IHS
Improved Distributed Hypercube Sampling

IHS is a FORTRAN90 library, using double precision arithmetic, which carries out the improved distributed hypercube sampling algorithm.

N Points in an M dimensional Latin hypercube are to be selected. Each of the M coordinate dimensions is discretized to the values 1 through N. The points are to be chosen in such a way that no two points have any coordinate value in common. This is a standard Latin hypercube requirement, and there are many solutions.

This algorithm differs in that it tries to pick a solution which has the property that the points are "spread out" as evenly as possible. It does this by determining an optimal even spacing, and using the duplication factor D to allow it to choose the best of the various options available to it (the more duplication, the better chance of optimization).

One drawback to this algorithm is that it requires an internal real distance array of dimension D * N * N. For a relatively moderate problem with N = 1000, this can exceed the easily accessible memory. Moreover, the program is inherently quadratic in execution time as well as memory; the computation of the I-th point in the set of N requires a consideration of the value of the coordinates used up by the previous points, and the distances from each of those points to the candidates for the next point.

Related Data and Programs:

CVT computes elements of a Centroidal Voronoi Tessellation.

FAURE computes elements of a Faure quasirandom sequence.

GRID computes elements of a grid dataset.

HALTON computes elements of a Halton quasirandom sequence.

HAMMERSLEY computes elements of a Hammersley quasirandom sequence.

HEX_GRID computes elements of a hexagonal grid dataset.

HEX_GRID_ANGLE computes elements of an angled hexagonal grid dataset.

IHS is also available in a C++ version and a MATLAB version.

LATIN_CENTER computes elements of a Latin Hypercube dataset, choosing center points.

LATIN_EDGE computes elements of a Latin Hypercube dataset, choosing edge points.

LATIN_RANDOM computes elements of a Latin Hypercube dataset, choosing points at random.

LCVT computes a latinized Centroidal Voronoi Tessellation.

NIEDERREITER2 computes elements of a Niederreiter quasirandom sequence with base 2.

NORMAL is a FORTRAN90 library which computes elements of a sequence of pseudorandom normally distributed values.

SOBOL computes elements of a Sobol quasirandom sequence.

UNIFORM computes elements of a uniform pseudorandom sequence.

VAN_DER_CORPUT computes elements of a van der Corput quasirandom sequence.

Reference:

1. Brian Beachkofski, Ramana Grandhi,
   Improved Distributed Hypercube Sampling,
   American Institute of Aeronautics and Astronautics Paper 2002-1274.

Source Code:

• ihs.f90, the source code.
• ihs.csh, commands to compile the source code.

Examples and Tests:

• ihs_prb.f90, a sample calling program.
• ihs_prb.csh, commands to compile and run the sample program.
• ihs_prb_output.txt, the output file.

List of Routines:

• COVARIANCE does a covariance calculation for IHS solutions.
• GET_SEED returns a seed for the random number generator.
• GET_UNIT returns a free FORTRAN unit number.
• I4_UNIFORM returns a scaled pseudorandom I4.
• I4VEC_UNIFORM returns a scaled pseudorandom I4VEC.
• IHS implements the improved distributed hypercube sampling algorithm.
• IHS_WRITE writes an IHS dataset to a file.
• R4_UNIFORM_01 returns a unit pseudorandom R4.
• R8_UNIFORM_01 returns a unit pseudorandom R8.
• R8VEC_STD returns the standard deviation of a real vector.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TIMESTRING writes the current YMDHMS date into a string.

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