- advection_pde, an Octave 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, an Octave code which sets up and solves the Allen-Cahn reaction-diffusion partial differential equation (PDE) in 1 space dimension and time.
- allen_cahn_pde_test
- allen_cahn_pde_etdrk4 an Octave 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 an Octave 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, an Octave 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, an Octave 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
- animation_test, an Octave code which demonstrates how to create an animation in the form of a GIF.
- anishchenko_ode, an Octave code which sets up and solves the Anishchenko ordinary differential equation (ODE), which has chaotic behavior and an attractor.
- anishchenko_ode_test
- annulus_distance, an Octave code which estimates the typical distance between a pair of points randomly selected inside a circular annulus.
- annulus_distance_test
- annulus_grid, an Octave code which computes a grid of points over the interior of a circular annulus.
- annulus_grid_test
- annulus_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of an annulus centered at the origin.
- annulus_integrals_test
- annulus_monte_carlo, an Octave 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, an Octave 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, an Octave 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, an Octave code which interactively approximates a function f(x) in the interval [a,b] by constructing a Bernstein polynomial.
- approx_bernstein_test
- approx_chebyshev, an Octave 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 minimax polynomial.
- approx_chebyshev_test
- approx_leastsquares, an Octave 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, an Octave code which estimates the arclength of curves of the form (x,f(x)) or (x(t),y(t)).
- arclength_test
- arenstorf_ode, an Octave 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, an Octave code which shows how to count and report command line arguments;
- args_test
- arneodo_ode, an Octave code which sets up and solves the Arneodo ordinary differential equation (ODE), which has chaotic behavior and an attractor.
- arneodo_ode_test
- artery_pde, an Octave code which solves a partial differential equation (PDE) in one spatial dimension and time, that models the displacement of arterial walls under pressure.
- artery_pde_test
- asa_2011_geometry, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which evaluates the incomplete Gamma function, by G Bhattacharjee. This is a version of Applied Statistics Algorithm 32.
- asa032_test
- asa047, an Octave 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, an Octave 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, an Octave code which implements the K-means data clustering algorithm, by David Sparks. This is a version of Applied Statistics Algorithm 58.
- asa058_test
- asa063, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which evaluates the digamma or psi function, by Jose Bernardo. This is a version of Applied Statistics Algorithm 103.
- asa103_test
- asa109, an Octave code which inverts the incomplete Beta function, by Cran, Martin and Thomas. This is a version of Applied Statistics Algorithm 109.
- asa109_test
- asa111, an Octave 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, an Octave 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, an Octave code which evaluates the trigamma function, by BE Schneider. This is a version of Applied Statistics Algorithm 121.
- asa121_test
- asa136, an Octave code which implements a clustering algorithm, by Hartigan and Wong. This is a version of Applied Statistics Algorithm 136.
- asa136_test
- asa144, an Octave code which randomly generates an RxC contingency table, by James Boyett. This is a version of Applied Statistics Algorithm 144.
- asa144_test
- asa147, an Octave code which evaluates the incomplete Gamma function, by Chi Leung Lau. This is a version of Applied Statistics Algorithm 147.
- asa147_test
- asa152, an Octave 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, an Octave code which randomly generates an RxC contingency table, by Michael Patefield; This is a version of Applied Statistics Algorithm 159.
- asa159_test
- asa172, an Octave 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, an Octave code which implements a random number generator (RNG), by Wichman and Hill. This is a version of Applied Statistics Algorithm 183.
- asa183_test
- asa226, an Octave 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, an Octave code which evaluates the incomplete Gamma function, by Shea. This is a version of Applied Statistics Algorithm 239.
- asa239_test
- asa241, an Octave 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, an Octave 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, an Octave code which evaluates the logarithm of the Gamma function, by Allan Mcleod; this is a version of Applied Statistics Algorithm 245.
- asa245_test
- asa266, an Octave code which evaluates various properties of the Dirichlet Probability Density Function (PDF); This is a version of Applied Statistics Algorithm 266.
- asa266_test
- asa299, an Octave 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, an Octave 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, an Octave 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, an Octave code which applies the Atbash substitution cipher to a string of text.
- atbash_test
- atkinson, an Octave code which contains examples from the text 'Elementary Numerical Analysis', by Atkinson.
- atkinson_test
- autocatalytic_ode, an Octave code which sets up and solves the autocatalytic ordinary differential equation (ODE), which has chaotic behavior and an attractor.
- autocatalytic_ode_test
- axon_ode, an Octave 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, an Octave code which carries out a backtrack search for a set of binary decisions, using reverse communication (RC).
- backtrack_binary_rc_test
- backward_euler, an Octave 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, an Octave 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_distance, an Octave 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, an Octave code which computes a grid of points over the interior of the unit ball in 3D.
- ball_grid_test
- ball_integrals, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which solves one or more ordinary differential equations (ODE) using BDF2, the (implicit) backward difference formula of order 2, using fsolve() to solve the implicit equation.
- bdf2_test
- bellman_ford, an Octave 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, an Octave code which looks at some simple cases of approximation of a function f(x) by a Bernstein polynomial.
- bernstein_approximation_test
- bernstein_polynomial, an Octave code which evaluates the Bernstein polynomials;
- bernstein_polynomial_test
- besselj, an Octave code which evaluates Bessel J functions of noninteger order;
- besselj_test
- besselzero, an Octave code which computes the zeros of Bessel functions j or y, by Greg van Winckel and Jason Nicholson.
- besselzero_test
- beta_nc, an Octave code which evaluates the cumulative density function (CDF) of the noncentral Beta distribution;
- beta_nc_test
- bezier_surface, an Octave code which reads, writes, prints and manipulates the data that defines a Bezier surface;
- bezier_surface_test
- bezier_surface_display, an Octave code which displays a Bezier surface;
- bezier_surface_display_test
- bicg, an Octave code which implements the biconjugate gradient method (BICG), which estimates the solution of a large sparse nonsymmetric linear system.
- bicg_test
- biharmonic_cheby1d, an Octave 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_fd1d, an Octave 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, an Octave code which deals with the biharmonic equation in two dimensions, whose simplest form is uxxxx + 2uxxyy + uyyyy = f.
- biharmonic_fd2d_test
- biochemical_linear_ode, an Octave code which sets up and solves a linear biochemical ordinary differential equation (ODE).
- biochemical_linear_ode_test
- biochemical_nonlinear_ode, an Octave code which sets up and solves a nonlinear biochemical ordinary differential equation (ODE).
- biochemical_nonlinear_ode_test
- bioconvection_ode, an Octave 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, an Octave code which evaluates some formulas for the shapes of bird eggs.
- bird_egg_test
- bisection, an Octave 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, an Octave 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, an Octave 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, an Octave code which implements some simple approaches to the Black-Scholes option valuation theory, by Desmond Higham.
- black_scholes_test
- blend, an Octave code which carries out 1D/2D/3D blending interpolation;
- blend_test
- blood_pressure_ode, an Octave 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, an Octave 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, an Octave 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.
- boundary_locus, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which displays a box plot, over integer pairs of data, of a function defined by two formulas.
- box_display_test
- box_distance, an Octave code which estimates the distribution and expected value of the distance between two points picked uniformly at random within a box.
- box_distance_test
- box_games, an Octave code which assists in the display of game boards (checkers, cellular automatons, life);
- box_games_test
- box_plot, an Octave code which displays a box plot of data that consists of pairs of integers;
- box_plot_test
- brownian_motion_simulation, an Octave code which simulates Brownian motion in an M dimensional region.
- brownian_motion_simulation_test
- broyden, an Octave code which implements the Broyden iterative method for nonlinear equations, by Tim Kelley.
- broyden_test
- brusselator_ode, an Octave code which sets up and solves the Brusselator ordinary differential equation (ODE) system.
- brusselator_ode_test
- buckling_spring, an Octave code which plots solutions of the buckling spring equations.
- buckling_spring_test
- burgers_exact, an Octave code which evaluates exact solutions of the time-dependent 1D viscous Burgers equation.
- burgers_exact_test
- burgers_steady_viscous, an Octave 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, an Octave 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, an Octave 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, an Octave code which demonstrates how signed integers can be stored as binary vectors, and arithmetic can be performed on them.
- bvec_test
- bvp_fd, an Octave code which demonstrates the use of the finite difference method (FDM) to solve a boundary value problem (BVP).
- bvp_fd_test
- bvp_shooting_test, an Octave code which demonstrates the use of the shooting method to solve a boundary value problem (BVP).
- c8lib, an Octave code which implements certain elementary functions for complex 64 bit ("C8") variables;
- c8lib_test
- caesar, an Octave code which applies a Caesar Shift Cipher to a string of text.
- caesar_test
- calpak, an Octave code which computes various simple calendrical quantities. It works with various calendars including Egyptian, English, French Revolutionary, Gregorian, Julian, and Julian Ephemeris Date. It converts a date from one calendar to another. It returns the day of the week for a given date. It converts from day-number/year to day/month/year format. It calculates the time difference between two dates.
- calpak_test
- candy_count, an Octave 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, an Octave code which plots data from a model of a 2D capacitor, computed by FreeFem++() and transferred using the ffmatlib() library.
- capacitor_3d_test, an Octave code which plots data from a model of a 3D capacitor, computed by FreeFem++() and transferred using the ffmatlib() library.
- casino_simulation, an Octave 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, an Octave code which solves one or more ordinary differential equations (ODE) using the Cauchy method.
- cauchy_method_test
- cauchy_principal_value, an Octave code which uses Gauss-Legendre quadrature to estimate the Cauchy Principal Value (CPV) of certain singular integrals.
- cauchy_principal_value_test
- caustic, an Octave 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, an Octave code which displays a single velocity field solution for the driven cavity;
- cavity_flow_display_test
- cc_display, an Octave code which displays the points used in a 2D Clenshaw-Curtis quadrature rule;
- cc_display_test
- ccl_test, an Octave 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, an Octave code which defines a Clenshaw Curtis Nested (CCN) quadrature rule.
- ccn_rule_test
- ccs_io an Octave code which reads and writes sparse linear systems stored in the Compressed Column Storage (CCS) format.
- ccs_io_test
- ccs_to_st an Octave code which converts a sparse matrix from Compressed Column Storage (CCS) to sparse triplet (ST) format.
- ccs_to_st_test
- ccvt_reflect, an Octave 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, an Octave code which prints or plots the evolution of Cellular Automaton rule #30.
- cellular_automaton_test
- cg, an Octave 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_ne, an Octave 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, an Octave 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, an Octave code which implements the conjugate gradient squared (CGS) method for solving a nonsymmetric sparse linear system A*x=b.
- cg_squared_test
- change_diophantine, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which computes the Chebyshev interpolant/approximant to a given function over an interval.
- chebyshev_test
- chebyshev_interp_1d, an Octave 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_polynomial, an Octave code which considers the Chebyshev polynomials T(i,x), U(i,x), V(i,x) and W(i,x).
- chebyshev_polynomial_test
- chebyshev_series, an Octave 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, an Octave code which tests the polynomial exactness of Gauss-Chebyshev type 1 quadrature rules.
- chebyshev1_exactness_test
- chebyshev1_rule, an Octave code which computes and writes out a Gauss-Chebyshev type 1 quadrature rule of given order.
- chebyshev1_rule_test
- chebyshev2_exactness, an Octave code which tests the polynomial exactness of Gauss-Chebyshev type 2 quadrature rules.
- chebyshev2_exactness_test
- chebyshev2_rule, an Octave code which computes and writes out a Gauss-Chebyshev type 2 quadrature rule of given order.
