Python Source
-
allen_cahn_pde,
a Python code which
sets up and solves the Allen-Cahn reaction-diffusion
partial differential equations (PDE) in one space
dimension and time.
-
alpert_rule,
a Python code which
can set up an Alpert quadrature rule to approximate the
integrals of functions which are
regular, log(x) singular, or 1/sqrt(x) singular.
-
analemma,
a Python 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.
-
animation_test,
a Python code which
computes a sequence of solutions to a partial differential equation,
using matplotlib, displaying each solution to the screen WITHOUT
requiring the user to hit RETURN to see the next image.
-
annulus_monte_carlo,
a Python code which
uses the Monte Carlo method to estimate the integral of a function
over the interior of a circular annulus in 2D.
-
annulus_rule,
a Python code which
computes a quadrature rule for estimating integrals of a function
over the interior of a circular annulus in 2D.
-
arenstorf_ode,
a Python code which
describes an ordinary differential equation (ODE) which defines
a stable periodic orbit of a spacecraft around the Earth and the Moon.
-
args,
a Python code which
reports the command line arguments with which it was invoked;
-
asa047,
a Python 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;
-
asa053,
a Python code which
produces sample matrices from the Wishart distribution,
by William Smith and Ronald Hocking.
This is a version of Applied Statistics Algorithm 53.
-
asa063,
a Python code which
evaluates the incomplete Beta function,
by KL Majumder and G Bhattacharjee.
This is a version of Applied Statistics Algorithm 63;
-
asa082,
a Python code which
computes the determinant of an orthogonal matrix;
this is Applied Statistics Algorithm 82,
by J C Gower.
-
asa103,
a Python code which
evaluates the digamma or psi function,
by Jose Bernardo;
this is a version of Applied Statistics Algorithm 103;
-
asa183,
a Python code which
implements a random number generator (RNG),
by Wichman and Hill;
this is a version of Applied Statistics Algorithm 183;
-
asa241,
a Python code which
computes the inverse of the normal cumulative density function (CDF),
by Michael Wichura;
this is a version of Applied Statistics Algorithm 241;
-
atbash,
a Python code which
applies the Atbash substitution cipher to a string of text.
-
backtrack_binary_rc,
a Python code which
carries out a backtrack search for a set of binary decisions, using
reverse communication (RC).
-
backward_euler,
a Python code which
solves one or more ordinary differential equations (ODE)
using the backward Euler method.
-
ball_distance,
a Python code which
considers the problem of describing the typical value of the distance
between a pair of points randomly selected from the interior of
the unit ball in 3D.
-
ball_grid,
a Python code which
computes grid points inside a 3D ball.
-
ball_integrals,
a Python code which
returns the exact value of the integral of any monomial
over the interior of the unit ball in 3D.
-
ball_monte_carlo,
a Python code which
applies a Monte Carlo method to estimate integrals of a function
over the interior of the unit ball in 3D;
-
bank,
a Python 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.
-
barycentric_interp_1d,
a Python 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.
-
bellman_ford,
a Python 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.
-
bernstein_polynomial,
a Python code which
evaluates the Bernstein polynomials;
-
besselj,
a Python code which
evaluates Bessel J functions of noninteger order;
-
bicycle_lock,
a Python code which
simulates the process of determining the secret combination of
a bicycle lock, an integer between 000 and 999.
-
biochemical_linear_ode,
a Python code which
defines a linear biochemical ordinary differential equation (ODE).
-
biochemical_nonlinear_ode,
a Python code which
defines a nonlinear biochemical ordinary differential equation (ODE).
-
bisect,
a Python 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 classes.
-
bisection_rc,
a Python code which
seeks a solution to the nonlinear equation F(X)=0 using bisection
within a user-supplied change of sign interval [A,B].
The procedure is written using reverse communication (RC).
-
black_scholes,
a Python code which
implements some simple approaches to
the Black-Scholes option valuation theory,
by Desmond Higham.
-
blas1_d,
a Python code which
constitutes the Level 1 Basic Linear Algebra Subprograms (BLAS),
for vector-vector operations
using double precision real arithmetic,
by Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh.
-
blowup_ode,
a Python code which
considers an ordinary differential equation (ODE) y'=y^2.
whose solution "blows up" in finite time.
-
boundary_word,
a Python code which
works with a polyomino that is described by its boundary word,
a sequence of U/D/L/R symbols that indicate how to trace out
its boundary.
-
brownian_motion_simulation,
a Python code which
simulates Brownian motion in an M dimensional region.
-
brusselator_ode,
a Python code which
defines the Brusselator ordinary differential equation (ODE) system.
-
burgers_solution,
a Python code which
evaluates exact solutions of the
time-dependent 1D viscous Burgers equation.
-
bvec,
a Python code which
demonstrates how signed integers can be stored as
binary vectors, and arithmetic can be performed on them.
-
c4lib,
a Python code which
implements certain elementary functions for
single precision complex (C4) variables;
-
c8lib,
a Python code which
implements certain elementary functions for
double precision complex (C8) variables;
-
caesar,
a Python code which
applies a Caesar Shift Cipher to a string of text.
-
calpak,
a Python code which
makes various calendar calculations;
-
cauchy_principal_value,
a Python code which
uses Gauss-Legendre quadrature to estimate the Cauchy Principal Value
(CPV) of certain singular integrals.
-
cfd_barba,
a Python code which
contains some of the iPython workbooks
associated with the "12 Steps to Navier-Stokes" presentation
by Lorena Barba.
-
cg,
a Python code which
implements a simple version of the conjugate gradient (CG) method
for solving a system of linear equations of the form A*x=b,
suitable for situations in which the matrix A is positive definite
(only real, positive eigenvalues) and symmetric.
-
cg_rc,
a Python code which
implements the conjugate gradient (CG) method for solving
a positive definite sparse linear system A*x=b,
using reverse communication (RC).
-
change_making,
a Python code which
considers the change making problem,
in which a given sum is to be formed using coins of various denominations.
