Python Source
-
alpert_rule,
a library 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 program 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.
-
annulus_monte_carlo,
a library 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 library which
computes a quadrature rule for estimating integrals of a function
over the interior of a circular annulus in 2D.
-
args,
a script which
reports the command line arguments with which it was invoked;
-
asa047,
a library 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 library 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 library which
evaluates the incomplete Beta function,
by KL Majumder and G Bhattacharjee.
This is a version of Applied Statistics Algorithm 63;
-
asa103,
a library which
evaluates the digamma or psi function,
by Jose Bernardo;
this is a version of Applied Statistics Algorithm 103;
-
asa183,
a library which
implements a random number generator (RNG),
by Wichman and Hill;
this is a version of Applied Statistics Algorithm 183;
-
asa241,
a library 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 library which
applies the Atbash substitution cipher to a string of text.
-
backtrack_binary_rc,
a library which
carries out a backtrack search for a set of binary decisions, using
reverse communication (RC).
-
ball_grid,
a library which
computes grid points inside a 3D ball.
-
ball_integrals,
a library which
returns the exact value of the integral of any monomial
over the interior of the unit ball in 3D.
-
ball_monte_carlo,
a library which
applies a Monte Carlo method to estimate integrals of a function
over the interior of the unit ball in 3D;
-
bank,
a library 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 library 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 library 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 library which
evaluates the Bernstein polynomials;
-
besselj,
a library which
evaluates Bessel J functions of noninteger order;
-
bicycle_lock,
a library which
simulates the process of determining the secret combination of
a bicycle lock, an integer between 000 and 999.
-
bisect,
a library 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 library 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 library which
implements some simple approaches to
the Black-Scholes option valuation theory,
by Desmond Higham.
-
blas1_d,
a library 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.
-
brownian_motion_simulation,
a library which
simulates Brownian motion in an M dimensional region.
-
burgers_solution,
a library which
evaluates exact solutions of the
time-dependent 1D viscous Burgers equation.
-
bvec,
a library which
demonstrates how signed integers can be stored as
binary vectors, and arithmetic can be performed on them.
-
c4lib,
a library which
implements certain elementary functions for
single precision complex (C4) variables;
-
c8lib,
a library which
implements certain elementary functions for
double precision complex (C8) variables;
-
caesar,
a library which
can apply a Caesar Shift Cipher to a string of text.
-
calpak,
a library which
makes various calendar calculations;
-
cauchy_principal_value,
a library which
uses Gauss-Legendre quadrature to estimate the Cauchy Principal Value
(CPV) of certain singular integrals.
-
cfd_barba,
a library which
contains Python scripts of some of the iPython workbooks
associated with the "12 Steps to Navier-Stokes" presentation
by Lorena Barba.
-
cg,
a library 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 library 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 library which
considers the change making problem,
in which a given sum is to be formed using coins of various denominations.
-
chebyshev_interp_1d,
a library which
determines the combination of Chebyshev polynomials which
interpolates a set of data, so that p(x(i)) = y(i).
-
chebyshev_polynomial,
a library 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.
-
chrpak,
a library which
manipulates characters and strings;
-
circle_arc_grid,
a program which
computes grid points along a circular arc.
-
circle_integrals,
a library which
returns the exact value of the integral of any monomial
over the circumference of the unit circle in 2D.
-
circle_monte_carlo,
a library which
applies a Monte Carlo method to estimate the integral of a function
along the circumference of the unit circle in 2D;
-
clausen,
a library which
evaluates a Chebyshev interpolant to the Clausen function Cl2(x).
-
collatz_recursive,
a library which
demonstrates recursive programming by considering
the simple Collatz 3n+1 problem.
-
combination_lock,
a program which
simulates the process of determining the secret combination of a lock.
-
combo,
a library 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 library 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,
a program which
demonstrates some simple features involved in the use of
complex numbers in programming.
-
condition,
a library which
implements methods of computing or estimating
the condition number of a matrix.
-
continued_fraction
a library which
implements some simple algorithms for dealing with simple and
generalized continued fractions.
