Determinant of factorized matrices #1785
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ricardoV94
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linalg
| match core_op: | ||
| case Cholesky(): | ||
| L = client.outputs[0] | ||
| new_det = matrix_diagonal_product(L) ** 2 |
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TODO: Add the positive tag here.
Possibly also rewrite for log(x ** 2) -> log(x) * 2, when we know x is positive
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This all seemed out of scope so I didn't address it. Positive tagging isn't used systematically and I'd rather we have a plan for doing that.
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Still missing tests and a couple other things. I wanted to first get #1786 in (which I think is still not ready either) |
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I approved to poke you towards finishing it :) |
jessegrabowski
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I used claude to add tests. I think it did a reasonable job. |
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I also rebased, so if you want to keep working on it be aware of that. |
| assert_equal_computations([rewritten], [expected]) | ||
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| def test_local_log_prod_to_sum_log_no_rewrite(): |
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nitpick: this can be part of the first test above, as another parametrization where the expected graph is the same as the original one
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| assert len(det_nodes_no_opt) == 1 | ||
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| fn_opt = function( |
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Where these tests hard to pattern match with the rewrite_graph -> assert_equal_computations mold?
| assert_equal_computations([rewritten], [expected]) | ||
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| def test_det_of_factorized_matrix_no_rewrite_without_abs(): |
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Same nit about being a parametrization above. I am not sure myself I prefer that way, just raising if you have a clear preference
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| # Test graph that only has det_X | ||
| f = function([X], [det_X]) | ||
| f.dprint() |
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Probably added by me
| f.dprint() |
2 participants
The old
local_det_cholrewrite is extended to cover more cases of a matrix that is factorized elsewhere, not just with Cholesky, but also LU, LUFactor, or SVD, QR (the latter two only if the sign isn't needed)A new rewrite is added for the determinant of a factorization itself. The logic is slightly different, for instance det(LUFactor) is non-sensical, and the determinant for some outputs of SVD/ QR can always be computed even if the determinant of the whole factorization cannot.
Also extended the rewrite of log(prod(x)) to sum(log(x)), which should increase the stability of many of these when we want the log determinant (or log(abs(determintant))).
Still missing tests
Closes #1679
Related to #573