses the finite element method (FEM) and explicit time stepping to solve the time dependent heat equation in 1D.
- fem1d_heat_explicit_test
- fem1d_heat_implicit, a MATLAB code which uses the finite element method (FEM) and implicit time stepping to solve the time dependent heat equation in 1D.
- fem1d_heat_implicit_test
- fem1d_heat_steady, a MATLAB code which uses the finite element method (FEM) to solve the steady (time independent) 1D heat equation;
- fem1d_heat_steady_test
- fem1d_lagrange, a MATLAB 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 MATLAB code which applies the finite element method (FEM), with piecewise linear (PWL) basis functions, to a nonlinear two point boundary value problem (BVP) in 1D;
- fem1d_nonlinear_test
- fem1d_pack, a MATLAB code which contains utilities for 1D finite element method (FEM) calculations.
- fem1d_pack_test
- fem1d_pmethod, a MATLAB 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 MATLAB 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 MATLAB 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
- fem1d_spectral_numeric, a MATLAB code which applies the spectral finite element method (FEM) to solve the problem u'' = - pi^2 sin(x) over [-1,+1] with zero boundary conditions, using as basis elements the functions x^n*(x-1)*(x+1), and carrying out the integration numerically, using the quad() function, by Miro Stoyanov.
- fem1d_spectral_numeric_test
- fem2d_bvp_linear, a MATLAB code which applies the finite element method (FEM), with piecewise linear (PWL) 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 MATLAB code which applies the finite element method (FEM), with piecewise quadratic (PWQ) 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 MATLAB 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 MATLAB code which applies the finite element method (FEM) to the time dependent heat equation on an arbitrary triangulated region in 2D;
- fem2d_heat_test
- fem2d_heat_rectangle, a MATLAB code which applies the finite element method (FEM) for the time-dependent heat equation on a triangulated rectangle in 2D;
- fem2d_heat_rectangle_test
- fem2d_heat_sparse, a MATLAB code which applies the finite element method (FEM) to the heat equation on an arbitrary triangulated region in 2D, using a sparse storage matrix format;
- fem2d_heat_sparse_test
- fem2d_mesh_display, a MATLAB code which reads a FEM model of a 2D mesh of elements of any uniform order and displays a plot of the elements and nodes, with optional numbering.
- fem2d_mesh_display_test
- fem2d_pack, a MATLAB code which performs simple 2D finite element method (FEM) computations;
- fem2d_pack_test
- fem2d_poisson_rectangle, a MATLAB 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 MATLAB 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_predator_prey_fast, a MATLAB code which implements a finite element method (FEM) for a time and 2D space dependent predator-prey system, on an arbitrary triangulated region, with a variety of possible boundary conditions, incorporating some optimizations, by Marcus Garvie.
- fem2d_predator_prey_fast_test
- fem2d_project, a MATLAB code which projects a function f(x,y), given as data, into a given finite element method (FEM) space of piecewise linear triangular elements.
- fem2d_project_test
- fem2d_project_function, a MATLAB code which projects a function f(x,y), given as a formula, into a given finite element method (FEM) space of piecewise linear triangular elements.
- fem2d_project_function_test
- fem2d_sample, a MATLAB code which samples a finite element method (FEM) function, defined by three text files describing the nodes, triangles, and coefficients, at arbitrary points.
- fem2d_sample_test
- fem2d_scalar_display, a MATLAB code which reads information about nodes, elements and nodal values for a 2D finite element method (FEM) and creates a surface plot of U(X,Y).
- fem2d_scalar_display_test
- fem2d_scalar_display_brief, a MATLAB code which reads information about nodes, elements and nodal values for a 2D finite element method (FEM) and creates a surface plot of U(X,Y), in 5 lines of code.
- fem2d_scalar_display_brief_test
- fem2d_scalar_display_gpl, a MATLAB code which reads information about nodes, elements and nodal values for a 2D finite element method (FEM) and creates a GPL file describing a surface plot of U(X,Y), to be displayed by gnuplot().
- fem2d_scalar_display_gpl_test,
- fem3d_pack, a MATLAB code which contains utilities for 3D finite element method (FEM) calculations.
- fem3d_pack_test
- fem3d_project, a MATLAB code which projects a function f(x,y,z), given as a data, into a given space of piecewise linear tetrahedral elements for use in the finite element method (FEM).
- fem3d_project_test
- fem3d_sample, a MATLAB code library which evaluates a function defined on a 3D tetrahedral mesh as part of the finite element method (FEM).
- fem3d_sample_test
- fern, a MATLAB code which computes and displays the Barnsley fractal fern.
- fern_test
- feynman_kac_1d, a MATLAB code which demonstrates the use of the Feynman-Kac algorithm to solve the Poisson equation in a 1D interval by averaging stochastic paths to the boundary.
- feynman_kac_1d_test
- feynman_kac_2d, a MATLAB code which demonstrates the use of the Feynman-Kac algorithm to solve the Poisson equation in a 2D ellipse by averaging stochastic paths to the boundary.
- feynman_kac_2d_test
- feynman_kac_3d, a MATLAB code which demonstrates the use of the Feynman-Kac algorithm to solve the Poisson equation in a 3D ellipsoid by averaging stochastic paths to the boundary.
- feynman_kac_3d_test
- ffmatlib, a MATLAB code which allows the user to plot finite element method (FEM) results that have been computed by FreeFem++().
- fft_serial, a MATLAB code which computes a Fast Fourier Transform (FFT), and is intended as a starting point for implementing a parallel version.
- fft_serial_test
- fibonacci_spiral, a MATLAB code which displays points on a Fibonacci spiral, suggesting the arrangement of seeds in a sunflower, for instance.
- fibonacci_spiral_test
- file_increment, a MATLAB code which increments every entry of an integer array which is stored in a file.
- file_increment_test
- file_name_sequence, a MATLAB 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_test, a MATLAB 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 MATLAB code which approximates integrals which include an oscillatory factor of sin(k*x) or cos(k*x).
- filon_rule_test
- filum, a MATLAB code which handles files and filenames;
- filum_test
- fire_simulation, a MATLAB code which simulates a forest fire over a rectangular array of trees, starting at a single random location.
- fire_simulation_test
- fisher_exact, a MATLAB code which returns an exact solution of the Kolmogorov Petrovsky Piskonov Fisher partial differential equation (PDE) ut=uxx+u*(1-u).
- fisher_exact_test
- fitzhugh_nagumo_ode, a MATLAB code which sets up and solves the Fitzhugh-Nagumo system of ordinary differential equations (ODE).
- fitzhugh_nagumo_ode_test
- flame_exact, a MATLAB 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
- flame_ode, a MATLAB code which sets up and solves 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_ode_test
- flies_simulation, a MATLAB code which simulates an experiment in which two flies land on a plate of radius 1. By repeating the experiment many times, the average distance between the flies is to be estimated.
- flies_simulation_test
- florida_cvt_geo, a MATLAB code which creates a centroidal Voronoi Tessellation (CVT) of the state of Florida, based solely on geometric considerations.
- florida_cvt_geo_test
- florida_cvt_pop, a MATLAB code which creates a centroidal Voronoi Tessellation (CVT) of the state of Florida, based on population considerations.
- florida_cvt_pop_test
- floyd, a MATLAB code which implements the Floyd algorithm for finding the shortest distance between pairs of nodes on a directed graph.
- floyd_test
- fly_simulation, a MATLAB code which simulates an experiment in which a fly lands on a plate of radius 1. By repeating the experiment many times, the average distance of the fly from the center is to be estimated.
- fly_simulation_test
- fmincon_test, a MATLAB code which calls fmincon(), which seeks the minimizer of a scalar function of multiple variables, within a region specified by linear constraints and bounds. fmincon() is part of the MATLAB Optimization Toolbox.
- fn, a MATLAB code which evaluates elementary and special functions using Chebyshev polynomials, including Airy, Bessel I, Bessel J, Bessel K, Bessel Y, beta, confluent hypergeometric, cosine integral, the Dawson integral, digamma (psi), error, exponential integral, gamma, hyperbolic cosine integral, hyperbolic sine integral, incomplete gamma, log gamma, logarithmic integral, Pochhammer, psi, sine integral, Spence;, by Wayne Fullerton.
- fn_test
- football_dynamic, a MATLAB code which uses dynamic programming to count the ways of achieving a given score in football.
- football_dynamic_test
- four_fifths, a MATLAB code which searches for a solution to the problem of finding four fifth powers that sum to a fifth power, that is, integers a, b, c, d and e such that a^5+b^5+c^5+d^5=e^5. Euler conjectured that no solution was possible.
- four_fifths_test
- fractal_coastline, a MATLAB code which uses perturbed Bezier interpolation to create a fractal coastline from a crude outline of a state, country, island, or even any general closed polygonal curve.
- fractal_coastline_test
- freefem_msh_io, a MATLAB code which reads and writes files used by the FreeFem finite element program to store mesh information.
- freefem_msh_io_test
- fsolve_test, a MATLAB code which calls fsolve() which seeks the solution x of one or more nonlinear equations f(x)=0.
- full_deck_simulation, a MATLAB code which simulates a process in which a random card is drawn from a deck of 52, and then replaced, continuing until every card has been seen at least once.
- full_deck_simulation_test
- gamblers_ruin_simulation, a MATLAB code which simulates a game in which a gambler never stops playing until all money is lost.
- gamblers_ruin_simulation_test
- gauss_seidel, a MATLAB code which implements the Gauss-Seidel iteration for linear systems.
- gauss_seidel_test
- gauss_seidel_poisson_1d, a MATLAB code which demonstrates how the linear system for a discretized version of the steady 1D Poisson equation can be solved by the Gauss-Seidel iteration.
- gauss_seidel_poisson_1d_test
- gauss_seidel_stochastic, a MATLAB code which uses a stochastic version of the Gauss-Seidel iteration to solve a linear system with a symmetric positive definite (SPD) matrix.
- gauss_seidel_stochastic_test
- gaussian, a MATLAB code which evaluates the Gaussian function and its derivatives.
- gaussian_test,
- gaussian_2d, a MATLAB code which evaluates a general Gaussian function of a 2D argument.
- gaussian_2d_test,
- gaussian_prime_spiral, a MATLAB code which computes a twisting spiral path along the Gaussian primes, and displays a plot of the total trajectory.
- gaussian_prime_spiral_test
- ge_to_crs, a MATLAB code which converts a matrix from General (GE) to Compressed Row Storage (CRS) format.
- ge_to_crs_test
- gegenbauer_cc, a MATLAB code which computes the Gegenbauer weighted integral of a function f(x) using a Clenshaw-Curtis approach.
- gegenbauer_cc_test
- gegenbauer_exactness, a MATLAB code which tests the polynomial exactness of Gauss-Gegenbauer quadrature rules.
- gegenbauer_exactness_test
- gegenbauer_polynomial, a MATLAB code which evaluates the Gegenbauer polynomial and associated functions.
- gegenbauer_polynomial_test
- gegenbauer_rule, a MATLAB code which computes and writes out a Gauss-Gegenbauer quadrature rule of given order.
- gegenbauer_rule_test
- gen_hermite_exactness, a MATLAB code which tests the polynomial exactness of generalized Gauss-Hermite quadrature rules.
- gen_hermite_exactness_test
- gen_hermite_rule, a MATLAB 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 MATLAB code which tests the polynomial exactness of generalized Gauss-Laguerre quadrature rules.
- gen_laguerre_exactness_test
- gen_laguerre_rule, a MATLAB code which prints a generalized Gauss-Laguerre quadrature rule of given order and parameter value.
- gen_laguerre_rule_test
- geometry, a MATLAB 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 MATLAB code which computes Delaunay triangulations, Voronoi diagrams, and other information, by Barry Joe.
- geompack_test
- gl_fast_rule, a MATLAB 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 MATLAB code which finds a global minimum of a scalar function of a scalar variable, without the use of derivative information, by Richard Brent.
- glomin_test
- glycolysis_ode, a MATLAB code which sets up a pair of ordinary differential equations (ODE) that model the biochemical process of glycolysis, for which a limit cycle exists.
- glycolysis_ode_test
- gmres, a MATLAB code which implements the generalized minimum residual (GMRES) method for solving a nonsymmetric sparse linear system A*x=b.
- gmres_test
- gmsh_io, a MATLAB code which reads or writes files created by the gmsh() program for 1D, 2D or 3D meshes used by the finite element method (FEM).
- gmsh_io_test
- gmsh_to_fem, a MATLAB code which reads a mesh data file created by the gmsh() program and writes a pair of node and element files that correspond to the FEM format.
- gmsh_to_fem_test
- gnuplot_test, a MATLAB code which uses gnuplot() to create various kinds of plots.
- gpl_display, a MATLAB code which tries to read the data in a typical gnuplot() GPL file, describing a 1D, 2D or 3D curve, or a surface Z(X,Y) defined on a regular grid, a triangular grid, or an irregular quadrilateral grid, displays it in a more attractive way than gnuplot() does.
- gpl_display_test
- gradient_descent, a MATLAB code which uses gradient descent to solve a linear least squares (LLS) problem.
- gradient_descent_test
- gram_polynomial, a MATLAB code which evaluates the Gram polynomials, also known as the discrete Chebyshev polyomials and associated functions.
- gram_polynomial_test
- gram_schmidt, a MATLAB code which implements the Gram-Schmidt process to orthogonalize and normalize a set of vectors.
- gram_schmidt_test
- graph_adj, a MATLAB 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_representation, a MATLAB code which expresses the representation of an abstract mathematical graph in several ways.
- graph_representation_test
- graphics_test, a MATLAB code which demonstrates a variety of graphics displays, including bar plots, contour plots, filled polygons, histograms, line plots, scatter plots, surface plots, tree diagrams, vector plots.
- gray_code_display, a MATLAB code which computes the Hamming distance tables for both the binary and Gray codes, and displays 3D plots that illustrate how the Gray code does a better job of providing nearby representations for nearby numbers.
- gray_code_display_test
- gray_scott_movie, a MATLAB code which solves versions of the partial differential equation (PDE) known as the Gray-Scott reaction diffusion equation, converting the solutions to a sequence of graphics frames, which are then assembled into a movie.
- gray_scott_movie_test
- gray_scott_pde, a MATLAB code which solves the partial differential equation (PDE) known as the Gray-Scott reaction diffusion equation, displaying a sequence of solutions as time progresses.
- gray_scott_pde_test
- grazing_ode, a MATLAB code which sets up and solves ordinary differential equations (ODE) that model the populations of an edible plant, and the herbivore that grazes on it.
- grazing_ode_test
- grf_display, a MATLAB code which reads a grf file defining a mathematical graph and displays it.
- grf_display_test
- grf_io, a MATLAB code which reads or writes a grf file which represents a mathematical graph;
- grf_io_test
- grid_display, a MATLAB code which reads a file of points on a grid or sparse grid, displays the grid and saves the image in a png file;
- grid_display_test
- gridlines, a MATLAB code which gives the user more control over drawing gridlines on a graph than the builtin grid command.
- gridlines_test
- grids_display, a MATLAB code which reads two files of grids or sparse grids, displaying the first with hollow blue dots, the second with solid red dots.
- grids_display_test
- gurobi_solution_read, a MATLAB code which reads a file created by the optimization package GUROBI, representing the solution of a polyomino tiling problem, and writes out a simple ASCII file to be read by load().
- gurobi_solution_read_test
- haar_transform, a MATLAB code which computes the Haar transform of 1d or 2d data.
- haar_transform_test
- halton, a MATLAB code which computes elements of a Halton Quasi Monte Carlo (QMC) sequence, using a simple interface.
- halton_test
- hammersley, a MATLAB code which computes elements of a Hammersley Quasi Monte Carlo (QMC) sequence, using a simple interface.
- hammersley_test
- hamming, a MATLAB code which implements some simple versions of Hamming codes which detects and correct errors in data.
- hamming_test
- hand_area, a MATLAB code which estimates the area of a curve which outlines a hand.
- hand_area_test
- hand_data, a MATLAB code which carries out some numerical exercises based on data that came from tracing several points on a hand.
- hand_data_test
- hand_mesh2d, a MATLAB code which reads in a set of points which outline a human hand, and calls mesh2d(), which is able to create a fine triangular mesh of the region outlined by the points.
- hand_mesh2d_test
- hankel_cholesky, a MATLAB code which computes the upper Cholesky factor R of a symmetric positive definite (SPD) Hankel matrix so that H = R' * R.
- hankel_cholesky_test
- hankel_inverse, a MATLAB code which computes the inverse of a Hankel matrix.
- hankel_inverse_test
- hankel_spd, a MATLAB code which computes a lower triangular matrix L which is the Cholesky factor of a symmetric positive definite (SPD) Hankel matrix H, that is, H = L * L'.
- hankel_spd_test
- hb_io, a MATLAB code which reads and writes sparse linear systems stored in the Harwell Boeing (HB) format for sparse matrices.
- hb_io_test
- hb_to_mm, a MATLAB code which converts a sparse matrix from Harwell Boeing (HB) to Matrix Market (MM) format.
- hb_to_mm_test
- hb_to_msm, a MATLAB code which converts a sparse matrix stored in a Harwell Boeing (HB) format to MATLAB sparse matrix (MSM) format;
- hb_to_msm_test
- hb_to_st, a MATLAB code which converts a sparse matrix from Harwell Boeing (HB) format to Sparse Triplet (ST) format.
- hb_to_st_test
- heartbeat_ode, a MATLAB code which sets up and solves an ordinary differential equation (ODE) describing the beating of the heart, as suggested by Zeeman.
- heartbeat_ode_test
- heat_transfer_test, a MATLAB code which plots data from the computation of heat distribution on a metal disk, as computed by FreeFem++() and transferred using the ffmatlib() library.
