MATLAB Source Codes
-
advection_pde,
a MATLAB code which
solves the advection partial differential equation (PDE)
dudt + c * dudx = 0 in one spatial dimension, with
a constant velocity c, and periodic boundary conditions, using the
FTCS method, forward time difference, centered space difference.
-
advection_pde_test
-
allen_cahn_pde,
a MATLAB code which
sets up and solves the Allen-Cahn reaction-diffusion
system of partial differential equations (PDE)
du/dt = nu * uxx - u * (u^2-1) / (2*xi)
in 1 space dimension and time.
-
allen_cahn_pde_test
-
allen_cahn_pde_etdrk4
a MATLAB code which
uses the exponential time differencing (ETD) RK4 method
to solve the Allen-Cahn system of stiff ordinary differential
equations (ODE), by Aly-Khan Kassam, Lloyd Trefethen.
-
allen_cahn_pde_etdrk4_test
-
allen_cahn_pde_euler
a MATLAB code which
uses the Euler method to solve the Allen-Cahn PDE as a
system of stiff ordinary differential equations (ODE),
by Aly-Khan Kassam, Lloyd Trefethen.
-
allen_cahn_pde_euler_test
-
alpert_rule,
a MATLAB code which
sets up an Alpert quadrature rule for functions which are
regular, log(x) singular, or 1/sqrt(x) singular.
-
alpert_rule_test
-
analemma,
a MATLAB code which
evaluates the equation of time, a formula for the difference between
the uniform 24 hour day and the actual position of the sun,
based on a C program by Brian Tung.
-
analemma_test
-
animation_test,
a MATLAB code which
demonstrates how to create an animation in the form of a GIF.
-
anishchenko_ode,
a MATLAB code which
sets up and solves the Anishchenko ordinary differential equation
(ODE), which has chaotic behavior and an attractor.
-
anishchenko_ode_test
-
annulus_distance,
a MATLAB code which
estimates the typical distance
between a pair of points randomly selected inside a circular
annulus.
-
annulus_distance_test
-
annulus_grid,
a MATLAB code which
computes a grid of points
over the interior of a circular annulus.
-
annulus_grid_test
-
annulus_integrals,
a MATLAB code which
returns the exact value of the integral of any monomial
over the interior of a circular annulus centered at the origin.
-
annulus_integrals_test
-
annulus_monte_carlo,
a MATLAB code which
uses the Monte Carlo method to estimate the integral of a function
over the interior of a circular annulus in 2D.
-
annulus_monte_carlo_test
-
annulus_rule,
a MATLAB code which
computes a quadrature rule for estimating integrals of a function
over the interior of a circular annulus in 2D.
-
annulus_rule_test
-
aperiodic_tile,
a MATLAB code which
constructs several steps in the aperiodic tiling of the plane,
using the monotile T(1,1), displaying the result graphically,
by Henning Voss.
-
aperiodic_tile_test
-
approx_bernstein,
a MATLAB code which
interactively approximates a function f(x) in the interval [a,b]
by constructing a Bernstein polynomial.
-
approx_bernstein_test
-
approx_chebyshev,
a MATLAB code which
interactively approximates a function f(x) in the interval [a,b]
by constructing a Chebyshev polynomial interpolant that is often
a good estimate of the minmax polynomial.
-
approx_chebyshev_test
-
approx_leastsquares,
a MATLAB code which
interactively approximates a function f(x) in the interval [a,b]
by constructing an m-degree polynomial which minimizes the square
root of the sum of the squares of the error with n sample data points.
-
approx_leastsquares_test
-
arclength,
a MATLAB code which
estimates the arclength of curves of the form (x,f(x)) or
(x(t),y(t)).
-
arclength_test
-
area_under_curve,
a MATLAB code which
displays the area under a curve, that is, the points (x,y)
between the X axis and the curve Y=F(X).
-
area_under_curve_test
-
arenstorf_ode,
a MATLAB code which
sets up and solves an ordinary differential equation (ODE) which
defines a stable periodic orbit of a spacecraft around the Earth
and the Moon.
-
arenstorf_ode_test
-
args,
a function which
shows how to count and report command line arguments;
-
args_test
-
arneodo_ode,
a MATLAB code which
sets up and solves the Arneodo ordinary differential equation
(ODE), which has chaotic behavior and an attractor.
-
arneodo_ode_test
-
arpack_test,
a MATLAB code which
calls arpack(), which
computes eigenvalues and eigenvectors of large
sparse matrices, accessible via the built-in eigs() command;
-
artery_pde,
a MATLAB code which
solves a partial differential equation (PDE)
that models the displacement of arterial walls under pressure.
-
artery_pde_test
-
asa_geometry_2011,
a MATLAB code which
was used during labs, demonstrations,
and lectures associated with the Geometry Algorithms portion of
the class Algorithms for Science Applications II, as taught
at the Scientific Computing Department, Florida State University,
Spring Semester 2011.
-
asa_2011_geometry_test
-
asa_graphs_2011,
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_images_2011,
a MATLAB code which
was used during labs, demonstrations,
and lectures associated with the Image Algorithms portion of
the class Algorithms for Science Applications II, as taught
at the Scientific Computing Department, Florida State University,
Spring Semester 2011.
-
asa005,
a MATLAB code which
evaluates the Cumulative Density Function (CDF) of the noncentral T
Probability Density Function (PDF), by BE Cooper.
This is a version of Applied Statistics Algorithm 5;
-
asa005_test
-
asa006,
a MATLAB code which
computes the Cholesky factorization of a symmetric positive
definite (SPD) matrix, by Michael Healy.
This is a version of Applied Statistics Algorithm 6;
-
asa006_test
-
asa007,
a MATLAB code which
computes the inverse of a symmetric positive definite (SPD) matrix,
by Michael Healy.
This is a version of Applied Statistics Algorithm 7.
-
asa007_test
-
asa032,
a MATLAB code which
evaluates the incomplete Gamma function,
by G Bhattacharjee.
This is a version of Applied Statistics Algorithm 32.
-
asa032_test
-
asa047,
a MATLAB code which
minimizes a scalar function of several variables
using the Nelder-Mead algorithm,
by R ONeill.
This is a version of Applied Statistics Algorithm 47.
-
asa047_test
-
asa053,
a MATLAB code which
produces sample matrices from the Wishart distribution,
by William Smith and Ronald Hocking.
This is a version of Applied Statistics Algorithm 53.
-
asa053_test
-
asa058,
a MATLAB code which
implements the K-means data clustering algorithm,
by David Sparks.
This is a version of Applied Statistics Algorithm 58.
-
asa058_test
-
asa063,
a MATLAB code which
evaluates the incomplete Beta function,
by KL Majumder and G Bhattacharjee.
This is a version of Applied Statistics Algorithm 63.
-
asa063_test
-
asa066,
a MATLAB code which
evaluates the Cumulative Density Function (CDF) of the normal
probability distribution, by David Hill.
This is a version of Applied Statistics Algorithm 66.
-
asa066_test
-
asa076,
a MATLAB code which
evaluates the Owen T function, needed to compute the
Cumulative Density Function (CDF) of the
noncentral T distribution,
by Young and Minder.
This is a version of Applied Statistics Algorithm 76.
-
asa076_test
-
asa082,
a MATLAB code which
computes the determinant of an orthogonal matrix;
this is a version of Applied Statistics Algorithm 82,
by J C Gower.
-
asa082_test
-
asa091,
a MATLAB code which
evaluates the percentage points of the Chi-Squared distribution,
by Best and Roberts.
This is a version of Applied Statistics Algorithm 91.
-
asa091_test
-
asa103,
a MATLAB code which
evaluates the digamma or psi function,
by Jose Bernardo.
This is a version of Applied Statistics Algorithm 103.
-
asa103_test
-
asa109,
a MATLAB code which
inverts the incomplete Beta function,
by Cran, Martin and Thomas.
This is a version of Applied Statistics Algorithm 109.
-
asa109_test
-
asa111,
a MATLAB code which
evaluates the percentage points of the normal distribution,
by Beasley and Springer.
This is a version of Applied Statistics Algorithm 111.
-
asa111_test
-
asa113,
a MATLAB code which
implements a clustering algorithm using transfers and swaps,
by Banfield and Bassill.
This is a version of Applied Statistics Algorithm 113.
-
asa113_test
-
asa121,
a MATLAB code which
evaluates the trigamma function,
by BE Schneider.
This is a version of Applied Statistics Algorithm 121.
-
asa121_test
-
asa136,
a MATLAB code which
implements a clustering algorithm,
by Hartigan and Wong.
This is a version of Applied Statistics Algorithm 136.
-
asa136_test
-
asa144,
a MATLAB code which
randomly generates an RxC contingency table,
by James Boyett.
This is a version of Applied Statistics Algorithm 144.
-
asa144_test
-
asa147,
a MATLAB code which
evaluates the incomplete Gamma function,
by Chi Leung Lau.
This is a version of Applied Statistics Algorithm 147.
-
asa147_test
-
asa152,
a MATLAB code which
evaluates the Probability Density Function (PDF)
and Cumulative Density Function
(CDF) associated with the hypergeometric distribution,
by Richard Lund;
this is a version of Applied Statistics Algorithm 152.
-
asa152_test
-
asa159,
a MATLAB code which
randomly generates an RxC contingency table,
by Michael Patefield;
This is a version of Applied Statistics Algorithm 159.
-
asa159_test
-
asa172,
a MATLAB code which
generates all M-dimensional indices in a given range,
simulating the behavior of an arbitrary number of nested loops,
by OFlaherty and MacKenzie.
this is a version of Applied Statistics Algorithm 172;
-
asa172_test
-
asa183,
a MATLAB code which
implements a random number generator (RNG),
by Wichman and Hill.
This is a version of Applied Statistics Algorithm 183.
-
asa183_test
-
asa226,
a MATLAB code which
evaluates the Cumulative Density Function (CDF)
of the noncentral Beta distribution,
by Russell Lenth.
This is a version of Applied Statistics Algorithm 226.
-
asa226_test
-
asa239,
a MATLAB code which
evaluates the incomplete Gamma function,
by Shea.
This is a version of Applied Statistics Algorithm 239.
-
asa239_test
-
asa241,
a MATLAB code which
evaluates the percentage points of the normal distribution,
by Michael Wichura.
This is a version of Applied Statistics Algorithm 241.
-
asa241_test
-
asa243,
a MATLAB code which
evaluates the Cumulative Density Function (CDF)
of the noncentral T distribution,
by Russell Lenth;
this is a version of Applied Statistics Algorithm 243.
-
asa243_test
-
asa245,
a MATLAB code which
evaluates the logarithm of the Gamma function,
by Allan Mcleod;
this is a version of Applied Statistics Algorithm 245.
-
asa245_test
-
asa266,
a MATLAB code which
evaluates various properties of
the Dirichlet Probability Density Function (PDF);
This is a version of Applied Statistics Algorithm 266.
-
asa266_test
-
asa299,
a MATLAB code which
computes the lattice points in an M-dimensional simplex,
by Chasalow and Brand;
this is a version of Applied Statistics Algorithm 299;
-
asa299_test
-
asa310,
a MATLAB code which
computes the Cumulative Density Function (CDF)
of the noncentral Beta distribution, by Chattamvelli and Shanmugam;
this is a version of Applied Statistics Algorithm 310.
-
asa310_test
-
asa314,
a MATLAB code which
computes the inverse of a matrix whose elements are subject to
modulo arithmetic,
by Roger Payne.
This is a version of Applied Statistics Algorithm 314;
-
asa314_test
-
atbash,
a MATLAB code which
applies the Atbash substitution cipher to a string of text.
-
atbash_test
-
atkinson,
a MATLAB code which
contains examples from the text 'Elementary Numerical Analysis',
by Atkinson.
-
atkinson_test
-
autocatalytic_ode,
a MATLAB code which
sets up and solves the autocatalytic ordinary differential equation
(ODE), which has chaotic behavior and an attractor.
-
autocatalytic_ode_test
-
axon_ode,
a MATLAB code which
sets up and solves the ordinary differential equations (ODE) for the
Hodgkin-Huxley model of an axon.
-
axon_ode_test
-
backtrack_binary_rc,
a MATLAB code which
carries out a backtrack search for a set of binary decisions, using
reverse communication (RC).
-
backtrack_binary_rc_test
-
backward_euler,
a MATLAB code which
solves one or more ordinary differential equations (ODE)
using the (implicit) backward Euler method, using fsolve()
for the implicit equation.
-
backward_euler_test
-
backward_euler_fixed,
a MATLAB code which
solves one or more ordinary differential equations (ODE)
using the (implicit) backward Euler method, using a fixed
point iteration for the implicit equation.
-
backward_euler_fixed_test
-
ball_and_stick_display,
a MATLAB code which
demonstrates the creation of a 3D ball and stick image;
-
ball_and_stick_display_test
-
ball_distance,
a MATLAB code which
computes the expected value of the distance
between a pair of points randomly selected from the interior
of the unit ball in 3D.
-
ball_distance_test
-
ball_grid,
a MATLAB code which
computes a grid of points
over the interior of the unit ball in 3D.
-
ball_grid_test
-
ball_integrals,
a MATLAB code which
returns the exact value of the integral of any monomial
over the interior of the unit ball in 3D.
-
ball_integrals_test
-
ball_monte_carlo,
a MATLAB code which
applies a Monte Carlo method to estimate integrals of a function
over the interior of the unit ball in 3D;
-
ball_monte_carlo_test
-
ball_positive_distance,
a MATLAB code which
computes the expected value of the distance
between a pair of points randomly selected from the interior
of the unit positive ball in 3D.
-
ball_positive_distance_test
-
bank,
a MATLAB code which
computes the check digit associated with a US Bank Routing Number
check digit, or reports whether a 9-digit code is actually valid.
-
bank_test
-
barycentric_interp_1d,
a MATLAB code which
defines and evaluates the barycentric Lagrange polynomial p(x)
which interpolates a set of data, so that p(x(i)) = y(i).
The barycentric approach means that very high degree polynomials can
safely be used.
-
barycentric_interp_1d_test
-
bdf2,
a MATLAB code which
solves one or more ordinary differential equations (ODE)
using the (implicit) backward difference formula of order 2 (BDF2),
using fsolve() to solve the implicit equation.
-
bdf2_test
-
bellman_ford,
a MATLAB code which
implements the Bellman-Ford algorithm for finding the shortest
distance from a given node to all other nodes in a directed graph
whose edges have been assigned real-valued lengths.
-
bellman_ford_test
-
bernstein_approximation,
a MATLAB code which
looks at some simple cases of approximation of a function f(x)
by a Bernstein polynomial.
-
bernstein_approximation_test
-
bernstein_polynomial,
a MATLAB code which
evaluates the Bernstein polynomials;
-
bernstein_polynomial_test
-
besselj,
a MATLAB code which
evaluates Bessel J functions of noninteger order;
-
besselj_test
-
besselzero,
a MATLAB code which
computes the zeros of Bessel functions j or y,
by Greg van Winckel and Jason Nicholson.
-
besselzero_test
-
beta_nc,
a MATLAB code which
evaluates the cumulative density function (CDF) of
the noncentral Beta distribution;
-
beta_nc_test
-
bezier_surface,
a MATLAB code which
reads, writes, prints and manipulates
the data that defines a Bezier surface;
-
bezier_surface_test
-
bezier_surface_display,
a MATLAB code which
displays a Bezier surface;
-
bezier_surface_display_test
-
bicg,
a MATLAB code which
implements the biconjugate gradient method (BICG), which
estimates the solution of a large sparse nonsymmetric linear system.
-
bicg_test
-
biharmonic_cheby1d,
a MATLAB code which
uses Chebyshev methods to solve the biharmonic
equation over an interval, a fourth order two point boundary
value problem (BVP) in one spatial dimension.
-
biharmonic_cheby1d_test
-
biharmonic_exact,
a MATLAB code which
evaluates exact solutions w(x,y) to the biharmonic equation
del^2 w = 0 or wxxxx + 2 wxxyy + wyyyy = 0
-
biharmonic_exact_test
-
biharmonic_fd1d,
a MATLAB code which
applies the finite difference method to solve the biharmonic
equation over an interval, a fourth order two point boundary
value problem (BVP) in one spatial dimension.
-
biharmonic_fd1d_test
-
biharmonic_fd2d,
a MATLAB code which
deals with the biharmonic equation in two dimensions, whose
simplest form is uxxxx + 2uxxyy + uyyyy = f.
-
biharmonic_fd2d_test
-
biochemical_linear_ode,
a MATLAB code which
sets up and solves a linear biochemical ordinary differential
equation (ODE).
-
biochemical_linear_ode_test
-
biochemical_nonlinear_ode,
a MATLAB code which
sets up and solves a nonlinear biochemical ordinary differential
equation (ODE).
-
biochemical_nonlinear_ode_test
-
bioconvection_ode,
a MATLAB code which
approximates solutions to a system of
ordinary differential equations (ODE) which
model a bioconvection problem, and which are related to
the Lorenz system.
-
bioconvection_ode_test
-
bird_egg,
a MATLAB code which
evaluates some formulas for the shapes of bird eggs.
-
bird_egg_test
-
bisection,
a MATLAB code which
applies the bisection method to seek a root of f(x)
over a change-of-sign interval a <= x <= b.
-
bisection_test
-
bisection_integer,
a MATLAB code which
seeks an integer solution to the equation F(X)=0,
using bisection within a user-supplied change of sign
interval [a,b].
-
bisection_integer_test
-
bisection_rc,
a MATLAB code which
seeks a solution to the equation F(X)=0 using bisection
within a user-supplied change of sign interval [a,b].
The procedure is written using reverse communication (RC).
-
bisection_rc_test
-
black_scholes,
a MATLAB code which
implements some simple approaches to
the Black-Scholes option valuation theory,
by Desmond Higham.
-
black_scholes_test
-
blend,
a MATLAB code which
carries out 1D/2D/3D blending interpolation;
-
blend_test
-
blood_pressure_ode,
a MATLAB code which
sets up and solves an ordinary differential equation (ODE)
which models the variation in blood pressure in the human artery.
-
blood_pressure_ode_test
-
blowup_ode,
a MATLAB code which
sets up and solves an ordinary differential equation (ODE) y'=y^2.
whose solution "blows up" in finite time.
-
blowup_ode_test
-
boat,
a MATLAB code which
considers the boat tiling puzzle, a smaller version of the eternity
puzzle. The boat puzzle specifies a region R composed of 756
30-60-90 triangles, and a set of 21 "tiles", each consisting of 36
30-60-90 triangles, and seeks an arrangement of the tiles that
exactly covers the region.
-
boat_test
-
boat_cplex_test
a BASH code which
calls cplex(), to read the LP file defining the boat tiling problem,
solve the linear programming problem, and write the solution to
a file.
-
boat_gurobi_test
a BASH code which
calls gurobi(), to read the LP file defining the boat tiling
problem, solve the linear programming problem, and write the
solution to a file.
-
boomerang,
a MATLAB code which
considers the boomerang tiling puzzle, a smaller version of the
eternity puzzle. The puzzle specifies a region R composed of 2376
30-60-90 triangles, and a set of 66 "tiles", each consisting of 36
30-60-90 triangles, and seeks an arrangement of the tiles that
exactly covers the region.
-
boomerang_test
-
boomerang_cplex_test
a BASH code which
calls cplex(), to read the LP file defining the boomerang tiling
problem, solve the linear programming problem, and write the
solution to a file.
-
boundary_locus,
a MATLAB code which
uses the boundary locus method to display the region of
absolute stability for a solver of ordinary differential
equations (ODE).
-
boundary_locus_test
-
boundary_locus2,
a MATLAB code which
uses the boundary locus method to plot the boundary of the
absolute stability region for a solver of ordinary differential
equations (ODE), based on a procedure by Randall Leveque.
-
boundary_locus2_test
-
boundary_word_drafter,
a MATLAB code which
describes the outline of an object using a string of symbols that
represent the sequence of steps tracing out the boundary,
on a grid of drafters, or 30-60-90 triangles. The objects include
tiles for the eternity, serenity and trinity puzzles, and the
hat and turtle aperiodic monotiles.
-
boundary_word_drafter_test
-
boundary_word_equilateral,
a MATLAB code which
describes the outline of an object on a grid of equilateral
triangles, using a string of symbols that represent the
sequence of steps tracing out the boundary.
-
boundary_word_equilateral_test
-
boundary_word_hexagon,
a MATLAB code which
describes the outline of an object on a grid of hexagons,
using a string of symbols that represent the sequence of steps
tracing out the boundary.
-
boundary_word_hexagon_test
-
boundary_word_right,
a MATLAB code which
describes the outline of an object on a grid of isoceles right
triangles, using a string of symbols that represent the sequence
of steps tracing out the boundary.
-
boundary_word_right_test
-
boundary_word_square,
a MATLAB code which
describes the outline of an object on a grid of squares,
using a string of symbols that represent the sequence of steps
tracing out the boundary.
-
boundary_word_square_test
-
box_behnken,
a MATLAB code which
computes a Box-Behnken design,
that is, a set of arguments to sample the behavior
of a function of multiple parameters;
-
box_behnken_test
-
box_display,
a MATLAB code which
displays a box plot, over integer pairs of data, of a function
defined by two formulas.
-
box_display_test
-
box_distance,
a MATLAB code which
estimates the distribution and expected value of the distance between
two points picked uniformly at random within a 3D box.
-
box_distance_test
-
box_flow,
a MATLAB code which
solves the Navier Stokes equations (NSE) in a 2D rectangular region,
replacing the continuity equation with a pressure Poisson equation
(PPE), by John Cornthwaite.
-
box_flow_test
-
box_games,
a MATLAB code which
assists in the display of game boards (checkers, cellular
automatons, Conway's game of life);
-
box_games_test
-
box_plot,
a MATLAB code which
displays a box plot of data that consists of pairs of integers;
-
box_plot_test
-
brc_data,
a MATLAB code which
creates a file of randomly generated temperature readings to be
associated with weather stations at 413 world cities. A file like
this, with 1 billion records, is used for the billion
record challenge (BRC).
-
brc_data_test
-
brc_naive,
a MATLAB code which
reads a file of randomly generated temperature readings, associated
with weather stations at 413 world cities, and computes the minimum,
mean, and maximum temperature for each weather station. It also reports
the total execution time. Processing such a data file with one billion
records is the substance of the billion record challenge (BRC).
-
brc_naive_test
-
brownian_motion_simulation,
a MATLAB code which
simulates Brownian motion in an M dimensional region.
-
brownian_motion_simulation_test
-
broyden,
a MATLAB code which
implements the Broyden iterative method for nonlinear equations,
by Tim Kelley.
-
broyden_test
-
brusselator_ode,
a MATLAB code which
sets up and solves the Brusselator ordinary differential
equation (ODE) system.
-
brusselator_ode_test
-
buckling_spring,
a MATLAB code which
plots solutions of the buckling spring equations.
-
buckling_spring_test
-
burgers_pde_etdrk4,
a MATLAB code which
uses the exponential time differencing (ETD) RK4 method
to solve the Burgers PDE as a system of stiff ordinary differential
equations (ODE), by Aly-Khan Kassam, Lloyd Trefethen.
-
burgers_pde_etdrk4_test
-
burgers_exact,
a MATLAB code which
evaluates exact solutions
of the time-dependent 1D viscous Burgers equation.
-
burgers_exact_test
-
burgers_steady_viscous,
a MATLAB code which
solves the steady (time-independent) viscous Burgers equation
using the finite difference method (FDM) applied to the
conservative form of the equation, using the Newton method to
solve the resulting nonlinear system.
-
burgers_steady_viscous_test
-
burgers_time_inviscid,
a MATLAB code which
solves the time-dependent inviscid Burgers equation
using the finite difference method (FDM), and one of six solution
methods.
-
burgers_time_inviscid_test
-
burgers_time_viscous,
a MATLAB code which
solves the time-dependent viscous Burgers equation
using the finite difference method (FDM) applied to the
conservative form of the equation.
-
burgers_time_viscous_test
-
bvec,
a MATLAB code which
demonstrates how signed integers can be stored as
binary vectors, and arithmetic can be performed on them.
-
bvec_test
-
bvp_fd,
a MATLAB code which
demonstrates the use of the finite difference method (FDM)
to solve a boundary value problem (BVP).
-
bvp_fd_test
-
bvp_shooting_test,
a MATLAB code which
demonstrates the use of the shooting method
to solve a boundary value problem (BVP).
-
bvp4c_test,
a MATLAB code which
calls bvp4c(), which
solves boundary value problems (BVP) in one spatial dimension.
-
bwlabel_test,
a MATLAB code which
calls bwlabel(), which
is given a binary matrix, and organizes the 1 values into
labeled clusters, using 4-way or 8-way connectivity.
-
c8lib,
a MATLAB code which
implements certain elementary functions for
complex 64 bit ("C8") variables;
-
c8lib_test
-
caesar,
a MATLAB code which
applies a Caesar Shift Cipher to a string of text.
-
caesar_test
-
calendar_nyt,
a MATLAB code which
shows the correspondence between dates and the New York Times
volume and issue number;
-
calendar_nyt_test
-
calpak,
a MATLAB code which
computes various simple calendrical quantities. It can work with
various calendars including Egyptian, English, French Revolutionary,
Gregorian, Julian, and Julian Ephemeris Date. It can convert a
date from one calendar to another. It can return the day of the week
for a given date. It can convert from day-number/year to day/month/year
format. It can calculate the time difference between two dates.
-
calpak_test
-
candy_count,
a MATLAB code which
counts the types of candy in a rectangular container, which might be
a vector, matrix, or 3D box. The candy is assumed to have C possible
types, and to have been entered into the container in a cycle that
begins with type 1. While the vector case is easy, it is already
difficult to come up with a general formula for the MxN matrix case.
-
candy_count_test
-
capacitor_2d_test,
a MATLAB code which
plots data from a model of a 2D capacitor, computed by FreeFem++()
and transferred using the ffmatlib() library.
-
capacitor_3d_test,
a MATLAB code which
plots data from a model of a 3D capacitor, computed by FreeFem++()
and transferred using the ffmatlib() library.
-
casino_simulation,
a MATLAB code which
simulates a casino game that gives you 20% of your bet for heads,
and only takes 17% for tails. How much will you end up winning?
-
casino_simulation_test
-
cauchy_method,
a MATLAB code which
solves one or more ordinary differential equations (ODE)
using the Cauchy method.
-
cauchy_method_test
-
cauchy_principal_value,
a MATLAB code which
uses Gauss-Legendre quadrature to estimate the Cauchy Principal
Value (CPV) of certain singular integrals.
-
cauchy_principal_value_test
-
caustic,
a MATLAB code which
generates an image of a caustic, by drawing n equally spaced points in
a circle, and then connecting specific pairs of points using a spacing
parameter m.
-
caustic_test
-
cavity_flow_display,
a MATLAB code which
displays a single velocity field solution for the driven cavity;
-
cavity_flow_display_test
-
cavity_flow_movie,
a MATLAB code which
animates the velocity solutions for the driven cavity;
-
cavity_flow_movie_test
-
cc_display,
a MATLAB code which
displays the points used in a 2D Clenshaw-Curtis quadrature rule;
-
cc_display_test
-
cc_project,
a MATLAB code which
computes generalized Clenshaw-Curtis quadrature rules
for semi-infinite and infinite intervals, by John Boyd.
-
cc_project_test
-
ccl_test,
a MATLAB code which
estimates the Lebesgue constants for sets of points in [-1,+1]
computed in several ways. The program is probably of limited
interest except as an example of an application of the
lebesgue_constant() function.
-
ccn_rule,
a MATLAB code which
defines a Clenshaw Curtis Nested (CCN) quadrature rule.
-
ccn_rule_test
-
ccs_io
a MATLAB code which
reads and writes sparse linear systems
stored in the Compressed Column Storage (CCS) format.
-
ccs_io_test
-
ccs_to_st
a MATLAB code which
converts a sparse matrix from Compressed Column Storage (CCS) to
sparse triplet (ST) format.
-
ccs_to_st_test
-
ccvt_reflect,
a MATLAB code which
calculates a Constrained Centroidal Voronoi Tessellation (CCVT)
for points constrained to lie in a box, with some points pushed
towards the boundary;
-
ccvt_reflect_test
-
cell,
a MATLAB code which
defines a cell array, a generalization of an array which
compactly stores and retrieves vector or matrix data of
varying size, such as the rows of a triangular matrix.
-
cell_test
-
cellular_automaton,
a MATLAB code which
prints or plots the evolution of Cellular Automaton rule #30.
-
cellular_automaton_test
-
cg,
a MATLAB code which
implements a simple version of the conjugate gradient (CG) method
for solving a system of linear equations of the form A*x=b,
suitable for situations in which the matrix A is
symmetric positive definite (SPD).
-
cg_test
-
cg_lab_triangles,
a MATLAB code which
was a computer lab
assignment on computational geometry and triangles;
-
cg_lab_triangles_test
-
cg_ne,
a MATLAB code which
implements the conjugate gradient method (CG) for the normal
equations, where the matrix A is not symmetric positive
definite (SPD). In this case, it is attempted to set up and solve
the normal equations A'*A*x=A'*b.
-
cg_ne_test
-
cg_rc,
a MATLAB code which
implements the conjugate gradient (CG) method for solving
a symmetric positive definite (SPD) sparse linear system A*x=b,
using reverse communication (RC).
-
cg_rc_test
-
cg_squared,
a MATLAB code which
implements the conjugate gradient squared (CGS) method for solving
a nonsymmetric sparse linear system A*x=b.
-
cg_squared_test
-
chain_letter_tree,
a MATLAB code which
analyzes a similarity matrix for 11 versions of a single chain
letter and produces a dendrogram or tree diagram that suggests
the degrees of relatedness and the evolutionary history of the
letters.
-
change_diophantine,
a MATLAB code which
sets up a Diophantine equation to solve the change making problem,
which counts the number of ways a given sum can be formed
using coins of various denominations.
-
change_diophantine_test
-
change_dynamic,
a MATLAB code which
uses dynamic programming to solve the change making problem,
in which a given sum is to be formed using coins of various
denominations.
-
change_dynamic_test
-
change_greedy,
a MATLAB code which
uses the greedy method to seek a solution to the change making problem,
which tries to match a given amount by selecting coins of various
denominations.
-
change_greedy_test
-
change_polynomial,
a MATLAB code which
uses a polynomial multiplication algorithm to count the ways of making
various sums using a given number of coins.
-
change_polynomial_test
-
chebyshev,
a MATLAB code which
computes the Chebyshev interpolant/approximant to a given function
over an interval.
-
chebyshev_test
-
chebyshev_interp_1d,
a MATLAB code which
determines the combination of Chebyshev polynomials which
interpolates a set of data, so that p(x(i)) = y(i).
-
chebyshev_interp_1d_test
-
chebyshev_matrix,
a MATLAB code which
defines the Chebyshev differentiation matrix,
by Lloyd Trefethen.
-
chebyshev_matrix_test
-
chebyshev_polynomial,
a MATLAB code which
considers the Chebyshev polynomials T(i,x), U(i,x), V(i,x)
and W(i,x).
-
chebyshev_polynomial_test
-
chebyshev_series,
a MATLAB code which
evaluates a Chebyshev series approximating a function f(x),
while efficiently computing one, two, three or four derivatives of the
series, by Manfred Zimmer.
-
chebyshev_series_test
-
chebyshev1_exactness,
a MATLAB code which
tests the polynomial exactness of
Gauss-Chebyshev type 1 quadrature rules.
-
chebyshev1_exactness_test
-
chebyshev1_rule,
a MATLAB code which
computes and writes out a Gauss-Chebyshev type 1 quadrature rule
of given order.
-
chebyshev1_rule_test
-
chebyshev2_exactness,
a MATLAB code which
tests the polynomial exactness of Gauss-Chebyshev type 2
quadrature rules.
-
chebyshev2_exactness_test
-
chebyshev2_rule,
a MATLAB code which
computes and writes out a Gauss-Chebyshev type 2 quadrature rule
of given order.
-
chebyshev2_rule_test
-
chen_ode,
a MATLAB code which
sets up and solves the Chen system
of ordinary differential equations (ODE).
-
chen_ode_test
-
cheney_kincaid,
a MATLAB code which
contains examples from the text 'Numerical Mathematics and Computing',
by Cheney and Kincaid.
-
cheney_kincaid_test
-
chinese_remainder_theorem,
a MATLAB code which
demonstrates the Chinese remainder theorem, for reconstructing a
number based on its remainders against a set of bases.
-
chinese_remainder_theorem_test
-
chirikov_iteration,
a MATLAB code which
applies the Chirikov map repeatedly to a given (x,y)
initial condition.
-
chirikov_iteration_test
-
chladni_figures,
a MATLAB code which
creates Chladni figures of the eigenmodes of a thin vibrating
plate, by Martin Gander and Felix Kwok.
-
chladni_figures_test
-
chrominoes,
a MATLAB code which
searches for tilings of a polygonal region using polyominoes,
in which a coloring scheme is used to reduce the problem size
and quickly eliminate certain arrangements.
-
chrominoes_test
-
chrpak,
a MATLAB code which
manipulates characters and strings;
-
chrpak_test
-
chuckaluck_simulation,
a MATLAB code which
simulates the Chuck-a-Luck gambling game.
-
chuckaluck_simulation_test
-
circle_arc_grid,
a MATLAB code which
computes grid points along a circular arc.
