LATINIZE
Force a Dataset to be a Latin Hypercube

LATINIZE is a library of MATLAB functions 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 MATLAB library of routines for Latin Square datasets choosing the center of each square.

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

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

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

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

TABLE_LATINIZE is an interactive MATLAB 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:

• dtable_data_read.m, reads a double precision table dataset from a file.
• dtable_data_write.m, writes a double precision table dataset to a file.
• dtable_header_read.m, reads header data from a file.
• dtable_header_write.m, writes header data to a file.
• dtable_latinize.m, latinizes a double precision table dataset.
• dtable_latinized_write.m, writes a double precision latinized table dataset to a file.
• file_column_count.m, counts the number of columns in the first line of a file.
• file_name_ext_swap.m, replaces the current "extension" of a file name.
• file_row_count.m, counts the number of row records in a file.
• r8_epsilon.m, returns the R8 machine precision.
• r8mat_transpose_print.m, prints an R8MAT, tranposed.
• r8mat_transpose_print_some.m, prints some of an R8MAT, tranposed.
• r8vec_sort_heap_index_a.m, does an indexed heap ascending sort of an R8VEC.
• s_len_trim.m, returns the length of a string to the last nonblank.
• s_word_count.m counts the number of "words" in a string.
• timestamp.m prints the current YMDHMS date as a time stamp.
• timestring.m writes the current YMDHMS date into a string.

Examples and Tests:

• latinize_test.m, runs all the tests.
• latinize_test01.m, carries out the latinization operation on a single file.
• latinize_test.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.

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