- heated_plate, a MATLAB code which solves the steady state heat equation in a 2D rectangular region, and is intended as a starting point for a parallel version.
- heated_plate_test
- hello, a MATLAB code which prints out "Hello, world!".
- hello_test
- hello_parfor, a MATLAB code which uses the parfor() statement for parallel execution and simply prints "Hello, world!" multiple times.
- hello_parfor_test
- helmholtz_exact, a MATLAB code which evaluates an exact formula for the solution of the Helmholtz equation, a sort of eigenvalue equation that can arise after separation of variables is a applied to the wave equation. This example considers a problem in which Z(x,y) represents the vertical deflection of the surface of a vibrating circular membrane such as a drumhead.
- helmholtz_exact_test
- henon_heiles_ode, a MATLAB code which sets up and solves the Henon-Heiles system of ordinary differential equations (ODE) which model the motion of a star around the galactic center.
- henon_heiles_ode_test
- henon_orbit, a MATLAB code which computes the orbit of the Henon map for various sets of initial data.
- henon_orbit_test
- hermite_cubic, a MATLAB code which computes the value, derivatives or integral of a Hermite cubic polynomial, or manipulates an interpolating function made up of piecewise Hermite cubic polynomials.
- hermite_cubic_test
- hermite_exactness, a MATLAB code which tests the polynomial exactness of Gauss-Hermite quadrature rules to estimate the integral of a function with density exp(-x^2) over the interval (-oo,+oo).
- hermite_exactness_test
- hermite_integrands, a MATLAB code which defines test integrands for Hermite integrals with density exp(-x^2) over the interval (-oo,+oo).
- hermite_integrands_test
- hermite_interpolant, a MATLAB code which computes the Hermite interpolant, a polynomial that matches function values and derivatives.
- hermite_interpolant_test
- hermite_polynomial, a MATLAB code which evaluates the physicist's Hermite polynomial, the probabilist's Hermite polynomial, the Hermite function, and related functions.
- hermite_polynomial_test
- hermite_product_display, a MATLAB code which displays an image of a function created by the Cartesian product of two Hermite polynomials, such as f(x,y) = h(3,x) * h(1,y).
- hermite_product_display_test
- hermite_product_polynomial, a MATLAB code which defines Hermite product polynomials, creating a multivariate polynomial as the product of univariate Hermite polynomials.
- hermite_product_polynomial_test
- hermite_rule, a MATLAB code which returns a Gauss-Hermite quadrature rule to estimate the integral of a function with density exp(-x^2) over the interval (-oo,+oo).
- hermite_rule_test
- hexagon_integrals, a MATLAB code which returns the exact value of the integral of a monomial over the interior of a hexagon in 2D.
- hexagon_integrals_test
- hexagon_lyness_rule, a MATLAB code which computes one of 13 Lyness quadrature rules over the interior of the unit hexagon.
- hexagon_lyness_rule_test
- hexagon_monte_carlo, a MATLAB code which applies a Monte Carlo method to estimate the integral of a function over the interior of a hexagon in 2D;
- hexagon_monte_carlo_test
- hexagon_stroud_rule, a MATLAB code which computes one of four Stroud quadrature rules over the interior of the unit hexagon.
- hexagon_stroud_rule_test
- hexahedron_jaskowiec_rule, a MATLAB 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 MATLAB code which returns a symmetric Witherden quadrature rule for the hexahedron, with exactness up to total degree 11.
- hexahedron_witherden_rule_test
- high_card_parfor, a MATLAB 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 parfor() to carry out the computation in parallel.
- high_card_parfor_test
- high_card_simulation, a MATLAB 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.
- high_card_simulation_test
- hilbert_curve, a MATLAB code which computes the sequence of discrete Hilbert curves whose limit is a space-filling curve.
- hilbert_curve_test
- hilbert_curve_display, a MATLAB code which plots a Hilbert curve of given order.
- hilbert_curve_display_test
- histogram_data_2d_sample, a MATLAB code which demonstrates how to construct a Probability Density Function (PDF) from sample data over a 2D domain, and then to use that PDF to create new samples.
- histogram_data_2d_sample_test
- histogram_discrete, a MATLAB code which tries to make a histogram of data without using bins.
- histogram_discrete_test
- histogram_display, a MATLAB code 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;
- histogram_display_test
- histogram_pdf_sample, a MATLAB code which demonstrates how sampling can be done by starting with the formula for a PDF, creating a histogram, constructing a histogram for the CDF, and then sampling.
- histogram_pdf_sample_test
- histogram_pdf_2d_sample, a MATLAB code which demonstrates how uniform sampling of a 2D region with respect to some known Probability Density Function (PDF) can be approximated by decomposing the region into rectangles, approximating the PDF by a piecewise constant (PWC) function, constructing a histogram for the CDF, and then sampling.
- histogram_pdf_2d_sample_test
- histogramize, a MATLAB code which takes a vector of data and organizes it into a histogram of a given number of bins with given width and range, which can be displayed as a bar chart.
- histogramize_test
- hits, a MATLAB code which uses the HITS algorithm to assign authority and hub indices to a set of nodes in a directed network.
- hits_test
- house, a MATLAB code which includes a line segment outline of a house, and some programs to show how linear transformations affect the shape, by Cleve Moler.
- house_test
- human_data, a MATLAB code which starts with an image of simple outline of a human body, tabulates a sequence of points on the outline, creating numerical data defining the boundary. It is then able to fill the region with mesh points and triangulate the region. This allows the region to be analyzed by the finite element method (FEM).
- human_data_test
- humps, a MATLAB code which evaluates the humps() function, its first and second derivatives and its antiderivative.
- humps_test
- humps_ode, a MATLAB code which sets up and solves an ordinary differential equation (ODE) whose solution is a double hump curve.
- humps_ode_test
- hyper_2f1, a MATLAB code which evaluates the hypergeometric functions 2F1(a,b,c;x) for real parameters a, b, c, and real or complex argument x.
- hyper_2f1_test
- hyperball_distance, a MATLAB code which computes the expected value of the distance between a pair of points randomly selected from the interior of the unit hyperball in M dimensions.
- hyperball_distance_test
- hyperball_integrals, a MATLAB 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 MATLAB 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
- hyperball_positive_distance, a MATLAB code which computes the expected value of the distance between a pair of points randomly selected from the interior of the unit positive hyperball in M dimensions.
- hyperball_positive_distance_test
- hypercube_distance, a MATLAB code which estimates the expected value of the distance between a pair of points randomly selected in the M-dimensional unit hypercube.
- hypercube_distance_test
- hypercube_exactness, a MATLAB 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 MATLAB code which computes a grid of points over the interior of a hypercube in M dimensions.
- hypercube_grid_test
- hypercube_integrals, a MATLAB 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 MATLAB 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
- hypercube_surface_distance, a MATLAB code which estimates the expected value of the distance between a pair of points randomly selected on the surface of the unit hypercube in D dimensions.
- hypercube_surface_distance_test
- hypergeom_test, a MATLAB code which calls hypergeom(), which is a built-in MATLAB function which evaluates the generalized hypergeometric functions pFq(z), for integer p and q.
- hypersphere, a MATLAB 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_angle, a MATLAB code which considers the problem of describing the typical value of the angle between a pair of points randomly selected on the unit hypersphere in M dimensions. Since by symmetry, this will be zero, we instead look at the average of the absolute value of the dot product, and the corresponding angle. In dimension 1, we have average dot product of 1, and angle 0. As the dimension increases, the average dot product rapidly decreases to 0, while the average angle goes to 90 degrees.
- hypersphere_angle_test
- hypersphere_distance, a MATLAB code which computes the expected value of the distance between a pair of points randomly selected on the surface of the unit hypersphere in M dimensions.
- hypersphere_distance_test
- hypersphere_integrals, a MATLAB 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 MATLAB 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
- hypersphere_positive_distance, a MATLAB code which computes the expected value of the distance between a pair of points randomly selected on the surface of the unit positive hypersphere in M dimensions.
- hypersphere_positive_distance_test
- i4lib, a MATLAB code which contains utilities using single precision integer (I4) arithmetic.
- i4lib_test
- i4mat_rref2, a MATLAB code which computes a version of the reduced row echelon form of an integer matrix.
- i4mat_rref2_test
- ice_io, a MATLAB code which reads or writes an ICE dataset, which defines a 3D grid, using the netcdf() file format.
- ice_io_test
- ice_to_medit, a MATLAB code which reads a netcdf() file containing an ICE dataset and rewrites the information as a medit() MESH file.
- ice_to_medit_test
- ill_bvp, a MATLAB code which defines an ill conditioned boundary value problem (BVP), and calls on bvp4c() to solve it with various values of the conditioning parameter.
- ill_bvp_test
- image_boundary, a MATLAB code which reports the pixels which form the boundary between the black and white regions of a simple image.
- image_boundary_test
- image_contrast, a MATLAB code which applies image processing techniques to increase the contrast in an image.
- image_contrast_test
- image_decimate, a MATLAB code which drops the even rows and columns from an image.
- image_decimate_test
- image_denoise, a MATLAB code which applies simple filtering operations to a noisy image.
- image_denoise_test
- image_diffuse, a MATLAB code which uses diffusion to smooth out an image.
- image_diffuse_test
- image_double, a MATLAB code which doubles the height and width of an image by repeating each row and column.
- image_double_test
- image_edge, a MATLAB code which detects edges in an image.
- image_edge_test
- image_mesh, a MATLAB code which starts with a list of points that bound some region, and calls mesh2d() to create a mesh of the interior.
- image_mesh_test
- image_noise, a MATLAB code which adds noise to an image.
- image_noise_test
- image_normalize, a MATLAB code which reads image data from a file, converts it (if necessary) to grayscale, resizes it to H pixels by W pixels.
- image_normalize_test
- image_quantization, a MATLAB code which uses kmeans() to reduce the number of colors or shades of gray in an image.
- image_quantization_test
- image_rgb_to_gray, a MATLAB code which makes a grayscale version of an RGB image.
- image_rgb_to_gray_test
- image_sample, a MATLAB code which allows the user to specify an image file to be displayed. The user may then use the mouse to select points on the image. The coordinates of each point are saved to a file. Selection ends with a double click. An example is supplied, which outlines the boundary of an aneurysm.
- image_sample_test
- image_threshold, a MATLAB code which makes a black and white version of a grayscale image by setting all pixels below or above a threshold value to black or white.
- image_threshold_test
- imshow_numeric, a MATLAB code which accepts a numeric 2D array and displays it as a grayscale image.
- imshow_numeric_test
- index, a MATLAB code which converts an M-dimensional vector index to a one-dimensional vector index; it handles zero and one based indexing schemes, as well as column major and row major conventions.
- index_test
- insurance_simulation, a MATLAB code which simulates a highly simplified model of term life insurance, in which a customer agrees to pay an annual fee for a given number of years, so that if the customer dies within that term, the family receives a large payout.
- insurance_simulation_test
- interp, a MATLAB code which parameterizes and interpolates data;
- interp_test
- interp_chebyshev, a MATLAB code which interactively uses n Chebyshev spaced nodes in the interval [a,b] to interpolate a function f(x) with a polynomial.
- interp_chebyshev_test
- interp_equal, a MATLAB code which interactively uses n equally spaced nodes in the interval [a,b] to interpolate a function f(x) with a polynomial.
- interp_equal_test
- interp_ncs, a MATLAB code which interactively constructs a natural cubic spline (NCS) interpolant to a function f(x), using the 'zero second derivative' end condition.
- interp_ncs_test
- interp_spline, a MATLAB code which interactively constructs a cubic spline interpolant to a function f(x), using the 'not-a-knot' end condition.
- interp_spline_test
- interp_spline_data, a MATLAB code which interactively constructs a cubic spline interpolant to (x,y) data, using the 'not-a-knot' end condition.
- interp_spline_data_test
- interp_trig, a MATLAB code which interactively uses n equally spaced nodes in the interval [a,b] to interpolate a function f(x) with a trigonometric polynomial.
- interp_trig_test
- iplot, a MATLAB code which interactively plots a function f(x) over a domain a ≤ x ≤ b;
- iplot_test
- is_gaussian_prime, a MATLAB code which is true if a given complex number c is a Gaussian prime.
- is_gaussian_prime_test
- is_prime, a MATLAB code which is true if a given integer n is prime.
- is_prime_test
- isbn, a MATLAB code which determines the check digit for an International Standard Book Number (ISBN) or reports whether a given ISBN is valid.
- isbn_test
- ising_2d_simulation, a MATLAB code which simulates the evolution of a 2D array of positive and negative charges, each of which is likely to flip to be in agreement with neighbors.
- ising_2d_simulation_test
- jaccard_distance, a MATLAB code which computes the Jaccard distance between two sets.
- jaccard_distance_test
- jacobi, a MATLAB code which implements the Jacobi iteration for the iterative solution of linear systems.
- jacobi_test
- jacobi_eigenvalue, a MATLAB code which implements the Jacobi iteration for the iterative determination of the eigenvalues and eigenvectors of a real symmetric matrix.
- jacobi_eigenvalue_test
- jacobi_exactness, a MATLAB code which tests the polynomial exactness of rules for integrals with a Jacobi weight function.
- jacobi_exactness_test
- jacobi_poisson_1d, a MATLAB code which uses Jacobi iteration to solve the linear system for a discretized steady 1D Poisson equation.
- jacobi_poisson_1d_test
- jacobi_polynomial, a MATLAB code which evaluates the Jacobi polynomial and associated functions.
- jacobi_polynomial_test
- jacobi_rule, a MATLAB code which computes a Gauss-Jacobi quadrature rule.
- jacobi_rule_test
- jai_alai_simulation, a MATLAB code which simulates a sequence matches of the game of jai alai.
- jai_alai_simulation_test
- jordan_matrix, a MATLAB code which returns a random matrix in Jordan canonical form.
- jordan_matrix_test
- joukowsky_transform, a MATLAB code which applies the Joukowsky transform to data, mapping between a circle in the complex plane and various airfoil shapes.
- joukowsky_transform_test
- julia_set, a MATLAB code which computes and plots a Julia set, the set of points in the complex plane that remain bounded under a mapping of the form f(z) = z^2+c.
- julia_set_test
- jumping_bean_simulation, a MATLAB code which simulates the motion of several jumping beans which prefer cooler locations.
- jumping_bean_simulation_test
- kdv_etdrk4, a MATLAB code which uses the exponential time differencing (ETD) RK4 method to solve the Korteweg-deVries (KdV) partial differential equation (PDE), by Aly-Khan Kassam, Lloyd Trefethen.
- kdv_etdrk4_test
- kdv_exact, a MATLAB code which evaluates exact solutions of the Korteweg-deVries (KdV) partial differential equation (PDE).
- kdv_exact_test
- kdv_ift, a MATLAB code which uses the Inverse Fourier Transform (IFT) method to solve the Korteweg-deVries (KdV) partial differential equation (PDE), by Aly-Khan Kassam, Lloyd Trefethen.
- kdv_ift_test
- kelley, a MATLAB code which implements iterative methods for linear and nonlinear problems, by Tim Kelley.
- kelley_test
- kepler_ode, a MATLAB code which sets up and solves the ordinary differential equations (ODE) for a Kepler two-body gravitational system.
- kepler_ode_test
- kepler_perturbed_ode, a MATLAB code which sets up and solves the ordinary differential equations (ODE) for a perturbed Kepler two-body gravitational system.
- kepler_perturbed_ode_test
- keyword_test, a MATLAB code which accepts named keywords, using the Name/Value paired argument convention.
- kmeans, a MATLAB code which handles the K-Means problem, which organizes a set of N points in M dimensions into K clusters;
- kmeans_test
- kmeans_fast, a MATLAB code which contains several different algorithms for the K-Means problem, which organizes a set of N points in M dimensions into K clusters, by Charles Elkan.
- kmeans_fast_test
- knapsack_01_brute, a MATLAB code which uses brute force to solve small versions of the 0/1 knapsack problem;
- knapsack_01_brute_test
- knapsack_dynamic, a MATLAB code which uses dynamic programming to solve a knapsack problem.
- knapsack_dynamic_test
- knapsack_greedy, a MATLAB code which uses a greedy algorithm to estimate a solution of the knapsack problem;
- knapsack_greedy_test
- kronrod_rule, a MATLAB code which computes a Gauss and Gauss-Kronrod pair of quadrature rules of arbitrary order, by Robert Piessens, Maria Branders.
- kronrod_rule_test
- kursiv_pde_etdrk4, a MATLAB code which uses the exponential time differencing (ETD) RK4 method to solve the Kuratomo-Sivashinsky PDE as a system of stiff ordinary differential equations (ODE), by Aly-Khan Kassam, Lloyd Trefethen.
- kursiv_pde_etdrk4_test
- lagrange_approx_1d, a MATLAB code which defines and evaluates the Lagrange polynomial p(x) of degree m which approximates a set of nd data points (x(i),y(i)).
- lagrange_approx_1d_test
- lagrange_basis_display, a MATLAB code which displays the basis functions associated with a given set of nodes used with the Lagrange interpolation scheme.
- lagrange_basis_display_test
- lagrange_interp_1d, a MATLAB code which defines and evaluates the Lagrange polynomial p(x) which interpolates a set of data depending on a 1D argument, so that p(x(i)) = y(i).
- lagrange_interp_1d_test
- lagrange_interp_2d, a MATLAB code which defines and evaluates the Lagrange polynomial p(x,y) which interpolates a set of data depending on a 2D argument that was evaluated on a product grid, so that p(x(i),y(j)) = z(i,j).
- lagrange_interp_2d_test
- lagrange_interp_nd, a MATLAB code which defines and evaluates the Lagrange polynomial p(x) which interpolates a set of data depending on an M dimensional argument that was evaluated on a product grid, so that p(x(i)) = z(i).