-
circle_arc_grid_test
-
circle_circles_packing,
a MATLAB code which
tries to randomly pack as many non-overlapping circles of equal size
into a larger circle, with a typical final coverage density of
about 0.547. This is an
example of random sequential adsorption (RSA).
-
circle_circles_packing_test
-
circle_distance,
a MATLAB code which
computes the expected value of the distance
between a pair of points randomly selected on the circumference
of the unit circle in 2D.
-
circle_distance_test
-
circle_grid_display
a MATLAB code which
reads a matrix of integers, and draws a corresponding
grid of circles filled with color.
-
circle_grid_display_test
-
circle_integrals,
a MATLAB code which
returns the exact value of the integral of any monomial
over the circumference of the unit circle in 2D.
-
circle_integrals_test
-
circle_map,
a MATLAB code which
illustrates how a matrix maps points on the unit circle
to an ellipse.
-
circle_map_test
-
circle_monte_carlo,
a MATLAB code which
applies a Monte Carlo method to estimate the integral of a function
along the circumference of the unit circle in 2D;
-
circle_monte_carlo_test
-
circle_positive_distance,
a MATLAB code which
estimates the mean and variance of the distance between
a random pair of points on the circumference
of the unit positive circle in 2D.
-
circle_positive_distance_test
-
circle_rule,
a MATLAB code which
computes quadrature rules for the unit circle in 2D,
to approximate integrals of f(x,y) over the
circumference of the circle of radius 1 and center (0,0).
-
circle_rule_test
-
circle_segment,
a MATLAB code which
carries out computations associated with a circle segment, including
height, angle, area, centroid, sampling, and quadrature.
-
circle_segment_test
-
circles,
a MATLAB code which
draws one or more circles,
while controlling the center locations, radii, colors, edge
colors, and transparency, by Chad Greene.
-
circles_test
-
cities,
a MATLAB code which
works with city-to-city distance matrices;
-
cities_test
-
clausen,
a MATLAB code which
evaluates a Chebyshev interpolant to the Clausen function Cl2(x).
-
clausen_test
-
clenshaw_curtis_rule,
a MATLAB code which
implements a Clenshaw Curtis quadrature rule;
-
clenshaw_curtis_rule_test
-
clock_solitaire_simulation,
a MATLAB code which
simulates the game of clock solitaire. The deck is dealt into 13
piles of 4 cards each. Repeatedly, the top card a pile is removed,
and its rank indicates the next pile to consider. Game continues
until an empty pile is reached. The game is won if all piles are
empty. The quantity of interest is the probability of winning.
-
clock_solitaire_simulation_test
-
closest_pair_brute,
a MATLAB code which
uses brute force to solve a 2D version of the closest pair problem.
-
closest_pair_brute_test
-
closest_pair_divcon,
a MATLAB code which
uses a divide and conquer approach to solve a 2D version of
the closest pair problem.
-
closest_pair_divcon_test
-
closest_point_brute,
a MATLAB code which
uses brute force to find the nearest of a set of N points in D
dimensions to a given test point. This is sometimes called a
nearest neighbor calculation.
-
closest_point_brute_test
-
cnoise,
a MATLAB code which
generates samples of noise obeying a 1/f^alpha power law,
by Miroslav Stoyanov.
-
cnoise_test
-
cobweb_plot,
a MATLAB code which
displays a cobweb plot illustrating the process of function
iteration.
-
cobweb_plot_test
-
coin_simulation,
a MATLAB code which
looks at ways of simulating or visualizing the results of
many tosses of a fair or biased coin.
-
coin_simulation_test
-
collatz,
a MATLAB code which
computes and analyzes the Collatz
sequence, also known as the hailstone sequence or 3n+1 sequence;
-
collatz_test
-
collatz_parfor,
a MATLAB code using the parfor() statement
for parallel execution,
to find the longest Collatz sequence in the range 1 through N.
-
collatz_parfor_test
-
collatz_polynomial,
a MATLAB code which
implements the Collatz polynomial iteration, a polynomial analog of
the numerical iteration that is also known as the 3n+1 conjecture or
the hailstone sequence.
-
collatz_polynomial_test
-
collatz_recursive,
a MATLAB code which
demonstrates recursive programming by considering
the simple Collatz 3n+1 problem.
-
collatz_recursive_test
-
collocation,
a MATLAB code which
demonstrates the use of collocation
to produce a function g(x) that satisfies the same constraints
as a function f(x), but only at a discrete set of points.
-
collocation_test
-
colored_noise,
a MATLAB code which
generates samples of noise obeying a 1/f^alpha power law.
-
colored_noise_test
-
combo,
a MATLAB code which
ranks, unranks, enumerates, lists and
randomly selects balanced sequences, cycles, graphs, Gray codes,
subsets, partitions, permutations, restricted growth functions,
Pruefer codes and trees.
-
combo_test
-
companion_matrix,
a MATLAB code which
computes the companion matrix for a polynomial.
The polynomial may be represented in the standard monomial basis,
or as a sum of Chebyshev, Gegenbauer, Hermite, Laguerre, or Lagrange
basis polynomials. All the roots of the polynomial can be determined as
the eigenvalues of the corresponding companion matrix.
-
companion_matrix_test
-
compass_search,
a MATLAB code which
seeks the minimizer of a scalar function of several variables
using compass search,
a direct search algorithm that does not use derivatives.
-
compass_search_test
-
complex_numbers_test,
a MATLAB code which
demonstrates some of the features of using complex
numbers.
-
components,
a MATLAB code which
organizes contiguous cells into labeled clusters, for a
1D, 2D, or 3D array. This code has uses in image analysis
and percolation simulation.
-
components_test
-
condition,
a MATLAB code which
implements methods of computing or estimating
the condition number of a matrix.
-
condition_test
-
conservation_ode,
a MATLAB code which
monitors the conservation of a quantity
that should be constant, during the solution of an
ordinary differential equation (ODE).
-
conservation_ode_test
-
conte_deboor,
a MATLAB code which
contains examples from the text 'Elementary Numerical Analysis'
by Conte and deBoor.
-
conte_deboor_test
-
continuation,
a MATLAB code which
implements the continuation method for a simple 2D problem,
involving finding a point on the unit circle, and then
finding a sequence of nearby points that trace out the full
curve, using only the information available in the implicit
definition of the curve from the function f(x,y)=x^2+y^2-1.
-
continuation_test
-
continued_fraction
a MATLAB code which
implements some simple algorithms for dealing with simple and
generalized continued fractions.
-
continued_fraction_test
-
contour_gradient,
a MATLAB code which
displays contours and gradient vectors for a function f(x,y).
-
contour_gradient_test
-
contour_gradient_3d,
a MATLAB code which
displays contours and gradient vectors for a function f(x,y)
in a 3D display.
-
contour_gradient_3d_test
-
contour_sequence4,
a MATLAB code which
creates images suitable for animation
from one XY file and a sequence of u(x,y) data files;
-
contour_sequence4_test
-
control_bio,
a MATLAB code which
optimizes a given cost functional of a biological model
using optimal control,
based on work by Suzanne Lenhart and John Workman.
-
control_bio_test
-
control_bio_homework,
a MATLAB code which
handles several homework problems for a biological control class.
-
convective_rolls_test,
a MATLAB code which
plots data describing the convective rolling behavior of a fluid
being heated from below, as computed by FreeFem++()
and transferred using the ffmatlib() library.
-
convective_rolls_movie_test,
a MATLAB code which
animates data describing the convective rolling behavior of a fluid
being heated from below, as computed by FreeFem++()
and transferred using the ffmatlib() library.
-
convergence,
a MATLAB code which
is given a sequence of approximation errors and estimates the order
of convergence, assuming the results correspond to a
a sequence of decreasing mesh sizes h, or increasing mesh counts n.
-
convergence_test
-
convhull_test,
a MATLAB code which
demonstrates the use of the built-in function convhull()
for the computation of the convex hull of a set of 2D points.
-
coordinate_search,
a MATLAB code which
seeks the minimizer of a scalar function of several variables,
by Jeff Borggaard.
-
coordinate_search_test
-
cordic,
a MATLAB code which
computes a few special functions using the CORDIC algorithm.
-
cordic_test
-
correlation,
a MATLAB code which
contains statistical correlation functions.
-
correlation_test
-
cosine_transform,
a MATLAB code which
demonstrates some simple properties of the discrete cosine
transform (DCT).
-
cosine_transform_test
-
counterfeit_detection,
a MATLAB code which
considers problems in which one or more counterfeit coins
are to be identified by the fact that they do not have the
standard weight.
-
counterfeit_detection_test
-
cplex_solution_read,
a MATLAB code which
extracts solution data from a cplex() result file.
-
cplex_solution_read_test
-
cpr,
a MATLAB code which
implements the Chebyshev Proxy Rootfinder (CPR) to locate all the
real zeros of a smooth real function f(x) within an interval [a,b],
by John Boyd.
-
cpr_test
-
craps_simulation,
a MATLAB code which
simulates the gambling game of craps, in which a player rolls two dice.
On the first roll, the player wins immediately if a 7 or 11 is rolled,
and loses immediately if a 2, 3 or 12 is rolled. Otherwise, the sum
of the dice on this first roll is called the point. The player now
continues to roll the dice, winning if the point is rolled again,
and losing if a 7 is rolled.
-
craps_simulation_test
-
crs_io,
a MATLAB code which
reads and writes sparse linear systems
stored in the Compressed Row Storage (CRS) format.
-
crs_io_test
-
cube_arbq_rule,
a MATLAB code which
returns quadrature rules,
with exactness up to total degree 15,
over the interior of the symmetric cube in 3D,
by Hong Xiao and Zydrunas Gimbutas.
-
cube_arbq_rule_test
-
cube_distance,
a MATLAB code which
computes the expected value of the distance
between a pair of points randomly selected in the interior
of the unit cube in 3D.
-
cube_distance_test
-
cube_exactness,
a MATLAB code which
investigates the polynomial exactness of quadrature rules
over the interior of a cube in 3D.
-
cube_exactness_test
-
cube_felippa_rule,
a MATLAB code which
returns a Felippa quadrature rule for approximating integrals
over the interior of a cube in 3D.
-
cube_felippa_rule_test
-
cube_grid,
a MATLAB code which
computes a grid of points
over the interior of a cube in 3D.
-
cube_grid_test
-
cube_integrals,
a MATLAB code which
returns the exact value of the integral of any monomial
over the interior of the unit cube in 3D.
-
cube_integrals_test
-
cube_monte_carlo,
a MATLAB code which
applies a Monte Carlo method to estimate the integral of a function
over the interior of the unit cube in 3D.
-
cube_monte_carlo_test
-
cube_surface_distance,
a MATLAB code which
estimates the expected value of the distance
between a pair of points randomly selected
on the surface of the unit cube.
-
cube_surface_distance_test
-
cuda_loop,
a MATLAB code which
shows how, in a CUDA program running on a Graphics Processing
Unit (GPU), the choice of block and thread factors determines
the allocation of tasks to processors.
-
cuda_loop_test
-
cvt,
a MATLAB code which
computes an N-point Centroidal Voronoi Tessellation (CVT)
in M dimensions;
-
cvt_test
-
cvt_1_movie,
a MATLAB code which
creates a movie of the evolution of a
Centroidal Voronoi Tessellation (CVT) in the unit square;
-
cvt_1_movie_test
-
cvt_2_movie,
a MATLAB code which
animates the generation of a Centroidal Voronoi Tessellation (CVT)
in the unit square, which includes a random "rebirth"
at every iteration.
-
cvt_2_movie_test
-
cvt_3_movie,
a MATLAB code which
animates the generation of a Centroidal Voronoi Tessellation
(CVT) for the "holey pie" region.
-
cvt_3_movie_test
-
cvt_4_movie,
a MATLAB code which
creates a Centroidal Voronoi Tessellation (CVT) movie in
the unit square,
with a density function that drives points to the corners;
-
cvt_4_movie_test
-
cvt_1d_lloyd,
a MATLAB code which
computes an N-point Centroidal Voronoi Tessellation (CVT)
within the interval [0,1], under a uniform density,
using the Lloyd method to compute the Voronoi regions exactly.
-
cvt_1d_lloyd_test
-
cvt_1d_lumping,
a MATLAB code which
allows the user to carry out a lumped version of the Lloyd iterative
algorithm for a centroidal Voronoi Tessellation (CVT() in the
interval [-1,+1], and is applied to investigate a relationship
between a CVT and the Chebyshev Zero nodes.
-
cvt_1d_lumping_test
-
cvt_1d_nonuniform,
a MATLAB code which
computes an N-point Centroidal Voronoi Tessellation (CVT)
in 1 dimension, under a nonuniform density,
and plots the evolution of the locations of the generators
during the iteration;
-
cvt_1d_nonuniform_test
-
cvt_1d_sampling,
a MATLAB code which
computes an N-point Centroidal Voronoi Tessellation (CVT)
within the interval [0,1], under a uniform density,
using sampling to estimate the Voronoi regions.
-
cvt_1d_sampling_test
-
cvt_2d_lumping,
a MATLAB code which
computes an N-point Centroidal Voronoi Tessellation (CVT)
within the unit square [-1,1]^2, under a Chebyshev density,
using weighted sampling (lumping) to estimate the Voronoi regions.
-
cvt_2d_lumping_test
-
cvt_2d_sampling,
a MATLAB code which
computes an N-point Centroidal Voronoi Tessellation (CVT)
within the unit square [0,1]x[0,1], under a uniform density,
using sampling to estimate the Voronoi regions.
-
cvt_2d_sampling_test
-
cvt_3d_lumping,
a MATLAB code which
computes an N-point Centroidal Voronoi Tessellation (CVT)
within the unit cube [-1,1]^3, under a Chebyshev density,
using weighted sampling (lumping) to estimate the Voronoi regions.
-
cvt_3d_lumping_test
-
cvt_3d_sampling,
a MATLAB code which
computes an N-point Centroidal Voronoi Tessellation (CVT)
within the unit cube [0,1]^3, under a uniform density,
using sampling to estimate the Voronoi regions.
-
cvt_3d_sampling_test
-
cvt_basic,
a MATLAB code which
calculates a Centroidal Voronoi Tessellation (CVT) in a square
with uniform density. It is intended as an introduction to the
cvt_square_uniform() code.
-
cvt_basic_test
-
cvt_box,
a MATLAB code which
calculates a Centroidal Voronoi Tessellation (CVT)
constrained to a box region, with points projected to the boundary;
-
cvt_box_test
-
cvt_circle_nonuniform,
a MATLAB code which
demonstrates the computation of a centroidal Voronoi Tessellation
(CVT) over a circular region, using a nonuniform density.
-
cvt_circle_nonuniform_test
-
cvt_circle_uniform,
a MATLAB code which
computes a centroidal Voronoi Tessellation (CVT)
over a circular region, using a uniform density.
-
cvt_circle_uniform_test
-
cvt_corn,
a MATLAB code which
studies a 2D model of the growth of a corn kernel, by treating
the surface and interior biological cells as points to be
organized by a Centroidal Voronoi Tessellation (CVT)
with a nonuniform density; during a sequence of growth steps,
new biological cells are randomly added to the surface and
interior.
-
cvt_corn_test
-
cvt_corn_movie,
a MATLAB code which
makes a movie in which the growth of a corn kernel is simulated
using a Centroidal Voronoi Tessellation (CVT).
-
cvt_corn_movie_test
-
cvt_ellipse_uniform,
a MATLAB code which
iteratively calculates a Centroidal Voronoi Tessellation (CVT)
over an ellipse, with a uniform density.
-
cvt_ellipse_uniform_test
-
cvt_metric,
a MATLAB code which
computes a Centroidal Voronoi Tessellation (CVT) under a
spatially varying metric;
-
cvt_metric_test
-
cvt_square_nonuniform,
a MATLAB code which
iteratively calculates a Centroidal Voronoi Tessellation (CVT)
over a square, with a nonuniform density.
-
cvt_square_nonuniform_test
-
cvt_square_pdf_discrete,
a MATLAB code which
iteratively calculates a Centroidal Voronoi Tessellation (CVT)
over a square, with a density determined from a discrete PDF.
-
cvt_square_pdf_discrete_test
-
cvt_square_uniform,
a MATLAB code which
iteratively calculates a Centroidal Voronoi Tessellation (CVT)
over a square, with a uniform density.
-
cvt_square_uniform_test
-
cvt_triangle_uniform,
a MATLAB code which
iteratively calculates a Centroidal Voronoi Tessellation (CVT)
over a triangle, with a uniform density.
-
cvt_triangle_uniform_test
-
cvtm_1d,
a MATLAB code which
estimates a mirror-periodic centroidal Voronoi Tessellation (CVTM)
in the periodic interval [0,1], using a version of the Lloyd
iteration.
-
cvtm_1d_test
-
cvtp,
a MATLAB code which
creates a periodic Centroidal Voronoi Tessellation (CVTP).
-
cvtp_test
-
cvtp_1d,
a MATLAB code which
estimates a periodic centroidal Voronoi Tessellation (CVTP) in the
periodic interval [0,1], using a version of the Lloyd iteration.
-
cvtp_1d_test
-
cycle_brent,
a MATLAB code which
carries out an iterated function evaluation,
and seeks to determine the nearest element of a cycle,
and the cycle length, using the Brent method.
-
cycle_brent_test
-
cycle_floyd,
a MATLAB code which
carries out an iterated function evaluation,
and seeks to determine the nearest element of a cycle,
and the cycle length, using the Floyd method.
-
cycle_floyd_test
-
cyclic_reduction,
a MATLAB code which
solves a tridiagonal linear system using cyclic reduction;
-
cyclic_reduction_test
-
delaunay_test,
a MATLAB code which
calls the built-in delaunay() function, which
computes the Delaunay triangulation of a set of points.
-
delsq,
a MATLAB code which
is given a grid G, and returns a corresponding sparse matrix D that
defines the Laplacian operator on G. MATLAB includes a built-in
version of this function.
-
delsq_test
-
dfield9,
a MATLAB code which
allows a user to interactively specify the right hand side of an
ordinary differential equation (ODE). The program then displays
the corresponding direction field. If the user clicks on any point
in the image as an initial condition, the program displays the
corresponding solution curve. The original version of this code
was by John Polking.
-
dg1d_advection,
a MATLAB code which
uses the Discontinuous Galerkin Method (DG) to approximate a
solution of the advection equation.
The original version of the code was written by Jan Hesthaven
and Tim Warburton.
-
dg1d_advection_test
-
dg1d_burgers,
a MATLAB code which
uses the Discontinuous Galerkin Method (DG) to approximate a
solution of the unsteady 1D Burgers equation.
The original version of the code was written by Jan Hesthaven
and Tim Warburton.
-
dg1d_burgers_test
-
dg1d_heat,
a MATLAB code which
uses the Discontinuous Galerkin Method (DG) to approximate a
solution of the unsteady 1D heat equation.
The original version of the code was written by Jan Hesthaven
and Tim Warburton.
-
dg1d_heat_test
-
dg1d_maxwell,
a MATLAB code which
uses the Discontinuous Galerkin Method (DG) to approximate a
solution of the Maxwell equations.
The original version of the code was written by Jan Hesthaven
and Tim Warburton.
-
dg1d_maxwell_test
-
dg1d_poisson,
a MATLAB code which
applies the discontinuous Galerkin method (DG) to a 1D version of
the Poisson equation;
the original version of the code was written by Beatrice Riviere.
-
dg1d_poisson_test
-
diaphony,
a MATLAB code which
reads a file of N points in M dimensions and computes its diaphony,
a measure of point dispersion.
-
diaphony_test
-
dice_simulation,
a MATLAB code which
simulates N tosses of M dice, making a histogram of the resulting sums.
-
dice_simulation_test
-
dictionary_code,
a MATLAB code which
demonstates how a text file can be compressed and decompressed
using a dictionary code.
-
dictionary_code_test
-
diff_test,
a MATLAB code which
calls diff(), which
computes differences in a vector of data,
which can be scaled to estimate derivatives of equally spaced data.
-
diff_center,
a MATLAB code which
interactively uses centered differences to estimate the derivative
of a function f(x), using a stepsize h.
-
diff_center_test
-
diff_forward,
a MATLAB code which
interactively uses forward differences to estimate the derivative
of a function f(x), using a stepsize h.
-
diff_forward_test
-
diff2_center,
a MATLAB code which
interactively uses centered differences to estimate the second
derivative of a function f(x), using a stepsize h.
-
diff2_center_test
-
differ,
a MATLAB code which
is given function values at equally spaced locations, and the
order of a derivative, and uses the finite difference method (FDM)
to compute a linear combination of these function values which
approximated that derivative.
-
differ_test
-
diffusion_pde,
a MATLAB code which
solves the diffusion partial differential equation (PDE)
dudt = mu * d2udx2
in one spatial dimension and time, with
a constant diffusion coefficient mu, and periodic or zero Neumann
boundary conditions,
using the forward time centered space (FTCS) solver or ode45().
-
diffusion_pde_test
-
digital_dice,
a MATLAB code which
carries out the probability simulations
described in "Digital Dice", by Paul Nahin;
-
digital_dice_test
-
digraph_adj,
a MATLAB code which
carries out operations on abstract digraphs, a kind of graph with
directed edges, described by an adjacency matrix.
-
digraph_adj_test
-
dijkstra,
a MATLAB code which
implements a simple version of the Dijkstra minimum distance
algorithm for graphs.
-
dijkstra_test
-
diophantine,
a MATLAB code which
finds one solution of a Diophantine equation in any number of
variables.
-
diophantine_test
-
diophantine_nd,
a MATLAB code which
is given a Diophantine equation in N variables, and
returns all nonnegative solutions, or all strictly positive
solutions.
-
diophantine_nd_doc
-
diophantine_nd_test
-
discrete_pdf_sample_2d,
a MATLAB code which
demonstrates how to construct a Probability Density Function (PDF)
from a table of sample data, and then to use that PDF to create
new samples.
-
discrete_pdf_sample_2d_test
-
disk_distance,
a MATLAB code which
computes the expected value of the distance
between a pair of points randomly selected from the interior of the
unit disk in 2D.
-
disk_distance_test
-
disk_grid,
a MATLAB code which
computes grid points within the interior of
a disk of user specified radius and center in 2D,
using gnuplot() to create an image of the grid.
-
disk_grid_test
-
disk_integrals,
a MATLAB code which
returns the exact value of the integral of any monomial
over the interior of a disk of radius R centered at the origin.
-
disk_integrals_test
-
disk_monte_carlo,
a MATLAB code which
applies a Monte Carlo method to estimate integrals of a function
over the interior of a disk of radius R centered at the origin.
-
disk_monte_carlo_test
-
disk_positive_distance,
a MATLAB code which
computes the expected value of the distance
between a pair of points randomly selected from the interior of the
unit positive disk in 2D.
-
disk_positive_distance_test
-
disk_rule,
a MATLAB code which
computes quadrature rules for the general disk in 2D.
-
disk_rule_test
-
disk01_integrals,
a MATLAB code which
returns the exact value of the integral of any monomial
over the interior of the unit disk in 2D.
-
disk01_integrals_test
-
disk01_integrands,
a MATLAB code which
defines several test integrals over the unit disk, making it
possible to check the accuracy of quadrature rules.
-
disk01_integrands_test
-
disk01_monte_carlo,
a MATLAB code which
applies a Monte Carlo method to estimate integrals of a function
over the interior of the unit disk in 2D;
-
disk01_monte_carlo_test
-
disk01_rule,
a MATLAB code which
computes quadrature rules for the unit disk in 2D.
-
disk01_rule_test
-
disk01_positive_monte_carlo,
a MATLAB code which
applies a Monte Carlo method to estimate the integral of a function
over the interior of the unit positive disk in 2D;
-
disk01_positive_monte_carlo_test
-
disk01_positive_rule,
a MATLAB code which
computes quadrature rules for the unit positive disk in 2D.
-
disk01_positive_rule_test
-
dist_plot,
a MATLAB code which
makes contour plots of the distance function,
as defined and used in Persson and Strang's
distmesh() code;
-
dist_plot_test
-
distance_to_position,
a MATLAB code which
estimates the positions of cities which minimizes the discrepancy
with a city-to-city distance table.
-
distance_to_position_test
-
distance_to_position_sphere,
a MATLAB code which
estimates the positions of cities on a sphere (such as the earth)
based on a city-to-city distance table.
-
distance_to_position_sphere_test
-
distmesh,
a MATLAB code which
carries out a method of mesh generation;
by Per-Olof Persson and Gilbert Strang.
-
distmesh_test
-
distmesh_3d,
a MATLAB code which
carries out a method of mesh generation in 3D,
by Per-Olof Persson and Gilbert Strang.
-
distmesh_3d_test
-
divdif,
a MATLAB code which
creates, prints and manipulates divided difference polynomials from
a table of values (x,f(x)). The code can compute the coefficients of
the Newton and power sum forms of the interpolating polynomial. It
can compute the derivative or antiderivate polynomial. It can compute
the form of the Lagrange basis polynomials. It can compute the
points and weights for Newton Cotes quadrature rules. It can compute
the weights for a Lagrange interpolation scheme.
-
divdif_test
-
doomsday,
a MATLAB code which
is given the year, month and day of a date, and uses
John Conway's doomsday algorithm
to determine the corresponding day of the week.
-
doomsday_test
-
dosage_ode,
a MATLAB code which
sets up and solves a system of ordinary differential equations
(ODE) to simulate the blood levels of a medicinal drug that should
stay between medicinal and toxic limits.
-
dosage_ode_test
-
dot_l2,
a MATLAB code which
interactively estimates the L2 dot product of two functions:
dot_l2(f(x),g(x))_= integral ( a <= x <= b ) f(x) g(x) dx
-
dot_l2_test
-
double_c_data,
a MATLAB code which
generates, plots and writes out 2D data that forms two interlocking
"C" shapes.
-
double_c_data_test
-
double_well_ode,
a MATLAB code which
sets up and solves an ordinary differential equation (ODE)
which models the motion of a particle in a double well potential.
-
double_well_ode_test
-
dream,
a MATLAB code which
implements the DREAM algorithm for accelerating
Markov Chain Monte Carlo (MCMC) convergence using differential
evolution,
using five user functions to define the problem, by Guannan Zhang.
-
dream_test
-
duel_simulation,
a MATLAB code which
simulates N repetitions of a duel between two players, each of
whom has a known firing accuracy.
-
duel_simulation_test
-
dueling_idiots,
a MATLAB code which
carries out the probability simulations
described in "Dueling Idiots", by Paul Nahin;
-
dueling_idiots_test
-
duffing_ode,
a MATLAB code which
sets up and solves a second-order ordinary differential equation (ODE)
whose solution can exhibit chaotic behavior.
-
duffing_ode_test
-
e_spigot,
a MATLAB code which
produces any number of digits of the decimal expansion of e.
-
e_spigot_test
-
earth_sphere,
a MATLAB code which
displays a 3D image of the earth, including oceans, continents,
and topography,
by Clay Thompson and Will Campbell.
-
earth_sphere_test
-
edge,
a MATLAB code which
defines some test functions in 1D, 2D and 3D
for the detection of edges or discontinuities.
-
edge_test
-
eigenfaces,
a MATLAB code which
applies principal component analysis (PCA) to a set of images.
-
eigenfaces_test
-
eigs_test,
a MATLAB code which
calls eigs(), which
is a built-in system function which computes the eigenvalues and
eigenvectors of a matrix.
-
elfun,
a MATLAB code which
evaluates elliptic integrals, include Bulirsch's integrals cel(),
cel1(), cel2(), cel3(), Carlson integrals rc(), rd(), rf(), rg(), rj(),
and Jacobi functions cn(), dn(), sn(),
by Milan Batista.
-
elfun_test
-
ellipse,
a MATLAB code which
carries out geometric calculations for ellipses and ellipsoids,
including area, distance to a point, eccentricity, perimeter,
points along the perimeter, random sampling, conversion between
standard and quadratic forms.
-
ellipse_test
-
ellipse_distance,
a MATLAB code which
computes the expected value of the distance
between a pair of points randomly selected on the circumference
of the ellipse (x/a)^2+(y/b)^2=1 in 2D.
-
ellipse_distance_test
-
ellipse_grid,
a MATLAB code which
computes a grid of points
over the interior of an ellipse in 2D.
-
ellipse_grid_test
-
ellipse_monte_carlo,
a MATLAB code which
uses the Monte Carlo method to estimate the value of integrals
over the interior of an ellipse in 2D.
-
ellipse_monte_carlo_test
-
ellipsoid,
a MATLAB code which
carries out geometric calculations for ellipsoids, including
area, random sampling, and volume.
-
ellipsoid_test
-
ellipsoid_grid,
a MATLAB code which
computes a grid of points
over the interior of an ellipsoid in 3D.
-
ellipsoid_grid_test
-
ellipsoid_monte_carlo,
a MATLAB code which
uses the Monte Carlo method to estimate the value of integrals
over the interior of an ellipsoid in M dimensions.
-
ellipsoid_monte_carlo_test
-
elliptic_integral,
a MATLAB code which
evaluates complete elliptic integrals of first, second and third
kind, using the Carlson elliptic integral functions.
-
elliptic_integral_test
-
epicycloid,
a MATLAB code which
computes, plots and tabulates an epicycloid curve.
-
epicycloid_test
-
equidistribution,
investigates equidistribution properties relating to density functions
and point sets.
-
equidistribution_test
-
eros,
a MATLAB code which
implements elementary row operations (EROs) for the
interactive solution of a system of linear equations.
-
eros_test
-
errors,
a MATLAB code which
illustrates the failure of numerical algorithms;
-
errors_test
-
eternity,
a MATLAB code which
considers the eternity puzzle, an irregular dodecagon that is to be
tiled by 209 pieces, each formed by 12 contiguous 30-60-90 triangles,
known as polydrafters.
-
eternity_test
-
eternity_hexity,
a MATLAB code which
evaluates and manipulates a six-fold parity quantity associated with
grids and tiles used in the Eternity puzzle.
-
eternity_hexity_test
-
eternity_tile,
a MATLAB code which
considers the individual tiles of the eternity puzzle,
209 distinct pieces, each formed by 36
contiguous 30-60-90 triangles, known as polydrafters,
as well as tiles for the serenity and trinity puzzles,
and the hat and turtle aperiodic monotile.
-
eternity_tile_test
-
euclid,
a MATLAB code which
investigates various versions of Euclid's algorithm for computing
the greatest common divisor (GCD) of two integers.
-
euclid_test
-
euler,
a MATLAB code which
solves one or more ordinary differential equations (ODE)
using the forward Euler method.
-
euler_test
-
exactness,
a MATLAB code which
investigates the exactness of quadrature rules that estimate the
integral of a function with a density, such as 1, exp(-x) or
exp(-x^2), over an interval such as [-1,+1], [0,+oo) or (-oo,+oo).
-
exactness_test
-
exm,
a MATLAB code which
contains scripts and data discussed in the electronic textbook
"Experiments with Matlab", by Cleve Moler,
including easter, Fast Fourier Transforms, Fibonacci numbers,
the fractal fern, the game of Life, magic matrices,
the Mandelbrot set, Morse code,
Music, Ordinary Differential Equations, the page rank algorithm,
planetary orbits, predator prey equations,
the shallow water equations, Sudoku puzzles.
-
exm_test
-
exp_ode,
a MATLAB code which
sets up and solves an ordinary differential equation (ODE)
whose solution is an exponential function.
-
exp_ode_test
-
faces_average,
a MATLAB code which
averages several images of the same face;
-
faces_average_test
-
fair_dice_simulation,
a MATLAB code which
simulates N tosses of 2 dice, making a histogram of the resulting sums.
-
fair_dice_simulation_test
-
faure,
a MATLAB code which
computes the Faure M dimensional Quasi Mont Carlo (QMC) sequence;
-
faure_test
-
fd_predator_prey,
a MATLAB code which
solves a time-dependent predator prey system using the
finite difference method (FDM).
-
fd_predator_prey_test
-
fd_to_tec,
a MATLAB code which
converts finite difference method (FDM) models into tecplot() ASCII files.
-
fd_to_tec_test
-
fd1d_advection_diffusion_steady,
a MATLAB code which
applies the finite difference method (FDM) to solve the
steady advection diffusion equation v*ux-k*uxx=0 in
one spatial dimension, with constant velocity v and diffusivity k.
-
fd1d_advection_diffusion_steady_test
-
fd1d_advection_ftcs,
a MATLAB code which
applies the finite difference method (FDM) to solve the time-dependent
advection equation ut = - c * ux in one spatial dimension, with
a constant velocity, using the forward time centered space (FTCS)
difference scheme.
-
fd1d_advection_ftcs_test
-
fd1d_advection_lax,
a MATLAB code which
applies the finite difference method (FDM) to solve the time-dependent
advection equation ut = - c * ux in one spatial dimension, with
a constant velocity, using the Lax method to approximate the
time derivative.
-
fd1d_advection_lax_test
-
fd1d_advection_lax_wendroff,
a MATLAB code which
applies the finite difference method (FDM) to solve the time-dependent
advection equation ut = - c * ux in one spatial dimension, with
a constant velocity, using the Lax-Wendroff method to approximate the
time derivative.
-
fd1d_advection_lax_wendroff_test
-
fd1d_burgers_lax,
a MATLAB code which
applies the finite difference method (FDM) and the Lax Wendroff method
to solve the non-viscous time-dependent Burgers equation
in one spatial dimension.
