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.

On output, each row of the table will have the properties that:

1. the minimum and maximum row values are the same as on input;
2. the row contains N evenly spaced values between the minimum and maximum.
3. in each row, the elements retain their ordering.

Licensing:

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

Languages

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

Related Data and Programs:

LATIN_CENTER, a FORTRAN90 library which computes a Latin Square by choosing the center of each square.

LATIN_COVER, a FORTRAN90 library which produces N Latin squares which cover an NxN square, or NxN Latin cubes which cover an NxNxN cube.

LATIN_EDGE, a FORTRAN90 library which computes a Latin Square by choosing the edge of each square.

LATIN_RANDOM, a FORTRAN90 library which computes a Latin Square by choosing a random point of each square.

TABLE_LATINIZE, a 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.
2. Yuki Saka, Max Gunzburger, John Burkardt,
   Latinized, Improved LHS, and CVT Point Sets in Hypercubes,
   International Journal of Numerical Analysis and Modeling,
   Volume 4, Number 3-4, 2007, pages 729-743,

Source Code:

• latinize.f90, the source code.

Examples and Tests:

• latinize_test.f90, the test code.
• latinize_test.txt, the output file.

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 ( kind = 4 ) value of a base 10 digit.
• 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_DATA_READ reads data from an R8MAT file.
• R8MAT_HEADER_READ reads the header from an R8MAT file.
• R8MAT_LATINIZE "Latinizes" a real table dataset.
• 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.
• R8MAT_WRITE writes an R8MAT file.
• 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.

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