-
chebyshev_interp_1d,
a Python code which
determines the combination of Chebyshev polynomials which
interpolates a set of data, so that p(x(i)) = y(i).
-
chebyshev_polynomial,
a Python code which
considers the Chebyshev polynomials T(i,x), U(i,x), V(i,x) and W(i,x).
Functions are provided to evaluate the polynomials, determine their
zeros, produce their polynomial coefficients, produce related
quadrature rules, project other functions onto these polynomial
bases, and integrate double and triple products of the polynomials.
-
chinese_remainder_theorem,
a Python code which
demonstrates the Chinese remainder theorem, for reconstructing a
number based on its remainders against a set of bases.
-
chrpak,
a Python code which
manipulates characters and strings;
-
chuckaluck_simulation,
a Python code which
simulates the Chuck-a-Luck gambling game.
-
circle_arc_grid,
a Python code which
computes grid points along a circular arc.
-
circle_distance,
a Python code which
considers the problem of describing the typical value of the distance
between a pair of points randomly selected on the circumference
of the unit circle.
-
circle_integrals,
a Python code which
returns the exact value of the integral of any monomial
over the circumference of the unit circle in 2D.
-
circle_monte_carlo,
a Python code which
applies a Monte Carlo method to estimate the integral of a function
along the circumference of the unit circle in 2D;
-
clausen,
a Python code which
evaluates a Chebyshev interpolant to the Clausen function Cl2(x).
-
cobweb_plot,
a Python library which
displays a cobweb plot illustrating the process of function iteration,
by John D Cook.
-
collatz_recursive,
a Python code which
demonstrates recursive programming by considering
the simple Collatz 3n+1 problem.
-
combination_lock,
a Python code which
simulates the process of determining the secret combination of a lock.
-
combo,
a Python code which
includes routines for ranking, unranking, enumerating and
randomly selecting balanced sequences, cycles, graphs, Gray codes,
subsets, partitions, permutations, restricted growth functions,
Pruefer codes and trees.
-
compass_search,
a Python code which
seeks the minimizer of a scalar function of several variables
using compass search, a direct search algorithm
that does not use derivatives.
-
complex_numbers_test
-
condition,
a Python code which
implements methods of computing or estimating
the condition number of a matrix.
-
continued_fraction
a Python code which
implements some simple algorithms for dealing with simple and
generalized continued fractions.
-
cordic,
a Python code which
computes a few special functions using the CORDIC algorithm.
-
cosine_transform,
a Python code which
demonstrates some simple properties of the discrete cosine transform
(DCT).
-
counterfeit_detection,
a Python 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.
-
csv_test,
a Python code which
tests the csv() library
for reading and writing Comma Separated Value (CSV) data files.
-
cube_distance,
a Python code which
considers the problem of describing the typical value of the distance
between a pair of points randomly selected in the interior
of the unit cube in 3D.
-
cube_grid,
a Python code which
computes a grid of points
over the interior of a cube in 3D.
-
cube_integrals,
a Python code which
returns the exact value of the integral of any monomial
over the interior of the unit cube in 3D.
-
cube_monte_carlo,
a Python code which
applies a Monte Carlo method to estimate the integral of a function
over the interior of the unit cube in 3D.
-
cuda_loop,
a Python code which
shows how, in a CUDA program, the choice of block and
thread factors determines the allocation of tasks to processors.
-
cvt_1d_lloyd,
a Python code which
computes an N-point Centroidal Voronoi Tessellation (CVT)
within the interval [0,1], under a uniform density,
using the Lloyd iteration to compute the Voronoi regions exactly.
-
cvt_2d_sampling,
a Python 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.
-
cvxopt_svm,
a Python code which
solves a support vector machine (SVM) problem by formulating it
as a quadratic programming problem to be solved by cvxopt().
-
cvxopt_test
-
cycle_brent,
a Python 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_floyd,
a Python 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.
-
delaunay_test,
a Python code which
demonstrates the use of the scipy.spatial function Delaunay(),
to compute a Voronoi diagram, and matplotlib.pyplot.triplot(),
to display it.
-
dg1d_poisson,
a Python code which
applies the discontinuous Galerkin method (DG) to a 1D version of
the Poisson equation,
based on a code by Beatrice Riviere.
-
dijkstra,
a Python code which
implements a simple version of the Dijkstra minimum distance algorithm
for graphs.
-
diophantine_nd,
a Python code which
is given a Diophantine equation in N variables, and
returns all nonnegative solutions, or all strictly positive solutions.
-
disk_distance,
a Python code which
considers the problem of describing the typical value of the distance
between a pair of points randomly selected inside the unit disk.
-
disk_grid,
a Python code which
computes grid points within the interior of
a disk of user specified radius and center in 2D,
using matplotlib to create an image of the grid.
-
disk_monte_carlo,
a Python code which
applies a Monte Carlo (MC) method to estimate integrals of a function
over the interior of the general disk in 2D;
-
disk_rule,
a Python code which
computes a quadrature rule
over the interior of the general disk in 2D.
-
disk01_integrals,
a Python code which
returns the exact value of the integral of any monomial
over the interior of the unit disk in 2D.
-
disk01_monte_carlo,
a Python code which
applies a Monte Carlo method to estimate integrals of a function
over the interior of the unit disk in 2D;
-
disk01_quarter_monte_carlo,
a Python code which
applies a Monte Carlo method to estimate integrals of a function
over the interior of the unit quarter disk in 2D;
-
disk01_rule,
a Python code which
computes a quadrature rule
to approximate the integral of a function
over the interior of the unit disk in 2D,
with radius 1 and center (0,0).
-
dolfin-convert,
a Python code which
can convert mesh file from Gmsh, MEDIT, METIS or SCOTCH format to an
XML format suitable for use by DOLFIN or FENICS,
by Anders Logg.
-
doomsday,
a Python 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.
-
dosage_ode,
a Python code which
uses a system of ordinary differential equations (ODE) to
simulate the blood levels of a medicinal drug that should
stay between medicinal and toxic limits.