-
fd1d_burgers_lax_test
-
fd1d_burgers_leap,
a MATLAB code which
applies the finite difference method (FDM) and the leapfrog approach
to solve the non-viscous time-dependent Burgers equation
in one spatial dimension.
-
fd1d_burgers_leap_test
-
fd1d_bvp,
a MATLAB code which
applies the finite difference method (FDM)
to a two point boundary value problem (BVP) in one spatial dimension.
-
fd1d_bvp_test
-
fd1d_display,
a MATLAB code which
reads a pair of files defining a 1D
finite difference method (FDM) of a function, and plots the data.
-
fd1d_display_test
-
fd1d_heat_explicit,
a MATLAB code which
implements a finite difference method (FDM), explicit in time,
to solve the time dependent 1D heat equation;
-
fd1d_heat_explicit_test
-
fd1d_heat_implicit,
a MATLAB code which
implements a finite difference method (FDM), implicit in time,
to solve the time dependent 1D heat equation;
-
fd1d_heat_implicit_test
-
fd1d_heat_steady,
a MATLAB code which
implements a finite difference method (FDM) for the steady
(time independent) 1D heat equation;
-
fd1d_heat_steady_test
-
fd1d_poisson,
a MATLAB code which
solves a Poisson equation over a user-specified discretized interval,
with given functions f(x) (right hand side) and g(x) (Dirichlet
boundary conditions), using the Finite Difference Method (FDM).
-
fd1d_poisson_test
-
fd1d_predator_prey,
a MATLAB code which
implements the finite difference method (FDM) for a predator-prey
system with time and 1D spatial dependence, by Marcus Garvie.
-
fd1d_predator_prey_test
-
fd1d_predator_prey_plot,
a MATLAB code which
plots solutions of the predator prey differential equations,
by Marcus Garvie.
-
fd1d_predator_prey_plot_test
-
fd1d_wave,
a MATLAB code which
applies the finite difference method (FDM) to solve the time-dependent
wave equation utt = c * uxx in one spatial dimension.
-
fd1d_wave_test
-
fd2d_convergence_test,
a MATLAB code which
calls fd2d_poisson(), which
repeatedly solves a Poisson equation on a sequence of finer meshes,
so that the relationship between mesh size H and error norm E can
be explored.
-
fd2d_heat_steady,
a MATLAB code which
implements a finite difference method (FDM) for the steady
(time independent) 2D heat equation;
-
fd2d_heat_steady_test
-
fd2d_poisson,
a MATLAB code which
solves a Poisson equation over a user-specified discretized rectangle,
with given functions f(x,y) (right hand side) and g(x,y) (Dirichlet
boundary conditions), using the Finite Difference Method (FDM).
-
fd2d_poisson_test
-
fd2d_predator_prey,
a MATLAB code which
implements a finite difference method (FDM) for a
time and 2D space dependent predator-prey system,
by Marcus Garvie.
-
fd2d_predator_prey_test
-
fd3d_poisson,
a MATLAB code which
solves a Poisson equation over a user-specified discretized 3d block,
with given functions f(x,y,z) (right hand side) and g(x,y,z)
(Dirichlet boundary conditions), using the Finite Difference
Method (FDM).
-
fd3d_poisson_test
-
fem_basis,
a MATLAB code which
defines and evaluates finite element method (FEM) basis functions
for any degree in an M dimensional simplex (1D interval, 2D triangle,
3D tetrahedron, and higher dimensional generalizations.)
-
fem_basis_test
-
fem_basis_q4_display,
a MATLAB code which
displays any single finite element method (FEM) basis function
associated with an arbitrary linear quadrilateral Q4 mesh;
-
fem_basis_q4_display_test
-
fem_basis_t3_display,
a MATLAB code which
displays a basis function for the finite element method (FEM)
associated with an arbitrary 3-node triangle T3 mesh;
-
fem_basis_t3_display_test
-
fem_basis_t4_display,
a MATLAB code which
displays a basis function for the finite element method (FEM)
associated with an arbitrary 4-node triangle T4 mesh;
-
fem_basis_t4_display_test
-
fem_basis_t6_display,
a MATLAB code which
displays a basis function for the finite element method (FEM)
associated with an arbitrary 6-node triangle T6 mesh;
-
fem_basis_t6_display_test
-
fem_io,
a MATLAB code which
reads or writes FEM files,
which describe the nodes, elements, and function values
associated with a finite element method (FEM) model;
-
fem_io_test
-
fem_neumann,
a MATLAB code which
sets up a time-dependent reaction-diffusion equation in 1D,
with Neumann boundary conditions,
discretized using the finite element method (FEM).
-
fem_neumann_test
-
fem_to_gmsh,
a MATLAB code which
reads a pair of FEM files defining node coordinates and elements,
of a 1D, 2D or 3D mesh, namely
a file of node coordinates and a file of elements defined by
node indices, and creates a gmsh() MESH file.
-
fem_to_gmsh_test
-
fem_to_medit,
a MATLAB code which
reads a set of FEM files defining the node coordinates, boundary
nodes, and elements of a finite element mesh, and rewrites the
data as a medit() MESH file.
-
fem_to_medit_test
-
fem_to_tec,
a MATLAB code which
converts FEM models into tecplot() ASCII files.
-
fem_to_tec_test
-
fem_to_triangle,
a MATLAB code which
reads FEM files defining a 2D mesh of triangles, namely
a file of node coordinates and a file of elements defined by
node indices, and creates a corresponding pair of node
and element files for use by Jonathan Shewchuk's triangle() program.
-
fem_to_triangle_test
-
fem_to_xml,
a MATLAB code which
reads a pair of FEM files defining node coordinates and elements,
of a 1D, 2D or 3D mesh, namely
a file of node coordinates and a file of elements defined by
node indices, and creates a corresponding XML file for input
to dolfin() or fenics().
-
fem_to_xml_test
-
fem1d,
a MATLAB code which
applies the finite element method (FEM),
using piecewise linear basis functions, to a linear
two point boundary value problem (BVP) in 1D;
-
fem1d_test
-
fem1d_adaptive,
a MATLAB code which
uses an adaptive mesh when
applying the finite element method (FEM),
with piecewise linear basis functions, to a linear
two point boundary value problem (BVP) in 1D;
-
fem1d_adaptive_test
-
fem1d_approximate,
a MATLAB code which
uses a given finite element method (FEM) mesh and
piecewise linear (PWL) basis functions
to approximate a set of data points,
while controlling the variation in the derivative.
-
fem1d_approximate_test
-
fem1d_bvp_linear,
a MATLAB code which
applies the finite element method (FEM), with piecewise linear (PWL)
elements, to a two point boundary value problem (BVP) in one
spatial dimension, and compares the computed and exact solutions
with the L2 and seminorm errors.
-
fem1d_bvp_linear_test
-
fem1d_bvp_quadratic,
a MATLAB code which
applies the finite element method (FEM),
with piecewise quadratic (PWQ) elements,
to a two point boundary value problem (BVP) in one spatial dimension,
and compares the computed and exact solutions
with the L2 and seminorm errors.
-
fem1d_bvp_quadratic_test
-
fem1d_display,
a MATLAB code which
reads three files defining a 1D arbitrary degree basis function
associated with the finite element method (FEM),
and displays a plot.
-
fem1d_display_test
-
fem1d_function_10_display,
a MATLAB code which
reads three files defining a 1D piecewise linear finite element
method (FEM) function and displays a plot.
-
fem1d_display_function_10_test
-
fem1d_heat_explicit,
a MATLAB code which
uses the finite element method (FEM) and explicit time stepping
to solve the time dependent heat equation in 1D.
-
fem1d_heat_explicit_test
-
fem1d_heat_implicit,
a MATLAB code which
uses the finite element method (FEM) and implicit time stepping
to solve the time dependent heat equation in 1D.
-
fem1d_heat_implicit_test
-
fem1d_heat_steady,
a MATLAB code which
uses the finite element method (FEM) to solve the steady
(time independent) 1D heat equation;
-
fem1d_heat_steady_test
-
fem1d_lagrange,
a MATLAB code which
sets up the matrices and vectors associated with the finite element
method (FEM) solution of a boundary value problem (BVP) -u''+u=f(x),
using Lagrange basis polynomials.
-
fem1d_lagrange_test
-
fem1d_nonlinear,
a MATLAB code which
applies the finite element method (FEM),
with piecewise linear (PWL) basis functions, to a nonlinear
two point boundary value problem (BVP) in 1D;
-
fem1d_nonlinear_test
-
fem1d_pack,
a MATLAB code which
contains utilities for 1D finite element method (FEM) calculations.
-
fem1d_pack_test
-
fem1d_pmethod,
a MATLAB code which
applies the p-method version of
the finite element method (FEM) to a linear
two point boundary value problem (BVP) in 1D;
-
fem1d_pmethod_test
-
fem1d_project,
a MATLAB code which
projects data into a finite element space, including the least squares
approximation of data, or the projection of a finite element solution
from one mesh to another.
-
fem1d_project_test
-
fem1d_sample,
a MATLAB code which
samples a scalar or vector finite element function of one variable,
defined by FEM files,
returning interpolated values at the sample points.
-
fem1d_sample_test
-
fem1d_spectral_numeric,
a MATLAB code which
applies the spectral finite element method (FEM) to solve the problem
u'' = - pi^2 sin(x) over [-1,+1] with zero boundary conditions,
using as basis elements the functions x^n*(x-1)*(x+1),
and carrying out the integration numerically,
using the quad() function,
by Miro Stoyanov.
-
fem1d_spectral_numeric_test
-
fem2d_bvp_linear,
a MATLAB code which
applies the finite element method (FEM),
with piecewise linear (PWL) elements,
to a 2D boundary value problem (BVP) in a rectangle,
and compares the computed and exact solutions
with the L2 and seminorm errors.
-
fem2d_bvp_linear_test
-
fem2d_bvp_quadratic,
a MATLAB code which
applies the finite element method (FEM),
with piecewise quadratic (PWQ) elements,
to a 2D boundary value problem (BVP) in a rectangle,
and compares the computed and exact solutions
with the L2 and seminorm errors.
-
fem2d_bvp_quadratic_test
-
fem2d_bvp_serene,
a MATLAB code which
applies the finite element method (FEM), with serendipity elements,
to a 2D boundary value problem (BVP) in a rectangle,
and compares the computed and exact solutions
with the L2 and seminorm errors.
-
fem2d_bvp_serene_test
-
fem2d_heat,
a MATLAB code which
applies the finite element method (FEM) to the time dependent
heat equation on an arbitrary triangulated region in 2D;
-
fem2d_heat_test
-
fem2d_heat_rectangle,
a MATLAB code which
applies the finite element method (FEM) for the time-dependent
heat equation on a triangulated rectangle in 2D;
-
fem2d_heat_rectangle_test
-
fem2d_heat_sparse,
a MATLAB code which
applies the finite element method (FEM) to the heat equation
on an arbitrary triangulated region in 2D, using a sparse
storage matrix format;
-
fem2d_heat_sparse_test
-
fem2d_mesh_display,
a MATLAB code which
reads a FEM model of a 2D mesh of elements of any uniform order
and displays a plot of the elements and nodes,
with optional numbering.
-
fem2d_mesh_display_test
-
fem2d_pack,
a MATLAB code which
performs simple 2D finite element method (FEM) computations;
-
fem2d_pack_test
-
fem2d_poisson_rectangle,
a MATLAB code which
solves the 2D Poisson equation on a rectangle,
using the finite element method (FEM),
and piecewise quadratic triangular elements.
-
fem2d_poisson_rectangle_test
-
fem2d_poisson_rectangle_linear,
a MATLAB code which
solves the 2D Poisson equation on a rectangle,
using the finite element method (FEM),
and piecewise linear triangular elements.
-
fem2d_poisson_rectangle_linear_test
-
fem2d_predator_prey_fast,
a MATLAB code which
implements a finite element method (FEM) for a
time and 2D space dependent predator-prey system,
on an arbitrary triangulated region,
with a variety of possible boundary conditions,
incorporating some optimizations,
by Marcus Garvie.
-
fem2d_predator_prey_fast_test
-
fem2d_project,
a MATLAB code which
projects a function f(x,y), given as data,
into a given finite element method (FEM) space
of piecewise linear triangular elements.
-
fem2d_project_test
-
fem2d_project_function,
a MATLAB code which
projects a function f(x,y), given as a formula,
into a given finite element method (FEM) space
of piecewise linear triangular elements.
-
fem2d_project_function_test
-
fem2d_sample,
a MATLAB code which
samples a finite element method (FEM) function, defined by
three text files describing the nodes, triangles, and coefficients,
at arbitrary points.
-
fem2d_sample_test
-
fem2d_scalar_display,
a MATLAB code which
reads information about nodes, elements and nodal values for a
2D finite element method (FEM) and creates a surface plot of U(X,Y).
-
fem2d_scalar_display_test
-
fem2d_scalar_display_brief,
a MATLAB code which
reads information about nodes, elements and nodal values for a
2D finite element method (FEM) and creates a surface plot of U(X,Y),
in 5 lines of code.
-
fem2d_scalar_display_brief_test
-
fem2d_scalar_display_gpl,
a MATLAB code which
reads information about nodes, elements and nodal values for a
2D finite element method (FEM) and creates a GPL file describing
a surface plot of U(X,Y), to be displayed by gnuplot().
-
fem2d_scalar_display_gpl_test,
-
fem3d_pack,
a MATLAB code which
contains utilities for 3D finite element method (FEM) calculations.
-
fem3d_pack_test
-
fem3d_project,
a MATLAB code which
projects a function f(x,y,z), given as a data,
into a given space of piecewise linear tetrahedral elements
for use in the finite element method (FEM).
-
fem3d_project_test
-
fem3d_sample,
a MATLAB code library which
evaluates a function defined on a 3D tetrahedral mesh as part of
the finite element method (FEM).
-
fem3d_sample_test
-
fern,
a MATLAB code which
computes and displays the Barnsley fractal fern.
-
fern_test
-
feynman_kac_1d,
a MATLAB code which
demonstrates the use of the Feynman-Kac algorithm
to solve the Poisson equation in a 1D interval by averaging
stochastic paths to the boundary.
-
feynman_kac_1d_test
-
feynman_kac_2d,
a MATLAB code which
demonstrates the use of the Feynman-Kac algorithm
to solve the Poisson equation in a 2D ellipse by averaging
stochastic paths to the boundary.
-
feynman_kac_2d_test
-
feynman_kac_3d,
a MATLAB code which
demonstrates the use of the Feynman-Kac algorithm
to solve the Poisson equation in a 3D ellipsoid by averaging
stochastic paths to the boundary.
-
feynman_kac_3d_test
-
ffmatlib,
a MATLAB code which
allows the user to plot finite element method (FEM) results
that have been computed by FreeFem++().
-
fft_serial,
a MATLAB code which
computes a Fast Fourier Transform (FFT), and is intended as
a starting point for implementing a parallel version.
-
fft_serial_test
-
fibonacci_spiral,
a MATLAB code which
displays points on a Fibonacci spiral, suggesting the arrangement
of seeds in a sunflower, for instance.
-
fibonacci_spiral_test
-
file_increment,
a MATLAB code which
increments every entry of an integer array which is stored in a file.
-
file_increment_test
-
file_name_sequence,
a MATLAB code which
demonstrates ways to generate a sequence of filenames, which can
be useful when generating a sequence of still snapshots
to be animated later.
-
file_name_sequence_test
-
files_multiple_test,
a MATLAB code which
demonstrates how a program can open multiple output files at one time,
and write data to any one specific file it chooses.
-
filon_rule,
a MATLAB code which
approximates integrals which include an
oscillatory factor of sin(k*x) or cos(k*x).
-
filon_rule_test
-
filum,
a MATLAB code which
handles files and filenames;
-
filum_test
-
fire_simulation,
a MATLAB code which
simulates a forest fire over a rectangular array of trees,
starting at a single random location.
-
fire_simulation_test
-
fisher_exact,
a MATLAB code which
returns an exact solution of the Kolmogorov Petrovsky Piskonov Fisher
partial differential equation (PDE) ut=uxx+u*(1-u).
-
fisher_exact_test
-
fisher_pde_ftcs,
a MATLAB code which
estimates a solution of the Kolmogorov Petrovsky Piskonov Fisher
partial differential equation (PDE) ut=uxx+u*(1-u), using the
forward time centered space (FTCS) method, with an oscillating
Dirichlet condition on the left, and a zero Neumann condition
on the right. An animation of the solution is created.
-
fisher_pde_ftcs_test
-
fitzhugh_nagumo_ode,
a MATLAB code which
sets up and solves the Fitzhugh-Nagumo system of
ordinary differential equations (ODE).
-
fitzhugh_nagumo_ode_test
-
flame_exact,
a MATLAB code which
returns the exact solution of an ordinary differential equation (ODE)
which models the growth of a ball of flame in a combustion process.
The exact solution is defined in terms of the Lambert W function.
-
flame_exact_test
-
flame_ode,
a MATLAB code which
sets up and solves an ordinary differential equation (ODE)
which models the growth of a ball of flame in a combustion process.
The exact solution is defined in terms of the Lambert W function.
-
flame_ode_test
-
flies_simulation,
a MATLAB code which
simulates an experiment in which two flies land on a plate of radius 1.
By repeating the experiment many times, the average distance between
the flies is to be estimated.
-
flies_simulation_test
-
florida_cvt_geo,
a MATLAB code which
creates a centroidal Voronoi Tessellation (CVT) of
the state of Florida, based solely on geometric considerations.
-
florida_cvt_geo_test
-
florida_cvt_pop,
a MATLAB code which
creates a centroidal Voronoi Tessellation (CVT) of
the state of Florida, based on population considerations.
-
florida_cvt_pop_test
-
floyd,
a MATLAB code which
implements the Floyd algorithm for finding the shortest distance
between pairs of nodes on a directed graph.
-
floyd_test
-
fly_simulation,
a MATLAB code which
simulates an experiment in which a fly lands on a plate of radius 1.
By repeating the experiment many times, the average distance of the
fly from the center is to be estimated.
-
fly_simulation_test
-
fmincon_test,
a MATLAB code which
calls fmincon(), which
seeks the minimizer of a scalar function of multiple variables,
within a region specified by linear constraints and bounds.
fmincon() is part of the MATLAB Optimization Toolbox.
-
fn,
a MATLAB code which
evaluates elementary and special functions using Chebyshev polynomials,
including Airy, Bessel I, Bessel J, Bessel K, Bessel Y, beta,
confluent hypergeometric, cosine integral, the Dawson integral,
digamma (psi), error, exponential integral, gamma, hyperbolic cosine
integral, hyperbolic sine integral, incomplete gamma, log gamma,
logarithmic integral, Pochhammer, psi, sine integral, Spence;,
by Wayne Fullerton.
-
fn_test
-
football_dynamic,
a MATLAB code which
uses dynamic programming to count the ways of achieving
a given score in football.
-
football_dynamic_test
-
four_fifths,
a MATLAB code which
searches for a solution to the problem of finding
four fifth powers that sum to a fifth power, that is, integers a,
b, c, d and e such that a^5+b^5+c^5+d^5=e^5. Euler conjectured
that no solution was possible.
-
four_fifths_test
-
fractal_coastline,
a MATLAB code which
uses perturbed Bezier interpolation to create a fractal coastline
from a crude outline of a state, country, island, or even
any general closed polygonal curve.
-
fractal_coastline_test
-
freefem_msh_io,
a MATLAB code which
reads and writes files used by the FreeFem finite element program
to store mesh information.
-
freefem_msh_io_test
-
fsolve_test,
a MATLAB code which
calls fsolve() which
seeks the solution x of one or more nonlinear equations f(x)=0.
-
full_deck_simulation,
a MATLAB code which
simulates a process in which a random card is drawn from
a deck of 52, and then replaced, continuing until every
card has been seen at least once.
-
full_deck_simulation_test
-
gamblers_ruin_simulation,
a MATLAB code which
simulates a game in which a gambler never stops playing until
all money is lost.
-
gamblers_ruin_simulation_test
-
gauss_seidel,
a MATLAB code which
implements the Gauss-Seidel iteration for linear systems.
-
gauss_seidel_test
-
gauss_seidel_poisson_1d,
a MATLAB code which
demonstrates how the linear system for a discretized version of the
steady 1D Poisson equation can be solved by the Gauss-Seidel
iteration.
-
gauss_seidel_poisson_1d_test
-
gauss_seidel_stochastic,
a MATLAB code which
uses a stochastic version of the Gauss-Seidel iteration to solve
a linear system
with a symmetric positive definite (SPD) matrix.
-
gauss_seidel_stochastic_test
-
gaussian,
a MATLAB code which
evaluates the Gaussian function and its derivatives.
-
gaussian_test,
-
gaussian_2d,
a MATLAB code which
evaluates a general Gaussian function of a 2D argument.
-
gaussian_2d_test,
-
gaussian_prime_spiral,
a MATLAB code which
computes a twisting spiral path along the Gaussian primes,
and displays a plot of the total trajectory.
-
gaussian_prime_spiral_test
-
ge_to_crs,
a MATLAB code which
converts a matrix from General (GE) to
Compressed Row Storage (CRS) format.
-
ge_to_crs_test
-
gegenbauer_cc,
a MATLAB code which
computes the Gegenbauer weighted integral of a function f(x)
using a Clenshaw-Curtis approach.
-
gegenbauer_cc_test
-
gegenbauer_exactness,
a MATLAB code which
tests the polynomial exactness of Gauss-Gegenbauer quadrature rules.
-
gegenbauer_exactness_test
-
gegenbauer_polynomial,
a MATLAB code which
evaluates the Gegenbauer polynomial and associated functions.
-
gegenbauer_polynomial_test
-
gegenbauer_rule,
a MATLAB code which
computes and writes out a Gauss-Gegenbauer quadrature rule
of given order.
-
gegenbauer_rule_test
-
gen_hermite_exactness,
a MATLAB code which
tests the polynomial
exactness of generalized Gauss-Hermite quadrature rules.
-
gen_hermite_exactness_test
-
gen_hermite_rule,
a MATLAB code which
computes and writes out a generalized Gauss-Hermite quadrature rule of
given order and parameter value.
-
gen_hermite_rule_test
-
gen_laguerre_exactness,
a MATLAB code which
tests the polynomial exactness of generalized Gauss-Laguerre
quadrature rules.
-
gen_laguerre_exactness_test
-
gen_laguerre_rule,
a MATLAB code which
prints a generalized Gauss-Laguerre quadrature rule
of given order and parameter value.
-
gen_laguerre_rule_test
-
geometry,
a MATLAB code which
performs geometric calculations in 2, 3 and M dimensional space,
including the computation of angles, areas, containment, distances,
intersections, lengths, and volumes.
-
geometry_test
-
geompack,
a MATLAB code which
computes Delaunay triangulations, Voronoi diagrams,
and other information, by Barry Joe.
-
geompack_test
-
gl_fast_rule,
a MATLAB code which
carries out the rapid computation of the Kth value and weight of
an N point Gauss-Legendre quadrature rule,
by Ignace Bogaert.
-
gl_fast_rule_test
-
glomin,
a MATLAB code which
finds a global minimum of a scalar function of a scalar variable,
without the use of derivative information,
by Richard Brent.
-
glomin_test
-
glycolysis_ode,
a MATLAB code which
sets up a pair of ordinary differential equations (ODE)
that model the biochemical process of glycolysis, for which
a limit cycle exists.
-
glycolysis_ode_test
-
gmres,
a MATLAB code which
implements the generalized minimum residual (GMRES) method for
solving a nonsymmetric sparse linear system A*x=b.
-
gmres_test
-
gmsh_io,
a MATLAB code which
reads or writes files created by the gmsh()
program for 1D, 2D or 3D meshes
used by the finite element method (FEM).
-
gmsh_io_test
-
gmsh_to_fem,
a MATLAB code which
reads a mesh data file created by the gmsh() program
and writes a pair of node and element files that correspond
to the FEM format.
-
gmsh_to_fem_test
-
gnuplot_test,
a MATLAB code which
uses gnuplot() to create various kinds of plots.
-
gpl_display,
a MATLAB code which
tries to read the data in a typical gnuplot() GPL file,
describing a 1D, 2D or 3D curve, or a surface Z(X,Y) defined
on a regular grid, a triangular grid, or an irregular quadrilateral
grid, displays it in a more attractive way than gnuplot() does.
-
gpl_display_test
-
gradient_descent,
a MATLAB code which
uses gradient descent to solve a linear least squares (LLS) problem.
-
gradient_descent_test
-
gram_polynomial,
a MATLAB code which
evaluates the Gram polynomials, also known as the discrete
Chebyshev polyomials and associated functions.
-
gram_polynomial_test
-
gram_schmidt,
a MATLAB code which
implements the Gram-Schmidt process to orthogonalize and normalize
a set of vectors.
-
gram_schmidt_test
-
graph_adj,
a MATLAB code which
carries out operations on abstract graphs, with undirected edges,
represented by an adjacency matrix. Operations include breadth-first
search, the computation of a minimum spanning tree,
an Euler or Hamilton circuit, blocks, chromatic polynomial,
or transitive closure.
-
graph_adj_test
-
graph_dist,
a MATLAB code which
carries out operations on abstract graphs, defined by undirected
edges with an associated distance matrix.
-
graph_dist_test
-
graph_representation,
a MATLAB code which
expresses the representation of an abstract mathematical graph
in several ways.
-
graph_representation_test
-
graphics_test,
a MATLAB code which
demonstrates a variety of graphics displays, including
bar plots, contour plots, filled polygons, histograms, line plots,
scatter plots, surface plots, tree diagrams, vector plots.
-
gray_code_display,
a MATLAB code which
computes the Hamming distance tables
for both the binary and Gray codes,
and displays 3D plots that illustrate how the Gray code does a better
job of providing nearby representations for nearby numbers.
-
gray_code_display_test
-
gray_scott_movie,
a MATLAB code which
solves versions of the partial differential equation (PDE) known
as the Gray-Scott reaction diffusion equation, converting the
solutions to a sequence of graphics frames, which are then
assembled into a movie.
-
gray_scott_movie_test
-
gray_scott_pde,
a MATLAB code which
solves the partial differential equation (PDE) known
as the Gray-Scott reaction diffusion equation, displaying
a sequence of solutions as time progresses.
-
gray_scott_pde_test
-
grazing_ode,
a MATLAB code which
sets up and solves ordinary differential equations (ODE)
that model the populations of an edible plant, and the
herbivore that grazes on it.
-
grazing_ode_test
-
grf_display,
a MATLAB code which
reads a grf file defining a mathematical graph and
displays it.
-
grf_display_test
-
grf_io,
a MATLAB code which
reads or writes a grf file which represents a mathematical graph;
-
grf_io_test
-
grid_display,
a MATLAB code which
reads a file of points on a grid or sparse grid, displays the
grid and saves the image in a png file;
-
grid_display_test
-
gridlines,
a MATLAB code which
gives the user more control over drawing gridlines on a graph
than the builtin grid command.
-
gridlines_test
-
grids_display,
a MATLAB code which
reads two files of grids or sparse grids, displaying the
first with hollow blue dots, the second with solid red dots.
-
grids_display_test
-
gurobi_solution_read,
a MATLAB code which
reads a file created by the optimization package GUROBI, representing
the solution of a polyomino tiling problem, and writes out a simple
ASCII file to be read by load().
-
gurobi_solution_read_test
-
gyroscope_ode,
a MATLAB code which
sets up the ordinary differential equations (ODE) that simulate
the angular attitude and rotational speed of a gyroscope.
-
gyroscope_ode_test
-
haar_transform,
a MATLAB code which
computes the Haar transform of 1d or 2d data.
-
haar_transform_test
-
halton,
a MATLAB code which
computes elements of a Halton Quasi Monte Carlo (QMC) sequence,
using a simple interface.
-
halton_test
-
hammersley,
a MATLAB code which
computes elements of a Hammersley Quasi Monte Carlo (QMC) sequence,
using a simple interface.
-
hammersley_test
-
hamming,
a MATLAB code which
implements some simple versions of Hamming codes which detects
and correct errors in data.
-
hamming_test
-
hand_area,
a MATLAB code which
estimates the area of a curve which outlines a hand.
-
hand_area_test
-
hand_data,
a MATLAB code which
carries out some numerical exercises based on data that came from
tracing several points on a hand.
-
hand_data_test
-
hand_mesh2d,
a MATLAB code which
reads in a set of points which outline a human hand,
and calls mesh2d(), which is able to create a fine triangular
mesh of the region outlined by the points.
-
hand_mesh2d_test
-
hankel_cholesky,
a MATLAB code which
computes the upper Cholesky factor R of a symmetric positive
definite (SPD) Hankel matrix so that H = R' * R.
-
hankel_cholesky_test
-
hankel_inverse,
a MATLAB code which
computes the inverse of a Hankel matrix.
-
hankel_inverse_test
-
hankel_spd,
a MATLAB code which
computes a lower triangular matrix L which is the Cholesky factor
of a symmetric positive definite (SPD) Hankel matrix H, that is,
H = L * L'.
-
hankel_spd_test
-
hb_io,
a MATLAB code which
reads and writes sparse linear systems stored in the Harwell Boeing (HB)
format for sparse matrices.
-
hb_io_test
-
hb_to_mm,
a MATLAB code which
converts a sparse matrix from Harwell Boeing (HB)
to Matrix Market (MM) format.
-
hb_to_mm_test
-
hb_to_msm,
a MATLAB code which
converts a sparse matrix stored in a
Harwell Boeing (HB) format to MATLAB sparse matrix (MSM) format;
-
hb_to_msm_test
-
hb_to_st,
a MATLAB code which
converts a sparse matrix from Harwell Boeing (HB) format
to Sparse Triplet (ST) format.
-
hb_to_st_test
-
heartbeat_ode,
a MATLAB code which
sets up and solves an ordinary differential equation
(ODE) describing the beating of the heart, as suggested by Zeeman.
-
heartbeat_ode_test
-
heat_transfer_test,
a MATLAB code which
plots data from the computation of heat distribution
on a metal disk, as computed by FreeFem++()
and transferred using the ffmatlib() library.
-
heated_plate,
a MATLAB code which
solves the steady state heat equation in a 2D
rectangular region, and is intended as
a starting point for a parallel version.
-
heated_plate_test
-
hello,
a MATLAB code which
prints out "Hello, world!".
-
hello_test
-
hello_parfor,
a MATLAB code which
uses the parfor() statement for parallel execution
and simply prints "Hello, world!" multiple times.
-
hello_parfor_test
-
helmholtz_exact,
a MATLAB code which
evaluates an exact formula for the solution of the Helmholtz equation,
a sort of eigenvalue equation that can arise after separation of
variables is a applied to the wave equation. This example considers
a problem in which Z(x,y) represents the vertical deflection of
the surface of a vibrating circular membrane such as a drumhead.
-
helmholtz_exact_test
-
henon_heiles_ode,
a MATLAB code which
sets up and solves the Henon-Heiles system of ordinary differential
equations (ODE) which model the motion of a star around the
galactic center.
-
henon_heiles_ode_test
-
henon_orbit,
a MATLAB code which
computes the orbit of the Henon map for various sets of initial data.
-
henon_orbit_test
-
hermite_cubic,
a MATLAB code which
computes the value, derivatives or integral
of a Hermite cubic polynomial,
or manipulates an interpolating function made up of
piecewise Hermite cubic polynomials.
-
hermite_cubic_test
-
hermite_exactness,
a MATLAB code which
tests the polynomial exactness of Gauss-Hermite quadrature rules
to estimate the integral of a function with density exp(-x^2)
over the interval (-oo,+oo).
-
hermite_exactness_test
-
hermite_integrands,
a MATLAB code which
defines test integrands for Hermite integrals
with density exp(-x^2) over the interval (-oo,+oo).
-
hermite_integrands_test
-
hermite_interpolant,
a MATLAB code which
computes the Hermite interpolant, a polynomial that matches
function values and derivatives.
-
hermite_interpolant_test
-
hermite_polynomial,
a MATLAB code which
evaluates the physicist's Hermite polynomial,
the probabilist's Hermite polynomial,
the Hermite function, and related functions.
-
hermite_polynomial_test
-
hermite_product_display,
a MATLAB code which
displays an image of a function created by the Cartesian product
of two Hermite polynomials, such as f(x,y) = h(3,x) * h(1,y).
-
hermite_product_display_test
-
hermite_product_polynomial,
a MATLAB code which
defines Hermite product polynomials, creating a multivariate
polynomial as the product of univariate Hermite polynomials.
-
hermite_product_polynomial_test
-
hermite_rule,
a MATLAB code which
returns a Gauss-Hermite quadrature rule
to estimate the integral of a function with density exp(-x^2)
over the interval (-oo,+oo).
-
hermite_rule_test
-
hexagon_integrals,
a MATLAB code which
returns the exact value of the integral of a monomial
over the interior of a hexagon in 2D.
-
hexagon_integrals_test
-
hexagon_lyness_rule,
a MATLAB code which
computes one of 13 Lyness quadrature rules over the interior
of the unit hexagon.
-
hexagon_lyness_rule_test
-
hexagon_monte_carlo,
a MATLAB code which
applies a Monte Carlo method to estimate the integral of a function
over the interior of a hexagon in 2D;
-
hexagon_monte_carlo_test
-
hexagon_stroud_rule,
a MATLAB code which
computes one of four Stroud quadrature rules over the interior
of the unit hexagon.
