Javadoc
Given a 3x3 array "matrix0", this function replaces it with the
LU decomposition of a row-wise permutation of itself. The input
parameters are "matrix0" and "dimen". The array "matrix0" is also
an output parameter. The vector "row_perm[3]" is an output
parameter that contains the row permutations resulting from partial
pivoting. The output parameter "even_row_xchg" is 1 when the
number of row exchanges is even, or -1 otherwise. Assumes data
type is always double.
This function is similar to luDecomposition, except that it
is tuned specifically for 3x3 matrices.