我有一个2400 x 2400的数据数组，看起来像这样：
data = [[-2.302670298082603040e-01 -2.304885241061924717e-01 -2.305029774024092148e-01 -2.304807100897505734e-01 -2.303702531336284665e-01 -2.307144352067780346e-01...
[-2.302670298082603040e-01 -2.304885241061924717e-01 -2.305029774024092148e-01 -2.304807100897505734e-01 -2.303702531336284665e-01 -2.307144352067780346e-01...
...
并且我正在尝试拟合以下2D高斯函数：
def Gauss2D(x, mux, muy, sigmax, sigmay, amplitude, offset, rotation):
assert len(x) == 2
X = x[0]
Y = x[1]
A = (np.cos(rotation)**2)/(2*sigmax**2) + (np.sin(rotation)**2)/(2*sigmay**2)
B = (np.sin(rotation*2))/(4*sigmay**2) - (np.sin(2*rotation))/(4*sigmax**2)
C = (np.sin(rotation)**2)/(2*sigmax**2) + (np.cos(rotation)**2)/(2*sigmay**2)
G = amplitude*np.exp(-((A * (X - mux) ** 2) + (2 * B * (X - mux) * (Y - muy)) + (C * (Y - muy) ** 2))) + offset
return G
读取此数据。因此，我将自变量（坐标）的域定义如下：
vert = np.arange(2400, dtype=float)
horiz = np.arange(2400, dtype=float)
HORIZ, VERT = np.meshgrid(horiz, vert)
，并作为参数的初始估算值：
po = np.asarray([1200., 1200., 300., 300., 0.14, 0.22, 0.], dtype=float)
这样我可以进行以下调整：
popt, pcov = curve_fit(Gauss2D, (HORIZ, VERT), data, p0=po)
这将返回以下错误消息，而我却没有最清楚的线索：
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
ValueError: object too deep for desired array
---------------------------------------------------------------------------
error Traceback (most recent call last)
<ipython-input-11-ebba75332bfa> in <module>()
----> 1 curve_fit(Gauss2D, (HORIZ, VERT), data, p0=po)
/home/harrythegenius/anaconda3/lib/python3.6/site-packages/scipy/optimize/minpack.py in curve_fit(f, xdata, ydata, p0, sigma, absolute_sigma, check_finite, bounds, method, jac, **kwargs)
734 # Remove full_output from kwargs, otherwise we're passing it in twice.
735 return_full = kwargs.pop('full_output', False)
--> 736 res = leastsq(func, p0, Dfun=jac, full_output=1, **kwargs)
737 popt, pcov, infodict, errmsg, ier = res
738 cost = np.sum(infodict['fvec'] ** 2)
/home/harrythegenius/anaconda3/lib/python3.6/site-packages/scipy/optimize/minpack.py in leastsq(func, x0, args, Dfun, full_output, col_deriv, ftol, xtol, gtol, maxfev, epsfcn, factor, diag)
385 maxfev = 200*(n + 1)
386 retval = _minpack._lmdif(func, x0, args, full_output, ftol, xtol,
--> 387 gtol, maxfev, epsfcn, factor, diag)
388 else:
389 if col_deriv:
error: Result from function call is not a proper array of floats.