-
hexagon_stroud_rule_test
-
hexahedron_jaskowiec_rule,
a MATLAB code which
returns a symmetric Jaskowiec quadrature rule for the hexahedron,
with exactness up to total degree 21.
-
hexahedron_jaskowiec_rule_test
-
hexahedron_witherden_rule,
a MATLAB code which
returns a symmetric Witherden quadrature rule for the hexahedron,
with exactness up to total degree 11.
-
hexahedron_witherden_rule_test
-
high_card_parfor,
a MATLAB code which
simulates a situation in which you see the cards in a deck one by one,
and must select the one you think is the highest and stop,
using parfor() to carry out the computation in parallel.
-
high_card_parfor_test
-
high_card_simulation,
a MATLAB code which
simulates a situation in which you see the cards in a deck one by one,
and must select the one you think is the highest and stop.
-
high_card_simulation_test
-
hilbert_curve,
a MATLAB code which
computes the sequence of discrete Hilbert curves whose limit
is a space-filling curve.
-
hilbert_curve_test
-
hilbert_curve_3d,
a MATLAB code which
converts 3D Hilbert curve data between spatial coordinates of a
lattice point (x,y,z) and the linear coordinate H which describes
the ordering of that point on the curve.
-
hilbert_curve_3d_test
-
hilbert_curve_display,
a MATLAB code which
plots a Hilbert curve of given order.
-
hilbert_curve_display_test
-
histogram_data_2d_sample,
a MATLAB code which
demonstrates how to construct a Probability Density Function (PDF)
from sample data over a 2D domain,
and then to use that PDF to create new samples.
-
histogram_data_2d_sample_test
-
histogram_discrete,
a MATLAB code which
tries to make a histogram of data without using bins.
-
histogram_discrete_test
-
histogram_display,
a MATLAB code which
makes a bar plot of a set of data stored
as columns in a file; the first column is the X values, and
all the other columns are Y values to be shown as a stack of bars;
-
histogram_display_test
-
histogram_pdf_sample,
a MATLAB code which
demonstrates how sampling can be done by starting with the
formula for a PDF, creating a histogram, constructing a
histogram for the CDF, and then sampling.
-
histogram_pdf_sample_test
-
histogram_pdf_2d_sample,
a MATLAB code which
demonstrates how uniform sampling of a 2D region with respect to some
known Probability Density Function (PDF) can be approximated by
decomposing the region into rectangles, approximating the PDF by
a piecewise constant (PWC) function, constructing a histogram for
the CDF, and then sampling.
-
histogram_pdf_2d_sample_test
-
histogramize,
a MATLAB code which
takes a vector of data and organizes it into a histogram of a
given number of bins with given width and range,
which can be displayed as a bar chart.
-
histogramize_test
-
hits,
a MATLAB code which
uses the HITS algorithm to assign authority and hub indices to
a set of nodes in a directed network.
-
hits_test
-
house,
a MATLAB code which
includes a line segment outline of a house, and some programs to
show how linear transformations affect the shape,
by Cleve Moler.
-
house_test
-
human_data,
a MATLAB code which
starts with an image of simple outline of a human body,
tabulates a sequence of points on the outline,
creating numerical data defining the boundary. It is then able
to fill the region with mesh points and triangulate the region.
This allows the region to be analyzed by the finite element
method (FEM).
-
human_data_test
-
humps,
a MATLAB code which
evaluates the humps() function, its first and second derivatives
and its antiderivative.
-
humps_test
-
humps_ode,
a MATLAB code which
sets up and solves an ordinary differential equation (ODE)
whose solution is a double hump curve.
-
humps_ode_test
-
hyper_2f1,
a MATLAB code which
evaluates the hypergeometric functions 2F1(a,b,c;x) for real
parameters a, b, c, and real or complex argument x.
-
hyper_2f1_test
-
hyperball_distance,
a MATLAB code which
computes the expected value of the distance
between a pair of points randomly selected from the interior of
the unit hyperball in M dimensions.
-
hyperball_distance_test
-
hyperball_integrals,
a MATLAB code which
returns the exact value of the integral of any monomial
over the interior of the unit hyperball in M dimensions.
-
hyperball_integrals_test
-
hyperball_monte_carlo,
a MATLAB code which
applies a Monte Carlo method to estimate the integral of a function
over the interior of the unit ball in M dimensions;
-
hyperball_monte_carlo_test
-
hyperball_positive_distance,
a MATLAB code which
computes the expected value of the distance
between a pair of points randomly selected from the interior of
the unit positive hyperball in M dimensions.
-
hyperball_positive_distance_test
-
hypercube_distance,
a MATLAB code which
estimates the expected value of the distance
between a pair of points randomly selected
in the M-dimensional unit hypercube.
-
hypercube_distance_test
-
hypercube_exactness,
a MATLAB code which
tests the polynomial exactness of a quadrature rule
over the interior of the unit hypercube in M dimensions.
-
hypercube_exactness_test
-
hypercube_grid,
a MATLAB code which
computes a grid of points
over the interior of a hypercube in M dimensions.
-
hypercube_grid_test
-
hypercube_integrals,
a MATLAB code which
returns the exact value of the integral of any monomial
over the interior of the unit hypercube in M dimensions.
-
hypercube_integrals_test
-
hypercube_monte_carlo,
a MATLAB code which
applies a Monte Carlo method to estimate the integral of a function
over the interior of the unit hypercube in M dimensions.
-
hypercube_monte_carlo_test
-
hypercube_surface_distance,
a MATLAB code which
estimates the expected value of the distance
between a pair of points randomly selected
on the surface of the unit hypercube in D dimensions.
-
hypercube_surface_distance_test
-
hypergeom_test,
a MATLAB code which
calls hypergeom(), which
is a built-in MATLAB function which
evaluates the generalized hypergeometric functions pFq(z),
for integer p and q.
-
hypersphere,
a MATLAB code which
carries out various operations for an M dimensional hypersphere,
including converting between Cartesian and spherical coordinates,
stereographic projection, sampling the surface of the sphere, and
computing the surface area and volume.
-
hypersphere_test
-
hypersphere_angle,
a MATLAB code which
considers the problem of describing the typical value of the angle
between a pair of points randomly selected on the unit hypersphere
in M dimensions. Since by symmetry, this will be zero, we instead look
at the average of the absolute value of the dot product, and the
corresponding angle. In dimension 1, we have average dot product
of 1, and angle 0. As the dimension increases, the average dot product
rapidly decreases to 0, while the average angle goes to 90 degrees.
-
hypersphere_angle_test
-
hypersphere_distance,
a MATLAB code which
computes the expected value of the distance
between a pair of points randomly selected on the surface
of the unit hypersphere in M dimensions.
-
hypersphere_distance_test
-
hypersphere_integrals,
a MATLAB code which
returns the exact value of the integral of any monomial
over the surface of the unit hypersphere in M dimensions.
-
hypersphere_integrals_test
-
hypersphere_monte_carlo,
a MATLAB code which
applies a Monte Carlo method to estimate the integral of a function
on the surface of the unit sphere in M dimensions;
-
hypersphere_monte_carlo_test
-
hypersphere_positive_distance,
a MATLAB code which
computes the expected value of the distance
between a pair of points randomly selected on the surface
of the unit positive hypersphere in M dimensions.
-
hypersphere_positive_distance_test
-
i4lib,
a MATLAB code which
contains utilities using single precision integer (I4)
arithmetic.
-
i4lib_test
-
i4mat_rref2,
a MATLAB code which
computes a version of the reduced row echelon form of an
integer matrix.
-
i4mat_rref2_test
-
ice_io,
a MATLAB code which
reads or writes an ICE dataset, which defines a 3D grid,
using the netcdf() file format.
-
ice_io_test
-
ice_to_medit,
a MATLAB code which
reads a netcdf() file containing an ICE dataset and rewrites the
information as a medit() MESH file.
-
ice_to_medit_test
-
ill_bvp,
a MATLAB code which
defines an ill conditioned boundary value problem (BVP), and calls on
bvp4c() to solve it with various values of the conditioning parameter.
-
ill_bvp_test
-
image_boundary,
a MATLAB code which
reports the pixels which form the boundary between the black and
white regions of a simple image.
-
image_boundary_test
-
image_contrast,
a MATLAB code which
applies image processing techniques to increase the contrast
in an image.
-
image_contrast_test
-
image_decimate,
a MATLAB code which
drops the even rows and columns from an image.
-
image_decimate_test
-
image_denoise,
a MATLAB code which
applies simple filtering operations to a noisy image.
-
image_denoise_test
-
image_diffuse,
a MATLAB code which
uses diffusion to smooth out an image.
-
image_diffuse_test
-
image_double,
a MATLAB code which
doubles the height and width of an image by repeating each row
and column.
-
image_double_test
-
image_edge,
a MATLAB code which
detects edges in an image.
-
image_edge_test
-
image_mesh,
a MATLAB code which
starts with a list of points that bound some region,
and calls mesh2d() to create a mesh of the interior.
-
image_mesh_test
-
image_noise,
a MATLAB code which
adds noise to an image.
-
image_noise_test
-
image_normalize,
a MATLAB code which
reads image data from a file, converts it (if necessary) to
grayscale, resizes it to H pixels by W pixels.
-
image_normalize_test
-
image_quantization,
a MATLAB code which
uses kmeans() to reduce the
number of colors or shades of gray in an image.
-
image_quantization_test
-
image_rgb_to_gray,
a MATLAB code which
makes a grayscale version of an RGB image.
-
image_rgb_to_gray_test
-
image_sample,
a MATLAB code which
allows the user to specify an image file to be displayed.
The user may then use the mouse to select points on the image.
The coordinates of each point are saved to a file.
Selection ends with a double click. An example is supplied,
which outlines the boundary of an aneurysm.
-
image_sample_test
-
image_threshold,
a MATLAB code which
makes a black and white version of a grayscale image
by setting all pixels below or above a threshold value
to black or white.
-
image_threshold_test
-
imshow_numeric,
a MATLAB code which
accepts a numeric 2D array and displays it as a grayscale image.
-
imshow_numeric_test
-
index,
a MATLAB code which
converts an M-dimensional vector index to a one-dimensional vector index;
it handles zero and one based indexing schemes, as well as column major
and row major conventions.
-
index_test
-
insurance_simulation,
a MATLAB code which
simulates a highly simplified model of term life insurance,
in which a customer agrees to pay an annual fee for a given
number of years, so that if the customer dies within that term,
the family receives a large payout.
-
insurance_simulation_test
-
interp,
a MATLAB code which
parameterizes and interpolates data;
-
interp_test
-
interp_chebyshev,
a MATLAB code which
interactively uses n Chebyshev spaced nodes in the interval [a,b]
to interpolate a function f(x) with a polynomial.
-
interp_chebyshev_test
-
interp_equal,
a MATLAB code which
interactively uses n equally spaced nodes in the interval [a,b]
to interpolate a function f(x) with a polynomial.
-
interp_equal_test
-
interp_ncs,
a MATLAB code which
interactively constructs a natural cubic spline (NCS) interpolant
to a function f(x), using the 'zero second derivative' end condition.
-
interp_ncs_test
-
interp_spline,
a MATLAB code which
interactively constructs a cubic spline interpolant to a function
f(x), using the 'not-a-knot' end condition.
-
interp_spline_test
-
interp_spline_data,
a MATLAB code which
interactively constructs a cubic spline interpolant to (x,y) data,
using the 'not-a-knot' end condition.
-
interp_spline_data_test
-
interp_trig,
a MATLAB code which
interactively uses n equally spaced nodes in the interval [a,b]
to interpolate a function f(x) with a trigonometric polynomial.
-
interp_trig_test
-
iplot,
a MATLAB code which
interactively plots a function f(x) over a domain a ≤ x ≤ b;
-
iplot_test
-
is_gaussian_prime,
a MATLAB code which
is true if a given complex number c is a Gaussian prime.
-
is_gaussian_prime_test
-
is_prime,
a MATLAB code which
is true if a given integer n is prime.
-
is_prime_test
-
isbn,
a MATLAB code which
determines the check digit for an International Standard Book Number
(ISBN) or reports whether a given ISBN is valid.
-
isbn_test
-
ising_2d_simulation,
a MATLAB code which
simulates the evolution of a 2D array of positive and negative
charges, each of which is likely to flip to be in agreement
with neighbors.
-
ising_2d_simulation_test
-
jaccard_distance,
a MATLAB code which
computes the Jaccard distance between two sets.
-
jaccard_distance_test
-
jacobi,
a MATLAB code which
implements the Jacobi iteration for the iterative solution of
linear systems.
-
jacobi_test
-
jacobi_eigenvalue,
a MATLAB code which
implements the Jacobi iteration for the iterative determination
of the eigenvalues and eigenvectors of a real symmetric matrix.
-
jacobi_eigenvalue_test
-
jacobi_exactness,
a MATLAB code which
tests the polynomial exactness of rules for integrals with
a Jacobi weight function.
-
jacobi_exactness_test
-
jacobi_poisson_1d,
a MATLAB code which
uses Jacobi iteration to solve the linear system for a discretized
steady 1D Poisson equation.
-
jacobi_poisson_1d_test
-
jacobi_polynomial,
a MATLAB code which
evaluates the Jacobi polynomial and associated functions.
-
jacobi_polynomial_test
-
jacobi_rule,
a MATLAB code which
computes a Gauss-Jacobi quadrature rule.
-
jacobi_rule_test
-
jai_alai_simulation,
a MATLAB code which
simulates a sequence matches of the game of jai alai.
-
jai_alai_simulation_test
-
jordan_matrix,
a MATLAB code which
returns a random matrix in Jordan canonical form.
-
jordan_matrix_test
-
joukowsky_transform,
a MATLAB code which
applies the Joukowsky transform to data, mapping between a circle
in the complex plane and various airfoil shapes.
-
joukowsky_transform_test
-
julia_set,
a MATLAB code which
computes and plots a Julia set,
the set of points in the complex plane that remain bounded
under a mapping of the form f(z) = z^2+c.
-
julia_set_test
-
jumping_bean_simulation,
a MATLAB code which
simulates the motion of several jumping beans which prefer
cooler locations.
-
jumping_bean_simulation_test
-
kdv_etdrk4,
a MATLAB code which
uses the exponential time differencing (ETD) RK4 method to
solve the Korteweg-deVries (KdV) partial differential equation (PDE),
by Aly-Khan Kassam, Lloyd Trefethen.
-
kdv_etdrk4_test
-
kdv_exact,
a MATLAB code which
evaluates exact solutions of the Korteweg-deVries (KdV)
partial differential equation (PDE).
-
kdv_exact_test
-
kdv_ift,
a MATLAB code which
uses the Inverse Fourier Transform (IFT) method to solve the
Korteweg-deVries (KdV) partial differential equation (PDE),
by Aly-Khan Kassam, Lloyd Trefethen.
-
kdv_ift_test
-
kelley,
a MATLAB code which
implements iterative methods for linear and nonlinear problems,
by Tim Kelley.
-
kelley_test
-
kepler_ode,
a MATLAB code which
sets up and solves the ordinary differential equations (ODE) for a
Kepler two-body gravitational system.
-
kepler_ode_test
-
kepler_perturbed_ode,
a MATLAB code which
sets up and solves the ordinary differential equations (ODE) for a
perturbed Kepler two-body gravitational system.
-
kepler_perturbed_ode_test
-
keyword_test,
a MATLAB code which
accepts named keywords, using the Name/Value paired argument
convention.
-
kmeans,
a MATLAB code which
handles the K-Means problem,
which organizes a set of N points in M dimensions into K clusters;
-
kmeans_test
-
kmeans_fast,
a MATLAB code which
contains several different algorithms for the K-Means problem,
which organizes a set of N points in M dimensions into K clusters,
by Charles Elkan.
-
kmeans_fast_test
-
knapsack_01_brute,
a MATLAB code which
uses brute force to solve small versions of the 0/1 knapsack problem,
in which a knapsack of limited weight capacity is to be packed as
full as possible, selecting items from a set of varying weights;
-
knapsack_01_brute_test
-
knapsack_brute,
a MATLAB code which
uses brute force to solve small versions of the knapsack problem,
in which N items are available, each with given value and weight.
A thief's knapsack can carry no more than Wmax pounds. The thief
seeks a selection of items to carry in the knapsack of maximum
total value.
-
knapsack_brute_test
-
knapsack_dynamic,
a MATLAB code which
uses dynamic programming to solve a knapsack problem.
-
knapsack_dynamic_test
-
knapsack_greedy,
a MATLAB code which
uses a greedy algorithm to estimate a solution of the knapsack problem;
-
knapsack_greedy_test
-
knapsack_random,
a MATLAB code which
randomly chooses a subset of N items, each with given value and weight.
It then evaluates whether this is a feasible solution to a
problem in which a thief's knapsack can carry no more than Wmax pounds,
and it is desired to maximum the total value of the selected items.
-
knapsack_random_test
-
knapsack_rational,
a MATLAB code which
solves the rational knapsack problem, in which a knapsack of limited
weight capacity is filled with profitable items. This variation of
the knapsack problem allows a fractional part of an item to
be included in the knapsack. The result is an upper bound on the
maximum possible profit for the knapsack problem.
-
knapsack_rational_test
-
knapsack_values,
a MATLAB code which
returns some simple examples of the knapsack problem,
in which N items are available, each with given value V and weight W.
A thief's knapsack can carry no more than K pounds. The thief
seeks a selection S of items to carry in the knapsack of maximum
total value.
-
knapsack_values_test
-
kronrod_rule,
a MATLAB code which
computes a Gauss and Gauss-Kronrod pair of quadrature rules
of arbitrary order,
by Robert Piessens, Maria Branders.
-
kronrod_rule_test
-
kursiv_pde_etdrk4,
a MATLAB code which
uses the exponential time differencing (ETD) RK4 method
to solve the Kuratomo-Sivashinsky PDE as a system of stiff ordinary
differential equations (ODE), by Aly-Khan Kassam, Lloyd Trefethen.
-
kursiv_pde_etdrk4_test
-
lagrange_approx_1d,
a MATLAB code which
defines and evaluates the Lagrange polynomial p(x) of degree m
which approximates a set of nd data points (x(i),y(i)).
-
lagrange_approx_1d_test
-
lagrange_basis_display,
a MATLAB code which
displays the basis functions associated with a given set of nodes used
with the Lagrange interpolation scheme.
-
lagrange_basis_display_test
-
lagrange_interp_1d,
a MATLAB code which
defines and evaluates the Lagrange polynomial p(x)
which interpolates a set of data depending on a 1D argument,
so that p(x(i)) = y(i).
-
lagrange_interp_1d_test
-
lagrange_interp_2d,
a MATLAB code which
defines and evaluates the Lagrange polynomial p(x,y)
which interpolates a set of data depending on a 2D argument
that was evaluated on a product grid,
so that p(x(i),y(j)) = z(i,j).
-
lagrange_interp_2d_test
-
lagrange_interp_nd,
a MATLAB code which
defines and evaluates the Lagrange polynomial p(x)
which interpolates a set of data depending on an M dimensional
argument that was evaluated on a product grid,
so that p(x(i)) = z(i).
-
lagrange_interp_nd_test
-
lagrange_nd,
a MATLAB code which
implements several multivariate Lagrange interpolation schemes
developed by Tomas Sauer.
-
lagrange_nd_test
-
laguerre_exactness,
a MATLAB code which
tests the polynomial exactness of Gauss-Laguerre quadrature rules
for integrating functions with density exp(-x) over [0,+oo).
-
laguerre_exactness_test
-
laguerre_integrands,
a MATLAB code which
implements test problems for
approximate integration over a semi-infinite interval,
often carried out using Gauss-Laguerre quadrature.
-
laguerre_integrands_test
-
laguerre_polynomial,
a MATLAB code which
evaluates the Laguerre polynomial,
the generalized Laguerre polynomials,
and the Laguerre function.
-
laguerre_polynomial_test
-
laguerre_product,
a MATLAB code which
computes weighted integrals of products of Laguerre polynomials.
-
laguerre_product_test
-
laguerre_rule,
a MATLAB code which
returns a Gauss-Laguerre quadrature rule of given order.
-
laguerre_rule_test
-
lambert_w,
a MATLAB code which
evaluates Lambert's W function.
-
lambert_w_test
-
langford_ode,
a MATLAB code which
sets up and solves the Langford system
of ordinary differential equations (ODE).
-
langford_ode_test
-
laplace_periodic_test,
a MATLAB code which
plots data from the solution of the Laplace equation in a square
with periodic boundary conditions, computed by FreeFem++()
and transferred using the ffmatlib() library.
-
laplacian,
a MATLAB code which
evaluates a discretized approximation to the Laplacian operator
on data on an evenly spaced grid, within a circle, an interval,
or a torus. For the case of the interval, the data may be supplied
on an unevenly spaced grid.
-
laplacian_test
-
laplacian_matrix,
a MATLAB code which
carries out computations related to the discrete
Laplacian operator, including full or sparse evaluation,
evaluation for unequally spaced data sampling points,
application to a set of data samples, solution of associated
linear systems, eigenvalues and eigenvectors, and extension
to 2D and 3D geometry.
-
laplacian_matrix_test
-
latin_center,
a MATLAB code which
computes N points in an M dimensional Latin Center square;
-
latin_center_test
-
latin_cover,
a MATLAB code which
produces N Latin squares which cover an NxN square, or NxN Latin cubes
which cover an NxNxN cube.
-
latin_cover_test
-
latin_edge,
a MATLAB code which
returns N points in an M dimensional Latin Edge square;
-
latin_edge_test
-
latin_random,
a MATLAB code which
returns N points in an M dimensional Latin Random square;
-
latin_random_test
-
latinize,
a MATLAB code which
adjusts N points in M dimensions to form a Latin hypercube;
-
latinize_test
-
lattice_rule,
a MATLAB code which
returns lattice rules for M dimensional integration;
-
lattice_rule_test
-
leapfrog,
a MATLAB code which
uses the leapfrog method to solve a second order ordinary
differential equation (ODE) of the form y''=f(t,y).
-
leapfrog_test
-
least_squares_approximant,
a MATLAB code which
finds a polynomial approximant to data using linear least
squares (LLS).
-
least_squares_approximant_test
-
lebesgue,
a MATLAB code which
is given nodes in 1D, plots the Lebesgue function, and estimates
the Lebesgue constant, which measures the maximum magnitude of
the potential error of Lagrange polynomial interpolation.
-
lebesgue_test
-
legendre_exactness,
a MATLAB code which
tests the monomial exactness of quadrature rules for the Legendre
problem of integrating a function with density 1
over the interval [-1,+1].
-
legendre_exactness_test
-
legendre_fast_rule,
a MATLAB code which
uses a fast (order N) algorithm to compute a Gauss-Legendre
quadrature rule of given order.
-
legendre_fast_rule_test
-
legendre_polynomial,
a MATLAB code which
evaluates the Legendre polynomial and associated functions.
-
legendre_polynomial_test
-
legendre_product,
a MATLAB code which
computes weighted integrals of products of Legendre polynomials.
-
legendre_product_test
-
legendre_product_display,
a MATLAB code which
displays the points in a 2D Gauss-Legendre product quadrature rule;
-
legendre_product_display_test
-
legendre_product_polynomial,
a MATLAB code which
defines Legendre product polynomials, creating a multivariate
polynomial as the product of univariate Legendre polynomials.
-
legendre_product_polynomial_test
-
legendre_rule,
a MATLAB code which
returns a Gauss-Legendre quadrature rule of given order.
-
legendre_rule_test
-
legendre_shifted_polynomial,
a MATLAB code which
evaluates the shifted Legendre polynomial, with the domain [0,1].
-
legendre_shifted_polynomial_test
-
levels,
a MATLAB code which
makes a contour plot,
choosing the contour levels using random sampling.
-
levels_test
-
levenshtein_distance,
a MATLAB code which
returns the Levenshtein distance between two strings.
-
levenshtein_distance_test
-
levenshtein_matrix,
a MATLAB code which
returns the Levenshtein distance matrix defined by two strings.
-
levenshtein_matrix_test
-
life,
a MATLAB code which
computes a few steps of the evolution of John Conway's Game of Life,
intended as a starting point for implementing a parallel version.
-
life_test
-
lights_out,
a MATLAB code which
analyzes the "Lights Out" game, in which lights on a 5x5 board are
randomly lit up. Pushing a light reverses its status, as well as
the status of the north, south, east and west neighbor lights.
The user seeks to push buttons in such a way that
all the lights are turned off.
-
lights_out_test
-
lights_out_game,
a MATLAB code which
sets up the "Lights Out" game, lighting up a few squares on
a grid. An interactive user must then try to press squares
in such a way that all the lights are turned off.
-
lindberg_exact,
a MATLAB code which
evaluates the exact solution of the Lindberg ordinary differential
equations (ODE), a system that is extremely difficult to solve
accurately.
-
lindberg_exact_test
-
lindberg_ode,
a MATLAB code which
sets up and solves a system of 4 ordinary differential equations
(ODE) which are very stiff.
-
lindberg_ode_test
-
line_cvt_lloyd,
a MATLAB code which
applies the Lloyd iteration repeatedly to a set of N points,
to compute a Centroidal Voronoi Tessellation (CVT)
over the interior of a line segment in 1D.
-
line_cvt_lloyd_test
-
line_distance,
a MATLAB code which
computes the expected value of the distance
between a pair of points randomly selected in the unit line segment.
-
line_distance_test
-
line_fekete_rule,
a MATLAB code which
estimates the location of N Fekete points, for polynomial
interpolation or quadrature,
over the interior of a line segment in 1D.
-
line_fekete_rule_test
-
line_felippa_rule,
a MATLAB code which
returns a Felippa quadrature rule for approximating integrals
over the interior of a line segment in 1D.
-
line_felippa_rule_test
-
line_grid,
a MATLAB code which
computes a grid of points
over the interior of a line segment in 1D.
-
line_grid_test
-
line_integrals,
a MATLAB code which
returns the exact value of the integral of any monomial
over the length of the unit line in 1D.
-
line_integrals_test
-
line_lines_packing,
a MATLAB code which
tries to randomly pack as many non-overlapping equal line segments
as possible into a larger line segment,
estimating Renyi's parking constant of 0.7475979202. This is an
example of random sequential adsorption (RSA).
-
line_lines_packing_test
-
line_monte_carlo,
a MATLAB code which
applies a Monte Carlo method to estimate the integral of a function
over the length of the unit line in 1D.
-
line_monte_carlo_test
-
line_ncc_rule,
a MATLAB code which
computes a Newton Cotes Closed (NCC) quadrature rule,
using equally spaced points,
over the interior of a line segment in 1D.
-
line_ncc_rule_test
-
line_nco_rule,
a MATLAB code which
computes a Newton Cotes Open (NCO) quadrature rule,
using equally spaced points,
over the interior of a line segment in 1D.
-
line_nco_rule_test
-
linear_algebra,
a MATLAB code which
carries out various linear algebra operations for matrices
stored in a variety of formats.
-
linpack_bench,
a MATLAB code which
is a version of the LINPACK benchmark;
-
linpack_bench_test
-
linpack_bench_backslash,
a MATLAB code which
is a version of the LINPACK benchmark using the "backslash"
linear system solver;
-
linpack_bench_backslash_test
-
linpack_d,
a MATLAB code which
factors and solves linear systems using real 64 bit arithmetic,
by Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart.
The matrix and vector data is assumed to be real.
-
linpack_d_test
-
linpack_z,
a MATLAB code which
factors and solves linear systems
using complex 64 bit arithmetic,
by Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart.
The matrix and vector data is assumed to be complex.
-
linpack_z_test
-
lissajous,
a MATLAB code which
displays a Lissajous figure,
of the form x = sin ( a1 t + b1 ), y = sin ( a2 t + b2 ).
-
lissajous_test
-
llsq,
a MATLAB code which
solves the linear least squares (LLS) problem.
It finds the "best" straight line to match a set of data points.
More precisely, it finds the quantities "a" and "b" defining
the straight line y=a*x+b, which minimizes the root-mean-square
(RMS) error to the data.
-
llsq_test
-
load_test,
a MATLAB code which
calls the load() function, which
reads data from a file into a variable.
-
lobatto_polynomial,
a MATLAB code which
evaluates Lobatto polynomials, which are similar to Legendre
polynomials except that they are 0 at both endpoints.
-
lobatto_polynomial_test
-
local_min,
a MATLAB code which
finds a local minimum of a scalar function of a scalar variable,
without the use of derivative information,
by Richard Brent.
-
local_min_test
-
local_min_rc,
a MATLAB code which
finds a local minimum of a scalar function of a scalar variable,
without the use of derivative information,
using reverse communication (RC),
by Richard Brent.
-
local_min_rc_test
-
locker_simulation,
a MATLAB code which
simulates the locker problem, in which gym users have left
their wallets in lockers; someone has scrambled all the lockers,
and the gym users need a strategy that maximizes the chance
that everyone will find their wallet by searching a limited
number of lockers.
-
locker_simulation_test
-
log_norm,
a MATLAB code which
computes the logarithmic norm of a matrix, for norms 1, 2 and oo.
-
log_norm_test
-
log_normal,
a MATLAB code which
returns quantities related to the log normal Probability
Distribution Function (PDF).
-
log_normal_test
-
log_normal_truncated_ab,
a MATLAB code which
returns quantities related to the log normal Probability
Distribution Function (PDF) truncated to the interval [a,b].
-
log_normal_truncated_ab_test
-
logistic_bifurcation,
a MATLAB code which
plots the bifurcation diagram for the logistic equation,
by John D Cook.
-
logistic_bifurcation_test
-
logistic_exact,
a MATLAB code which
evaluates an exact solution of the logistic equation,
an ordinary differential equation (ODE)
which models population growth in the face of a limited carrying capacity.
-
logistic_exact_test
-
logistic_ode,
a MATLAB code which
sets up and solves an ordinary differential equation (ODE)
which models population growth in the face of a limited carrying
capacity.
-
logistic_ode_test
-
lorenz_ode,
sets up and solves the Lorenz system of ordinary differential
equations (ODE), which exhibit sensitive dependence on the
initial conditions.
-
lorenz_ode_test
-
lorenz_ode_cluster_test,
takes N points on a trajectory of solutions to the Lorenz system
of ordinary differential equations (ODE),
and applies the K-Means algorithm to organize the data into
K clusters.
-
lorenz_ode_sensitivity_test,
a MATLAB code which
demonstrates sensitivity to initial conditions in the Lorenz system,
of ordinary differential equations (ODE),
using an approach suggested by John D Cook.
-
luhn,
a MATLAB code which
computes the Luhn check digit for a string, and validates a string.
-
luhn_test
-
machar,
a MATLAB code which
computes the appropriate values of arithmetic constants for a given machine,
by William Cody.
-
machar_test
-
machine,
a MATLAB code which
returns values of arithmetic constants for a given machine.
-
machine_test
-
mackey_glass_dde,
a MATLAB code which
sets up and solves the Mackey-Glass Delay Differential Equation (DDE),
which models dynamical diseases such as irregular breathing apnea
and chronic myelogenous leukemia, and produces a strange chaotic
attractor.
-
mackey_glass_dde_test
-
magic_matrix,
a MATLAB code which
computes a magic matrix, for any odd order n, such that all rows and
columns have the same sum.
-
magic_matrix_test
-
mandelbrot,
a MATLAB code which
generates an image of the Mandelbrot set;
-
mandelbrot_test
-
mandelbrot_orbit,
a MATLAB code which
generates the Mandelbrot iterates arising from a single
starting point;
-
mandelbrot_orbit_test
-
maple_area,
a MATLAB code which
takes the list of pixels that form the boundary of the image
of a maple leaf within a picture, and uses grid, Monte Carlo,
and Quasi Monte Carlo (QMC) sampling to estimate the area of the leaf.
-
maple_area_test
-
maple_boundary,
a MATLAB code which
reads an image of a maple leaf and extracts the list of pixels
that form the boundary.
-
maple_boundary_test
-
mario,
a MATLAB code which
creates a sort of "needlepoint" image of Mario, as an array of
colored squares.
-
mario_test
-
markov_letters,
a MATLAB code which
counts the occurences of letter pairs in a text.
-
markov_letters_test
-
matlab_test,
a MATLAB code which
illustrates the use of scripts and M-files;
-
matlab_combinatorics,
a MATLAB code which
considers a variety of problems in combinatorics involving
counting, combinations, permutations, and so on.
-
matlab_commandline,
a MATLAB code which
illustrates how to execute code from the UNIX command line, that is,
not with the usual command window.
-
matlab_compiler,
a MATLAB code which
illustrates the use of the compiler, which allows you
to run an application outside of the Matlab environment.
-
matlab_distance,
a MATLAB code which
estimates the typical distance between a pair of points
randomly selected from the surface or interior of a
geometric object such as a circle, disk, sphere, cube,
and between other nongeometric pairs of items.
-
matlab_exact,
a MATLAB code which
evaluates exact solutions to a few selected examples of
ordinary differential equations (ODE) and partial differential
equations (PDE).
-
matlab_graphics,
a MATLAB code which
demonstrates a few issues that arise when producing graphic
images.
-
matlab_grid,
a MATLAB code which
generates a regular grid of points inside a variety of regions
in one, two, three or many dimensions.