-
duel_simulation,
a Python code which
simulates N repetitions of a duel between two players, each of
whom has a known firing accuracy.
-
ellipse_grid,
a Python code which
computes grid points
over the interior of an ellipse in 2D.
-
ellipse_monte_carlo,
a Python code which
uses the Monte Carlo method to estimate the value of integrals
over the interior of an ellipse in 2D.
-
ellipsoid_grid,
a Python code which
computes a grid of points
over the interior of an ellipsoid in 3D.
-
ellipsoid_monte_carlo,
a Python code which
uses the Monte Carlo method to estimate the value of integrals
over the interior of an ellipsoid in M dimensions.
-
elliptic_integral,
a Python code which
evaluates complete elliptic integrals of first, second and third kind,
using the Carlson elliptic integral functions.
-
euler,
a Python code which
solves one or more ordinary differential equations (ODE)
using the forward Euler method.
-
exactness,
a Python 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).
-
exp_ode,
a Python code which
sets up an ordinary differential equation (ODE)
whose solution is an exponential function.
-
fastgl,
a Python code which
carries out the rapid computation of the Kth value and weight of
an N point Gauss-Legendre quadrature rule for approximating
the integral of a function over the interval [-1,+1],
by Ignace Bogaert.
-
fd_predator_prey,
a Python code which
solves a time-dependent predator prey system using the
finite difference method (FDM).
-
fd1d_advection_lax_wendroff,
a Python 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,
creating a graphics file with matplotlib.
-
fd1d_bvp,
a Python code which
applies the finite difference method (FDM)
to a two point boundary value problem (BVP) in one spatial dimension.
-
fd1d_heat_explicit,
a Python code which
implements a finite difference method (FDM), explicit in time,
to solve the time dependent 1D heat equation;
-
fd1d_heat_implicit,
a Python code which
implements a finite difference method (FDM), implicit in time,
to solve the time dependent 1D heat equation;
-
fd2d_heat_steady,
a Python code which
implements a finite difference method (FDM) for the steady
(time independent) 2D heat equation;
-
fem_basis,
a Python code which
can define and evaluate 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_to_xml,
a Python 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.
-
fem1d,
a Python code which
applies the finite element method (FEM) to a boundary value problem
(BVP) in one spatial dimension, using a procedural approach.
-
fem1d_bvp_linear,
a Python code which
applies the finite element method (FEM), with piecewise linear elements,
to a two point boundary value problem (BVP) in one spatial dimension,
and compares the computed and exact solutions
with the L2 and seminorm errors.
-
fem1d_bvp_quadratic,
a Python code which
applies the finite element method (FEM),
with piecewise quadratic elements,
to a two point boundary value problem (BVP) in one spatial dimension,
and compares the computed and exact solutions
with the L2 and seminorm errors.
-
fem1d_classes,
a Python code which
defines classes useful for solving a boundary value problem (BVP)
of the form u''+2u'+u=f in 1 spatial dimension,
using the finite element method (FEM),
by Mike Sussman.
-
fem1d_heat_explicit,
a Python code which
uses the finite element method (FEM) and explicit time stepping
to solve the time dependent heat equation in 1D.
-
fem1d_model,
a Python code which
applies the finite element method (FEM) to a boundary value problem
(BVP) in one spatial dimension, using a procedural approach.
-
fem2d_bvp_linear,
a Python code which
applies the finite element method (FEM),
with piecewise bilinear elements,
to a 2D boundary value problem (BVP) in a rectangle.
-
file_name_sequence,
a Python 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.
-
filum,
a Python code which
performs various operations on files;
-
fire_simulation,
a Python code which
simulates a forest fire over a rectangular array of trees,
starting at a single random location. It is intended as a starting
point for the development of a parallel version.
-
flame_ode,
a Python code which
solves an ordinary differential equation (ODE) which models
the growth of a ball of flame in a combustion process.
-
florida_cvt_geo,
Python codes which
explore the creation of a centroidal Voronoi Tessellation (CVT) of
the state of Florida, based solely on geometric considerations.
-
florida_cvt_pop,
Python codes which
explore the creation of a centroidal Voronoi Tessellation (CVT) of
the state of Florida, based on population considerations.
-
fn,
a Python code which
evaluates elementary and special functions using
Chebyshev polynomials; functions include Airy, Bessel I, J, K and Y,
beta, confluent hypergeometric, error, gamma, log gamma, Pochhammer,
Spence; integrals include hyperbolic cosine, cosine, Dawson,
exponential, logarithmic, hyperbolic sine, sine; by Wayne Fullerton.
-
four_fifths,
a Python 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. The code is by Brian Hayes.
-
freefem_msh_io,
a Python code which
can read and write files used by the FreeFem++ finite element program
to store mesh information.
-
fsolve_test,
a Python code which
calls fsolve() which
seeks the solution x of one or more nonlinear equations f(x)=0.
-
gegenbauer_cc,
a Python code which
computes the Gegenbauer weighted integral of a function f(x)
using a Clenshaw-Curtis approach.
-
gegenbauer_polynomial,
a Python code which
evaluates the Gegenbauer polynomial and associated functions.
-
geometry,
a Python code which
performs geometric calculations in 2, 3 and M dimensional space,
including the computation of angles, areas, containment, distances,
intersections, lengths, and volumes.
-
gmgsolve,
a Python code which
applies one step of the V-cycle of the geometric multigrid method,
by Mike Sussman.
-
graphics_test,
Python codes which
illustrate how various kinds of data can be displayed
and analyzed graphically, using the matplotlib() graphics package.
-
graphviz_test
-
haar,
a Python code which
computes the Haar transform of data.
-
halton,
a Python code which
computes elements of a Halton Quasi Monte Carlo (QMC) sequence,
using a simple interface.
-
hammersley,
a Python code which
computes elements of a Hammersley Quasi Monte Carlo (QMC) sequence,
using a simple interface.
-
hankel_cholesky,
a Python code which
computes the upper Cholesky factor R of a nonnegative definite
symmetric H matrix so that H = R' * R.
