IHS
Improved Distributed Hypercube Sampling

IHS is a C++ library which carries out the improved distributed hypercube sampling (IHS) 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.

Languages:

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

Related Data and Programs:

BOX_BEHNKEN, a C++ library which computes a Box-Behnken design, that is, a set of arguments to sample the behavior of a function of multiple parameters;

CVT, a C++ library which computes elements of a Centroidal Voronoi Tessellation.

FAURE, a C++ library which computes elements of a Faure quasirandom sequence.

GRID, a C++ library which computes elements of a grid sequence.

HALTON, a C++ library which computes elements of a Halton quasirandom sequence.

HAMMERSLEY, a C++ library which computes elements of a Hammersley quasirandom sequence.

HEX_GRID, a C++ library which computes elements of a hexagonal grid dataset.

LATIN_CENTER, a C++ library which computes elements of a Latin Hypercube dataset, choosing center points.

LATIN_EDGE, a C++ library which computes elements of a Latin Hypercube dataset, choosing edge points.

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

LCVT, a C++ library which computes a latinized Centroidal Voronoi Tessellation.

NIEDERREITER2, a C++ library which computes elements of a Niederreiter quasirandom sequence using base 2.

NORMAL, a C++ library which computes elements of a sequence of pseudorandom normally distributed values.

SOBOL, a C++ library which computes elements of a Sobol quasirandom sequence.

TABLE_QUALITY, a C++ program which measures the dispersion quality of points in a dataset read from a file.

UNIFORM, a C++ library which computes elements of a uniform pseudorandom sequence.

VAN_DER_CORPUT, a C++ 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:

• ihs.cpp, the source code.
• ihs.hpp, the include file.
• ihs.sh, commands to compile the source code.

Examples and Tests:

• ihs_prb.cpp, a sample calling program.
• ihs_prb.sh, commands to compile and run the sample program.
• ihs_prb_output.txt, the output from a run of the sample program.

List of Routines:

• COVARIANCE does a covariance calculation for IHS solutions.
• DIGIT_TO_CH returns the base 10 digit character corresponding to a digit.
• GET_SEED returns a random seed for the random number generator.
• I4_LOG_10 returns the whole part of the logarithm base 10 of an integer.
• I4_MAX returns the maximum of two integers.
• I4_MIN returns the smaller of two integers.
• I4_TO_S converts an integer to a string.
• I4_UNIFORM returns a scaled pseudorandom I4.
• IHS implements the improved distributed hypercube sampling algorithm.
• IHS_WRITE writes an IHS dataset to a file.
• R4_ABS returns the absolute value of an R4.
• R4_NINT returns the nearest integer to an R4.
• R8_EPSILON returns the R8 round off unit.
• R8_HUGE returns a "huge" R8.
• R8_UNIFORM_01 is a portable pseudorandom number generator.
• R8VEC_AVERAGE returns the average of an R8VEC.
• R8VEC_STD returns the standard deviation of an R8VEC.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TIMESTRING returns the current YMDHMS date as a string.

You can go up one level to the C++ source codes.