Determinant of factorized matrices #1785
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| [det] = node.outputs | ||
| [x] = node.inputs | ||
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| only_used_by_abs = all( |
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Any Op that that maps (-1, 1) to the same value is actually fine, At the very least should include square as well
ricardoV94
added
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
| case QR(): | ||
| R = client.outputs[-1] | ||
| # if mode == "economic", R may not be square and this rewrite could hide a shape error | ||
| # That's why it's tagged as `shape_unsafe` |
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This rewrite isn't tagged shape_unsafe
| new_det = ones(x.shape[:-2], dtype=det.dtype) | ||
| case QR(): | ||
| # if mode == "economic", Q/R may not be square and this rewrite could hide a shape error | ||
| # That's why it's tagged as `shape_unsafe` |
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Is it worth handling this case in a separate rewrite so as to not tag the others as shape_unsafe (since they aren't)
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I've thought about that as well. That's almost always the case, only a subset of the matching cases is actually unsafe in a rewrite.
OTOH the tag is mostly a debug thing, if you're getting an odd result or shape error you may want to exclude to see if it goes away or the error is more obvious.
You never really want to exclude them at the end of the day
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