第01章 统计学习方法概论 - 使用最小二乘法拟和曲线 - 实现fitting函数

import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import leastsq

def real_func(x):
    return np.sin(2*np.pi*x)

def fit_func(p, x):
    f = np.poly1d(p)
    return f(x)

def residuals_func(p, x, y):
    return fit_func(p, x) - y

x = np.linspace(0, 1, 10)
x_points = np.linspace(0, 1, 1000)
y_ = real_func(x)
y = [np.random.normal(0, 0.1) + y1 for y1 in y_]

def fitting(M=0):
    p_init = np.random.rand(M + 1)
    p_lsq = leastsq(residuals_func, p_init, args=(x, y))
    print('Fitting Parameters:', p_lsq[0])
    plt.plot(x_points, real_func(x_points), label='real')
    plt.plot(x_points, fit_func(p_lsq[0], x_points), label='fitted curve')
    plt.plot(x, y, 'bo', label='noise')
    plt.legend()
    return p_lsq