- chebyshev2_rule_test
- chen_ode, an Octave code which sets up and solves the Chen system of ordinary differential equations (ODE).
- chen_ode_test
- cheney_kincaid, an Octave code which contains examples from the text 'Numerical Mathematics and Computing', by Cheney and Kincaid.
- cheney_kincaid_test
- chinese_remainder_theorem, an Octave 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, an Octave code which applies the Chirikov map repeatedly to a given (x,y) initial condition.
- chirikov_iteration_test
- chladni_figures, an Octave code which creates Chladni figures of the eigenmodes of a thin vibrating plate, by Martin Gander and Felix Kwok.
- chladni_figures_test
- chrpak, an Octave code which manipulates characters and strings;
- chrpak_test
- chuckaluck_simulation, an Octave code which simulates the Chuck-a-Luck gambling game.
- chuckaluck_simulation_test
- circle_arc_grid, an Octave code which computes grid points along a circular arc.
- circle_arc_grid_test
- circle_distance, an Octave 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 an Octave code which reads a matrix of integers, and draws a corresponding grid of circles filled with color.
- circle_grid_display_test
- circle_integrals, an Octave 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, an Octave code which illustrates how a matrix maps points on the unit circle to an ellipse.
- circle_map_test
- circle_monte_carlo, an Octave 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, an Octave 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, an Octave 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, an Octave code which carries out computations associated with a circle segment, including height, angle, area, centroid, sampling, and quadrature.
- circle_segment_test
- circles, an Octave code which draws one or more circles, while controlling the center locations, radii, colors, edge colors, and transparency, by Chad Greene.
- circles_test
- cities, an Octave code which works with city-to-city distance matrices;
- cities_test
- clausen, an Octave code which evaluates a Chebyshev interpolant to the Clausen function Cl2(x).
- clausen_test
- clenshaw_curtis_rule, an Octave code which implements a Clenshaw Curtis quadrature rule;
- clenshaw_curtis_rule_test
- clock_solitaire_simulation, an Octave 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, an Octave 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, an Octave code which generates samples of noise obeying a 1/f^alpha power law, by Miroslav Stoyanov.
- cnoise_test
- cobweb_plot, an Octave code which displays a cobweb plot illustrating the process of function iteration.
- cobweb_plot_test
- coin_simulation, an Octave code which looks at ways of simulating or visualizing the results of many tosses of a fair or biased coin.
- coin_simulation_test
- collatz, an Octave code which computes and analyzes the Collatz sequence, also known as the hailstone sequence or 3n+1 sequence;
- collatz_test
- collatz_polynomial, an Octave 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, an Octave code which demonstrates recursive programming by considering the simple Collatz 3n+1 problem.
- collatz_recursive_test
- collocation, an Octave 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, an Octave code which generates samples of noise obeying a 1/f^alpha power law.
- colored_noise_test
- combo, an Octave 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, an Octave 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, an Octave 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
- components, an Octave 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, an Octave code which implements methods of computing or estimating the condition number of a matrix.
- condition_test
- conservation_ode, an Octave 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, an Octave code which contains examples from the text 'Elementary Numerical Analysis' by Conte and deBoor.
- conte_deboor_test
- continuation, an Octave 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 an Octave code which implements some simple algorithms for dealing with simple and generalized continued fractions.
- continued_fraction_test
- control_bio, an Octave 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, an Octave 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.
- convhull_test, an Octave 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, an Octave code which seeks the minimizer of a scalar function of several variables, by Jeff Borggaard.
- coordinate_search_test
- cordic, an Octave code which computes a few special functions using the CORDIC algorithm.
- cordic_test
- correlation, an Octave code which contains statistical correlation functions.
- correlation_test
- cosine_transform, an Octave code which demonstrates some simple properties of the discrete cosine transform (DCT).
- cosine_transform_test
- counterfeit_detection, an Octave 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, an Octave code which extracts solution data from a cplex() result file.
- cplex_solution_read_test
- cpr, an Octave 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, an Octave 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, an Octave code which reads and writes sparse linear systems stored in the Compressed Row Storage (CRS) format.
- crs_io_test
- cube_arbq_rule, an Octave 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, an Octave 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, an Octave code which investigates the polynomial exactness of quadrature rules over the interior of a cube in 3D.
- cube_exactness_test
- cube_felippa_rule, an Octave code which returns a Felippa quadrature rules for approximating integrals over the interior of a cube in 3D.
- cube_felippa_rule_test
- cube_grid, an Octave code which computes a grid of points over the interior of a cube in 3D.
- cube_grid_test
- cube_integrals, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which computes an N-point Centroidal Voronoi Tessellation (CVT) in M dimensions;
- cvt_test
- cvt_1d_lloyd, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which computes a centroidal Voronoi Tessellation (CVT) over a circular region, using a uniform density.
- cvt_circle_uniform_test
- cvt_corn, an Octave 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_ellipse_uniform, an Octave code which iteratively calculates a Centroidal Voronoi Tessellation (CVT) over an ellipse, with a uniform density.
- cvt_ellipse_uniform_test
- cvt_square_nonuniform, an Octave code which iteratively calculates a Centroidal Voronoi Tessellation (CVT) over a square, with a nonuniform density.
- cvt_square_nonuniform_test
- cvt_square_pdf_discrete, an Octave 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, an Octave code which iteratively calculates a Centroidal Voronoi Tessellation (CVT) over a square, with a uniform density.
- cvt_square_uniform_test
- cvt_triangle_uniform, an Octave code which iteratively calculates a Centroidal Voronoi Tessellation (CVT) over a triangle, with a uniform density.
- cvt_triangle_uniform_test
- cvtm_1d, an Octave 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, an Octave code which creates a periodic Centroidal Voronoi Tessellation (CVTP).
- cvtp_test
- cvtp_1d, an Octave 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, an Octave 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, an Octave 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, an Octave code which solves a tridiagonal linear system using cyclic reduction;
- cyclic_reduction_test
- delaunay_test, an Octave code which calls the built-in delaunay() function, which computes the Delaunay triangulation of a set of points.
- delsq, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which reads a file of N points in M dimensions and computes its diaphony, a measure of point dispersion.
- diaphony_test
- dice_simulation, an Octave code which simulates N tosses of M dice, making a histogram of the resulting sums.
- dice_simulation_test
- dictionary_code, an Octave code which demonstates how a text file can be compressed and decompressed using a dictionary code.
- dictionary_code_test
- diff_forward, an Octave code which interactively uses forward differences to estimate the derivative of a function f(x), using a stepsize h.
- diff_forward_test
- diff_test, an Octave 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, an Octave code which interactively uses centered differences to estimate the derivative of a function f(x), using a stepsize h.
- diff_center_test
- diff_forward, an Octave code which interactively uses forward differences to estimate the derivative of a function f(x), using a stepsize h.
- diff_forward_test
- diff2_center, an Octave code which interactively uses centered differences to estimate the second derivative of a function f(x), using a stepsize h.
- diff2_center_test
- differ, an Octave 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, an Octave 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, an Octave code which carries out probability simulations described in "Digital Dice", by Paul Nahin;
- digital_dice_test
- dijkstra, an Octave code which implements a simple version of the Dijkstra minimum distance algorithm for graphs.
- dijkstra_test
- diophantine, an Octave code which finds one solution of a diophantine equation in any number of variables.
- diophantine_test
- diophantine_nd, an Octave code which is given a Diophantine equation in N variables, and returns all nonnegative solutions, or all strictly positive solutions.
- diophantine_nd_test
- discrete_pdf_sample_2d, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which applies a Monte Carlo method to estimate integrals of a function over the interior of the general disk in 2D.
- disk_monte_carlo_test
- disk_positive_distance, an Octave 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, an Octave code which computes quadrature rules for the general disk in 2D.
- disk_rule_test
- disk01_integrals, an Octave 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, an Octave 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, an Octave code which applies a Monte Carlo method to estimate integrals of a function over the interior of the unit disk in 2D;
- disk01_monte_carlo_test
- disk01_positive_monte_carlo, an Octave 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, an Octave code which computes a quadrature rule over the interior of the unit positive disk in 2D, with radius 1 and center (0,0).
- disk01_positive_rule_test
- disk01_rule, an Octave code which computes quadrature rules for the unit disk in 2D.
- disk01_rule_test
- dist_plot, an Octave code which makes contour plots of the distance function, as defined and used in Persson and Strang's distmesh() code;
- dist_plot_test
- distmesh, an Octave code which carries out a method of mesh generation; by Per-Olof Persson and Gilbert Strang.
- distmesh_test
- distmesh_3d, an Octave code which carries out a method of mesh generation in 3D, by Per-Olof Persson and Gilbert Strang.
- distmesh_3d_test
- divdif, an Octave code which uses divided differences to compute the polynomial interpolant to a given set of data.
- divdif_test
- doomsday, an Octave 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, an Octave 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
- double_c_data, an Octave code which generates, plots and writes out 2D data that forms two interlocking "C" shapes.
- double_c_data_test
- double_well_ode, an Octave 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, an Octave 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, an Octave code which simulates N repetitions of a duel between two players, each of whom has a known firing accuracy.
- duel_simulation_test
- dueling_idiots, an Octave code which carries out the probability simulations described in "Dueling Idiots", by Paul Nahin;
- dueling_idiots_test
- duffing_ode, an Octave code which sets up and solves a second-order ordinary differential equation (ODE) whose solution can exhibit chaotic behavior.
- duffing_ode_test
- e_spigot, an Octave code which produces any number of digits of the decimal expansion of e.
- e_spigot_test
- edge, an Octave code which defines some test functions in 1D, 2D and 3D for the detection of edges or discontinuities.
- edge_test
- eigs_test, an Octave code which calls eigs(), which is a built-in system function which computes the eigenvalues and eigenvectors of a matrix.
- elfun, an Octave 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, an Octave 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, an Octave 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, an Octave code which computes a grid of points over the interior of an ellipse in 2D.
- ellipse_grid_test
- ellipse_monte_carlo, an Octave 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, an Octave code which carries out geometric calculations for ellipsoids, including area, random sampling, conversion between standard and quadratic forms.
- ellipsoid_test
- ellipsoid_grid, an Octave code which computes a grid of points over the interior of an ellipsoid in 3D.
- ellipsoid_grid_test
- ellipsoid_monte_carlo, an Octave 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, an Octave code which evaluates complete elliptic integrals of first, second and third kind, using the Carlson elliptic integral functions.
- elliptic_integral_test
- epicycloid, an Octave code which plots an epicycloid curve.
- epicycloid_test
- equidistribution, an Octave code which investigates equidistribution properties relating to density functions and point sets.
- equidistribution_test
- eros, an Octave code which implements elementary row operations (ERO) for the interactive solution of a system of linear equations.
- eros_test
- errors, an Octave code which illustrates the failure of numerical algorithms;
- errors_test
- eternity, an Octave 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, an Octave 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, an Octave 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 monotiles.
- eternity_tile_test
- euclid, an Octave code which investigates various versions of Euclid's algorithm for computing the greatest common divisor (GCD) of two integers.
- euclid_test
- euler, an Octave code which solves one or more ordinary differential equations (ODE) using the forward Euler method.
- euler_test
- exactness, an Octave 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, an Octave 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, an Octave code which sets up and solves an ordinary differential equation (ODE) whose solution is an exponential function.
- exp_ode_test
- faces_average, an Octave code which averages several images of the same face;
- faces_average_test
- fair_dice_simulation, an Octave code which simulates N tosses of 2 dice, making a histogram of the resulting sums.
