ValueError: object too deep for desired array

强人锁男

我打算将二维高斯函数拟合到显示激光束的图像上，以得到其参数如FWHM和位置。到目前为止，我试图理解如何在Python中定义一个二维高斯函数，以及如何将x和y变量传递给它。
我编写了一个小脚本，它定义了这个函数，绘制了它，给它添加了一些噪声，然后尝试使用curve_fit来匹配它。一切似乎都在工作，除了最后一个步骤，我试图使我的模型函数适应嘈杂的数据。这是我的代码:

1. import scipy.optimize as opt
   
2. import numpy as np
   
3. import pylab as plt
   
4. 
   
5. 
   
6. #define model function and pass independant variables x and y as a list
   
7. def twoD_Gaussian((x,y), amplitude, xo, yo, sigma_x, sigma_y, theta, offset):
   
8.     xo = float(xo)
   
9.     yo = float(yo)   
   
10.     a = (np.cos(theta)**2)/(2*sigma_x**2) + (np.sin(theta)**2)/(2*sigma_y**2)
    
11.     b = -(np.sin(2*theta))/(4*sigma_x**2) + (np.sin(2*theta))/(4*sigma_y**2)
    
12.     c = (np.sin(theta)**2)/(2*sigma_x**2) + (np.cos(theta)**2)/(2*sigma_y**2)
    
13.     return offset + amplitude*np.exp( - (a*((x-xo)**2) + 2*b*(x-xo)*(y-yo) + c*((y-yo)**2)))
    
14. 
    
15. # Create x and y indices
    
16. x = np.linspace(0, 200, 201)
    
17. y = np.linspace(0, 200, 201)
    
18. x,y = np.meshgrid(x, y)
    
19. 
    
20. #create data
    
21. data = twoD_Gaussian((x, y), 3, 100, 100, 20, 40, 0, 10)
    
22. 
    
23. # plot twoD_Gaussian data generated above
    
24. plt.figure()
    
25. plt.imshow(data)
    
26. plt.colorbar()
    
27. 
    
28. # add some noise to the data and try to fit the data generated beforehand
    
29. initial_guess = (3,100,100,20,40,0,10)
    
30. 
    
31. data_noisy = data + 0.2*np.random.normal(size=len(x))
    
32. 
    
33. popt, pcov = opt.curve_fit(twoD_Gaussian, (x,y), data_noisy, p0 = initial_guess)
    

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得到一个错误
ValueError: object too deep for desired array
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "C:\Python\WinPython-64bit-2.7.6.2\python-2.7.6.amd64\lib\site-packages\spyderlib\widgets\externalshell\sitecustomize.py", line 540, in runfile
    execfile(filename, namespace)
  File "E:/Work Computer/Software/Python/Fitting scripts/2D Gaussian function fit/2D_Gaussian_LevMarq_v2.py", line 39, in <module>
    popt, pcov = opt.curve_fit(twoD_Gaussian, (x,y), data_noisy, p0 = initial_guess)
  File "C:\Python\WinPython-64bit-2.7.6.2\python-2.7.6.amd64\lib\site-packages\scipy\optimize\minpack.py", line 533, in curve_fit
    res = leastsq(func, p0, args=args, full_output=1, **kw)
  File "C:\Python\WinPython-64bit-2.7.6.2\python-2.7.6.amd64\lib\site-packages\scipy\optimize\minpack.py", line 378, in leastsq
    gtol, maxfev, epsfcn, factor, diag)
minpack.error: Result from function call is not a proper array of floats.

蛋蛋超人

twoD_Gaussian输出为1D。您可以做的是在最后一行的末尾添加.ravel()，如下所示:

1. def twoD_Gaussian((x, y), amplitude, xo, yo, sigma_x, sigma_y, theta, offset):
   
2.     xo = float(xo)
   
3.     yo = float(yo)   
   
4.     a = (np.cos(theta)**2)/(2*sigma_x**2) + (np.sin(theta)**2)/(2*sigma_y**2)
   
5.     b = -(np.sin(2*theta))/(4*sigma_x**2) + (np.sin(2*theta))/(4*sigma_y**2)
   
6.     c = (np.sin(theta)**2)/(2*sigma_x**2) + (np.cos(theta)**2)/(2*sigma_y**2)
   
7.     g = offset + amplitude*np.exp( - (a*((x-xo)**2) + 2*b*(x-xo)*(y-yo)
   
8.                             + c*((y-yo)**2)))
   
9.     return g.ravel()
   

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需要重新构造用于绘图的输出，例如:

1. # Create x and y indices
   
2. x = np.linspace(0, 200, 201)
   
3. y = np.linspace(0, 200, 201)
   
4. x, y = np.meshgrid(x, y)
   
5. 
   
6. #create data
   
7. data = twoD_Gaussian((x, y), 3, 100, 100, 20, 40, 0, 10)
   
8. 
   
9. # plot twoD_Gaussian data generated above
   
10. plt.figure()
    
11. plt.imshow(data.reshape(201, 201))
    
12. plt.colorbar()
    
13. Do the fitting as before:
    
14. # add some noise to the data and try to fit the data generated beforehand
    
15. initial_guess = (3,100,100,20,40,0,10)
    
16. 
    
17. data_noisy = data + 0.2*np.random.normal(size=data.shape)
    
18. 
    
19. popt, pcov = opt.curve_fit(twoD_Gaussian, (x, y), data_noisy, p0=initial_guess)
    
20. And plot the results:
    
21. data_fitted = twoD_Gaussian((x, y), *popt)
    
22. 
    
23. fig, ax = plt.subplots(1, 1)
    
24. ax.hold(True)
    
25. ax.imshow(data_noisy.reshape(201, 201), cmap=plt.cm.jet, origin='bottom',
    
26.     extent=(x.min(), x.max(), y.min(), y.max()))
    
27. ax.contour(x, y, data_fitted.reshape(201, 201), 8, colors='w')
    
28. plt.show()
    

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马猴烧酒

1. def twoD_Gaussian(xdata_tuple, amplitude, xo, yo, sigma_x, sigma_y, theta, offset):
   
2.     (x, y) = xdata_tuple                                                        
   
3.     xo = float(xo)                                                              
   
4.     yo = float(yo)                                                              
   
5.     a = (np.cos(theta)**2)/(2*sigma_x**2) + (np.sin(theta)**2)/(2*sigma_y**2)   
   
6.     b = -(np.sin(2*theta))/(4*sigma_x**2) + (np.sin(2*theta))/(4*sigma_y**2)   
   
7.     c = (np.sin(theta)**2)/(2*sigma_x**2) + (np.cos(theta)**2)/(2*sigma_y**2)   
   
8.     g = offset + amplitude*np.exp( - (a*((x-xo)**2) + 2*b*(x-xo)*(y-yo)         
   
9.                         + c*((y-yo)**2)))                                   
   
10.     return g.ravel()
    

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德国骨科

curve_fit()希望xdata的维度为(2,n*m)而不是(2,n,m)。ydata应该分别有形状(n*m)而不是(n,m)。因此，可以使用ravel()将2D数组压平:

1. xdata = np.vstack((xx.ravel(),yy.ravel()))
   
2. ydata = data_noisy.ravel()
   
3. popt, pcov = opt.curve_fit(twoD_Gaussian, xdata, ydata, p0=initial_guess)
   

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