Added three functions for linalg: SVD, Least Squares and PseudoInverse #258
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…meric!), Least Squares and PseudoInverse
| matrix = to_mpmath_matrix(m) | ||
| U, S, V = mp.svd(matrix) | ||
| S = mp.diag(S) | ||
| print(U, S, V) |
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Sympy implements the singular value decomposition for exact inputs, see here. We should probably us this version if the argument is exact and the mpmath version otherwise. Edit: Can never get the md hyperlink syntax right. |
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Also, we have a helper class function for wrapping Sympy functions. It's called There's also I'm happy to help with this. Let me know if you have any questions. |
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Hey, actually the function you're linking is the one I am using. But if you look closely, it's the mpmath Matrix package of sympy and unfortunately not the sympy Matrix... Took me some time to realize, too. So I guess at least sympy doesn't have a algebraic solution up to now. |
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Oh, you're right sorry. I see there's an Sympy issue sympy/sympy#6832 to track this missing functionality. The only option we have is to provide the numerical SVD (as you've done). |
| </dl> | ||
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| >> SingularValueDecomposition[{{1, 2}, {2, 3}, {3, 4}}] | ||
| = {{-11 / 6, -1 / 3, 7 / 6}, {4 / 3, 1 / 3, -2 / 3}} |
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This test is failing (because we get inexact answers). It's nice to have the tests pass, and unfortunately in the current system there's no way to mark a test as xfail. I'd suggest adding a Line before this test explaining why the results are inexact, and then testing the inexact results.
Let me know if that's unclear.
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Ideally I'd like to get this one into 0.9 too. |
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Opened #321. |
SVD is only numeric and implemented via mpmath. Not sure if that's acceptable or not? Might need a check, too.