cholesky_solve.h File Reference

Solve Ax = b for symmetric positive-definite A via Cholesky decomposition. More...

#include "config.h"
#include "utilities/expected.h"
#include "matrix_traits.h"
#include "simple_type_traits.h"
#include "algorithms/decomposition/cholesky.h"
#include "algorithms/solvers/triangular_solve.h"

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Namespaces
namespace	matrix_algorithms

Functions
template<typename T , my_size_t N>
Expected< FusedVector< T, N >, MatrixStatus >	matrix_algorithms::cholesky_solve (const FusedMatrix< T, N, N > &A, const FusedVector< T, N > &b)
	Solve Ax = b for symmetric positive-definite A via Cholesky decomposition.

Detailed Description

Solve Ax = b for symmetric positive-definite A via Cholesky decomposition.

Chains cholesky() → forward_substitute() → transposed back substitution to solve Ax = b without forming the inverse. Zero dynamic allocation.

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ALGORITHM

Cholesky solve (Ax = b, A symmetric positive-definite):

1. Decompose A = LLᵀ via cholesky(A)
2. Solve Ly = b via forward substitution
3. Solve Lᵀx = y via back substitution (accessing L transposed in-place)

Complexity: O(N³/3 + N²) — dominated by Cholesky for large N.

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FAILURE MODES

Forwards all errors from cholesky():

• MatrixStatus::NotSymmetric — input fails isSymmetric() check
• MatrixStatus::NotPositiveDefinite — diagonal ≤ tol during factorization

From forward_substitute():

• MatrixStatus::Singular — zero diagonal (should not occur if cholesky succeeded)

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