[AUD-012][High] Reject nonsymmetric and non-finite Cholesky input

[gabrielsantosphilips]

Audit finding

• ID: AUD-012
• Status: Verified defect
• Severity: High
• Confidence: High
• Audited revision: 2f479320d805a1f9f35ebe4afaaeeded48913a94

Problem

CholeskyDecomposition::TryFactor() reads only the lower triangle and never validates symmetry or finite values.

Source:

numerical-toolbox-cpp/numerical/math/CholeskyDecomposition.hpp

Lines 42 to 65 in 2f47932

	OPTIMIZE_FOR_SPEED constexpr std::optional<SquareMatrix<T, N>> CholeskyDecomposition<T, N>::TryFactor(const SquareMatrix<T, N>& a)
	{
	SquareMatrix<T, N> l{};
	for (std::size_t i = 0; i < N; ++i)
	{
	for (std::size_t j = 0; j <= i; ++j)
	{
	const float sum = ToFloat(a.at(i, j)) - detail::CholeskyInnerProduct(l, i, j);
	if (i != j)
	l.at(i, j) = T(sum / ToFloat(l.at(j, j)));
	else if (sum <= std::numeric_limits<float>::epsilon() * math::Abs(ToFloat(a.at(i, i))))
	return std::nullopt;
	else
	l.at(i, j) = T(math::Sqrt(sum));
	}
	}
	return l;
	}
	template<typename T, std::size_t N>
	OPTIMIZE_FOR_SPEED constexpr SquareMatrix<T, N> CholeskyDecomposition<T, N>::Factor(const SquareMatrix<T, N>& a)

Reproduction

[[4,100],[2,3]] returns an engaged optional. Its factor reconstructs [[4,2],[2,3]], not the supplied matrix. NaN pivots can also bypass the <= rejection comparison.

Acceptance criteria

• Reject nonsymmetric input using a scale-aware float tolerance.
• Reject NaN and infinite values.
• Preserve a recoverable failure result through callers.
• Add A = L L^T reconstruction, nonsymmetric, NaN, and ill-conditioning tests.