BOX_BEHNKEN
Box-Behnken Sampling

BOX_BEHNKEN is a FORTRAN77 library which returns a set of sample argument values to be used to analyze the behavior of a function.

Given DIM_NUM parameters, each of which is prescribed to lie between a minimum and maximum range, and a function taking these parameters as arguments, this program returns a table of sets of argument values that may be used to sample the function's behavior.

One sample point is the average. All other sample points are generated by setting a single spatial coordinate to its average value, and all other spatial coordinates to either the minimum or maximum. In this way, 1 + DIM_NUM*2**(DIM_NUM-1) points are generated.

Licensing:

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

Languages:

BOX_BEHNKEN is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

CVT, a FORTRAN90 library which computes elements of a Centroidal Voronoi Tessellation.

FAURE, a FORTRAN90 library which computes elements of a Faure sequence.

GRID, a FORTRAN90 library which computes elements of a grid sequence.

HALTON, a FORTRAN90 library which computes elements of a Halton sequence.

HAMMERSLEY, a FORTRAN90 library which computes elements of a Hammersley sequence.

HEX_GRID, a FORTRAN90 library which computes elements of a hexagonal grid dataset.

HEX_GRID_ANGLE, a FORTRAN90 library which computes elements of an angled hexagonal grid dataset.

IHS, a FORTRAN90 library which computes elements of an improved distributed Latin hypercube dataset.

LATIN_CENTER, a FORTRAN90 library which computes elements of a Latin Hypercube dataset, choosing center points.

LATIN_EDGE, a FORTRAN90 library which computes elements of a Latin Hypercube dataset, choosing edge points.

LATIN_RANDOM, a FORTRAN90 library which computes elements of a Latin Hypercube dataset, choosing points at random.

LATINIZE, a FORTRAN90 library which can "latinize" a dataset.

LCVT, a FORTRAN90 library which computes a latinized Centroidal Voronoi Tessellation.

NIEDERREITER2, a FORTRAN90 library which computes elements of a Niederreiter sequence using base 2.

SOBOL, a FORTRAN90 library which computes elements of a Sobol sequence.

TABLE_LATINIZE, a FORTRAN90 program which reads a table file containing a set of data, and writes out a corresponding "latinized" version.

TOMS647, a FORTRAN90 library which implements a version of ACM TOMS algorithm 647, for evaluating Faure, Halton and Sobol sequences.

UNIFORM, a FORTRAN77 library which computes elements of a uniform pseudorandom sequence.

VAN_DER_CORPUT, a FORTRAN90 library which computes elements of a (1 dimensional) van der Corput sequence.

Reference:

1. George Box, Donald Behnken,
   Some new three level designs for the study of quantitative variables,
   Technometrics,
   Volume 2, pages 455-475, 1960.

Source Code:

• box_behnken.f, the source code.
• box_behnken.sh, commands to compile the source code.

Examples and Tests:

• box_behnken_prb.f, a sample calling program.
• box_behnken_prb.sh, commands to compile and run the sample program.
• box_behnken_prb_output.txt, the output file.
• box_behnken_04_33.txt, contains a Box-Behnken dataset of 33 values for 4 parameters.

List of Routines:

• BOX_BEHNKEN returns a Box-Behnken design for the given number of factors.
• BOX_BEHNKEN_SIZE returns the size of a Box-Behnken design.
• GET_UNIT returns a free FORTRAN unit number.
• R8MAT_TRANSPOSE_PRINT prints an R8MAT, transposed.
• R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT transposed.
• R8MAT_WRITE writes a R8MAT file.
• S_LEN_TRIM returns the length of a string to the last nonblank.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.

You can go up one level to the FORTRAN77 source codes.