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Fix bugs and improve robustness of SelfAdjointEigenSolver, improve test coverage

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libeigen/eigen!2396

Co-authored-by: Rasmus Munk Larsen <rmlarsen@gmail.com>
This commit is contained in:
Rasmus Munk Larsen
2026-04-07 21:08:29 -07:00
parent bde3a68bae
commit 110530a4d8
6 changed files with 1519 additions and 162 deletions
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155
test/bdcsvd.cpp
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@@ -15,6 +15,7 @@
#define EIGEN_RUNTIME_NO_MALLOC
#include "main.h"
#include "tridiag_test_matrices.h"
#include <Eigen/SVD>
#define SVD_DEFAULT(M) BDCSVD<M>
@@ -146,148 +147,26 @@ void verify_bidiagonal_vs_matrix_svd(const Matrix<RealScalar, Dynamic, 1>& diag,
template <typename RealScalar>
void bdcsvd_bidiagonal_hard_cases() {
using std::abs;
using std::cos;
using std::pow;
using std::sin;
typedef Matrix<RealScalar, Dynamic, 1> VectorXr;
Eigen::internal::set_is_malloc_allowed(true);
const RealScalar eps = NumTraits<RealScalar>::epsilon();
// Use the shared tridiagonal test matrix generators.
// Each generator fills (diag, offdiag) which we treat as (diagonal, superdiagonal)
// of a bidiagonal matrix.
test::for_all_tridiag_test_matrices<RealScalar>(
[](const auto& diag, const auto& offdiag) { verify_bidiagonal_svd<RealScalar>(diag, offdiag); });
// Test sizes: cover n=1, very small, below/above algoSwap (16), and larger.
const int sizes[] = {1, 2, 3, 5, 10, 16, 20, 50, 100};
const int numSizes = sizeof(sizes) / sizeof(sizes[0]);
// Additional SVD-specific test: identity with cross-validation against full matrix SVD.
test::for_tridiag_sizes<RealScalar>([](auto& diag, auto& offdiag) {
test::tridiag_identity(diag, offdiag);
verify_bidiagonal_vs_matrix_svd<RealScalar>(diag, offdiag);
});
for (int si = 0; si < numSizes; ++si) {
const Index n = sizes[si];
VectorXr diag(n), superdiag(n > 1 ? n - 1 : 0);
// 1. Identity: d=[1,...,1], e=[0,...,0]
diag.setOnes();
superdiag.setZero();
verify_bidiagonal_svd<RealScalar>(diag, superdiag);
verify_bidiagonal_vs_matrix_svd<RealScalar>(diag, superdiag);
// 2. Zero: d=[0,...,0], e=[0,...,0]
diag.setZero();
superdiag.setZero();
verify_bidiagonal_svd<RealScalar>(diag, superdiag);
// 3. Scalar (only meaningful for n=1, but runs for all)
if (n == 1) {
diag(0) = RealScalar(3.14);
verify_bidiagonal_svd<RealScalar>(diag, superdiag);
}
// 4. Golub-Kahan: d=[1,...,1], e=[1,...,1]
diag.setOnes();
if (n > 1) superdiag.setOnes();
verify_bidiagonal_svd<RealScalar>(diag, superdiag);
// 5. Kahan matrix: d_i = s^(i-1), e_i = -c*s^(i-1)
// Clamp exponents so condition number stays bounded by 1/eps.
{
const RealScalar theta = RealScalar(0.3);
const RealScalar s = sin(theta);
const RealScalar c = cos(theta);
using std::log;
const RealScalar maxPower = -log(eps) / (-log(s));
for (Index i = 0; i < n; ++i) diag(i) = pow(s, numext::mini(RealScalar(i), maxPower));
for (Index i = 0; i < n - 1; ++i) superdiag(i) = -c * pow(s, numext::mini(RealScalar(i), maxPower));
verify_bidiagonal_svd<RealScalar>(diag, superdiag);
}
// 6. Geometric decay diagonal: d_i = 0.5^i, e=[0,...,0]
// Clamp so condition number stays bounded by 1/eps.
{
using std::log;
const RealScalar base = RealScalar(0.5);
const RealScalar maxPower = -log(eps) / (-log(base));
for (Index i = 0; i < n; ++i) diag(i) = pow(base, numext::mini(RealScalar(i), maxPower));
superdiag.setZero();
verify_bidiagonal_svd<RealScalar>(diag, superdiag);
}
// 7. Geometric decay superdiagonal: d=[1,...,1], e_i = 0.5^i
diag.setOnes();
for (Index i = 0; i < n - 1; ++i) superdiag(i) = pow(RealScalar(0.5), RealScalar(i));
verify_bidiagonal_svd<RealScalar>(diag, superdiag);
// 8. Clustered at 1: d_i = 1 + i*eps, e=[0,...,0]
for (Index i = 0; i < n; ++i) diag(i) = RealScalar(1) + RealScalar(i) * eps;
superdiag.setZero();
verify_bidiagonal_svd<RealScalar>(diag, superdiag);
// 9. Two clusters: half ≈ 1, half ≈ eps
for (Index i = 0; i < n; ++i) diag(i) = (i < n / 2) ? RealScalar(1) : eps;
superdiag.setZero();
verify_bidiagonal_svd<RealScalar>(diag, superdiag);
// 10. Single tiny singular value: d=[1,...,1,eps], e=[eps^2,...]
