Cholesky decomposition for symmetric positive-definite matrices. More...
#include "config.h"#include "utilities/expected.h"#include "matrix_traits.h"#include "math/math_utils.h"#include "simple_type_traits.h"
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Namespaces | |
| namespace | matrix_algorithms |
Functions | |
| template<typename MatrixType > | |
| Expected< MatrixType, MatrixStatus > | matrix_algorithms::cholesky (const MatrixType &A, typename MatrixType::value_type tol=typename MatrixType::value_type(PRECISION_TOLERANCE)) |
| Compute the Cholesky decomposition of a symmetric positive-definite matrix. | |
| template<typename MatrixType > | |
| MatrixType | matrix_algorithms::cholesky_or_die (const MatrixType &A) |
| Cholesky decomposition — abort on failure. | |
Detailed Description
Cholesky decomposition for symmetric positive-definite matrices.
Computes the lower-triangular factor L such that A = L · Lᵀ. Returns the result wrapped in Expected so that callers can distinguish success from well-defined failure modes (not symmetric, not positive definite) without exceptions or dynamic allocation.
ALGORITHM
For a symmetric positive-definite matrix A of size N×N, the Cholesky decomposition computes a lower-triangular matrix L such that A = LLᵀ.
For each row i = 0 … N−1:
For each column j = 0 … i:
If i == j (diagonal):
L(i,i) = sqrt( A(i,i) − Σ_{k=0}^{j-1} L(i,k)² )
Else (below diagonal):
L(i,j) = ( A(i,j) − Σ_{k=0}^{j-1} L(i,k)·L(j,k) ) / L(j,j)
Complexity: O(N³/3) multiplications, O(N) square roots.
FAILURE MODES
- MatrixStatus::NotSymmetric — input fails isSymmetric() check
- MatrixStatus::NotPositiveDefinite — a diagonal element ≤ tol during factorization
The tolerance parameter tol controls the diagonal threshold:
- tol = PRECISION_TOLERANCE (default): strict, rejects near-zero diagonals
- tol = 0: relaxed, allows exact-zero diagonals (semi-definite matrices)
- tol < 0: permissive, allows slightly negative diagonals (numerical noise)
