Low rank normalization

[odunbar]

Purpose

Closes #225

Content

• Based on the idea that the covariance defines geometrically a linear transformation from white noise to the data noise, ensemble covariance C can be viewed as C = R S S R^{-1} where R is a rotation, and S is the sqrt of the singular values of C. The transformation from white data to the actual data samples is C^{1/2} = RS and it's "whitening" inverse is C^{-1/2} = S^{-1}R^{-1} = S^{-1}R^T as R is a rotation. For rank deficient C, we take the normalization to be instead Sinv R^T where Sinv is Diagonal with the first rank(C) entries equal to S^{-1}, and zero otherwise.
• Added tests to check the covariances become close to the identity in full or low-dim subspace after normalization
• Changed an input-dim consistency check to account for new dimension change

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• I have read and checked the items on the review checklist.

[eviatarbach]

Thank you for addressing this! LGTM.

[odunbar]

bors r+

[bors]

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