# SIMPLEX_MONTE_CARLO Monte Carlo Integral Estimates over the Unit Simplex in M Dimensions

SIMPLEX_MONTE_CARLO is a Python library which uses the Monte Carlo method to estimate the integral of a function F(X) over the interior of the unit simplex in M dimensions.

The interior of the unit simplex in M dimensions is defined by the constraints:

```        0 <= X(1:M)
sum ( 1 <= I <= M ) X(I) <= 1
```
The functions F(X) are monomials, having the form
```        F(X) = product ( 1 <= I <= M ) X(I)^E(I)
```
where the exponents are nonnegative integers.

### Languages:

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

### Related Data and Programs:

BALL_MONTE_CARLO, a Python library 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 Python library 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 Python library 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 Python library which uses the Monte Carlo method to estimate integrals over the interior of a disk in 2D.

DISK01_MONTE_CARLO, a Python library which uses the Monte Carlo method to estimate integrals over the interior of the unit disk in 2D.

DISK01_QUARTER_MONTE_CARLO, a Python library 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 Python library which uses the Monte Carlo method to estimate the value of integrals over the interior of an ellipse in 2D.

ELLIPSOID_MONTE_CARLO a Python library 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 Python library 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 Python 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_MONTE_CARLO, a Python library which applies a Monte Carlo method to estimate the integral of a function on the surface of the unit sphere in M dimensions;

LINE_MONTE_CARLO, a Python library which applies a Monte Carlo method to estimate the integral of a function over the length of the unit line segment in 1D;

POLYGON_MONTE_CARLO, a Python library 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 Python library which applies a Monte Carlo method to estimate integrals of a function over the interior of the unit pyramid in 3D;

SIMPLEX_GRID, a Python library which generates a regular grid of points over the interior of an arbitrary simplex in M dimensions.

SIMPLEX_INTEGRALS, a Python library which returns the exact value of the integral of any monomial over the interior of the unit simplex in M dimensions.

SPHERE_MONTE_CARLO, a Python library which applies a Monte Carlo method to estimate the integral of a function on the surface of the unit sphere in 3D;

SQUARE_MONTE_CARLO, a Python library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit square in 2D.

TETRAHREDRON_MONTE_CARLO, a Python library which uses the Monte Carlo method to estimate integrals over the interior of the unit tetrahedron in 3D.

TRIANGLE01_MONTE_CARLO, a Python library which uses the Monte Carlo method to estimate integrals over the interior of the unit triangle in 2D.

WEDGE_MONTE_CARLO, a Python library which uses the Monte Carlo method to estimate integrals over the interior of the unit wedge in 3D.

### Source Code:

You can go up one level to the Python source codes.

Last revised on 13 November 2016