- lagrange_interp_nd_test
- lagrange_nd, a MATLAB code which implements several multivariate Lagrange interpolation schemes developed by Tomas Sauer.
- lagrange_nd_test
- laguerre_exactness, a MATLAB code which tests the polynomial exactness of Gauss-Laguerre quadrature rules for integrating functions with density exp(-x) over [0,+oo).
- laguerre_exactness_test
- laguerre_integrands, a MATLAB code which implements test problems for approximate integration over a semi-infinite interval, often carried out using Gauss-Laguerre quadrature.
- laguerre_integrands_test
- laguerre_polynomial, a MATLAB code which evaluates the Laguerre polynomial, the generalized Laguerre polynomials, and the Laguerre function.
- laguerre_polynomial_test
- laguerre_product, a MATLAB code which computes weighted integrals of products of Laguerre polynomials.
- laguerre_product_test
- laguerre_rule, a MATLAB code which returns a Gauss-Laguerre quadrature rule of given order.
- laguerre_rule_test
- lambert_w, a MATLAB code which evaluates Lambert's W function.
- lambert_w_test
- langford_ode, a MATLAB code which sets up and solves the Langford system of ordinary differential equations (ODE).
- langford_ode_test
- laplace_periodic_test, a MATLAB code which plots data from the solution of the Laplace equation in a square with periodic boundary conditions, computed by FreeFem++() and transferred using the ffmatlib() library.
- laplacian, a MATLAB 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 a set of data samples, solution of associated linear systems, eigenvalues and eigenvectors, and extension to 2D and 3D geometry.
- laplacian_test
- latin_center, a MATLAB code which computes N points in an M dimensional Latin Center square;
- latin_center_test
- latin_cover, a MATLAB 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 MATLAB code which returns N points in an M dimensional Latin Edge square;
- latin_edge_test
- latin_random, a MATLAB code which returns N points in an M dimensional Latin Random square;
- latin_random_test
- latinize, a MATLAB code which adjusts N points in M dimensions to form a Latin hypercube;
- latinize_test
- lattice_rule, a MATLAB code which returns lattice rules for M dimensional integration;
- lattice_rule_test
- leapfrog, a MATLAB code which uses the leapfrog method to solve a second order ordinary differential equation (ODE) of the form y''=f(t,y).
- leapfrog_test
- least_squares_approximant, a MATLAB code which finds a polynomial approximant to data using linear least squares (LLS).
- least_squares_approximant_test
- lebesgue, a MATLAB code which is given nodes in 1D, plots the Lebesgue function, and estimates the Lebesgue constant, which measures the maximum magnitude of the potential error of Lagrange polynomial interpolation.
- lebesgue_test
- legendre_exactness, a MATLAB code which tests the monomial exactness of quadrature rules for the Legendre problem of integrating a function with density 1 over the interval [-1,+1].
- legendre_exactness_test
- legendre_fast_rule, a MATLAB code which uses a fast (order N) algorithm to compute a Gauss-Legendre quadrature rule of given order.
- legendre_fast_rule_test
- legendre_polynomial, a MATLAB code which evaluates the Legendre polynomial and associated functions.
- legendre_polynomial_test
- legendre_product, a MATLAB code which computes weighted integrals of products of Legendre polynomials.
- legendre_product_test
- legendre_product_display, a MATLAB code which displays the points in a 2D Gauss-Legendre product quadrature rule;
- legendre_product_display_test
- legendre_product_polynomial, a MATLAB code which defines Legendre product polynomials, creating a multivariate polynomial as the product of univariate Legendre polynomials.
- legendre_product_polynomial_test
- legendre_rule, a MATLAB code which returns a Gauss-Legendre quadrature rule of given order.
- legendre_rule_test
- legendre_shifted_polynomial, a MATLAB code which evaluates the shifted Legendre polynomial, with the domain [0,1].
- legendre_shifted_polynomial_test
- levels, a MATLAB code which makes a contour plot, choosing the contour levels using random sampling.
- levels_test
- levenshtein_distance, a MATLAB code which returns the Levenshtein distance between two strings.
- levenshtein_distance_test
- levenshtein_matrix, a MATLAB code which returns the Levenshtein distance matrix defined by two strings.
- levenshtein_matrix_test
- life, a MATLAB code which computes a few steps of the evolution of John Conway's Game of Life, intended as a starting point for implementing a parallel version.
- life_test
- lights_out, a MATLAB code which sets up the "Lights Out" game, lighting up a few squares on a grid. An interactive user must then try to press squares in such a way that all the lights are turned off.
- lindberg_exact, a MATLAB code which evaluates the exact solution of the Lindberg ordinary differential equations (ODE), a system that is extremely difficult to solve accurately.
- lindberg_exact_test
- lindberg_ode, a MATLAB code which sets up and solves a system of 4 ordinary differential equations (ODE) which are very stiff.
- lindberg_ode_test
- line_cvt_lloyd, a MATLAB code which applies the Lloyd iteration repeatedly to a set of N points, to compute a Centroidal Voronoi Tessellation (CVT) over the interior of a line segment in 1D.
- line_cvt_lloyd_test
- line_distance, a MATLAB code which computes the expected value of the distance between a pair of points randomly selected in the unit line segment.
- line_distance_test
- line_fekete_rule, a MATLAB 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 MATLAB code which returns a Felippa quadrature rule for approximating integrals over the interior of a line segment in 1D.
- line_felippa_rule_test
- line_grid, a MATLAB code which computes a grid of points over the interior of a line segment in 1D.
- line_grid_test
- line_integrals, a MATLAB 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 MATLAB 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 MATLAB 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 MATLAB 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
- line_packing, a MATLAB code which tries to randomly pack as many non-overlapping equal line segments as possible into a larger line segment, estimating Renyi's parking constant of 0.7475979202.
- line_packing_test
- linear_algebra, a MATLAB code which carries out various linear algebra operations for matrices stored in a variety of formats.
- linpack_bench, a MATLAB code which is a version of the LINPACK benchmark;
- linpack_bench_test
- linpack_bench_backslash, a MATLAB code which is a version of the LINPACK benchmark using the "backslash" linear system solver;
- linpack_bench_backslash_test
- linpack_d, a MATLAB code which factors and solves linear systems using real 64 bit 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 MATLAB code which factors and solves linear systems using complex 64 bit arithmetic, by Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart. The matrix and vector data is assumed to be complex.
- linpack_z_test
- lissajous, a MATLAB code which displays a Lissajous figure, of the form x = sin ( a1 t + b1 ), y = sin ( a2 t + b2 ).
- lissajous_test
- llsq, a MATLAB code which solves the linear least squares (LLS) problem. It finds the "best" straight line to match a set of data points. More precisely, it finds the quantities "a" and "b" defining the straight line y=a*x+b, which minimizes the root-mean-square (RMS) error to the data.
- llsq_test
- load_test, a MATLAB code which calls the load() function, which reads data from a file into a variable.
- lobatto_polynomial, a MATLAB code which evaluates Lobatto polynomials, which are similar to Legendre polynomials except that they are 0 at both endpoints.
- lobatto_polynomial_test
- local_min, a MATLAB 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 MATLAB 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
- locker_simulation, a MATLAB code which simulates the locker problem, in which gym users have left their wallets in lockers; someone has scrambled all the lockers, and the gym users need a strategy that maximizes the chance that everyone will find their wallet by searching a limited number of lockers.
- locker_simulation_test
- log_norm, a MATLAB code which computes the logarithmic norm of a matrix, for norms 1, 2 and oo.
- log_norm_test
- log_normal, a MATLAB code which returns quantities related to the log normal Probability Distribution Function (PDF).
- log_normal_test
- log_normal_truncated_ab, a MATLAB 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_bifurcation, a MATLAB code which plots the bifurcation diagram for the logistic equation, by John D Cook.
- logistic_bifurcation_test
- logistic_exact, a MATLAB 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
- logistic_ode, a MATLAB code which sets up and solves an ordinary differential equation (ODE) which models population growth in the face of a limited carrying capacity.
- logistic_ode_test
- lorenz_ode, sets up and solves the Lorenz system of ordinary differential equations (ODE), which exhibit sensitive dependence on the initial conditions.
- lorenz_ode_test
- lorenz_ode_cluster_test, takes N points on a trajectory of solutions to the Lorenz system of ordinary differential equations (ODE), and applies the K-Means algorithm to organize the data into K clusters.
- lorenz_ode_sensitivity_test, a MATLAB code which demonstrates sensitivity to initial conditions in the Lorenz system, of ordinary differential equations (ODE), using an approach suggested by John D Cook.
- luhn, a MATLAB code which computes the Luhn check digit for a string, and validates a string.
- luhn_test
- machar, a MATLAB code which computes the appropriate values of arithmetic constants for a given machine, by William Cody.
- machar_test
- machine, a MATLAB code which returns values of arithmetic constants for a given machine.
- machine_test
- mackey_glass_dde, a MATLAB code which sets up and solves the Mackey-Glass Delay Differential Equation (DDE), which models dynamical diseases such as irregular breathing apnea and chronic myelogenous leukemia, and produces a strange chaotic attractor.
- mackey_glass_dde_test
- magic_matrix, a MATLAB code which computes a magic matrix, for any odd order n, such that all rows and columns have the same sum.
- magic_matrix_test
- mandelbrot, a MATLAB code which generates an image of the Mandelbrot set;
- mandelbrot_test
- mandelbrot_orbit, a MATLAB code which generates the Mandelbrot iterates arising from a single starting point;
- mandelbrot_orbit_test
- maple_area, a MATLAB code which takes the list of pixels that form the boundary of the image of a maple leaf within a picture, and uses grid, Monte Carlo, and Quasi Monte Carlo (QMC) sampling to estimate the area of the leaf.
- maple_area_test
- maple_boundary, a MATLAB code which reads an image of a maple leaf and extracts the list of pixels that form the boundary.
- maple_boundary_test
- mario, a MATLAB code which creates a sort of "needlepoint" image of Mario, as an array of colored squares.
- mario_test
- markov_letters, a MATLAB code which counts the occurences of letter pairs in a text.
- markov_letters_test
- matlab_test, a MATLAB code which illustrates the use of scripts and M-files;
- matlab_combinatorics, a MATLAB code which considers a variety of problems in combinatorics involving counting, combinations, permutations, and so on.
- matlab_commandline, a MATLAB code which illustrates how to execute code from the UNIX command line, that is, not with the usual command window.
- matlab_compiler, a MATLAB code which illustrates the use of the compiler, which allows you to run an application outside of the Matlab environment.
- matlab_distance, a MATLAB code which estimates the typical distance between a pair of points randomly selected from the surface or interior of a geometric object such as a circle, disk, sphere, cube, and between other nongeometric pairs of items.
- matlab_exact, a MATLAB code which evaluates exact solutions to a few selected examples of ordinary differential equations (ODE) and partial differential equations (PDE).
- matlab_graphics, a MATLAB code which demonstrates a few issues that arise when producing graphic images.
- matlab_grid, a MATLAB code which generates a regular grid of points inside a variety of regions in one, two, three or many dimensions.
- matlab_kmeans_test, a MATLAB code which calls the built in kmeans() function, which clusters N sets of M-dimensional data into K clusters.
- matlab_map, a MATLAB code which uses the mapping toolbox to draw maps of the world, countries, the US, or individual states.
- matlab_mistake, a MATLAB code which illustrates some simple but devious programming mistakes.
- matlab_monte_carlo, a MATLAB code which uses Monte Carlo sampling to estimate areas and integrals.
- matlab_movie, a MATLAB code which creates a movie or animation by generating a sequence of graphics frames and then stringing them together.
- matlab_ode, a MATLAB code which sets up various systems of ordinary differential equations (ODE).
- matlab_os, a MATLAB code which illustrates how the system command can be used to issue commands to the computer operating system (UNIX or DOS);
- matlab_plots, a MATLAB code which uses plotting to illustrate a mathematical structure, such as an iterative map, a fractal, a curve or surface.
- matlab_polynomial, a MATLAB code which analyzes a variety of polynomial families, returning the polynomial values, coefficients, derivatives, integrals, roots, or other information.
- matlab_random_test, a MATLAB code which demonstrates random number generation.
- matlab_rule, a MATLAB 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).
- matlab_simulation, a MATLAB 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.
- matrix_analyze, a MATLAB code which reports whether a matrix has various properties.
- matrix_analyze_test
- matrix_assemble_parfor, a MATLAB code which demonstrates the parfor() parallel programming feature by assembling the Hilbert matrix in a parallel loop.
- matrix_assemble_parfor_test
- matrix_chain_brute, a MATLAB 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 MATLAB 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 MATLAB code which computes the exponential of a matrix.
- matrix_exponential_test
- mcnuggets, a MATLAB code which counts M(N), the number of ways a given number N of Chicken McNuggets can be assembled, given that they are only available in packages of 6, 9, and 20.
- mcnuggets_test
- mcnuggets_diophantine, a MATLAB code which uses Diophantine methods to find the ways a given number N of Chicken McNuggets can be assembled, given that they are only available in packages of 6, 9, and 20.
- mcnuggets_diophantine_test
- md, a MATLAB code which carries out a molecular dynamics simulation, and is intended as a starting point for implementing a parallel version.
- md_test
- md_fast, a MATLAB code which carries out a molecular dynamics simulation; it is a version of md() that has been revised to take advantage of vectorization.
- md_fast_test
- md_parfor, a MATLAB code which runs the md() molecular dynamics program, running in parallel using parfor().
- md_parfor_test
- medit_mesh_io, a MATLAB code which reads or writes medit() MESH files defining a finite element mesh.
- medit_mesh_io_test
- medit_to_fem, a MATLAB code which reads a medit() MESH file and writes a corresponding pair of node and element files that correspond to the FEM format.
- medit_to_fem_test
- medit_to_ice, a MATLAB code which reads a medit() MESH file containing an ICE dataset and rewrites the information as a netcdf() file.
- medit_to_ice_test
- memory, a MATLAB code which declares and uses a sequence of larger and larger arrays, to see what the memory limits are on a given computer.
- memory_test
- mesh_bandwidth, a MATLAB code which returns the geometric bandwidth associated with a mesh of elements of any order and in a space of M dimensions.
- mesh_bandwidth_test
- mesh_boundary, a MATLAB code which is given a mesh of a 2D region, formed by polygonal elements, and determines a sequence of pairs of polygonal vertices that define the boundary of the region.
- mesh_boundary_test
- mesh_display, a MATLAB code which plots the nodes and elements of a polygonal mesh, with optional numbering.
- mesh_display_test
- mesh_etoe, a MATLAB code which uses ETOV, the mesh element-to-vertex connectivity, to construct ETOE, the element-to-element connectivity.
- mesh_etoe_test
- mesh_vtoe, a MATLAB code which uses ETOV, the mesh element-to-vertex connectivity, to construct VTOE, the vertex-to-element connectivity.
- mesh_vtoe_test
- mesh2d, a MATLAB code which automatically creates a triangular mesh for a given polygonal region, by Darren Engwirda.
- mesh2d_test
- mesh2d_to_medit, a MATLAB code which accepts the nodes and triangles of a mesh created by mesh2d() and creates a corresponding medit() MESH file.
- mesh2d_to_medit_test
- mesh2d_write, a MATLAB code which writes mesh2d() node and element data to files.
- mesh2d_write_test
- mgmres, a MATLAB 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 MATLAB 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 MATLAB 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 MATLAB code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method, with fsolve() solving the implicit equation, and a fixed time step.
- midpoint_test
- midpoint_adaptive, a MATLAB 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.
- midpoint_adaptive_test
- midpoint_explicit, a MATLAB code which solves one or more ordinary differential equations (ODE) using the (explicit) midpoint method, also called the modified Euler method, and using a fixed time step.
- midpoint_explicit_test
- midpoint_fixed, a MATLAB code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method, using a simple fixed-point iteration to solve the implicit equation, and using a fixed time step.
- midpoint_fixed_test
- mm_io, a MATLAB code which reads and writes sparse linear systems stored in the Matrix Market (MM) format.
- mm_io_test
- mm_to_hb, a MATLAB code which reads the sparse matrix information from an Matrix Market (MM) file and writes a corresponding Harwell Boeing (HB) file.
- mm_to_hb_test
- mm_to_msm, a MATLAB code which reads a Matrix Market (MM) file defining a sparse matrix, and creates a corresponding matrix in MATLAB sparse matrix (MSM) format.
- mm_to_msm_test
- mm_to_st, a MATLAB code which reads the sparse matrix information from a Matrix Market (MM) file and writes a corresponding Sparse Triplet (ST) file.
- mm_to_st_test
- mnist_neural, a MATLAB code which constructs a neural network in order to classify images of digits.
- mnist_neural_test
- monoalphabetic, a MATLAB code which applies a monoalphabetic substitution cipher to a string of text.
- monoalphabetic_test
- monomial, a MATLAB 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_symmetrize, a MATLAB code which symmetrizes the coefficients of equivalent monomials in a polynomial.
- monomial_symmetrize_test
- monomial_value, a MATLAB code which evaluates a monomial in M dimensions.
- monomial_value_test
- monopoly_matrix, a MATLAB code which computes the adjacency and transition matrices for the game of Monopoly.
- monopoly_matrix_test
- monty_hall_simulation, a MATLAB code which simulates the "Let's Make a Deal" game in which Monty Hall has hidden a prize behind one of several doors, and the user wins the prize if the correct door is selected.
- monty_hall_simulation_test
- mortality, a MATLAB code which processes some sample mortality data.