- fair_dice_simulation_test
- faure, an Octave code which computes the Faure M dimensional Quasi Mont Carlo (QMC) sequence;
- faure_test
- fd_predator_prey, an Octave code which solves a time-dependent predator prey system using the finite difference method (FDM).
- fd_predator_prey_test
- fd1d_advection_diffusion_steady, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which implements a finite difference method (FDM) for the steady (time independent) 1D heat equation;
- fd1d_heat_steady_test
- fd1d_poisson, an Octave 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, an Octave 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, an Octave code which plots solutions of the predator prey differential equations, by Marcus Garvie.
- fd1d_predator_prey_plot_test
- fd1d_wave, an Octave 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, an Octave 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, an Octave code which implements a finite difference method (FDM) for the steady (time independent) 2D heat equation;
- fd2d_heat_steady_test
- fd2d_poisson, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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_triangle, an Octave 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, an Octave 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, an Octave 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, an Octave code which uses an adaptive mesh when applying the finite element method (FEM), with piecewise linear (PWL) basis functions, to a linear two point boundary value problem (BVP) in 1D;
- fem1d_adaptive_test
- fem1d_approximate, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which uses the finite element method (FEM) to solve the steady (time independent) 1D heat equation;
- fem1d_heat_steady_test
- fem1d_lagrange, an Octave 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, an Octave 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, an Octave code which contains utilities for 1D finite element method (FEM) calculations.
- fem1d_pack_test
- fem1d_pmethod, an Octave 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, an Octave 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, an Octave code which samples a scalar or vector finite element function of one variable, defined by FEM files, returning interpolated values at the sample points.
- fem1d_sample_test
- fem2d_bvp_linear, an Octave 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
- fem1d_bvp_quadratic, an Octave 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
- fem2d_bvp_serene, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which performs simple 2D finite element method (FEM) computations;
- fem2d_pack_test
- fem2d_poisson_rectangle, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which contains utilities for 3D finite element method (FEM) calculations.
- fem3d_pack_test
- fem3d_project, an Octave 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, an Octave code library which evaluates a function defined on a 3D tetrahedral mesh as part of the finite element method (FEM).
- fem3d_sample_test
- fern, an Octave code which computes and displays the Barnsley fractal fern.
- fern_test
- feynman_kac_1d, an Octave 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, an Octave 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, an Octave 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, an Octave code which allows the user to plot finite element method (FEM) results that have been computed by FreeFem++().
- fft_serial, an Octave 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, an Octave code which displays points on a Fibonacci spiral, suggesting the arrangement of seeds in a sunflower, for instance.
- fibonacci_spiral_test
- file_increment, an Octave code which increments every entry of an integer array which is stored in a file.
- file_increment_test
- file_name_sequence, an Octave 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, an Octave 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, an Octave code which approximates integrals which include an oscillatory factor of sin(k*x) or cos(k*x).
- filon_rule_test
- filum, an Octave code which handles files and filenames;
- filum_test
- fire_simulation, an Octave code which simulates a forest fire over a rectangular array of trees, starting at a single random location.
- fire_simulation_test
- fisher_exact, an Octave 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, an Octave code which sets up and solves the Fitzhugh-Nagumo system of ordinary differential equations (ODE).
- fitzhugh_nagumo_ode_test
- flame_exact, an Octave 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, an Octave 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, an Octave 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
- floyd, an Octave code which implements the Floyd algorithm for finding the shortest distance between pairs of nodes on a directed graph.
- floyd_test
- fly_simulation, an Octave 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
- fn, an Octave 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, an Octave code which uses dynamic programming to count the ways of achieving a given score in football.
- football_dynamic_test
- four_fifths, an Octave 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, an Octave 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, an Octave code which reads and writes files used by the FreeFem finite element program to store mesh information.
- freefem_msh_io_test
- fsolve_test, an Octave code which calls fsolve() which seeks the solution x of one or more nonlinear equations f(x)=0.
- full_deck_simulation, an Octave 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, an Octave code which simulates a game in which a gambler never stops playing until all money is lost.
- gamblers_ruin_simulation_test
- gauss_seidel, an Octave code which implements the Gauss-Seidel iteration for linear systems.
- gauss_seidel_test
- gauss_seidel_poisson_1d, an Octave 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, an Octave 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, an Octave code which evaluates the Gaussian function and its derivatives.
- gaussian_test,
- gaussian_2d, an Octave code which evaluates a general Gaussian function of a 2D argument.
- gaussian_2d_test,
- gaussian_prime_spiral, an Octave 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, an Octave code which converts a matrix from General (GE) to Compressed Row Storage (CRS) format.
- ge_to_crs_test
- gegenbauer_cc, an Octave code which computes the Gegenbauer weighted integral of a function f(x) using a Clenshaw-Curtis approach.
- gegenbauer_cc_test
- gegenbauer_exactness, an Octave code which tests the polynomial exactness of Gauss-Gegenbauer quadrature rules.
- gegenbauer_exactness_test
- gegenbauer_polynomial, an Octave code which evaluates the Gegenbauer polynomial and associated functions.
- gegenbauer_polynomial_test
- gegenbauer_rule, an Octave code which computes and writes out a Gauss-Gegenbauer quadrature rule of given order.
- gegenbauer_rule_test
- gen_hermite_exactness, an Octave code which tests the polynomial exactness of generalized Gauss-Hermite quadrature rules.
- gen_hermite_exactness_test
- gen_hermite_rule, an Octave 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, an Octave code which tests the polynomial exactness of generalized Gauss-Laguerre quadrature rules.
- gen_laguerre_exactness_test
- gen_laguerre_rule, an Octave code which computes and writes out a generalized Gauss-Laguerre quadrature rule of given order and parameter value.
- gen_laguerre_rule_test
- geometry, an Octave 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, an Octave code which computes Delaunay triangulations, Voronoi diagrams, and other information, by Barry Joe.
- geompack_test
- gl_fast_rule, an Octave 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, an Octave 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, an Octave 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, an Octave code which implements the generalized minimum residual (GMRES) method for solving a nonsymmetric sparse linear system A*x=b.
- gmres_test
- gmsh_io, an Octave 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, an Octave 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, an Octave code which uses gnuplot() to create various kinds of plots.
- gpl_display, an Octave 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() is capable of.
- gpl_display_test
- gradient_descent, an Octave code which uses gradient descent to solve a linear least squares (LLS) problem.
- gradient_descent_test
- gram_polynomial, an Octave code which evaluates the Gram polynomials, also known as the discrete Chebyshev polyomials and associated functions.
- gram_polynomial_test
- gram_schmidt, an Octave code which implements the Gram-Schmidt process to orthogonalize and normalize a set of vectors.
- gram_schmidt_test
- graph_adj, an Octave code which carries out operations on abstract graphs, with undirected edges, described 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, an Octave code which determines various representations of a graph.
- graph_representation_test
- graphics_test, an Octave code which graphically displays various kinds of data.
- grazing_ode, an Octave code which sets up and solves a pair of ordinary differential equations (ODE) that model the populations of an edible plant, and the herbivore that grazes on it.
- gray_code_display, an Octave 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
- grazing_ode_test
- grf_display, an Octave code which reads a GRF file defining a mathematical graph and displays an image of it.
- grf_display_test
- grf_io, an Octave code which reads or writes a grf file which represents a mathematical graph;
- grf_io_test
- grid_display, an Octave 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, an Octave code which gives the user more control over drawing gridlines on a graph than is available through the builtin grid() command.
- gridlines_test
- grids_display, an Octave 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, an Octave 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, an Octave code which computes the Haar transform of 1d or 2d data.
- haar_transform_test
- halton, an Octave code which computes elements of a Halton Quasi Monte Carlo (QMC) sequence, using a simple interface.
- halton_test
- hammersley, an Octave code which computes elements of a Hammersley Quasi Monte Carlo (QMC) sequence, using a simple interface.
- hammersley_test
- hamming, an Octave code which implements some simple versions of Hamming codes which detects and correct errors in data.
- hamming_test
- hand_area, an Octave code which estimates the area of a curve which outlines a hand.
- hand_area_test
- hand_data, an Octave code which carries out some numerical exercises based on data that came from tracing several points on a hand.
- hand_data_test
- hand_mesh2d, an Octave 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, an Octave code which computes the upper Cholesky factor R of a symmetric positive definite (SPD) Hankel matrix H so that H = R' * R.
- hankel_cholesky_test
- hankel_inverse, an Octave code which computes the inverse of a Hankel matrix.
- hankel_inverse_test
- hankel_spd, an Octave 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, an Octave code which reads and writes sparse linear systems stored in the Harwell Boeing (HB) format for sparse matrices.
- hb_io_test
- hb_to_mm, an Octave code which converts a sparse matrix from Harwell Boeing (HB) to Matrix Market (MM) format.
- hb_to_mm_test
- hb_to_msm, an Octave 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, an Octave code which converts a sparse matrix from Harwell Boeing (HB) format to Sparse Triplet (ST) format.
- hb_to_st_test
- heartbeat_ode, an Octave 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, an Octave 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, an Octave 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, an Octave code which prints out "Hello, world!".
- hello_test
- helmholtz_exact, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which defines test integrands for Hermite integrals with density exp(-x^2) over the interval (-oo,+oo).
- hermite_integrands_test
- hermite_interpolant, an Octave code which computes the Hermite interpolant, a polynomial that matches function values and derivatives.
- hermite_interpolant_test
- hermite_polynomial, an Octave 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, an Octave 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, an Octave code which defines Hermite product polynomials, creating a multivariate polynomial as the product of univariate Hermite polynomials.
- hermite_rule, an Octave code which computes and writes out a Gauss-Hermite quadrature rule to estimate the integral of a function with density exp(-x^2) over the interval (-oo,+oo).
- hexagon_integrals, an Octave 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, an Octave code which computes one of 13 Lyness quadrature rules over the interior of the unit hexagon.
- hexagon_lyness_rule_test
- hexagon_monte_carlo, an Octave 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, an Octave code which computes one of four Stroud quadrature rules over the interior of the unit hexagon.
- hexagon_stroud_rule_test
- hexahedron_jaskowiec_rule, an Octave 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, an Octave code which returns a symmetric Witherden quadrature rule for the hexahedron, with exactness up to total degree 11.
- hexahedron_witherden_rule_test
- high_card_simulation, an Octave 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, an Octave code which computes the sequence of discrete Hilbert curves whose limit is a space-filling curve.
- hilbert_curve_test
- hilbert_curve_display, an Octave code which plots a Hilbert curve of given order.
- hilbert_curve_display_test
- histogram_data_2d_sample, an Octave 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, an Octave code which tries to make a histogram of data without using bins.
- histogram_discrete_test
- histogram_pdf, an Octave code which creates a histogram plot of a set of data, normalized to estimate the probability density function (PDF).
- histogram_pdf_test
- histogram_pdf_2d_sample, an Octave 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, an Octave code which takes a vector of data and organizes it into a histogram of a given number of bins with given width and range, to be displayed as a bar chart.
- histogramize_test
- hits, an Octave code which uses the HITS algorithm to assign authority and hub indices to a set of nodes in a directed network.
- hits_test
- house, an Octave 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, an Octave 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, an Octave code which evaluates the humps() function, its first and second derivatives and its antiderivative.
- humps_test
- humps_ode, an Octave code which sets up and solves an ordinary differential equation (ODE) whose solution is a double hump curve.
- humps_ode_test
- hyper_2f1, an Octave code which evaluates the hypergeometric functions 2F1(a,b,c;x) for real parameters a, b, c and argument x. This function is simply a wrapper for the Gnu Scientific Library function gsl_sf_hyperg_2F1().