-
hankel_cholesky,
a Python code which
computes the upper Cholesky factor R of a nonnegative definite
symmetric Hankel matrix so that H = R' * R.
-
hankel_spd,
a Python 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'.
-
hdf5_test,
a Python code which
demonstrates the use of the HDF5 library and file format.
-
hello,
a Python code which
prints "Hello, world!".
-
hello_mpi,
a Python code which
prints out "Hello, world!",
carried out in parallel using MPI and MPI4PY.
-
henon_heiles_ode,
a Python code which
solves the Henon-Heiles system of ordinary differential equations (ODE)
which model the motion of a star around the galactic center.
-
hilbert_curve,
a Python code which
computes the sequence of discrete Hilbert curves whose limit
is a space-filling curve.
-
humps_ode,
a Python code which
solves an ordinary differential equation (ODE)
whose solution is a double hump curve.
-
hyperball_distance,
a Python code which
considers the problem of describing the typical value of the distance
between a pair of points randomly selected from the interior of the
unit hyperball in M dimensions.
-
hyperball_integrals,
a Python code which
returns the exact value of the integral of any monomial
over the interior of the unit hyperball in M dimensions.
-
hyperball_monte_carlo,
a Python code which
applies a Monte Carlo method to estimate the integral of a function
over the interior of the unit ball in M dimensions;
-
hypercube_grid,
a Python code which
computes a grid of points
over the interior of a hypercube in M dimensions.
-
hypercube_integrals,
a Python code which
returns the exact value of the integral of any monomial
over the interior of the unit hypercube in M dimensions.
-
hypercube_monte_carlo,
a Python code which
applies a Monte Carlo method to estimate the integral of a function
over the interior of the unit hypercube in M dimensions.
-
hypersphere_distance,
a Python code which
considers the problem of describing the typical value of the distance
between a pair of points randomly selected from the surface of the unit
hypersphere in M dimensions.
-
hypersphere_integrals,
a Python code which
returns the exact value of the integral of any monomial
over the surface of the unit hypersphere in M dimensions.
-
hypersphere_monte_carlo,
a Python code which
applies a Monte Carlo method to estimate the integral of a function
on the surface of the unit sphere in M dimensions;
-
i4lib,
a Python code which
contains many utility routines, using single precision integer (I4)
arithmetic.
-
i8lib,
a Python code which
contains many utility routines, using double precision integer (I8)
arithmetic.
-
isbn,
a Python code which
determines the check digit for an International Standard Book Number
(ISBN), or reports whether a given ISBN is valid.
-
jacobi,
a Python code which
implements the Jacobi iteration for the iterative solution of
linear systems.
-
jacobi_eigenvalue,
a Python code which
implements the Jacobi iteration for the iterative determination
of the eigenvalues and eigenvectors of a real symmetric matrix.
-
kepler_ode,
a Python code which
defines the ordinary differential equations (ODE) for a
Kepler two-body gravitational system.
-
knapsack_01,
a Python code which
uses brute force to solve small versions of the 0/1 knapsack problem;
-
kronrod,
a Python code which
computes a Gauss and Gauss-Kronrod pair of quadrature rules
of arbitrary order for the approximation of the integral of
a function over the interval [-1,+1],
by Robert Piessens, Maria Branders.
-
lagrange_interp_1d,
a Python 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).
-
latin_random,
a Python code which
computes Latin Random Squares of N points in M dimensions;
-
lebesgue,
a Python code which
is given a set of nodes in 1D, and
plots the Lebesgue function, and estimates the Lebesgue constant,
which measures the maximum magnitude of the potential error
of Lagrange polynomial interpolation.
-
legendre_polynomial,
a Python code which
evaluates the Legendre polynomial and associated functions.
-
legendre_product_polynomial,
a Python code which
defines Legendre product polynomials, creating a multivariate
polynomial as the product of univariate Legendre polynomials.
-
legendre_shifted_polynomial,
a Python code which
evaluates the shifted Legendre polynomial, with the domain [0,1].
-
levenshtein,
a Python code which
returns the Levenshtein distance between two strings.
-
line_distance,
a Python code which
considers the problem of describing the typical value of the distance
between a pair of points randomly selected in the unit line segment.
-
line_grid,
a Python code which
computes a grid of points
over the interior of a line segment in 1D.
-
line_integrals,
a Python code which
returns the exact value of the integral of any monomial
over the length of the unit line in 1D.
-
line_monte_carlo,
a Python code which
applies a Monte Carlo method to estimate the integral of a function
over the length of the unit line in 1D.
-
linpack_d,
a Python code which
factors and solves linear systems
using double precision real arithmetic,
by Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart.
-
linplus_c8,
a Python code which
carries out some linear algebra operations on complex matrices.
-
llsq,
a Python code which
solves the simple linear least squares (LLS) problem of finding the
formula of a straight line y=a*x+b which minimizes the root mean
square error to a set of N data points.
-
loadtxt_test,
a Python program which
calls the numpy function loadtxt() to extract numeric data from a
text file.
-
local_min_rc,
a Python 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.
-
log_normal,
a Python code which
returns quantities related to the log normal Probability
Distribution Function (PDF).
-
log_normal_truncated_ab,
a Python code which
returns quantities related to the log normal Probability
Distribution Function (PDF) truncated to the interval [A,B].
-
logistic_bifurcation,
a Python code which
computes the bifurcation diagram for the logistic equation,
by John Cook.
-
lorenz_ode,
a Python code which
approximates solutions to the Lorenz system
of ordinary differential equations (ODE),
creating graphics files using matplotlib.
-
lorenz_ode_sensitivity_test,
a Python 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 Python code which
can compute the Luhn check digit for a string, or verify a string,
as used for error detection in credit card numbers.
