Module cholesky 

low level implementation of the various cholesky-like decompositions

Modules

lblt

the bunch kaufman decomposition of a self-adjoint matrix $a$ is such that: $$P A P^\top = LBL^H$$ where $P$ is a permutation matrix, $B$ is a block diagonal matrix, with $1\times 1$ or $2 \times 2 $ diagonal blocks, and $L$ is a unit lower triangular matrix

ldlt

the $L D L^\top$ decomposition of a self-adjoint positive definite matrix $A$ is such that: $$A = L D L^H$$ where $L$ is a unit lower triangular matrix, and $D$ is a diagonal matrix

llt

the $L L^\top$ decomposition of a self-adjoint positive definite matrix $A$ is such that: $$A = L L^H$$ where $L$ is a lower triangular matrix

llt_pivoting

the pivoted $L L^\top$ decomposition of a self-adjoint positive definite matrix $A$ is such that: $$P A P^\top = L L^H$$ where $L$ is a unit lower triangular matrix and $P$ is a permutation matrix