- hyper_2f1_test
- hyperball_distance, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which computes a grid of points over the interior of a hypercube in M dimensions.
- hypercube_grid_test
- hypercube_integrals, an Octave 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, an Octave 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, an Octave 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
- hypersphere, an Octave 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_distance, an Octave 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_distance_test
- hypersphere_distance, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which contains many utility routines, using single precision integer (I4) arithmetic.
- i4lib_test
- i4mat_rref2, an Octave code which computes a version of the reduced row echelon form of an integer matrix.
- i4mat_rref2_test
- image_mesh, an Octave 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_sample, an Octave 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 RETURN. An example is supplied, which outlines the boundary of an aneurysm.
- image_sample_test
- index, an Octave 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, an Octave 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, an Octave code which parameterizes and interpolates data;
- interp_test
- is_gaussian_prime, an Octave code which is true if a given complex number c is a Gaussian prime.
- is_gaussian_prime_test
- is_prime, an Octave code which implements various versions of the sieve of Eratosthenes to determine whether a given integer is prime.
- is_prime_test
- isbn, an Octave 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, an Octave 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, an Octave code which computes the Jaccard distance between two sets.
- jaccard_distance_test
- jacobi, an Octave code which implements the Jacobi iteration for the iterative solution of linear systems.
- jacobi_test
- jacobi_eigenvalue, an Octave 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, an Octave code which tests the polynomial exactness of rules for integrals with a Jacobi weight function.
- jacobi_exactness_test
- jacobi_poisson_1d, an Octave code which uses Jacobi iteration to solve the linear system for a discretized steady 1D Poisson equation.
- jacobi_poisson_1d_test
- jacobi_polynomial, an Octave code which evaluates the Jacobi polynomial and associated functions.
- jacobi_polynomial_test
- jacobi_rule, an Octave code which computes and writes out a Gauss-Jacobi quadrature rule of given order.
- jacobi_rule_test
- jai_alai_simulation, an Octave code which simulates matches of jai alai.
- jai_alai_simulation_test
- jordan_matrix, an Octave code which returns a random matrix in Jordan canonical form.
- jordan_matrix_test
- julia_set, an Octave 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
- kdv_etdrk4, an Octave code which uses the ETDRK4 method to solve the Korteweg-deVries (KdV) partial differential equation (PDE), by Aly-Khan Kassam, Lloyd Trefethen.
- kdv_etdrk4_test
- kdv_exact, an Octave code which evaluates an exact solution of the Korteweg-deVries (KdV) partial differential equation (PDE).
- kdv_exact_test
- kdv_ift, an Octave 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, an Octave code which implements iterative methods for linear and nonlinear problems, including Arnoldi iteration, Broyden's method, conjugate gradient, GMRES, Krylov iteration, Newton-Krylov nonlinear solver, line search for minimization, transpose-free quasi-minimal residual solver for sparse linear systems, by Tim Kelley.
- kelley_test
- kepler_ode, an Octave code which sets up and solves the ordinary differential equations (ODE) for a Kepler two-body gravitational system.
- kepler_ode_test
- kepler_perturbed_ode, an Octave 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, an Octave code which accepts named keywords, using the Name/Value paired argument convention.
- kmeans, an Octave code which handles the K-Means problem, which organizes a set of N points in M dimensions into K clusters;
- kmeans_test
- kmeans_fast, an Octave 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, an Octave code which uses brute force to solve small versions of the 0/1 knapsack problem;
- knapsack_01_brute_test
- knapsack_dynamic, an Octave code which uses dynamic programming to solve a knapsack problem.
- knapsack_dynamic_test
- knapsack_greedy, an Octave code which uses a greedy algorithm to estimate a solution of the knapsack problem;
- knapsack_greedy_test
- kronrod_rule, an Octave code which computes a Gauss and Gauss-Kronrod pair of quadrature rules of arbitrary order, by Robert Piessens, Maria Branders.
- kronrod_rule_test
- lagrange_approx_1d, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which implements several multivariate Lagrange interpolation schemes developed by Tomas Sauer.
- lagrange_nd_test
- laguerre_exactness, an Octave 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, an Octave 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, an Octave code which evaluates the Laguerre polynomial, the generalized Laguerre polynomials, and the Laguerre function.
- laguerre_polynomial_test
- laguerre_product, an Octave code which computes weighted integrals of products of Laguerre polynomials.
- laguerre_product_test
- laguerre_rule, an Octave code which computes and prints a Gauss-Laguerre quadrature rule of a given order for estimating the integral of a function with density exp(-x) over the interval [0,+oo).
- laguerre_rule_test
- lambert_w, an Octave code which evaluates Lambert's W function.
- lambert_w_test
- langford_ode, an Octave code which sets up and solves the Langford system of ordinary differential equations (ODE).
- langford_ode_test
- laplace_periodic_test, an Octave 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, an Octave 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, an Octave code which computes N points in an M dimensional Latin Center square;
- latin_center_test
- latin_cover, an Octave 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, an Octave code which returns N points in an M dimensional Latin Edge square;
- latin_edge_test
- latin_random, an Octave code which returns N points in an M dimensional Latin Random square;
- latin_random_test
- latinize, an Octave code which adjusts N points in M dimensions to form a Latin hypercube;
- latinize_test
- lattice_rule, an Octave code which returns lattice rules for M dimensional integration;
- lattice_rule_test
- leapfrog, an Octave 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, an Octave code which finds a polynomial approximant to data using linear least squares (LLS).
- least_squares_approximant_test
- lebesgue, an Octave 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, an Octave 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, an Octave code which uses a fast (order N) algorithm to compute a Gauss-Legendre quadrature rule of given order.
- legendre_fast_rule_test
- legendre_polynomial, an Octave code which evaluates the Legendre polynomial and associated functions.
- legendre_polynomial_test
- legendre_product, an Octave code which computes weighted integrals of products of Legendre polynomials.
- legendre_product_test
- legendre_product_display, an Octave code which displays the points used in a 2D Gauss-Legendre quadrature rule;
- legendre_product_display_test
- legendre_product_polynomial, an Octave code which defines Legendre product polynomials, creating a multivariate polynomial as the product of univariate Legendre polynomials.
- legendre_product_polynomial_test
- legendre_rule, an Octave code which writes out a Gauss-Legendre quadrature rule of given order.
- legendre_rule_test
- legendre_shifted_polynomial, an Octave code which evaluates the shifted Legendre polynomial, with the domain [0,1].
- legendre_shifted_polynomial_test
- levenshtein_distance, an Octave code which returns the Levenshtein distance between two strings.
- levenshtein_distance_test
- levenshtein_matrix, an Octave code which returns the Levenshtein distance matrix defined by two strings.
- levenshtein_matrix_test
- lindberg_exact, an Octave 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, an Octave code which sets up and solves a system of 4 ordinary differential equations (ODE) which are very stiff.
- lindberg_ode_test
- line_cvt_lloyd, an Octave 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, an Octave 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, an Octave 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, an Octave code which returns a Felippa quadrature rules for approximating integrals over the interior of a line segment in 1D.
- line_felippa_rule_test
- line_grid, an Octave code which computes a grid of points over the interior of a line segment in 1D.
- line_grid_test
- line_integrals, an Octave 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, an Octave 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, an Octave 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, an Octave code which computes a Newton Cotes Open (NCO) quadrature rule, using equally spaced points, over the interior of a line segment in 1D.
- line_nco_rule_test
- linear_algebra, an Octave code which carries out various linear algebra operations for matrices stored in a variety of formats.
- linpack_d, an Octave 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, an Octave 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, an Octave code which plots a Lissajous figure, of the form x = sin ( a1 t + b1 ), y = sin ( a2 t + b2 ).
- lissajous_test
- llsq, an Octave 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, an Octave code which calls the load() function, which reads data from a file into a variable.
- lobatto_polynomial, an Octave code which evaluates Lobatto polynomials similar to Legendre polynomials except that they are 0 at both endpoints.
- lobatto_polynomial_test
- local_min, an Octave 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, an Octave 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, an Octave 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, an Octave code which computes the logarithmic norm of a matrix, for norms 1, 2 and oo.
- log_norm_test
- log_normal, an Octave code which returns quantities related to the log normal Probability Distribution Function (PDF).
- log_normal_test
- log_normal_truncated_ab, an Octave 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, an Octave code which plots the bifurcation diagram for the logistic equation, by John D Cook.
- logistic_bifurcation_test
- logistic_exact, an Octave 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, an Octave 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, an Octave code which sets up and solves the Lorenz system of ordinary differential equations (ODE).
- lorenz_ode_test
- luhn, an Octave code which computes the Luhn check digit for a string, and validates a string.
- luhn_test
- machar, an Octave code which computes the appropriate values of arithmetic constants for a given machine, by William Cody.
- machar_test
- machine, an Octave code which returns values of arithmetic constants for a given machine.
- machine_test
- magic_matrix, an Octave 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, an Octave code which generates an image of the Mandelbrot set;
- mandelbrot_test
- mandelbrot_orbit, an Octave code which generates the Mandelbrot iterates arising from a single starting point;
- mandelbrot_orbit_test
- maple_area, an Octave 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
- mario, an Octave code which creates a sort of "needlepoint" image of Mario, as an array of colored squares.
- mario_test
- markov_letters, an Octave code which counts the occurences of letter pairs in a text.
- markov_letters_test
- matrix_analyze, an Octave code which reports whether a matrix has various properties.
- matrix_analyze_test
- matrix_chain_brute, an Octave 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, an Octave 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, an Octave code which computes the exponential of a matrix.
- matrix_exponential_test
- mcnuggets, an Octave 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, an Octave 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, an Octave code which carries out a molecular dynamics simulation, and is intended as a starting point for implementing a parallel version.
- md_test
- md_fast, an Octave 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
- medit_mesh_io, an Octave code which reads or writes medit() MESH files defining a finite element mesh.
- medit_mesh_io_test
- medit_to_fem, an Octave 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
- memory, an Octave 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, an Octave 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, an Octave 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, an Octave code which plots the nodes and elements of a polygonal mesh, with optional numbering.
- mesh_display_test
- mesh_etoe, an Octave code which uses ETOV, the mesh element-to-vertex connectivity, to construct ETOE, the element-to-element connectivity.
- mesh_etoe_test
- mesh_vtoe, an Octave code which uses ETOV, the mesh element-to-vertex connectivity, to construct VTOE, the vertex-to-element connectivity.
- mesh_vtoe_test
- mesh2d, an Octave code which automatically creates a triangular mesh for a given polygonal region, by Darren Engwirda.
- mesh2d_test
- mesh2d_to_medit, an Octave 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, an Octave code which writes mesh2d() node and element data to files.
- mesh2d_write_test
- mgmres, an Octave 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, an Octave 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, an Octave 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, an Octave code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method.
- midpoint_test
- midpoint_adaptive, an Octave 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, an Octave code which solves one or more ordinary differential equations (ODE) using the (explicit) midpoint method, also called the modified Euler method.
- midpoint_explicit_test
- midpoint_fixed, an Octave 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.
- midpoint_fixed_test
- mm_io, an Octave code which reads and writes sparse linear systems stored in the Matrix Market (MM) format.
- mm_io_test
- mm_to_hb, an Octave 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, an Octave 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, an Octave 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
- monoalphabetic, an Octave code which applies a monoalphabetic substitution cipher to a string of text.
- monoalphabetic_test
- monomial, an Octave 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, an Octave code which symmetrizes the coefficients of equivalent monomials in a polynomial.
- monomial_symmetrize_test
- monomial_value, an Octave code which evaluates a monomial in M dimensions.