-
machar,
a Python code which
dynamically computes the values of
various machine characteristic constants,
by William Cody;
-
machine,
a Python code which
returns tabulated values of
the constants associated with computer arithmetic;
-
mandelbrot,
a Python code which
generates a Portable Network Graphics (PNG) image of the
Mandelbrot set;
-
mario,
a Python code which
creates a sort of "needlepoint" image of Mario, as an array of
colored squares.
-
matrix_exponential,
a Python code which
demonstrates some simple approaches to the problem of computing the
exponential of a matrix.
-
md,
a Python code which
carries out a molecular dynamics (MD) simulation, intended as
a starting point for implementing a parallel version.
-
midpoint,
a Python code which
solves one or more ordinary differential equations (ODE)
using the midpoint method.
-
monomial,
a Python 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 in a given range.
-
monomial_value,
a Python code which
evaluates a monomial in M dimensions.
-
movie_test,
a Python code which
creates a movie file from a sequence of solutions to a
partial differential equation, using matplotlib.
-
naca,
a Python code which
can take the parameters of certain NACA airfoils and return the
coordinates of a sequence of points that outline the wing shape.
-
nas,
a Python code which
runs the NASA kernel benchmark.
-
navier_stokes_2d_exact,
a Python code which
evaluates an exact solution to the incompressible time-dependent
Navier-Stokes equations (NSE) over an arbitrary domain in 2D.
-
navier_stokes_3d_exact,
a Python code which
evaluates an exact solution to the incompressible time-dependent
Navier-Stokes equations (NSE) over an arbitrary domain in 3D.
-
nearest_interp_1d,
a Python code which
interpolates a set of data using a piecewise constant interpolant
defined by the nearest neighbor criterion,
creating graphics files for processing by matplotlib.
-
newton,
a Python code which
applies the Newton method to solve a single nonlinear equation f(x)=0.
-
newton_interp_1d,
a Python code which
finds a polynomial interpolant to data using Newton divided
differences.
-
ngrams,
a Python code which
can analyze a string or text against the observed frequency of
"ngrams" (particular sequences of n letters) in English text.
-
normal,
a Python code which
implements a random number generator (RNG) for normally distributed
values;
-
normal_ode,
a Python code which
sets up an ordinary differential equation (ODE)
defining the normal probability density function (PDF).
-
normal01_multivariate_distance,
a Python code which
considers the problem of describing the typical value of the distance
between a pair of points randomly selected from an isotropic
standard normal distribution in M dimensions.
-
ode_euler,
a Python code which
applies the Euler method to estimate the solution
of an ordinary differential equation y'=f(x,y), over the
interval [a,b], with initial condition y(a)=ya, using n steps.
-
oscillator_ode,
a Python code which
defines the highly oscillatory ordinary differential equation (ODE).
-
owen,
a Python code which
evaluates the Owen T function;
-
padua,
a Python code which
returns the coordinates of the 2D Padua points,
as well as interpolation weights or quadrature weights,
and images of the points graphics files.
-
pariomino,
a Python code which
considers pariominoes, which are polyominoes with a
checkerboard parity.
-
partition_problem,
a Python code which
seeks solutions of the partition problem, splitting a set of
integers into two subsets with equal sum.
-
pbma_io,
a Python code which
reads or writes ASCII Portable Bit Map (PBM) 2D graphics files;
-
pbmb_io,
a Python code which
reads or writes a binary Portable Bit Map (PBM) 2D graphics file;
-
pdflib,
a Python 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.
-
pendulum_double_ode,
a Python code which
defines the double pendulum ordinary differential equation (ODE).
-
pendulum_nonlinear_ode,
a Python code which
sets up 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_ode,
a Python code which
sets up 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.
-
perceptron,
a Python code which
demonstrates the calculation of a classifier of linearly separable data
using the perceptron algorithm.
-
pgma_io,
a Python code which
reads or writes ASCII Portable Gray Map (PGM) 2D graphics files;
-
pgmb_io,
a Python code which
reads or writes a binary Portable Gray Map (PGM) 2D graphics file;
-
pink_noise,
a Python code which
computes a pink noise signal obeying a 1/f power law.
-
pip3_test
-
polpak,
a Python code which
evaluates a variety of mathematical functions, including
Chebyshev, Gegenbauer, Hermite, Jacobi, Laguerre,
Legendre polynomials, and the Collatz sequence.
-
polygon_grid,
a Python code which
generates a grid of points
over the interior of a polygon in 2D.
-
polygon_integrals,
a Python code which
returns the exact value of the integral of any monomial
over the interior of a polygon in 2D.
-
polygon_monte_carlo,
a Python code which
applies a Monte Carlo method to estimate the integral of a function
over the interior of a polygon in 2D.
-
polygon_properties,
a Python 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, diameter, distance to a point,
inradius, lattice area, nearest point in set, outradius, uniform
sampling.
-
polygon_triangulate,
a Python code which
triangulates a possibly nonconvex polygon in 2D,
and which can use gnuplot to display the external edges and
internal diagonals of the triangulation.
-
polynomial,
a Python code which
adds, multiplies, differentiates, evaluates and prints multivariate
polynomials in a space of M dimensions.
-
polynomials,
a Python code which
defines multivariate polynomials over rectangular domains, for
which certain information is to be determined, such as the maximum
and minimum values.
-
polyomino_parity,
a Python code which
uses parity considerations to determine whether a given set of
polyominoes can tile a specified region.
-
polyominoes,
a Python code which
manipulates polyominoes and tilings.
-
ppma_io,
a Python code which
reads or writes an ASCII Portable Pixel Map (PPM) 2D graphics file;
-
ppmb_io,
a Python code which
reads or writes a binary Portable Pixel Map (PPM) 2D graphics file;
-
praxis,
a Python code which
minimizes a scalar function of several variables, without
requiring derivative information,
by Richard Brent.
-
predator_prey_ode,
a Python code which
solves a time-dependent predator-prey system
of ordinary differential equations (ODE).
-
prime,
a Python code which
counts the number of primes between 1 and N,
intended as a starting point for a parallel version.
-
prime_mpi,
a Python code which
counts the number of primes between 1 and N,
carried out in parallel using MPI and MPI4PY.