- mortality_test
- msm_to_hb, a MATLAB code which writes a MATLAB sparse matrix (MSM) to a Harwell Boeing (HB) file;
- msm_to_hb_test
- msm_to_mm, a MATLAB code which writes a MATLAB sparse matrix (MSM) to a Matrix Market (MM) file;
- msm_to_mm_test
- msm_to_st, a MATLAB code which writes a MATLAB sparse matrix (MSM) to a Sparse Triplet (ST) file;
- msm_to_st_test
- mxm, a MATLAB code which sets up a matrix multiplication problem A=B*C of arbitrary size, and compares the time required for IJK, IKJ, JIK, JKI, KIJ and KJI orderings of the loops.
- mxm_test
- naca, a MATLAB code which takes the parameters of certain NACA airfoils and returns the coordinates of a sequence of points that outline the wing shape. The shape can be displayed with MATLAB graphics.
- naca_test
- nas, a MATLAB code which runs the NASA kernel benchmark.
- nas_test
- navier_stokes_2d_exact, a MATLAB 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 MATLAB 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
- navier_stokes_mesh2d, a MATLAB code which handles meshes for several 2D test problems involving the Navier Stokes equations (NSE) for fluid flow, provided by Leo Rebholz.
- navier_stokes_mesh2d_test
- navier_stokes_mesh3d, a MATLAB code which handles meshes for several 3D test problems involving the Navier Stokes equations (NSE) for fluid flow, provided by Leo Rebholz.
- navier_stokes_mesh3d_test
- ncm, a MATLAB code which accompanies the textbook "Numerical Computing with MATLAB", by Cleve Moler, and illustrates algorithms for the 3n+1 problem, blackjack, eigenvalue computations, fast Fourier transforms, Fibonacci numbers, file encryption, the flame differential equation, the fractal fern, the Lorenz differential equation, a membrane partial differential equation, minimization of a scalar function, ordinary differential equations, the pendulum differential equation, piecewise cubic Hermite interpolation, polynomial interpolation, quadrature for approximate integration, random number generation, tridiagonal linear system solution, the singular value decomposition, solution of a nonlinear equation.
- ncm_test
- nearest_interp_1d, a MATLAB code which interpolates a set of data using a piecewise constant (PWC) interpolant defined by the nearest neighbor criterion.
- nearest_interp_1d_test
- neighbor_risk, a MATLAB code which records information about neighboring pairs of territories in the game of RISK.
- neighbor_risk_test
- neighbor_states, a MATLAB code which records information about pairs of US states which are neighbors.
- neighbor_states_test
- nelder_mead, a MATLAB code which implements the Nelder-Mead algorithm for the minimization of a scalar function of several variables, by Jeff Borggaard.
- nelder_mead_test
- netcdf_test, a MATLAB code which reads and writes netcdf files.
- neural_network, a MATLAB code which illustrates the use of neural networks for deep learning, using back propagation and stochastic gradient descent, by Catherine Higham and Desmond Higham.
- neural_network_test
- newton_interp_1d, a MATLAB code which finds a polynomial interpolant to data using Newton divided differences.
- newton_interp_1d_test
- newton_rc, a MATLAB code which solves a system of nonlinear equations by Newton's method, using reverse communication (RC).
- newton_rc_test
- niederreiter2, a MATLAB code which computes the Niederreiter M dimensional Quasi Mont Carlo (QMC) sequence, base 2;
- niederreiter2_test
- nintlib, a MATLAB code which implements approximate integration (quadrature) in M dimensions;
- nintlib_test
- nonlin_bisect, a MATLAB code which interactively uses bisection to seek a zero of a function f(x) within a domain a ≤ x ≤ b;
- nonlin_bisect_test
- nonlin_fixed_point, a MATLAB code which interactively uses fixed point iteration x=g(x) to seek a zero of a function f(x) given a starting point x0 and iterations it;
- nonlin_fixed_point_test
- nonlin_newton, a MATLAB code which interactively uses the Newton method to find the zero of a function, given formulas for f(x), f'(x), and a starting point.
- nonlin_newton_test
- nonlin_regula, a MATLAB code which interactively uses the regula falsi method to seek a zero of a function f(x) within a change of sign interval [a,b];
- nonlin_regula_test
- nonlin_secant, a MATLAB code which interactively uses the secant method to seek a zero of a function f(x) given two starting estimates a and b.
- nonlin_secant_test
- nonlin_snyder, a MATLAB code which interactively uses the Snyder method to seek a zero of a function f(x) within a change of sign interval [a,b];
- nonlin_snyder_test
- norm_l1, a MATLAB code which interactively estimates the L1 norm of a function over an interval [A,B], with the function entered as a string.
- norm_l1_test
- norm_l2, a MATLAB code which interactively estimates the L2 norm of a function over an interval [A,B], with the function entered as a string.
- norm_l2_test
- norm_loo, a MATLAB code which interactively estimates the L-infinity norm of a function over an interval [A,B], with the function entered as a string.
- norm_loo_test
- norm_rms, a MATLAB code which interactively estimates the root mean square (RMS) norm of a function over an interval [A,B], with the function entered as a string.
- norm_rms_test
- normal, a MATLAB code which implements normal random number generators (RNG) for real and complex arithmetic, for scalars, vectors, and matrices.
- normal_test
- normal_dataset, a MATLAB code which creates a multivariate normal random dataset and writes it to a file.
- normal_dataset_test
- normal_ode, a MATLAB code which sets up and solves an ordinary differential equation (ODE) defining the normal probability density function (PDF).
- normal_ode_test
- normal01_multivariate_distance, a MATLAB code which computes the expected value of the distance between a pair of points randomly selected from an isotropic standard normal distribution in M dimensions.
- normal01_multivariate_distance_test
- numgrid, a MATLAB code which defines and numbers a subset of the nodes in a regular nxn grid of the [-1,+1]x[-1,+1] unit square. MATLAB includes a built-in version of this function.
- numgrid_test
- obj_display, a MATLAB code which displays an OBJ 3D graphics file;
- obj_display_test
- obj_io, a MATLAB code which reads and writes the data in an OBJ 3D graphics file;
- obj_io_test
- obj_to_tri_surface, a MATLAB code which reads an OBJ 3D graphics file and extracts the surface mesh data as a TRI_SURFACE dataset.
- obj_to_tri_surface_test
- octopus, a MATLAB code which contains some Octave utilities.
- octopus_test
- ode_euler, a MATLAB code which interactively applies the Euler method to estimate the solution of an ordinary differential equation (ODE) y'=f(x,y), over the interval [a,b], with initial condition y(a)=ya, using n steps.
- ode_euler_test
- ode_euler_backward, a MATLAB code which interactively applies the backward Euler method to estimate the solution of an ordinary differential equation (ODE) y'=f(x,y), over the interval [a,b], with initial condition y(a)=ya, using n steps.
- ode_euler_backward_test
- ode_euler_system, a MATLAB code which interactively applies the Euler method to estimate the solution of a system of ordinary differential equations (ODE) y'=f(x,y), over the interval [a,b], with initial condition y(a)=ya, using n steps.
- ode_euler_system_test
- ode_midpoint, a MATLAB code which interactively applies the midpoint method to estimate the solution of an ordinary differential equation (ODE) y'=f(x,y), over the interval [a,b], with initial condition y(a)=ya, using n steps.
- ode_midpoint_test
- ode_midpoint_system, a MATLAB code which interactively applies the midpoint method to estimate the solution of a system of ordinary differential equations (ODE) y'=f(x,y), over the interval [a,b], with initial condition y(a)=ya, using n steps.
- ode_midpoint_system_test
- ode_rk4, a MATLAB code which interactively applies a fourth order Runge-Kutta method to estimate the solution of an ordinary differential equation (ODE) y'=f(x,y), over the interval [a,b], with initial condition y(a)=ya, using n steps.
- ode_rk4_test
- ode_trapezoidal, a MATLAB code which interactively applies the trapezoidal method to estimate the solution of an ordinary differential equation (ODE) y'=f(x,y), over the interval [a,b], with initial condition y(a)=ya, using n steps.
- ode_trapezoidal_test
- ode_sweep_parfor, a MATLAB code which demonstrates how the parfor() command parallelizes the computation of a grid of solutions to a parameterized system of ordinary differential equations (ODE).
- ode_sweep_parfor_test
- ode_trapezoidal, a MATLAB code which interactively applies the trapezoidal method to estimate the solution of an ordinary differential equation (ODE) y'=f(x,y), over the interval [a,b], with initial condition y(a)=ya, using n steps.
- ode_trapezoidal_test
- ode23_test, a MATLAB code which calls ode23(), which is a built-in function for the adaptive solution of systems of ordinary differential equations (ODE) using a pair of Runge-Kutta solvers of orders 2 and 3.
- ode45_test, a MATLAB code which calls ode45(), which is a built-in function for the adaptive solution of systems of ordinary differential equations (ODE) using a pair of Runge-Kutta solvers of orders 4 and 5.
- opt_golden, a MATLAB code which interactively estimates a minimizer of a function f(x) over the interval [a,b], assuming f(x) is unimodular (U-shaped) over the interval [a,b].
- opt_golden_test
- opt_gradient_descent, a MATLAB code which interactively seeks a local minimum of a function f(x), given a formula for the derivative f'(x), a starting point x0, and a stepsize factor gamma.
- opt_gradient_descent_test
- opt_quadratic, a MATLAB code which interactively uses quadratic interpolation to estimate a critical point of a function f(x) given three starting points, an iteration limit n, and tolerances for x and y.
- opt_quadratic_test
- opt_sample, a MATLAB code which interactively estimates the minimum and maximum of a function f(x) over an interval [a,b], using n random sample values, with the function entered as a string.
- opt_sample_test
- oregonator_ode, a MATLAB code which sets up and solves the ordinary differential equations (ODE) for the Oregonator, a model of the Belousov-Zhabotinsky chemical reaction.
- oregonator_ode_test
- ornstein_uhlenbeck, a MATLAB code which approximates solutions of the Ornstein-Uhlenbeck stochastic differential equation (SDE) using the Euler method, the Euler-Maruyama method, and the Milstein method.
- ornstein_uhlenbeck_test
- oscillator_ode, a MATLAB code which sets up and solves the highly oscillatory ordinary differential equation (ODE).
- oscillator_ode_test
- outliers_test, a MATLAB code which uses the isoutlier() function, and other techniques, to identify outliers in data.
- ozone_ode, a MATLAB code which sets up and solves a stiff system of four ordinary differential equations (ODE) that simulate the daily variation in atmospheric ozone concentration.
- ozone_ode_test
- ozone2_ode, a MATLAB code which sets up and solves a stiff system of four ordinary differential equations (ODE) that simulate the daily variation in atmospheric ozone concentration. This version of the ozone ODE includes a nitrogen oxide source term.
- ozone2_ode_test
- padua, a MATLAB code which returns the coordinates of the 2D Padua points, as well as interpolation weights or quadrature weights, and images of the points.
- padua_test
- pagerank, a MATLAB code which uses the eigenvalue (power method) and surfer (Markov Chain Monte Carlo MCMC) approaches to ranking web pages.
- pagerank_test
- pagerank2, a MATLAB code which considers a specific application of the page rank algorithm.
- pagerank2_test
- pariomino, a MATLAB code which considers pariominoes, which are polyominoes with a checkerboard parity, and the determination of tilings of a region using a specific set of pariominoes.
- pariomino_test
- partial_digest, a MATLAB code which seeks solutions of the partial digest problem.
- partial_digest_test
- partition_brute, a MATLAB 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
- partition_greedy, a MATLAB code which uses a greedy algorithm to seek a solution of the partition problem, in which a given set of integers is to be split into two groups whose sums are as close as possible.
- partition_greedy_test
- patterson_rule, a MATLAB 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 MATLAB code which reads or writes graphics files that use the ASCII Portable Bit Map (PBM) format.
- pbma_io_test
- pce_burgers, a MATLAB code which solves a version of the time-dependent viscous Burgers equation, with uncertain viscosity, using a polynomial chaos expansion (PCE) in terms of Hermite polynomials, by Gianluca Iaccarino.
- pce_burgers_test
- pce_legendre, a MATLAB code which sets up the system matrix for a polynomial chaos expansion (PCE), using Legendre polynomials with a linear factor, applied to a 2D partial differential equation (PDE) with a stochastic diffusion coefficient.
- pce_legendre_test
- pce_ode_hermite, a MATLAB code which sets up a simple scalar ordinary differential equation (ODE) for exponential decay with an uncertain decay rate, using a polynomial chaos expansion (PCE) in terms of Hermite polynomials.
- pce_ode_hermite_test
- pdepe_test, a MATLAB code which uses pdepe(), which solves an initial boundary value problem (IBVP) in one spatial dimension.
- pdflib, a MATLAB 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
- peak_movie, a MATLAB code which creates a sequence of frames, and then an animation or movie from the data displayed by the peaks() function.
- peak_movie_test
- pendulum_comparison_ode, a MATLAB code which compares the linear and nonlinear ordinary differential equations (ODE) that represent the behavior of a pendulum of length L under a gravitational force of strength G.
- pendulum_comparison_ode_test
- pendulum_double_ode, a MATLAB code which sets up and solves the double pendulum ordinary differential equation (ODE).
- pendulum_double_ode_test
- pendulum_double_ode_movie, a MATLAB code which solves the double pendulum ordinary differential equation (ODE) for a given set of initial conditions and parameters, and makes a movie of the results.
- pendulum_double_ode_movie_test
- pendulum_elastic_ode a MATLAB code which sets up and solves the ordinary differential equations (ODE) that represent the behavior of a nonlinear elastic pendulum, with gravitational force G, spring constant K, unstretched length L, and mass M.
- pendulum_elastic_ode_test
- pendulum_nonlinear_exact, a MATLAB code which evaluates an exact formula for the solution of the the ordinary differential equations (ODE) that represent the behavior of a nonlinear pendulum of length L under a gravitational force of strength G.
- pendulum_nonlinear_exact_test
- pendulum_nonlinear_ode, a MATLAB code which sets up and solves the ordinary differential equations (ODE) that represent a nonlinear model of the behavior of a pendulum of length L under a gravitational force of strength G.
- pendulum_nonlinear_ode_test
- pendulum_ode, a MATLAB code which sets up and solves the ordinary differential equations (ODE) that represent a linear model of the behavior of a pendulum of length L under a gravitational force of strength G.
- pendulum_ode_test
- pendulum_ode_period, a MATLAB code which sets up and solves a system of ordinary differential equations (ODE) that represent the behavior of a linear pendulum of length L under a gravitational force of strength G, in order to estimate the period of oscillation.
- pendulum_ode_period_test
- pentominoes, a MATLAB code which forms or plots any of the 12 members of the pentomino family, shapes formed from 5 adjacent squares.
- pentominoes_test
- perceptron_test, a MATLAB code which calculates a classifier of linearly separable data using the perceptron algorithm.
- percolation_simulation, a MATLAB code which simulates a percolation system. A rectangular region is decomposed into a grid of MxN squares. Each square may be porous or solid. We are interested in a path of porous squares connecting the top and bottom, or the left and right boundaries. The original MATLAB code was written by Ian Cooper.
- percolation_simulation_test
- permutation_distance, a MATLAB code which estimates the expected value of the Ulam distance between a pair of randomly selected permutations of the same order.
- permutation_distance_test
- persistence, a MATLAB 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 MATLAB code which reads or writes graphics files that use the ASCII Portable Gray Map (PGM) format.
- pgma_io_test
- pi_spigot, a MATLAB code which produces any number of digits of the decimal expansion of pi.
- pi_spigot_test
- pic, a MATLAB code which uses the Particle In Cell (PIC) method to simulate the motion of electrically charged particles past a plate, and is intended as a starting point for implementing a parallel version.
- pic_test
- pink_noise, a MATLAB code which computes a pink noise signal obeying a 1/f power law.
- pink_noise_test
- plasma_matrix, a MATLAB code which sets up a matrix associated with a problem in plasma physics.
- plasma_matrix_test
- ply_io, a MATLAB code which reads or writes a 3D graphics file in PLY format, by Greg Turk;
- ply_io_test
- poisson_1d_multigrid, a MATLAB code which applies the multigrid method to a discretized version of the 1D Poisson equation.
- poisson_1d_multigrid_test
- poisson_2d, a MATLAB code which solves the Poisson equation in a rectangle, using finite differences and Jacobi iteration.
- poisson_2d_test
- poisson_ell_test, a MATLAB code which plots data from a solution of the Poisson equation in the L-shaped region, as computed by FreeFem++() and transferred using the ffmatlib() library.
- poisson_simulation, a MATLAB code which simulates a Poisson process in which events randomly occur with an average waiting time of Lambda.
- poisson_simulation_test
- polar_ode, a MATLAB code which sets up and solves an ordinary differential equation (ODE) whose variable is complex, and whose solution should be viewed in a polar coordinate plot.
- polar_ode_test
- polpak, a MATLAB 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 MATLAB 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_average, a MATLAB code which demonstrates a process of repeatedly averaging and normalizing the vertices of a polygon, illustrating a property of the power method.
- polygon_average_test
- polygon_distance, a MATLAB code which computes the expected value of the distance between a pair of points randomly selected from the interior of a polygon in 2D.
- polygon_distance_test
- polygon_grid, a MATLAB code which generates a grid of points over the interior of a polygon in 2D.
- polygon_grid_test
- polygon_integrals, a MATLAB 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 MATLAB 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 MATLAB code which triangulates a (possibly nonconvex) polygon in 2D, based on a C program by Joseph ORourke;
- polygon_triangulate_test
- polygonal_surface_display, a MATLAB code which displays a surface in 3D described as a set of polygons;
- polygonal_surface_display_test
- polyiamonds, a MATLAB code which works with polyiamonds, simple shapes constructed by edgewise connections of congruent equilateral triangles.