- monomial_value_test
- monopoly_matrix, an Octave code which computes the adjacency and transition matrices for the game of Monopoly.
- monopoly_matrix_test
- monty_hall_simulation, an Octave 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, an Octave code which processes some sample mortality data.
- mortality_test
- msm_to_hb, an Octave code which writes a MATLAB sparse matrix (MSM) to a Harwell Boeing (HB) file;
- msm_to_hb_test
- msm_to_mm, an Octave code which writes a MATLAB sparse matrix (MSM) to a Matrix Market (MM) file;
- msm_to_mm_test
- msm_to_st, an Octave code which writes a MATLAB sparse matrix (MSM) to a Sparse Triplet (ST) file;
- msm_to_st_test
- mxm, an Octave 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, an Octave 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 graphically.
- naca_test
- nas, an Octave code which runs the NASA kernel benchmark.
- nas_test
- navier_stokes_2d_exact, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which records information about neighboring pairs of territories in the game of RISK.
- neighbor_risk_test
- neighbor_states, an Octave code which records information about pairs of US states which are neighbors.
- neighbor_states_test
- neural_network, an Octave 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, an Octave code which finds a polynomial interpolant to data using Newton divided differences.
- newton_interp_1d_test
- newton_rc, an Octave code which solves a system of nonlinear equations by Newton's method, using reverse communication (RC).
- newton_rc_test
- niederreiter2, an Octave code which computes the Niederreiter M dimensional Quasi Mont Carlo (QMC) sequence, base 2;
- niederreiter2_test
- nintlib, an Octave code which implements approximate integration (quadrature) in M dimensions;
- nintlib_test
- normal, an Octave code which implements normal random number generators (RNG) for real and complex arithmetic, for scalars, vectors, and matrices.
- normal_test
- normal_dataset, an Octave code which creates a multivariate normal random dataset and writes it to a file.
- normal_dataset_test
- normal_ode, an Octave code which sets up and solves an ordinary differential equation (ODE) defining the normal probability density function (PDF).
- normal_ode_test
- normal01_multivariate_distance, an Octave 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, an Octave code which defines and numbers a subset of the nodes in a regular nxn grid of the [-1,+1]x[-1,+1] unit square.
- numgrid_test
- obj_display, an Octave code which displays an OBJ 3D graphics file;
- obj_display_test
- obj_io, an Octave code which reads and writes the data in an OBJ 3D graphics file;
- obj_io_test
- obj_to_tri_surface, an Octave code which reads an OBJ 3D graphics file and extracts the surface mesh data as a TRI_SURFACE dataset.
- obj_to_tri_surface_test
- octave_combinatorics, an Octave code which considers a variety of problems in combinatorics involving counting, combinations, permutations, and so on.
- octave_distance, an Octave 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.
- octave_exact, an Octave code which evaluates exact solutions to a few selected examples of ordinary differential equations (ODE) and partial differential equations (PDE).
- octave_grid, an Octave code which generates a regular grid of points inside a variety of regions in one, two, three or many dimensions.
- octave_monte_carlo, an Octave code which uses Monte Carlo sampling to estimate areas and integrals.
- octave_ode, an Octave code which sets up various systems of ordinary differential equations (ODE).
- octave_plots, an Octave code which uses plotting to illustrate a mathematical structure, such as an iterative map, a fractal, a curve or surface.
- octave_polynomial, an Octave code which analyzes a variety of polynomial families, returning the polynomial values, coefficients, derivatives, integrals, roots, or other information.
- octave_simulation, an Octave 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.
- octopus, an Octave code which contains some Octave-specific utilities.
- octopus_test
- ode23_test, an Octave 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, an Octave 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.
- oregonator_ode, an Octave code which sets up and solves the ordinary differential equations (ODE) that define the Oregonator, a model of the Belousov-Zhabotinsky chemical reaction.
- oregonator_ode_test
- ornstein_uhlenbeck, an Octave 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, an Octave code which sets up and solves the highly oscillatory ordinary differential equation (ODE).
- oscillator_ode_test
- owen, an Octave code which evaluates the Owen T function.
- owen_test
- ozone_ode, an Octave 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, an Octave 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, an Octave 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, an Octave code which uses the eigenvalue (power method) and surfer (Markov Chain Monte Carlo MCMC) approaches to ranking web pages.
- pagerank_test
- pagerank2, an Octave code which considers a specific application of the page rank algorithm.
- pagerank2_test
- pariomino, an Octave code which considers pariominoes, which are polyominoes with a checkerboard parity.
- pariomino_test
- partial_digest, an Octave code which seeks solutions of the partial digest problem.
- partial_digest_test
- partition_brute, an Octave 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, an Octave 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, an Octave 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, an Octave code which reads or writes graphics files that use the ASCII Portable Bit Map (PBM) format.
- pbma_io_test
- pce_burgers, an Octave 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, an Octave 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, an Octave 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
- pdflib, an Octave 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
- pendulum_comparison_ode, an Octave 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, an Octave code which sets up and solves the double pendulum ordinary differential equation (ODE).
- pendulum_double_ode_test
- pendulum_elastic_ode an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which forms or plots any of the 12 members of the pentomino family, shapes formed from 5 adjacent squares.
- pentominoes_test
- perceptron_test, an Octave code which calculates a classifier of linearly separable data using the perceptron algorithm.
- percolation_simulation, an Octave 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 code was written by Ian Cooper.
- percolation_simulation_test
- permutation_distance, an Octave 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, an Octave code which demonstrates how to initialize, get, or set data stored within a function, using static/persistent/saved/local memory.
- persistence_test
- pgma_io, an Octave code which reads or writes graphics files that use the ASCII Portable Gray Map (PGM) format.
- pgma_io_test
- pi_spigot, an Octave code which produces any number of digits of the decimal expansion of pi.
- pi_spigot_test
- pic, an Octave 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, an Octave code which computes a pink noise signal obeying a 1/f power law.
- pink_noise_test
- plasma_matrix, an Octave code which sets up a matrix associated with a problem in plasma physics.
- plasma_matrix_test
- poisson_1d_multigrid, an Octave code which applies the multigrid method to a discretized version of the 1D Poisson equation.
- poisson_1d_multigrid_test
- poisson_2d, an Octave code which solves the Poisson equation in a rectangle, using finite differences and Jacobi iteration.
- poisson_2d_test
- poisson_ell_test, an Octave 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, an Octave code which simulates a Poisson process in which events randomly occur with an average waiting time of Lambda.
- poisson_simulation_test
- polar_ode, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which generates a grid of points over the interior of a polygon in 2D.
- polygon_grid_test
- polygon_integrals, an Octave 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, an Octave 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, an Octave code which triangulates a (possibly nonconvex) polygon in 2D, based on a C program by Joseph ORourke;
- polygon_triangulate_test
- polyiamonds, an Octave code which works with polyiamonds, simple shapes constructed by edgewise connections of congruent equilateral triangles.
- polyiamonds_test
- polynomial, an Octave code which adds, multiplies, differentiates, evaluates and prints multivariate polynomials in a space of M dimensions.
- polynomial_test
- polynomial_conversion, an Octave code which converts representations of a polynomial between monomial, Bernstein, Chebyshev, Gegenbauer, Hermite, Laguerre and Legendre forms.
- polynomial_conversion_test
- polynomial_multiply, an Octave code which multiplies two polynomials p(x) and q(x).
- polynomial_multiply_test
- polynomial_resultant, an Octave code which computes the resultant R of univariate polynomials P and Q.
- polynomial_resultant_test
- polynomial_root_bound, an Octave code which computes the Cauchy bound on the magnitude of all roots of a polynomial with complex coefficients.
- polynomial_root_bound_test
- polynomials, an Octave 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, an Octave code which uses parity considerations to determine whether a given set of polyominoes can tile a specified region.
- polyomino_parity_test
- polyominoes, an Octave 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, an Octave 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, an Octave code which carries out the power method for finding a dominant eigenvalue and its eigenvector.
- power_method_test
- power_rule, an Octave code which constructs a power rule, that is, a product quadrature rule from identical 1D factor rules.
- power_rule_test
- ppma_io, an Octave code which reads or writes graphics files that use the ASCII Portable Pixel Map (PPM) format.
- ppma_io_test
- praxis, an Octave code which minimizes a scalar function of several variables, without requiring derivative information, by Richard Brent.
- praxis_test
- predator_prey_ode, an Octave code which sets up and solves a time-dependent predator-prey system of ordinary differential equations (ODE).
- predator_prey_ode_test
- predator_prey_ode_period, an Octave 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, an Octave 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_pi, an Octave code which evaluates Pi(n), the number of primes less than or equal to an integer n.
- prime_pi_test
- prime_plot, an Octave code which displays a box plot of the prime and composite numbers.
- prime_plot_test
- prism_jaskowiec_rule, an Octave 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, an Octave 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, an Octave 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, an Octave code which creates an M dimensional quadrature rule from a product of distinct 1d quadrature rules;
- product_rule_test
- pwc_plot_1d, an Octave 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, an Octave 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, an Octave code which approximates a set of data using a piecewise linear (PWL) function.
- pwl_approx_1d_test
- pwl_interp_1d, an Octave code which interpolates a set of data using a piecewise linear (PWL) function.
- pwl_interp_1d_test
- pwl_interp_2d, an Octave code which evaluates a piecewise linear (PWL) interpolant to data defined on a regular 2D grid.
- pwl_interp_2d_test
- pwl_interp_2d_scattered, an Octave 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, an Octave 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, an Octave 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, an Octave code which returns a Felippa quadrature rule for approximating integrals over the interior of a pyramid in 3D.
- pyramid_felippa_rule_test
- pyramid_grid, an Octave code which computes a grid of points over the interior of the unit pyramid in 3D;
- pyramid_grid_test
- pyramid_integrals, an Octave 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, an Octave 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, an Octave 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, an Octave code which computes a conical product quadrature rule over the interior of the unit pyramid in 3D.
- pyramid_rule_test
- pyramid_witherden_rule, an Octave 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, an Octave 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, an Octave code which rapidly defines certain quadrature rules for approximating an integral;
- quad_fast_rule_test
- quad_rule, an Octave code which defines quadrature rules for approximating an integral;
- quad_rule_test
- quad2d, an Octave 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 an Octave 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, an Octave 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
- quadrature_golub_welsch, an Octave code which computes the points and weights of a Gaussian quadrature rule using the Golub-Welsch procedure.
- quadrature_golub_welsch_test
- quadrature_least_squares, an Octave 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, an Octave 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, an Octave 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, an Octave code which carries out geometric calculations on quadrilaterals, including angles, area, distances, nearest point, point containment, perimeter, and random generation.
- quadrilateral_test
- quadrilateral_mesh, an Octave code which handles meshes of quadrilaterals over a 2D region;
- quadrilateral_mesh_test
- quadrilateral_mesh_order1_display, an Octave code which plots piecewise constant (PWC) data associated with a mesh of quadrilaterals;
- quadrilateral_mesh_order1_display_test
- quadrilateral_surface_display, an Octave 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, an Octave code which returns a symmetric Witherden quadrature rule for the quadrilateral, with exactness up to total degree 21.
- quadrilateral_witherden_rule_test
- quality, an Octave code which measures the dispersion of pointsets in M dimensions;
- quality_test
- quasiperiodic_ode, an Octave code which sets up and solves a system of ordinary differential equations (ODE) for a problem with a quasiperiodic solution.
- quasiperiodic_ode_test
- quaternions, an Octave code which carries out some simple arithmetic operations for quaternions.
- quaternions_test
- r8_scale, an Octave code which computes the "next" and "previous" real numbers.
