GRID_DATASET
Generate Grid Datasets

GRID_DATASET is a FORTRAN90 program which creates a grid dataset.

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);

Usage:

grid_dataset m n seed center

• m is the spatial dimension;
• n is the number of points to generate;
• seed is the random number generator seed;
• center is the centering option.

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:

FAURE_DATASET, a FORTRAN90 program which creates a Faure quasirandom dataset;

GRID is a FORTRAN90 library which can define a grid dataset. GRID_DATASET needs a compiled copy of that library in order to build the program.

GRID is a dataset directory which contains a number of sample grid datasets.

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

NIEDERREITER2_DATASET, a FORTRAN90 program which creates a Niederreiter quasirandom dataset with base 2;

NORMAL_DATASET is a FORTRAN90 program which generates a dataset of multivariate normal pseudorandom values and writes them to a file.

SOBOL_DATASET is a FORTRAN90 program which computes a Sobol quasirandom sequence and writes it to a file.

TABLE_DISCREPANCY is a C++ program which can read a TABLE file of points (presumed to lie in the unit hypercube) and compute bounds on the star discrepancy, a measure of dispersion.

UNIFORM_DATASET is a FORTRAN90 program which generates a dataset of multivariate uniform pseudorandom values and writes them to a file.

VAN_DER_CORPUT_DATASET is a FORTRAN90 program which creates a van der Corput quasirandom sequence and writes it to a file.

Source Code:

• grid_dataset.f90, the source code.
• grid_dataset.csh, commands to compile and load the source code.

List of Routines:

• MAIN is the main program for GRID_DATASET.
• GET_SEED returns a seed for the random number generator.
• GET_UNIT returns a free FORTRAN unit number.
• GRID_GENERATE generates a grid dataset.
• GRID_SIDE finds the smallest grid containing at least N points.
• I4_HUGE returns a "huge" I4.
• KSUB_RANDOM2 selects a random subset of size K from a set of size N.
• R8_UNIFORM_01 returns a unit pseudorandom R8.
• R8MAT_WRITE writes an R8MAT file.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TUPLE_NEXT_FAST computes the next element of a tuple space, "fast".

You can go up one level to the FORTRAN90 source codes.