def error_norm(self, comp_cov, norm='frobenius', scaling=True,
squared=True):
"""Computes the Mean Squared Error between two covariance estimators.
(In the sense of the Frobenius norm).
Parameters
----------
comp_cov : array-like, shape = [n_features, n_features]
The covariance to compare with.
norm : str
The type of norm used to compute the error. Available error types:
- 'frobenius' (default): sqrt(tr(A^t.A))
- 'spectral': sqrt(max(eigenvalues(A^t.A))
where A is the error ``(comp_cov - self.covariance_)``.
scaling : bool
If True (default), the squared error norm is divided by n_features.
If False, the squared error norm is not rescaled.
squared : bool
Whether to compute the squared error norm or the error norm.
If True (default), the squared error norm is returned.
If False, the error norm is returned.
Returns
-------
The Mean Squared Error (in the sense of the Frobenius norm) between
`self` and `comp_cov` covariance estimators.
"""
# compute the error
error = comp_cov - self.covariance_
# compute the error norm
if norm == "frobenius":
squared_norm = np.sum(error ** 2)
elif norm == "spectral":
squared_norm = np.amax(linalg.svdvals(np.dot(error.T, error)))
else:
raise NotImplementedError(
"Only spectral and frobenius norms are implemented")
# optionally scale the error norm
if scaling:
squared_norm = squared_norm / error.shape[0]
# finally get either the squared norm or the norm
if squared:
result = squared_norm
else:
result = np.sqrt(squared_norm)
return result
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