Python曲线拟合(polyfit , curve_fit, interp1d插值)

np.polyfit 多项式拟合

在python中，Numpy.polyfit()是一个在多项式函数内拟合数据的方法。当最小二乘法的拟合条件很差时，polyfit会发出RankWarning。

对散点进行多项式拟合并打印出拟合函数以及拟合后的图形程序如下

例1

在这个程序中，首先，导入matplotlib和numpy库。设置x、y、p和t的值。然后，使用这个x、y、p和t的值，通过拟合绘制多项式。

import numpy as np
import matplotlib.pyplot as plt

np.random.seed(46)
x = np.linspace(0, 1, 25)
y = np.cos(x) + 0.3 * np.random.rand(25)
p = np.poly1d(np.polyfit(x, y, 4))
t = np.linspace(0, 1, 250)
plt.plot(x, y, 'o', t, p(t), '-')
plt.show()

例2

在这个程序中，也是如此，首先，导入matplotlib和numpy库。设置x和y的值。然后，计算多项式并设置x和y的新值。一旦完成，使用函数polyfit()拟合多项式。

import numpy as np
import matplotlib.pyplot as plt

np.random.seed(12)
x = np.linspace(-20, 20, 10)
y = 3.6 * pow(x, 3) + 8.3 * pow(x, 2) + 5.1 * pow(x, 1) + 5
func = np.polyfit(x, y, 4)
xn = np.linspace(-20, 20, 1000)
yn = np.poly1d(func)
plt.plot(xn, yn(xn), x, y, 'o')
plt.show()

curve_fit () 自定义函数拟合

能拟合的函数不止下面这些，只要你写出想要使用的函数的表达式，就可以得到函数的参数！！！

import numpy as np  # NumPy https://numpy.org/
import matplotlib.pyplot as plt  # Matplotlib https://matplotlib.org/
from scipy.optimize import curve_fit  # https://www.scipy.org/

# 三次 - 跟前面所说的poly_fit一个意思
def func_poly_3(x, a, b, c , d):
    return a*x*x*x + b*x*x + c*x + d
# 幂函数
def func_power(x, a, b):
    return x**a + b
# 指数函数
def func_exp(x, a, b):
    return a**x + b

def Hyperb(x, a1, a2, qi):
    y = qi / np.power(1 + a1 * a2 * x, 1 / a2)
    return y

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popt, pcov = curve_fit(func_poly_3, xdata, ydata, method='lm',maxfev = 8866)

plot1 = plt.plot(np.array(xdata), ydata, 'r*', label='original values')
plot2 = plt.plot(np.array(xdata), [func_poly_3(i, *popt) for i in xdata], 'b', label='curvefit values')

plt.show()

scipy.interpolate.interpnd 插值拟合

前两种都限于你得提前知道待拟合的是什么函数, 可不可以通过大量的点插值得到函数呢?

python的scipy.interpolate模块有一维插值函数interp1d，二维插值函数interp2d，多维插值函数interpnd.

在此只对一维插值做演示.

import numpy as np
from scipy.interpolate import interp1d
import matplotlib.pyplot as plt

xdata=[1.0, 1.0185728, 1.0371457, 1.0557185, 1.0742913, 1.0928641, 1.111437, 1.1300098, 1.1485826, 1.1671554, 1.1857283, 1.2043011, 1.2228739, 1.2414467, 1.2600196, 1.2785924, 1.2971652, 1.315738, 1.3343109, 1.3528837, 1.3714565, 1.3900293, 1.4086022, 1.427175, 1.4457478, 1.4643206, 1.4828935, 1.5014663, 1.5200391, 1.5386119, 1.5571848, 1.5757576, 1.5943304, 1.6129032, 1.6314761, 1.6500489, 1.6686217, 1.6871945, 1.7057674, 1.7243402, 1.742913, 1.7614858, 1.7800587, 1.7986315, 1.8172043, 1.8357771, 1.85435, 1.8729228, 1.8914956, 1.9100684, 1.9286413, 1.9472141, 1.9657869, 1.9843597, 2.0029326, 2.0215054, 2.0400782, 2.058651, 2.0772239, 2.0957967, 2.1143695, 2.1329423, 2.1515152, 2.170088, 2.1886608, 2.2072336, 2.2258065, 2.2443793, 2.2629521, 2.2815249, 2.3000978, 2.3186706, 2.3372434, 2.3558162, 2.3743891, 2.3929619, 2.4115347, 2.4301075, 2.4486804, 2.4672532, 2.485826, 2.5043988, 2.5229717, 2.5415445, 2.5601173, 2.5786901, 2.597263, 2.6158358, 2.6344086, 2.6529814, 2.6715543, 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# method: 插值方法: 可选 {‘linear’, ‘nearest’, ‘cubic’} 之一
# ‘linear’: 分段线性, ‘nearest’: 最近邻点, ‘cubic’: 三次样条（cubic spline）插值
func = interp1d(xdata, ydata, kind='cubic')
x_new = np.linspace(start=min(xdata), stop=max(xdata), num=10)
y_new = func(x_new)
plot1 = plt.plot(xdata, ydata, 'r', label='original values')
plt.scatter(x_new, y_new)  # 此时即为平滑曲线
plt.show()

References

NumPy polyfit | How polyfit function work in NumPy with examples? (educba.com)

python - 如何修复 numpy 中的“polyfit 可能状况不佳”？- 堆栈溢出 (stackoverflow.com)

python数据处理一：使用curve_fit实现曲线拟合_耐心的小黑的博客-CSDN博客_curve_fit python

Python数据处理——绘制函数图形以及数据拟合 - 何爱平 - 博客园 (cnblogs.com)

数学建模：插值与拟合—插值问题的python求解_Charle4Leclerc的博客-CSDN博客