GRID
Random Points on a Uniform Grid

GRID is a set of MATLAB routines to randomly select N points on a uniform grid in the unit hypercube in M-dimensional space.

Note that, unless N is an Mth power of an integer, the program must generate a regular grid with too many points, and then omit some. Choosing which points to omit is done with a random number generator, whose actions are controlled by SEED.

The actual placement of the grid within the unit hypercube leaves some options for the use. It is easiest to describe the options in the 1 dimensional case, and in terms of where the first and last grid point are. Assuming we have N evenly spaced points to place between 0 and 1, the centering options are

• CENTER = 1: first point is 0.0, last point is 1.0;
• CENTER = 2: first point is 1/(N+1), last point is N/(N+1);
• CENTER = 3: first point is 0, last point is (N-1)/N;
• CENTER = 4: first point is 1/N, last point is 1;
• CENTER = 5: first point is 1/(2*N), last point is (2*N-1)/(2*N);

Related Data and Programs:

CLENSHAW_CURTIS is a MATLAB library which can set up a Clenshaw Curtis quadrature grid in multiple dimensions.

CVT is a library of MATLAB routines which computes elements of a Centroidal Voronoi Tessellation.

FAURE is a library of MATLAB routines which computes elements of a Faure quasirandom sequence.

GRID is also available in a C++ version and a FORTRAN90 version.

GRID_DATASET is an interactive MATLAB program which allows the user to specify a grid dataset.

HALTON is a library of MATLAB routines which computes elements of a Halton quasirandom sequence.

HAMMERSLEY is a library of MATLAB routines which computes elements of a Hammersley quasirandom sequence.

HEX_GRID is a library of MATLAB routines which computes elements of a hexagonal grid dataset.

IHS is a library of MATLAB routines which computes elements of an improved distributed Latin hypercube dataset.

LATIN_CENTER is a library of MATLAB routines which computes elements of a Latin Hypercube dataset, choosing center points.

LATIN_EDGE is a library of MATLAB routines which computes elements of a Latin Hypercube dataset, choosing edge points.

LATIN_RANDOM is a library of MATLAB routines which computes elements of a Latin Hypercube dataset, choosing points at random.

LCVT is a library of MATLAB routines which computes a latinized Centroidal Voronoi Tessellation.

NIEDERREITER2 is a library of MATLAB routines which computes elements of a Niederreiter quasirandom sequence with base 2.

SOBOL is a library of MATLAB routines which computes elements of a Sobol quasirandom sequence.

SPARSE_GRID is a MATLAB library of routines for generating points on sparse grids.

UNIFORM is a library of MATLAB routines which computes elements of a uniform pseudorandom sequence.

VAN_DER_CORPUT is a library of MATLAB routines which computes elements of a van der Corput quasirandom sequence.

Source Code:

• get_seed.m, returns a seed for the random number generator.
• grid_generate.m, generates a grid dataset.
• grid_side.m, finds the smallest M-D grid containing at least N points.
• grid_write.m, writes a grid dataset to a file.
• ksub_random2.m, selects a random subset of size K from a set of size N.
• r8_epsilon.m, returns the machine precision.
• r8_uniform_01.m, returns a double precision pseudorandom number.
• timestamp.m, prints the current YMDHMS date as a timestamp.
• timestring.m, returns the current YMDHMS date as a string.
• tuple_next_fast.m, computes the next element of a tuple space, "fast".

Examples and Tests:

• grid_test.m, runs all the problems.
• grid_test.out, output from all the problems.
• grid_test_01.m, tests GRID_GENERATE.

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