BUG: TestLstsqMatrix, residuals not calculated properly for square tests #29851
Description
Describe the issue:
When running numpy/matrixlib/tests/test_matrix_linalg.py in parallel threads (see #29552 for more information about running tests in parallel), in the TestLstsqMatrix class, the tests test_sq_cases and test_empty_sq_cases will occasionally fail.
Looking at the error messages, it looks like the residuals for these square tests are not being calculated properly when ran under parallel threads.
Reproduce the code example:
pip install pytest-run-parallel
spin test numpy/matrixlib/tests/test_matrix_linalg.py::TestLstsqMatrix -- --parallel-threads=autoError message:
Large traceback, link to gist: https://gist.github.com/bwhitt7/fba632611b3b5cd127190d47eee34cb0Python and NumPy Versions:
Python: 3.14.0rc3+ free-threading build
NumPy: 2.4.0.dev
Runtime Environment:
[{'numpy_version': '2.4.0.dev0+git20250930.0f46b6e',
'python': '3.14.0rc3+ free-threading build (heads/3.14:c76fd771b5c, Sep 25 '
'2025, 10:25:46) [GCC 13.3.0]',
'uname': uname_result(system='Linux', node='SPACE', release='6.6.87.2-microsoft-standard-WSL2', version='#1 SMP PREEMPT_DYNAMIC Thu Jun 5 18:30:46 UTC 2025', machine='x86_64')},
{'simd_extensions': {'baseline': ['SSE', 'SSE2', 'SSE3'],
'found': ['SSSE3',
'SSE41',
'POPCNT',
'SSE42',
'AVX',
'F16C',
'FMA3',
'AVX2'],
'not_found': ['AVX512F',
'AVX512CD',
'AVX512_KNL',
'AVX512_KNM',
'AVX512_SKX',
'AVX512_CLX',
'AVX512_CNL',
'AVX512_ICL',
'AVX512_SPR']}},
{'architecture': 'Haswell',
'filepath': '/usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so',
'internal_api': 'openblas',
'num_threads': 24,
'prefix': 'libopenblas',
'threading_layer': 'pthreads',
'user_api': 'blas',
'version': '0.3.26'}]
Context for the issue:
I'm working on making the NumPy test suite more thread safe and exposing thread safety issues like this.