MiniTensor: fix log() failure on ill-conditioned SPD tensors

[lxmota]

@trilinos/minitensor

Motivation

For SPD tensors with condition number above ~1e10, minitensor::log() (inverse scaling and squaring) can abort in debug builds and write out of bounds in release builds. Root cause chain, verified with a debugger on a captured input:

1. The fully expanded 3x3 determinant used by the Denman–Beavers scaling in sqrt_dbp cancels catastrophically: for the tensor in the added regression test (eigenvalues 1e6, 1, 1e-6; unit determinant) the six terms are of order 1e15 and the computed determinant is exactly 0.0.
2. The scaling factor g = 1/det^(1/6) becomes Inf and floods the iterates X and M with Inf.
3. inverse_full_pivot → solve_full_pivot: elimination produces Inf/Inf = NaN, and the next pivot search finds no pivot because NaN comparisons are false.
4. With asserts enabled, the run aborts at the pivot_row < dimension assert; with -DNDEBUG the subsequent S(pivot_row, j) /= t with pivot_row == dimension is an out-of-bounds write.

In a 500-sample sweep per condition number, log() aborted on 22% of random SPD tensors at condition 1e12 and 39% at 1e14.

Changes

• sqrt_dbp: skip the determinant scaling when the computed determinant is zero or the scaling factor is non-finite. The scaling only accelerates convergence, so skipping it affects iteration count, not correctness.
• solve_full_pivot: replace the pivot-search asserts with MT_ERROR_EXIT so a singular or non-finite matrix produces a clean failure instead of memory corruption in release builds.
• New regression test MiniTensor.LogIllConditioned with the captured tensor whose expanded determinant cancels to exactly zero.

Related Issues

None filed; found during an accuracy/performance study of log() vs log_sym() on SPD tensors.

Testing

• Full test_01.cc gtest suite (33 tests including the new one) passes on Linux x86-64, GCC 16, serial Kokkos.
• With the fix, 500-sample sweeps at conditions 1e12 and 1e14 complete 500/500 (previously 391/500 and 307/500), with relative errors identical to the unpatched code on the samples that previously succeeded (median ~1e-6 at 1e12 against an independent 80-bit eigendecomposition reference).
• The alternative of switching the ISS pipeline to inverse_fast23 was also evaluated and rejected: it divides by the same cancellation-prone determinant, and NaN passes its assert(det != 0), turning the failure into an infinite loop.

[github-actions]

CDash for AT2 results

Reproducing CI builds locally

CI builds can be reproduced locally in a container.

Requirements: Python 3.9+, Podman, CMake

Steps:

• Check out the branch of the PR locally.
• Run commonTools/pr_reproducer/reproducer.sh.