-
prob,
a Python code which
evaluates, samples, inverts, and characterizes a number of
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.
-
pwl_interp_1d,
a Python code which
interpolates a set of data using a piecewise linear function in 1D.
-
pwl_interp_2d,
a Python code which
interpolates a set of data using a piecewise linear function in 2D.
-
py_test,
Python codes which
illustrate various features of Python programming.
-
python_intrinsics_test,
a Python code which
demonstrates some of the intrinsic functions in the Python language.
-
python_mistake,
Python codes which
illustrate mistakes caused by Python,
encouraged by Python, or made difficult to spot because of Python.
-
pytorch_test,
Python codes which
illustrate certain features of pytorch.
-
pyramid_grid,
a Python code which
computes a grid of points
over the interior of the unit pyramid in 3D;
-
pyramid_monte_carlo,
a Python code which
applies a Monte Carlo (MC) method to estimate integrals of a function
over the interior of the unit pyramid in 3D;
-
quad_mpi,
a Python code which
approximates an integral using a quadrature rule,
carried out in parallel using MPI and MPI4PY.
-
quad_serial,
a Python code which
applies a quadrature rule to estimate an integral,
intended as a starting point for parallelization exercises.
-
quadex_ode
a Python code which
solves a stiff ordinary differential equation (ODE), whose
exact solution is a parabola, but for which errors grow exponentially.
-
quadrule,
a Python code which
implements rules for approximate integration (quadrature)
in one dimension;
-
quasiperiodic_ode,
a Python code which
sets up a system of
ordinary differential equations (ODE) for a problem with a
quasiperiodic solution.
-
quaternions,
a Python code which
carries out some simple arithmetic operations for quaternions.
-
r83,
a Python code which
contains linear algebra routines for r83 matrices
(real, 64 bit, tridiagonal 3xN format).
-
r8col,
a Python code which
contains utility routines for an R8COL, that is,
a double precision real MxN array, considered as N column vectors,
each of length M. The data may be thought of as a matrix of
multiple columns, and many operations will be carried out columnwise.
-
r8ge,
a Python code which
contains linear algebra routines for R8GE matrices
(real, 64 bit, General format).
-
r8lib,
a Python code which
contains many utility routines, using double precision real (R8)
arithmetic.
-
r8lt,
a Python code which
contains linear algebra routines for R8LT matrices
(real, 64 bit, Lower Triangular).
-
r8poly,
a Python code which
contains a number of utilities for polynomials with R8 coefficients,
that is, using double precision or 64 bit real arithmetic.
-
r8row,
a Python code which
contains utility routines for an R8ROW, that is,
an double precision real MxN array, considered as M row vectors,
each of length N. The data may be thought of as a matrix of
multiple rows, and many operations will be carried out rowwise.
-
r8st,
a Python code which
contains linear algebra routines for R8ST matrices
(real, 64 bit, Sparse Triplet (ST)).
-
r8ut,
a Python code which
contains linear algebra routines for R8UT matrices
(real, 64 bit, Upper Triangular).
-
randlc,
a Python code which
implements a random number generator (RNG)
used by the NAS Benchmark programs.
-
random_data,
a Python code which
uses a random number generator (RNG) to sample points for
various probability distributions, spatial dimensions, and geometries,
including the M-dimensional cube, ellipsoid, simplex and sphere.
-
random_matrix_eigenvalues,
a Python code which
demonstrates how, for certain probability density functions (PDF),
a symmetric matrix with entries sampled from that PDF will have
eigenvalues distributed according to the Wigner semicircle distribution.
-
random_sorted,
a Python code which
generates vectors of random values which are already sorted.
-
ranlib,
a Python 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.
-
rbf_interp_1d,
a Python code which
defines and evaluates
radial basis function (RBF) interpolants to 1D data.
-
rbf_interp_2d,
a Python code which
defines radial basis function (RBF) interpolants to 2D data.
-
ripple_ode,
a Python code which
solves an ordinary differential equation (ODE) whose family of
solutions start as ripples and end as hyperbolas.
-
rk4,
a Python 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.
-
rkf45,
a Python code which
implements the Runge-Kutta-Fehlberg (RKF) solver for the approximate
solution of an ordinary differential equation (ODE) system.
-
rnglib,
a Python code which
implements a random number generator (RNG) with splitting facilities,
allowing multiple independent streams to be computed,
by L'Ecuyer and Cote.
-
robertson_ode,
a Python code which
sets up a system of three nonlinear stiff ordinary differential
equations (ODE) characterizing an autocatalytic chemical reaction.
-
roessler_ode,
a Python code which
defines the right hand side of the Roessler ODE system.
-
root_rc,
a Python code which
seeks a solution of a scalar nonlinear equation f(x)=0,
using reverse communication (RC), by Gaston Gonnet.
-
roots_rc,
a Python code which
seeks solutions of a system of nonlinear equations,
using reverse communication (RC), by Gaston Gonnet.
-
rot13,
a Python code which
makes a copy of a file which has
been encoded using the ROT13 coding and a ROT5 coding for digits.
-
row_echelon_integer,
a Python 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.
-
rubber_band_ode,
a Python code which
defines and solves a set of ordinary differential equations (ODE)
describing a mass suspended by a spring and rubber band, which
can exhibit chaotic behavior.
-
sammon_data,
a Python code which
generates six examples of M dimensional datasets for cluster analysis.
-
satisfy,
a Python code which
demonstrates, for a particular circuit, an exhaustive search
for solutions of the circuit satisfiability problem.
-
search_mpi,
a Python code which
searches integers between A and B for a solution J such that F(J)=C,
carried out in parallel using MPI and MPI4PY.
-
search_serial,
a Python code which
searches integers between A and B for a solution J such that F(J)=C,
intended as a starting point for parallelization exercises.
-
sftpack,
a Python code which
implements the slow Fourier transform (SFT), intended as a teaching
tool and comparison with the fast Fourier transform (FFT).