-
cordic,
a library which
computes a few special functions using the CORDIC algorithm.
-
cosine_transform,
a library which
demonstrates some simple properties of the discrete cosine transform
(DCT).
-
counterfeit_detection,
a library 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.
-
cube_grid,
a library which
computes a grid of points
over the interior of a cube in 3D.
-
cube_integrals,
a library which
returns the exact value of the integral of any monomial
over the interior of the unit cube in 3D.
-
cube_monte_carlo,
a library 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 library which
shows how, in a CUDA program, the user's choice of block and
thread factors determines the allocation of tasks to processors.
-
cvt_1d_lloyd,
a program which
computes an N-point Centroidal Voronoi Tessellation (CVT)
within the interval [0,1], under a uniform density,
using Lloyd's method to compute the Voronoi regions exactly.
-
cvt_2d_sampling,
a program 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 program which
solves a support vector machine (SVM) problem by formulating it
as a quadratic programming problem to be solved by cvxopt().
-
cycle_brent,
a library which
carries out an iterated function evaluation, and seeks to determine
the nearest element of a cycle, and the cycle's length,
using Brent's method.
-
cycle_floyd,
a library which
carries out an iterated function evaluation, and seeks to determine
the nearest element of a cycle, and the cycle's length,
using Floyd's method.
-
delaunay_test,
a script 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 program which
applies the discontinuous Galerkin method (DG) to a 1D version of
the Poisson equation,
based on a MATLAB code by Beatrice Riviere.
-
dijkstra,
a library which
implements a simple version of Dijkstra's minimum distance algorithm
for graphs.
-
disk_grid,
a library 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 library 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 library which
computes a quadrature rule
over the interior of the general disk in 2D.
-
disk01_integrals,
a library which
returns the exact value of the integral of any monomial
over the interior of the unit disk in 2D.
-
disk01_monte_carlo,
a library 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 library 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 library 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_test,
scripts which
are used with the DOLFIN library to set up and solve
a wide variety of problems using the finite element method (FEM).
-
dolfin-convert,
a program 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 library 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.
-
drug_dosage,
a program which
simulates the variation in the blood levels of
a medicinal drug being administered at specific dosages and times over
a course of treatment. The level should rise about a given medicinal
level for some time, but stay below the toxic level.
-
duel_simulation,
a program which
simulates N repetitions of a duel between two players, each of
whom has a known firing accuracy.
-
ellipse_grid,
a library which
computes grid points
over the interior of an ellipse in 2D.
-
ellipse_monte_carlo,
a library which
uses the Monte Carlo method to estimate the value of integrals
over the interior of an ellipse in 2D.
-
ellipsoid_grid,
a library which
computes a grid of points
over the interior of an ellipsoid in 3D.
-
ellipsoid_monte_carlo,
a library which
uses the Monte Carlo method to estimate the value of integrals
over the interior of an ellipsoid in M dimensions.
-
elliptic_integral,
a library which
evaluates complete elliptic integrals of first, second and third kind,
using Carlson's elliptic integral functions.
-
exactness,
a library 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).
-
fastgl,
a library 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 program which
solves a time-dependent predator prey system using the
finite difference method (FDM).
-
fd1d_advection_lax_wendroff,
a program 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_heat_explicit,
a library which
implements a finite difference method (FDM), explicit in time,
to solve the time dependent 1D heat equation;
-
fd1d_heat_implicit,
a program which
implements a finite difference method (FDM), implicit in time,
to solve the time dependent 1D heat equation;
-
fd2d_heat_steady,
a program which
implements a finite difference method (FDM) for the steady
(time independent) 2D heat equation;
-
fem_basis,
a library 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,
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 program 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 program 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 program 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 library 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 program which
uses the finite element method (FEM) and explicit time stepping
to solve the time dependent heat equation in 1D.
-
fem2d_bvp_linear,
a program 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 program 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 library which
performs various operations on files;
-
fire_serial,
a program 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.
-
florida_cvt_geo,
programs which
explore the creation of a centroidal Voronoi Tessellation (CVT) of
the state of Florida, based solely on geometric considerations.
