import matplotlib.pyplot as plt
import numpy as np
from numpy.random import normal
from scipy.optimize import curve_fit
x_data = np.linspace(0, 2*np.pi, 30)
y_data = np.sin(x_data) + normal(0, 0.2, 30)
def func(x, a, b, c, d):
return a * np.sin(b*x + c) + d
parameter, covariance_matrix = curve_fit(func, x_data, y_data)
x = np.linspace(min(x_data), max(x_data), 1000)
plt.plot(x_data, y_data, 'rx', label='data')
plt.plot(x, func(x, *parameter), 'b-', label='fit') # the star is to unpack the parameter array
plt.show()
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
import math
xdata = np.array([2.65, 2.80, 2.96, 3.80, 3.90, 4.60, 4.80, 4.90, 5.65, 5.92])
ydata = np.sin(xdata)
def func(x,p1,p2,p3): # HERE WE DEFINE A SIN FUNCTION THAT WE THINK WILL FOLLOW THE DATA DISTRIBUTION
return p1*np.sin(x*p2+p3)
# Here you give the initial parameters for p0 which Python then iterates over
# to find the best fit
popt, pcov = curve_fit(func,xdata,ydata,p0=(1.0,1.0,1.0)) #THESE PARAMETERS ARE USER DEFINED
print(popt) # This contains your two best fit parameters
# Performing sum of squares
p1 = popt[0]
p2 = popt[1]
p3 = popt[2]
residuals = ydata - func(xdata,p1,p2,p3)
fres = sum(residuals**2)
print(fres) #THIS IS YOUR CHI-SQUARE VALUE!
xaxis = np.linspace(1,7,100) # we can plot with xdata, but fit will not look good
curve_y = func(xaxis,p1,p2,p3)
plt.plot(xdata,ydata,'*')
plt.plot(xaxis,curve_y,'-')
plt.show()
当然它不会绘制任何东西,
curve_fit
不会绘制。在文档中,
curve_fit
的返回值是一个带有估计参数的数组和一个带有估计协方差矩阵的2d数组。您必须自己绘制带有估计参数的拟合函数。我也建议用
a*sin(bx +c) +d
来拟合,因为b和c是不相关的。这是有效的:
结果是:
我有一个示例代码,其中包含正弦曲线形式的数据和适合数据的用户定义函数。
代码如下:
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