- r8_scale_test
- r83, an Octave code which contains linear algebra routines for r83 matrices (real, 64 bit, tridiagonal 3xN format).
- r83_test
- r83_np, an Octave code which contains linear algebra routines for r83_np matrices (real, 64 bit, tridiagonal 3xN format, nonpivoting factorization).
- r83_np_test
- r83p, an Octave code which contains linear algebra routines for r83p matrices (real, 64 bit, tridiagonal periodic format).
- r83p_test
- r83s, an Octave code which contains linear algebra routines for r83s matrices (real, 64 bit, tridiagonal scalar format).
- r83s_test
- r83t, an Octave code which contains linear algebra routines for r83t matrices (real, 64 bit, tridiagonal Mx3 format).
- r83t_test
- r83v, an Octave code which contains linear algebra routines for r83v matrices (real, 64 bit, tridiagonal three vector format).
- r83v_test
- r85, an Octave code which contains linear algebra routines for r85 matrices (real, 64 bit, pentadiagonal format).
- r85_test
- r8bb, an Octave code which contains linear algebra routines for r8bb matrices (real, 64 bit, border banded format).
- r8bb_test
- r8blt, an Octave code which contains linear algebra routines for r8blt matrices (real, 64 bit, band lower triangular format).
- r8blt_test
- r8bto, an Octave code which contains linear algebra routines for r8bto matrices (real, 64 bit, block Toeplitz format).
- r8bto_test
- r8but, an Octave code which contains linear algebra routines for r8but matrices (real, 64 bit, band upper triangular format).
- r8but_test
- r8cb, an Octave code which contains linear algebra routines for r8cb matrices (real, 64 bit, Compressed Band format).
- r8cb_test
- r8cbb, an Octave code which contains linear algebra routines for r8cbb matrices (real, 64 bit, Compressed Border Banded format).
- r8cbb_test
- r8ccs, an Octave code which contains linear algebra routines for r8ccs matrices: real, 64 bit, Compressed Column Storage (CCS) format.
- r8ccs_test
- r8ci, an Octave code which contains linear algebra routines for r8ci matrices (real, 64 bit, circulant format).
- r8ci_test
- r8col, an Octave 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, an Octave code which contains linear algebra routines for R8CRS matrices: real, 64 bit, Compressed Row Storage (CRS) format.
- r8crs_test
- r8gb, an Octave code which contains linear algebra routines for r8gb matrices (real, 64 bit, General Banded format).
- r8gb_test
- r8gd, an Octave code which contains linear algebra routines for r8gd matrices (real, 64 bit, general diagonal format).
- r8gd_test
- r8ge, an Octave code which contains linear algebra routines for R8GE matrices (real, 64 bit, General format).
- r8ge_test
- r8ge_np, an Octave code which contains nonpivoting linear algebra routines for r8ge_np matrices (real, 64 bit, General Nonpivoting format).
- r8ge_np_test
- r8lib, an Octave code which contains many utility routines, using double precision real (R8) arithmetic.
- r8lib_test
- r8lt, an Octave code which contains linear algebra routines for R8LT matrices: real, 64 bit, Lower Triangular.
- r8lt_test
- r8ltt, an Octave code which contains linear algebra routines for r8ltt matrices (real, 64 bit, lower triangular Toeplitz format).
- r8ltt_test
- r8ncf, an Octave code which contains linear algebra routines for r8ncf matrices (real, 64 bit, nonsymmetric coordinate format).
- r8ncf_test
- r8pbl, an Octave code which contains linear algebra routines for r8pbl matrices (real, 64 bit, symmetric positive definite (SPD) band lower format).
- r8pbl_test
- r8pbu, an Octave code which contains linear algebra routines for r8pbu matrices (real, 64 bit, symmetric positive definite (SPD) band upper format).
- r8pbu_test
- r8po, an Octave code which contains linear algebra routines for r8po matrices (real, 64 bit, symmetric positive definite (SPD) format).
- r8po_test
- r8poly, an Octave 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, an Octave code which contains linear algebra routines for r8pp matrices (real, 64 bit, symmetric positive definite (SPD) packed format).
- r8pp_test
- r8ri, an Octave code which contains linear algebra routines for r8ri matrices (real, 64 bit, row indexed format).
- r8ri_test
- r8row, an Octave 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, an Octave code which contains linear algebra routines for r8sd matrices (real, 64 bit, symmetric diagonal format).
- r8sd_test
- r8sm, an Octave code which contains linear algebra routines for r8sm matrices (real, 64 bit, Sherman-Morrison A-u*v' format).
- r8sm_test
- r8sr, an Octave code which carries out linear algebra operations for r8sr matrices (real, 64 bit, diagonal + compressed row offdiagonal format).
- r8sr_test
- r8ss, an Octave code which carries out linear algebra operations for r8ss matrices (real, 64 bit, symmetric skyline format).
- r8ss_test
- r8st, an Octave code which contains linear algebra routines for R8ST matrices: real, 64 bit, Sparse Triplet.
- r8st_test
- r8sto, an Octave code which contains linear algebra routines for r8sto matrices (real, 64 bit, symmetric Toeplitz N format).
- r8sto_test
- r8to, an Octave code which contains linear algebra routines for r8to matrices (real, 64 bit, Toeplitz 2*N-1 format).
- r8to_test
- r8ut, an Octave code which contains linear algebra routines for r8ut matrices: real, 64 bit, Upper Triangular.
- r8ut_test
- r8utp, an Octave code which carries out linear algebra operations on r8utp matrices, real 64 bit, Upper Triangular Packed format.
- r8utp_test
- r8utt, an Octave code which contains linear algebra routines for r8utt matrices (real, 64 bit, upper triangular Toeplitz format).
- r8utt_test
- r8vm, an Octave code which contains linear algebra routines for r8vm matrices (real, 64 bit, vandermonde format).
- r8vm_test
- randlc, an Octave code which implements a random number generator (RNG) used by the nas() benchmarks.
- randlc_test
- random_data, an Octave 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, an Octave code which generates vectors of random values which are already sorted.
- random_sorted_test
- random_walk_1d_simulation, an Octave code which simulates a random walk in a 1-dimensional region.
- random_walk_1d_simulation_test
- random_walk_2d_avoid_simulation, an Octave code which simulates a self-avoiding random walk in a 2-dimensional region.
- random_walk_2d_avoid_simulation_test
- random_walk_2d_simulation, an Octave code which simulates a random walk in a 2-dimensional region.
- random_walk_2d_simulation_test
- random_walk_3d_simulation, an Octave code which simulates a random walk in a 3-dimensional region.
- random_walk_3d_simulation_test
- ranlib, an Octave 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, an Octave code which defines and evaluates radial basis function (RBF) interpolants to 1D data.
- rbf_interp_1d_test
- rbf_interp_2d, an Octave code which defines radial basis function (RBF) interpolants to 2D data.
- rbf_interp_2d_test
- rbf_interp_nd, an Octave code which defines and evaluates radial basis function (RBF) interpolants to M dimensional data.
- rbf_interp_nd_test
- reaction_ode, an Octave 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, an Octave 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, an Octave 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
- rectangle_distance, an Octave 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, an Octave code which plots data from an interesting region that was meshed by FreeFem++() and transferred using the ffmatlib() library.
- rejection_sample, an Octave code which demonstrates acceptance/rejection sampling.
- rejection_sample_test
- rigid_body_ode, an Octave 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, an Octave code which creates, plots, or saves data generated by sampling a number of concentric, possibly overlapping rings.
- ring_data_test
- ripple_ode, an Octave 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, an Octave code which returns the transition and adjacency matrix for the game of RISK.
- risk_matrix_test
- rk12, an Octave 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, an Octave code which defines an adaptive ordinary differential equation (ODE) solver, using Runge-Kutta (RK) solvers of order 1 and 2.
- rk12_adapt_test
- rk23, an Octave code which applies Runge-Kutta (RK) solvers of order 2 and 3 to a system of ordinary differential equations (ODE);
- rk23_test
- rk34, an Octave code which applies Runge-Kutta (RK) solvers of order 3 and 4 to a system of ordinary differential equations (ODE);
- rk34_test
- rk4, an Octave 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, an Octave code which applies Runge-Kutta (RK) solvers of order 4 and 5 to a system of ordinary differential equations (ODE);
- rk45_test
- rkf45, an Octave code which applies a Runge-Kutta-Fehlberg (RKF) solver to a system of ordinary differential equations (ODE);
- rkf45_test
- rng_cliff, an Octave code which computes a sequence of values from the Cliff random number generator (RNG).
- rng_cliff_test
- rnglib, an Octave 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, an Octave 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, an Octave code which sets up and solves the 3D Roessler system of ordinary differential equations (ODE).
- roessler_ode_test
- root_rc, an Octave 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, an Octave code which seeks solutions of a system of nonlinear equations, using reverse communication (RC), by Gaston Gonnet.
- roots_rc_test
- rot13, an Octave code which enciphers a string using the ROT13 cipher for letters, and the ROT5 cipher for digits.
- rot13_test
- roulette_simulation, an Octave code which simulates the spinning of a roulette wheel and the evaluation of certain common roulette bets.
- roulette_simulation_test
- row_echelon_integer, an Octave 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, an Octave code which calls rref() for the reduced row echelon form (RREF) of a matrix, which can be singular or rectangular.
- rubber_band_ode, an Octave code which sets up and solves a set of ordinary differential equations (ODE) describing a mass suspended by a spring and rubber band, which exhibits chaotic behavior.
- rubber_band_ode_test
- rucklidge_ode, an Octave 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, an Octave code which generates six M dimensional datasets for cluster analysis.
- sammon_data_test
- sandia_cubature, an Octave code which computes M-dimensional quadrature rules for certain regions and weight functions.
- sandia_cubature_test
- sandia_rules, an Octave 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, an Octave code which explores a generalized construction method for sparse grids.
- sandia_sgmgg_test
- sandia_sparse, an Octave 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, an Octave 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
- sawtooth_ode, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which illustrates properties of stochastic differential equations (SDE), and common algorithms for their analysis, by Desmond Higham;
- sde_test
- search_test, an Octave code which searches integers between A and B for a value J such that F(J) = C.
- sensitive_ode, an Octave code which sets up a second order ordinary differential equation (ODE) which exhibits sensitive dependence on the initial condition.
- sensitive_ode_test
- serenity, an Octave 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, an Octave code which implements various set theoretic operations.
- set_theory_test
- sftpack, an Octave code which implements the slow Fourier transform (SFT), intended as a teaching tool and comparison with the Fast Fourier Transform (FFT).
- sftpack_test
- shepard_interp_1d, an Octave code which defines and evaluates Shepard interpolants to 1D data, based on inverse distance weighting.
- shepard_interp_1d_test
- shepard_interp_2d, an Octave code which defines and evaluates Shepard interpolants to 2D data, based on inverse distance weighting.
- shepard_interp_2d_test
- shepard_interp_nd, an Octave code which defines and evaluates Shepard interpolants to M dimensional data, based on inverse distance weighting.
- shepard_interp_nd_test
- sigmoid_derivative, an Octave code which evaluates derivatives of any order for the sigmoid function s(x)=1/(1+exp(-x)).
- sigmoid_derivative_test
- simplex_coordinates, an Octave code which computes the Cartesian coordinates of the vertices of a regular simplex in M dimensions.
- simplex_coordinates_test
- simplex_gm_rule, an Octave 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, an Octave code which generates a regular grid of points over the interior of an arbitrary simplex in M dimensions.
- simplex_grid_test
- simplex_integrals, an Octave 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, an Octave 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, an Octave 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, an Octave code which demonstrates properties of the discrete sine transform (DST).