-
florida_cvt_pop,
programs which
explore the creation of a centroidal Voronoi Tessellation (CVT) of
the state of Florida, based on population considerations.
-
fn,
a library 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 library 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 library which
can read and write files used by the FreeFem++ finite element program
to store mesh information.
-
gegenbauer_cc,
a library which
computes the Gegenbauer weighted integral of a function f(x)
using a Clenshaw-Curtis approach.
-
gegenbauer_polynomial,
a library which
evaluates the Gegenbauer polynomial and associated functions.
-
geometry,
a library 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 library which
can apply one step of the V-cycle of the geometric multigrid method,
by Mike Sussman.
-
graphics_test,
programs which
illustrate how various kinds of data can be displayed
and analyzed graphically.
-
grid,
a library which
randomly selects N distinct points from a uniform grid
in the unit hypercube in M-dimensional space.
-
haar,
a library which
computes the Haar transform of data.
-
halton,
a library which
computes elements of a Halton Quasi Monte Carlo (QMC) sequence,
using a simple interface.
-
hammersley,
a library which
computes elements of a Hammersley Quasi Monte Carlo (QMC) sequence,
using a simple interface.
-
hankel_cholesky,
a library which
computes the upper Cholesky factor R of a nonnegative definite
symmetric H matrix so that H = R' * R.
-
hankel_pds,
a library which
can compute a lower triangular matrix L which is the Cholesky factor
of a positive definite (symmetric) Hankel matrix H, that is,
H = L * L'.
-
hdf5_test,
scripts which
demonstrate the use of the HDF5 library and file format.
-
hello,
a script which
prints "Hello, world!".
-
hello_mpi,
a script which
prints out "Hello, world!",
carried out in parallel using MPI and MPI4PY.
-
hilbert_curve,
a library which
computes the sequence of discrete Hilbert curves whose limit
is a space-filling curve.
-
hyperball_integrals,
a library 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 library 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 library which
computes a grid of points
over the interior of a hypercube in M dimensions.
-
hypercube_integrals,
a library 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 library which
applies a Monte Carlo method to estimate the integral of a function
over the interior of the unit hypercube in M dimensions.
-
hypersphere_integrals,
a library 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 library 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 library which
contains many utility routines, using single precision integer (I4)
arithmetic.
-
i8lib,
a library which
contains many utility routines, using double precision integer (I8)
arithmetic.
-
isbn,
a library which
can determine the check digit for an International Standard Book Number
or report whether a given ISBN is valid.
-
jacobi,
a program which
implements the Jacobi iteration for the iterative solution of
linear systems.
-
jacobi_eigenvalue,
a library which
implements the Jacobi iteration for the iterative determination
of the eigenvalues and eigenvectors of a real symmetric matrix.
-
knapsack_01,
a library which
uses brute force to solve small versions of the 0/1 knapsack problem;
-
kronrod,
a library which
can compute 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 library 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 library which
computes Latin Random Squares of N points in M dimensions;
-
lebesgue,
a library 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 library which
evaluates the Legendre polynomial and associated functions.
-
legendre_product_polynomial,
a library which
defines Legendre product polynomials, creating a multivariate
polynomial as the product of univariate Legendre polynomials.
-
legendre_shifted_polynomial,
a library which
evaluates the shifted Legendre polynomial, with the domain [0,1].
-
levenshtein,
a library which
returns the Levenshtein distance between two strings.
-
line_grid,
a library which
computes a grid of points
over the interior of a line segment in 1D.
-
line_integrals,
a library which
returns the exact value of the integral of any monomial
over the length of the unit line in 1D.
-
line_monte_carlo,
a library 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 library which
factors and solves linear systems
using double precision real arithmetic,
by Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart.
-
linplus_c8,
a library which
carries out some linear algebra operations on complex matrices.
-
llsq,
a library 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 script which
calls the numpy function loadtxt() to extract numeric data from a
text file.
-
local_min_rc,
a library 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 library which
returns quantities related to the log normal Probability
Distribution Function (PDF).
