GRID
Random Points on a Uniform Grid

GRID is a MATLAB library which randomly selects N distinct 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);

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

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 MATLAB library which computes elements of a Centroidal Voronoi Tessellation.

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

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

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

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

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

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

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

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

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

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

LATTICE is a MATLAB library which approximates multidimensional integrals using lattice rules.

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

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

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

SPARSE_GRID is a MATLAB library which generates points on sparse grids.

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

VAN_DER_CORPUT is a MATLAB library 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_output.txt, the output file.
• grid_test_01.m, tests GRID_GENERATE.

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