-
shallow_water_1d,
a Python code which
simulates the evolution of a 1D fluid governed by the
time-dependent shallow water equations.
-
shepard_interp_1d,
a Python code which
defines and evaluates Shepard interpolants to 1D data,
based on inverse distance weighting.
-
simplex_coordinates,
a Python code which
computes the Cartesian coordinates of the vertices of
a regular simplex in M dimensions.
-
simplex_gm_rule,
a Python 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_grid,
a Python code which
generates a regular grid of points
over the interior of an arbitrary simplex in M dimensions.
-
simplex_integrals,
a Python code which
returns the exact value of the integral of any monomial
over the interior of the unit simplex in M dimensions.
-
simplex_monte_carlo,
a Python code which
uses the Monte Carlo method to estimate an integral
over the interior of the unit simplex in M dimensions.
-
sine_transform,
a Python code which
demonstrates simple properties of the discrete sine transform (DST).
-
sir_ode,
a Python code which
sets up the ordinary differential equations (ODE) which
simulate the spread of a disease
using the Susceptible/Infected/Recovered (SIR) model.
-
snakes_and_ladders,
a Python code which
simulates the game of Snakes and Ladders, and estimates
the average number of moves in a one-player game.
-
sobol,
a Python code which
computes elements of a Sobol Quasi Monte Carlo (QMC) sequence.
-
solve,
a Python code which
demonstrates how Gauss elimination can be used to solve a
linear system A*x=b.
-
sort_rc,
a Python code which
can sort a list of any kind of objects,
using reverse communication (RC).
-
sphere_distance,
a Python code which
considers the problem of describing the typical value of the distance
between a pair of points randomly selected from the surface of
the unit sphere in 3D.
-
sphere_fibonacci_grid,
a Python code which
uses a Fibonacci spiral to create a grid of points
on the surface of the unit sphere in 3D.
-
sphere_integrals,
a Python code which
returns the exact value of the integral of any monomial
over the surface of the unit sphere in 3D.
-
sphere_llq_grid,
a Python code which
uses longitudes and latitudes to create grids of points,
lines, and quadrilaterals
on the surface of the unit sphere in 3D.
-
sphere_llt_grid,
a Python code which
uses longitudes and latitudes to create grids of points,
lines, and triangles
on the surface of the unit sphere in 3D.
-
sphere_monte_carlo,
a Python code which
applies a Monte Carlo method to estimate the integral of a function
on the surface of the unit sphere in 3D.
-
sphere_ode,
a Python code which
sets up the ordinary differential equations (ODE) which
model motion on the surface of a sphere.
-
spiral_data,
a Python code which
computes a velocity vector field that satisfies the continuity
equation, writing the data to a file that can be plotted
by gnuplot.
-
square_distance,
a Python code which
considers the problem of describing the typical value of the distance
between a pair of points randomly selected inside the unit square.
-
square_grid,
a Python code which
computes a grid of points
over the interior of a square in 2D.
-
square_integrals,
a Python 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_minimal_rule,
a Python 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_monte_carlo,
a Python code which
applies a Monte Carlo method to estimate the integral of a function
over the interior of the unit square in 2D.
-
st_io
a Python code which
reads and writes sparse linear systems
stored in the Sparse Triplet (ST) format.
-
stiff_ode,
a Python code which
considers an ordinary differential equation (ODE) which is
an example of a stiff ODE.
-
stochastic_diffusion,
a Python code which
implements several versions of a stochastic diffusivity coefficient.
-
stokes_2d_exact,
a Python code which
evaluates exact solutions to the incompressible steady
Stokes equations over the unit square in 2D.
-
subset,
a Python 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_sum,
a Python code which
seeks solutions of the subset sum problem.
-
svd_snowfall,
a Python code which
reads a file containing historical snowfall data and
analyzes the data with the Singular Value Decomposition (SVD),
displaying the results using gnuplot.
-
svd_test,
a Python code which
demonstrates the calculation of
the singular value decomposition (SVD) and some of its properties;
-
table_io,
a Python code which
reads and writes files (not very much here yet.)
-
test_eigen,
a Python code which
implements test matrices for eigenvalue analysis.
-
test_interp,
a Python code which
defines test problems for interpolation,
provided as a set of (x,y(x)) data.
-
test_interp_1d,
a Python code which
defines test problems for interpolation of data y(x),
which depends on a 1D argument.
-
test_interp_2d,
a Python code which
defines test problems for interpolation of data z(x,y),
which depends on a 2D argument.
-
test_lls,
a Python code which
implements linear least squares test problems of the form A*x=b.
-
test_mat,
a Python code which
defines test matrices for which some of the determinant, eigenvalues,
inverse, null vectors, P*L*U factorization or linear system solution
are already known, including the Vandermonde and Wathen matrix.
-
test_matrix_exponential,
a Python code which
defines a set of test cases for computing the matrix exponential.
-
test_min,
a Python code which
implements test problems for
minimization of a scalar function of a scalar variable.
-
test_nonlin,
a Python code which
implements test problems for the solution
of systems of nonlinear equations.
-
test_optimization,
a Python code which
implements test problems for optimization
of a scalar function of several variables,
as described by Molga and Smutnicki.
-
test_values,
a Python code which
returns selected values of some special functions;
-
test_zero,
a Python code which
defines some functions f(x) suitable for testing
software that solves f(x)=0;
-
tester,
a BASH script which runs the test codes.
-
tetrahedron_grid,
a Python code which
computes a grid of points
over the interior of a tetrahedron in 3D.
-
tetrahedron_integrals,
a Python code which
returns the exact value of the integral of any monomial
over the interior of the unit tetrahedron in 3D.
-
tetrahedron_monte_carlo,
a Python code which
uses the Monte Carlo method to estimate an integral
over the interior of the unit tetrahedron in 3D.
-
three_body_ode,
a Python code which
defines 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.
-
timer_test,
a Python code which
tests various timers.
-
timestamp,
a Python code which
prints the current YMDHMS date as a timestamp.
