Module cholesky 

Dynamic-size, caller-owned-buffer decompositions (nalgebra-parity, zero-heap). Cholesky decomposition A = L·Lᵀ for symmetric positive-definite matrices.

Functionality parity with nalgebra’s linalg::cholesky, implemented in the qualia idiom: zero allocation, operating on caller-owned row-major slices with explicit dimension. No DMatrix, no heap, no dependency.

Cholesky is the fast, numerically-stable path for SPD systems (covariance solves, least-squares normal equations, Kalman updates, interior-point steps).

Functions

cholesky_determinant

Determinant of an SPD matrix from its Cholesky factor: det(A) = Π L[i][i]².

cholesky_factor

Compute the lower-triangular Cholesky factor L of the n×n symmetric positive-definite matrix a (row-major), writing L row-major into l (lower triangle filled, strictly-upper zeroed). a and l must each be length n*n.

cholesky_solve

Solve A·x = b for SPD A, given its Cholesky factor l (from cholesky_factor): forward-substitute L·y = b, then back-substitute Lᵀ·x = y. l is n*n; b and x are length n. The solution is written into x (which is also used as scratch for y).