在数据框列上应用curve_fit(Apply curve_fit on dataframe columns)

 我有一个带有多列的pandas.DataFrame ，我想对每个列应用一个curve_fit函数。 我希望输出是一个数据框，其最佳值适合列中的数据（目前，我对它们的协方差不感兴趣）。 
 
 df具有以下结构： 
 
    a  b  c
0   0  0  0
1   0  0  0
2   0  0  0
3   0  0  0
4   0  0  0
5   0  0  0
6   1  0  1
7   1  1  1
8   1  1  1
9   1  1  1
10  1  1  1
11  1  1  1
12  1  1  1
13  1  1  1
14  2  1  2
15  6  2  6
16  7  2  7
17  8  2  8
18  9  2  9
19  7  2  7
 
 我已经定义了一个适合数据的函数，如下所示： 
 
def sigmoid(x, a, x0, k):
     y = a / (1 + np.exp(-k*(x-x0)))
     return y

def fitdata(dataseries):
    popt, pcov=curve_fit(sigmoid, dataseries.index, dataseries)
    return popt
 
 我可以应用该函数并获得一个数组作为回报： 
 
result_a=fitdata(df['a'])
In []: result_a
Out[]: array([  8.04197008,  14.48710063,   1.51668241])
 
 如果我尝试df.apply函数我得到以下错误： 
 
fittings=df.apply(fitdata)
ValueError: Shape of passed values is (3, 3), indices imply (3, 20)
 
 最终我希望输出看起来像： 
 
           a          b          c
0   8.041970   2.366496   8.041970
1  14.487101  12.006009  14.487101
2   1.516682   0.282359   1.516682
 
 这可以用类似的东西来完成吗？ 

I have a pandas.DataFrame with with multiple columns and I would like to apply a curve_fit function to each of them. I would like the output to be a dataframe with the optimal values fitting the data in the columns (for now, I am not interested in their covariance).
 
The df has the following structure:
 
    a  b  c
0   0  0  0
1   0  0  0
2   0  0  0
3   0  0  0
4   0  0  0
5   0  0  0
6   1  0  1
7   1  1  1
8   1  1  1
9   1  1  1
10  1  1  1
11  1  1  1
12  1  1  1
13  1  1  1
14  2  1  2
15  6  2  6
16  7  2  7
17  8  2  8
18  9  2  9
19  7  2  7
 
I have defined a function to fit to the data as so:
 
def sigmoid(x, a, x0, k):
     y = a / (1 + np.exp(-k*(x-x0)))
     return y

def fitdata(dataseries):
    popt, pcov=curve_fit(sigmoid, dataseries.index, dataseries)
    return popt
 
I can apply the function and get an array in return:
 
result_a=fitdata(df['a'])
In []: result_a
Out[]: array([  8.04197008,  14.48710063,   1.51668241])
 
If I try to df.apply the function I get the following error:
 
fittings=df.apply(fitdata)
ValueError: Shape of passed values is (3, 3), indices imply (3, 20)
 
Ultimately I would like the output to look like:
 
           a          b          c
0   8.041970   2.366496   8.041970
1  14.487101  12.006009  14.487101
2   1.516682   0.282359   1.516682
 
Can this be done with something similar to apply?