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TRANSFORM>SYMMETRIZE

PURPOSE Change an unsymmetric matrix into a symmetric matrix by using one of a variety of criteria.

DESCRIPTION Produces a symmetric square matrix by one of the following methods. Replace xij and xji by their maximum, minimum, average, sum, absolute difference, product or xij/xji (provided xji is non zero) i < j. Alternatively make the lower triangle equal the upper triangle or the upper triangle equal the lower triangle.

The routine also produces a symmetric matrix with binary values on all off-diagonal by replacing xij and xji by 1 if xij > xji for i j. The > operation in xij > xji can be replaced by , =, <, .
 
If the data has missing values 

PARAMETERS
Input dataset:
Name of file containing matrix to be symmetrized. Data type: Square matrix.

Symmetrizing method (Default = Maximum).
Choices are:
   
Maximum - Replace xij and xji by max(xij,xji), i < j.
Minimum - Replace xij and xji by min(xij,xji), i < j.
Average - Replace xij and xji by (xij + xji)/2, i < j.
Sum - Replace xij and xji by xij + xji, i < j.
Difference - Replace xij and xji by abs(xij - xji), i < j.
Product - Replace xij and xji by xijxji, i < j.
Division - Replace xij and xji by xij/xji, i < j provided xji is non zero.
Lower Half - Replace xij by xji, i < j.
Upper Half - Replace xji by xij, i < j.
Upper > Lower - Replace xij and xji by 1 if xij > xji, by 0 otherwise, i < j.
Upper Lower - Replace xij and xji by 1 if xij xji, by 0 otherwise, i < j.
Upper = Lower - Replace xij and xji by 1 if xij = xji, by 0 otherwise, i < j.
Upper Lower - Replace xij and xji by 1 if xij xji, by 0 otherwise, i < j.
Upper < Lower - Replace xij and xji by 1 if xij < xji, by 0 otherwise, i < j.

Handle missing
Specify how to treat missing data in the symmetrization process. Choose the non-missing value allows the user to reduce or even eliminate the number of missing values in the data. Both missing means that if either value is missing then this is recorded as missing in the symmetrized data.

Output dataset (Default = 'Symmetrize').
Name of file containing symmetrized data.
 
LOG FILE Symmetrized matrix.

TIMING O(N^2).

COMMENTS None.