Optimized arithmetic methods for strided triangular matrices #52571
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jishnub
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Dec 25, 2023
Since the values stored in the parent corresponding to the structural zeros of a tridiagonal matrix aren't well-defined, using it in `ldiv!` is a footgun that may lead to heisenbugs (one seen in https://buildkite.com/julialang/julia-master/builds/31285#018c7cc7-6c77-41ac-a01b-1c7d14cb1b15). This PR changes it to using the tridiagonal matrix directly in `ldiv!`, which should lead to predictable results, and be bug-free. The failing tests for #52571 pass locally with this change.
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Although this PR improves performance and resolves several issues, I don't really like the hacky nature of the new methods that are specifically working around bugs with using a partly initialized |
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Ready to go? I still like it. 😉 |
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Looks good to me. Perhaps we should update the branch to ensure that the tests are passing? Unfortunately my computer has broken down, so progress has stalled |
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Test failures appear unrelated, so should be good |
KristofferC
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Jan 5, 2024
Since the values stored in the parent corresponding to the structural zeros of a tridiagonal matrix aren't well-defined, using it in `ldiv!` is a footgun that may lead to heisenbugs (one seen in https://buildkite.com/julialang/julia-master/builds/31285#018c7cc7-6c77-41ac-a01b-1c7d14cb1b15). This PR changes it to using the tridiagonal matrix directly in `ldiv!`, which should lead to predictable results, and be bug-free. The failing tests for #52571 pass locally with this change. (cherry picked from commit ef549ae)
KristofferC
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that referenced
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Jan 5, 2024
Since the values stored in the parent corresponding to the structural zeros of a tridiagonal matrix aren't well-defined, using it in `ldiv!` is a footgun that may lead to heisenbugs (one seen in https://buildkite.com/julialang/julia-master/builds/31285#018c7cc7-6c77-41ac-a01b-1c7d14cb1b15). This PR changes it to using the tridiagonal matrix directly in `ldiv!`, which should lead to predictable results, and be bug-free. The failing tests for #52571 pass locally with this change. (cherry picked from commit ef549ae)
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This uses broadcasting for operations like
A::UpperTriangular + B::UpperTriangularin case the parents areStridedMatrixes. Looping only over the triangular part is usually faster for large matrices, where presumably memory is the bottleneck.Some performance comparisons, using
-U1.011 ms (3 allocations: 7.63 MiB)559.680 μs (3 allocations: 7.63 MiB)U + U/U - U971.740 μs (3 allocations: 7.63 MiB)560.063 μs (3 allocations: 7.63 MiB)U + U1/U - U13.014 ms (9 allocations: 22.89 MiB)944.772 μs (3 allocations: 7.63 MiB)U1 + U14.509 ms (12 allocations: 30.52 MiB)1.687 ms (3 allocations: 7.63 MiB)U1 - U13.357 ms (9 allocations: 22.89 MiB)1.763 ms (3 allocations: 7.63 MiB)I've retained the existing methods as fallback, in case there's current code that works without broadcasting.