- polyiamonds_test
- polynomial, a MATLAB code which adds, multiplies, differentiates, evaluates and prints multivariate polynomials in a space of M dimensions.
- polynomial_test
- polynomial_conversion, a MATLAB code which converts representations of a polynomial between monomial, Bernstein, Chebyshev, Gegenbauer, Hermite, Laguerre and Legendre forms.
- polynomial_conversion_test
- polynomial_multiply, a MATLAB code which multiplies two polynomials p(x) and q(x).
- polynomial_multiply_test
- polynomial_resultant, a MATLAB code which computes the resultant R of univariate polynomials P and Q.
- polynomial_resultant_test
- polynomial_resultant_symbolic_test, a MATLAB code which calls the symbolic function resultant(), which computes the resultant R of univariate polynomials P and Q.
- polynomial_root_bound, a MATLAB code which computes the Cauchy bound on the magnitude of all roots of a polynomial with complex coefficients.
- polynomial_root_bound_test
- polynomials, a MATLAB 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
- polyomino_parity, a MATLAB code which uses parity considerations to determine whether a given set of polyominoes tile a specified region.
- polyomino_parity_test
- polyominoes, a MATLAB code which defines, solves, and plots a variety of polyomino tiling problems, which are solved by a direct algebraic approach, instead of the more typical brute-force or backtracking methods.
- polyominoes_test
- porous_medium_exact, a MATLAB 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 MATLAB code which carries out the power method for finding a dominant eigenvalue and its eigenvector.
- power_method_test
- power_rule, a MATLAB code which constructs a power rule, that is, a product quadrature rule from identical 1D factor rules.
- power_rule_test
- pplane9, a MATLAB code which allows a user to interactively explore the phase plane of a system of autonomous ordinary differential equations. On starting the program, the user is given an interface in which to enter the equations and the screen limits, as well as a graphics screen on which the direction field is shown. Clicking any point in the graphics screen results in a trace of the phase plane curve through that point. The program is by Hugh Harvey and George Williams. With every new release of MATLAB, this program breaks again!
- ppma_io, a MATLAB code which reads or writes graphics files that use the ASCII Portable Pixel Map (PPM) format.
- ppma_io_test
- pram, a MATLAB code which considers the pram puzzle, a smaller version of the eternity puzzle. The pram puzzle specifies a region R composed of 2304 30-60-90 triangles, and a set of 64 "tiles", consisting of 36 30-60-90 triangles, and seeks an arrangement of the tiles that exactly covers the region.
- pram_test
- pram_cplex_test a BASH code which calls cplex(), to read the LP file defining the pram tiling problem, solve the linear programming problem, and write the solution to a file.
- pram_view, a MATLAB code which considers the pram puzzle, and applies a given set of rotations, reflections and translations to the 64 tiles in order to reconstruct the pram region, thus verifying a known solution to the problem, as well as the correctness of the tile definitions.
- praxis, a MATLAB code which minimizes a scalar function of several variables, without requiring derivative information, by Richard Brent.
- praxis_test
- predator_prey_ode, a MATLAB code which sets up and solves a time-dependent predator-prey system of ordinary differential equations (ODE), for which a limit cycle exists.
- predator_prey_ode_test
- predator_prey_ode_period, a MATLAB code which sets up and solves a time-dependent predator-prey system of ordinary differential equations (ODE) in order to estimate the period of the limit cycle.
- predator_prey_ode_period_test
- prime, a MATLAB 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_parfor, a MATLAB code which counts primes between 1 and N, running in parallel using the parfor() feature of MATLAB.
- prime_parfor_test
- prime_pi, a MATLAB code which evaluates Pi(n), the number of primes less than or equal to an integer n.
- prime_pi_test
- prime_plot, a MATLAB code which displays a box plot of the prime and composite numbers.
- prime_plot_test
- prism_jaskowiec_rule, a MATLAB 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 MATLAB 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 MATLAB 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 MATLAB code which creates an M dimensional quadrature rule from a product of distinct 1d quadrature rules;
- product_rule_test
- profile_data, a MATLAB code which carries out some numerical exercises based on data that came from tracing the profile of a face.
- profile_data_test
- puzzles, a MATLAB code which solves simple puzzles;
- pwc_plot_1d, a MATLAB code which converts the definition of a piecewise constant (PWC) function of a 1D argument into plottable data.
- pwc_plot_1d_test
- pwc_plot_2d, a MATLAB code which converts the definition of a piecewise constant (PWC) function of a 2D argument into plottable data.
- pwc_plot_2d_test
- pwl_approx_1d, a MATLAB code which approximates a set of data using a piecewise linear (PWL) function.
- pwl_approx_1d_test
- pwl_interp_1d, a MATLAB code which interpolates a set of data using a piecewise linear (PWL) function.
- pwl_interp_1d_test
- pwl_interp_2d, a MATLAB code which evaluates a piecewise linear (PWL) interpolant to data defined on a regular 2D grid.
- pwl_interp_2d_test
- pwl_interp_2d_scattered, a MATLAB code which evaluates a piecewise linear (PWL) interpolant to data which is available at an irregularly arranged set of points.
- pwl_interp_2d_scattered_test
- pwl_product_integral, a MATLAB code which calculates the exact value of the integral of the product of two piecewise linear (PWL) functions f(x) and g(x).
- pwl_product_integral_test
- pyramid_exactness, a MATLAB code which investigates the polynomial exactness of a quadrature rule over the interior of the unit pyramid in 3D.
- pyramid_exactness_test
- pyramid_felippa_rule, a MATLAB 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 MATLAB code which computes a grid of points over the interior of the unit pyramid in 3D;
- pyramid_grid_test
- pyramid_integrals, a MATLAB 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 MATLAB 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 MATLAB 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 MATLAB code which computes a conical product quadrature rule over the interior of the unit pyramid in 3D.
- pyramid_rule_test
- pyramid_witherden_rule, a MATLAB 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 MATLAB code which computes the linear least squares (LLS) solution of a system A*x=b using the QR factorization.
- qr_solve_test
- quad_fast_rule, a MATLAB code which rapidly defines certain quadrature rules for approximating an integral;
- quad_fast_rule_test
- quad_gauss, a MATLAB code which interactively uses an n-point Gauss quadrature rule to estimate the integral of a function f(x) in the interval [a,b].
- quad_gauss_test
- quad_monte_carlo, a MATLAB code which interactively uses n random samples to estimate the integral of a function f(x) in the interval [a,b].
- quad_monte_carlo_test
- quad_parfor, a MATLAB code which estimates an integral using quadrature, using parfor() to enable parallel execution.
- quad_parfor_test
- quad_rule, a MATLAB code which defines quadrature rules for approximating an integral;
- quad_rule_test
- quad_trapezoid, a MATLAB code which interactively applies a trapezoid rule using n intervals to estimate the integral of a function f(x) over an interval [a,b].
- quad_trapezoid_test
- quad2d, a MATLAB code which estimates an integral over a 2D rectangle using quadrature, intended as the starting point for program optimization or parallelization.
- quad2d_test
- quadex_ode a MATLAB code which sets up and solves a stiff ordinary differential equation (ODE), whose exact solution is a parabola, but for which errors grow exponentially.
- quadex_ode_test
- quadmom, a MATLAB 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
- quadprog_test, calls quadprog() to solve problems in quadratic programming.
- quadrature_golub_welsch, a MATLAB code which computes the points and weights of a Gaussian quadrature rule using the Golub-Welsch procedure.
- quadrature_golub_welsch_test
- quadrature_least_squares, a MATLAB 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 MATLAB 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 MATLAB 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, a MATLAB code which carries out geometric calculations on quadrilaterals, including angles, area, distances, nearest point, point containment, perimeter, and random generation.
- quadrilateral_test
- quadrilateral_mesh, a MATLAB code which handles meshes of quadrilaterals over a 2D region;
- quadrilateral_mesh_test
- quadrilateral_mesh_order1_display, a MATLAB code which plots piecewise constant (PWC) data associated with a mesh of quadrilaterals;
- quadrilateral_mesh_order1_display_test
- quadrilateral_mesh_rcm, a MATLAB code which computes the Reverse Cuthill McKee (RCM) reordering for nodes in a mesh of 4-node quadrilaterals.
- quadrilateral_mesh_rcm_test
- quadrilateral_surface_display, a MATLAB code which plots piecewise bilinear data associated with a quadrilateral_surface, that is, a 3D surface defined by a quadrilateral mesh;
- quadrilateral_surface_display_test
- quadrilateral_witherden_rule, a MATLAB code which returns a symmetric Witherden quadrature rule for the quadrilateral, with exactness up to total degree 21.
- quadrilateral_witherden_rule_test
- quality, a MATLAB code which measures the dispersion of pointsets in M dimensions;
- quality_test
- quasiperiodic_ode, a MATLAB code which sets up and solves a system of ordinary differential equations (ODE) for a problem with a quasiperiodic solution.
- quasiperiodic_ode_test
- quaternions, a MATLAB code which carries out some simple arithmetic operations for quaternions.
- quaternions_test
- r8_scale, a MATLAB code which computes the "next" and "previous" real numbers.
- r8_scale_test
- r83, a MATLAB code which contains linear algebra routines for r83 matrices (real, 64 bit, tridiagonal 3xN format).
- r83_test
- r83_np, a MATLAB code which contains linear algebra routines for r83_np matrices (real, 64 bit, tridiagonal 3xN format, nonpivoting factorization).
- r83_np_test
- r83p, a MATLAB code which contains linear algebra routines for r83p matrices (real, 64 bit, tridiagonal periodic format).
- r83p_test
- r83s, a MATLAB code which contains linear algebra routines for r83s matrices (real, 64 bit, tridiagonal scalar format).
- r83s_test
- r83t, a MATLAB code which contains linear algebra routines for r83t matrices (real, 64 bit, tridiagonal Mx3 format).
- r83t_test
- r83v, a MATLAB code which contains linear algebra routines for r83v matrices (real, 64 bit, tridiagonal three vector format).
- r83v_test
- r85, a MATLAB code which contains linear algebra routines for r85 matrices (real, 64 bit, pentadiagonal format).
- r85_test
- r8bb, a MATLAB code which contains linear algebra routines for r8bb matrices (real, 64 bit, border banded format).
- r8bb_test
- r8blt, a MATLAB code which contains linear algebra routines for r8blt matrices (real, 64 bit, band lower triangular format).
- r8blt_test
- r8bto, a MATLAB code which contains linear algebra routines for r8bto matrices (real, 64 bit, block Toeplitz format).
- r8bto_test
- r8but, a MATLAB code which contains linear algebra routines for r8but matrices (real, 64 bit, band upper triangular format).
- r8but_test
- r8cb, a MATLAB code which contains linear algebra routines for r8cb matrices (real, 64 bit, Compressed Band format).
- r8cb_test
- r8cbb, a MATlAB code which contains linear algebra routines for r8cbb matrices (real, 64 bit, Compressed Border Banded format).
- r8cbb_test
- r8ccs, a MATLAB code which contains linear algebra routines for r8ccs matrices: real, 64 bit, Compressed Column Storage (CCS) format.
- r8ccs_test
- r8ci, a MATLAB code which contains linear algebra routines for r8ci matrices (real, 64 bit, circulant format).
- r8ci_test
- r8col, a MATLAB code which contains utility routines for an R8COL, that is, a real 64 bit 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
- r8crs, a MATLAB code which contains linear algebra routines for R8CRS matrices: real, 64 bit, Compressed Row Storage (CRS) format.
- r8crs_test
- r8gb, a MATLAB code which contains linear algebra routines for r8gb matrices (real, 64 bit, General Banded format).
- r8gb_test
- r8gd, a MATLAB code which contains linear algebra routines for r8gd matrices (real, 64 bit, general diagonal format).
- r8gd_test
- r8ge, a MATLAB code which contains linear algebra routines for R8GE matrices (real, 64 bit, General format).
- r8ge_test
- r8ge_np, a MATLAB code which contains nonpivoting linear algebra routines for r8ge_np matrices (real, 64 bit, General Nonpivoting format).
- r8ge_np_test
- r8lib, a MATLAB code which contains utilities for real 64 bit (R8) arithmetic.
- r8lib_test
- r8lt, a MATLAB code which contains linear algebra routines for R8LT matrices: real, 64 bit, Lower Triangular.
- r8lt_test
- r8ltt, a MATLAB code which contains linear algebra routines for r8ltt matrices (real, 64 bit, lower triangular Toeplitz format).
- r8ltt_test
- r8ncf, a MATLAB code which contains linear algebra routines for r8ncf matrices (real, 64 bit, nonsymmetric coordinate format).
- r8ncf_test
- r8pbl, a MATLAB code which contains linear algebra routines for r8pbl matrices (real, 64 bit, symmetric positive definite (SPD) band lower format).
- r8pbl_test
- r8pbu, a MATLAB code which contains linear algebra routines for r8pbu matrices (real, 64 bit, symmetric positive definite (SPD) band upper format).
- r8pbu_test
- r8po, a MATLAB code which contains linear algebra routines for r8po matrices (real, 64 bit, symmetric positive definite (SPD) format).
- r8po_test
- r8poly, a MATLAB 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 MATLAB code which contains linear algebra routines for r8pp matrices (real, 64 bit, symmetric positive definite (SPD) packed format).
- r8pp_test
- r8ri, a MATLAB code which contains linear algebra routines for r8ri matrices (real, 64 bit, row indexed format).
- r8ri_test
- r8row, a MATLAB code which contains utility routines for an R8ROW, that is, a real 64 bit 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 MATLAB code which contains linear algebra routines for r8sd matrices (real, 64 bit, symmetric diagonal format).
- r8sd_test
- r8sm, a MATLAB code which contains linear algebra routines for r8sm matrices (real, 64 bit, Sherman-Morrison A-u*v' format).
- r8sm_test
- r8sr, a MATLAB code which carries out linear algebra operations for r8sr matrices (real, 64 bit, diagonal + compressed row offdiagonal format).
- r8sr_test
- r8ss, a MATLAB code which carries out linear algebra operations for r8ss matrices (real, 64 bit, symmetric skyline format).
- r8ss_test
- r8st, a MATLAB code which contains linear algebra routines for R8ST matrices: real, 64 bit, Sparse Triplet.
- r8st_test
- r8sto, a MATLAB code which contains linear algebra routines for r8sto matrices (real, 64 bit, symmetric Toeplitz N format).
- r8sto_test
- r8to, a MATLAB code which contains linear algebra routines for r8to matrices (real, 64 bit, Toeplitz 2*N-1 format).
- r8to_test
- r8ut, a MATLAB code which contains linear algebra routines for r8ut matrices: real, 64 bit, Upper Triangular.
- r8ut_test
- r8utp, a MATLAB code which carries out linear algebra operations on r8utp matrices, real 64 bit, Upper Triangular Packed format.
- r8utp_test
- r8utt, a MATLAB code which contains linear algebra routines for r8utt matrices (real, 64 bit, upper triangular Toeplitz format).
- r8utt_test
- r8vm, a MATLAB code which contains linear algebra routines for r8vm matrices (real, 64 bit, vandermonde format).
- r8vm_test
- randlc, a MATLAB code which implements a random number generator (RNG) used by the nas() benchmarks.
- randlc_test
- random_data, a MATLAB 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 annulus, cube, ellipse, ellipsoid, polygon, simplex and sphere.
- random_data_test
- random_sorted, a MATLAB code which generates vectors of random values which are already sorted.
- random_sorted_test
- random_walk_1d_simulation, a MATLAB code which simulates a random walk in a 1-dimensional region.
- random_walk_1d_simulation_test
- random_walk_2d_avoid_simulation, a MATLAB code which simulates a self-avoiding random walk in a 2-dimensional region.
- random_walk_2d_avoid_simulation_test
- random_walk_2d_simulation, a MATLAB code which simulates a random walk in a 2-dimensional region.
- random_walk_2d_simulation_test
- random_walk_3d_simulation, a MATLAB code which simulates a random walk in a 3-dimensional region.
- random_walk_3d_simulation_test
- ranlib, a MATLAB code 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
- rbf_interp_1d, a MATLAB code which defines and evaluates radial basis function (RBF) interpolants to 1D data.
- rbf_interp_1d_test
- rbf_interp_2d, a MATLAB code which defines radial basis function (RBF) interpolants to 2D data.
- rbf_interp_2d_test
- rbf_interp_nd, a MATLAB code which defines and evaluates radial basis function (RBF) interpolants to M dimensional data.
- rbf_interp_nd_test
- reaction_ode, a MATLAB code which sets up and solves the ordinary differential equations (ODE) which model a simple chemical reaction A+B --k--> C.
- reaction_ode_test
- reaction_twoway_ode, a MATLAB code which sets up and solves the ordinary differential equations (ODE) which model a two-way chemical reaction between species W1 and W2.
- reaction_twoway_ode_test
- reactor simulation, a MATLAB 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 program was provided as an example with the book "Numerical Methods and Software."
- reactor simulation_test
- readmatrix_test, a MATLAB code which calls readmatrix(), a built-in function which reads a data file containing numeric data in columns; it can also skip one or more initial rows, read only a specified set of columns, to avoid dealing with text input.
- readtable_test, a MATLAB code which calls readtable(), a built-in function which reads a data file containing data in columns, with some data being numeric and some text.
- rectangle_distance, a MATLAB code which estimates the distribution and expected value of the distance between two points picked uniformly at random within a rectangle.
- rectangle_distance_test
- region_test, a MATLAB code which plots data from an interesting region that was meshed by FreeFem++() and transferred using the ffmatlib() library.
- rejection_sample, a MATLAB code which demonstrates acceptance/rejection sampling.
