qml.kernels.threshold_matrix

threshold_matrix(K)

Remove negative eigenvalues from the given kernel matrix.

This method yields the closest positive semi-definite matrix in any unitarily invariant norm, e.g. the Frobenius norm.

Parameters

K (array[float]) – Kernel matrix, assumed to be symmetric.

Returns

Kernel matrix with cropped negative eigenvalues.

Return type

array[float]

Example:

Consider a symmetric matrix with both positive and negative eigenvalues:

>>> K = np.array([[0, 1, 0], [1, 0, 0], [0, 0, 2]])
>>> np.linalg.eigvalsh(K)
array([-1.,  1.,  2.])

We then can threshold/truncate the eigenvalues of the matrix via

>>> K_thresh = qml.kernels.threshold_matrix(K)
>>> np.linalg.eigvalsh(K_thresh)
array([0.,  1.,  2.])

If the input matrix does not have negative eigenvalues, threshold_matrix does not have any effect.

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