Module ldlt 

Symmetric Indefinite Factorization (LDL^T / Bunch-Kaufman).

Computes P * A * P^T = L * D * L^T where:

• P is a permutation matrix (encoded in pivot_info)
• L is unit lower triangular
• D is block diagonal with 1x1 and 2x2 blocks

Algorithm — Bunch-Kaufman Pivoting

At each step, the algorithm decides whether to use a 1x1 or 2x2 pivot by examining the magnitudes of diagonal and off-diagonal elements:

1. Let alpha = (1 + sqrt(17)) / 8 (~0.6404).
2. Find lambda = max |A[i, k]| for i != k (largest off-diagonal in column k).
3. If |A[k,k]| >= alpha * lambda: use 1x1 pivot at position k.
4. Otherwise, find sigma = max |A[i, r]| for i != r, where r is the row achieving lambda.
5. If |A[k,k]| * sigma >= alpha * lambda^2: use 1x1 pivot.
6. If |A[r,r]| >= alpha * sigma: use 1x1 pivot at position r (with swap).
7. Otherwise: use 2x2 pivot at positions (k, r).

This guarantees bounded element growth in L.

Structs

LdltResult

LDL^T factorization result.

Functions

ldlt

Computes the Bunch-Kaufman LDL^T factorization of a symmetric indefinite matrix.

ldlt_solve

Solves A * x = b using the LDL^T factorization.