playing devil's advocate I'd say use Algorithmic Differentiation instead of finite differences ;) that would probably speed things up quite a lot.
On Tue, May 4, 2010 at 11:36 PM, Davide Lasagna <lasagnadav...@gmail.com> wrote: > If your x data are equispaced I would do something like this > def derive( func, x): > """ > Approximate the first derivative of function func at points x. > """ > # compute the values of y = func(x) > y = func(x) > # compute the step > dx = x[1] - x[0] > # kernel array for second order accuracy centered first derivative > kc = np.array([-1.0, +0.0, +1.0]) / 2 / dx > # kernel array for second order accuracy left and right first derivative > kl = np.array([-3.0, +4.0, -1.0]) / 2 / dx > kr = np.array([+1.0, -4.0, +3.0]) / 2 / dx > # correlate it with the original array, > # note that only the valid computation are performed > derivs_c = np.correlate( y, kc, mode='valid' ) > derivs_r = np.correlate( y[-3:], kr, mode='valid' ) > derivs_l = np.correlate( y[:+3], kl, mode='valid' ) > return np.r_[derivs_l, derivs_c, derivs_r] > This is actually quite fast: on my machine (1.7GHz) i have this. >>>>:x = np.linspace(0,2*np.pi, 1e6) >>>>:func = lambda x: np.sin(x) >>>>:timeit derive(func, x) > 10 loops, best of 3: 177 ms per loop > I'm curious if someone comes up with something faster. > > Regards, > Davide > > On 4 May 2010 22:17, <josef.p...@gmail.com> wrote: >> >> On Tue, May 4, 2010 at 4:06 PM, gerardob <gberbeg...@gmail.com> wrote: >> > >> > Hello, I have written a very simple code that computes the gradient by >> > finite >> > differences of any general function. Keeping the same idea, I would like >> > modify the code using numpy to make it faster. >> > Any ideas? >> > Thanks. >> > >> > def grad_finite_dif(self,x,user_data = None): >> > assert len(x) == self.number_variables >> > points=[] >> > for j in range(self.number_variables): >> > points.append(x.copy()) >> > >> > points[len(points)-1][j]=points[len(points)-1][j]+0.0000001 >> > delta_f = [] >> > counter=0 >> > for j in range(self.number_variables): >> > >> > delta_f.append((self.eval(points[counter])-self.eval(x))/0.0000001) >> >> it looks like your are evaluating the same point several times >> self.eval(x) >> >> > counter = counter + 1 >> > return array(delta_f) >> >> That's what I used as a pattern for a gradient function >> >> #from scipy.optimize >> def approx_fprime(xk,f,epsilon,*args): >> f0 = f(*((xk,)+args)) >> grad = np.zeros((len(xk),), float) >> ei = np.zeros((len(xk),), float) >> for k in range(len(xk)): >> ei[k] = epsilon >> grad[k] = (f(*((xk+ei,)+args)) - f0)/epsilon >> ei[k] = 0.0 >> return grad >> >> Josef >> >> > -- >> > View this message in context: >> > http://old.nabble.com/Improvement-of-performance-tp28452458p28452458.html >> > Sent from the Numpy-discussion mailing list archive at Nabble.com. >> > >> > _______________________________________________ >> > 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 > > > _______________________________________________ > 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
