IHS
Improved Distributed Hypercube Sampling

IHS is a MATLAB library 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 N 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.

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:

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 a MATLAB library which computes elements of a grid sequence.

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

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.

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 using base 2.

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

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

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

TABLE_QUALITY is a MATLAB program which measures the dispersion quality of points in a dataset read from a file.

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 1D van der Corput sequence.

Reference:

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

Source Code:

• covariance.m, does a covariance calculation for IHS solutions.
• get_seed.m, returns a seed for the random number generator.
• i4_uniform.m, returns a random integer in a given range.
• ihs.m, implements the improved hypercube sampling algorithm.
• ihs_write.m, writes an IHS dataset to a file.
• r8_epsilon.m, returns the machine precision.
• r8_uniform_01.m, returns a pseudorandom double precision value in [0,1].
• r8vec_std.m, returns the standard deviation of a double precision vector.
• timestamp.m, prints the current YMDHMS date as a time stamp.
• timestring.m, returns the current YMDHMS date as a string.

Examples and Tests:

• ihs_prb.m, runs all the tests.
• ihs_test01.m, demonstrates IHS for several dimensions.
• ihs_test02.m, demonstrates IHS for several duplication values.
• ihs_test03.m, demonstrates IHS for several numbers of points.
• ihs_test04.m, demonstrates IHS for several random number seeds.
• ihs_test_output.txt, the output from all the tests.

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