Add nearest correlation matrix function

[tommyod]

• Implements the H-weighted (elementwise weighting) nearest correlation matrix in function nearest_correlation_matrix()
• Remove old function _nearest_positive_definite()
• Add back diagonal check == 1.0 in Iman Conover, since it now passes for inputs from this new function (whereas before it failed on output from _nearest_positive_definite())
• Replace usage in the main function

I am unsure about these lines. I added them as an extra fail-safe, but adding some slack on the constraint X >> 0 (X must be in the cone of positive symmetric definite matrices) by adjusting it to X - eps * I >> 0 seems to work well. So the code below is never triggered on my random test cases. That being said, if it triggers it could save a user from an unfortunate situation in the future. Any thoughts on this would be appreciated. If you are agnostic, then I say we keep it - it makes a the code more robust at a not-too-high cost. I have no strong opinion however.

  # We might get small eigenvalues due to numerics. Attempt to fix this by
  # recursively calling the solver with smaller values of epsilon. This is
  # an extra fail-safe that is very rarely triggered on actual data.
  is_symmetric = np.allclose(X, X.T)
  is_PD = np.linalg.eig(X).eigenvalues.min() > 0
  if not (is_symmetric and is_PD) and (eps > 1e-14):
      if verbose:
          print(f"Recursively calling solver with eps := {eps} / 10")
      return nearest_correlation_matrix(G, weights=H, eps=eps / 10, verbose=verbose)

  return X

[dafeda]

This looks great.
As for the recursion, I don't mind it at all, but should we consider adding max recursion depth somehow?