Added a .pinv() method to MultiVectors plus tests #367
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| @_cached_property | ||
| def pinv_func(self): | ||
| """ | ||
| Get a function that returns left-pseudoinverse using a computational |
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Is the left pseudo-inverse equal to the right pseudo-inverse (i.e., can you find a counterexample where it isn't?)
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Good question. I can't come up with a counter example. Something interesting and perhaps related I noticed is that if I replace the original np.linalg.solve with np.linalg.lstsq I get for the test example
Expected :0.5 + (3002399751580329.5^e2) - (0.5^e3) - (0.75^e13) - (3002399751580329.5^e23)
Actual :0.5 - (0.5^e3)
I think it is save to say that this is undesired behavior. The pinv function clearly behaves much gentler. And in the numpy docs I see no mention of left and right actually, so perhaps we should leave that distinction altogether? Since it seems to return the input element anyway in case of singular behavior I don't see how that could be different left and right.
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CI failures can be ignored. Thanks for the PR, I think I like the |
PR implementing #366.
I've added a method
.pinv()to multivectors, which returns the pseudoinverse instead of the normal inverse. Identical to the matrix inverse method but when invoked on singular elements this does not throw an error but instead returns the original element, because well... it's singular.