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LU Decomposition in NRiC
The routines ludcmp() and lubksb() perform LU decomposition and backsubstitution respectively.
Can easily compute A-1 (solve for the identity matrix column by column) and det(A) (find the product of the diagonal elements of the LU decomposed matrix) - see NRiC 2.3.
WARNING: for large matrices, computing det(A) can overflow or underflow the computer's floating-point dynamic range.