- rejection_sample_test
- rigid_body_ode, a MATLAB code which sets up and solves the ordinary differential equations (ODE) representing the Euler equations for a rigid body with three unequal moments of inertia, originally proposed by Fred Krogh.
- rigid_body_ode_test
- ring_data, a MATLAB code which creates, plots, or saves data generated by sampling a number of concentric, possibly overlapping rings.
- ring_data_test
- ripple_ode, a MATLAB code which sets up and solves an ordinary differential equation (ODE) whose solutions start as ripples and end as hyperbolas.
- ripple_ode_test
- risk_matrix, a MATLAB code which returns the transition and adjacency matrix for the game of RISK.
- risk_matrix_test
- rk12, a MATLAB code which solves an ordinary differential equation (ODE) using a Runge-Kutta (RK) method of order 2, estimating the local error with a Runge-Kutta method of order 1.
- rk12_test
- rk12_adapt, a MATLAB code which defines an adaptive ordinary differential equation (ODE) solver, using Runge-Kutta (RK) solvers of order 1 and 2.
- rk12_adapt_test
- rk23, a MATLAB code which applies Runge-Kutta (RK) solvers of order 2 and 3 to a system of ordinary differential equations (ODE);
- rk23_test
- rk34, a MATLAB code which applies Runge-Kutta (RK) solvers of order 3 and 4 to a system of ordinary differential equations (ODE);
- rk34_test
- rk4, a MATLAB code which applies the fourth order Runge-Kutta (RK) algorithm to estimate the solution of an ordinary differential equation (ODE) at the next time step.
- rk4_test
- rk45, a MATLAB code which applies Runge-Kutta (RK) solvers of order 4 and 5 to a system of ordinary differential equations (ODE);
- rk45_test
- rkf45, a MATLAB code which applies a Runge-Kutta-Fehlberg (RKF) solver to a system of ordinary differential equations (ODE);
- rkf45_test
- rng_cliff, a MATLAB code which computes a sequence of values from the Cliff random number generator (RNG).
- rng_cliff_test
- rnglib, a MATLAB 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
- robertson_ode, a MATLAB code which sets up and solves a system of three nonlinear stiff ordinary differential equations (ODE) characterizing an autocatalytic chemical reaction.
- robertson_ode_test
- roessler_ode, a MATLAB code which sets up and solves the right hand side of the 3D Roessler system of ordinary differential equations (ODE).
- roessler_ode_test
- root_rc, a MATLAB code which seeks a solution of a scalar nonlinear equation f(x)=0, using reverse communication (RC), by Gaston Gonnet.
- root_rc_test
- roots_rc, a MATLAB code which seeks solutions of a system of nonlinear equations, using reverse communication (RC), by Gaston Gonnet.
- roots_rc_test
- rot13, a MATLAB code which enciphers a string using the ROT13 cipher for letters, and the ROT5 cipher for digits.
- rot13_test
- roulette_simulation, a MATLAB code which simulates the spinning of a roulette wheel and the evaluation of certain common roulette bets.
- roulette_simulation_test
- row_echelon_integer, a MATLAB 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
- rref_test, a MATLAB code which calls rref() for the reduced row echelon form (RREF) of a matrix, which can be singular or rectangular.
- rubber_band_ode, a MATLAB code which sets up and solves a set of ordinary differential equat ions (ODE) describing a mass suspended by a spring and rubber band, which exhibits chaotic behavior.
- rubber_band_ode_test
- rucklidge_ode, a MATLAB code which sets up and solves the Rucklidge ordinary differential equation (ODE), a model of double convection which embodies a transition to chaos.
- rucklidge_ode_test
- sammon_data, a MATLAB code which generates six M dimensional datasets for cluster analysis.
- sammon_data_test
- sandia_cubature, a MATLAB code which computes M-dimensional quadrature rules for certain regions and weight functions.
- sandia_cubature_test
- sandia_rules, a MATLAB 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 MATLAB code which explores a generalized construction method for sparse grids.
- sandia_sgmgg_test
- sandia_sparse, a MATLAB 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 MATLAB 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_parfor, a MATLAB code which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfiability problem, running in parallel using the parfor() feature.
- satisfy_parfor_test
- sawtooth_ode, a MATLAB code which sets up and solves an ordinary differential equation (ODE) driven by a right hand side which is a sawtooth function (periodic, discontinuous, piecewise linear).
- sawtooth_ode_test
- schroedinger_linear_pde, a MATLAB code which sets up and solves the complex partial differential equation (PDE) known as Schroedinger's linear equation: dudt = i uxx, in one spatial dimension, with Neumann boundary conditions.
- schroedinger_linear_pde_test
- schroedinger_nonlinear_pde, a MATLAB code which sets up and solves the complex partial differential equation (PDE) known as Schroedinger's nonlinear equation: dudt = i uxx + i gamma * |u|^2 u, in one spatial dimension, with Neumann boundary conditions.
- schroedinger_nonlinear_pde_test
- scip_solution_read, a MATLAB code which reads a file created by the integer programming package scip(), representing the solution of a polyomino tiling problem, and writes out a simple ASCII file.
- scip_solution_read_test
- sde, a MATLAB code which illustrates properties of stochastic differential equations (SDE), and common algorithms for their analysis, by Desmond Higham;
- sde_test
- search_test, a MATLAB code which searches integers between A and B for a value J such that F(J) = C.
- sensitive_ode, a MATLAB code which sets up a second order ordinary differential equation (ODE) which exhibits sensitive dependence on the initial condition.
- sensitive_ode_test
- serenity, a MATLAB code which considers the serenity puzzle, a smaller version of the eternity puzzle. The serenity puzzle specifies a dodecagonal region R composed of 288 30-60-90 triangles, and a set of 8 "tiles", each consisting of 36 30-60-90 triangles, and seeks an arrangement of the tiles that exactly covers the region.
- serenity_test
- serenity_cplex_test a BASH code which calls cplex(), to read the LP file defining the serenity tiling problem, solve the linear programming problem, and write the solution to a file.
- serenity_gurobi_test a BASH code which calls gurobi(), to read the LP file defining the serenity tiling problem, solve the linear programming problem, and write the solution to a file.
- set_theory, a MATLAB code which implements set theory operations such as union, intersection, complement, symmetric difference.
- set_theory_test
- sftpack, a MATLAB code which implements the slow Fourier transform (SFT), intended as a teaching tool and comparison with the Fast Fourier Transform (FFT).
- sftpack_test
- shallow_water_1d, a MATLAB code which simulates the evolution of a 1D fluid governed by the time-dependent shallow water equations (SWE).
- shallow_water_1d_test
- shallow_water_1d_display, a MATLAB code which displays a solution of the shallow water equations (SWE) in 1D, generally as computed by the program shallow_water_1d().
- shallow_water_1d_display_test
- shallow_water_1d_movie, a MATLAB code which solves the partial differential equation (PDE) known as the shallow water equations (SWE), converting the solutions to a sequence of graphics frames, which are then assembled into a movie.
- shallow_water_1d_movie_test
- shepard_interp_1d, a MATLAB code which defines and evaluates Shepard interpolants to 1D data, based on inverse distance weighting.
- shepard_interp_1d_test
- shepard_interp_2d, a MATLAB code which defines and evaluates Shepard interpolants to 2D data, based on inverse distance weighting.
- shepard_interp_2d_test
- shepard_interp_nd, a MATLAB code which defines and evaluates Shepard interpolants to M dimensional data, based on inverse distance weighting.
- shepard_interp_nd_test
- sigmoid_derivative, a MATLAB code which evaluates derivatives of any order for the sigmoid function s(x)=1/(1+exp(-x)).
- sigmoid_derivative_test
- simplex_coordinates, a MATLAB code which computes the Cartesian coordinates of the vertices of a regular simplex in M dimensions.
- simplex_coordinates_test
- simplex_gm_rule, a MATLAB code which defines Grundmann-Moeller quadrature rules over the interior of a triangle in 2D, a tetrahedron in 3D, or over the interior of the simplex in M dimensions.
- simplex_gm_rule_test
- simplex_grid, a MATLAB code which generates a regular grid of points over the interior of an arbitrary simplex in M dimensions.
- simplex_grid_test
- simplex_integrals, a MATLAB 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 MATLAB 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 MATLAB 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 MATLAB code which demonstrates properties of the discrete sine transform (DST).
- sine_transform_test
- single_linkage_test, a MATLAB code which uses the MATLAB single linkage clustering functions.
- sir_ode, a MATLAB code which sets up and solves the ordinary differential equations (ODE) which simulate the spread of a disease using the Susceptible/Infected/Recovered (SIR) model.
- sir_ode_test
- sir_simulation, a MATLAB code which simulates the spread of a disease through a hospital room of M by N beds, using the Susceptible/Infected/Recovered (SIR) model.
- sir_simulation_test
- sling_ode, a MATLAB code which sets up and solves a system of ordinary differential equations (ODE) for which the exact circular solution can only be approximated for a short interval before it decays to zero.
- sling_ode_test
- snakes_and_ladders, a MATLAB code which provides tools for studying the game of Snakes and Ladders.
- snakes_and_ladders_simulation, a MATLAB code which simulates a one-player game of Snakes and Ladders, to produce histograms of the count, PDF and CDF estimates for the length of a one-player game.
- snakes_and_ladders_simulation_test
- snakes_game, a MATLAB code which simulates a one-player version of the game of Snakes and Ladders, by Mina Aymin.
- snakes_matrix, a MATLAB code which returns the transition matrix for the game of Snakes and Ladders.
- snakes_matrix_test
- snakes_probability, a MATLAB code which computes the game length probabilities for the game of Snakes and Ladders, by Desmond Higham and Nicholas Higham.
- snakes_probability_test
- sncndn, a MATLAB code which evaluates the Jacobi elliptic functions sn(u,m), cn(u,m), and dn(u,m).
- sncndn_test
- sobol, a MATLAB code which generates elements of the Sobol M dimensional Quasi Mont Carlo (QMC) sequence, by Bennett Fox.
- sobol_test
- solve, a MATLAB code which uses Gauss elimination to solve a linear system A*x=b.
- solve_test
- sor, a MATLAB code which uses the successive over-relaxation (SOR) iteration to solve a linear system of equations.
- sor_test
- sort_rc, a MATLAB code which sorts a list of any kind of objects, using reverse communication (RC).
- sort_rc_test
- sort_test, a MATLAB code which calls the sort() function to sort objects of several types.
- sparse_test, a MATLAB code which tests the sparse() function for creating sparse matrices and carrying out linear algebraic functions on them;
- sparse_display, a MATLAB code which reads information defining a matrix of numbers and displays the sparsity pattern or location of the nonzero elements using gnuplot(). This operation is already available in the built-in MATLAB spy() function.
- sparse_display_test
- sparse_grid_cc, a MATLAB code which creates sparse grids based on Clenshaw-Curtis (CC) quadrature rules.
- sparse_grid_cc_test
- sparse_grid_gl, a MATLAB code which creates sparse grids based on Gauss-Legendre (GL) rules.
- sparse_grid_gl_test
- sparse_grid_hermite, a MATLAB code which creates sparse grids based on Gauss-Hermite rules.
- sparse_grid_hermite_test
- sparse_grid_hw, a MATLAB 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 MATLAB code which creates sparse grids based on Gauss-Laguerre rules.
- sparse_grid_laguerre_test
- sparse_grid_mixed, a MATLAB code which creates a sparse grid dataset based on a mixed set of 1D factor rules.
- sparse_grid_mixed_test
- sparse_grid_total_poly, a MATLAB code which investigates the total polynomial approximation using sparse grids.
- sparse_grid_total_poly_test
- sparse_interp_nd, a MATLAB code which defines a sparse interpolant to a function f(x) of a M dimensional argument.
- sparse_interp_nd_test
- sparse_parfor, a MATLAB code which constructs a sparse matrix by evaluating individual blocks in parallel with the parfor() command, and then assembled on a single processor using the sparse() command, by Gene Cliff.
- sparse_parfor_test
- spd_test, a MATLAB code which performs a few tests on a real matrix to determine whether it is symmetric positive definite (SPD).
- sphere_cubed_grid, a MATLAB 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 MATLAB code which carries out the Centroidal Voronoi Tessellation (CVT) iteration on the surface of the unit sphere in 3D.
- sphere_cvt_test
- sphere_delaunay, a MATLAB code which computes the Delaunay triangulation of points on the surface of the unit sphere in 3D.
- sphere_delaunay_test
- sphere_distance, a MATLAB code which computes the expected value of the distance between a pair of points randomly selected on the surface of the unit sphere in 3D.
- sphere_distance_test
- sphere_exactness, a MATLAB code which tests the polynomial exactness of a quadrature rule on the surface of the unit sphere in 3D.
- sphere_exactness_test
- sphere_fibonacci_grid, a MATLAB 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 MATLAB code which provides a number of ways of generating 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 MATLAB 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 MATLAB code which computes Lebedev quadrature rules on the surface of the unit sphere in 3D.
- sphere_lebedev_rule_test
- sphere_lebedev_rule_display, a MATLAB code which reads a file defining a Lebedev quadrature rule on the surface of the unit sphere in 3D and displays the point locations.
- sphere_lebedev_rule_display_test
- sphere_llq_grid, a MATLAB 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 MATLAB 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 MATLAB 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_positive_distance, a MATLAB code which computes the expected value of the distance between a pair of points randomly selected on the surface of the unit positive sphere in 3D.
- sphere_positive_distance_test
- sphere_quad, a MATLAB code which uses triangulation to approximate an integral on the surface of the unit sphere in 3D.
- sphere_quad_test
- sphere_stereograph, a MATLAB 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_stereograph_display, a MATLAB code which computes and displays the results of several stereographic projections between points on the surface of the unit sphere in 3D and a plane.
- sphere_stereograph_display_test
- sphere_triangle_monte_carlo, a MATLAB 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 MATLAB 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 MATLAB code which computes the Voronoi diagram of points on the surface of the unit sphere in 3D.
- sphere_voronoi_test
- spinterp, a MATLAB code 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.
- spinterp_test
- spiral_exact, a MATLAB code which computes a 2D velocity vector field that is an exact solution of the continuity equation.
- spiral_exact_test
- spiral_pde, a MATLAB code which solves a pair of reaction-diffusion partial differential equations (PDE) over a rectangular domain with periodic boundary condition, whose solution is known to evolve into a pair of spirals.
- spiral_pde_test
- spiral_pde_movie, a MATLAB code which solves a pair of reaction-diffusion partial differential equations (PDE) over a rectangular domain with periodic boundary condition, whose solution is known to evolve into a pair of spirals. The sequence of solutions is bundled into a movie.
- spiral_pde_movie_test
- spline, a MATLAB code which interpolates and approximates via splines;
- spline_test
- spquad, a MATLAB code which computes the points and weights of a sparse grid quadrature rule for an M-dimensional integral, based on the Clenshaw-Curtis quadrature rule, by Greg von Winckel.
- spquad_test
- spring_double_ode, a MATLAB code which sets up and solves a system of ordinary differential equations (ODE) for a system in which a mass is connected by a spring to a mass connected by a spring to a fixed support.
- spring_double_ode_test
- spring_ode, a MATLAB code which sets up and solves a system of ordinary differential equations (ODE) for the motion of a spring with mass m, damping b, and stiffness k.
- spring_ode_test
- spring_sweep_ode, a MATLAB code which computes a grid of solutions to a parameterized system of ordinary differential equations (ODE) that represent the motion of a spring with mass m, damping b, and stiffness k.
- spring_sweep_ode_test
- square_arbq_rule, a MATLAB 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_distance, a MATLAB code which computes the expected value of the distance between a pair of points randomly selected from the interior of the unit square in 2D.
- square_distance_test
- square_exactness, a MATLAB code which investigates the polynomial exactness of quadrature rules for f(x,y) over the interior of a rectangle in 2D.
- square_exactness_test
- square_felippa_rule, a MATLAB code which returns Felippa quadrature rules for approximating integrals over the interior of a square in 2D.
- square_felippa_rule_test
- square_grid, a MATLAB code which computes a grid of points over the interior of a square in 2D.
- square_grid_test
- square_hex_grid, a MATLAB code which computes a hexagonal grid of points over the interior of a square in 2D.
- square_hex_grid_test
- square_integrals, a MATLAB 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 MATLAB 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 MATLAB 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_surface_distance, a MATLAB code which estimates the expected value of the distance between a pair of points randomly selected on the surface of the unit square.
- square_surface_distance_test
- square_symq_rule, a MATLAB code which returns symmetric quadrature rules, with exactness up to total degree 20, over the interior of the square in 2D, by Hong Xiao and Zydrunas Gimbutas.
- square_symq_rule_test
- squircle_ode, a MATLAB code which sets up and solves a system of ordinary differential equations (ODE) for a pair of functions that generalize the sine and cosine, and whose phase portrait is a squircle (a sort of squared circle).
- squircle_ode_test
- st_io, a MATLAB code which reads and writes sparse linear systems stored in the Sparse Triplet (ST) format.
- st_io_test
- st_to_ccs, a MATLAB 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 MATLAB code which converts sparse matrix data from Sparse Triplet (ST) format to Harwell Boeing (HB) format;
- st_to_hb_test
- st_to_mm, a MATLAB code which converts sparse matrix data from Sparse Triplet (ST) format to Matrix Market (MM) format;
- st_to_mm_test
- st_to_msm, a MATLAB code which reads a Sparse Triplet (ST) file and creates a corresponding MATLAB Sparse Matrix (MSM).
- st_to_msm_test
- steinerberger, a MATLAB code which evaluates the Steinerberger function, a continuous function with discontinuous derivative, which is very hard to accurately plot, integrate, minimize, or interpolate.
