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Replace empirical product test tolerances with principled Higham-Mary bounds

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libeigen/eigen!2292

Co-authored-by: Rasmus Munk Larsen <rmlarsen@gmail.com>
This commit is contained in:
Rasmus Munk Larsen
2026-03-20 11:03:58 -07:00
parent 821ab7d3e6
commit 8a47aa334b
3 changed files with 102 additions and 25 deletions
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14
test/product.h
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@@ -97,8 +97,12 @@ void product(const MatrixType& m) {
// begin testing Product.h: only associativity for now
// (we use Transpose.h but this doesn't count as a test for it)
{
// Increase tolerance, since coefficients here can get relatively large.
RealScalar tol = RealScalar(2) * get_test_precision(m1);
// Associativity: (m1 * m1^T) * m2 vs m1 * (m1^T * m2).
// Two chained products with inner dims cols and rows. Intermediate entries
// of m1*m1^T are O(sqrt(cols)), amplifying the second product's error.
// Probabilistic bound (Higham & Mary 2019): ~lambda * sqrt(k) * epsilon
// per inner product, times sqrt(cols) amplification from chained product.
RealScalar tol = product_tolerance<Scalar>((std::max)(rows, cols), 3);
VERIFY(verifyIsApprox((m1 * m1.transpose()) * m2, m1 * (m1.transpose() * m2), tol));
}
m3 = m1;
@@ -289,8 +293,10 @@ void product(const MatrixType& m) {
// regression for blas_trais
{
// Increase test tolerance, since coefficients can get relatively large.
RealScalar tol = RealScalar(2) * get_test_precision(square);
// Triple products of rows x rows matrices. Each side computes 2-3
// products with inner dim = rows. Probabilistic bound with amplification
// from chained products with O(sqrt(rows)) intermediate entries.
RealScalar tol = product_tolerance<Scalar>(rows, 4);
VERIFY(
verifyIsApprox(square * (square * square).transpose(), square * square.transpose() * square.transpose(), tol));
VERIFY(verifyIsApprox(square * (-(square * square)), -square * square * square, tol));