Add entropy analysis singular vectors

[charlesmartin14]

We would like to extend the entropy analysis of eigenvectors to add the
Entropy Analysis of Singular Vectors of W

Currently we analyze the eigenvectors of X = W^{T}W (or sometimes X=WW^{T})
I would like to extend this to perform SVD on W=USV^{W} and perform the same analysis on the U and V left and right singular vectors

Note: when X=W^{T}W then the eigenvectors of X correspond to the left singular vectors U
(and when X=WW^{T}) then we analyzing V)

Recently, however, we have found that the entropies (and other metrics) of the U and V vectors can be very different

To make this as easy as possible:

I propose simply refactoring the method
apply_analyze_eigenvectors(self, ww_layer, params=None):

into
apply_analyze_singularvectors(self, ww_layer, params=None):
and
plot_singularvector_metrics(svals, vec_entropies, loc_ratios, part_ratios, type=LEFT|RIGHT)

Then we modify the main method so that instead of computing

evals, V = eig_full(X, method=params[SVD_METHOD])
            all_evals.extend(evals)

We compute the full SVD, and generate the metrics for the U and V singular vectors, and provide the same plots for both

This should take an hour or so to code, not counting unit tests

Additional extensions

• save the U and V metrics in the layer for use later in a new method
• possibly change /extend the entropy to be normalized by the number of bins so entropies can be compared across different layers
• add the SVDShuffling method which is like SVDSmoothing, but uses the full SVD (rather than Truncated SVD) and shuffles the bulk eigenvalues rather than simply dropping them
• Allow SVDShuffling and/or SVDSmoothing to select vectors to retain by the entropy metrics ( i.e. N lowest entropy left and right singular vectors, etc)