diag.setOnes();
diag(n - 1) = eps;
for (Index i = 0; i < n - 1; ++i) superdiag(i) = eps * eps;
verify_bidiagonal_svd<RealScalar>(diag, superdiag);
// 11. Graded: d_i = 10^(-i), e_i = 10^(-i)
for (Index i = 0; i < n; ++i) diag(i) = pow(RealScalar(10), -RealScalar(i));
for (Index i = 0; i < n - 1; ++i) superdiag(i) = pow(RealScalar(10), -RealScalar(i));
verify_bidiagonal_svd<RealScalar>(diag, superdiag);
// 12. Nearly diagonal: random diag, eps * random superdiag
diag = VectorXr::Random(n).cwiseAbs() + VectorXr::Constant(n, RealScalar(0.1));
for (Index i = 0; i < n - 1; ++i) superdiag(i) = eps * (RealScalar(0.5) + abs(internal::random<RealScalar>()));
verify_bidiagonal_svd<RealScalar>(diag, superdiag);
// 13. All equal: d=[c,...,c], e=[c,...,c]
diag.setConstant(RealScalar(2.5));
if (n > 1) superdiag.setConstant(RealScalar(2.5));
verify_bidiagonal_svd<RealScalar>(diag, superdiag);
// 14. Wilkinson: d_i = |n/2 - i|, e=[1,...,1]
for (Index i = 0; i < n; ++i) diag(i) = abs(RealScalar(n / 2) - RealScalar(i));
if (n > 1) superdiag.setOnes();
verify_bidiagonal_svd<RealScalar>(diag, superdiag);
// 15. Overflow/underflow: alternating big/tiny diagonal, tiny/big superdiagonal
{
const RealScalar big = (std::numeric_limits<RealScalar>::max)() / RealScalar(1000);
const RealScalar tiny = (std::numeric_limits<RealScalar>::min)() * RealScalar(1000);
for (Index i = 0; i < n; ++i) diag(i) = (i % 2 == 0) ? big : tiny;
for (Index i = 0; i < n - 1; ++i) superdiag(i) = (i % 2 == 0) ? tiny : big;
verify_bidiagonal_svd<RealScalar>(diag, superdiag);
}
// 16. Prescribed condition number: d_i = kappa^(-i/(n-1)), e_i = eps * random
if (n > 1) {
const RealScalar kappa = RealScalar(1) / eps;
for (Index i = 0; i < n; ++i) diag(i) = pow(kappa, -RealScalar(i) / RealScalar(n - 1));
for (Index i = 0; i < n - 1; ++i) superdiag(i) = eps * abs(internal::random<RealScalar>());
verify_bidiagonal_svd<RealScalar>(diag, superdiag);
}
// 17. Rank-deficient: d=[1,..,0,..,0,..,1], e=[0,...,0]
for (Index i = 0; i < n; ++i) diag(i) = (i < n / 3 || i >= 2 * n / 3) ? RealScalar(1) : RealScalar(0);
superdiag.setZero();
verify_bidiagonal_svd<RealScalar>(diag, superdiag);
// 18. Arrowhead stress: d_i = linspace(1, n), e_i = 1/(i+1)
for (Index i = 0; i < n; ++i) diag(i) = RealScalar(1) + RealScalar(i);
for (Index i = 0; i < n - 1; ++i) superdiag(i) = RealScalar(1) / RealScalar(i + 1);
verify_bidiagonal_svd<RealScalar>(diag, superdiag);
// 19. Repeated singular values: d=[1,2,3,1,2,3,...], e=[0,...,0]
for (Index i = 0; i < n; ++i) diag(i) = RealScalar((i % 3) + 1);
superdiag.setZero();
verify_bidiagonal_svd<RealScalar>(diag, superdiag);
// 20. Glued identity: d=[1,...,1], e=0 except e[n/2-1]=eps
diag.setOnes();
superdiag.setZero();
if (n > 2) superdiag(n / 2 - 1) = eps;
verify_bidiagonal_svd<RealScalar>(diag, superdiag);
// Additional SVD-specific test: scalar for n=1.
{
typedef Matrix<RealScalar, Dynamic, 1> VectorXr;
VectorXr diag(1), offdiag(0);
diag(0) = RealScalar(3.14);
verify_bidiagonal_svd<RealScalar>(diag, offdiag);
}
}