**line_monte_carlo**,
a MATLAB code which
uses the Monte Carlo method to estimate the integral of a function
over the length of the unit line in 1D.

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

**line_monte_carlo** is available in
a C version and
a C++ version and
a FORTRAN90 version and
a MATLAB version and
a Python version.

annulus_monte_carlo a MATLAB code which uses the monte carlo method to estimate the integral of a function over the interior of a circular annulus in 2d.

ball_monte_carlo, a MATLAB code which applies a monte carlo method to estimate integrals of a function over the interior of the unit ball in 3d;

circle_monte_carlo, a MATLAB code which applies a monte carlo method to estimate the integral of a function on the circumference of the unit circle in 2d;

cube_monte_carlo, a MATLAB code which applies a monte carlo method to estimate the integral of a function over the interior of the unit cube in 3d;

disk_monte_carlo, a MATLAB code which uses the monte carlo method to estimate integrals over the interior of the general disk in 2d.

disk01_monte_carlo, a MATLAB code which uses the monte carlo method to estimate integrals over the interior of the unit disk in 2d.

disk01_quarter_monte_carlo, a MATLAB code which applies a monte carlo method to estimate the integral of a function over the interior of the unit quarter disk in 2d;

ellipse_monte_carlo a MATLAB code which uses the monte carlo method to estimate the value of integrals over the interior of an ellipse in 2d.

ellipsoid_monte_carlo a MATLAB code which uses the monte carlo method to estimate the value of integrals over the interior of an ellipsoid in m dimensions.

hyperball_monte_carlo, a MATLAB code which applies a monte carlo method to estimate the integral of a function over the interior of the unit hyperball in m dimensions;

hypercube_monte_carlo, a MATLAB code which applies a monte carlo method to estimate the integral of a function over the interior of the unit hypercube in m dimensions;

hypersphere_monte_carlo, a MATLAB code which applies a monte carlo method to estimate the integral of a function on the surface of the unit hypersphere in m dimensions;

line_fekete_rule, a MATLAB code which approximates the location of fekete points in an interval [a,b]. a family of sets of fekete points, indexed by size n, represents an excellent choice for defining a polynomial interpolant.

line_felippa_rule, a MATLAB code which returns the points and weights of a felippa quadrature rule over the interior of a line segment in 1d.

line_grid, a MATLAB code which computes a grid of points over the interior of a line segment in 1d.

line_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the length of the unit line in 1d.

line_ncc_rule, a MATLAB code which computes a newton cotes closed (ncc) quadrature rule for the line, that is, for an interval of the form [a,b], using equally spaced points which include the endpoints.

line_nco_rule, a MATLAB code which computes a newton cotes open (nco) quadrature rule, using equally spaced points, over the interior of a line segment in 1d.

polygon_monte_carlo, a MATLAB code which applies a monte carlo method to estimate the integral of a function over the interior of a polygon in 2d.

pyramid_monte_carlo, a MATLAB code which applies a monte carlo method to estimate integrals of a function over the interior of the unit pyramid in 3d;

simplex_monte_carlo, a MATLAB code which uses the monte carlo method to estimate integrals over the interior of the unit simplex in m dimensions.

sphere_monte_carlo, a MATLAB code which applies a monte carlo method to estimate the integral of a function on the surface of the unit sphere in 3d;

sphere_triangle_monte_carlo, a MATLAB code which applies a monte carlo method to estimate the integral of a function over a spherical triangle on the surface of the unit sphere in 3d;

square_monte_carlo, a MATLAB code which applies a monte carlo method to estimate the integral of a function over the interior of the unit square in 2d;

tetrahedron_monte_carlo, a MATLAB code which uses the monte carlo method to estimate integrals over the interior of the unit tetrahedron in 3d.

triangle_monte_carlo, a MATLAB code which uses the monte carlo method to estimate integrals over the interior of a triangle in 2d.

triangle01_monte_carlo, a MATLAB code which uses the monte carlo method to estimate integrals over the interior of the unit triangle in 2d.

wedge_monte_carlo, a MATLAB code which uses the monte carlo method to estimate integrals over the interior of the unit wedge in 3d.

- line01_length.m length of the unit line in 1D.
- line01_monomial_integral.m monomial integral over the unit line in 1D.
- line01_sample_ergodic.m ergodically samples the unit line in 1D.
- line01_sample_random.m randomly samples the unit line in 1D.
- monomial_value_1d.m evaluates a monomial in 1D.