Module cholesky_factorizer 

Cholesky factorization and linear solves for symmetric positive-definite matrices.

This module provides a CholeskyFactorizer type for computing and storing the Cholesky factorization of a square matrix

$$A = L L^\intercal$$

where $L$ is lower triangular.

The matrix is provided as a flat slice in row-major order. Internally, the computed Cholesky factor L is also stored in row-major order in a dense Vec<T>. Only the lower-triangular part is meaningful after factorization.

Once a factorization has been computed with CholeskyFactorizer::factorize, the stored factor can be reused to solve linear systems of the form

$$A x = b$$

via CholeskyFactorizer::solve.

Requirements

The input matrix must:

• be square of dimension n × n
• be stored in row-major order
• be symmetric positive definite

If the matrix is not positive definite, factorization fails with CholeskyError::NotPositiveDefinite.

Errors

The module uses CholeskyError to report the following conditions:

• CholeskyError::DimensionMismatch when the input matrix or right-hand side has an incompatible size
• CholeskyError::NotPositiveDefinite when factorization fails because the matrix is not positive definite
• CholeskyError::NotFactorized when attempting to solve a system before a valid factorization has been computed

Example

use optimization_engine::CholeskyFactorizer;

let a = vec![
    4.0_f64, 1.0,
    1.0,     3.0,
];

let b = vec![1.0_f64, 2.0];

let mut factorizer = CholeskyFactorizer::new(2);
factorizer.factorize(&a).unwrap();

let x = factorizer.solve(&b).unwrap();

assert!((x[0] - 0.0909090909).abs() < 1e-10);
assert!((x[1] - 0.6363636364).abs() < 1e-10);

Notes

• The implementation is generic over T: Float.
• Storage is preallocated when constructing the factorizer with CholeskyFactorizer::new.
• The factorizer keeps the computed factor internally so that multiple right-hand sides can be solved efficiently after a single factorization.

Structs

CholeskyFactorizer

Cholesky factoriser

Enums

CholeskyError

Cholesky errors