Added a function to generate random positive semi definite operator. #1013
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@vprusso This PR implements the function to generate a random positive semidefinite operator and is ready for a review. Additionally, I have an issue with the documentation. In the example section the matrix shape is deformed. Please assist me in rectifying it. |
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| Generate a positive semi-definite operator of dimension 3. | ||
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| >>> dim = 3 |
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The example should showcase the use of the function. Not a redefinition of the whole thing.
| >>> random_mat = random_mat / np.trace(random_mat) | ||
| >>> random_mat | ||
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| [[0.35636099 0.17920518 0.14620245] |
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If the matrices are not formatting well for you, refer to any other function that uses matrices in toqito for reference.
| .. bibliography:: | ||
| :filter: docname in docnames | ||
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| :param dim (int): The dimension of the operator. |
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The types provided in the type-hinting args, so don't need to state these here.
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| :return (np.ndarray): A random positive semi-definite operator with dimensions dim x dim. | ||
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| :raises ValueError: If dim is not a positive integer. |
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When does a value get raised? This comment is incorrect.
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| A positive semi-definite operator is a Hermitian operator that has only real and non-negative eigenvalues. | ||
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| This function generates a random positive semi-definite operator by constructing a symmetric matrix, |
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This docstring needs to be written more clearly. For instance "eigenvalues" (not "eigen values"), statements like "The resultant of the function ..." could be worded more clearly, "creates a symmetry matrix" (it's not a "symmetry matrix" it's a "symmetric matrix", etc.
| import numpy as np | ||
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| def random_psd_operator(dim: int) -> np.ndarray: | ||
| r''' Generate a random positive semi definite operator. |
| import numpy as np | ||
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| def random_psd_operator(dim: int) -> np.ndarray: | ||
| r''' Generate a random positive semi definite operator. |
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"semidefinite" not "semi definite"
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| ''' | ||
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| random_mat = np.random.rand(dim, dim) |
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The way this function is written is difficult to follow. Something more concise could be:
mat = (np.random.rand(dim, dim) + np.random.rand(dim, dim).T) / 2
vals, vecs = np.linalg.eigh(mat)
mat = vecs @ np.diag(np.abs(vals)) @ vecs.T
return mat / np.trace(mat)| assert_equal(rand_psd_operator.shape, (dim, dim)) | ||
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| # Check if the matrix is a valid density matrix | ||
| assert is_density(rand_psd_operator), "Matrix should be a valid density matrix" |
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Why does a random PSD matrix need to have trace 1? This would only be true if we were generating a random density matrix.
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Thank you for your feedback. I will review and address the suggested changes. |
Description
Closes #652
Changes