使用scipy.optimize.curve_fit拟合2D高斯函数-ValueError和minpack.error [英] Fitting a 2D Gaussian function using scipy.optimize.curve_fit - ValueError and minpack.error
问题描述
我打算将2D高斯函数拟合到显示激光束的图像上,以获取其参数,例如FWHM
和位置.到目前为止,我试图了解如何在Python中定义2D高斯函数以及如何将x和y变量传递给它.
I intend to fit a 2D Gaussian function to images showing a laser beam to get its parameters like FWHM
and position. So far I tried to understand how to define a 2D Gaussian function in Python and how to pass x and y variables to it.
我编写了一个小脚本,该脚本定义了该函数,对其进行了绘制,给它添加了一些噪点,然后尝试使用curve_fit
使其适合它.除了最后一步,我尝试将模型函数拟合到嘈杂的数据之外,其他所有内容似乎都正常工作.这是我的代码:
I've written a little script which defines that function, plots it, adds some noise to it and then tries to fit it using curve_fit
. Everything seems to work except the last step in which I try to fit my model function to the noisy data. Here is my code:
import scipy.optimize as opt
import numpy as np
import pylab as plt
#define model function and pass independant variables x and y as a list
def twoD_Gaussian((x,y), amplitude, xo, yo, sigma_x, sigma_y, theta, offset):
xo = float(xo)
yo = float(yo)
a = (np.cos(theta)**2)/(2*sigma_x**2) + (np.sin(theta)**2)/(2*sigma_y**2)
b = -(np.sin(2*theta))/(4*sigma_x**2) + (np.sin(2*theta))/(4*sigma_y**2)
c = (np.sin(theta)**2)/(2*sigma_x**2) + (np.cos(theta)**2)/(2*sigma_y**2)
return offset + amplitude*np.exp( - (a*((x-xo)**2) + 2*b*(x-xo)*(y-yo) + c*((y-yo)**2)))
# Create x and y indices
x = np.linspace(0, 200, 201)
y = np.linspace(0, 200, 201)
x,y = np.meshgrid(x, y)
#create data
data = twoD_Gaussian((x, y), 3, 100, 100, 20, 40, 0, 10)
# plot twoD_Gaussian data generated above
plt.figure()
plt.imshow(data)
plt.colorbar()
# add some noise to the data and try to fit the data generated beforehand
initial_guess = (3,100,100,20,40,0,10)
data_noisy = data + 0.2*np.random.normal(size=len(x))
popt, pcov = opt.curve_fit(twoD_Gaussian, (x,y), data_noisy, p0 = initial_guess)
这是使用winpython 64-bit
Python 2.7
运行脚本时收到的错误消息:
Here is the error message I get when running the script using winpython 64-bit
Python 2.7
:
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.
我做错了什么?我是如何将自变量传递给模型function/curve_fit
的?
What is it that am I doing wrong? Is it how I pass the independent variables to the model function/curve_fit
?
推荐答案
twoD_Gaussian
的输出必须为一维.您可以做的是在最后一行的末尾添加.ravel()
,如下所示:
The output of twoD_Gaussian
needs to be 1D. What you can do is add a .ravel()
onto the end of the last line, like this:
def twoD_Gaussian((x, y), amplitude, xo, yo, sigma_x, sigma_y, theta, offset):
xo = float(xo)
yo = float(yo)
a = (np.cos(theta)**2)/(2*sigma_x**2) + (np.sin(theta)**2)/(2*sigma_y**2)
b = -(np.sin(2*theta))/(4*sigma_x**2) + (np.sin(2*theta))/(4*sigma_y**2)
c = (np.sin(theta)**2)/(2*sigma_x**2) + (np.cos(theta)**2)/(2*sigma_y**2)
g = offset + amplitude*np.exp( - (a*((x-xo)**2) + 2*b*(x-xo)*(y-yo)
+ c*((y-yo)**2)))
return g.ravel()
显然,您需要重塑输出以进行打印,例如:
You'll obviously need to reshape the output for plotting, e.g:
# Create x and y indices
x = np.linspace(0, 200, 201)
y = np.linspace(0, 200, 201)
x, y = np.meshgrid(x, y)
#create data
data = twoD_Gaussian((x, y), 3, 100, 100, 20, 40, 0, 10)
# plot twoD_Gaussian data generated above
plt.figure()
plt.imshow(data.reshape(201, 201))
plt.colorbar()
像以前一样进行拟合:
# add some noise to the data and try to fit the data generated beforehand
initial_guess = (3,100,100,20,40,0,10)
data_noisy = data + 0.2*np.random.normal(size=data.shape)
popt, pcov = opt.curve_fit(twoD_Gaussian, (x, y), data_noisy, p0=initial_guess)
并绘制结果:
data_fitted = twoD_Gaussian((x, y), *popt)
fig, ax = plt.subplots(1, 1)
ax.hold(True)
ax.imshow(data_noisy.reshape(201, 201), cmap=plt.cm.jet, origin='bottom',
extent=(x.min(), x.max(), y.min(), y.max()))
ax.contour(x, y, data_fitted.reshape(201, 201), 8, colors='w')
plt.show()
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