-
matlab_integrals,
a MATLAB code which
returns the exact value of the integral of any monomial
over the surface or interior of some geometric object,
including a line, quadrilateral, box, circle, disk, sphere,
ball and others.
-
matlab_kmeans_test,
a MATLAB code which
calls the built in kmeans() function, which
clusters N sets of M-dimensional data into K clusters.
-
matlab_map,
a MATLAB code which
uses the mapping toolbox to draw maps of
the world, countries, the US, or individual states.
-
matlab_mistake,
a MATLAB code which
illustrates some simple but devious programming mistakes.
-
matlab_monte_carlo,
a MATLAB code which
uses Monte Carlo sampling to estimate areas and integrals.
-
matlab_movie,
a MATLAB code which
creates a movie or animation by generating a sequence of
graphics frames and then stringing them together.
-
matlab_ode,
a MATLAB code which
sets up various systems of ordinary differential equations (ODE).
-
matlab_ode_solver,
a MATLAB code which
solves one or more differential equations (ODE) using a method of a
particular order, either explicit or implicit. Some methods require
a nonlinear equation solver. Some methods used a fixed stepsize,
while others adapt the stepsize based on an error estimate.
-
matlab_os,
a MATLAB code which
illustrates how the system command can be used to
issue commands to the computer operating system (UNIX or DOS);
-
matlab_plots,
a MATLAB code which
uses plotting to illustrate a mathematical structure, such as
an iterative map, a fractal, a curve or surface.
-
matlab_polynomial,
a MATLAB code which
analyzes a variety of polynomial families, returning the polynomial
values, coefficients, derivatives, integrals, roots, or other
information.
-
matlab_random_test,
a MATLAB code which
demonstrates random number generation.
-
matlab_rule,
a MATLAB code which
computes a quadrature rule which
estimates the integral of a function f(x), which might be defined over
a one dimensional region (a line) or more complex shapes such as
a circle, a triangle, a quadrilateral, a polygon, or a higher
dimensional region, and which might include an associated weight
function w(x).
-
matlab_simulation,
a MATLAB code which
uses simulation to study card games, contests, and other processes
which have a random element. Usually, the purpose is to try to
predict the average behavior of the system over many trials.
-
matrix_analyze,
a MATLAB code which
reports whether a matrix has various properties.
-
matrix_analyze_test
-
matrix_assemble_parfor,
a MATLAB code which
demonstrates the parfor() parallel programming
feature by assembling the Hilbert matrix in a parallel loop.
-
matrix_assemble_parfor_test
-
matrix_chain_brute,
a MATLAB code which
finds the cost of the most efficient ordering to use when
multiplying a sequence of matrices, using brute force.
-
matrix_chain_brute_test
-
matrix_chain_dynamic,
a MATLAB code which
finds the cost of the most efficient ordering to use when
multiplying a sequence of matrices, using dynamic programming.
-
matrix_chain_dynamic_test
-
matrix_exponential,
a MATLAB code which
computes the exponential of a matrix.
-
matrix_exponential_test
-
mcnuggets,
a MATLAB code which
counts M(N), the number of ways a given number N of Chicken
McNuggets can be assembled, given that they are only available
in packages of 6, 9, and 20.
-
mcnuggets_test
-
mcnuggets_diophantine,
a MATLAB code which
uses Diophantine methods to find the ways a given number N of Chicken
McNuggets can be assembled, given that they are only available
in packages of 6, 9, and 20.
-
mcnuggets_diophantine_test
-
md,
a MATLAB code which
carries out a molecular dynamics simulation, and is intended as
a starting point for implementing a parallel version.
-
md_test
-
md_fast,
a MATLAB code which
carries out a molecular dynamics simulation; it is a version of md()
that has been revised to take advantage of vectorization.
-
md_fast_test
-
md_parfor,
a MATLAB code which
runs the md() molecular dynamics program,
running in parallel using parfor().
-
md_parfor_test
-
medit_mesh_io,
a MATLAB code which
reads or writes medit() MESH files defining a finite element mesh.
-
medit_mesh_io_test
-
medit_to_fem,
a MATLAB code which
reads a medit() MESH file
and writes a corresponding pair of node and element files that
correspond to the FEM format.
-
medit_to_fem_test
-
medit_to_ice,
a MATLAB code which
reads a medit() MESH file containing an ICE dataset and rewrites the
information as a netcdf() file.
-
medit_to_ice_test
-
memory,
a MATLAB code which
declares and uses a sequence of larger and larger arrays,
to see what the memory limits are on a given computer.
-
memory_test
-
mesh_bandwidth,
a MATLAB code which
returns the geometric bandwidth associated with a mesh of
elements of any order and in a space of M dimensions.
-
mesh_bandwidth_test
-
mesh_boundary,
a MATLAB code which
is given a mesh of a 2D region, formed by polygonal elements,
and determines a sequence of pairs of polygonal vertices that
define the boundary of the region.
-
mesh_boundary_test
-
mesh_display,
a MATLAB code which
plots the nodes and elements of a polygonal mesh, with optional
numbering.
-
mesh_display_test
-
mesh_etoe,
a MATLAB code which
uses ETOV, the mesh element-to-vertex connectivity,
to construct ETOE, the element-to-element connectivity.
-
mesh_etoe_test
-
mesh_vtoe,
a MATLAB code which
uses ETOV, the mesh element-to-vertex connectivity,
to construct VTOE, the vertex-to-element connectivity.
-
mesh_vtoe_test
-
mesh2d,
a MATLAB code which
automatically creates a triangular mesh for a given polygonal
region, by Darren Engwirda.
-
mesh2d_test
-
mesh2d_to_medit,
a MATLAB code which
accepts the nodes and triangles of a mesh created by mesh2d()
and creates a corresponding medit() MESH file.
-
mesh2d_to_medit_test
-
mesh2d_write,
a MATLAB code which
writes mesh2d() node and element data to files.
-
mesh2d_write_test
-
mgmres,
a MATLAB code which
applies the restarted Generalized Minimum Residual (GMRES) algorithm
to solve a sparse linear system, using Compressed Row Storage (CRS) or
sparse triplet (ST) format, by Lili Ju.
-
mgmres_test
-
mgs,
a MATLAB code which
is an obscure legacy code, which the student is encouraged to
study, understand, and document. This example is due to Diane O'Leary.
-
mgs_test
-
mhd_exact,
a MATLAB code which
evaluates Hartmann's exact formula for a solution of the
magnetohydrodynamic (MHD) fluid flow equations in 2D.
-
mhd_exact_test
-
middle_square,
a MATLAB code which
implements the middle square algorithm for generating random integers.
This is a very early method, attributed to von Neumann, which actually
is deeply flawed, with short cycles.
-
middle_square_test
-
midpoint,
a MATLAB code which
solves one or more ordinary differential equations (ODE)
using the (implicit) midpoint method, with fsolve() solving
the implicit equation, and a fixed time step.
-
midpoint_test
-
midpoint_adaptive,
a MATLAB code which
solves one or more ordinary differential equations (ODE)
using the (implicit) midpoint method, with fsolve() solving
the implicit equation, and an adaptive time step.
Plots of the solution and timestep history are created.
-
midpoint_adaptive_test
-
midpoint_explicit,
a MATLAB code which
solves one or more ordinary differential equations (ODE)
using the (explicit) midpoint method, also called the
modified Euler method, and using a fixed time step.
-
midpoint_explicit_test
-
midpoint_fixed,
a MATLAB code which
solves one or more ordinary differential equations (ODE)
using the (implicit) midpoint method, using a simple fixed-point
iteration to solve the implicit equation, and using a fixed time step.
-
midpoint_fixed_test
-
mm_io,
a MATLAB code which
reads and writes sparse linear systems stored
in the Matrix Market (MM) format.
-
mm_io_test
-
mm_to_hb,
a MATLAB code which
reads the sparse matrix information from an Matrix Market (MM) file
and writes a corresponding Harwell Boeing (HB) file.
-
mm_to_hb_test
-
mm_to_msm,
a MATLAB code which
reads a Matrix Market (MM) file defining a sparse matrix, and creates
a corresponding matrix in MATLAB sparse matrix (MSM) format.
-
mm_to_msm_test
-
mm_to_st,
a MATLAB code which
reads the sparse matrix information from a Matrix Market (MM) file
and writes a corresponding Sparse Triplet (ST) file.
-
mm_to_st_test
-
mnist_neural,
a MATLAB code which
constructs a neural network in order to classify images of digits.
-
mnist_neural_test
-
monoalphabetic,
a MATLAB code which
applies a monoalphabetic substitution cipher to a string of text.
-
monoalphabetic_test
-
monomial,
a MATLAB code which
enumerates, lists, ranks, unranks and randomizes multivariate
monomials in a space of M dimensions, with total degree less than N,
equal to N, or lying within a given range.
-
monomial_test
-
monomial_symmetrize,
a MATLAB code which
symmetrizes the coefficients of equivalent monomials in a polynomial.
-
monomial_symmetrize_test
-
monomial_value,
a MATLAB code which
evaluates a monomial in M dimensions.
-
monomial_value_test
-
monopoly_matrix,
a MATLAB code which
computes the adjacency and transition matrices for the game
of Monopoly.
-
monopoly_matrix_test
-
monty_hall_simulation,
a MATLAB code which
simulates the "Let's Make a Deal" game in which Monty Hall has
hidden a prize behind one of several doors, and the user wins
the prize if the correct door is selected.
-
monty_hall_simulation_test
-
mortality,
a MATLAB code which
processes some sample mortality data.
-
mortality_test
-
msm_to_hb,
a MATLAB code which
writes a MATLAB sparse matrix (MSM) to a Harwell Boeing (HB) file;
-
msm_to_hb_test
-
msm_to_mm,
a MATLAB code which
writes a MATLAB sparse matrix (MSM) to a Matrix Market (MM) file;
-
msm_to_mm_test
-
msm_to_st,
a MATLAB code which
writes a MATLAB sparse matrix (MSM) to a Sparse Triplet (ST) file;
-
msm_to_st_test
-
mxm,
a MATLAB code which
sets up a matrix multiplication problem A=B*C of arbitrary size,
and compares the time required for IJK, IKJ, JIK, JKI, KIJ and KJI
orderings of the loops.
-
mxm_test
-
naca,
a MATLAB code which
takes the parameters of certain NACA airfoils and returns the
coordinates of a sequence of points that outline the wing shape.
The shape can be displayed with MATLAB graphics.
-
naca_test
-
nas,
a MATLAB code which
runs the NASA kernel benchmark.
-
nas_test
-
navier_stokes_2d_exact,
a MATLAB code which
evaluates an exact solution to the incompressible time-dependent
Navier-Stokes equations (NSE) over an arbitrary domain in 2D.
-
navier_stokes_2d_exact_test
-
navier_stokes_3d_exact,
a MATLAB code which
evaluates an exact solution to the incompressible time-dependent
Navier-Stokes equations (NSE) over an arbitrary domain in 3D.
-
navier_stokes_3d_exact_test
-
navier_stokes_mesh2d,
a MATLAB code which
handles meshes for several
2D test problems involving the Navier Stokes equations (NSE)
for fluid flow, provided by Leo Rebholz.
-
navier_stokes_mesh2d_test
-
navier_stokes_mesh3d,
a MATLAB code which
handles meshes for several
3D test problems involving the Navier Stokes equations (NSE)
for fluid flow, provided by Leo Rebholz.
-
navier_stokes_mesh3d_test
-
ncm,
a MATLAB code which
accompanies the textbook "Numerical Computing with MATLAB",
by Cleve Moler, and illustrates algorithms for
the 3n+1 problem, blackjack, eigenvalue computations,
fast Fourier transforms, Fibonacci numbers, file encryption,
the flame differential equation, the fractal fern,
the Lorenz differential equation, a membrane partial
differential equation,
minimization of a scalar function,
ordinary differential equations, the pendulum differential equation,
piecewise cubic Hermite interpolation, polynomial interpolation,
quadrature for approximate integration,
random number generation,
tridiagonal linear system solution, the singular value
decomposition, solution of a nonlinear equation.
-
ncm_test
-
nearest_interp_1d,
a MATLAB code which
interpolates a set of data using a piecewise constant (PWC)
interpolant defined by the nearest neighbor criterion.
-
nearest_interp_1d_test
-
nearest_neighbor,
a MATLAB code which
is given two sets of M-dimensional points R and S;
For each point in S, it finds the closest point in R.
The code is by Richard Brown.
-
nearest_neighbor_test
-
neighbor_risk,
a MATLAB code which
records information about neighboring pairs of territories
in the game of RISK.
-
neighbor_risk_test
-
neighbor_states,
a MATLAB code which
records information about pairs of US states which are neighbors.
-
neighbor_states_test
-
neighbors_to_metis_graph,
a MATLAB code which
reads a file describing the neighbor
structure of a mesh of triangles or tetrahedrons, and writes a
metis_graph() file suitable for input to one of the family of
programs based on metis();
-
neighbors_to_metis_graph_test
-
nelder_mead,
a MATLAB code which
implements the Nelder-Mead algorithm for the minimization of a
scalar function of several variables, by Jeff Borggaard.
-
nelder_mead_test
-
nested_sequence_display,
a MATLAB code which
displays nested sequences.
-
nested_sequence_display_test
-
netcdf_test,
a MATLAB code which
reads and writes netcdf files.
-
neural_network,
a MATLAB code which
illustrates the use of neural networks for deep learning,
using back propagation and stochastic gradient descent,
by Catherine Higham and Desmond Higham.
-
neural_network_test
-
newton_interp_1d,
a MATLAB code which
finds a polynomial interpolant to data using Newton divided
differences.
-
newton_interp_1d_test
-
newton_rc,
a MATLAB code which
solves a system of nonlinear equations
by Newton's method, using reverse communication (RC).
-
newton_rc_test
-
niederreiter2,
a MATLAB code which
computes the Niederreiter M dimensional
Quasi Mont Carlo (QMC) sequence, base 2;
-
niederreiter2_test
-
nint_exactness_mixed,
a MATLAB code which
measures the exactness of an M-dimensional quadrature rule
based on a mixture of 1D quadrature rule factors.
-
nint_exactness_mixed_test
-
nintlib,
a MATLAB code which
implements approximate integration (quadrature) in M dimensions;
-
nintlib_test
-
nonlin_bisect,
a MATLAB code which
interactively uses bisection to seek a zero of a function f(x)
within a domain a ≤ x ≤ b;
-
nonlin_bisect_test
-
nonlin_fixed_point,
a MATLAB code which
interactively uses fixed point iteration x=g(x) to seek a zero of a
function f(x) given a starting point x0 and iterations it;
-
nonlin_fixed_point_test
-
nonlin_newton,
a MATLAB code which
interactively uses the Newton method to find the zero of a function,
given formulas for f(x), f'(x), and a starting point.
-
nonlin_newton_test
-
nonlin_regula,
a MATLAB code which
interactively uses the regula falsi method to seek a zero
of a function f(x) within a change of sign interval [a,b];
-
nonlin_regula_test
-
nonlin_secant,
a MATLAB code which
interactively uses the secant method to seek a zero of a function f(x)
given two starting estimates a and b.
-
nonlin_secant_test
-
nonlin_snyder,
a MATLAB code which
interactively uses the Snyder method to seek a zero
of a function f(x) within a change of sign interval [a,b];
-
nonlin_snyder_test
-
norm_l1,
a MATLAB code which
interactively estimates the L1 norm of a function over an interval [A,B],
with the function entered as a string.
-
norm_l1_test
-
norm_l2,
a MATLAB code which
interactively estimates the L2 norm of a function over an interval [A,B],
with the function entered as a string.
-
norm_l2_test
-
norm_loo,
a MATLAB code which
interactively estimates the L-infinity norm of a function over
an interval [A,B],
with the function entered as a string.
-
norm_loo_test
-
norm_rms,
a MATLAB code which
interactively estimates the root mean square (RMS) norm of a function
over an interval [A,B],
with the function entered as a string.
-
norm_rms_test
-
normal,
a MATLAB code which
implements normal random number generators (RNG) for
real and complex arithmetic, for scalars, vectors, and matrices.
-
normal_test
-
normal_dataset,
a MATLAB code which
creates a multivariate normal random dataset and writes it to a file.
-
normal_dataset_test
-
normal_ode,
a MATLAB code which
sets up and solves an ordinary differential equation (ODE)
defining the normal probability density function (PDF).
-
normal_ode_test
-
normal01_multivariate_distance,
a MATLAB code which
computes the expected value of the distance
between a pair of points randomly selected from an isotropic
standard normal distribution in M dimensions.
-
normal01_multivariate_distance_test
-
numgrid,
a MATLAB code which
defines and numbers a subset of the nodes in a regular nxn grid
of the [-1,+1]x[-1,+1] unit square. MATLAB includes a built-in
version of this function.
-
numgrid_test
-
obj_display,
a MATLAB code which
displays an OBJ 3D graphics file;
-
obj_display_test
-
obj_io,
a MATLAB code which
reads and writes the data in an OBJ 3D graphics file;
-
obj_io_test
-
obj_to_tri_surface,
a MATLAB code which
reads an OBJ 3D graphics file and extracts
the surface mesh data as a TRI_SURFACE dataset.
-
obj_to_tri_surface_test
-
octopus,
a MATLAB code which
contains some Octave utilities.
-
octopus_test
-
ode_euler,
a MATLAB code which
interactively applies the Euler method to estimate the solution
of an ordinary differential equation (ODE) y'=f(x,y),
over the interval [a,b],
with initial condition y(a)=ya, using n steps.
-
ode_euler_test
-
ode_euler_backward,
a MATLAB code which
interactively applies the backward Euler method to estimate the solution
of an ordinary differential equation (ODE) y'=f(x,y),
over the interval [a,b],
with initial condition y(a)=ya, using n steps.
-
ode_euler_backward_test
-
ode_euler_system,
a MATLAB code which
interactively applies the Euler method to estimate the solution
of a system of ordinary differential equations (ODE) y'=f(x,y), over
the interval [a,b], with initial condition y(a)=ya, using n steps.
-
ode_euler_system_test
-
ode_midpoint,
a MATLAB code which
interactively applies the midpoint method to estimate the solution
of an ordinary differential equation (ODE) y'=f(x,y),
over the interval [a,b],
with initial condition y(a)=ya, using n steps.
-
ode_midpoint_test
-
ode_midpoint_system,
a MATLAB code which
interactively applies the midpoint method to estimate the solution
of a system of ordinary differential equations (ODE) y'=f(x,y),
over the interval [a,b],
with initial condition y(a)=ya, using n steps.
-
ode_midpoint_system_test
-
ode_rk4,
a MATLAB code which
interactively applies a fourth order Runge-Kutta method to estimate
the solution of an ordinary differential equation (ODE) y'=f(x,y),
over the interval [a,b],
with initial condition y(a)=ya, using n steps.
-
ode_rk4_test
-
ode_trapezoidal,
a MATLAB code which
interactively applies the trapezoidal method to estimate
the solution of an ordinary differential equation (ODE) y'=f(x,y),
over the interval [a,b],
with initial condition y(a)=ya, using n steps.
-
ode_trapezoidal_test
-
ode_sweep_parfor,
a MATLAB code which
demonstrates how the parfor() command parallelizes
the computation of a grid of solutions to a parameterized system of
ordinary differential equations (ODE).
-
ode_sweep_parfor_test
-
ode_trapezoidal,
a MATLAB code which
interactively applies the trapezoidal method to estimate the solution
of an ordinary differential equation (ODE) y'=f(x,y),
over the interval [a,b],
with initial condition y(a)=ya, using n steps.
-
ode_trapezoidal_test
-
ode23_test,
a MATLAB code which
calls ode23(), which
is a built-in function for the adaptive solution of systems of
ordinary differential equations (ODE) using a pair of
Runge-Kutta solvers of orders 2 and 3.
-
ode45_test,
a MATLAB code which
calls ode45(), which
is a built-in function for the adaptive solution of systems of
ordinary differential equations (ODE) using a pair of
Runge-Kutta solvers of orders 4 and 5.
-
opt_golden,
a MATLAB code which
interactively estimates a minimizer of a function f(x)
over the interval [a,b], assuming f(x) is unimodular (U-shaped)
over the interval [a,b].
-
opt_golden_test
-
opt_gradient_descent,
a MATLAB code which
interactively seeks a local minimum of a function f(x),
given a formula for the derivative f'(x), a starting point x0,
and a stepsize factor gamma.
-
opt_gradient_descent_test
-
opt_quadratic,
a MATLAB code which
interactively uses quadratic interpolation to estimate a critical
point of a function f(x) given three starting points, an iteration
limit n, and tolerances for x and y.
-
opt_quadratic_test
-
opt_sample,
a MATLAB code which
interactively estimates the minimum and maximum of a function f(x)
over an interval [a,b], using n random sample values,
with the function entered as a string.
-
opt_sample_test
-
oregonator_ode,
a MATLAB code which
sets up and solves the ordinary differential equations (ODE) for
the Oregonator, a model of the Belousov-Zhabotinsky
chemical reaction.
-
oregonator_ode_test
-
ornstein_uhlenbeck,
a MATLAB code which
approximates solutions of the Ornstein-Uhlenbeck
stochastic differential equation (SDE)
using the Euler method, the Euler-Maruyama method,
and the Milstein method.
-
ornstein_uhlenbeck_test
-
oscillator_ode,
a MATLAB code which
sets up and solves the highly oscillatory ordinary differential
equation (ODE).
-
oscillator_ode_test
-
outliers_test,
a MATLAB code which
uses the isoutlier() function, and other techniques, to identify
outliers in data.
-
ozone_ode,
a MATLAB code which
sets up and solves a stiff system of four ordinary differential
equations (ODE) that simulate the daily variation in atmospheric
ozone concentration.
-
ozone_ode_test
-
ozone2_ode,
a MATLAB code which
sets up and solves a stiff system of four ordinary differential
equations (ODE) that simulate the daily variation in atmospheric ozone
concentration. This version of the ozone ODE includes a nitrogen
oxide source term.
-
ozone2_ode_test
-
padua,
a MATLAB code which
returns the coordinates of the 2D Padua points,
as well as interpolation weights or quadrature weights,
and images of the points.
-
padua_test
-
pagerank,
a MATLAB code which
uses the eigenvalue (power method) and surfer
(Markov Chain Monte Carlo MCMC)
approaches to ranking web pages.
-
pagerank_test
-
pagerank2,
a MATLAB code which
considers a specific application of the page rank algorithm.
-
pagerank2_test
-
paraheat_functional,
a MATLAB code which
sets up and solves a parameterized steady heat equation
in a 2D spatial domain, using diffusivity parameterized by vc,
and reporting selected solution values vs,
using a functional framework vs=f(vc).
-
paraheat_functional_test
-
pariomino,
a MATLAB code which
considers pariominoes, which are polyominoes with a checkerboard
parity, and the determination of tilings of a region using a specific
set of pariominoes.
-
pariomino_test
-
partial_digest,
a MATLAB code which
seeks solutions of the partial digest problem.
-
partial_digest_test
-
partition_brute,
a MATLAB code which
uses a brute force algorithm to seek solutions of the partition problem,
splitting a set of integers into two subsets with equal sum.
-
partition_brute_test
-
partition_greedy,
a MATLAB code which
uses a greedy algorithm to seek a solution of the partition problem,
in which a given set of integers is to be split into two groups whose
sums are as close as possible.
-
partition_greedy_test
-
patterson_rule,
a MATLAB code which
returns the points and weights of a 1D Gauss-Patterson quadrature
rule of order 1, 3, 7, 15, 31, 63, 127, 255 or 511.
-
patterson_rule_test
-
pbma_io,
a MATLAB code which
reads or writes graphics files that use the ASCII
Portable Bit Map (PBM) format.
-
pbma_io_test
-
pce_burgers,
a MATLAB code which
solves a version of the time-dependent viscous Burgers equation,
with uncertain viscosity, using a polynomial chaos expansion (PCE)
in terms of Hermite polynomials, by Gianluca Iaccarino.
-
pce_burgers_test
-
pce_legendre,
a MATLAB code which
sets up the system matrix for a polynomial chaos expansion (PCE),
using Legendre polynomials with a linear factor, applied to a 2D
partial differential equation (PDE) with a stochastic diffusion
coefficient.
-
pce_legendre_test
-
pce_ode_hermite,
a MATLAB code which
sets up a simple scalar ordinary differential equation (ODE)
for exponential decay with an uncertain decay rate,
using a polynomial chaos expansion (PCE) in terms of Hermite polynomials.
-
pce_ode_hermite_test
-
pdepe_test,
a MATLAB code which
uses pdepe(), which
solves an initial boundary value problem (IBVP) in one spatial
dimension.
-
pdflib,
a MATLAB code which
evaluates Probability Density Functions (PDF)
and produces random samples from them,
including beta, binomial, chi, exponential, gamma, inverse chi,
inverse gamma, multinomial, normal, scaled inverse chi, and uniform.
-
pdflib_test
-
peak_movie,
a MATLAB code which
creates a sequence of frames, and then an animation or movie
from the data displayed by the peaks() function.
-
peak_movie_test
-
pendulum_comparison_ode,
a MATLAB code which
compares the linear and nonlinear ordinary differential equations
(ODE) that represent the behavior of a pendulum of length L
under a gravitational force of strength G.
-
pendulum_comparison_ode_test
-
pendulum_double_ode,
a MATLAB code which
sets up and solves the double pendulum ordinary differential
equation (ODE).
-
pendulum_double_ode_test
-
pendulum_double_ode_movie,
a MATLAB code which
solves the double pendulum ordinary differential equation (ODE)
for a given set of initial conditions and parameters, and makes
a movie of the results.
-
pendulum_double_ode_movie_test
-
pendulum_elastic_ode
a MATLAB code which
sets up and solves the ordinary differential equations (ODE) that
represent the behavior of a nonlinear elastic pendulum, with
gravitational force G, spring constant K, unstretched length L,
and mass M.
-
pendulum_elastic_ode_test
-
pendulum_nonlinear_exact,
a MATLAB code which
evaluates an exact formula for the solution of the
the ordinary differential equations (ODE) that represent
the behavior of a nonlinear pendulum of length L under a
gravitational force of strength G.
-
pendulum_nonlinear_exact_test
-
pendulum_nonlinear_ode,
a MATLAB code which
sets up and solves the ordinary differential equations (ODE)
that represent a nonlinear model of the behavior
of a pendulum of length L under a gravitational force of strength G.
-
pendulum_nonlinear_ode_test
-
pendulum_ode,
a MATLAB code which
sets up and solves the ordinary differential equations (ODE) that
represent a linear model of the behavior
of a pendulum of length L under a gravitational force of strength G.
-
pendulum_ode_test
-
pendulum_ode_period,
a MATLAB code which
sets up and solves a system of
ordinary differential equations (ODE) that represent the behavior
of a linear pendulum of length L under a gravitational force of
strength G, in order to estimate the period of oscillation.
-
pendulum_ode_period_test
-
pentominoes,
a MATLAB code which
forms or plots any of the 12 members of the pentomino family,
shapes formed from 5 adjacent squares.
-
pentominoes_test
-
perceptron_test,
a MATLAB code which
calculates a classifier of linearly separable data
using the perceptron algorithm.
-
percolation_simulation,
a MATLAB code which
simulates a percolation system. A rectangular region is decomposed
into a grid of MxN squares. Each square may be porous or solid.
We are interested in a path of porous squares connecting the top and
bottom, or the left and right boundaries. The original MATLAB code
was written by Ian Cooper.
-
percolation_simulation_test
-
permutation_distance,
a MATLAB code which
estimates the expected value of the Ulam distance
between a pair of randomly selected permutations of the same order.
-
permutation_distance_test
-
persistence,
a MATLAB code which
demonstrates how to initialize, get, or set data stored
within a function, using static/persistent/saved/local memory.
-
persistence_test
-
pgma_io,
a MATLAB code which
reads or writes graphics files that use the ASCII
Portable Gray Map (PGM) format.
-
pgma_io_test
-
pi_spigot,
a MATLAB code which
produces any number of digits of the decimal expansion of pi.
-
pi_spigot_test
-
pic,
a MATLAB code which
uses the Particle In Cell (PIC) method to simulate the motion of
electrically charged particles past a plate, and is intended as
a starting point for implementing a parallel version.
-
pic_test
-
pink_noise,
a MATLAB code which
computes a pink noise signal obeying a 1/f power law.
-
pink_noise_test
-
plasma_matrix,
a MATLAB code which
sets up a matrix associated with a problem in plasma physics.
-
plasma_matrix_test
-
ply_display,
a MATLAB code which
displays an image of a 3D graphics file in PLY format;
-
ply_display_test
-
ply_io,
a MATLAB code which
reads or writes a 3D graphics file in PLY format,
by Greg Turk;
-
ply_io_test
-
ply_to_tri_surface,
a MATLAB code which
reads a PLY file describing a 3D polygonal mesh, and reformulates
the surface mesh data as 3D mesh of triangles, a TRI_SURFACE dataset.
-
ply_to_tri_surface_test
-
poisson_1d,
a MATlAB code which
solves a discretized version of the Poisson equation -uxx = f(x)
on the interval a ≤ x ≤ b, with Dirichlet boundary conditions
u(a) = ua, u(b) = ub.
The linear system is solved using Gauss-Seidel iteration.
-
poisson_1d_test
-
poisson_1d_multigrid,
a MATLAB code which
applies the multigrid method to a discretized version of the
1D Poisson equation.
-
poisson_1d_multigrid_test
-
poisson_2d,
a MATLAB code which
solves the Poisson equation in a rectangle,
using finite differences and Jacobi iteration.
-
poisson_2d_test
-
poisson_ell_test,
a MATLAB code which
plots data from a solution of the Poisson equation in the
L-shaped region, as computed by FreeFem++()
and transferred using the ffmatlib() library.
-
poisson_simulation,
a MATLAB code which
simulates a Poisson process in which events randomly occur with an
average waiting time of Lambda.
-
poisson_simulation_test
-
polar_ode,
a MATLAB code which
sets up and solves an ordinary differential equation (ODE)
whose variable is complex, and whose solution should be viewed
in a polar coordinate plot.
-
polar_ode_test
-
polpak,
a MATLAB code which
evaluates a variety of mathematical functions, polynomials, and
sequences, including Bell, Benford, Bernoulli, Bernstein, Cardan,
Catalan, Charlier, Chebyshev, Collatz, Delannoy, Euler, Fibonacci,
Gegenbauer, Gudermannian, Harmonic, Hermite, Hofstadter,
Hypergeometric 2F1, Jacobi,
Krawtchouk, Laguerre, Lambert, Legendre, Lerch, Meixner, Mertens,
Moebius, Motzkin, Phi, Stirling Number, Tau, Tribonacci, Zernike.
-
polpak_test
-
polygon,
a MATLAB code which
computes properties of an arbitrary polygon in the plane, defined
by a sequence of vertices, including interior angles, area, centroid,
containment of a point, convexity, counter clockwise ordering,
diameter, distance to a point, inradius, lattice area, nearest point
in set, outradius, uniform sampling, and triangulation.
-
polygon_test
-
polygon_average,
a MATLAB code which
demonstrates a process of repeatedly averaging and normalizing the
vertices of a polygon, illustrating a property of the power method.
-
polygon_average_test
-
polygon_distance,
a MATLAB code which
computes the expected value of the distance
between a pair of points randomly selected from the interior of
a polygon in 2D.
-
polygon_distance_test
-
polygon_grid,
a MATLAB code which
generates a grid of points
over the interior of a polygon in 2D.
-
polygon_grid_test
-
polygon_integrals,
a MATLAB code which
returns the exact value of the integral of any monomial
over the interior of a polygon in 2D.
-
polygon_integrals_test
-
polygon_minkowski,
a MATLAB code which
converts polygons between the vertex representation and the Minkowski
representation, which uses a sequence of (non-unit) normal vectors.
-
polygon_minkowski_test
-
polygon_monte_carlo,
a MATLAB code which
applies a Monte Carlo method to estimate the integral of a function
over the interior of a polygon in 2D.
-
polygon_monte_carlo_test
-
polygon_triangulate,
a MATLAB code which
triangulates a (possibly nonconvex) polygon in 2D,
based on a C program by Joseph ORourke;
-
polygon_triangulate_test
-
polygonal_surface_display,
a MATLAB code which
displays a surface in 3D described as a set of polygons;
-
polygonal_surface_display_test
-
polyiamonds,
a MATLAB code which
works with polyiamonds, simple shapes constructed by edgewise
connections of congruent equilateral triangles.
-
polyiamonds_test
-
polynomial,
a MATLAB code which
adds, multiplies, differentiates, evaluates and prints multivariate
polynomials in a space of M dimensions.
-
polynomial_test
-
polynomial_conversion,
a MATLAB code which
converts representations of a polynomial between monomial, Bernstein,
Chebyshev, Gegenbauer, Hermite, Laguerre and Legendre forms.
-
polynomial_conversion_test
-
polynomial_multiply,
a MATLAB code which
multiplies two polynomials p(x) and q(x).
-
polynomial_multiply_test
-
polynomial_resultant,
a MATLAB code which
computes the resultant R of univariate polynomials P and Q.
-
polynomial_resultant_test
-
polynomial_resultant_symbolic_test,
a MATLAB code which
calls the symbolic function resultant(), which
computes the resultant R of univariate polynomials P and Q.
-
polynomial_root_bound,
a MATLAB code which
computes the Cauchy bound on the magnitude of all roots
of a polynomial with complex coefficients.
