梯度下降步数统计

def gradient_ascent_points(f,xstart,ystart,rate=1,tolerance=1e-6):
    x = xstart
    y = ystart
    xs, ys = [x], [y]
    grad = approx_gradient(f,x,y)
    while length(grad) > tolerance:
        x += rate * grad[0]
        y += rate * grad[1]
        grad = approx_gradient(f,x,y)
        xs.append(x)
        ys.append(y)
    return xs, ys