数值分析实验之曲线最小二乘拟合含有噪声扰动（python实现）

 1 import numpy as np
 2 import matplotlib.pyplot as plt
 3 import math
 4 #定义x、y散点坐标
 5 x = np.arange(0.0, 10.0,0.1)
 6 x = np.array(x)
 7 print(‘x is :\n‘,x)
 8 num = np.sin(x)+np.random.randn(100)
 9 y = np.array(num)
10 print(‘y is :\n‘,y)
11 f1 = np.polyfit(x, y, 1)#用1次多项式拟合，若要多次拟合，相应的改变这个常数即可
12 print(‘f1 is :\n‘,f1)
13 
14 p1 = np.poly1d(f1)
15 print(‘p1 is :\n‘,p1)
16 
17 #也可使用yvals=np.polyval(f1, x)
18 yvals = p1(x)  #拟合y值
19 print(‘yvals is :\n‘,yvals)
20 #绘图
21 plot1 = plt.plot(x, y, ‘s‘,label=‘original values‘,color="blue")
22 plot2 = plt.plot(x, yvals, ‘r‘,label=‘polyfit values‘,color="red")
23 plt.xlabel(‘x‘)
24 plt.ylabel(‘y‘)
25 plt.legend(loc=4) #指定legend的位置右下角
26 plt.title(‘polyfitting‘)
27 plt.show()

 1 import numpy as np
 2 import matplotlib.pyplot as plt
 3 import math
 4 from scipy.optimize import curve_fit
 5 
 6 #自定义函数 
 7 def func(x, a, b):
 8     return a*np.sin(x)+b
 9 
10 #定义x、y散点坐标
11 x = np.arange(0.0, 10.0,0.1)
12 x = np.array(x)
13 num = np.sin(x)+np.random.randn(100)
14 y = np.array(num)
15 
16 #非线性最小二乘法拟合
17 popt, pcov = curve_fit(func, x, y)
18 #获取popt里面是拟合系数
19 print(popt)
20 a = popt[0]
21 b = popt[1]
22 #c = popt[2]
23 #d = popt[3]
24 #e = popt[4]
25 yvals = func(x,a,b) #拟合y值
26 print(‘popt:‘, popt)
27 print(‘系数a:‘, a)
28 print(‘系数b:‘, b)
29 #print(‘系数c:‘, c)
30 #print(‘系数d:‘, d)
31 #print(‘系数e:‘, e)
32 print(‘系数pcov:‘, pcov)#方差
33 print(‘系数yvals:‘, yvals)#x代入拟合出的函数得到的函数值
34 #绘图
35 plot1 = plt.plot(x, y, ‘s‘,label=‘original values‘,color="purple")
36 x_test = np.arange(0.0, 10.0, 0.01)
37 y_test = func(x_test,a,b)
38 plot2 = plt.plot(x_test, y_test, ‘r‘,label=‘polyfit values‘,color="red")
39 plt.xlabel(‘x‘)
40 plt.ylabel(‘y‘)
41 plt.legend(loc=4) #指定legend的位置右下角
42 plt.title(‘curve_fit‘)
43 plt.show()

 1 import numpy as np
 2 import matplotlib.pyplot as plt
 3 import math
 4 from scipy.optimize import curve_fit
 5 
 6 #自定义函数 
 7 def func(x, a, b, c, d):
 8     return a*np.sin(b*x+c)+d
 9 
10 #定义x、y散点坐标
11 x = np.arange(0.0, 10.0,0.1)
12 x = np.array(x)
13 num = np.sin(x)+np.random.randn(100)
14 y = np.array(num)
15 
16 #非线性最小二乘法拟合
17 popt, pcov = curve_fit(func, x, y)
18 #获取popt里面是拟合系数
19 print(popt)
20 a = popt[0]
21 b = popt[1]
22 c = popt[2]
23 d = popt[3]
24 yvals = func(x,a,b,c,d) #拟合y值
25 print(‘popt:‘, popt)
26 print(‘系数a:‘, a)
27 print(‘系数b:‘, b)
28 print(‘系数c:‘, c)
29 print(‘系数d:‘, d)
30 print(‘系数pcov:‘, pcov)#方差
31 print(‘系数yvals:‘, yvals)#x代入拟合出的函数得到的函数值
32 #绘图
33 plot1 = plt.plot(x, y, ‘s‘,label=‘original values‘,color=‘orange‘)
34 x_test = np.arange(0.0, 10.0, 0.01)
35 y_test = func(x_test,a,b,c,d)
36 plot2 = plt.plot(x_test, y_test, ‘r‘,label=‘polyfit values‘,color=‘brown‘)
37 plt.xlabel(‘x‘)
38 plt.ylabel(‘y‘)
39 plt.legend(loc=4) #指定legend的位置右下角
40 plt.title(‘curve_fit‘)
41 plt.show()