-
polynomial_root_bound_test
-
polynomials,
a MATLAB code which
defines multivariate polynomials over rectangular domains, for
which certain information is to be determined, such as the maximum
and minimum values.
-
polynomials_test
-
polyomino_parity,
a MATLAB code which
uses parity considerations to determine whether a given set of
polyominoes tile a specified region.
-
polyomino_parity_test
-
polyominoes,
a MATLAB code which
defines, solves, and plots a variety of polyomino tiling problems,
which are solved by a direct algebraic approach, instead of the
more typical brute-force or backtracking methods.
-
polyominoes_test
-
porous_medium_exact,
a MATLAB code which
returns an exact solution of the porous medium equation (PME),
dudt=Del^2(u^m), a partial differential equation (PDE) related
to the diffusion equation, based on the Barenblatt solution.
-
porous_medium_exact_test
-
power_method,
a MATLAB code which
carries out the power method for finding a dominant eigenvalue
and its eigenvector.
-
power_method_test
-
power_rule,
a MATLAB code which
constructs a power rule, that is, a product quadrature rule
from identical 1D factor rules.
-
power_rule_test
-
pplane9,
a MATLAB code which
allows a user to interactively explore the phase plane of a system
of autonomous ordinary differential equations. On starting the
program, the user is given an interface in which to enter the
equations and the screen limits, as well as a graphics screen
on which the direction field is shown. Clicking any point in
the graphics screen results in a trace of the phase plane curve
through that point.
The program is by Hugh Harvey and George Williams.
With every new release of MATLAB, this program breaks again!
-
ppma_io,
a MATLAB code which
reads or writes graphics files that use the ASCII
Portable Pixel Map (PPM) format.
-
ppma_io_test
-
pram,
a MATLAB code which
considers the pram puzzle, a smaller version of the eternity
puzzle. The pram puzzle specifies a region R composed of 2304
30-60-90 triangles, and a set of 64 "tiles",
consisting of 36 30-60-90 triangles, and seeks an arrangement
of the tiles that exactly covers the region.
-
pram_test
-
pram_cplex_test
a BASH code which
calls cplex(), to read the LP file defining the pram tiling problem,
solve the linear programming problem, and write the solution to a file.
-
pram_view,
a MATLAB code which
considers the pram puzzle, and applies a given set of rotations,
reflections and translations to the 64 tiles in order to reconstruct
the pram region, thus verifying a known solution to the problem,
as well as the correctness of the tile definitions.
-
praxis,
a MATLAB code which
minimizes a scalar function of several variables, without
requiring derivative information,
by Richard Brent.
-
praxis_test
-
predator_prey_ode,
a MATLAB code which
sets up and solves a time-dependent predator-prey system
of ordinary differential equations (ODE),
for which a limit cycle exists.
-
predator_prey_ode_test
-
predator_prey_ode_period,
a MATLAB code which
sets up and solves a time-dependent predator-prey system
of ordinary differential equations (ODE) in order to estimate
the period of the limit cycle.
-
predator_prey_ode_period_test
-
prime,
a MATLAB code which
counts the number of primes between 1 and N,
and is intended as a starting point for a parallel version.
-
prime_test
-
prime_factors,
a MATLAB code which
returns a list of the prime factors of an integer.
-
prime_factors_test
-
prime_fermat,
a MATLAB code which
applies Fermat's primality test to an integer n, which always
correctly identifies primes, but sometimes also accepts nonprimes.
Nonetheless, the test is useful for weeding out most nonprimes.
The accuracy of the test can be improved by running it for several
bases.
-
prime_fermat_test
-
prime_parfor,
a MATLAB code which
counts primes between 1 and N,
running in parallel using the parfor() feature of MATLAB.
-
prime_parfor_test
-
prime_pi,
a MATLAB code which
evaluates Pi(n), the number of primes less than or equal to an integer n.
-
prime_pi_test
-
prime_plot,
a MATLAB code which
displays a box plot of the prime and composite numbers.
-
prime_plot_test
-
prism_jaskowiec_rule,
a MATLAB code which
returns symmetric quadrature rules, with exactness up to total
degree 20, over the interior of a prism with triangular base,
by Jan Jaskowiec, Natarajan Sukumar.
-
prism_jaskowiec_rule_test
-
prism_witherden_rule,
a MATLAB code which
returns a symmetric Witherden quadrature rule for a prism with
triangular base, with exactness up to total degree 10.
-
prism_witherden_rule_test
-
prob,
a MATLAB code which
evaluates, samples, inverts, and characterizes
Probability Density Functions (PDF)
and Cumulative Density Functions (CDF), including anglit, arcsin,
benford, birthday, bernoulli, beta_binomial, beta, binomial, bradford,
burr, cardiod, cauchy, chi, chi squared, circular, cosine, deranged,
dipole, dirichlet mixture, discrete, empirical, english sentence and
word length, error, exponential, extreme values, f, fisk, folded normal,
frechet, gamma, generalized logistic, geometric, gompertz, gumbel,
half normal, hypergeometric, inverse gaussian, laplace, levy, logistic,
log normal, log series, log uniform, lorentz, maxwell, multinomial,
nakagami, negative binomial, normal, pareto, planck, poisson,
power, quasigeometric, rayleigh, reciprocal, runs, sech, semicircular,
student t, triangle, uniform, von mises, weibull, zipf.
-
prob_test
-
product_rule,
a MATLAB code which
creates an M dimensional quadrature rule
from a product of distinct 1d quadrature rules;
-
product_rule_test
-
profile_data,
a MATLAB code which
carries out some numerical exercises based on data that came from
tracing the profile of a face.
-
profile_data_test
-
puzzles,
a MATLAB code which
solves simple puzzles;
-
pwc_plot_1d,
a MATLAB code which
converts the definition of a piecewise constant (PWC) function
of a 1D argument into plottable data.
-
pwc_plot_1d_test
-
pwc_plot_2d,
a MATLAB code which
converts the definition of a piecewise constant (PWC) function
of a 2D argument into plottable data.
-
pwc_plot_2d_test
-
pwl_approx_1d,
a MATLAB code which
approximates a set of data using a piecewise linear (PWL) function.
-
pwl_approx_1d_test
-
pwl_interp_1d,
a MATLAB code which
interpolates a set of data using a piecewise linear (PWL) function.
-
pwl_interp_1d_test
-
pwl_interp_2d,
a MATLAB code which
evaluates a piecewise linear (PWL) interpolant to data defined on
a regular 2D grid.
-
pwl_interp_2d_test
-
pwl_interp_2d_scattered,
a MATLAB code which
evaluates a piecewise linear (PWL) interpolant to data which is available
at an irregularly arranged set of points.
-
pwl_interp_2d_scattered_test
-
pwl_product_integral,
a MATLAB code which
calculates the exact value of the integral of the product of two
piecewise linear (PWL) functions f(x) and g(x).
-
pwl_product_integral_test
-
pyramid_exactness,
a MATLAB code which
investigates the polynomial exactness of a quadrature rule
over the interior of the unit pyramid in 3D.
-
pyramid_exactness_test
-
pyramid_felippa_rule,
a MATLAB code which
returns a Felippa quadrature rule for approximating integrals
over the interior of a pyramid in 3D.
-
pyramid_felippa_rule_test
-
pyramid_grid,
a MATLAB code which
computes a grid of points
over the interior of the unit pyramid in 3D;
-
pyramid_grid_test
-
pyramid_integrals,
a MATLAB code which
returns the exact value of the integral of any monomial
over the interior of the unit pyramid in 3D.
-
pyramid_integrals_test
-
pyramid_jaskowiec_rule,
a MATLAB code which
returns quadrature rules, with exactness up to total degree 20,
over the interior of a pyramid in 3D,
by Jan Jaskowiec, Natarajan Sukumar.
-
pyramid_jaskowiec_rule_test
-
pyramid_monte_carlo,
a MATLAB code which
applies a Monte Carlo method to estimate integrals of a function
over the interior of the unit pyramid in 3D;
-
pyramid_monte_carlo_test
-
pyramid_rule,
a MATLAB code which
computes a conical product quadrature rule
over the interior of the unit pyramid in 3D.
-
pyramid_rule_test
-
pyramid_witherden_rule,
a MATLAB code which
returns a Witherden quadrature rule, with exactness up to total
degree 10, over the interior of a pyramid.
-
pyramid_witherden_rule_test
-
qr_solve,
a MATLAB code which
computes the linear least squares (LLS) solution of a system A*x=b
using the QR factorization.
-
qr_solve_test
-
quad_fast_rule,
a MATLAB code which
rapidly defines certain quadrature rules
for approximating an integral;
-
quad_fast_rule_test
-
quad_gauss,
a MATLAB code which
interactively uses an n-point Gauss quadrature rule to estimate
the integral of a function f(x) in the interval [a,b].
-
quad_gauss_test
-
quad_monte_carlo,
a MATLAB code which
interactively uses n random samples to estimate
the integral of a function f(x) in the interval [a,b].
-
quad_monte_carlo_test
-
quad_parfor,
a MATLAB code which
estimates an integral using quadrature,
using parfor() to enable parallel execution.
-
quad_parfor_test
-
quad_rule,
a MATLAB code which
defines quadrature rules for approximating an integral;
-
quad_rule_test
-
quad_serial,
a MATLAB code which
applies a quadrature rule to estimate an integral,
intended as a starting point for parallelization exercises.
-
quad_serial_test
-
quad_trapezoid,
a MATLAB code which
interactively applies a trapezoid rule using n intervals
to estimate the integral of a function f(x) over an interval [a,b].
-
quad_trapezoid_test
-
quad2d,
a MATLAB code which
estimates an integral over a 2D rectangle using quadrature,
intended as the starting point for program optimization
or parallelization.
-
quad2d_test
-
quadex_ode
a MATLAB code which
sets up and solves a stiff ordinary differential equation (ODE), whose
exact solution is a parabola, but for which errors grow exponentially.
-
quadex_ode_test
-
quadmom,
a MATLAB code which
computes a Gaussian quadrature rule for a weight function rho(x)
based on the Golub-Welsch procedure that only requires knowledge
of the moments of rho(x).
-
quadmom_test
-
quadprog_test,
calls quadprog() to solve problems in quadratic programming.
-
quadrature_golub_welsch,
a MATLAB code which
computes the points and weights of a Gaussian quadrature rule using
the Golub-Welsch procedure.
-
quadrature_golub_welsch_test
-
quadrature_least_squares,
a MATLAB code which
computes weights for sub-interpolatory quadrature rules,
that is, it estimates integrals by integrating a polynomial that
approximates the function data in a least squares sense.
-
quadrature_least_squares_test
-
quadrature_weights_vandermonde,
a MATLAB code which
computes the weights of a quadrature rule using the Vandermonde
matrix, assuming that the points have been specified.
-
quadrature_weights_vandermonde_test
-
quadrature_weights_vandermonde_2d,
a MATLAB code which
computes the weights of a 2D quadrature rule using the Vandermonde
matrix, assuming that the points have been specified.
-
quadrature_weights_vandermonde_2d_test
-
quadrilateral,
a MATLAB code which
carries out geometric calculations on quadrilaterals, including
angles, area, distances, nearest point, point containment, perimeter,
and random generation.
-
quadrilateral_test
-
quadrilateral_mesh,
a MATLAB code which
handles meshes of quadrilaterals over a 2D region;
-
quadrilateral_mesh_test
-
quadrilateral_mesh_order1_display,
a MATLAB code which
plots piecewise constant (PWC) data associated
with a mesh of quadrilaterals;
-
quadrilateral_mesh_order1_display_test
-
quadrilateral_mesh_rcm,
a MATLAB code which
computes the Reverse Cuthill McKee (RCM) reordering
for nodes in a mesh of 4-node quadrilaterals.
-
quadrilateral_mesh_rcm_test
-
quadrilateral_surface_display,
a MATLAB code which
plots piecewise bilinear data associated with a quadrilateral_surface,
that is, a 3D surface defined by a quadrilateral mesh;
-
quadrilateral_surface_display_test
-
quadrilateral_witherden_rule,
a MATLAB code which
returns a symmetric Witherden quadrature rule for the quadrilateral,
with exactness up to total degree 21.
-
quadrilateral_witherden_rule_test
-
quality,
a MATLAB code which
measures the dispersion of pointsets in M dimensions;
-
quality_test
-
quasiperiodic_ode,
a MATLAB code which
sets up and solves a system of
ordinary differential equations (ODE) for a problem with a
quasiperiodic solution.
-
quasiperiodic_ode_test
-
quaternions,
a MATLAB code which
carries out some simple arithmetic operations for quaternions.
-
quaternions_test
-
r8_scale,
a MATLAB code which
computes the "next" and "previous" real numbers.
-
r8_scale_test
-
r83,
a MATLAB code which
contains linear algebra routines for r83 matrices
(real, 64 bit, tridiagonal 3xN format).
-
r83_test
-
r83_np,
a MATLAB code which
contains linear algebra routines for r83_np matrices
(real, 64 bit, tridiagonal 3xN format, nonpivoting factorization).
-
r83_np_test
-
r83p,
a MATLAB code which
contains linear algebra routines for r83p matrices
(real, 64 bit, tridiagonal periodic format).
-
r83p_test
-
r83s,
a MATLAB code which
contains linear algebra routines for r83s matrices
(real, 64 bit, tridiagonal scalar format).
-
r83s_test
-
r83t,
a MATLAB code which
contains linear algebra routines for r83t matrices
(real, 64 bit, tridiagonal Mx3 format).
-
r83t_test
-
r83v,
a MATLAB code which
contains linear algebra routines for r83v matrices
(real, 64 bit, tridiagonal three vector format).
-
r83v_test
-
r85,
a MATLAB code which
contains linear algebra routines for r85 matrices
(real, 64 bit, pentadiagonal format).
-
r85_test
-
r8bb,
a MATLAB code which
contains linear algebra routines for r8bb matrices
(real, 64 bit, border banded format).
-
r8bb_test
-
r8blt,
a MATLAB code which
contains linear algebra routines for r8blt matrices
(real, 64 bit, band lower triangular format).
-
r8blt_test
-
r8bto,
a MATLAB code which
contains linear algebra routines for r8bto matrices
(real, 64 bit, block Toeplitz format).
-
r8bto_test
-
r8but,
a MATLAB code which
contains linear algebra routines for r8but matrices
(real, 64 bit, band upper triangular format).
-
r8but_test
-
r8cb,
a MATLAB code which
contains linear algebra routines for r8cb matrices
(real, 64 bit, Compressed Band format).
-
r8cb_test
-
r8cbb,
a MATlAB code which
contains linear algebra routines for r8cbb matrices
(real, 64 bit, Compressed Border Banded format).
-
r8cbb_test
-
r8ccs,
a MATLAB code which
contains linear algebra routines for r8ccs matrices:
real, 64 bit, Compressed Column Storage (CCS) format.
-
r8ccs_test
-
r8ci,
a MATLAB code which
contains linear algebra routines for r8ci matrices
(real, 64 bit, circulant format).
-
r8ci_test
-
r8col,
a MATLAB code which
contains utility routines for an R8COL, that is,
a real 64 bit MxN array, considered as N column vectors,
each of length M. The data may be thought of as a matrix of
multiple columns, and many operations will be carried out
columnwise.
-
r8col_test
-
r8crs,
a MATLAB code which
contains linear algebra routines for R8CRS matrices:
real, 64 bit, Compressed Row Storage (CRS) format.
-
r8crs_test
-
r8gb,
a MATLAB code which
contains linear algebra routines for r8gb matrices
(real, 64 bit, General Banded format).
-
r8gb_test
-
r8gd,
a MATLAB code which
contains linear algebra routines for r8gd matrices
(real, 64 bit, general diagonal format).
-
r8gd_test
-
r8ge,
a MATLAB code which
contains linear algebra routines for R8GE matrices
(real, 64 bit, General format).
-
r8ge_test
-
r8ge_np,
a MATLAB code which
contains nonpivoting linear algebra routines for r8ge_np matrices
(real, 64 bit, General Nonpivoting format).
-
r8ge_np_test
-
r8lib,
a MATLAB code which
contains utilities for real 64 bit (R8) arithmetic.
-
r8lib_test
-
r8lt,
a MATLAB code which
contains linear algebra routines for R8LT matrices:
real, 64 bit, Lower Triangular.
-
r8lt_test
-
r8ltt,
a MATLAB code which
contains linear algebra routines for r8ltt matrices
(real, 64 bit, lower triangular Toeplitz format).
-
r8ltt_test
-
r8ncf,
a MATLAB code which
contains linear algebra routines for r8ncf matrices
(real, 64 bit, nonsymmetric coordinate format).
-
r8ncf_test
-
r8pbl,
a MATLAB code which
contains linear algebra routines for r8pbl matrices
(real, 64 bit, symmetric positive definite (SPD) band lower format).
-
r8pbl_test
-
r8pbu,
a MATLAB code which
contains linear algebra routines for r8pbu matrices
(real, 64 bit, symmetric positive definite (SPD) band upper format).
-
r8pbu_test
-
r8po,
a MATLAB code which
contains linear algebra routines for r8po matrices
(real, 64 bit, symmetric positive definite (SPD) format).
-
r8po_test
-
r8poly,
a MATLAB code which
operates on real polynomials, including evaluation, differentiation,
integration, multiplication, synthetic division, shifting the
base, computing a power, taking the norm. It also defines
Chebyshev, Lagrange and Legendre polynomials.
-
r8poly_test
-
r8pp,
a MATLAB code which
contains linear algebra routines for r8pp matrices
(real, 64 bit, symmetric positive definite (SPD) packed format).
-
r8pp_test
-
r8ri,
a MATLAB code which
contains linear algebra routines for r8ri matrices
(real, 64 bit, row indexed format).
-
r8ri_test
-
r8row,
a MATLAB code which
contains utility routines for an R8ROW, that is,
a real 64 bit MxN array, considered as M row vectors,
each of length N. The data may be thought of as a matrix of
multiple rows, and many operations will be carried out rowwise.
-
r8row_test
-
r8sd,
a MATLAB code which
contains linear algebra routines for r8sd matrices
(real, 64 bit, symmetric diagonal format).
-
r8sd_test
-
r8sm,
a MATLAB code which
contains linear algebra routines for r8sm matrices
(real, 64 bit, Sherman-Morrison A-u*v' format).
-
r8sm_test
-
r8sr,
a MATLAB code which
carries out linear algebra operations for r8sr matrices
(real, 64 bit, diagonal + compressed row offdiagonal format).
-
r8sr_test
-
r8ss,
a MATLAB code which
carries out linear algebra operations for r8ss matrices
(real, 64 bit, symmetric skyline format).
-
r8ss_test
-
r8st,
a MATLAB code which
contains linear algebra routines for R8ST matrices:
real, 64 bit, Sparse Triplet.
-
r8st_test
-
r8sto,
a MATLAB code which
contains linear algebra routines for r8sto matrices
(real, 64 bit, symmetric Toeplitz N format).
-
r8sto_test
-
r8to,
a MATLAB code which
contains linear algebra routines for r8to matrices
(real, 64 bit, Toeplitz 2*N-1 format).
-
r8to_test
-
r8ut,
a MATLAB code which
contains linear algebra routines for r8ut matrices:
real, 64 bit, Upper Triangular.
-
r8ut_test
-
r8utp,
a MATLAB code which
carries out linear algebra operations on r8utp matrices,
real 64 bit, Upper Triangular Packed format.
-
r8utp_test
-
r8utt,
a MATLAB code which
contains linear algebra routines for r8utt matrices
(real, 64 bit, upper triangular Toeplitz format).
-
r8utt_test
-
r8vm,
a MATLAB code which
contains linear algebra routines for r8vm matrices
(real, 64 bit, vandermonde format).
-
r8vm_test
-
randlc,
a MATLAB code which
implements a random number generator (RNG)
used by the nas() benchmarks.
-
randlc_test
-
random_data,
a MATLAB code which
uses a random number generator (RNG) to sample points distributed
according to various probability density functions (PDF),
spatial dimensions, and geometries, including the
annulus, cube, ellipse, ellipsoid, polygon, simplex and sphere.
-
random_data_test
-
random_sorted,
a MATLAB code which
generates vectors of random values which are already sorted.
-
random_sorted_test
-
random_walk_1d_simulation,
a MATLAB code which
simulates a random walk in a 1-dimensional region.
-
random_walk_1d_simulation_test
-
random_walk_2d_avoid_simulation,
a MATLAB code which
simulates a self-avoiding random walk in a 2-dimensional region.
-
random_walk_2d_avoid_simulation_test
-
random_walk_2d_simulation,
a MATLAB code which
simulates a random walk in a 2-dimensional region.
-
random_walk_2d_simulation_test
-
random_walk_3d_simulation,
a MATLAB code which
simulates a random walk in a 3-dimensional region.
-
random_walk_3d_simulation_test
-
ranlib,
a MATLAB code which
produces random samples from Probability Density Functions
(PDF), including Beta, Chi-square Exponential, F, Gamma,
Multivariate normal, Noncentral chi-square, Noncentral F,
Univariate normal, random permutations, Real uniform, Binomial,
Negative Binomial, Multinomial, Poisson and Integer uniform,
by Barry Brown and James Lovato.
-
ranlib_test
-
rbf_interp_1d,
a MATLAB code which
defines and evaluates
radial basis function (RBF) interpolants to 1D data.
-
rbf_interp_1d_test
-
rbf_interp_2d,
a MATLAB code which
defines radial basis function (RBF) interpolants to 2D data.
-
rbf_interp_2d_test
-
rbf_interp_nd,
a MATLAB code which
defines and evaluates radial basis function (RBF) interpolants
to M dimensional data.
-
rbf_interp_nd_test
-
rcm,
a MATLAB code which
applies the Reverse Cuthill McKee (RCM) algorithm for
reordering the nodes of a graph, and reducing the bandwidth of a
corresponding sparse matrix;
-
rcm_test
-
reaction_ode,
a MATLAB code which
sets up and solves the ordinary differential equations (ODE) which model a
simple chemical reaction A+B --k--> C.
-
reaction_ode_test
-
reaction_twoway_ode,
a MATLAB code which
sets up and solves the ordinary differential equations (ODE) which
model a two-way chemical reaction between species W1 and W2.
-
reaction_twoway_ode_test
-
reactor simulation,
a MATLAB code which
is a simple Monte Carlo simulation of the shielding effect of a
slab of a certain thickness in front of a neutron source. This
program was provided as an example with the book "Numerical
Methods and Software."
-
reactor simulation_test
-
readmatrix_test,
a MATLAB code which calls readmatrix(), a built-in function which
reads a data file containing numeric data in columns; it can also
skip one or more initial rows, read only a specified set of columns,
to avoid dealing with text input.
-
readtable_test,
a MATLAB code which calls readtable(), a built-in function which
reads a data file containing data in columns, with some data
being numeric and some text.
-
rectangle_distance,
a MATLAB code which
estimates the distribution and expected value of the distance between
two points picked uniformly at random within a rectangle.
-
rectangle_distance_test
-
region_test,
a MATLAB code which
plots data from an interesting region that was meshed
by FreeFem++() and transferred using the ffmatlib() library.
-
rejection_sample,
a MATLAB code which
demonstrates acceptance/rejection sampling.
-
rejection_sample_test
-
rigid_body_ode,
a MATLAB code which
sets up and solves the ordinary differential equations (ODE)
representing the Euler equations for a rigid body with three
unequal moments of inertia, originally proposed by Fred Krogh.
-
rigid_body_ode_test
-
ring_data,
a MATLAB code which
creates, plots, or saves data generated by sampling a number of
concentric, possibly overlapping rings.
-
ring_data_test
-
ripple_ode,
a MATLAB code which
sets up and solves an ordinary differential equation (ODE) whose
solutions start as ripples and end as hyperbolas.
-
ripple_ode_test
-
risk_matrix,
a MATLAB code which
returns the transition and adjacency matrix for the game of RISK.
-
risk_matrix_test
-
rk1,
a MATLAB code which
solves one or more ordinary differential equations (ODE)
using an explicit Runge-Kutta method of order 1, usually known
as Euler's explicit method.
-
rk1_test
-
rk1_implicit,
a MATLAB code which
solves one or more ordinary differential equations (ODE)
using the Runge-Kutta order 1 implicit method, using fsolve()
to solve the implicit equation, and using a fixed time step.
rk1_implicit() is commonly called the backward Euler method.
-
rk1_implicit_test
-
rk12,
a MATLAB code which
solves an ordinary differential equation (ODE) using a Runge-Kutta
(RK) method of order 2, estimating the local error with a
Runge-Kutta method of order 1.
-
rk12_test
-
rk12_adapt,
a MATLAB code which
defines an adaptive ordinary differential equation (ODE)
solver, using Runge-Kutta (RK) solvers of order 1 and 2.
-
rk12_adapt_test
-
rk2,
a MATLAB code which
solves one or more ordinary differential equations (ODE)
using an explicit Runge-Kutta method of order 2,
also known as Heun's method, the modified Euler method,
or the explicit midpoint method.
-
rk2_test
-
rk2_implicit,
a MATLAB code which
solves one or more ordinary differential equations (ODE)
using the Runge-Kutta order 2 implicit method, using fsolve()
to solve the implicit equation, and using a fixed time step.
rk2_implicit() is also known as the implicit midpoint method.
-
rk2_implicit_test
-
rk23,
a MATLAB code which
applies Runge-Kutta (RK) solvers of order 2 and 3 to a system of
ordinary differential equations (ODE);
-
rk23_test
-
rk34,
a MATLAB code which
applies Runge-Kutta (RK) solvers of order 3 and 4 to a system of
ordinary differential equations (ODE);
-
rk34_test
-
rk4,
a MATLAB code which
applies the fourth order Runge-Kutta (RK) algorithm to estimate the
solution of an ordinary differential equation (ODE)
at the next time step.
-
rk4_test
-
rk45,
a MATLAB code which
applies Runge-Kutta (RK) solvers of order 4 and 5 to a system of
ordinary differential equations (ODE);
-
rk45_test
-
rkf45,
a MATLAB code which
applies a Runge-Kutta-Fehlberg (RKF) solver to a system of
ordinary differential equations (ODE);
-
rkf45_test
-
rng_cliff,
a MATLAB code which
computes a sequence of values from the Cliff random number
generator (RNG).
-
rng_cliff_test
-
rnglib,
a MATLAB code which
implements a random number generator (RNG) with splitting
facilities, allowing multiple independent streams to be computed,
by L'Ecuyer and Cote.
-
rnglib_test
-
robertson_ode,
a MATLAB code which
sets up and solves a system of three nonlinear stiff ordinary
differential equations (ODE) characterizing an autocatalytic
chemical reaction.
-
robertson_ode_test
-
roessler_ode,
a MATLAB code which
sets up and solves the right hand side of the 3D Roessler system
of ordinary differential equations (ODE).
-
roessler_ode_test
-
root_rc,
a MATLAB code which
seeks a solution of a scalar nonlinear equation f(x)=0,
using reverse communication (RC), by Gaston Gonnet.
-
root_rc_test
-
roots_rc,
a MATLAB code which
seeks solutions of a system of nonlinear equations,
using reverse communication (RC), by Gaston Gonnet.
-
roots_rc_test
-
rot13,
a MATLAB code which
enciphers a string using the ROT13 cipher for letters, and the
ROT5 cipher for digits.
-
rot13_test
-
roulette_simulation,
a MATLAB code which
simulates the spinning of a roulette wheel and the evaluation of
certain common roulette bets.
-
roulette_simulation_test
-
row_echelon_integer,
a MATLAB code which
carries out the exact computation of the integer row echelon form
(IREF) and integer reduced row echelon form (IRREF) of an integer
matrix.
-
row_echelon_integer_test
-
rref_test,
a MATLAB code which
calls rref() for the reduced row echelon form (RREF)
of a matrix, which can be singular or rectangular.
-
rubber_band_ode,
a MATLAB code which
sets up and solves a set of ordinary differential equat ions (ODE)
describing a mass suspended by a spring and rubber band, which
exhibits chaotic behavior.
-
rubber_band_ode_test
-
rucklidge_ode,
a MATLAB code which
sets up and solves the Rucklidge ordinary differential equation (ODE),
a model of double convection which embodies a transition to chaos.
-
rucklidge_ode_test
-
sammon_data,
a MATLAB code which
generates six M dimensional datasets for cluster analysis.
-
sammon_data_test
-
sandia_cubature,
a MATLAB code which
computes M-dimensional quadrature rules
for certain regions and weight functions.
-
sandia_cubature_test
-
sandia_rules,
a MATLAB code which
produces 1D quadrature rules of
Chebyshev, Clenshaw Curtis, Fejer 2, Gegenbauer, generalized Hermite,
generalized Laguerre, Hermite, Jacobi, Laguerre, Legendre
and Patterson types.
-
sandia_rules_test
-
sandia_sgmgg,
a MATLAB code which
explores a generalized construction method for sparse grids.
-
sandia_sgmgg_test
-
sandia_sparse,
a MATLAB code which
produces a M-dimensional sparse grid, based on a variety of 1D
quadrature rules; only isotropic grids are generated, that is, the same
rule is used in each dimension, and the same maximum order is used in
each dimension.
-
sandia_sparse_test
-
satisfy_brute,
a MATLAB code which
uses brute force to find all assignments of values to a set of
logical variables which make a complicated logical statement true.
-
satisfy_brute_test
-
satisfy_parfor,
a MATLAB code which
demonstrates, for a particular circuit, an exhaustive search
for solutions of the circuit satisfiability problem,
running in parallel using the parfor() feature.
-
satisfy_parfor_test
-
sawtooth_ode,
a MATLAB code which
sets up and solves an ordinary differential equation (ODE) driven
by a right hand side which is a sawtooth function (periodic,
discontinuous, piecewise linear).
-
sawtooth_ode_test
-
schroedinger_linear_pde,
a MATLAB code which
sets up and solves the complex partial differential equation (PDE)
known as Schroedinger's linear equation:
dudt = i uxx, in one spatial dimension,
with Neumann boundary conditions.
-
schroedinger_linear_pde_test
-
schroedinger_nonlinear_pde,
a MATLAB code which
sets up and solves the complex partial differential equation (PDE)
known as Schroedinger's nonlinear equation:
dudt = i uxx + i gamma * |u|^2 u, in one spatial dimension,
with Neumann boundary conditions.
-
schroedinger_nonlinear_pde_test
-
scip_solution_read,
a MATLAB code which
reads a file created by the integer programming package scip(),
representing the solution of a polyomino tiling problem, and writes
out a simple ASCII file.
-
scip_solution_read_test
-
sde,
a MATLAB code which
illustrates properties of stochastic differential equations (SDE),
and common algorithms for their analysis,
by Desmond Higham;
-
sde_test
-
search_test,
a MATLAB code which
searches integers between A and B for a value J such that F(J) = C.
-
sensitive_ode,
a MATLAB code which
sets up a second order ordinary differential equation (ODE)
which exhibits sensitive dependence on the initial condition.
-
sensitive_ode_test
-
serenity,
a MATLAB code which
considers the serenity puzzle, a smaller version of the eternity
puzzle. The serenity puzzle specifies a dodecagonal region R
composed of 288 30-60-90 triangles, and a set of 8 "tiles",
each consisting of 36 30-60-90 triangles, and seeks an arrangement
of the tiles that exactly covers the region.
-
serenity_test
-
serenity_cplex_test
a BASH code which
calls cplex(), to read the LP file defining the serenity tiling
problem, solve the linear programming problem, and write the
solution to a file.
-
serenity_gurobi_test
a BASH code which
calls gurobi(), to read the LP file defining the serenity tiling
problem, solve the linear programming problem, and write the
solution to a file.
-
set_theory,
a MATLAB code which
implements set theory operations such as union, intersection,
complement, symmetric difference.
-
set_theory_test
-
sftpack,
a MATLAB code which
implements the slow Fourier transform (SFT), intended as a teaching
tool and comparison with the Fast Fourier Transform (FFT).
-
sftpack_test
-
shallow_water_1d,
a MATLAB code which
simulates the evolution of a 1D fluid governed by the
time-dependent shallow water equations (SWE).
-
shallow_water_1d_test
-
shallow_water_1d_display,
a MATLAB code which
displays a solution of the shallow water equations (SWE) in 1D,
generally as computed by the program shallow_water_1d().
-
shallow_water_1d_display_test
-
shallow_water_1d_movie,
a MATLAB code which
solves the partial differential equation (PDE) known
as the shallow water equations (SWE), converting the
solutions to a sequence of graphics frames, which are then
assembled into a movie.
-
shallow_water_1d_movie_test
-
shepard_interp_1d,
a MATLAB code which
defines and evaluates Shepard interpolants to 1D data,
based on inverse distance weighting.
-
shepard_interp_1d_test
-
shepard_interp_2d,
a MATLAB code which
defines and evaluates Shepard interpolants to 2D data,
based on inverse distance weighting.
-
shepard_interp_2d_test
-
shepard_interp_nd,
a MATLAB code which
defines and evaluates Shepard interpolants to M dimensional data,
based on inverse distance weighting.
-
shepard_interp_nd_test
-
sigmoid_derivative,
a MATLAB code which
evaluates derivatives of any order for the sigmoid function
s(x)=1/(1+exp(-x)).