我不明白“对象对于所需数组而言太深”的消息。我还看到了针对此错误消息的多种在线解决方案，其中可以通过确保传递给curve_fit的所有数据类型均为浮点型或通过检查数组的尺寸是否正确来解决此问题。我一次又一次地尝试了这两种方法，但这没什么区别。那么，这是怎么了？
答案 0 :(得分：0)
根据评论，这是一个使用curve_fit（）的3D表面装配工，具有3D散点图，3D表面图和轮廓图。
import numpy, scipy, scipy.optimize
import matplotlib
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm # to colormap 3D surfaces from blue to red
import matplotlib.pyplot as plt
graphWidth = 800 # units are pixels
graphHeight = 600 # units are pixels
# 3D contour plot lines
numberOfContourLines = 16
def SurfacePlot(func, data, fittedParameters):
f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
matplotlib.pyplot.grid(True)
axes = Axes3D(f)
x_data = data[0]
y_data = data[1]
z_data = data[2]
xModel = numpy.linspace(min(x_data), max(x_data), 20)
yModel = numpy.linspace(min(y_data), max(y_data), 20)
X, Y = numpy.meshgrid(xModel, yModel)
Z = func(numpy.array([X, Y]), *fittedParameters)
axes.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.coolwarm, linewidth=1, antialiased=True)
axes.scatter(x_data, y_data, z_data) # show data along with plotted surface
axes.set_title('Surface Plot (click-drag with mouse)') # add a title for surface plot
axes.set_xlabel('X Data') # X axis data label
axes.set_ylabel('Y Data') # Y axis data label
axes.set_zlabel('Z Data') # Z axis data label
plt.show()
plt.close('all') # clean up after using pyplot or else thaere can be memory and process problems
def ContourPlot(func, data, fittedParameters):
f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
axes = f.add_subplot(111)
x_data = data[0]
y_data = data[1]
z_data = data[2]
xModel = numpy.linspace(min(x_data), max(x_data), 20)
yModel = numpy.linspace(min(y_data), max(y_data), 20)
X, Y = numpy.meshgrid(xModel, yModel)
Z = func(numpy.array([X, Y]), *fittedParameters)
axes.plot(x_data, y_data, 'o')
axes.set_title('Contour Plot') # add a title for contour plot
axes.set_xlabel('X Data') # X axis data label
axes.set_ylabel('Y Data') # Y axis data label
CS = matplotlib.pyplot.contour(X, Y, Z, numberOfContourLines, colors='k')
matplotlib.pyplot.clabel(CS, inline=1, fontsize=10) # labels for contours
plt.show()
plt.close('all') # clean up after using pyplot or else thaere can be memory and process problems
def ScatterPlot(data):
f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
matplotlib.pyplot.grid(True)
axes = Axes3D(f)
x_data = data[0]
y_data = data[1]
z_data = data[2]
axes.scatter(x_data, y_data, z_data)
axes.set_title('Scatter Plot (click-drag with mouse)')
axes.set_xlabel('X Data')
axes.set_ylabel('Y Data')
axes.set_zlabel('Z Data')
plt.show()
plt.close('all') # clean up after using pyplot or else thaere can be memory and process problems
def func(data, a, alpha, beta):
t = data[0]
p_p = data[1]
return a * (t**alpha) * (p_p**beta)
if __name__ == "__main__":
xData = numpy.array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0])
yData = numpy.array([11.0, 12.1, 13.0, 14.1, 15.0, 16.1, 17.0, 18.1, 90.0])
zData = numpy.array([1.1, 2.2, 3.3, 4.4, 5.5, 6.6, 7.7, 8.0, 9.9])
data = [xData, yData, zData]
initialParameters = [1.0, 1.0, 1.0] # these are the same as scipy default values in this example
# here a non-linear surface fit is made with scipy's curve_fit()
fittedParameters, pcov = scipy.optimize.curve_fit(func, [xData, yData], zData, p0 = initialParameters)
ScatterPlot(data)
SurfacePlot(func, data, fittedParameters)
ContourPlot(func, data, fittedParameters)
print('fitted prameters', fittedParameters)
modelPredictions = func(data, *fittedParameters)
absError = modelPredictions - zData
SE = numpy.square(absError) # squared errors
MSE = numpy.mean(SE) # mean squared errors
RMSE = numpy.sqrt(MSE) # Root Mean Squared Error, RMSE
Rsquared = 1.0 - (numpy.var(absError) / numpy.var(zData))
print('RMSE:', RMSE)
print('R-squared:', Rsquared)
答案 1 :(得分：0)
好的，我已经解决了这个问题。我怀疑这是一个维度问题。
应用于2D数组的curve_fit的适当尺寸如下：
因此，我保持参数数组不变，但是对该函数进行了以下更改：
def Gauss2D(x, mux, muy, sigmax, sigmay, amplitude, offset, rotation):
assert len(x) == 2
X = x[0]
Y = x[1]
A = (np.cos(rotation)**2)/(2*sigmax**2) + (np.sin(rotation)**2)/(2*sigmay**2)
B = (np.sin(rotation*2))/(4*sigmay**2) - (np.sin(2*rotation))/(4*sigmax**2)
C = (np.sin(rotation)**2)/(2*sigmax**2) + (np.cos(rotation)**2)/(2*sigmay**2)
G = amplitude*np.exp(-((A * (X - mux) ** 2) + (2 * B * (X - mux) * (Y - muy)) + (C * (Y - muy) ** 2))) + offset
return G.ravel()
我将以下内容传递给x数据参数：
x = np.vstack((HORIZ.ravel(), VERT.ravel()))
，然后输入y数据参数：
y = data.ravel()
因此，我使用以下方法对其进行了优化：
curve_fit(Gauss2D, x, y, po)
效果很好。