Refactor functions in matrixtools.py #442
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| if not is_hermitian(mx, tol): | ||
| return False | ||
| if attempt_cholesky: | ||
| try: | ||
| _ = _spl.cholesky(mx) | ||
| return True # Cholesky succeeded | ||
| except _spl.LinAlgError: | ||
| pass # we fall back on eigenvalue decomposition | ||
| evals = _np.linalg.eigvalsh(mx) |
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The property of being positive semidefinite is generally ascribed to Hermitian matrices, since the value of the quadratic form
The new implementation starts with a check that the matrix is Hermitian. If we do have a Hermitian matrix then the fastest way to check if it's positive definite is a Cholesky decomposition. However, Cholesky will fail on matrices that are only positive semidefinite, so there is no point in trying Cholesky if we expect is_pos_def will regularly handle singular matrices. I've set the default behavior for attempt_cholesky to False. If we skip Cholesky or if Cholesky fails then we use Hermitian eigendecomposition.
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A couple of things:
- Should we ensure the docstring is consistent? It says PD in the first line, but return says PSD.
- Both implementations are clearly for PSD. Should the function name be
is_pos_semidefinstead? Pro is that it is more accurate, con is that it is an API change. While this is in matrixtools and therefore could have moderate/high user exposure, it seems like the only use is inis_valid_density_mxbelow (which also seems like it has low usage), so maybe the API change would go mostly unnoticed?
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In the context of quantum information I find people are lax about positive definite versus positive semidefinite, so I think the function name is fine. But I'll definitely change the docstring to be consistent about really checking that a matrix is PSD.
| def remove_dependent_cols(mx, tol=1e-7): | ||
| """ | ||
| Removes the linearly dependent columns of a matrix. | ||
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| Parameters | ||
| ---------- | ||
| mx : numpy.ndarray | ||
| The input matrix | ||
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| Returns | ||
| ------- | ||
| A linearly independent subset of the columns of `mx`. | ||
| """ | ||
| last_rank = 0; cols_to_remove = [] | ||
| for j in range(mx.shape[1]): | ||
| rnk = _np.linalg.matrix_rank(mx[:, 0:j + 1], tol) | ||
| if rnk == last_rank: | ||
| cols_to_remove.append(j) | ||
| else: | ||
| last_rank = rnk | ||
| #print("Removing %d cols" % len(cols_to_remove)) | ||
| return _np.delete(mx, cols_to_remove, axis=1) | ||
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This was called in one function (below), which I reimplemented to rely on independent_columns.
rileyjmurray
changed the title
Get the latest fixes for the ComplementPOVMEffect.to_vector() calls.
Forgot to pull latest develop before attempting the previous merge.
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Thanks for the great effort @rileyjmurray, as always! Also, I greatly appreciate your preemptive comments on some of the more technical changes, it makes it much easier to follow. :)
There is only one real action item here, for an additional unit test for the attempt_cholesky codepath in is_pos_def (and a small docstring update). However, I've also made some non-blocking comments/questions. I 👍'd any of your comments that I read and agreed with but had no active comments or action items for.
| if not is_hermitian(mx, tol): | ||
| return False | ||
| if attempt_cholesky: | ||
| try: | ||
| _ = _spl.cholesky(mx) | ||
| return True # Cholesky succeeded | ||
| except _spl.LinAlgError: | ||
| pass # we fall back on eigenvalue decomposition | ||
| evals = _np.linalg.eigvalsh(mx) |
There was a problem hiding this comment.
A couple of things:
- Should we ensure the docstring is consistent? It says PD in the first line, but return says PSD.
- Both implementations are clearly for PSD. Should the function name be
is_pos_semidefinstead? Pro is that it is more accurate, con is that it is an API change. While this is in matrixtools and therefore could have moderate/high user exposure, it seems like the only use is inis_valid_density_mxbelow (which also seems like it has low usage), so maybe the API change would go mostly unnoticed?
This PR resolves #429. I've provided detailed comments explaining my changes to
matrixtools.py. I've also removed some commented-out code.