问题
I'm trying to use scipy.optimize.curve_fit with a custom fit function (roughly following this tutorial):
# Fit function
def fit_function(x, y, x0, y0, A, FWHM):
return A*np.exp(1)*4*np.log(2)*((x+x0)**2 + (y+y0)**2)/FWHM**2*np.exp(-4*np.log(2)*((x+x0)**2 + (y+y0)**2)/FWHM**2)
# Open image file
img = Image.open('/home/user/image.tif')
# xdata
X, Y = img.size
xRange = np.arange(1, X+1)
yRange = np.arange(1, Y+1)
xGrid, yGrid = np.meshgrid(xRange, yRange)
xyGrid = np.vstack((xGrid.ravel(), yGrid.ravel()))
# ydata
imgArray = np.array(img)
imgArrayFlat = imgArray.ravel()
# Fitting
params_opt, params_cov = curve_fit(fit_function, xyGrid, imgArrayFlat)
For some reason, Jupyter Notebook keeps throwing this error and I can't locate the problem in the code:
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-61-eaa3ebdb6469> in <module>()
17 imgArrayFlat = imgArray.ravel() # Flatten 2D pixel data into 1D array for scipy.optimize.curve_fit
18
---> 19 params_opt, params_cov = curve_fit(doughnut, xyGrid, imgArrayFlat)
/usr/lib/python3/dist-packages/scipy/optimize/minpack.py in curve_fit(f, xdata, ydata, p0, sigma, absolute_sigma, check_finite, bounds, method, jac, **kwargs)
749 # Remove full_output from kwargs, otherwise we're passing it in twice.
750 return_full = kwargs.pop('full_output', False)
--> 751 res = leastsq(func, p0, Dfun=jac, full_output=1, **kwargs)
752 popt, pcov, infodict, errmsg, ier = res
753 cost = np.sum(infodict['fvec'] ** 2)
/usr/lib/python3/dist-packages/scipy/optimize/minpack.py in leastsq(func, x0, args, Dfun, full_output, col_deriv, ftol, xtol, gtol, maxfev, epsfcn, factor, diag)
384 m = shape[0]
385 if n > m:
--> 386 raise TypeError('Improper input: N=%s must not exceed M=%s' % (n, m))
387 if epsfcn is None:
388 epsfcn = finfo(dtype).eps
TypeError: Improper input: N=5 must not exceed M=2
I don't understand what N and M refer to, but I've read somewhere that this error gets thrown when there are fewer datapoints than parameters (underdetermined system) - which is not the case here as the image files have about 15 x 15 = 225 datapoints each. What might be causing the trouble?
回答1:
Probably you need to change the function to
def fit_function(X, x0, y0, A, FWHM):
x, y = X
return A*np.exp(1)*4*np.log(2)*((x+x0)**2 + (y+y0)**2)/FWHM**2*np.exp(-4*np.log(2)*((x+x0)**2 + (y+y0)**2)/FWHM**2)
because only the first variable is treated as independent.
Currently you send an array inside x variable which is np.vstack-ed from two 1D arrays, hence the M=2: you have two datapoints. In the function all other arguments are treated as parameters to optimize (including y!), hence the N=5.
来源：https://stackoverflow.com/questions/63432150/typeerror-improper-input-n-5-must-not-exceed-m-2