-
log_normal_truncated_ab,
a library which
returns quantities related to the log normal Probability
Distribution Function (PDF) truncated to the interval [A,B].
-
lorenz_ode,
a program which
approximates solutions to the Lorenz system
of ordinary differential equations (ODE's),
creating graphics files using matplotlib.
-
luhn,
a library 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 library which
dynamically computes the values of
various machine characteristic constants,
by William Cody;
-
machine,
a library which
returns tabulated values of
the constants associated with computer arithmetic;
-
mandelbrot,
a program which
generates a Portable Network Graphics (PNG) image of the
Mandelbrot set;
-
mario,
a program which
creates a sort of "needlepoint" image of Mario, as an array of
colored squares.
-
matrix_exponential,
a library which
demonstrates some simple approaches to the problem of computing the
exponential of a matrix.
-
md,
a program which
carries out a molecular dynamics (MD) simulation, intended as
a starting point for implementing a parallel version.
-
monomial,
a library 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 library which
evaluates a monomial in M dimensions.
-
naca,
a library which
can take the parameters of certain NACA airfoils and return the
coordinates of a sequence of points that outline the wing shape.
The shape can be displayed with MATLAB graphics.
-
nas,
a program which
runs the NASA kernel benchmark.
-
navier_stokes_2d_exact,
a library 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 library which
evaluates an exact solution to the incompressible time-dependent
Navier-Stokes equations (NSE) over an arbitrary domain in 3D.
-
nearest_interp_1d,
a library 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 library which
applies Newton's method to solve a single nonlinear equation f(x)=0.
-
newton_interp_1d,
a library which
finds a polynomial interpolant to data using Newton divided
differences.
-
ngrams,
a library which
can analyze a string or text against the observed frequency of
"ngrams" (particular sequences of n letters) in English text.
-
normal,
a library which
implements a random number generator (RNG) for normally distributed
values;
-
owens,
a library which
evaluates Owen's T function;
-
padua,
a library which
returns the coordinates of the 2D Padua points,
as well as interpolation weights or quadrature weights,
and images of the points graphics files.
-
partition_problem,
a library which
seeks solutions of the partition problem, splitting a set of
integers into two subsets with equal sum.
-
pbma_io,
a library which
reads or writes ASCII Portable Bit Map (PBM) 2D graphics files;
-
pbmb_io,
a library which
reads or writes a binary Portable Bit Map (PBM) 2D graphics file;
-
pdflib,
a library which
evaluates Probability Density Functions (PDF's)
and produces random samples from them,
including beta, binomial, chi, exponential, gamma, inverse chi,
inverse gamma, multinomial, normal, scaled inverse chi, and uniform.
-
pentominoes,
a library which
provides some utilities for manipulating pentominoes.
-
pgma_io,
a library which
reads or writes ASCII Portable Gray Map (PGM) 2D graphics files;
-
pgmb_io,
a library which
reads or writes a binary Portable Gray Map (PGM) 2D graphics file;
-
pink_noise,
a library which
computes a pink noise signal obeying a 1/f power law.
-
polpak,
a library which
evaluates a variety of mathematical functions, including
Chebyshev, Gegenbauer, Hermite, Jacobi, Laguerre,
Legendre polynomials, and the Collatz sequence.
-
polygon_grid,
a library which
generates a grid of points
over the interior of a polygon in 2D.
-
polygon_integrals,
a library which
returns the exact value of the integral of any monomial
over the interior of a polygon in 2D.
-
polygon_monte_carlo,
a library which
applies a Monte Carlo method to estimate the integral of a function
over the interior of a polygon in 2D.
-
polygon_properties,
a library 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 library 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 library which
adds, multiplies, differentiates, evaluates and prints multivariate
polynomials in a space of M dimensions.
-
polynomials,
a library which
defines multivariate polynomials over rectangular domains, for
which certain information is to be determined, such as the maximum
and minimum values.
-
polyomino_condense,
a program which
cleans up a matrix that represents a polyomino by setting all nonzero
entries to 1, and removing initial and final rows and columns of zeros.
