simplex_grid

simplex_grid, a MATLAB code which generates a grid of points over the interior of a simplex in M dimensions.

Licensing:

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

Languages:

simplex_grid 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:

simplex_grid_test

annulus_grid, a MATLAB code which computes a grid of points over the interior of a circular annulus.

asa299, a MATLAB code which computes the lattice points in an m-dimensional simplex, by chasalow and brand; this is a version of applied statistics algorithm 299;

fem_basis, a MATLAB code which can define basis functions for the finite element method (fem) for any degree in an m-dimensional simplex (1d interval, 2d triangle, 3d tetrahedron, and higher dimensional generalizations.)

matlab_grid, a MATLAB code which generates a regular grid of points inside a variety of regions in one, two, three or many dimensions.

simplex_coordinates, a MATLAB code which computes the cartesian coordinates of the vertices of a regular simplex in m dimensions.

simplex_gm_rule, a MATLAB code which defines grundmann-moeller quadrature rules over the interior of a simplex in m dimensions.

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

Source Code:

• comp_next_grlex.m, returns the next composition of an integer N into K parts, using the graded lexicographic ordering.
• comp_random.m, returns a random composition of an integer N into K parts.
• i4_uniform_ab.m, returns a random integer between A and B.
• i4mat_transpose_print.m, prints an I4MAT transposed.
• i4mat_transpose_print_some.m, prints some of an I4MAT transposed.
• ksub_random.m, returns a random subset of K items from a set of N items.
• r8mat_transpose_print.m, prints an R8MAT transposed.
• r8mat_transpose_print_some.m, prints some of an R8MAT transposed.
• simplex_grid_index_all.m, returns all the simplex grid indices.
• simplex_grid_index_next.m, returns the next simplex grid index.
• simplex_grid_index_sample.m, returns a random simplex grid index.
• simplex_grid_index_to_point.m, converts a simplex grid index to a physical point.
• simplex_grid_size.m, returns the size of a grid using N subintervals in each of M dimensions.