Module lu 

low level implementation of the various $LU$ decompositions

Modules

full_pivoting

the full pivoting $LU$ decomposition is such that: $$P A Q^\top = LU$$ where $P$ and $Q$ are permutation matrices, $L$ is a unit lower triangular matrix, and $U$ is an upper triangular matrix.

partial_pivoting

the partial pivoting $LU$ decomposition is such that: $$PA = LU$$ where $P$ is a permutation matrix, $L$ is a unit lower triangular matrix, and $U$ is an upper triangular matrix.