-
polyomino_embed,
a library which
is given matrices defining a region R and a polyomino P, and determines
the number of possible embeddings of the polyomino into the region, and
the translations necessary to achieve them.
-
polyomino_enumerate,
a library which
enumerates fixed and free polyominoes of orders 0 through 28.
-
polyomino_index,
a library which
is given a matrix defining a polyomino P, and determines
a correspondingly shaped matrix which contains an index for each
nonzero entry in P.
-
polyomino_lp_write,
a program which
writes an LP file describing a (binary) integer programming problem
related to the tiling of a region R by copies of polyomino
shapes, with possible reflections and rotations.
-
polyomino_transform,
a program which
transforms the matrix representing a polyomino by reflection and
rotation.
-
ppma_io,
a library which
reads or writes an ASCII Portable Pixel Map (PPM) 2D graphics file;
-
ppmb_io,
a library which
reads or writes a binary Portable Pixel Map (PPM) 2D graphics file;
-
praxis,
a library which
minimizes a scalar function of several variables, without
requiring derivative information,
by Richard Brent.
-
prime_mpi,
a script which
counts the number of primes between 1 and N,
carried out in parallel using MPI and MPI4PY.
-
prime_serial,
a script which
counts the number of primes between 1 and N,
intended as a starting point for a parallel version.
-
prob,
a library which
evaluates, samples, inverts, and characterizes a number of
Probability Density Functions (PDF's)
and Cumulative Density Functions (CDF's), 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 library which
interpolates a set of data using a piecewise linear function in 1D.
-
pwl_interp_2d,
a library which
interpolates a set of data using a piecewise linear function in 2D.
-
py,
a directory of example Python scripts.
-
python_mistake,
programs which illustrate mistakes caused by Python,
encouraged by Python, or made difficult to spot because of Python.
-
pyramid_grid,
a library which
computes a grid of points
over the interior of the unit pyramid in 3D;
-
pyramid_monte_carlo,
a library 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 script which
approximates an integral using a quadrature rule,
carried out in parallel using MPI and MPI4PY.
-
quad_serial,
a script which applies a quadrature rule to estimate an integral,
intended as a starting point for parallelization exercises.
-
quadrule,
a library which
implements rules for approximate integration (quadrature)
in one dimension;
-
quaternions,
a library which
carries out some simple arithmetic operations for quaternions.
-
r4lib,
a library which
contains many utility routines, using
single precision real (R4) arithmetic.
-
r8col,
a library which
contains utility routines for R8COL's, that is,
double precision real MxN arrays, 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 library which
contains linear algebra routines for R8GE matrices
(real, 64 bit, General format).
-
r8lib,
a library which
contains many utility routines, using double precision real (R8)
arithmetic.
-
r8poly,
a library which
contains a number of utilities for polynomials with R8 coefficients,
that is, using double precision or 64 bit real arithmetic.
-
r8row,
a library which
contains utility routines for R8ROW's, that is,
double precision real MxN arrays, 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.
-
randlc,
a library which
implements a random number generator (RNG)
used by the NAS Benchmark programs.
-
random_data,
a library 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 library which
demonstrates how, for certain probability density functions (PDF's),
a symmetric matrix with entries sampled from that PDF will have
eigenvalues distributed according to Wigner's semicircle distribution.
-
random_sorted,
a library which
generates vectors of random values which are already sorted.
-
ranlib,
a library which
produces random samples from Probability Density Functions (PDF's),
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 library which
defines and evaluates
radial basis function (RBF) interpolants to 1D data.
-
rbf_interp_2d,
a library which
defines radial basis function (RBF) interpolants to 2D data.
-
rk4,
a library 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 script which
implements the Runge-Kutta-Fehlberg (RKF) solver for the approximate
solution of an ordinary differential equation (ODE) system.
-
rnglib,
a library which
implements a random number generator (RNG) with splitting facilities,
allowing multiple independent streams to be computed,
by L'Ecuyer and Cote.
-
root_rc,
a library which
seeks a solution of a scalar nonlinear equation f(x)=0,
using reverse communication (RC), by Gaston Gonnet.
