TypeError: Improper input: N=5 must not exceed M=2

Question

我正在尝试将 scipy.optimize.curve_fit 与自定义拟合函数一起使用（大致遵循 this 教程）：

# 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)

由于某些原因，Jupyter Notebook 不断抛出此错误，我无法定位代码中的问题：

---------------------------------------------------------------------------
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

我不明白 N 和 M 指的是什么，但我在某处读到当数据点少于参数（未确定的系统）时会抛出此错误 - 这是不是这里的情况，因为每个图像文件大约有 15 x 15 = 225 个数据点。可能是什么问题造成的？

Answer 1

可能您需要将功能更改为

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)

因为只有第一个变量被视为独立的。

当前您在 x 变量内发送一个数组，该数组是从两个一维数组 np.vstack 编辑的，因此 M=2：您有两个数据点。在函数中，所有其他参数都被视为要优化的参数（包括 y！），因此 N=5.

TypeError: Improper input: N=5 must not exceed M=2

TypeError: Improper input: N=5 must not exceed M=2

arrays

curve-fitting

shapes

scipy

scipy-optimize