On 15 Sep 2014 05:49, "Sebastian Berg" <sebast...@sipsolutions.net> wrote: > For example the QR and eigvals does not allow it, but on the other hand > solve explicitly does (most probably never did, simply because lapack > does not). So I am wondering if there is some convention for this, or > what convention we should implement.
To me the obvious convention would be that whenever there's a unique obvious answer that satisfies the operation's invariants, then we should prefer to implement it (though possibly with low priority), even if this means papering over lapack edge cases. This is consistent with how e.g. we already define sum([]) and prod([]) and empty matrix products, etc. Of course this requires some thinking... e.g. the empty matrix is a null matrix, b/c given empty_vec = np.ones((0,)) empty_mat = np.ones((0, 0)) then we have empty_vec @ empty_mat @ empty_vec = empty_vec @ empty_vec = sum([]) = 0 and therefore empty_mat is not positive definite. np.linalg.cholesky raises an error on non-positive-definite matrices in general (e.g. try np.linalg.cholesky(np.zeros((1, 1)))), so I guess cholesky shouldn't handle empty matrices. For eigvals, I guess empty_mat @ empty_vec = empty_vec, meaning that empty_vec is a arguably an eigenvector with some indeterminate eigenvalue? Or maybe the fact that scalar * empty_vec = empty_vec for ever scalar means that empty_vec should be counted as a zero vector, and thus be ineligible to be an eigenvector. Saying that the empty matrix has zero eigenvectors or eigenvalues seems pretty intuitive. I don't see any trouble with defining qr for empty matrices either. -n _______________________________________________ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
