On 11/08/2010 01:38 PM, Joon wrote: > On Mon, 08 Nov 2010 13:23:46 -0600, Pauli Virtanen <p...@iki.fi> wrote: > > > Mon, 08 Nov 2010 13:17:11 -0600, Joon wrote: > >> I was wondering when it is better to store cholesky factor and use > it to > >> solve Ax = b, instead of storing the inverse of A. (A is a symmetric, > >> positive-definite matrix.) > >> > >> Even in the repeated case, if I have the inverse of A (invA) stored, > >> then I can solve Ax = b_i, i = 1, ... , n, by x = dot(invA, b_i). Is > >> dot(invA, b_i) slower than cho_solve(cho_factor, b_i)? > > > > Not necessarily slower, but it contains more numerical error. > > > > http://www.johndcook.com/blog/2010/01/19/dont-invert-that-matrix/ > > > >> I heard calculating the inverse is not recommended, but my > understanding > >> is that numpy.linalg.inv actually solves Ax = I instead of literally > >> calculating the inverse of A. It would be great if I can get some > >> intuition about this. > > > > That's the same thing as computing the inverse matrix. > > > > Oh I see. So I guess in invA = solve(Ax, I) and then x = dot(invA, b) > case, there are more places where numerical errors occur, than just > x = solve(Ax, b) case. > > Thank you, > Joon > > > Numpy uses SVD to get the (pseudo) inverse, which is usually very accurate at getting (pseudo) inverse.
There are a lot of misconceptions involved but ultimately it comes down to two options: If you need the inverse (like standard errors) then everything else is rather moot. If you are just solving a system then there are better numerical solvers available in speed and accuracy than using inverse or similar approaches. Bruce _______________________________________________ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