-
toeplitz_cholesky,
a Python code which
computes the Cholesky factorization of a nonnegative definite
symmetric Toeplitz matrix.
-
toms097,
a Python code which
computes the distance between all pairs of nodes in a directed graph
with weighted edges, using the Floyd algorithm.
This is a version of ACM TOMS algorithm 97.
-
toms112,
a Python code which
determines whether a point is contained in a polygon,
by Moshe Shimrat.
This is a version of ACM TOMS algorithm 112.
-
toms178,
a Python code which
seeks the minimizer of a function of several variables, using the
Hooke-Jeeves direct search method,
by Arthur Kaupe.
This is a version of ACM TOMS algorithm 178.
-
toms179,
a Python code which
calculates the incomplete Beta ratio,
by Oliver Ludwig.
This is a version of ACM TOMS algorithm 179.
-
toms243,
a Python code which
evaluates the logarithm of a complex value,
by David Collens.
This is a version of ACM TOMS algorithm 243.
-
toms515,
a Python code which
can select subsets of size K from a set of size N.
This is a version of ACM TOMS Algorithm 515,
by Bill Buckles, Matthew Lybanon.
-
toms577,
a Python code which
evaluates the Carlson elliptic integral functions RC, RD, RF and RJ.
This is a version of ACM TOMS algorithm 577.
-
toms655,
a Python code which
computes the weights for interpolatory quadrature rule;
this library is commonly called IQPACK,
by Sylvan Elhay and Jaroslav Kautsky.
This is a version of ACM TOMS algorithm 655.
(Only a small portion of this library has been implemented
in Python so far!)
-
toms743,
a Python code which
evaluates the Lambert W function.
This is a version of ACM TOMS algorithm 743,
by Barry, Barry and Culligan-Hensley.
-
toms923,
a Python code which
evaluates the Pfaffian for a dense or banded skew symmetric matrix,
by Michael Wimmer.
-
trapezoid,
a Python code which
solves one or more ordinary differential equations (ODE)
using the trapezoid method.
-
triangle_distance,
a Python code which
considers the problem of describing the typical value of the distance
between a pair of points randomly selected from the interior of a
triangle in 2D.
-
triangle_grid,
a Python code which
computes a grid of points
over the interior of a triangle in 2D.
-
triangle_integrals,
a Python code which
returns the exact value of the integral of any polynomial
over the interior of a general triangle in 2D.
-
triangle_interpolate,
a Python code which
shows how vertex data can be interpolated at any point
in the interior of a triangle.
-
triangle_monte_carlo,
a Python code which
uses the Monte Carlo method to estimate an integral
over the interior of a general triangle in 2D.
-
triangle_properties,
a Python code which
can compute properties, including angles, area, centroid, circumcircle,
edge lengths, incircle, orientation, orthocenter, and quality,
of a triangle in 2D.
-
triangle_twb_rule,
a Python code which
generates the points and weights of quadrature rules
over the interior of a triangle in 2D,
determined by Taylor, Wingate, and Bos.
-
triangle01_integrals,
a Python code which
returns the integral of any monomial
over the interior of the unit triangle in 2D.
-
triangle01_monte_carlo,
a Python code which
uses the Monte Carlo method to estimate the integral of any function
over the interior of the unit triangle in 2D.
-
truncated_normal,
a Python 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_rule,
a Python 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].
-
tsp_brute,
a Python code which
reads a file of city-to-city distances and solves a (small!)
traveling salesperson problem (TSP), using brute force.
-
two_body_ode,
a Python code which
defines 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.
-
ubvec,
a Python code which
demonstrates how nonnegative integers can be stored as
unsigned binary vectors, and arithmetic can be performed on them.
-
unicycle,
a Python code which
considers permutations containing a single cycle,
sometimes called cyclic permutations.
-
uniform,
a Python code which
contains uniform random number generators (RNG) for several
arithmetic types.
-
upc,
a Python code which
can compute the check digit associated with a uniform product code
(UPC), or it can report whether a 12-digit UPC is actually valid.
-
van_der_corput,
a Python code which
computes elements of the van der Corput
1-dimensional Quasi Monte Carlo (QMC) sequence,
using a simple interface.
-
vandermonde_interp_1d,
a Python code which
finds a polynomial interpolant to data y(x) of a 1D argument
by setting up and solving a linear system for the
polynomial coefficients involving the Vandermonde matrix,
creating graphics with matplotlib.
-
vanderpol_ode,
a Python code which
defines the right hand side of the van der Pol oscillator
ordinary differential equation (ODE).
-
voronoi_plot,
a Python 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_test,
a Python code which
demonstrates the use of the scipy.spatial function Voronoi(),
to compute a Voronoi diagram, and voronoi_plot_2d(), to display it.
-
walker_sample,
a Python code which
efficiently samples a discrete probability density function
(PDF) represented by a vector, using Walker sampling.
-
walsh,
a Python code which
implements versions of the Walsh and Haar transforms.
-
wathen,
a Python 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).
-
wedge_grid,
a Python code which
computes a grid of points
over the interior of the unit wedge in 3D.
-
wedge_integrals,
a Python code which
returns the exact value of the integral of any monomial
over the interior of the unit wedge in 3D.
-
wedge_monte_carlo,
a Python code which
uses the Monte Carlo method to estimate an integral
over the interior of the unit wedge in 3D.
-
weekday,
a Python 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_zeller,
a Python 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.
-
wtime,
a Python code which
shows how to return a reading of the wall clock time.
-
xml_to_fem,
a Python code which
reads an XML file created by dolfin() or fenics(), describing a mesh
in 1D, 2D, or 3D, and extracts two sets of information, namely,
the coordinates of nodes, and the indices of nodes that form each
element, which constitute a finite element method (FEM) mesh
of the geometry.
-
zero_rc,
a Python code which
seeks solutions of a scalar nonlinear equation f(x)=0,
or a system of nonlinear equations,
using reverse communication (RC).
-
zombie_ode,
a Python code which
sets up 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.
Last revised on 11 November 2020.