LATINIZE
Force a Dataset to be a Latin Hypercube

LATINIZE is a FORTRAN90 library which adjusts 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.

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:

LATIN_CENTER is a FORTRAN90 library of routines for Latin Square datasets choosing the center of each square.

LATIN_EDGE is a FORTRAN90 library of routines for Latin Square datasets choosing the edge of each square.

LATIN_RANDOM is a FORTRAN90 library of routines for Latin Square datasets choosing a random point of each square.

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

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

TABLE_LATINIZE is an interactive FORTRAN90 program which allows the user to name the input data file on the command line.

Reference:

1. Michael McKay, William Conover, Richard 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.f90, the source code.
• latinize.csh, commands to compile the source code.

Examples and Tests:

• latinize_prb.f90, the test code.
• latinize_prb.csh, commands to compile, link, load and run the test code.
• latinize_prb_output.txt, 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 a case insensitive comparison of two characters for equality.
• CH_TO_DIGIT returns the integer value of a base 10 digit.
• DTABLE_DATA_READ reads real table data from a file.
• DTABLE_DATA_WRITE writes a table dataset to a file.
• DTABLE_HEADER_READ reads header data from a file.
• DTABLE_HEADER_WRITE writes the table header data to a file.
• DTABLE_LATINIZE "Latinizes" a real table dataset.
• DTABLE_LATINIZED_WRITE writes a real latinized table dataset to a file.
• 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.
• GET_UNIT returns a free FORTRAN unit number.
• R8MAT_PRINT_SOME prints some of a DMAT.
• R8MAT_TRANSPOSE_PRINT prints a real matrix, transposed.
• R8MAT_TRANSPOSE_PRINT_SOME prints some of a real matrix, transposed.
• R8VEC_SORT_HEAP_INDEX_A does an indexed heap ascending sort of a real vector.
• S_BLANK_DELETE removes blanks from a string, left justifying the remainder.
• S_INDEX_LAST finds the LAST occurrence of a given substring.
• 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 writes the current YMDHMS date into a string.

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