Module ic0 

Incomplete Cholesky factorization with zero fill-in — IC(0).

Computes an approximate factorization A ~ L * L^T for symmetric positive- definite (SPD) matrices. The sparsity pattern of L matches the lower triangle of A (zero fill-in).

Algorithm

Uses a level-set parallel approach similar to ILU(0) but exploits symmetry:

1. Rows are grouped into dependency levels.
2. For each row i in a level and each lower-triangular column k < i: a_ij -= a_ik * a_jk for j in the intersection of row i columns and row k columns.
3. The diagonal is updated: a_ii = sqrt(a_ii).
4. Off-diagonal entries are scaled: a_ij /= a_ii for j > i.

Functions

ic0

Incomplete Cholesky(0) factorization: A ~ L * L^T.