LATINIZE
Force a Dataset to be a Latin Hypercube

LATINIZE is a library of C++ routines, using double precision arithmetic, which adjust an M dimensional dataset of N points so that it forms a Latin hypercube.

The algorithm is actually very simple. In each spatial dimension, the point coordinates are sorted, and then replaced by the appropriate values for a Latin hypercube. In particular, if there are four points, then in every coordinate, the four points will be assigned values of 1/8, 3/8, 5/8 and 7/8 (in some order). The hope is that if the initial dataset has some nice dispersion property, then the resulting adjusted dataset will inherit some of this dispersion as well; in particular, more dispersion than typically seen in an arbitrary Latin hypercube.

Related Data and Programs:

LATIN_CENTER is a C++ library of routines for Latin Square datasets choosing the center of each square.

LATIN_EDGE is a C++ library of routines for Latin Square datasets choosing the edge of each square.

LATIN_RANDOM is a C++ library of routines for Latin Square datasets choosing a random point of each square.

LATINIZE is also available in a FORTRAN90 version and a MATLAB version.

TABLE is the format used to store the input and output files used by the program.

TABLE_LATINIZE is an interactive C++ program which allows the name of the data file to be specified on the command line.

Reference:

1. M D McKay, W J Conover, R J Beckman,
   A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code,
   Technometrics,
   Volume 21, pages 239-245, 1979.

Source Code:

• latinize.C, the source code.
• latinize.H, the include file.
• latinize.csh, commands to compile the source code.

Examples:

• latinize_prb.C, the test code.
• latinize_prb.csh, commands to compile, link, load and run the test code.
• latinize_prb.out, printed output from a run of the test code.

CVT_02_00010 is a set of 10 CVT points in 2D:

• cvt_02_00010.txt, the original set of 10 points in 2D.
• cvt_02_00010.png, a PNG image of the points.
• cvt_02_00010.latin.txt, the latinized version of the dataset.
• cvt_02_00010.latin.png, a PNG image of the latinized points.

CVT_03_00007 is a set of 7 CVT points in 3D:

• cvt_03_00007.txt, 7 points in 3D.
• cvt_03_00007.latin.txt, the latinized version of the dataset.

CVT_03_00056 is a set of 56 CVT points in 3D:

• cvt_03_00056.txt, 56 points in 3D.
• cvt_03_00056.latin.txt, the latinized version of the dataset.

CVT_07_00100 is a set of 100 CVT points in 7D:

• cvt_07_00100.txt, 100 points in 7D.
• cvt_07_00100.latin.txt, the latinized version of the dataset.

List of Routines:

• CH_CAP capitalizes a single character.
• CH_EQI is true if two characters are equal, disregarding case.
• CH_TO_DIGIT returns the integer value of a base 10 digit.
• DTABLE_DATA_READ reads the real table data from a TABLE file.
• DTABLE_DATA_WRITE writes real table data to a TABLE file.
• DTABLE_HEADER_READ reads the header from a TABLE file.
• DTABLE_HEADER_WRITE writes the header of a TABLE file.
• DTABLE_LATINIZE "Latinizes" a real table dataset.
• DTABLE_PRINT prints a double precision matrix, with an optional title.
• DTABLE_PRINT_SOME prints some of a double precision matrix.
• DTABLE_TRANSPOSE_PRINT prints a real matrix, transposed.
• DTABLE_TRANSPOSE_PRINT_SOME prints some of a real matrix, transposed.
• FILE_COLUMN_COUNT counts the number of columns in the first line of a file.
• FILE_NAME_EXT_GET determines the "extension" of a file name.
• FILE_NAME_EXT_SWAP replaces the current "extension" of a file name.
• FILE_ROW_COUNT counts the number of row records in a file.
• I4_MAX returns the maximum of two integers.
• I4_MIN returns the smaller of two integers.
• R8_EPSILON returns the round off unit for doubleing arithmetic.
• R8VEC_SORT_HEAP_INDEX_A does an indexed heap ascending sort of a real vector.
• S_INDEX_LAST_C returns a pointer to the last occurrence of a given character.
• S_LEN_TRIM returns the length of a string to the last nonblank.
• S_TO_R8 reads an R8 from a string.
• S_TO_R8VEC reads an R8VEC from a string.
• S_WORD_COUNT counts the number of "words" in a string.
• 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.