-
roots_rc,
a library which
seeks solutions of a system of nonlinear equations,
using reverse communication (RC), by Gaston Gonnet.
-
rot13,
a program 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 library which
carries out the exact computation of the integer row echelon form (IREF)
and integer reduced row echelon form (IRREF) of an integer matrix.
-
sammon_data,
a program which
generates six examples of M dimensional datasets for cluster analysis.
-
satisfy,
a program which
demonstrates, for a particular circuit, an exhaustive search
for solutions of the circuit satisfiability problem.
-
search_mpi,
a script 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 script 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 library which
implements the slow Fourier transform (SFT), intended as a teaching
tool and comparison with the fast Fourier transform (FFT).
-
shallow_water_1d,
a program which
simulates the evolution of a 1D fluid governed by the
time-dependent shallow water equations.
-
shepard_interp_1d,
a library which
defines and evaluates Shepard interpolants to 1D data,
based on inverse distance weighting.
-
simplex_coordinates,
a library which
computes the Cartesian coordinates of the vertices of
a regular simplex in M dimensions.
-
simplex_gm_rule,
a library 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 library which
generates a regular grid of points
over the interior of an arbitrary simplex in M dimensions.
-
simplex_integrals,
a library 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 library which
uses the Monte Carlo method to estimate an integral
over the interior of the unit simplex in M dimensions.
-
sine_transform,
a library which
demonstrates simple properties of the discrete sine transform (DST).
-
snakes_and_ladders,
a library which
simulates the game of Snakes and Ladders, and estimates
the average number of moves in a one-player game.
-
sobol,
a library which
computes elements of a Sobol Quasi Monte Carlo (QMC) sequence.
-
solve,
a library which
demonstrates how Gauss elimination can be used to solve a
linear system A*x=b.
-
sort_rc,
a library which
can sort a list of any kind of objects,
using reverse communication (RC).
-
sparse_grid,
some classes and functions defining sparse grids,
by Jochen Garcke.
-
sphere_fibonacci_grid,
a library which
uses a Fibonacci spiral to create a grid of points
on the surface of the unit sphere in 3D.
-
sphere_integrals,
a library which
returns the exact value of the integral of any monomial
over the surface of the unit sphere in 3D.
-
sphere_llq_grid,
a library 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 library 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 library which
applies a Monte Carlo method to estimate the integral of a function
on the surface of the unit sphere in 3D.
-
spiral_data,
a library which
computes a velocity vector field that satisfies the continuity
equation, writing the data to a file that can be plotted
by gnuplot.
-
square_grid,
a library which
computes a grid of points
over the interior of a square in 2D.
-
square_integrals,
a library 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 library 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 library 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 library which
reads and writes sparse linear systems
stored in the Sparse Triplet (ST) format.
-
stochastic_diffusion,
functions which
implement several versions of a stochastic diffusivity coefficient.
-
stokes_2d_exact,
a library which
evaluates exact solutions to the incompressible steady
Stokes equations over the unit square in 2D.
-
subset,
a library 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 library which
seeks solutions of the subset sum problem.
-
svd_snowfall,
a program 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 program which
demonstrates the calculation of
the singular value decomposition (SVD) and some of its properties;
-
table_io,
functions which read and write files (not very much here yet.)
-
test_eigen,
a library which
implements test matrices for eigenvalue analysis.
-
test_interp,
a library which
defines test problems for interpolation,
provided as a set of (x,y(x)) data.
-
test_interp_1d,
a library which
defines test problems for interpolation of data y(x),
which depends on a 1D argument.
-
test_interp_2d,
a library which
defines test problems for interpolation of data z(x,y),
which depends on a 2D argument.
-
test_lls,
a library which
implements linear least squares test problems of the form A*x=b.
-
test_mat,
a library 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 library which
defines a set of test cases for computing the matrix exponential.
-
test_min,
a library which
implements test problems for
minimization of a scalar function of a scalar variable.
-
test_optimization,
a library which
implements test problems for optimization
of a scalar function of several variables,
as described by Molga and Smutnicki.