- steinerberger_test
- stetter_ode, a MATLAB code which sets up and solves an ordinary differential equation (ODE) for which a specific time step sequence causes the implicit trapezoidal method to be unstable, while the implicit midpoint method will be stable. Note that the right hand side function f(t,y) is periodic, discontinuous, and piecewise linear.
- stetter_ode_test
- stiff_ode, a MATLAB code which sets up and solves an ordinary differential equation (ODE) which is an example of a stiff ODE.
- stiff_ode_test
- stla_display, a MATLAB code which displays an ASCII stereolithography (STL) 3D graphics file;
- stla_display_test
- stla_io, a MATLAB code which reads and writes an ASCII stereolithography (STL) 3D graphics file;
- stla_io_test
- stla_to_tri_surface, a MATLAB code which reads an ASCII stereolithography (STL) 3D graphics file and extracts the surface mesh data as a TRI_SURFACE dataset.
- stla_to_tri_surface_test
- stla_to_tri_surface_fast, a MATLAB code which is a faster version of stla_to_tri_surface().
- stla_to_tri_surface_fast_test
- stochastic_diffusion, a MATLAB code which implements several versions of a stochastic diffusivity coefficient.
- stochastic_diffusion_test
- stochastic_heat2d, a MATLAB 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 MATLAB code which applies a Runge Kutta (RK) scheme to a stochastic ordinary differential equation (SDE).
- stochastic_rk_test
- stokes_2d_exact, a MATLAB code which evaluates exact solutions to the incompressible steady Stokes equations over the unit square in 2D.
- stokes_2d_exact_test
- string_pde, a MATLAB 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
- stroud, a MATLAB 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_test
- subset, a MATLAB 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_distance, a MATLAB code which estimates the expected value of the Hamming distance between a pair of randomly selected subsets of an M set.
- subset_distance_test
- subset_sum, a MATLAB 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 MATLAB 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 MATLAB code which seeks solutions of the subset sum problem, using a brute force approach.
- subset_sum_brute_test
- subset_sum_swap, a MATLAB 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
- sudoku, a MATLAB code which handles Sudoku puzzles;
- sudoku_test
- surf_test, calls surf(), which displays a 3D surface or contour plot for data of the form Z=F(X,Y).
- svd_basis, a MATLAB code which applies the singular value decomposition (SVD) to a collection of data vectors, extracting dominant modes;
- svd_basis_test
- svd_circle, a MATLAB code which analyzes a linear map of the unit circle caused by an arbitrary 2x2 matrix A, using the singular value decomposition (SVD).
- svd_circle_test
- svd_faces, a MATLAB code which applies singular value decomposition (SVD) analysis to a set of images.
- svd_faces_test
- svd_fingerprint, a MATLAB code which reads a file containing a fingerprint image and uses the singular value decomposition (SVD) to compute and display a series of low rank approximations to the image.
- svd_fingerprint_test
- svd_gray, a MATLAB code which reads a gray scale image, computes the Singular Value Decomposition (SVD), and constructs a series of low rank approximations to the image.
- svd_gray_test
- svd_lls, a MATLAB code which uses the singular value decomposition (SVD) to construct and plot the best affine and linear relationships in the sense of least square, between two vectors of data.
- svd_lls_test
- svd_powers, a MATLAB code which applies singular value decomposition (SVD) analysis to a set of powers x(i)^(j-1).
- svd_powers_test
- svd_snowfall, a MATLAB code which reads a file containing historical snowfall data and analyzes the data with the Singular Value Decomposition (SVD).
- svd_snowfall_test
- svd_sphere, a MATLAB code which analyzes a linear map of the unit sphere caused by an arbitrary 3x3 matrix A, using the singular value decomposition (SVD).
- svd_sphere_test
- svd_test, a MATLAB code which demonstrates the Singular Value Decomposition (SVD) for a simple example.
- svd_truncated_test, a MATLAB code which calls the "economy" version of the Singular Value Decomposition (SVD) of an M by N rectangular matrix, in cases where M is less than N or N is less than M.
- t_puzzle, a MATLAB code which considers the T puzzle, a set of 4 wooden pieces. The challenge is to arrange the pieces to form the shape of the letter T. Three other challenge shapes are an arrow, a rhombus, and a "fat" T.
- t_puzzle_test
- t_puzzle_cplex_test, a BASH code which calls cplex(), to read the LP file defining the T-puzzle tiling problem, solve the linear programming problem, and write the solution to a file.
- t_puzzle_gui, a MATLAB code which sets up a graphical user interface for the T puzzle, by Cleve Moler.
- t_puzzle_gurobi_test, a BASH code which calls gurobi(), to read the LP file defining the T-puzzle tiling problem, solve the linear programming problem, and write the solution to a file.
- table_io, a MATLAB code which reads and writes a simple table file;
- table_io_test
- task_division, a MATLAB code which implements a simple procedure for smoothly dividing T tasks among P processors; such a method can be useful in MPI and other parallel environments, particularly when T is not an exact multiple of P, and when the processors can be indexed starting from 0 or from 1.
- task_division_test
- tec_io, a MATLAB 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 MATLAB code which converts a tecplot() ASCII TEC file into an FEM model.
- tec_to_fem_test
- tec_to_vtk, a MATLAB code which converts a tecplot() TEC file into a set of VTK files.
- tec_to_vtk_test
- tennis_matrix, a MATLAB code which computes the transition matrix for a game of tennis, which has 17 distinct states.
- tennis_matrix_test
- tensor_grid_display, a MATLAB code which displays the grid points of a tensor product rule used for interpolation or quadrature, in 1D, 2D or 3D.
- tensor_grid_display_test
- test_approx, a MATLAB code which implements test problems for approximation, provided as a set of (x,y) data.
- test_approx_test
- test_con, a MATLAB code which implements test problems for numerical continuation.
- test_con_test
- test_eigen, a MATLAB code which implements test matrices for eigenvalue analysis.
- test_eigen_test
- test_int, a MATLAB code which implements test problems for approximate integration (quadrature) in one dimension.
- test_int_test
- test_int_2d, a MATLAB code which implements test problems for approximate integration (quadrature) in two dimensions.
- test_int_2d_test
- test_interp, a MATLAB code which defines test problems for interpolation, provided as a set of (x,y(x)) data.
- test_interp_test
- test_interp_1d, a MATLAB 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 MATLAB code which defines test problems for interpolation of data z(x,y), which depends on a 2D argument.
- test_interp_2d_test
- test_interp_fun, a MATLAB code which defines test problems for interpolation which are available in functional form.
- test_interp_fun_test
- test_interp_nd, a MATLAB code which defines test problems for interpolation of data z(x), depending on an M dimensional argument.
- test_interp_nd_test
- test_lls, a MATLAB code which implements linear least squares (LLS) test problems of the form A*x=b.
- test_lls_test
- test_matrix, a MATLAB 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 MATLAB code which defines a set of test cases for computing the matrix exponential.
- test_matrix_exponential_test
- test_min, a MATLAB code which implements test problems for minimization of a scalar function of a scalar variable.
- test_min_test
- test_nearest, a MATLAB code which tests the time complexity of various procedures for solving the nearest neighbor problem.
- test_nearest_test
- test_nint, a MATLAB code which defines test functions for M-dimensional quadrature routines.
- test_nint_test
- test_nonlin, a MATLAB code which implements test problems for the solution of systems of nonlinear equations.
- test_nonlin_test
- test_opt, a MATLAB code which implements test problems for optimization of a scalar function of several variables.
- test_opt_test
- test_opt_con, a MATLAB 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 MATLAB 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 MATLAB code which generates example cases of the partial digest problem.
- test_partial_digest_test
- test_triangulation, a MATLAB code which defines test problems for triangulation;
- test_triangulation_test
- test_values, a MATLAB 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, Julian Ephemeris Date, Kelvin, Laguerre, Laplace, Legendre, Lerch, Lobachevsky, Lobatto, Logarithmic integral, Log normal, McNugget numbers, Mertens, Mittag-Leffler, Moebius, Multinomial, Negative binomial, Nine J, Normal, Omega, Owen, Partition, Phi, Pi, Poisson, Polylogarithm, 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 MATLAB code which defines some functions f(x) suitable for testing software that solves a nonlinear equation f(x)=0;
- test_zero_test
- tester, a BASH script which runs the MATLAB tests.
- tet_mesh, a MATLAB code which works with tetrahedral meshes in 3D;
- tet_mesh_test
- tet_mesh_boundary, a MATLAB code which reads information defining a tetrahedral mesh of points in 3D, and determines the triangular faces that form the boundary of the mesh; it writes out files containing the nodes and elements defining this TRI_SURFACE data.
- tet_mesh_boundary_test
- tet_mesh_display, a MATLAB code which reads data defining a tetrahedral mesh, and displays a wireframe image of the nodes and edges;
- tet_mesh_display_test
- tet_mesh_l2q, a MATLAB code which reads information about a 4-node linear mesh of tetrahedrons and creates data defining a corresponding 10-node quadratic mesh of tetrahedrons;
- tet_mesh_l2q_test
- tet_mesh_q2l, a MATLAB code which reads information about a 10-node quadratic mesh of tetrahedrons and creates data defining a corresponding 4-node linear mesh of tetrahedrons;
- tet_mesh_q2l_test
- tet_mesh_quad, a MATLAB code which estimates the integral of a function over a region defined by a tetrahedral mesh.
- tet_mesh_quad_test
- tet_mesh_quality, a MATLAB code which computes various quality measures for a tetrahedral mesh of a set of nodes in 3D;
- tet_mesh_quality_test
- tet_mesh_rcm, a MATLAB code which computes the Reverse Cuthill McKee (RCM) reordering for the nodes of a mesh of tetrahedrons, using 4 or 10 node elements.
- tet_mesh_rcm_test
- tet_mesh_refine, a MATLAB code which refines a mesh of tetrahedrons;
- tet_mesh_refine_test
- tet_mesh_tet_neighbors, a MATLAB code which reads information about a tetrahedral mesh and lists the tetrahedrons adjacent to a given tetrahedron;
- tet_mesh_tet_neighbors_test
- tet_mesh_to_gmsh, a MATLAB code which write a gmsh() file describing a tetrahedral mesh;
- tet_mesh_to_gmsh_test
- tet_mesh_to_xml, a MATLAB code which write an XML file describing a tetrahedral mesh;
- tet_mesh_to_xml_test
- tet_mesh_volumes, a MATLAB code which computes the volume of each tetrahedron in a mesh of tetrahedrons;
- tet_mesh_volumes_test
- tetrahedron, a MATLAB code which carries out geometric calculations involving a general tetrahedron, including solid and facial angles, face areas, point containment, distances to a point, circumsphere and insphere, measures of shape quality, centroid, barycentric coordinates, edges and edge lengths, random sampling, and volumes.
- tetrahedron_test
- tetrahedron_arbq_rule, a MATLAB 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 MATLAB code which tests the polynomial exactness of a quadrature rule over the interior of a tetrahedron in 3D.
- tetrahedron_exactness_test
- tetrahedron_felippa_rule, a MATLAB 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 MATLAB code which computes a grid of points over the interior of a tetrahedron in 3D.
- tetrahedron_grid_test
- tetrahedron_integrals, a MATLAB 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 MATLAB 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 MATLAB code which defines a Keast quadrature rule, of degree of exactness 0 through 8, over the interior of the tetrahedron in 3D.
- tetrahedron_keast_rule_test
- tetrahedron_monte_carlo, a MATLAB 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 MATLAB 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 MATLAB code which defines Newton-Cotes open (NCO) quadrature rules over the interior of a tetrahedron in 3D.
- tetrahedron_nco_rule_test
- tetrahedron_slice_display, a MATLAB code which determines the intersection between a tetrahedron and a plane and displays the result.
- tetrahedron_slice_display_test
- tetrahedron_slice_movie, a MATLAB code which is given a tetrahedron and a vector, displays an evenly spaced sequence of planes that intersect the tetrahedron and are normal to the vector, and creates a movie of the process.
- tetrahedron_slice_movie_test
- tetrahedron_witherden_rule, a MATLAB 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 MATLAB code which uses the Monte Carlo method to estimate an integral over the interior of the unit tetrahedron in 3D.
- tetrahedron01_monte_carlo_test
- theodolite, a MATLAB code which presents the problem of estimating the location of an event which occurs in the sky, atmosphere, or the heavens, using nothing but the reported angle of observation from several stations; a nonlinear least squares (NLS) solver is needed.
- theodolite_test
- theta_method, a MATLAB code which solves one or more ordinary differential equations (ODE) using the theta method.
- theta_method_test
- three_body_ode, a MATLAB code which sets up and solves ordinary differential equations (ODE) that simulate 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
- tictoc_test, a MATLAB code which calls tic() and toc(), which compute elapsed time.
- timer_test, a MATLAB code which demonstrates and compares several ways of timing code execution.
- timestamp, a MATLAB code which prints the current YMDHMS date as a timestamp;
- timestamp_test
- toeplitz_cholesky, a MATLAB code which computes the Cholesky factorization of a symmetric positive definite (SPD) Toeplitz matrix.
- toeplitz_cholesky_test
- toeplitz_inverse, a MATLAB code which computes the inverse of a Toeplitz matrix.
- toeplitz_inverse_test
- toms097, a MATLAB 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 MATLAB 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 MATLAB 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 MATLAB code which evaluates the modified Beta function, by Oliver Ludwig. This is a version of ACM TOMS algorithm 179.
- toms179_test
- toms243, a MATLAB 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 MATLAB code which evaluates the logarithm of the Gamma function. This is a version of ACM TOMS algorithm 291.
- toms291_test
- toms443, a MATLAB 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 MATLAB code which manipulates Chebyshev series for interpolation and approximation; this is a version of ACM TOMS algorithm 446, by Roger Broucke.
- toms446_test
- toms462, a MATLAB 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
- toms515, a MATLAB 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
- toms577, a MATLAB code which evaluates the Carlson elliptic integral functions RC, RD, RF and RJ. This is a version of ACM TOMS algorithm 577;
- toms577_test
- toms655, a MATLAB 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
- toms743, a MATLAB code which evaluates the Lambert W function. This is a version of ACM TOMS algorithm 743, by Barry, Barry and Culligan-Hensley.
- toms743_test
- toms847, a MATLAB code which carries out piecewise linear (PWL) multidimensional hierarchical sparse grid interpolation; this is commonly called spinterp() (version 2.1); this is a version of ACM TOMS Algorithm 847, by Andreas Klimke;
- toms847_test
- toms866, a MATLAB code which is version 2.2 of the Incompressible Flow Iterative Solution Software (IFISS), for fluid flow governed by the Navier Stokes equations (NSE), by Howard Elman, Alison Ramage, David Silvester; this is a version of ACM TOMS algorithm 866.
- toms886, a MATLAB 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
- toms923, a MATLAB code which evaluates the Pfaffian for a dense or banded skew symmetric matrix, by Michael Wimmer.
- toms923_test
- tortoise, a MATLAB code which considers the tortoise tiling puzzle, a smaller version of the eternity puzzle. The puzzle specifies a region R composed of 1620 30-60-90 triangles, and a set of 45 "tiles", each consisting of 36 30-60-90 triangles, and seeks an arrangement of the tiles that exactly covers the region.
- tortoise_test
- tortoise_cplex_test a BASH code which calls cplex(), to read the LP file defining the tortoise tiling problem, solve the linear programming problem, and write the solution to a file.
- tortoise_gurobi_test a BASH code which calls gurobi(), to read the LP file defining the tortoise tiling problem, solve the linear programming problem, and write the solution to a file.
- tough_ode, a MATLAB code which sets up and solves a system of four ordinary differential equations (ODE) which is extremely difficult to solve accurately.
- tough_ode_test
- traffic_simulation, a MATLAB code which simulates the cars waiting to get through a traffic light.
- traffic_simulation_test
- trapezoidal, a MATLAB code which solves one or more ordinary differential equations (ODE) using the (implicit) trapezoidal method, and MATLAB's fsolve() to handle the implicit system.
- trapezoidal_test
- trapezoidal_explicit, a MATLAB code which solves one or more ordinary differential equations (ODE) using the (explicit) trapezoidal method.
- trapezoidal_explicit_test
- trapezoidal_fixed, a MATLAB code which solves one or more ordinary differential equations (ODE) using the (implicit) trapezoidal method, using the fixed point method.
- trapezoidal_fixed_test
- treepack, a MATLAB 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_display, a MATLAB code which displays a TRI_SURFACE describing a triangulated surface;
- tri_surface_display_test
- tri_surface_to_obj, a MATLAB code which reads a TRI_SURFACE dataset and extracts the surface mesh data as an OBJ file.
- tri_surface_to_obj_test
- tri_surface_to_stla, a MATLAB code which reads a TRI_SURFACE dataset and extracts the surface mesh data as an ASCII stereolithography (STL) file.
- tri_surface_to_stla_test
- triangle, a MATLAB code which computes properties of a triangle, including angles, area, centroid, circumcircle, edge lengths, incircle, orientation, orthocenter, quality, Cartesian to barycentric coordinates, barycentric coordinates to Cartesian. A point is treated as a (1,2) array, a list of points as an (n,2) array, and a triangle as a (3,2) array.
- triangle_test
- triangle_analyze, a MATLAB 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_display, a MATLAB code which displays the nodes and elements of a triangulation for which the data has been stored in NODE and ELE files by Jonathan Shewchuk's triangle() program.
- triangle_display_test
- triangle_distance, a MATLAB code which computes the expected value of the distance between a pair of points randomly selected from the interior of a triangle in 2D.
- triangle_distance_test
- triangle_dunavant_rule, a MATLAB code which returns a Dunavant quadrature rule over the interior of a triangle in 2D.