-
sigmoid_derivative_test
-
simplex_coordinates,
a MATLAB code which
computes the Cartesian coordinates of the vertices of
a regular simplex in M dimensions.
-
simplex_coordinates_test
-
simplex_gm_rule,
a MATLAB code which
defines Grundmann-Moeller quadrature rules
over the interior of a triangle in 2D, a tetrahedron in 3D, or
over the interior of the simplex in M dimensions.
-
simplex_gm_rule_test
-
simplex_grid,
a MATLAB code which
generates a regular grid of points
over the interior of an arbitrary simplex in M dimensions.
-
simplex_grid_test
-
simplex_integrals,
a MATLAB code which
returns the exact value of the integral of any monomial
over the interior of the unit simplex in M dimensions.
-
simplex_integrals_test
-
simplex_monte_carlo,
a MATLAB code which
uses the Monte Carlo method to estimate an integral
over the interior of the unit simplex in M dimensions.
-
simplex_monte_carlo_test
-
sine_gordon_exact,
a MATLAB code which
returns an exact solution of the Sine-Gordon equation,
a partial differential equation (PDE) of the form uxy=sin(u).
-
sine_gordon_exact_test
-
sine_transform,
a MATLAB code which
demonstrates properties of the discrete sine transform (DST).
-
sine_transform_test
-
single_linkage_test,
a MATLAB code which
uses the MATLAB single linkage clustering functions.
-
sir_ode,
a MATLAB code which
sets up and solves the ordinary differential equations (ODE) which
simulate the spread of a disease
using the Susceptible/Infected/Recovered (SIR) model.
-
sir_ode_test
-
sir_simulation,
a MATLAB code which
simulates the spread of a disease through a hospital room
of M by N beds, using the Susceptible/Infected/Recovered
(SIR) model.
-
sir_simulation_test
-
slap_io,
a MATLAB code which
reads and writes sparse matrix files in the SLAP format;
-
slap_io_test
-
sling_ode,
a MATLAB code which
sets up and solves a system of ordinary differential equations
(ODE) for which the exact circular solution can only be approximated
for a short interval before it decays to zero.
-
sling_ode_test
-
smolyak_display,
a MATLAB code which
displays the exactness diagram for a 2D Smolyak sparse grid,
by displaying and summing the exactness diagrams for the
component product rules.
-
smolyak_display_test
-
snakes_and_ladders,
a MATLAB code which
provides tools for studying the game of Snakes and Ladders.
-
snakes_and_ladders_simulation,
a MATLAB code which
simulates a one-player game of Snakes and Ladders, to
produce histograms of the count, PDF and CDF estimates for the
length of a one-player game.
-
snakes_and_ladders_simulation_test
-
snakes_game,
a MATLAB code which
simulates a one-player version of the game
of Snakes and Ladders, by Mina Aymin.
-
snakes_matrix,
a MATLAB code which
returns the transition matrix for the game of
Snakes and Ladders.
-
snakes_matrix_test
-
snakes_probability,
a MATLAB code which
computes the game length probabilities for the game of
Snakes and Ladders,
by Desmond Higham and Nicholas Higham.
-
snakes_probability_test
-
sncndn,
a MATLAB code which
evaluates the Jacobi elliptic functions sn(u,m), cn(u,m),
and dn(u,m).
-
sncndn_test
-
sobol,
a MATLAB code which
generates elements of the Sobol M dimensional Quasi Mont Carlo (QMC)
sequence, by Bennett Fox.
-
sobol_test
-
solve,
a MATLAB code which
uses Gauss elimination to solve a linear system A*x=b.
-
solve_test
-
sor,
a MATLAB code which
uses the successive over-relaxation (SOR) iteration
to solve a linear system of equations.
-
sor_test
-
sort_rc,
a MATLAB code which
sorts a list of any kind of objects,
using reverse communication (RC).
-
sort_rc_test
-
sort_test,
a MATLAB code which
calls the sort() function to sort objects of several types.
-
sparse_test,
a MATLAB code which
tests the sparse() function for creating sparse matrices
and carrying out linear algebraic functions on them;
-
sparse_count,
a MATLAB code which
analyzes sparse grids in which a single family
of 1D quadrature rules is used for all spatial dimensions,
with a variety of growth rules.
-
sparse_count_test
-
sparse_display,
a MATLAB code which
reads information defining a matrix of numbers and displays
the sparsity pattern or location of the nonzero elements using
gnuplot(). This operation is already available in the built-in
MATLAB spy() function.
-
sparse_display_test
-
sparse_grid_cc,
a MATLAB code which
creates sparse grids based on Clenshaw-Curtis (CC) quadrature rules.
-
sparse_grid_cc_test
-
sparse_grid_gl,
a MATLAB code which
creates sparse grids based on Gauss-Legendre (GL) rules.
-
sparse_grid_gl_test
-
sparse_grid_hermite,
a MATLAB code which
creates sparse grids based on Gauss-Hermite rules.
-
sparse_grid_hermite_test
-
sparse_grid_hw,
a MATLAB code which
creates sparse grids based on Gauss-Legendre, Gauss-Hermite,
Gauss-Patterson, or a nested variation of Gauss-Hermite rules,
by Florian Heiss and Viktor Winschel.
-
sparse_grid_hw_test
-
sparse_grid_laguerre,
a MATLAB code which
creates sparse grids based on Gauss-Laguerre rules.
-
sparse_grid_laguerre_test
-
sparse_grid_mixed,
a MATLAB code which
creates a sparse grid dataset based on a mixed set of 1D factor rules.
-
sparse_grid_mixed_test
-
sparse_grid_total_poly,
a MATLAB code which
investigates the total polynomial approximation
using sparse grids.
-
sparse_grid_total_poly_test
-
sparse_interp_nd,
a MATLAB code which
defines a sparse interpolant to a function f(x) of a
M dimensional argument.
-
sparse_interp_nd_test
-
sparse_parfor,
a MATLAB code which
constructs a sparse matrix by
evaluating individual blocks in parallel with the parfor()
command, and then assembled on a single processor using the
sparse() command,
by Gene Cliff.
-
sparse_parfor_test
-
spd_test,
a MATLAB code which
performs a few tests on a real matrix to determine whether it is
symmetric positive definite (SPD).
-
sphere_cubed_grid,
a MATLAB code which
uses the projection of a cube to create grids of points,
lines, and quadrilaterals
on the surface of the unit sphere in 3D.
-
sphere_cubed_grid_test
-
sphere_cvt,
a MATLAB code which
carries out the Centroidal Voronoi Tessellation (CVT) iteration
on the surface of the unit sphere in 3D.
-
sphere_cvt_test
-
sphere_delaunay,
a MATLAB code which
computes the Delaunay triangulation of points
on the surface of the unit sphere in 3D.
-
sphere_delaunay_test
-
sphere_distance,
a MATLAB code which
computes the expected value of the distance
between a pair of points randomly selected on the surface of the
unit sphere in 3D.
-
sphere_distance_test
-
sphere_exactness,
a MATLAB code which
tests the polynomial exactness of a quadrature rule
on the surface of the unit sphere in 3D.
-
sphere_exactness_test
-
sphere_fibonacci_grid,
a MATLAB code which
uses a Fibonacci spiral to create a grid of points
on the surface of the unit sphere in 3D.
-
sphere_fibonacci_grid_test
-
sphere_grid,
a MATLAB code which
provides a number of ways of generating grids of points, or of
points and lines, or of points and lines and faces,
on the surface of the unit sphere in 3D.
-
sphere_grid_test
-
sphere_integrals,
a MATLAB code which
returns the exact value of the integral of any monomial
over the surface of the unit sphere in 3D.
-
sphere_integrals_test
-
sphere_lebedev_rule,
a MATLAB code which
computes Lebedev quadrature rules
on the surface of the unit sphere in 3D.
-
sphere_lebedev_rule_test
-
sphere_lebedev_rule_display,
a MATLAB code which
reads a file defining a Lebedev quadrature rule
on the surface of the unit sphere in 3D
and displays the point locations.
-
sphere_lebedev_rule_display_test
-
sphere_llq_grid,
a MATLAB code which
uses longitudes and latitudes to create grids of points,
lines, and quadrilaterals
on the surface of the unit sphere in 3D.
-
sphere_llq_grid_test
-
sphere_llt_grid,
a MATLAB code which
uses longitudes and latitudes to create grids of points,
lines, and triangles
on the surface of the unit sphere in 3D.
-
sphere_llt_grid_test
-
sphere_monte_carlo,
a MATLAB code which
applies a Monte Carlo method to estimate the integral of a function
on the surface of the unit sphere in 3D.
-
sphere_monte_carlo_test
-
sphere_positive_distance,
a MATLAB code which
computes the expected value of the distance
between a pair of points randomly selected on the surface of the
unit positive sphere in 3D.
-
sphere_positive_distance_test
-
sphere_quad,
a MATLAB code which
uses triangulation to approximate an integral
on the surface of the unit sphere in 3D.
-
sphere_quad_test
-
sphere_stereograph,
a MATLAB code which
computes the stereographic mapping between points
on the surface of the unit sphere in 3D
and points on the plane Z = 1; a generalized mapping is
also available.
-
sphere_stereograph_test
-
sphere_stereograph_display,
a MATLAB code which
computes and displays the results of several stereographic
projections between points
on the surface of the unit sphere in 3D and a plane.
-
sphere_stereograph_display_test
-
sphere_triangle_monte_carlo,
a MATLAB code which
applies a Monte Carlo method to estimate the integral of a function
over a spherical triangle on the surface of the unit sphere in 3D;
-
sphere_triangle_monte_carlo_test
-
sphere_triangle_quad,
a MATLAB code which
uses quadrature to estimate the integral of a function
over a spherical triangle on the surface of the unit sphere in 3D.
-
sphere_triangle_quad_test
-
sphere_voronoi,
a MATLAB code which
computes the Voronoi diagram of points
on the surface of the unit sphere in 3D.
-
sphere_voronoi_test
-
spherical_harmonic,
a MATLAB code which
evaluates spherical harmonic functions.
-
spherical_harmonic_test
-
spinterp,
a MATLAB code which
carries out piecewise multilinear
hierarchical sparse grid interpolation, quadrature and optimization,
by Andreas Klimke;
an earlier version of this software is ACM TOMS Algorithm 847.
-
spinterp_test
-
spiral_exact,
a MATLAB code which
computes a 2D velocity vector field that is an exact solution
of the continuity equation.
-
spiral_exact_test
-
spiral_pde,
a MATLAB code which
solves a pair of reaction-diffusion partial differential equations
(PDE) over a rectangular domain with periodic boundary condition,
whose solution is known to evolve into a pair of spirals.
-
spiral_pde_test
-
spiral_pde_movie,
a MATLAB code which
solves a pair of reaction-diffusion partial differential equations
(PDE) over a rectangular domain with periodic boundary condition,
whose solution is known to evolve into a pair of spirals.
The sequence of solutions is bundled into a movie.
-
spiral_pde_movie_test
-
spline,
a MATLAB code which
interpolates and approximates via splines;
-
spline_test
-
spquad,
a MATLAB code which
computes the points and weights of a sparse grid quadrature rule
for an M-dimensional integral,
based on the Clenshaw-Curtis quadrature rule,
by Greg von Winckel.
-
spquad_test
-
spring_double_ode,
a MATLAB code which
sets up and solves a system of ordinary differential equations
(ODE) for a system in which a mass is connected by a spring to a mass
connected by a spring to a fixed support.
-
spring_double_ode_test
-
spring_ode,
a MATLAB code which
sets up and solves a system of ordinary differential equations (ODE)
for the motion of a spring with mass m, damping b, and stiffness k.
-
spring_ode_test
-
spring_sweep_ode,
a MATLAB code which
computes a grid of solutions to a parameterized system of
ordinary differential equations (ODE) that represent
the motion of a spring with mass m, damping b, and stiffness k.
-
spring_sweep_ode_test
-
square_arbq_rule,
a MATLAB code which
returns quadrature rules,
with exactness up to total degree 20,
over the interior of the symmetric square in 2D,
by Hong Xiao and Zydrunas Gimbutas.
-
square_arbq_rule_test
-
square_distance,
a MATLAB code which
computes the expected value of the distance
between a pair of points randomly selected from the interior of
the unit square in 2D.
-
square_distance_test
-
square_exactness,
a MATLAB code which
investigates the polynomial exactness of quadrature rules for f(x,y)
over the interior of a rectangle in 2D.
-
square_exactness_test
-
square_felippa_rule,
a MATLAB code which
returns Felippa quadrature rules for approximating integrals
over the interior of a square in 2D.
-
square_felippa_rule_test
-
square_grid,
a MATLAB code which
computes a grid of points
over the interior of a square in 2D.
-
square_grid_test
-
square_hex_grid,
a MATLAB code which
computes a hexagonal grid of points
over the interior of a square in 2D.
-
square_hex_grid_test
-
square_integrals,
a MATLAB code which
returns the exact value of the integral of any monomial
over the interior of the unit square or symmetric unit square in 2D.
-
square_integrals_test
-
square_minimal_rule,
a MATLAB code which
returns "almost minimal" quadrature rules,
with exactness up to total degree 55,
over the interior of the symmetric square in 2D,
by Mattia Festa and Alvise Sommariva.
-
square_minimal_rule_test
-
square_monte_carlo,
a MATLAB code which
applies a Monte Carlo method to estimate the integral of a function
over the interior of the unit square in 2D.
-
square_monte_carlo_test
-
square_surface_distance,
a MATLAB code which
estimates the expected value of the distance
between a pair of points randomly selected
on the surface of the unit square.
-
square_surface_distance_test
-
square_symq_rule,
a MATLAB code which
returns symmetric quadrature rules,
with exactness up to total degree 20,
over the interior of the square in 2D,
by Hong Xiao and Zydrunas Gimbutas.
-
square_symq_rule_test
-
squircle_ode,
a MATLAB code which
sets up and solves a system of
ordinary differential equations (ODE) for a pair of functions that
generalize the sine and cosine, and whose phase portrait is a
squircle (a sort of squared circle).
-
squircle_ode_test
-
st_io,
a MATLAB code which
reads and writes sparse linear systems
stored in the Sparse Triplet (ST) format.
-
st_io_test
-
st_to_ccs,
a MATLAB code which
converts sparse matrix data from Sparse Triplet (ST) format
to Compressed Column Storage (CCS) format;
-
st_to_ccs_test
-
st_to_hb,
a MATLAB code which
converts sparse matrix data from Sparse Triplet (ST) format
to Harwell Boeing (HB) format;
-
st_to_hb_test
-
st_to_mm,
a MATLAB code which
converts sparse matrix data from Sparse Triplet (ST) format
to Matrix Market (MM) format;
-
st_to_mm_test
-
st_to_msm,
a MATLAB code which
reads a Sparse Triplet (ST) file
and creates a corresponding MATLAB Sparse Matrix (MSM).
-
st_to_msm_test
-
steinerberger,
a MATLAB code which
evaluates the Steinerberger function, a continuous function
with discontinuous derivative, which is very hard to accurately
plot, integrate, minimize, or interpolate.
-
steinerberger_test
-
stetter_ode,
a MATLAB code which
sets up and solves an ordinary differential equation (ODE) for
which a specific time step sequence causes the implicit
trapezoidal method to be unstable, while the implicit midpoint
method will be stable. Note that the right hand side function
f(t,y) is periodic, discontinuous, and piecewise linear.
-
stetter_ode_test
-
stiff_ode,
a MATLAB code which
sets up and solves an ordinary differential equation (ODE) which is
an example of a stiff ODE.
-
stiff_ode_test
-
stla_display,
a MATLAB code which
displays an ASCII stereolithography (STL) 3D graphics file;
-
stla_display_test
-
stla_io,
a MATLAB code which
reads and writes an ASCII stereolithography (STL) 3D graphics file;
-
stla_io_test
-
stla_to_tri_surface,
a MATLAB code which
reads an ASCII stereolithography (STL) 3D graphics file and extracts
the surface mesh data as a TRI_SURFACE dataset.
-
stla_to_tri_surface_test
-
stla_to_tri_surface_fast,
a MATLAB code which
is a faster version of stla_to_tri_surface().
-
stla_to_tri_surface_fast_test
-
stochastic_diffusion,
a MATLAB code which
implements several versions of a stochastic diffusivity coefficient.
-
stochastic_diffusion_test
-
stochastic_heat2d,
a MATLAB code which
implements a finite difference method (FDM) for the steady
2D heat equation,
with a stochastic heat diffusivity coefficient.
-
stochastic_heat2d_test
-
stochastic_rk,
a MATLAB code which
applies a Runge Kutta (RK) scheme to
a stochastic ordinary differential equation (SDE).
-
stochastic_rk_test
-
stokes_2d_exact,
a MATLAB code which
evaluates exact solutions to the incompressible steady
Stokes equations over the unit square in 2D.
-
stokes_2d_exact_test
-
string_pde,
a MATLAB code which
sets up and solves the partial differential equations (PDE)
describing a vibrating string,
creating files that can be displayed by gnuplot().
-
string_pde_test
-
stroud_rule,
a MATLAB code which
defines quadrature rules for a variety of M-dimensional regions,
including the interior of the square, cube and hypercube, the pyramid,
cone and ellipse, the hexagon, the M-dimensional octahedron,
the circle, sphere and hypersphere, the triangle, tetrahedron
and simplex, and the surface of the circle, sphere and hypersphere.
-
stroud_rule_test
-
subpak,
a MATLAB code which
includes a number of utility routines.
-
subpak_test
-
subset,
a MATLAB code which
enumerates, generates, randomizes, ranks and unranks combinatorial
objects including combinations, compositions, Gray codes, index
sets, partitions, permutations, polynomials, subsets, and Young
tables. Backtracking routines are included to solve some
combinatorial problems.
-
subset_test
-
subset_distance,
a MATLAB code which
estimates the expected value of the Hamming distance
between a pair of randomly selected subsets of an M set.
-
subset_distance_test
-
subset_sum,
a MATLAB code which
seeks solutions of the subset sum problem, in which it is desired
to find a subset of integers which has a given sum.
-
subset_sum_test
-
subset_sum_backtrack,
a MATLAB code which
uses backtracking to find solutions of the subset sum problem,
in which it is desired to find a subset of integers which has a given sum.
-
subset_sum_backtrack_test
-
subset_sum_brute,
a MATLAB code which
seeks solutions of the subset sum problem,
using a brute force approach.
-
subset_sum_brute_test
-
subset_sum_swap,
a MATLAB code which
uses swapping to try to improve an initial estimated solution
of the subset sum problem, which seeks a subset of a set of integers
which has a given sum. Even when an exact solution exists, this
approach often only finds an approximate solution.
-
subset_sum_swap_test
-
sudoku,
a MATLAB code which
handles Sudoku puzzles;
-
sudoku_test
-
surf_test,
calls surf(), which
displays a 3D surface or contour plot for data
of the form Z=F(X,Y).
-
svd_basis,
a MATLAB code which
applies the singular value decomposition (SVD)
to a collection of data vectors, extracting dominant modes;
-
svd_basis_test
-
svd_circle,
a MATLAB code which
analyzes a linear map of the unit circle caused by an arbitrary
2x2 matrix A, using the singular value decomposition (SVD).
-
svd_circle_test
-
svd_faces,
a MATLAB code which
applies singular value decomposition (SVD) analysis
to a set of images.
-
svd_faces_test
-
svd_fingerprint,
a MATLAB code which
reads a file containing a fingerprint image and
uses the singular value decomposition (SVD) to
compute and display a series of low rank approximations
to the image.
-
svd_fingerprint_test
-
svd_gray,
a MATLAB code which
reads a gray scale image, computes the Singular Value
Decomposition (SVD), and constructs a series of low rank
approximations to the image.
-
svd_gray_test
-
svd_lls,
a MATLAB code which
uses the singular value decomposition (SVD) to construct and
plot the best affine and linear relationships in the sense of
least square, between two vectors of data.
-
svd_lls_test
-
svd_powers,
a MATLAB code which
applies singular value decomposition (SVD) analysis to a set of
powers x(i)^(j-1).
-
svd_powers_test
-
svd_snowfall,
a MATLAB code which
reads a file containing historical snowfall data and
analyzes the data with the Singular Value Decomposition (SVD).
-
svd_snowfall_test
-
svd_sphere,
a MATLAB code which
analyzes a linear map of the unit sphere caused by an arbitrary
3x3 matrix A, using the singular value decomposition (SVD).
-
svd_sphere_test
-
svd_test,
a MATLAB code which
demonstrates the Singular Value Decomposition (SVD) for
a simple example.
-
svd_truncated_test,
a MATLAB code which
calls the "economy" version of the
Singular Value Decomposition (SVD)
of an M by N rectangular matrix, in cases where M is less than N
or N is less than M.
-
t_puzzle,
a MATLAB code which
considers the T puzzle, a set of 4 wooden pieces. The challenge is to
arrange the pieces to form the shape of the letter T. Three other
challenge shapes are an arrow, a rhombus, and a "fat" T.
-
t_puzzle_test
-
t_puzzle_cplex_test,
a BASH code which
calls cplex(), to read the LP file defining the T-puzzle tiling problem,
solve the linear programming problem, and write the solution to a file.
-
t_puzzle_gui,
a MATLAB code which
sets up a graphical user interface for the T puzzle,
by Cleve Moler.
-
t_puzzle_gurobi_test,
a BASH code which
calls gurobi(), to read the LP file defining the T-puzzle tiling problem,
solve the linear programming problem, and write the solution to a file.
-
table_io,
a MATLAB code which
reads and writes a simple table file;
-
table_io_test
-
task_division,
a MATLAB code which
implements a simple procedure for smoothly dividing T tasks among
P processors; such a method can be useful in MPI and other parallel
environments, particularly when T is not an exact multiple of P,
and when the processors can be indexed starting from 0 or from 1.
-
task_division_test
-
tec_io,
a MATLAB code which
reads or writes a tecplot() ASCII TEC file containing a
model associated with the finite element method (FEM).
-
tec_io_test
-
tec_to_fem,
a MATLAB code which
converts a tecplot() ASCII TEC file into an FEM model.
-
tec_to_fem_test
-
tec_to_vtk,
a MATLAB code which
converts a tecplot() TEC file into a set of VTK files.
-
tec_to_vtk_test
-
tennis_matrix,
a MATLAB code which
computes the transition matrix for a game of tennis, which
has 17 distinct states.
-
tennis_matrix_test
-
tensor_grid_display,
a MATLAB code which
displays the grid points of a tensor product rule used for
interpolation or quadrature, in 1D, 2D or 3D.
-
tensor_grid_display_test
-
test_approx,
a MATLAB code which
implements test problems for approximation,
provided as a set of (x,y) data.
-
test_approx_test
-
test_con,
a MATLAB code which
implements test problems for
numerical continuation.
-
test_con_test
-
test_eigen,
a MATLAB code which
implements test matrices for eigenvalue analysis.
-
test_eigen_test
-
test_int,
a MATLAB code which
implements test problems for
approximate integration (quadrature) in one dimension.
-
test_int_test
-
test_int_2d,
a MATLAB code which
implements test problems for
approximate integration (quadrature) in two dimensions.
-
test_int_2d_test
-
test_interp,
a MATLAB code which
defines test problems for interpolation,
provided as a set of (x,y(x)) data.
-
test_interp_test
-
test_interp_1d,
a MATLAB code which
defines test problems for interpolation of data y(x),
which depends on a 1D argument.
-
test_interp_1d_test
-
test_interp_2d,
a MATLAB code which
defines test problems for interpolation of data z(x,y),
which depends on a 2D argument.
-
test_interp_2d_test
-
test_interp_fun,
a MATLAB code which
defines test problems for interpolation which are
available in functional form.
-
test_interp_fun_test
-
test_interp_nd,
a MATLAB code which
defines test problems for interpolation of data z(x),
depending on an M dimensional argument.
-
test_interp_nd_test
-
test_lls,
a MATLAB code which
implements linear least squares (LLS) test problems of the
form A*x=b.
-
test_lls_test
-
test_matrix,
a MATLAB code which
defines test matrices for which the condition number, determinant,
eigenvalues, eigenvectors, inverse, null vectors, P*L*U factorization
or linear system solution are known. Examples include the
Fibonacci, Hilbert, Redheffer, Vandermonde, Wathen and Wilkinson
matrices.
-
test_matrix_test
-
test_matrix_exponential,
a MATLAB code which
defines a set of test cases for computing the matrix exponential.
-
test_matrix_exponential_test
-
test_min,
a MATLAB code which
implements test problems for
minimization of a scalar function of a scalar variable.
-
test_min_test
-
test_nint,
a MATLAB code which
defines test functions for M-dimensional quadrature routines.
-
test_nint_test
-
test_nonlin,
a MATLAB code which
implements test problems for the solution
of systems of nonlinear equations.
-
test_nonlin_test
-
test_opt,
a MATLAB code which
implements test problems for optimization
of a scalar function of several variables.
-
test_opt_test
-
test_opt_con,
a MATLAB code which
defines test problems for the minimization of a scalar function of
several variables, with the search constrained to lie within a
specified hyper-rectangle.
-
test_opt_con_test
-
test_optimization,
a MATLAB code which
implements test problems for optimization
of a scalar function of several variables,
as described by Molga and Smutnicki.
-
test_optimization_test
-
test_partial_digest,
a MATLAB code which
generates example cases of the partial digest problem.
-
test_partial_digest_test
-
test_triangulation,
a MATLAB code which
defines test problems for triangulation;
-
test_triangulation_test
-
test_values,
a MATLAB code which
supplies test values of various mathematical functions, including
Abramowitz, AGM, Airy, Bell, Bernoulli, Bessel, Beta, Binomial,
Bivariate Normal, Catalan, Cauchy, Chebyshev, Chi Square, Clausen,
Clebsch Gordan, Collatz, Cosine integral, Dawson, Debye, Dedekind,
dilogarithm, Dixon elliptic functions, Exponential integral, Elliptic,
Error, Euler, Exponential integral, F probability, Fresnel, Frobenius,
Gamma, Gegenbauer, Goodwin, Gudermannian, Harmonic, Hermite,
Hypergeometric 1F1, Hypergeometric 2F1, inverse trigonometic,
Jacobi Elliptic functions sn(), cn(), dn(), the Julian Ephemeris Date,
Kelvin, Knapsack, Laguerre, Lambert W, Laplace, Legendre, Lerch, Lobachevsky,
Lobatto, Logarithmic integral, Log normal, McNugget numbers,
Mersenne primes, Mertens, Mittag-Leffler, Moebius,
Multinomial, Negative binomial, Nine J, Normal, Omega, Owen, Partition,
Phi, Pi, Poisson, Polylogarithm, Polynomial Resultant, Polyomino, Prime,
Psi, Rayleigh, Hyperbolic Sine integral, Sigma, Sine Power integral,
Sine integral, Six J, Sphere area, Sphere volume, Spherical harmonic,
Stirling, Stromgen, Struve, Student, Subfactorial, Student probability,
Three J, Transport, Trigamma, Truncated normal, van der Corput,
von Mises, Weibull, Wright Omega, Zeta.
-
test_values_test
-
test_zero,
a MATLAB code which
defines some functions f(x) suitable for testing
software that solves a nonlinear equation f(x)=0;
-
test_zero_test
-
tester,
a BASH script which runs the MATLAB tests.
-
tet_mesh,
a MATLAB code which
works with tetrahedral meshes in 3D;
-
tet_mesh_test
-
tet_mesh_boundary,
a MATLAB code which
reads information defining
a tetrahedral mesh of points in 3D, and determines the triangular
faces that form the boundary of the mesh; it writes out files
containing the nodes and elements defining this TRI_SURFACE data.
-
tet_mesh_boundary_test
-
tet_mesh_display,
a MATLAB code which
reads data defining a tetrahedral mesh,
and displays a wireframe image of the nodes and edges;
-
tet_mesh_display_test
-
tet_mesh_l2q,
a MATLAB code which
reads information about a 4-node linear mesh of tetrahedrons and
creates data defining a corresponding 10-node quadratic
mesh of tetrahedrons;
-
tet_mesh_l2q_test
-
tet_mesh_q2l,
a MATLAB code which
reads information about a 10-node quadratic mesh of tetrahedrons and
creates data defining a corresponding 4-node linear
mesh of tetrahedrons;
-
tet_mesh_q2l_test
-
tet_mesh_quad,
a MATLAB code which
estimates the integral of a function over a region defined by
a tetrahedral mesh.
-
tet_mesh_quad_test
-
tet_mesh_quality,
a MATLAB code which
computes various quality measures for a
tetrahedral mesh of a set of nodes in 3D;
-
tet_mesh_quality_test
-
tet_mesh_rcm,
a MATLAB code which
computes the Reverse Cuthill McKee (RCM) reordering for the nodes
of a mesh of tetrahedrons, using 4 or 10 node elements.
-
tet_mesh_rcm_test
-
tet_mesh_refine,
a MATLAB code which
refines a mesh of tetrahedrons;
-
tet_mesh_refine_test
-
tet_mesh_tet_neighbors,
a MATLAB code which
reads information about a tetrahedral mesh and lists
the tetrahedrons adjacent to a given tetrahedron;
-
tet_mesh_tet_neighbors_test
-
tet_mesh_to_gmsh,
a MATLAB code which
write a gmsh() file describing a tetrahedral mesh;
-
tet_mesh_to_gmsh_test
-
tet_mesh_to_xml,
a MATLAB code which
write an XML file describing a tetrahedral mesh;
-
tet_mesh_to_xml_test
-
tet_mesh_volumes,
a MATLAB code which
computes the volume of each tetrahedron in a mesh of tetrahedrons;
-
tet_mesh_volumes_test
-
tetrahedron,
a MATLAB code which
carries out geometric calculations involving a general tetrahedron,
including solid and facial angles, face areas,
point containment, distances to a point, circumsphere and insphere,
measures of shape quality, centroid, barycentric coordinates,
edges and edge lengths, random sampling, and volumes.
-
tetrahedron_test
-
tetrahedron_arbq_rule,
a MATLAB code which
returns quadrature rules,
with exactness up to total degree 15,
over the interior of a tetrahedron in 3D,
by Hong Xiao and Zydrunas Gimbutas.
-
tetrahedron_arbq_rule_test
-
tetrahedron_exactness,
a MATLAB code which
tests the polynomial exactness of a quadrature rule
over the interior of a tetrahedron in 3D.
-
tetrahedron_exactness_test
-
tetrahedron_felippa_rule,
a MATLAB code which
returns a Felippa quadrature rule for approximating integrals
over the interior of a tetrahedron in 3D.
-
tetrahedron_felippa_rule_test
-
tetrahedron_grid,
a MATLAB code which
computes a grid of points
over the interior of a tetrahedron in 3D.
-
tetrahedron_grid_test
-
tetrahedron_integrals,
a MATLAB code which
returns the exact value of the integral of any monomial
over the interior of the unit tetrahedron in 3D.
-
tetrahedron_integrals_test
-
tetrahedron_jaskowiec_rule,
a MATLAB code which
returns quadrature rules, with exactness up to total degree 20,
over the interior of a tetrahedron in 3D,
by Jan Jaskowiec, Natarajan Sukumar.
-
tetrahedron_jaskowiec_rule_test
-
tetrahedron_keast_rule,
a MATLAB code which
defines a Keast quadrature rule, of degree of exactness 0 through 8,
over the interior of the tetrahedron in 3D.
-
tetrahedron_keast_rule_test
-
tetrahedron_monte_carlo,
a MATLAB code which
uses the Monte Carlo method to estimate an integral
over the interior of a general tetrahedron in 3D.
-
tetrahedron_monte_carlo_test
-
tetrahedron_ncc_rule,
a MATLAB code which
defines Newton-Cotes closed (NCC) quadrature rules
over the interior of a tetrahedron in 3D.
-
tetrahedron_ncc_rule_test
-
tetrahedron_nco_rule,
a MATLAB code which
defines Newton-Cotes open (NCO) quadrature rules
over the interior of a tetrahedron in 3D.
-
tetrahedron_nco_rule_test
-
tetrahedron_slice_display,
a MATLAB code which
determines the intersection between a tetrahedron and a plane and
displays the result.
-
tetrahedron_slice_display_test
-
tetrahedron_slice_movie,
a MATLAB code which
is given a tetrahedron and a vector, displays an evenly spaced
sequence of planes that intersect the tetrahedron
and are normal to the vector, and creates a movie of the process.
-
tetrahedron_slice_movie_test
-
tetrahedron_witherden_rule,
a MATLAB code which
returns a symmetric Witherden quadrature rule for the tetrahedron,
with exactness up to total degree 10.
-
tetrahedron_witherden_rule_test
-
tetrahedron01_monte_carlo,
a MATLAB code which
uses the Monte Carlo method to estimate an integral
over the interior of the unit tetrahedron in 3D.
-
tetrahedron01_monte_carlo_test
-
theodolite,
a MATLAB code which
presents the problem of estimating the location of an event
which occurs in the sky, atmosphere, or the heavens, using nothing
but the reported angle of observation from several stations;
a nonlinear least squares (NLS) solver is needed.
-
theodolite_test
-
theta_method,
a MATLAB code which
solves one or more ordinary differential equations (ODE)
using the theta method.
-
theta_method_test
-
three_body_ode,
a MATLAB code which
sets up and solves ordinary differential equations (ODE) that
simulate the behavior of three planets, constrained to lie in a
plane, and moving under the influence of gravity,
by Walter Gander and Jiri Hrebicek.
