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export module linalgebra:cholesky;
import std;
import :error;
import :vector;
import :matrix;
import :triangular_solve;
export namespace linalgebra {
struct CholeskyResult {
Matrix L;
};
CholeskyResult cholesky_factor(const Matrix& A, double tolerance = 1e-12);
Vector cholesky_solve(const CholeskyResult& chol, const Vector& b);
} // namespace linalgebra
namespace linalgebra {
CholeskyResult cholesky_factor(const Matrix& A, double tolerance) {
if (A.rows() != A.cols()) {
std::ostringstream oss;
oss << "cholesky_factor requires a square matrix, got " << A.rows() << "x" << A.cols();
throw DimensionMismatchError(oss.str());
}
const std::size_t n = A.rows();
for (std::size_t i = 0; i < n; ++i) {
for (std::size_t j = i + 1; j < n; ++j) {
if (std::abs(A(i, j) - A(j, i)) > tolerance) {
throw LinAlgError("cholesky_factor requires a symmetric matrix");
}
}
}
Matrix L = Matrix::zeros(n, n);
for (std::size_t j = 0; j < n; ++j) {
double sum = A(j, j);
for (std::size_t k = 0; k < j; ++k) {
sum -= L(j, k) * L(j, k);
}
if (sum <= tolerance) {
std::ostringstream oss;
oss << "cholesky_factor: matrix is not positive definite (diagonal became "
<< sum << " at step " << j << ")";
throw LinAlgError(oss.str());
}
L(j, j) = std::sqrt(sum);
for (std::size_t i = j + 1; i < n; ++i) {
double s = A(i, j);
for (std::size_t k = 0; k < j; ++k) {
s -= L(i, k) * L(j, k);
}
L(i, j) = s / L(j, j);
}
}
return CholeskyResult{std::move(L)};
}
Vector cholesky_solve(const CholeskyResult& chol, const Vector& b) {
const std::size_t n = chol.L.rows();
if (b.size() != n) {
std::ostringstream oss;
oss << "cholesky_solve: rhs size " << b.size()
<< " does not match factorization size " << n;
throw DimensionMismatchError(oss.str());
}
const Vector y = forward_substitution(chol.L, b);
return backward_substitution(transpose(chol.L), y);
}
} // namespace linalgebra
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