用scipy.optimize.curve_fit - ValueError和minpack.error拟合二维高斯函数
用scipy.optimize.curve_fit - ValueError和minpack.error拟合二维高斯函数
提问于 2014-02-05 08:28:21
我打算将2D高斯函数拟合到显示激光束的图像中，以获得其参数，如FWHM和位置。到目前为止，我试图理解如何在Python中定义2D高斯函数，以及如何将x和y变量传递给它。
我已经编写了一个小脚本来定义该函数，绘制它，给它添加一些噪声，然后尝试使用curve_fit对其进行拟合。除了最后一步，我尝试将我的模型函数与嘈杂的数据相匹配，其他一切似乎都正常。下面是我的代码：
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)以下是使用winpython 64-bit Python 2.7运行脚本时收到的错误消息
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.我到底做错了什么？它是如何将自变量传递给模型function/curve_fit的
回答 3
Stack Overflow用户
回答已采纳
发布于 2014-02-05 09:14:19
twoD_Gaussian的输出需要为1D。您可以做的是在最后一行的末尾添加一个.ravel()，如下所示：
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，您需要重塑用于绘图的输出，例如：
# 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()像以前一样执行管件：
# 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()
Stack Overflow用户
发布于 2014-11-11 19:52:09
为了扩展Dietrich的答案，我在使用Python 3.4 (在Ubuntu 14.04上)运行建议的解决方案时得到了以下错误：
def twoD_Gaussian((x, y), amplitude, xo, yo, sigma_x, sigma_y, theta, offset):
^
SyntaxError: invalid syntax运行2to3建议了以下简单的修复方法：
def twoD_Gaussian(xdata_tuple, amplitude, xo, yo, sigma_x, sigma_y, theta, offset):
(x, y) = xdata_tuple
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()这是因为从Python3开始，将元组作为参数传递给函数时自动解包已被删除。有关详细信息，请参阅此处：PEP 3113
Stack Overflow用户
发布于 2014-02-05 09:09:05
curve_fit()希望xdata的维度为(2,n*m)，而不是(2,n,m)。ydata应分别具有shape (n*m)而不是(n,m)。所以你可以使用ravel()来展平你的2D数组：
xdata = np.vstack((xx.ravel(),yy.ravel()))
ydata = data_noisy.ravel()
popt, pcov = opt.curve_fit(twoD_Gaussian, xdata, ydata, p0=initial_guess)顺便说一句:我不确定带三角项的参数化是不是最好的。例如，在数值方面和大偏差下，采用所描述的here可能会更健壮一些。
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原文链接：
https://stackoverflow.com/questions/21566379
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