- triangle_dunavant_rule_test
- triangle_exactness, a MATLAB code which tests the polynomial exactness of a quadrature rule over the interior of a triangle in 2D.
- triangle_exactness_test
- triangle_fekete_rule, a MATLAB code which sets up one of seven Fekete rules for interpolation or quadrature over the interior of a triangle in 2D.
- triangle_fekete_rule_test
- triangle_felippa_rule, a MATLAB code which returns Felippa quadrature rules for approximating integrals over the interior of a triangle in 2D.
- triangle_felippa_rule_test
- triangle_grid, a MATLAB code which computes a grid of points over the interior of a triangle in 2D.
- triangle_grid_test
- triangle_histogram, a MATLAB code which computes histograms of data over the interior of a unit triangle in 2D.
- triangle_histogram_test
- triangle_integrals, a MATLAB 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_integrands, a MATLAB code which defines integrands for testing quadrature rules over a triangle.
- triangle_integrands_test
- triangle_interpolate, a MATLAB code which shows how vertex data can be interpolated at any point in the interior of a triangle.
- triangle_interpolate_test
- triangle_io, a MATLAB code which reads or writes files created by Jonathan Shewchuk's triangle() program.
- triangle_io_test
- triangle_lyness_rule, a MATLAB code which returns a Lyness-Jespersen quadrature rule over the interior of a triangle in 2D;
- triangle_lyness_rule_test
- triangle_monte_carlo, a MATLAB 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_quadrature_symmetry, a MATLAB code which determines the symmetries of a quadrature rule for a triangle.
- triangle_quadrature_symmetry_test
- triangle_refine, a MATLAB code which divides a triangle into c^2 copies of itself, and implements a simple centroid-based quadrature scheme.
- triangle_refine_test
- triangle_svg, a MATLAB 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 MATLAB code which returns symmetric quadrature rules, with precision up to 50, over the interior of a triangle, by Hong Xiao and Zydrunas Gimbutas.
- triangle_symq_rule_test
- triangle_symq_rule_convert a MATLAB code which takes quadrature rules for the equilateral triangle and converts them to the reference triangle (0,0), (1,0), (0,1).
- triangle_symq_rule_old, a MATLAB code which is based on the original Fortran77 code, which uses an equilateral triangle as the reference element, by Hong Xiao and Zydrunas Gimbutas.
- triangle_symq_rule_old_test
- triangle_symq_to_ref, a MATLAB code which creates quadrature rules defined on the half-unit square from symmetric quadrature rules defined on an equilateral triangle, defined by triangle_symq_rule(), by Hong Xiao and Zydrunas Gimbutas.
- triangle_symq_to_ref_test
- triangle_to_fem, a MATLAB 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 MATLAB 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 MATLAB code which reads the NODE and ELE files created by Jonathan Shewchuk's triangle() program to describe a triangular mesh in 2D, and writes a corresponding XML mesh file for use by dolfin() or fenics().
- triangle_to_xml_test
- triangle_twb_rule, a MATLAB 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 MATLAB code which returns quadrature rules of exactness 5, 10, 15, 20, 25 and 30 over the interior of the triangle in 2D.
- triangle_wandzura_rule_test
- triangle_witherden_rule, a MATLAB 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 MATLAB code which returns the integral of any monomial over the interior of the unit triangle in 2D.
- triangle01_integrals_test
- triangle01_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate an integral over the interior of the unit triangle in 2D.
- triangle01_monte_carlo_test-
- triangulate, a MATLAB code which triangulates a polygonal region, based on a C program by Joseph ORourke;
- triangulate_test
- triangulate_rectangle, a MATLAB code which sets up a grid of triangles in a rectangular region.
- triangulate_rectangle_test
- triangulation, a MATLAB code which computes the triangulation of a set of points in the plane, and performs various operations using a triangulation, including searching a Delaunay triangulation to find which triangle contains a given point.
- triangulation_test
- triangulation_boundary, a MATLAB code which starts with a triangulation of a simple shape, and determines the triangle edges that form the boundary, and a sequence of nodes that trace the boundary.
- triangulation_boundary_test
- triangulation_boundary_edges, a MATLAB code which reads data defining a triangulation, determines which edges lie on the boundary, organizes them into connected components, and writes this information to a file.
- triangulation_boundary_edges_test
- triangulation_boundary_nodes, a MATLAB code which reads data defining a triangulation, determines which nodes lie on the boundary, and writes their coordinates to a file;
- triangulation_boundary_nodes_test
- triangulation_delaunay_discrepancy, a MATLAB code which measures the amount by which a triangulation fails the local Delaunay test;
- triangulation_delaunay_discrepancy_test triangulation_display, a MATLAB code which displays the nodes and elements of a triangulation;
- triangulation_display_test
- triangulation_node_to_element, a MATLAB code which reads files describing a set of nodes, their triangulation, and the value of one or more quantities at each node, and outputs a file that averages the quantities for each element. This operation in effect creates an order1 finite element model of the data.
- triangulation_node_to_element_test
- triangulation_order1_display, a MATLAB code which plots piecewise constant (PWC) data associated with a triangulation;
- triangulation_order1_display_test
- triangulation_order3_contour, a MATLAB code which plots color contours of a piecewise linear (PWL) scalar quantity evaluated at the nodes of a 3-node triangle triangulation.
- triangulation_order3_contour_test
- triangulation_order6_contour, a MATLAB code which plots color contours of a piecwise quadratic (PWQ) scalar quantity evaluated at the nodes of a 6-node triangle triangulation.
- triangulation_order6_contour_test
- triangulation_plot, a MATLAB code which plots the nodes and elements of a triangulation as a PostScript file;
- triangulation_plot_test
- triangulation_quad, a MATLAB 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 MATLAB code which reads information about a triangulation and computes various quality measures;
- triangulation_quality_test
- triangulation_refine, a MATLAB code which refines a triangulation;
- triangulation_refine_test
- triangulation_refine_local, a MATLAB code which refines a triangulation locally; a single triangular element is replaced by four smaller triangles, and neighboring information is updated.
- triangulation_refine_local_test
- triangulation_svg, a MATLAB code which creates a Scalable Vector graphics (SVG) image of a triangulation, which can be displayed by a web browser.
- triangulation_svg_test
- triangulation_triangle_neighbors, a MATLAB code which reads data defining a triangulation, finds the three neighbor triangles for each triangle, and writes them to a file;
- triangulation_triangle_neighbors_test
- tridiagonal_solver, a MATLAB code which solves a tridiagonal linear system.
- tridiagonal_solver_test
- trig_interp, a MATLAB code which uses trigonometric functions for interpolation.
- trig_interp_test
- trig_interp_basis, a MATLAB code which evaluates the cardinal basis functions for trigonometric interpolation of equally spaced data.
- trig_interp_basis_test
- trinity, a MATLAB code which considers the trinity puzzle, a smaller version of the eternity puzzle. The trinity puzzle specifies a region R composed of 144 30-60-90 triangles, and a set of 4 "tiles", each consisting of 36 30-60-90 triangles, and seeks an arrangement of the tiles that exactly covers the region.
- trinity_test
- trinity_cplex_test a BASH code which calls cplex(), to read the LP file defining the trinity tiling problem, solve the linear programming problem, and write the solution to a file.
- trinity_gurobi_test a BASH code which calls gurobi(), to read the LP file defining the trinity tiling problem, solve the linear programming problem, and write the solution to a file.
- trinity_scip_test a BASH code which calls scip(), to read the LP file defining the trinity tiling problem, solve the linear programming problem, and write the solution to a file.
- truel_simulation, a MATLAB code which simulates N repetitions of a duel between three players, each of whom has a known firing accuracy.
- truel_simulation_test
- truncated_normal, a MATLAB 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 MATLAB code which computes a quadrature rule for a normal probability density function (PDF), sometimes called a Gaussian distribution, that has been truncated to [A,+oo), (-oo,B] or [a,b].
- truncated_normal_rule_test
- truncated_normal_sparse_grid, a MATLAB code which computes a sparse grid based on 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_sparse_grid_test
- tsp_brute, a MATLAB code which is given a table of city-to-city distances and solves a (small!) traveling salesperson problem (TSP), using brute force.
- tsp_brute_test
- tsp_descent, a MATLAB code which is given a table of city-to-city distances, chooses an initial tour at random, and then tries some simple variations to quickly find a tour of lower length, to solve the traveling salesperson problem (TSP).
- tsp_descent_test
- tsp_greedy, a MATLAB code which is given a table of city-to-city distances, and solves a small traveling salesperson problem (TSP) using the greedy algorithm. It picks a starting city at random, and then successively visits the nearest unvisited city.
- tsp_greedy_test
- tsp_moler, a MATLAB code which tries to optimize the traveling salesperson problem (TSP), written by Cleve Moler.
- tsp_moler_test
- tsp_random, a MATLAB code which seeks a solution of the Traveling Salesperson Problem (TSP), by accepting a table of city-to-city distances, and randomly generating round trips that visit every city, returning the tour of shortest length.
- tsp_random_test
- tumor_pde, a MATLAB code which solves the tumor angiogenesis partial differential equations (PDE) using MATLAB's pdepe() function.
- tumor_pde_test
- two_body_ode, a MATLAB code which sets up and solves ordinary differential equations (ODE) which simulate the behavior of two bodies, constrained to lie in a plane, moving under the influence of gravity, with one body much more massive than the other.
- two_body_ode_test
- ubvec, a MATLAB code which demonstrates how nonnegative integers can be stored as unsigned binary vectors, and arithmetic can be performed on them.
- ubvec_test
- ulam_spiral, a MATLAB code which displays the integers as a spiral of grid cells, with the primes highlighted, so show that they tend to fall along diagonals, as discovered by Stanislaw Ulam.
- ulam_spiral_test
- unicycle, a MATLAB code which considers permutations containing a single cycle, sometimes called cyclic permutations.
- unicycle_test
- uniform, a MATLAB code which implements a uniform random number generator (RNG) for a variety of arithmetic types.
- uniform_test
- unstable_ode, a MATLAB code which sets up and solves an unstable ordinary differential equation (ODE) which the backward Euler method incorrectly drives to zero.
- unstable_ode_test
- upc, a MATLAB code which determines the check digit for a Uniform product Code (UPC) or reports whether a given UPC is valid.
- upc_test
- urn_simulation, a MATLAB code which simulates the experiment of sampling K balls from an urn containing N balls of various colors.
- urn_simulation_test
- usa_box_plot, a MATLAB code which creates simplified maps of the USA in which each state appears as a box, and the placement of the boxes only roughly corresponds to the relative locations of states on an accurate map.
- usa_box_plot_test
- usa_cvt_geo, a MATLAB code which explores the creation of a centroidal Voronoi Tessellation (CVT) of the continental United States, based solely on geometric considerations.
- usa_cvt_geo_test
- usa_matrix, a MATLAB code which defines the adjacency matrix for US states, using a variety of matrix formats.
- usa_matrix_test
- van_der_corput, a MATLAB code which computes elements of the van der Corput 1-dimensional Quasi Mont Carlo (QMC) sequence, using a simple interface.
- van_der_corput_test
- vandermonde, a MATLAB code which implements the Bjork-Pereyra algorithm for accurate solution of linear systems involving the Vandermonde matrix.
- vandermonde_test
- vandermonde_approx_1d, a MATLAB 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 MATLAB 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 MATLAB code which finds a polynomial interpolant to data y(x) of a 1D argument by solving a linear system for the polynomial coefficients involving the Vandermonde matrix.
- vandermonde_interp_1d_test
- vandermonde_interp_2d, a MATLAB code which finds a polynomial interpolant to data z(x,y) of a 2D argument by solving a linear system for the polynomial coefficients involving the Vandermonde matrix.
- vandermonde_interp_2d_test
- vanderpol_ode, a MATLAB code which sets up and solves the van der Pol system of ordinary differential equations (ODE), for which a limit cycle exists.
- vanderpol_ode_test
- vanderpol_ode_period, a MATLAB code which sets up and solves the ordinary differential equations (ODE) defining the van der Pol oscillator in order to estimate the period of the limit cycle.
- vanderpol_ode_period_test
- variomino, a MATLAB code which considers variominoes, which are polyominoes in which each square has been assigned a positive label or "variety", and the determination of tilings of a region using a specific set of variominoes.
- variomino_test
- vector, a MATLAB code which considers a problem involving vectors, which can be considered to belong to equivalence classes, for which an arbitrary collection of coefficients must be gathered, averaged, and then scattered again.
- vector_test
- velocity_verlet, a MATLAB code which uses a version of the velocity Verlet method to solve a second order ordinary differential equation (ODE) of the form y''=f(t,y).
- velocity_verlet_test
- verlet_simulation, a MATLAB code which demonstates the use of Verlet integration to simulate simple problems in dynamics, involving changes in position and velocity.
- verlet_simulation_test
- vin, a MATLAB code which computes the check digit for a Vehicle Identification Number (VIN), or verifies that a given VIN is legitimate.
- vin_test
- voronoi_city, a MATLAB code which displays the steps involved in computing the Voronoi diagram of 3 points, which we think of as cities connected by roads.
- voronoi_city_test
- voronoi_display, a MATLAB code which computes and displays the Voronoi diagram of a set of points.
- voronoi_display_test
- voronoi_mountains, a MATLAB code 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.
- voronoi_mountains_test
- voronoi_neighbors, a MATLAB code which is given a set of points in the plane and determines the Voronoi adjacency structure, that is, the points which share an edge of the Voronoi diagram.
- voronoi_neighbors_test
- voronoi_plot, a MATLAB code which estimates the Voronoi neighborhoods of points using sampling, and with a distance based on the L1, L2, LInfinity or arbitrary LP norms;
- voronoi_plot_test
- voronoi_test, a MATLAB code which calls the built-in voronoi() function, which computes the Voronoi diagram of a set of points.
- vpa_test, a MATLAB code which uses the Variable Precision Arithmetic (VPA) feature of the Symbolic Math Toolbox to compute arbitrary precision quantities.
- walker_sample, a MATLAB code which efficiently samples a discrete probability vector using Walker sampling.
- walker_sample_test
- walsh_transform, a MATLAB code which implements the Walsh data transform.
- walsh_transform_test
- wathen_matrix, a MATLAB code which compares storage schemes (full, banded, sparse triplet, sparse) and solution strategies (A\x, Linpack, 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_pde, a MATLAB code which uses the finite difference method (FDM) in space, and the method of lines in time, to set up and solve the partial differential equations (PDE) known as the wave equations, utt = c uxx.
- wave_pde_test
- wavelet, a MATLAB code which does some simple calculations with wavelet transforms;
- wavelet_test
- web_matrix, a MATLAB code which stores sample matrices describing a web page network. These matrices are typically very sparse, and the examples here are stored using the sparse triplet (ST) format. They can be used to demonstrate pagerank and other graph algorithms.
- web_matrix_test
- wedge_exactness, a MATLAB 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 MATLAB 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 MATLAB code which computes a grid of points over the interior of the unit wedge in 3D.
- wedge_grid_test
- wedge_integrals, a MATLAB 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 MATLAB 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 MATLAB 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
- weekday_zeller, a MATLAB code which uses the Zeller congruence to determine the day of the week corresponding to a given date, such as 13 July 1989, Gregorian calendar, ... which was a Thursday.
- weekday_zeller_test
- welzl, a MATLAB code which computes the minimal bounding circle or sphere for a set of points, using algorithms by Welzl or Ritter, by Anton Semechko.
- welzl_test
- whale, a MATLAB code which considers the whale tiling puzzle, a smaller version of the eternity puzzle. The whale puzzle specifies a region R composed of 288 30-60-90 triangles, and a set of 8 "tiles", each consisting of 36 30-60-90 triangles, and seeks an arrangement of the tiles that exactly covers the region.
- whale_test
- whale_cplex_test a BASH code which calls cplex(), to read the LP file defining the whale tiling problem, solve the linear programming problem, and write the solution to a file.
- whale_gurobi_test a BASH code which calls gurobi(), to read the LP file defining the whale tiling problem, solve the linear programming problem, and write the solution to a file.
- will_you_be_alive, a MATLAB code which carries out the probability simulations described in "Will You Be Alive 10 Years From Now?" by Paul Nahin;
- will_you_be_alive_test
- wishart_matrix, a MATLAB code which produces sample matrices from the Wishart or Bartlett distributions, useful for sampling random covariance matrices.
- wishart_matrix_test
- wtime, a MATLAB code which returns a reading of the wall clock time in seconds.
- wtime_test
- xml2struct, a MATLAB code which reads a file containing XML data, and produces a corresponding MATLAB struct.
- xml2struct_test
- xyz_display, a MATLAB code which displays a 3D plot from a file of point coordinates.
- xyz_display_test
- zero_brent, a MATLAB code which seeks a solution of a scalar nonlinear equation f(x)=0, by Richard Brent.
- zero_brent_test
- zero_chandrupatla, a MATLAB 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 MATLAB 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 MATLAB 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 MATLAB code which seeks a root of a nonlinear equation using the Muller method, with complex arithmetic.
- zero_muller_test
- zero_rc, a MATLAB code which seeks a solution of a scalar nonlinear equation f(x)=0, using reverse communication (RC), by Richard Brent.
- zero_rc_test
- ziggurat, a MATLAB code which implements uniform, normal and exponential random number generators (RNG) using the ziggurat method, by Marsaglia and Tsang.
- ziggurat_test
- zombie_ode, a MATLAB code which sets up and solves a system of ordinary differential equations (ODE) for a generalized Susceptible-Infected-Recovered (SIR) disease model to simulate a zombie attack, developed by Philip Munz.
- zombie_ode_test
- zoomin, a MATLAB code which implements many procedures for finding the zero of a scalar nonlinear function.
- zoomin_test