[AUD-016][High] Propagate QR rank failure from regression APIs

[gabrielsantosphilips]

Audit finding

• ID: AUD-016
• Status: Verified defect
• Severity: High
• Confidence: High
• Audited revision: 2f479320d805a1f9f35ebe4afaaeeded48913a94

Problem

Linear and polynomial regression call QrDecomposition::Decompose() but discard its Boolean result before back substitution. Constant/collinear feature columns and repeated abscissae reach zero-diagonal triangular solves. Their void Fit() APIs cannot report failure.

Sources:

• numerical-toolbox-cpp/numerical/estimators/offline/LinearRegression.hpp

  Lines 48 to 66 in 2f47932

  	qr.Decompose(X_design);
  	coefficients = qr.SolveLeastSquares(y);
  	}
  	template<typename T, std::size_t Samples, std::size_t Features>
  	OPTIMIZE_FOR_SPEED
  	T
  	LinearRegression<T, Samples, Features>::Predict(const InputMatrix& X) const
  	{
  	T result = coefficients.at(0, 0);
  	for (size_t i = 0; i < Features; ++i)
  	result += X.at(i, 0) * coefficients.at(i + 1, 0);
  	return result;
  	}
  	template<typename T, std::size_t Samples, std::size_t Features>
  	const typename LinearRegression<T, Samples, Features>::CoefficientsMatrix& LinearRegression<T, Samples, Features>::Coefficients() const

• numerical-toolbox-cpp/numerical/estimators/offline/PolynomialFitting.hpp

  Lines 47 to 64 in 2f47932

  	qr.Decompose(v);
  	coefficients = qr.SolveLeastSquares(y);
  	}
  	template<typename T, std::size_t Samples, std::size_t Degree>
  	T PolynomialFitting<T, Samples, Degree>::Predict(T xVal) const
  	{
  	T acc = coefficients.at(Degree, 0);
  	for (std::size_t j = Degree; j > 0; --j)
  	acc = acc * xVal + coefficients.at(j - 1, 0);
  	return acc;
  	}
  	template<typename T, std::size_t Samples, std::size_t Degree>
  	const typename PolynomialFitting<T, Samples, Degree>::CoefficientsVector&
  	PolynomialFitting<T, Samples, Degree>::Coefficients() const
  	{
  	return coefficients;

Acceptance criteria

• Fit() exposes explicit success/failure or returns an optional result.
• Failed QR decomposition never proceeds to solve.
• Prior coefficients remain well-defined after failure.
• Add independent rank-deficient, repeated-abscissa, and near-collinear tests.

[gabrielfrasantos]

Fixed on claude/repo-issues-triage-pgbb6e. Breaking interface change — OfflineEstimator::Fit returns bool.

Reproduced both cases first. QrDecomposition::Decompose was already detecting rank deficiency correctly and returning false; the callers simply discarded it. With collinear features, LinearRegression produced coefficients (0, 0, 0.5) — plausible-looking and wrong. PolynomialFitting with repeated abscissae produced (-nan, -nan, -inf).

Both now check the result and return before back substitution, so a failed factorization never reaches a zero-diagonal triangular solve, and prior coefficients are left untouched rather than overwritten with NaN.

Migration. Fit returning bool changes the pure virtual in OfflineEstimator, so any out-of-tree implementation of that interface needs updating. LinearRegression is the only in-tree implementer. Fit is not marked [[nodiscard]], so existing call sites that ignore the result still compile — that is deliberate to keep the change survivable, but it does mean silent misuse stays possible. Say if you would rather have [[nodiscard]] and take the churn.

Tests added: CollinearFeaturesReportFailure, CoefficientsRemainWellDefinedAfterFailure, FullRankFeaturesReportSuccess, and repeated_abscissae_report_failure_without_nan_coefficients.

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