On Mon, Nov 8, 2010 at 12:00 PM, Joon <groups.and.li...@gmail.com> wrote: > Another question is, is it better to do cho_solve(cho_factor(A), b) than > solve(A, b)?
If A is symmetric positive definite, then using the cholesky decomposition should be somewhat faster than using a more general solver. (Because, basically, the cholesky decomposition routine "knows" that your matrix is symmetric, so it only has to "look at" half of it, while a generic solver routine has to "look at" your whole matrix regardless). And indeed, that seems to be the case in numpy: In [18]: A = np.random.normal(size=(500, 500)) In [19]: A = np.dot(A, A.T) In [20]: b = np.random.normal(size=(500, 1)) In [21]: %timeit solve(A, b) 1 loops, best of 3: 147 ms per loop In [22]: %timeit cho_solve(cho_factor(A), b) 10 loops, best of 3: 92.6 ms per loop Also of note -- going via the inverse is much slower: In [23]: %timeit dot(inv(A), b) 1 loops, best of 3: 419 ms per loop (I didn't check what happens if you have to solve the same set of equations many times with A fixed and b varying, but I would still use cholesky for that case. Also, note that for solve(), cho_solve(), etc., b can be a matrix, which lets you solve for many different b vectors simultaneously.) -- Nathaniel _______________________________________________ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