-
three_body_ode_test
-
tictoc_test,
a MATLAB code which
calls tic() and toc(), which
compute elapsed time.
-
timer_test,
a MATLAB code which
demonstrates and compares several ways of timing code execution.
-
timestamp,
a MATLAB code which
prints the current YMDHMS date as a timestamp;
-
timestamp_test
-
toeplitz_cholesky,
a MATLAB code which
computes the Cholesky factorization of a symmetric positive definite
(SPD) Toeplitz matrix.
-
toeplitz_cholesky_test
-
toeplitz_inverse,
a MATLAB code which
computes the inverse of a Toeplitz matrix.
-
toeplitz_inverse_test
-
toms097,
a MATLAB code which
computes the distance between all pairs of nodes in a directed graph
with weighted edges, using the Floyd algorithm.
-
toms097_test
-
toms112,
a MATLAB code which
determines whether a point is contained in a polygon,
by Moshe Shimrat.
This is a version of ACM TOMS algorithm 112.
-
toms112_test
-
toms178,
a MATLAB code which
optimizes a scalar functional of multiple variables
using the Hooke-Jeeves method, by Arthur Kaupe.
This is a version of ACM TOMS algorithm 178.
-
toms178_test
-
toms179,
a MATLAB code which
evaluates the modified Beta function,
by Oliver Ludwig.
This is a version of ACM TOMS algorithm 179.
-
toms179_test
-
toms243,
a MATLAB code which
evaluates the logarithm of a complex value,
by David Collens.
This is a version of ACM TOMS algorithm 243.
-
toms243_test
-
toms291,
a MATLAB code which
evaluates the logarithm of the Gamma function.
This is a version of ACM TOMS algorithm 291.
-
toms291_test
-
toms443,
a MATLAB code which
evaluates the Lambert W function,
by Fritsch, Shafer and Crowley.
This is a version of ACM TOMS algorithm 443.
-
toms443_test
-
toms446,
a MATLAB code which
manipulates Chebyshev series for interpolation and approximation;
this is a version of ACM TOMS algorithm 446,
by Roger Broucke.
-
toms446_test
-
toms462,
a MATLAB code which
evaluates the upper right tail of the bivariate normal
Probability Density Function (PDF); that is,
the probability that normal variables X and Y with correlation R will
satisfy H <= X and K <= Y;
this is a version of ACM TOMS algorithm 462.
-
toms462_test
-
toms515,
a MATLAB code which
selects subsets of size K from a set of size N.
This is a version of ACM TOMS Algorithm 515,
by Bill Buckles, Matthew Lybanon.
-
toms515_test
-
toms577,
a MATLAB code which
evaluates the Carlson elliptic integral functions RC, RD, RF and RJ.
This is a version of ACM TOMS algorithm 577;
-
toms577_test
-
toms655,
a MATLAB code which
computes the weights for interpolatory quadrature rules;
this is commonly called IQPACK,
by Sylvan Elhay and Jaroslav Kautsky.
This is a version of ACM TOMS algorithm 655.
-
toms655_test
-
toms743,
a MATLAB code which
evaluates the Lambert W function.
This is a version of ACM TOMS algorithm 743,
by Barry, Barry and Culligan-Hensley.
-
toms743_test
-
toms847,
a MATLAB code which
carries out piecewise linear (PWL) multidimensional hierarchical
sparse grid interpolation;
this is commonly called spinterp() (version 2.1);
this is a version of ACM TOMS Algorithm 847,
by Andreas Klimke;
-
toms847_test
-
toms866,
a MATLAB code which
is version 2.2 of the
Incompressible Flow Iterative Solution Software (IFISS),
for fluid flow governed by the Navier Stokes equations (NSE),
by Howard Elman, Alison Ramage, David Silvester;
this is a version of ACM TOMS algorithm 866.
-
toms886,
a MATLAB code which
defines the Padua points for interpolation in a 2D region,
including the rectangle, triangle, and ellipse,
by Marco Caliari, Stefano de Marchi, Marco Vianello.
This is a version of ACM TOMS algorithm 886.
-
toms886_test
-
toms923,
a MATLAB code which
evaluates the Pfaffian for a dense or banded skew symmetric matrix,
by Michael Wimmer.
-
toms923_test
-
tortoise,
a MATLAB code which
considers the tortoise tiling puzzle, a smaller version of the eternity
puzzle. The puzzle specifies a region R composed of 1620
30-60-90 triangles, and a set of 45 "tiles", each consisting of 36
30-60-90 triangles, and seeks an arrangement of the tiles that
exactly covers the region.
-
tortoise_test
-
tortoise_cplex_test
a BASH code which
calls cplex(), to read the LP file defining the tortoise tiling problem,
solve the linear programming problem, and write the solution to a file.
-
tortoise_gurobi_test
a BASH code which
calls gurobi(), to read the LP file defining the tortoise tiling problem,
solve the linear programming problem, and write the solution to a file.
-
tough_ode,
a MATLAB code which
sets up and solves a system of four ordinary differential
equations (ODE) which is extremely difficult to solve accurately.
-
tough_ode_test
-
traffic_simulation,
a MATLAB code which
simulates the cars waiting to get through a traffic light.
-
traffic_simulation_test
-
trapezoidal,
a MATLAB code which
solves one or more ordinary differential equations (ODE)
using the (implicit) trapezoidal method, and MATLAB's
fsolve() to handle the implicit system.
-
trapezoidal_test
-
trapezoidal_explicit,
a MATLAB code which
solves one or more ordinary differential equations (ODE)
using the (explicit) trapezoidal method.
-
trapezoidal_explicit_test
-
trapezoidal_fixed,
a MATLAB code which
solves one or more ordinary differential equations (ODE)
using the (implicit) trapezoidal method, using the fixed point method.
-
trapezoidal_fixed_test
-
treepack,
a MATLAB code which
defines, analyzes, and manipulates trees,
a simple kind of graph with no circuits.
Special cases include rooted and binary trees.
Representations include adjacency, arc, Pruefer code,
and parent.
Operations include center, diameter, eccentricity, enumeration,
generation one at a time, random selection, traversal.
-
treepack_test
-
tri_surface_display,
a MATLAB code which
displays a TRI_SURFACE describing a triangulated surface;
-
tri_surface_display_test
-
tri_surface_io,
a MATLAB code which
reads and writes the graphics information in a tri_surface file,
describing a surface in 3D consisting of a collection of connected
triangles;
-
tri_surface_io_test
-
tri_surface_to_obj,
a MATLAB code which
reads a TRI_SURFACE dataset and extracts
the surface mesh data as an OBJ file.
-
tri_surface_to_obj_test
-
tri_surface_to_ply,
a MATLAB code which
reads a TRI_SURFACE dataset and extracts
the surface mesh data as a PLY file.
-
tri_surface_to_ply_test
-
tri_surface_to_stla,
a MATLAB code which
reads a TRI_SURFACE dataset and extracts
the surface mesh data as an ASCII stereolithography (STL) file.
-
tri_surface_to_stla_test
-
triangle,
a MATLAB code which
computes properties of a triangle, including angles, area,
centroid, circumcircle, edge lengths, incircle, orientation,
orthocenter, quality, Cartesian to barycentric coordinates,
barycentric coordinates to Cartesian. A point is treated as
a (1,2) array, a list of points as an (n,2) array, and a triangle
as a (3,2) array.
-
triangle_test
-
triangle_analyze,
a MATLAB code which
reads a triangle defined in a file and computes angles, area,
centroid, circumcircle, edge lengths, incircle, orientation,
orthocenter, and quality.
-
triangle_analyze_test
-
triangle_display,
a MATLAB code which
displays the nodes and elements of a triangulation
for which the data has been
stored in NODE and ELE files by Jonathan Shewchuk's triangle() program.
-
triangle_display_test
-
triangle_distance,
a MATLAB code which
computes the expected value of the distance
between a pair of points randomly selected from the interior of
a triangle in 2D.
-
triangle_distance_test
-
triangle_dunavant_rule,
a MATLAB code which
returns a Dunavant quadrature rule
over the interior of a triangle in 2D.
-
triangle_dunavant_rule_test
-
triangle_exactness,
a MATLAB code which
tests the polynomial exactness of a quadrature rule
over the interior of a triangle in 2D.
-
triangle_exactness_test
-
triangle_fekete_rule,
a MATLAB code which
sets up one of seven Fekete rules
for interpolation or quadrature
over the interior of a triangle in 2D.
-
triangle_fekete_rule_test
-
triangle_felippa_rule,
a MATLAB code which
returns Felippa quadrature rules for approximating integrals
over the interior of a triangle in 2D.
-
triangle_felippa_rule_test
-
triangle_grid,
a MATLAB code which
computes a grid of points
over the interior of a triangle in 2D.
-
triangle_grid_test
-
triangle_histogram,
a MATLAB code which
computes histograms of data
over the interior of a unit triangle in 2D.
-
triangle_histogram_test
-
triangle_integrals,
a MATLAB code which
returns the exact value of the integral of any polynomial
over the interior of an arbitrary triangle in 2D.
-
triangle_integrals_test
-
triangle_integrands,
a MATLAB code which
defines integrands for testing quadrature rules over a triangle.
-
triangle_integrands_test
-
triangle_interpolate,
a MATLAB code which
shows how vertex data can be interpolated at any point
in the interior of a triangle.
-
triangle_interpolate_test
-
triangle_io,
a MATLAB code which
reads or writes files created by Jonathan Shewchuk's
triangle() program.
-
triangle_io_test
-
triangle_lyness_rule,
a MATLAB code which
returns a Lyness-Jespersen quadrature rule
over the interior of a triangle in 2D;
-
triangle_lyness_rule_test
-
triangle_monte_carlo,
a MATLAB code which
uses the Monte Carlo method to estimate an integral
over the interior of a general triangle in 2D.
-
triangle_monte_carlo_test
-
triangle_quadrature_symmetry,
a MATLAB code which
determines the symmetries of a quadrature rule for a triangle.
-
triangle_quadrature_symmetry_test
-
triangle_refine,
a MATLAB code which
divides a triangle into c^2 copies of itself, and implements
a simple centroid-based quadrature scheme.
-
triangle_refine_test
-
triangle_svg,
a MATLAB code which
uses Scalable Vector graphics (SVG) to plot a triangle and
any number of points, to illustrate quadrature rules and
sampling techniques.
-
triangle_svg_test
-
triangle_symq_rule,
a MATLAB code which
returns symmetric quadrature rules, with precision up to 50,
over the interior of a triangle,
by Hong Xiao and Zydrunas Gimbutas.
-
triangle_symq_rule_test
-
triangle_symq_rule_convert,
a MATLAB code which
takes quadrature rules defined for the equilateral triangle and
converts them to the reference triangle (0,0), (1,0), (0,1).
-
triangle_symq_rule_convert_test
-
triangle_symq_rule_original,
a MATLAB code which
is based on the original Fortran77 code, which uses an equilateral
triangle as the reference element,
by Hong Xiao and Zydrunas Gimbutas.
-
triangle_symq_rule_original_test
-
triangle_symq_to_ref,
a MATLAB code which
creates quadrature rules defined on the half-unit square from
symmetric quadrature rules defined on an equilateral triangle,
defined by triangle_symq_rule(), by Hong Xiao and Zydrunas Gimbutas.
-
triangle_symq_to_ref_test
-
triangle_to_fem,
a MATLAB code which reads the NODE and ELE files
created by Jonathan Shewchuk's triangle() program to
describe a triangular mesh, and writes a corresponding pair of
node and element files in the 2D FEM format.
-
triangle_to_fem_test
-
triangle_to_medit,
a MATLAB code which
reads the NODE and ELE files created by
Jonathan Shewchuk's triangle() program to describe a triangular mesh,
and writes a corresponding medit() MESH file.
-
triangle_to_medit_test
-
triangle_to_xml,
a MATLAB code which reads the NODE and ELE files created by
Jonathan Shewchuk's triangle() program to describe a triangular
mesh in 2D, and writes a corresponding XML mesh file for use
by dolfin() or fenics().
-
triangle_to_xml_test
-
triangle_twb_rule,
a MATLAB code which
generates the points and weights of quadrature rules
over the interior of a triangle in 2D,
determined by Taylor, Wingate, and Bos.
-
triangle_twb_rule_test
-
triangle_wandzura_rule,
a MATLAB code which
returns quadrature rules of exactness 5, 10, 15, 20, 25 and 30
over the interior of the triangle in 2D.
-
triangle_wandzura_rule_test
-
triangle_witherden_rule,
a MATLAB code which
returns a symmetric Witherden quadrature rule for the triangle,
with exactness up to total degree 20.
-
triangle_witherden_rule_test
-
triangle01_integrals,
a MATLAB code which
returns the integral of any monomial
over the interior of the unit triangle in 2D.
-
triangle01_integrals_test
-
triangle01_monte_carlo,
a MATLAB code which
uses the Monte Carlo method to estimate an integral
over the interior of the unit triangle in 2D.
-
triangle01_monte_carlo_test-
-
triangulate,
a MATLAB code which
triangulates a polygonal region,
based on a C program by Joseph ORourke;
-
triangulate_test
-
triangulate_rectangle,
a MATLAB code which
sets up a grid of triangles in a rectangular region.
-
triangulate_rectangle_test
-
triangulation,
a MATLAB code which
computes the triangulation of a set of points in the plane,
and performs various operations using a triangulation, including
searching a Delaunay triangulation to find
which triangle contains a given point.
-
triangulation_test
-
triangulation_boundary,
a MATLAB code which
starts with a triangulation of a simple shape, and
determines the triangle edges that form the boundary,
and a sequence of nodes that trace the boundary.
-
triangulation_boundary_test
-
triangulation_boundary_edges,
a MATLAB code which
reads data defining a triangulation, determines which edges
lie on the boundary, organizes them into connected components,
and writes this information to a file.
-
triangulation_boundary_edges_test
-
triangulation_boundary_nodes,
a MATLAB code which
reads data defining a triangulation, determines which nodes
lie on the boundary, and writes their coordinates to a file;
-
triangulation_boundary_nodes_test
-
triangulation_corner,
a MATLAB code which
patches triangulations so that no triangle has two sides on the boundary.
-
triangulation_corner_test
-
triangulation_delaunay_discrepancy,
a MATLAB code which
measures the amount by which a triangulation fails
the local Delaunay test;
-
triangulation_delaunay_discrepancy_test
-
triangulation_display,
a MATLAB code which
displays the nodes and elements of a triangulation;
-
triangulation_display_test
-
triangulation_histogram,
a MATLAB code which
computes histograms of data over a triangulation.
-
triangulation_histogram_test
-
triangulation_l2q,
a MATLAB code which
reads information about a 3-node linear triangulation and creates data
defining a corresponding 6-node quadratic triangulation;
-
triangulation_l2q_test
-
triangulation_mask,
a MATLAB code which
reads a triangulation and calls
a user-supplied routine to consider each triangle for deletion;
-
triangulation_mask_test
-
triangulation_node_to_element,
a MATLAB code which
reads files describing a set of nodes, their triangulation, and the
value of one or more quantities at each node, and outputs a file
that averages the quantities for each element. This operation
in effect creates an order1 finite element model of the data.
-
triangulation_node_to_element_test
-
triangulation_order1_display,
a MATLAB code which
plots piecewise constant (PWC) data associated with a triangulation;
-
triangulation_order1_display_test
-
triangulation_order3_contour,
a MATLAB code which
plots color contours of a piecewise linear (PWL) scalar
quantity evaluated at the nodes of a 3-node triangle triangulation.
-
triangulation_order3_contour_test
-
triangulation_order6_contour,
a MATLAB code which
plots color contours of a piecwise quadratic (PWQ) scalar
quantity evaluated at the nodes of a 6-node triangle triangulation.
-
triangulation_order6_contour_test
-
triangulation_orient,
a MATLAB code which
ensures that the triangles in
an order 3 or order 6 triangulation have positive orientation;
-
triangulation_orient_test
-
triangulation_plot,
a MATLAB code which
plots the nodes and elements of a triangulation as a
PostScript file;
-
triangulation_plot_test
-
triangulation_q2l,
a MATLAB code which
reads information about a 6-node quadratic triangulation
and creates data defining a corresponding 3-node linear triangulation;
-
triangulation_q2l_test
-
triangulation_quad,
a MATLAB code which
reads information about a triangulation and the value of a function at
the nodes and estimates the integral of the function
over the triangulated region.
-
triangulation_quad_test
-
triangulation_quality,
a MATLAB code which
reads information about a triangulation and computes various
quality measures;
-
triangulation_quality_test
-
triangulation_rcm,
a MATLAB code which
reads files describing a triangulation of nodes in 2D, and applies the
Reverse Cuthill McKee (RCM) algorithm
to produce a renumbering of the triangulation with a reduced
bandwidth.
-
triangulation_rcm_test
-
triangulation_refine,
a MATLAB code which
refines a triangulation;
-
triangulation_refine_test
-
triangulation_refine_local,
a MATLAB code which
refines a triangulation locally; a single triangular element is
replaced by four smaller triangles, and neighboring information
is updated.
-
triangulation_refine_local_test
-
triangulation_svg,
a MATLAB code which
creates a Scalable Vector graphics (SVG) image of a triangulation,
which can be displayed by a web browser.
-
triangulation_svg_test
-
triangulation_t3_to_t4,
a MATLAB code which
reads information about a 3-node triangulation and creates data
defining a corresponding 4-node triangulation (vertices + centroid);
-
triangulation_t3_to_t4_test
-
triangulation_triangle_neighbors,
a MATLAB code which
reads data defining a triangulation, finds the three neighbor
triangles for each triangle, and writes them to a file;
-
triangulation_triangle_neighbors_test
-
tridiagonal_solver,
a MATLAB code which
solves a tridiagonal linear system.
-
tridiagonal_solver_test
-
trig_interp,
a MATLAB code which
uses trigonometric functions for interpolation.
-
trig_interp_test
-
trig_interp_basis,
a MATLAB code which
evaluates the cardinal basis functions for trigonometric
interpolation of equally spaced data.
-
trig_interp_basis_test
-
trinity,
a MATLAB code which
considers the trinity puzzle, a smaller version of the eternity
puzzle. The trinity puzzle specifies a region R composed of 144
30-60-90 triangles, and a set of 4 "tiles",
each consisting of 36 30-60-90 triangles, and seeks an arrangement
of the tiles that exactly covers the region.
-
trinity_test
-
trinity_cplex_test
a BASH code which
calls cplex(), to read the LP file defining the trinity tiling problem,
solve the linear programming problem, and write the solution to a file.
-
trinity_gurobi_test
a BASH code which
calls gurobi(), to read the LP file defining the trinity tiling
problem, solve the linear programming problem, and write the
solution to a file.
-
trinity_scip_test
a BASH code which
calls scip(), to read the LP file defining the trinity tiling problem,
solve the linear programming problem, and write the solution to a file.
-
truel_simulation,
a MATLAB code which
simulates N repetitions of a duel between three players, each of
whom has a known firing accuracy.
-
truel_simulation_test
-
truncated_normal,
a MATLAB code which
works with the truncated normal distribution over [a,b], or
[A,+oo) or (-oo,B], returning the probability density function (PDF),
the cumulative density function (CDF), the inverse CDF, the mean,
the variance, and sample values.
-
truncated_normal_test
-
truncated_normal_rule,
a MATLAB code which
computes a quadrature rule for a
normal probability density function (PDF), sometimes called a
Gaussian distribution, that has been truncated to [A,+oo), (-oo,B]
or [a,b].
-
truncated_normal_rule_test
-
truncated_normal_sparse_grid,
a MATLAB code which
computes a sparse grid based on a normal probability density
function (PDF), also called a Gaussian distribution, that has been
truncated to [A,+oo), (-oo,B] or [A,B].
-
truncated_normal_sparse_grid_test
-
tsp_brute,
a MATLAB code which
is given a table of city-to-city distances and solves a (small!)
traveling salesperson problem (TSP), using brute force.
-
tsp_brute_test
-
tsp_descent,
a MATLAB code which
is given a table of city-to-city distances, chooses an initial tour
at random, and then tries some simple variations to quickly find
a tour of lower length, to solve the traveling salesperson
problem (TSP).
-
tsp_descent_test
-
tsp_greedy,
a MATLAB code which
is given a table of city-to-city distances, and solves a small
traveling salesperson problem (TSP) using the greedy algorithm.
It picks a starting city at random, and then successively visits
the nearest unvisited city.
-
tsp_greedy_test
-
tsp_moler,
a MATLAB code which
tries to optimize the traveling salesperson problem (TSP),
written by Cleve Moler.
-
tsp_moler_test
-
tsp_random,
a MATLAB code which
seeks a solution of the Traveling Salesperson Problem (TSP), by
accepting a table of city-to-city distances, and randomly generating
round trips that visit every city, returning the tour of
shortest length.
-
tsp_random_test
-
tumor_pde,
a MATLAB code which
solves the tumor angiogenesis partial differential equations (PDE)
using MATLAB's pdepe() function.
-
tumor_pde_test
-
two_body_ode,
a MATLAB code which
sets up and solves ordinary differential equations (ODE) which
simulate the behavior of two bodies, constrained to lie in a plane,
moving under the influence of gravity, with one body much more
massive than the other.
-
two_body_ode_test
-
ubvec,
a MATLAB code which
demonstrates how nonnegative integers can be stored as
unsigned binary vectors, and arithmetic can be performed on them.
-
ubvec_test
-
ulam_spiral,
a MATLAB code which
displays the integers as a spiral of grid cells, with the primes
highlighted, so show that they tend to fall along diagonals,
as discovered by Stanislaw Ulam.
-
ulam_spiral_test
-
unicycle,
a MATLAB code which
considers permutations containing a single cycle,
sometimes called cyclic permutations.
-
unicycle_test
-
uniform,
a MATLAB code which
implements a uniform random number generator (RNG) for a variety
of arithmetic types.
-
uniform_test
-
unstable_ode,
a MATLAB code which
sets up and solves an unstable ordinary differential equation (ODE)
which the backward Euler method incorrectly drives to zero.
-
unstable_ode_test
-
upc,
a MATLAB code which
determines the check digit for a Uniform product Code (UPC) or
reports whether a given UPC is valid.
-
upc_test
-
urn_simulation,
a MATLAB code which
simulates the experiment of sampling K balls from an urn containing
N balls of various colors.
-
urn_simulation_test
-
usa_box_plot,
a MATLAB code which
creates simplified maps of the USA in which each state
appears as a box, and the placement of the boxes only
roughly corresponds to the relative locations of states on
an accurate map.
-
usa_box_plot_test
-
usa_cvt_geo,
a MATLAB code which
explores the creation of a centroidal Voronoi Tessellation (CVT) of
the continental United States, based solely on geometric
considerations.
-
usa_cvt_geo_test
-
usa_matrix,
a MATLAB code which
defines the adjacency matrix for US states,
using a variety of matrix formats.
-
usa_matrix_test
-
van_der_corput,
a MATLAB code which
computes elements of the van der Corput
1-dimensional Quasi Mont Carlo (QMC) sequence,
using a simple interface.
-
van_der_corput_test
-
vandermonde,
a MATLAB code which
implements the Bjork-Pereyra algorithm for accurate solution of
linear systems involving the Vandermonde matrix.
-
vandermonde_test
-
vandermonde_approx_1d,
a MATLAB code which
finds a polynomial approximant to data y(x) of a 1D argument
by setting up and solving an overdetermined linear system
for the polynomial coefficients involving the Vandermonde matrix.
-
vandermonde_approx_1d_test
-
vandermonde_approx_2d,
a MATLAB code which
finds a polynomial approximant p(x,y) to data z(x,y) of a 2D argument
by setting up and solving an overdetermined linear system for the
polynomial coefficients involving the Vandermonde matrix.
-
vandermonde_approx_2d_test
-
vandermonde_interp_1d,
a MATLAB code which
finds a polynomial interpolant to data y(x) of a 1D argument
by solving a linear system for the polynomial coefficients
involving the Vandermonde matrix.
-
vandermonde_interp_1d_test
-
vandermonde_interp_2d,
a MATLAB code which
finds a polynomial interpolant to data z(x,y) of a 2D argument
by solving a linear system for the polynomial coefficients
involving the Vandermonde matrix.
-
vandermonde_interp_2d_test
-
vanderpol_ode,
a MATLAB code which
sets up and solves the van der Pol system of
ordinary differential equations (ODE),
for which a limit cycle exists.
-
vanderpol_ode_test
-
vanderpol_ode_period,
a MATLAB code which
sets up and solves the ordinary differential equations (ODE)
defining the van der Pol oscillator
in order to estimate the period of the limit cycle.
-
vanderpol_ode_period_test
-
variomino,
a MATLAB code which
considers variominoes, which are polyominoes in which each square
has been assigned a positive label or "variety",
and the determination of tilings of a region using a specific set of
variominoes.
-
variomino_test
-
vector,
a MATLAB code which
considers a problem involving vectors, which can be
considered to belong to equivalence classes,
for which an arbitrary collection of coefficients must be
gathered, averaged, and then scattered again.
-
vector_test
-
velocity_verlet,
a MATLAB code which
uses a version of the velocity Verlet method to solve
a second order ordinary differential equation (ODE)
of the form y''=f(t,y).
-
velocity_verlet_test
-
verlet_simulation,
a MATLAB code which
demonstates the use of Verlet integration to simulate simple
problems in dynamics, involving changes in position and velocity.
-
verlet_simulation_test
-
vin,
a MATLAB code which
computes the check digit for a Vehicle Identification Number (VIN),
or verifies that a given VIN is legitimate.
-
vin_test
-
voronoi_city,
a MATLAB code which
displays the steps involved in computing the Voronoi diagram
of 3 points, which we think of as cities connected by roads.
-
voronoi_city_test
-
voronoi_display,
a MATLAB code which
computes and displays the Voronoi diagram of a set of points.
-
voronoi_display_test
-
voronoi_mountains,
a MATLAB code which
makes a mountain plot of a Voronoi
diagram, that is, a surface plot of the distance from each
point to its nearest Voronoi generator.
-
voronoi_mountains_test
-
voronoi_neighbors,
a MATLAB code which
is given a set of points in the plane and determines the
Voronoi adjacency structure, that is, the points which
share an edge of the Voronoi diagram.
-
voronoi_neighbors_test
-
voronoi_plot,
a MATLAB code which
estimates the Voronoi neighborhoods of points using sampling,
and with a distance based on the L1, L2, LInfinity
or arbitrary LP norms;
-
voronoi_plot_test
-
voronoi_test,
a MATLAB code which
calls the built-in voronoi() function, which
computes the Voronoi diagram of a set of points.
-
vpa_test,
a MATLAB code which
uses the Variable Precision Arithmetic (VPA) feature of the
Symbolic Math Toolbox to compute arbitrary precision quantities.
-
walker_sample,
a MATLAB code which
efficiently samples a discrete probability vector using
Walker sampling.
-
walker_sample_test
-
walsh_transform,
a MATLAB code which
implements the Walsh data transform.
-
walsh_transform_test
-
wathen_matrix,
a MATLAB code which
compares storage schemes (full, banded, sparse triplet, sparse) and
solution strategies (A\x, Linpack, conjugate gradient) for linear
systems involving the Wathen matrix, which can arise when solving a
problem using the finite element method (FEM).
-
wathen_matrix_test
-
wave_pde,
a MATLAB code which
uses the finite difference method (FDM) in space, and the method of
lines in time, to set up and solve the partial differential
equations (PDE) known as the wave equations, utt = c uxx.
-
wave_pde_test
-
wavelet,
a MATLAB code which
does some simple calculations with wavelet transforms;
-
wavelet_test
-
web_matrix,
a MATLAB code which
stores sample matrices describing a web page network. These matrices
are typically very sparse, and the examples here are stored using the
sparse triplet (ST) format. They can be used to demonstrate
pagerank and other graph algorithms.
-
web_matrix_test
-
wedge_exactness,
a MATLAB code which
investigates the polynomial exactness of a quadrature rule
over the interior of the unit wedge in 3D.
-
wedge_exactness_test
-
wedge_felippa_rule,
a MATLAB code which
returns a Felippa quadrature rule for approximating integrals
over the interior of the unit wedge in 3D.
-
wedge_felippa_rule_test
-
wedge_grid,
a MATLAB code which
computes a grid of points
over the interior of the unit wedge in 3D.
-
wedge_grid_test
-
wedge_integrals,
a MATLAB code which
returns the exact value of the integral of any monomial
over the interior of the unit wedge in 3D.
-
wedge_integrals_test
-
wedge_monte_carlo,
a MATLAB code which
uses the Monte Carlo method to estimate an integral
over the interior of the unit wedge in 3D.
-
wedge_monte_carlo_test
-
weekday,
a MATLAB code which
determines the day of the week corresponding to a given date,
such as 14 October 1066, Julian calendar, ... which was a Saturday.
-
weekday_test
-
weekday_zeller,
a MATLAB code which
uses the Zeller congruence to determine the day of the week corresponding
to a given date, such as 13 July 1989, Gregorian calendar,
... which was a Thursday.
-
weekday_zeller_test
-
welzl,
a MATLAB code which
computes the minimal bounding circle or sphere for a set of points,
using algorithms by Welzl or Ritter,
by Anton Semechko.
-
welzl_test
-
whale,
a MATLAB code which
considers the whale tiling puzzle, a smaller version of the eternity
puzzle. The whale puzzle specifies a region R composed of 288
30-60-90 triangles, and a set of 8 "tiles", each consisting of 36
30-60-90 triangles, and seeks an arrangement of the tiles that
exactly covers the region.
-
whale_test
-
whale_cplex_test
a BASH code which
calls cplex(), to read the LP file defining the whale tiling problem,
solve the linear programming problem, and write the solution to a file.
-
whale_gurobi_test
a BASH code which
calls gurobi(), to read the LP file defining the whale tiling problem,
solve the linear programming problem, and write the solution to a file.
-
will_you_be_alive,
a MATLAB code which
carries out the probability simulations
described in "Will You Be Alive 10 Years From Now?"
by Paul Nahin;
-
will_you_be_alive_test
-
wishart_matrix,
a MATLAB code which
produces sample matrices from the Wishart or Bartlett distributions,
useful for sampling random covariance matrices.
-
wishart_matrix_test
-
wtime,
a MATLAB code which
returns a reading of the wall clock time in seconds.
-
wtime_test
-
xml2struct,
a MATLAB code which
reads a file containing XML data, and produces a corresponding
MATLAB struct.
-
xml2struct_test
-
xy_display,
a MATLAB code which
reads a set of 2D
points from a simple XY graphics file and plots them.
-
xy_io,
a MATLAB code which
reads and writes simple graphic files in the XY, XYL and XYF formats.
-
xy_io_test
-
xyf_display,
a MATLAB code which
reads XYF information
containing a list of 2D point coordinates, and the indices of points
that form faces, and displays a plot.
-
xyl_display,
a MATLAB code which
reads XYL information
containing a list of 2D point coordinates, and the indices of points
that form lines, and displays a plot.
-
xyz_display,
a MATLAB code which
displays a 3D plot from a file of (X,Y,Z) point coordinates.
-
xyz_display_test
-
xyz_io,
a MATLAB code which
reads and writes simple graphics files in the XYZ, XYZL and XYZF formats.
-
xyz_io_test
-
xyzf_display,
a MATLAB code which
reads XYZF information
containing a list of 3D point coordinates, and the indices of points
that form faces, and displays a plot in the MATLAB graphics window.
-
xyzl_display,
a MATLAB code which
reads XYZL information
containing a list of 3D point coordinates, and the indices of points
that form lines, and displays a plot.
-
zero_brent,
a MATLAB code which
seeks a solution of a scalar nonlinear equation f(x)=0,
by Richard Brent.
-
zero_brent_test
-
zero_chandrupatla,
a MATLAB code which
finds a zero of a scalar function of a scalar variable,
starting from a change of sign interval, using the
Chandrupatla method, which can converge faster than
bisection, regula falsi, or Brent's method,
by Tirupathi Chandrapatla.
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zero_chandrupatla_test
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zero_itp,
a MATLAB code which
finds a zero of a scalar function of a scalar variable,
starting from a change of sign interval, using the
Interpolate/Truncate/Project (ITP) method, which has
faster convergence than the bisection method.
-
zero_itp_test
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zero_laguerre,
a MATLAB code which
uses Laguerre's method to find the zero of a function.
The method needs first and second derivative information.
The method almost always works when the function is a polynomial.
-
zero_laguerre_test
-
zero_muller,
a MATLAB code which
seeks a root of a nonlinear equation using the Muller method,
with complex arithmetic.
-
zero_muller_test
-
zero_rc,
a MATLAB code which
seeks a solution of a scalar nonlinear equation f(x)=0,
using reverse communication (RC), by Richard Brent.
-
zero_rc_test
-
ziggurat,
a MATLAB code which
implements uniform, normal and exponential
random number generators (RNG) using the ziggurat method,
by Marsaglia and Tsang.
-
ziggurat_test
-
zombie_ode,
a MATLAB code which
sets up and solves a system of ordinary differential equations (ODE)
for a generalized Susceptible-Infected-Recovered (SIR) disease
model to simulate a zombie attack, developed by Philip Munz.
-
zombie_ode_test
-
zoomin,
a MATLAB code which
implements procedures for finding the zero of a
scalar nonlinear function.
-
zoomin_test
Last revised on 19 November 2024.