 1 import numpy as np
 2 import matplotlib.pyplot as plt
 3 import math
 4 from scipy.optimize import curve_fit
 5 
 6 #自定义函数 
 7 def func(x, a0,a1,a2,a3,a4,a5,a6,a7,a8,b1,b2,b3,b4,b5,b6,b7,b8,w):
 8     return  a0 + a1*np.cos(x*w) + b1*np.sin(x*w) +  9                a2*np.cos(2*x*w) + b2*np.sin(2*x*w) + a3*np.cos(3*x*w) + b3*np.sin(3*x*w) + 10                a4*np.cos(4*x*w) + b4*np.sin(4*x*w) + a5*np.cos(5*x*w) + b5*np.sin(5*x*w) + 11                a6*np.cos(6*x*w) + b6*np.sin(6*x*w) + a7*np.cos(7*x*w) + b7*np.sin(7*x*w) + 12                a8*np.cos(8*x*w) + b8*np.sin(8*x*w)
13 
14 #定义x、y散点坐标
15 x = np.arange(0.0, 10.0,0.1)
16 x = np.array(x)
17 num = np.sin(x)+np.random.randn(100)
18 y = np.array(num)
19 
20 #非线性最小二乘法拟合
21 popt, pcov = curve_fit(func, x, y)
22 #获取popt里面是拟合系数
23 print(popt)
24 a0 = popt[0]
25 a1 = popt[1]
26 a2 = popt[2]
27 a3 = popt[3]
28 a4 = popt[4]
29 a5 = popt[5]
30 a6 = popt[6]
31 a7 = popt[7]
32 a8 = popt[8]
33 b1 = popt[9]
34 b2 = popt[10]
35 b3 = popt[11]
36 b4 = popt[12]
37 b5 = popt[13]
38 b6 = popt[14]
39 b7 = popt[15]
40 b8 = popt[16]
41 w = popt[17]
42 yvals = func(x,a0,a1,a2,a3,a4,a5,a6,a7,a8,b1,b2,b3,b4,b5,b6,b7,b8,w) #拟合y值
43 print(‘popt:‘, popt)
44 print(‘系数a0:‘, a0)
45 print(‘系数a1:‘, a1)
46 print(‘系数a2:‘, a2)
47 print(‘系数a3:‘, a3)
48 print(‘系数a4:‘, a4)
49 print(‘系数a5:‘, a5)
50 print(‘系数a6:‘, a6)
51 print(‘系数a7:‘, a7)
52 print(‘系数a8:‘, a8)
53 print(‘系数b1:‘, b1)
54 print(‘系数b2:‘, b2)
55 print(‘系数b3:‘, b3)
56 print(‘系数b4:‘, b4)
57 print(‘系数b5:‘, b5)
58 print(‘系数b6:‘, b6)
59 print(‘系数b7:‘, b7)
60 print(‘系数b8:‘, b8)
61 print(‘系数w:‘, w)
62 print(‘系数pcov:‘, pcov)#方差
63 print(‘系数yvals:‘, yvals)#x代入拟合出的函数得到的函数值
64 #绘图
65 plot1 = plt.plot(x, y, ‘s‘,label=‘original values‘,color=‘yellow‘)
66 x_test = np.arange(0.0, 10.0, 0.01)
67 y_test = func(x_test,a0,a1,a2,a3,a4,a5,a6,a7,a8,b1,b2,b3,b4,b5,b6,b7,b8,w)
68 plot2 = plt.plot(x_test, y_test, ‘r‘,label=‘polyfit values‘,color=‘blue‘)
69 plt.xlabel(‘x‘)
70 plt.ylabel(‘y‘)
71 plt.legend(loc=4) #指定legend的位置右下角
72 plt.title(‘curve_fit‘)
73 plt.show()