- sine_transform_test
- sir_ode, an Octave 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, an Octave 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, an Octave 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, an Octave code which provides tools for studying the game of Snakes and Ladders.
- snakes_and_ladders_simulation, an Octave 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_matrix, an Octave code which returns the transition matrix for the game of Snakes and Ladders.
- snakes_matrix_test
- snakes_probability, an Octave code which computes the game length probabilities for the game of Snakes and Ladders, by Desmond Higham and Nicholas Higham.
- snakes_probability_test
- solve, an Octave code which uses Gauss elimination to solve a linear system A*x=b.
- solve_test
- sor, an Octave code which uses the successive over-relaxation (SOR) iteration to solve a linear system of equations.
- sor_test
- sort_test, an Octave code which calls the sort() function to sort objects of several types.
- sort_rc, an Octave code which sorts a list of any kind of objects, using reverse communication (RC).
- sort_rc_test
- sparse_test, an Octave code which tests the sparse() function for creating sparse matrices and carrying out linear algebraic functions on them;
- sparse_display, an Octave 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 matplotlib spy() function.
- sparse_display_test
- sparse_grid_cc, an Octave code which creates sparse grids based on Clenshaw-Curtis (CC) quadrature rules.
- sparse_grid_cc_test
- sparse_grid_gl, an Octave code which creates sparse grids based on Gauss-Legendre (GL) rules.
- sparse_grid_gl_test
- sparse_grid_hermite, an Octave code which creates sparse grids based on Gauss-Hermite rules.
- sparse_grid_hermite_test
- sparse_grid_hw, an Octave 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, an Octave code which creates sparse grids based on Gauss-Laguerre rules.
- sparse_grid_laguerre_test
- sparse_grid_mixed, an Octave code which creates a sparse grid dataset based on a mixed set of 1D factor rules.
- sparse_grid_mixed_test
- sparse_grid_total_poly, an Octave code which investigates the total polynomial approximation using sparse grids.
- sparse_grid_total_poly_test
- sparse_interp_nd, an Octave code which defines a sparse interpolant to a function f(x) of a M dimensional argument.
- sparse_interp_nd_test
- spd_test, an Octave code which performs a few tests on a real matrix to determine whether it is symmetric positive definite (SPD).
- sphere_cubed_grid, an Octave 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, an Octave code which carries out the Centroidal Voronoi Tessellation (CVT) iteration on the surface of the unit sphere in 3D.
- sphere_cvt_test
- sphere_delaunay, an Octave code which computes the Delaunay triangulation of points on the surface of the unit sphere in 3D.
- sphere_delaunay_test
- sphere_distance, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which computes Lebedev quadrature rules on the surface of the unit sphere in 3D.
- sphere_lebedev_rule_test
- sphere_lebedev_rule_display, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which uses triangulation to approximate an integral on the surface of the unit sphere in 3D.
- sphere_quad_test
- sphere_stereograph, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which computes the Voronoi diagram of points on the surface of the unit sphere in 3D.
- sphere_voronoi_test
- spiral_exact, an Octave code which computes a 2D velocity vector field that is an exact solution of the continuity equation.
- spiral_exact_test
- spline, an Octave code which interpolates and approximates via splines;
- spline_test
- spquad, an Octave 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_ode, an Octave 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_double_ode, an Octave 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_sweep_ode, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which returns a Felippa quadrature rules for approximating integrals over the interior of a square in 2D.
- square_felippa_rule_test
- square_grid, an Octave code which computes a grid of points over the interior of a square in 2D.
- square_grid_test
- square_hex_grid, an Octave code which computes a hexagonal grid of points over the interior of a square in 2D.
- square_hex_grid_test
- square_integrals, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which returns symmetric quadrature rules, with exactness up to total degree 20, over the interior of the symmetric square in 2D, by Hong Xiao and Zydrunas Gimbutas.
- square_symq_rule_test
- squircle_ode, an Octave 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, an Octave code which reads and writes sparse linear systems stored in the Sparse Triplet (ST) format.
- st_io_test
- st_to_ccs, an Octave code which converts sparse matrix data from Sparse Triplet (ST) format to Compressed Column Storage (CCS) format;
- st_to_ccs_test
- st_to_hb, an Octave code which converts sparse matrix data from Sparse Triplet (ST) format to Harwell Boeing (HB) format;
- st_to_hb_test
- st_to_mm, an Octave code which converts sparse matrix data from Sparse Triplet (ST) format to Matrix Market (MM) format;
- st_to_mm_test
- st_to_msm, an Octave code which reads a Sparse Triplet (ST) file and creates a corresponding MATLAB Sparse Matrix (MSM).
- st_to_msm_test
- steinerberger, an Octave 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, an Octave 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, an Octave code which sets up and solves an ordinary differential equation (ODE) which is an example of a stiff ODE.
- stiff_ode_test
- stla_display, an Octave code which displays an ASCII stereolithography (STL) 3D graphics file;
- stla_display_test
- stla_io, an Octave code which reads and writes an ASCII stereolithography (STL) 3D graphics file;
- stla_io_test
- stla_to_tri_surface, an Octave 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, an Octave code which is a faster version of stla_to_tri_surface().
- stla_to_tri_surface_fast_test
- stochastic_diffusion, an Octave code which implements several versions of a stochastic diffusivity coefficient.
- stochastic_diffusion_test
- stochastic_heat2d, an Octave 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, an Octave code which applies a Runge Kutta (RK) scheme to a stochastic ordinary differential equation (SDE).
- stochastic_rk_test
- stokes_2d_exact, an Octave code which evaluates exact solutions to the incompressible steady Stokes equations over the unit square in 2D.
- stokes_2d_exact_test
- string_pde, an Octave code which sets up and solves the partial differential equations (PDE) describing a vibrating string, creating files to be displayed by gnuplot().
- string_pde_test
- subset, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which seeks solutions of the subset sum problem, using a brute force approach.
- subset_sum_brute_test
- subset_sum_swap, an Octave code which uses swapping to try to improve an initial estimated solution of the subset sum problem, which seeks a subset of a set of integers which has a given sum. Even when an exact solution exists, this approach often only finds an approximate solution.
- subset_sum_swap_test
- svd_test, an Octave code which demonstrates the Singular Value Decomposition (SVD) for a simple example.
- svd_basis, an Octave code which applies the singular value decomposition (SVD) to a collection of data vectors, extracting dominant modes;
- svd_basis_test
- svd_circle, an Octave 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, an Octave code which applies singular value decomposition (SVD) analysis to a set of images.
- svd_faces_test
- svd_fingerprint, an Octave 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, an Octave 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, an Octave 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, an Octave code which applies singular value decomposition (SVD) analysis to a set of powers x(i)^(j-1).
- svd_powers_test
- svd_snowfall, an Octave code which reads a file containing historical snowfall data and analyzes the data with the Singular Value Decomposition (SVD).
- svd_snowfall_test
- svd_sphere, an Octave 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_truncated_test, an Octave 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.
- sympy_test, an Octave code which tests sympy(), the symbolic mathematics package.
- table_io, an Octave code which reads and writes a simple table file;
- table_io_test
- task_division, an Octave 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
- tennis_matrix, an Octave code which computes the transition matrix for a game of tennis, which has 17 distinct states.
- tennis_matrix_test
- tensor_grid_display, an Octave 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, an Octave code which implements test problems for approximation, provided as a set of (x,y) data.
- test_approx_test
- test_con, an Octave code which implements test problems for numerical continuation.
- test_con_test
- test_eigen, an Octave code which implements test matrices for eigenvalue analysis.
- test_eigen_test
- test_int, an Octave code which implements test problems for approximate integration (quadrature) in one dimension.
- test_int_test
- test_int_2d, an Octave code which implements test problems for approximate integration (quadrature) in two dimensions.
- test_int_2d_test
- test_interp, an Octave code which defines test problems for interpolation, provided as a set of (x,y(x)) data.
- test_interp_test
- test_interp_1d, an Octave code which defines test problems for interpolation of data y(x), which depends on a 1D argument.
- test_interp_1d_test
- test_interp_2d, an Octave 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, an Octave code which defines test problems for interpolation which are available in functional form.
- test_interp_fun_test
- test_interp_nd, an Octave code which defines test problems for interpolation of data z(x), depending on an M dimensional argument.
- test_interp_nd_test
- test_lls, an Octave code which implements linear least squares (LLS) test problems of the form A*x=b.
- test_lls_test
- test_matrix, an Octave 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, an Octave code which defines a set of test cases for computing the matrix exponential.
- test_matrix_exponential_test
- test_min, an Octave code which implements test problems for minimization of a scalar function of a scalar variable.
- test_min_test
- test_nearest, an Octave code which tests the time complexity of various procedures for solving the nearest neighbor problem.
- test_nearest_test
- test_nint, an Octave code which defines test functions for M-dimensional quadrature routines.
- test_nint_test
- test_nonlin, an Octave code which implements test problems for the solution of systems of nonlinear equations.
- test_nonlin_test
- test_opt, an Octave code which implements test problems for optimization of a scalar function of several variables.
- test_opt_test
- test_opt_con, an Octave 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, an Octave 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, an Octave code which generates example cases of the partial digest problem.
- test_partial_digest_test
- test_triangulation, an Octave code which defines test problems for triangulation;
- test_triangulation_test
- test_values, an Octave 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, 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, an Octave 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 Octave tests.
- tet_mesh, an Octave code which works with tetrahedral meshes in 3D;
- tet_mesh_test
- tet_mesh_boundary, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which estimates the integral of a function over a region defined by a tetrahedral mesh.
- tet_mesh_quad_test
- tet_mesh_quality, an Octave code which computes various quality measures for a tetrahedral mesh of a set of nodes in 3D;
- tet_mesh_quality_test
- tet_mesh_rcm, an Octave 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, an Octave code which refines a mesh of tetrahedrons;
- tet_mesh_refine_test
- tet_mesh_tet_neighbors, an Octave 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, an Octave code which write a gmsh() file describing a tetrahedral mesh;
- tet_mesh_to_gmsh_test
- tet_mesh_to_xml, an Octave code which write an XML file describing a tetrahedral mesh;
- tet_mesh_to_xml_test
- tet_mesh_volumes, an Octave code which computes the volume of each tetrahedron in a mesh of tetrahedrons;
- tet_mesh_volumes_test
- tetrahedron, an Octave 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, an Octave 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, an Octave code which tests the polynomial exactness of a quadrature rule over the interior of a tetrahedron in 3D.
- tetrahedron_exactness_test
- tetrahedron_felippa_rule, an Octave code which returns a Felippa quadrature rules for approximating integrals over the interior of a tetrahedron in 3D.
- tetrahedron_felippa_rule_test
- tetrahedron_grid, an Octave code which computes a grid of points over the interior of a tetrahedron in 3D.
- tetrahedron_grid_test
- tetrahedron_integrals, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which defines Newton-Cotes closed (NCC) quadrature rules over the interior of a tetrahedron in 3D.
- tetrahedron_ncc_rule_test
- tetrahedron_nco_rule, an Octave code which defines Newton-Cotes open (NCO) quadrature rules over the interior of a tetrahedron in 3D.
- tetrahedron_nco_rule_test
- tetrahedron_slice_display, an Octave code which determines the intersection between a tetrahedron and a plane and displays the result.
- tetrahedron_slice_display_test
- tetrahedron_witherden_rule, an Octave 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, an Octave code which uses the Monte Carlo method to estimate an integral over the interior of the unit tetrahedron in 3D.
