n_list = range(4, 50, 4) linf, l2 = [], [] xall = random.random(size=n_list[-1]) dall = exp(-3.0 * random.random(size=n_list[-1])) * 0.05 eall = random.normal(size=n_list[-1]) * dall for n in n_list: x = xall[:n] x = tan((x-0.5)*pi*0.8) / tan(0.4*pi) * 0.5 + 0.5 fx = exp(-((x-0.5)*16)**2) + eall[:n] dfx = dall[:n] # fx[:] = 0; fx[x>0.5] = 1 # fx = arctan(100*(x-0.5)) / 3.0 + 0.5 fy, sig = interp_1d_adaptive(y, x, fx, dfx, compute_sigma=True) fy_l = lagrange_1d(y, x, fx) if abs(fy_l).max() > 1.0E3: fy_l[:] = 0.0 sig[sig>1000] = 1000; sig[sig<-1000] = -1000 pylab.figure() pylab.plot(y, fy, 'b') pylab.plot(y, fy + sig, ':b') pylab.plot(y, fy - sig, ':b') pylab.plot(y, fy_l, '-.g') pylab.plot(y, fye, '--r') pylab.bar(x, x*0, bottom=fx, yerr=dfx, width=0) pylab.ylim([-0.2, 1.2]) linf.append(abs(fy-fye).max()) l2.append(sqrt(((fy-fye)**2).sum())) print n, linf[-1], l2[-1]
y = linspace(0, 1, 250) fye = exp(-((y-0.5)*16)**2) n_list = range(4, 50, 4) randx = random.random(size=n_list[-1]) randx = numpy.tan((randx-0.5)*pi*0.6) / numpy.tan(0.3*pi) * 0.5 + 0.5 linf, l2 = [], [] linf_m, l2_m = [], [] for n in n_list: # x = linspace(0, 1, n) x = numpy.array(sorted(randx[:n])) fx = exp(-((x-0.5)*16)**2) fy = floater_hormann_adaptive(y, x, fx) fy_m = interp_1d_adaptive(y, x, fx) pylab.figure() pylab.plot(y, fye, '--r') pylab.plot(y, fy, 'g') pylab.plot(y, fy_m, 'b') pylab.plot(x, fx, '+k') pylab.ylim([-0.2, 1.2]) linf.append(abs(fy-fye).max()) l2.append(sqrt(((fy-fye)**2).sum())) linf_m.append(abs(fy_m-fye).max()) l2_m.append(sqrt(((fy_m-fye)**2).sum())) print linf[-1], l2[-1], ' mine ', linf_m[-1], l2_m[-1] pylab.figure() pylab.semilogy(n_list, linf, '-+g') pylab.semilogy(n_list, l2, '-+g')
