tetrahedron01_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate the integral of a function F(X,Y,Z) over the interior of the unit tetrahedron in 3D.
The interior of the unit tetrahedron in 3D is defined by the constraints:
0 <= X 0 <= Y 0 <= Z X + Y + Z <= 1The functions F(X,Y,Z) are monomials, having the form
F(X,Y,Z) = X^E(1) * Y^E(2) * Z^E(3)where the exponents are nonnegative integers.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
tetrahedron01_monte_carlo is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.
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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.
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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;
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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;
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tetrahedron_ncc_rule, a MATLAB code which defines newton-cotes closed (ncc) quadrature rules over the interior of a tetrahedron in 3d.
tetrahedron_nco_rule, a MATLAB code which defines newton-cotes open (nco) quadrature rules over the interior of a tetrahedron in 3d.
tetrahedron01_monte_carlo_test
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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.