如何在使用 lmfit 进行最小化时修复 'The array returned by a function changed size between calls'？

Question

如何在使用 lmfit 进行最小化时修复错误 'The array returned by a function changed size between calls' 的代码？

请在下面找到我的代码：

import numpy as np
import pandas as pd
import lmfit as lf

#model needs to be fitted
x0 = 75
def func(params, x, Tsky):
    A = params['amp']
    w = params['width']
    t = params['thickness']
    v0 = params['mid_freq']
    b0 = params['b0']
    b1 = params['b1']
    b2 = params['b2']
    b3 = params['b3']
    b4 = params['b4']
    B = (4 * (x - v0)**2. / w**2.) * np.log(-1./t * np.log((1 + np.exp(-t))/2))
    T21 = -A * (1 - np.exp(-t * np.exp(B)))/(1 - np.exp(-t))
    model = T21 + b0 * ((x/x0)**(-2.5 + b1 + b2 * np.log(x/x0))) * np.exp(-b3*(x/x0)**-2.) + b4 *  (x/x0)**-2.
    return (Tsky-model)

#read the data
df = pd.read_csv('figure1_plotdata.csv')
data_list = df.T.values.tolist()
xdata = np.array(data_list[0])
Tsky = np.array(data_list[2])

#initial value of the parameters
params = lf.Parameters()
params.add('amp', value=0.2)
params.add('width', value=10)
params.add('thickness', value=5)
params.add('mid_freq', value=70)
params.add('b0', value=500)
params.add('b1', value=-0.5)
params.add('b2', value=-0.5)
params.add('b3', value=-0.5)
params.add('b4', value=500)

#minimize the function
out = lf.minimize(func, params, args=(xdata, Tsky), method='leastsq', kws=None, iter_cb=None, scale_covar=True, nan_policy='omit', calc_covar=True)

print(lf.fit_report(out))

错误信息如下：

File "/home/ankita/Dropbox/Python/Bowman_work/min.py", line 81, in <module>
    out = lf.minimize(func, params, args=(xdata, Tsky), method='leastsq', kws=None, iter_cb=None, scale_covar=True, nan_policy='omit', calc_covar=True)

  File "/home/ankita/anaconda3/lib/python3.7/site-packages/lmfit-0.9.13-py3.7.egg/lmfit/minimizer.py", line 2300, in minimize
    return fitter.minimize(method=method)

  File "/home/ankita/anaconda3/lib/python3.7/site-packages/lmfit-0.9.13-py3.7.egg/lmfit/minimizer.py", line 1949, in minimize
    return function(**kwargs)

  File "/home/ankita/anaconda3/lib/python3.7/site-packages/lmfit-0.9.13-py3.7.egg/lmfit/minimizer.py", line 1492, in leastsq
    lsout = scipy_leastsq(self.__residual, variables, **lskws)

  File "/home/ankita/anaconda3/lib/python3.7/site-packages/scipy/optimize/minpack.py", line 394, in leastsq
    gtol, maxfev, epsfcn, factor, diag)

**ValueError: The array returned by a function changed size between calls**

Answer 1

如果你用过

out = lf.minimize(func, params,...,nan_policy='raise')

您会看到出现异常，告诉您存在 NaN。当您使用 nan_policy='omit' 时，您的模型生成的任何此类 NaN 都会从残差数组中移除，因此数组的大小会在两次调用之间发生变化。拟合不能处理 NaN 或数组大小的变化——你必须消除它们。

特别是 np.log(x) 在 x<0 时是 NaN。您的 np.log() 有一个复杂的参数，该参数取决于参数 t 的值。如果对于 t 的某个值，该参数低于 0，则该模型具有 NaN 并且没有意义。您必须确保此参数不能低于 0。可能是使用

params.add('thickness', value=5, min=0)

足够了。但是您应该更详细地检查您的模型并确定它是否有意义。

我觉得你的模型很复杂。我猜不出这样的模型是从哪里来的。采用多个 np.exp() 和 np.log() 有点要求数值不稳定性。所以，我不知道简单地强制 t 为正是否会很合适，但它可能会为您指明正确的方向。

如何在使用 lmfit 进行最小化时修复 'The array returned by a function changed size between calls'？

How to fix 'The array returned by a function changed size between calls' while using lmfit for minimization?

python

minimization

anaconda

lmfit