- tetrahedron01_monte_carlo_test
- theta_method, an Octave code which solves one or more ordinary differential equations (ODE) using the theta method.
- theta_method_test
- three_body_ode, an Octave 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, an Octave code which calls tic() and toc(), which compute elapsed time.
- timer_test, an Octave code which demonstrates and compares several ways of timing code execution.
- timestamp, an Octave code which prints the current YMDHMS date as a timestamp;
- timestamp_test
- toeplitz_cholesky, an Octave code which computes the Cholesky factorization of a symmetric positive definite (SPD) Toeplitz matrix.
- toeplitz_cholesky_test
- toeplitz_inverse, an Octave code which computes the inverse of a Toeplitz matrix.
- toeplitz_inverse_test
- toms097, an Octave code which computes the distance between all pairs of nodes in a directed graph with weighted edges, using the Floyd algorithm. This is a version of ACM TOMS algorithm 97.
- toms097_test
- toms112, an Octave 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, an Octave 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, an Octave code which evaluates the modified Beta function, by Oliver Ludwig. This is a version of ACM TOMS algorithm 179.
- toms179_test
- toms243, an Octave code which evaluates the logarithm of a complex value, by David Collens. This is a version of ACM TOMS algorithm 243.
- toms243_test
- toms291, an Octave code which evaluates the logarithm of the Gamma function. This is a version of ACM TOMS algorithm 291.
- toms291_test
- toms443, an Octave code which evaluates the Lambert W function, by Fritsch, Shafer and Crowley. This is a version of ACM TOMS algorithm 443.
- toms443_test
- toms446, an Octave code which manipulates Chebyshev series for interpolation and approximation; this is a version of ACM TOMS algorithm 446, by Roger Broucke.
- toms446_test
- toms462, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which evaluates the Pfaffian for a dense or banded skew symmetric matrix, by Michael Wimmer.
- toms923_test
- tough_ode, an Octave 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, an Octave code which simulates the cars waiting to get through a traffic light.
- traffic_simulation_test
- trapezoidal, an Octave code which solves one or more ordinary differential equations (ODE) using the (implicit) trapezoidal method, and fsolve() for the implicit system.
- trapezoidal_test
- trapezoidal_explicit, an Octave code which solves one or more ordinary differential equations (ODE) using the (explicit) trapezoidal method.
- trapezoidal_explicit_test
- trapezoidal_fixed, an Octave code which solves one or more ordinary differential equations (ODE) using the (implicit) trapezoidal method, and a fixed point method for the implicit system.
- trapezoidal_fixed_test
- treepack, an Octave 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, an Octave code which displays a TRI_SURFACE object representing a triangulated surface;
- tri_surface_display_test
- tri_surface_to_obj, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which returns a Dunavant quadrature rule over the interior of a triangle in 2D.
- triangle_dunavant_rule_test
- triangle_exactness, an Octave code which tests the polynomial exactness of a quadrature rule over the interior of a triangle in 2D.
- triangle_exactness_test
- triangle_fekete_rule, an Octave code which returns a Fekete rule for interpolation or quadrature over the interior of a triangle in 2D.
- triangle_fekete_rule_test
- triangle_felippa_rule, an Octave code which returns a Felippa quadrature rule for approximating integrals over the interior of a triangle in 2D.
- triangle_felippa_rule_test
- triangle_grid, an Octave code which computes a grid of points over the interior of a triangle in 2D.
- triangle_grid_test
- triangle_histogram, an Octave code which computes histograms of data over the interior of a unit triangle in 2D.
- triangle_histogram_test
- triangle_integrals, an Octave 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, an Octave code which defines integrands for testing quadrature rules over a triangle.
- triangle_integrands_test
- triangle_interpolate, an Octave code which shows how vertex data can be interpolated at any point in the interior of a triangle.
- triangle_interpolate_test
- triangle_io, an Octave code which reads or writes files created by Jonathan Shewchuk's triangle() program.
- triangle_io_test
- triangle_lyness_rule, an Octave code which returns Lyness-Jespersen quadrature rules over the interior of a triangle in 2D;
- triangle_lyness_rule_test
- triangle_monte_carlo, an Octave code which uses the Monte Carlo method to estimate an integral over the interior of a general triangle in 2D.
- triangle_monte_carlo_test
- triangle_ncc_rule, an Octave code which defines Newton-Cotes Closed (NCC) quadrature rules over the interior of a triangle in 2D.
- triangle_ncc_rule_test
- triangle_nco_rule, an Octave code which defines Newton-Cotes Open (NCO) quadrature rules over the interior of a triangle in 2D.
- triangle_nco_rule_test
- triangle_quadrature_symmetry, an Octave code which determines the symmetries of a quadrature rule for a triangle.
- triangle_quadrature_symmetry_test
- triangle_refine, an Octave code which divides a triangle into c^2 copies of itself, and implements a simple centroid-based quadrature scheme.
- triangle_refine_test
- triangle_svg, an Octave 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, an Octave code which returns efficient symmetric quadrature rules, with exactness up to total degree 50, over the interior of a triangle in 2D, by Hong Xiao and Zydrunas Gimbutas.
- triangle_symq_rule_test
- triangle_symq_to_ref, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which returns a Wandzura quadrature rule of exactness 5, 10, 15, 20, 25 and 30 over the interior of the triangle in 2D.
- triangle_wandzura_rule_test
- triangle_witherden_rule, an Octave code which returns a symmetric Witherden quadrature rule for the triangle, with exactness up to total degree 20.
- triangle_witherden_rule_test
- triangle01_integrals, an Octave code which returns the integral of any monomial over the interior of the unit triangle in 2D.
- triangle01_integrals_test
- triangle01_monte_carlo, an Octave 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, an Octave code which triangulates a polygonal region, based on a C program by Joseph ORourke;
- triangulate_test
- triangulate_rectangle, an Octave code which sets up a grid of triangles in a rectangular region.
- triangulate_rectangle_test
- triangulation, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which measures the amount by which a triangulation fails the local Delaunay test;
- triangulation_delaunay_discrepancy_test
- triangulation_display, an Octave code which displays the nodes and elements of a triangulation;
- triangulation_display_test
- triangulation_node_to_element, an Octave 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, an Octave code which plots piecewise constant (PWC) data associated with a triangulation;
- triangulation_order1_display_test
- triangulation_order3_contour, an Octave 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, an Octave 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, an Octave code which plots the nodes and elements of a triangulation as a PostScript file;
- triangulation_plot_test
- triangulation_quad, an Octave 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, an Octave code which reads information about a triangulation and computes various quality measures;
- triangulation_quality_test
- triangulation_refine, an Octave code which refines a triangulation;
- triangulation_refine_test
- triangulation_svg, an Octave 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, an Octave 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, an Octave code which solves a tridiagonal linear system.
- tridiagonal_solver_test
- trig_interp, an Octave code which uses trigonometric functions for interpolation.
- trig_interp_test
- trig_interp_basis, an Octave code which evaluates the cardinal basis functions for trigonometric interpolation of equally spaced data.
- trig_interp_basis_test
- trinity, an Octave 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", T1, T2, T3 and T4, each consisting of 36 30-60-90 triangles, and seeks an arrangement of the four tiles that exactly covers the region.
- trinity_test
- truel_simulation, an Octave code which simulates N repetitions of a duel between three players, each of whom has a known firing accuracy.
- truel_simulation_test
- truncated_normal, an Octave 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, an Octave 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, an Octave 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, an Octave code which reads a file of city-to-city distances and solves a (small!) traveling salesperson problem (TSP), using brute force.
- tsp_brute_test
- tsp_descent, an Octave code which reads a file 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, an Octave code which reads a file 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, an Octave code which tries to optimize the traveling salesperson problem (TSP), written by Cleve Moler.
- tsp_moler_test
- tsp_random, an Octave 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
- two_body_ode, an Octave 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, an Octave code which demonstrates how nonnegative integers can be stored as unsigned binary vectors (UBVEC), and arithmetic can be performed on them.
- ubvec_test
- ulam_spiral, an Octave 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, an Octave code which considers permutations containing a single cycle, sometimes called cyclic permutations.
- unicycle_test
- uniform, an Octave code which implements a uniform random number generator (RNG) for a variety of arithmetic types.
- uniform_test
- unstable_ode, an Octave 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, an Octave code which determines the check digit for a Uniform product Code (UPC) or reports whether a given UPC is valid.
- upc_test
- urn_simulation, an Octave code which simulates the experiment of sampling K balls from an urn containing N balls of various colors.
- urn_simulation_test
- usa_box_plot, an Octave 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, an Octave 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, an Octave code which defines the adjacency matrix for US states, using a variety of matrix formats.
- usa_matrix_test
- van_der_corput, an Octave 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, an Octave code which implements the Bjork-Pereyra algorithm for accurate solution of linear systems involving the Vandermonde matrix.
- vandermonde_test
- vandermonde_approx_1d, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which sets up and solves the van der Pol system of ordinary differential equations (ODE).
- vanderpol_ode_test
- vanderpol_ode_period, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave code which demonstates the use of Verlet integration to simulate simple problems in dynamics, involving changes in position and velocity.
- verlet_simulation_test
- vin, an Octave code which computes the check digit for a Vehicle Identification Number (VIN), or verifies that a given VIN is legitimate.
- vin_test
- voronoi_display, an Octave code which computes and displays the Voronoi diagram of a set of points.
- voronoi_display_test
- voronoi_mountains, an Octave 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, an Octave 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, an Octave 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, an Octave code which calls the built-in voronoi() function, which computes the Voronoi diagram of a set of points.
- vpa_test, an Octave code which uses the Symbolic package to compute arbitrary precision quantities.
- walker_sample, an Octave code which efficiently samples a discrete probability vector using Walker sampling.
- walker_sample_test
- walsh_transform, an Octave code which implements the Walsh data transform.
- walsh_transform_test
- wathen_matrix, an Octave 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 arises when solving a problem using the finite element method (FEM).
- wathen_matrix_test
- wave_pde, an Octave 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, an Octave code which does some simple calculations with wavelet transforms;
- wavelet_test
- web_matrix, an Octave 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, an Octave 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, an Octave code which returns quadrature rules for approximating integrals over the interior of the unit wedge in 3D.
- wedge_felippa_rule_test
- wedge_grid, an Octave code which computes a grid of points over the interior of the unit wedge in 3D.
- wedge_grid_test
- wedge_integrals, an Octave 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, an Octave 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, an Octave 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, an Octave 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, an Octave 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
- will_you_be_alive, an Octave 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, an Octave code which produces sample matrices from the Wishart or Bartlett distributions, useful for sampling random covariance matrices.
- wishart_matrix_test
- wtime, an Octave code which returns a reading of the wall clock time in seconds.
- wtime_test
- xyz_display, an Octave code which displays a 3D plot from a file of point coordinates.
- xyz_display_test
- zero_brent, an Octave code which seeks a solution of a scalar nonlinear equation f(x)=0, by Richard Brent.
- zero_brent_test
- zero_chandrupatla, an Octave 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, an Octave 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, an Octave 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, an Octave code which seeks a root of a nonlinear equation using the Muller method, with complex arithmetic.
- zero_muller_test
- zero_rc, an Octave code which seeks a solution of a scalar nonlinear equation f(x)=0, using reverse communication (RC), by Richard Brent.
- zero_rc_test
- ziggurat, an Octave code which implements uniform, normal and exponential random number generators (RNG) using the ziggurat method, by Marsaglia and Tsang.
- ziggurat_test
- zombie_ode, an Octave 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, an Octave code which implements many procedures for finding the zero of a scalar nonlinear function.
- zoomin_test