Python基于最小二乘法实现曲线拟合示例基于最小二乘法实现曲线拟合示例
本文实例讲述了Python基于最小二乘法实现曲线拟合。分享给大家供大家参考，具体如下：
这里不手动实现最小二乘，调用scipy库中实现好的相关优化函数。
考虑如下的含有4个参数的函数式：
构造数据
import numpy as np
from scipy import optimize
import matplotlib.pyplot as plt
def logistic4(x, A, B, C, D):
return (A-D)/(1+(x/C)**B)+D
def residuals(p, y, x):
A, B, C, D = p
return y - logisctic4(x, A, B, C, D)
def peval(x, p):
A, B, C, D = p
return logistic4(x, A, B, C, D)
A, B, C, D = .5, 2.5, 8, 7.3
x = np.linspace(0, 20, 20)
y_true = logistic4(x, A, B, C, D)
y_meas = y_true + 0.2 * np.random.randn(len(y_true))
调用工具箱函数，进行优化
p0 = [1/2]*4
plesq = optimize.leastsq(residuals, p0, args=(y_meas, x))
# leastsq函数的功能其实是根据误差（y_meas-y_true）
# 估计模型（也即函数）的参数
绘图
plt.figure(figsize=(6, 4.5))
plt.plot(x, peval(x, plesq[0]), x, y_meas, 'o', x, y_true)
plt.legend(['Fit', 'Noisy', 'True'], loc='upper left')
plt.title('least square for the noisy data (measurements)')
for i, (param, true, est) in enumerate(zip('ABCD', [A, B, C, D], plesq[0])):
plt.text(11, 2-i*.5, '{} = {:.2f}, est({:.2f}) = {:.2f}'.format(param, true, param, est))
plt.savefig('./logisitic.png')
plt.show()
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