-
test_values,
a library which
returns selected values of some special functions;
-
test_zero,
a library which
defines some functions f(x) suitable for testing
software that solves f(x)=0;
-
tetrahedron_grid,
a library which
computes a grid of points
over the interior of a tetrahedron in 3D.
-
tetrahedron_integrals,
a library which
returns the exact value of the integral of any monomial
over the interior of the unit tetrahedron in 3D.
-
tetrahedron_monte_carlo,
a library which
uses the Monte Carlo method to estimate an integral
over the interior of the unit tetrahedron in 3D.
-
timer,
a library which
implements various real time and CPU time tests.
-
timestamp,
a script which
prints the current YMDHMS date as a timestamp.
-
toeplitz_cholesky,
a library which
computes the Cholesky factorization of a nonnegative definite
symmetric Toeplitz matrix.
-
toms097,
a library which
computes the distance between all pairs of nodes in a directed graph
with weighted edges, using Floyd's algorithm.
This is a version of ACM TOMS algorithm 97.
-
toms112,
a library which
determines whether a point is contained in a polygon,
by Moshe Shimrat.
This is a version of ACM TOMS algorithm 112.
-
toms178,
a library 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 library which
calculates the incomplete Beta ratio,
by Oliver Ludwig.
This is a version of ACM TOMS algorithm 179.
-
toms243,
a library which
evaluates the logarithm of a complex value,
by David Collens.
This is a version of ACM TOMS algorithm 243.
-
toms515,
a library 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 library which
evaluates Carlson's elliptic integral functions RC, RD, RF and RJ.
This is a version of ACM TOMS algorithm 577.
-
triangle_grid,
a library which
computes a grid of points
over the interior of a triangle in 2D.
-
triangle_integrals,
a library which
returns the exact value of the integral of any polynomial
over the interior of a general triangle in 2D.
-
triangle_interpolate,
a library which
shows how vertex data can be interpolated at any point
in the interior of a triangle.
-
triangle_monte_carlo,
a library which
uses the Monte Carlo method to estimate an integral
over the interior of a general triangle in 2D.
-
triangle_properties,
a library which
can compute properties, including angles, area, centroid, circumcircle,
edge lengths, incircle, orientation, orthocenter, and quality,
of a triangle in 2D.
-
triangle01_integrals,
a library which
returns the integral of any monomial
over the interior of the unit triangle in 2D.
-
triangle01_monte_carlo,
a library 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 library 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 program 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 program which
reads a file of city-to-city distances and solves a (small!)
traveling salesperson problem (TSP), using brute force.
-
ubvec,
a library which
demonstrates how nonnegative integers can be stored as
unsigned binary vectors, and arithmetic can be performed on them.
-
unicycle,
a library which
considers permutations containing a single cycle,
sometimes called cyclic permutations.
-
uniform,
a library which
contains uniform random number generators (RNG's) for several
arithmetic types.
-
upc,
is a library 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 library which
computes elements of the van der Corput
1-dimensional Quasi Monte Carlo (QMC) sequence,
using a simple interface.
-
vandermonde_interp_1d,
a library 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.
-
voronoi_plot,
a program 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 script 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 library which
efficiently samples a discrete probability density function
(PDF) represented by a vector, using Walker sampling.
-
walsh,
a library which
implements versions of the Walsh and Haar transforms.
-
wathen,
a library 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 library which
computes a grid of points
over the interior of the unit wedge in 3D.
-
wedge_integrals,
a library which
returns the exact value of the integral of any monomial
over the interior of the unit wedge in 3D.
-
wedge_monte_carlo,
a library which
uses the Monte Carlo method to estimate an integral
over the interior of the unit wedge in 3D.
-
weekday,
a library which
determines the day of the week corresponding to a given date,
such as 14 October 1066, Julian calendar, ... which was a Saturday.
-
wtime,
a library which
shows how to return a reading of the wall clock time.
-
xml_to_fem,
a script which
reads an XML file created by FENICS or DOLFIN, 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 library which
seeks solutions of a scalar nonlinear equation f(x)=0,
or a system of nonlinear equations,
using reverse communication (RC).
Last revised on 19 April 2019.