Class Lu

This is lifted from the JAMA package and adapted for this library from its PHP4 origin into PHP 5 and to fit the Chippyash\Matrix model You can find the JAMA package at http://www.phpmath.com/build02/JAMA/downloads/ My thanks to the original authors mentioned below

For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n unit lower triangular matrix L, an n-by-n upper triangular matrix U, and a permutation vector piv of length m so that A(piv,:) = L*U. If m < n, then L is m-by-m and U is m-by-n.

The LU decompostion with pivoting always exists, even if the matrix is singular, so the constructor will never fail. The primary use of the LU decomposition is in the solution of square systems of simultaneous linear equations. This will fail if isNonsingular() returns false.