eigenBounds

Code implementing the computation of bounds on eigenvalues/singular values of a matrix. Work in progress.

TO DO on Gao implementation:

1. Check if PRbound is implemented properly
2. See if periodic/pseudo-periodic signals can also use the factorization of covariance trick to get a bound (periodic signals naturaly have a dimensionality bound, but they do not fit within the given framework)
3. See if results can be extended to circulant matrices (i.e. periodic auto-correlations which do not taper off as time goes to infinity)

TO DO on psd matrix bound

1. Given a lower bound on sum of largest eigenvalues and rank, create the best possible bound -> DONE
2. Given a lower bound on sum of largest, and an upper bound on sum of lowest, create best possible bound: i.e. take max(lowerBound,tr(C)-upperBound), and if result is not a concave bound (it need not be), then generate the minimum cocave curve that is above the max() curve.