# -*- coding: cp936 -*-#optimization test, y = (x-3)^2from matplotlib.pyplot import figure, hold, plot, show, xlabel, ylabel, legenddef f(x):        "The function we want to minimize"        return (x-3)**2def f_grad(x):        "gradient of function f"        return 2*(x-3)x = 0y = f(x)err = 1.0maxIter = 300curve = [y]it = 0step = 0.1#下面展示的是我之前用的方法，看上去貌似还挺合理的，但是很慢while err > 1e-4 and it < maxIter:    it += 1    gradient = f_grad(x)    new_x = x - gradient * step    new_y = f(new_x)    new_err = abs(new_y - y)    if new_y > y: #如果出现divergence的迹象，就减小step size        step *= 0.8    err, x, y = new_err, new_x, new_y    print ‘err:‘, err, ‘, y:‘, y    curve.append(y)print ‘iterations: ‘, itfigure(); hold(True); plot(curve, ‘r*-‘)xlabel(‘iterations‘); ylabel(‘objective function value‘)#下面展示的是backtracking line search，速度很快x = 0y = f(x)err = 1.0alpha = 0.25beta = 0.8curve2 = [y]it = 0while err > 1e-4 and it < maxIter:    it += 1    gradient = f_grad(x)    step = 1.0    while f(x - step * gradient) > y - alpha * step * gradient**2:        step *= beta    x = x - step * gradient    new_y = f(x)    err = y - new_y    y = new_y    print ‘err:‘, err, ‘, y:‘, y    curve2.append(y)print ‘iterations: ‘, itplot(curve2, ‘bo-‘)legend([‘gradient descent I used‘, ‘backtracking line search‘])show()