square_monte_carlo

square_monte_carlo, a MATLAB code which estimates the integral of a function over the interior of the unit square in 2D.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

square_monte_carlo is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

square_monte_carlo_test

matlab_monte_carlo, a MATLAB code which uses Monte Carlo sampling to estimate areas and integrals.

square_arbq_rule, a MATLAB code which returns quadrature rules, with exactness up to total degree 20, over the interior of the symmetric square in 2d, by Hong Xiao and Zydrunas Gimbutas.

square_felippa_rule, a MATLAB code which returns the points and weights of a Felippa quadrature rule over the interior of a square in 2d.

square_grid, a MATLAB code which computes a grid of points over the interior of a square in 2d.

square_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit square in 2d.

square_minimal_rule, a MATLAB code which returns "almost minimal" quadrature rules, with exactness up to total degree 55, over the interior of the symmetric square in 2d, by Mattia Festa and Alvise Sommariva.

square_symq_rule, a MATLAB code which returns symmetric quadrature rules, with exactness up to total degree 20, over the interior of the symmetric square in 2d, by Hong Xiao and Zydrunas Gimbutas.

Source Code:

• monomial_value.m, evaluates a monomial.
• r8mat_uniform_01.m, returns a uniform pseudorandom R8MAT.
• square01_area.m, returns the area of the unit square in 2D.
• square01_monomial_integral.m, integrates a monomial in the unit square in 2D.
• square01_sample.m, samples points from the unit square in 2D.