Thanks, Nathaniel. Your reply was very helpful. -Joon
On Mon, 08 Nov 2010 15:47:22 -0600, Nathaniel Smith <n...@pobox.com> wrote: > 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 -- _______________________________________________ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
