Python: how to get element-wise standard deviation of multiple arrays in a dataframe

Question

I have a rather big dataframe (df) containing arrays and NaN in each cell, the first 3 rows look like this:

df:
                 A                B                C
X  [4, 8, 1, 1, 9]              NaN  [8, 2, 8, 4, 9]
Y  [4, 3, 4, 1, 5]  [1, 2, 6, 2, 7]  [7, 1, 1, 7, 8]
Z              NaN  [9, 3, 8, 7, 7]  [2, 6, 3, 1, 9]

I already know (thanks to piRSquared) how to take the element-wise mean over rows for each column so that I get this:

element_wise_mean:
A                        [4.0, 5.5, 2.5, 1.0, 7.0]
B                        [5.0, 2.5, 7.0, 4.5, 7.0]
C    [5.66666666667, 3.0, 4.0, 4.0, 8.66666666667]

Now I wonder how to get the respective standard deviation, any idea? