qml.kernels.displace_matrix

displace_matrix(K)

Remove negative eigenvalues from the given kernel matrix by adding a multiple of the identity matrix.

This method keeps the eigenvectors of the matrix intact.

Parameters

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

Returns

Kernel matrix with eigenvalues offset by adding the identity.

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 shift all eigenvalues of the matrix by adding the identity matrix multiplied with the absolute value of the smallest (the most negative, that is) eigenvalue:

>>> K_displaced = qml.kernels.displace_matrix(K)
>>> np.linalg.eigvalsh(K_displaced)
array([0.,  2.,  3.])

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

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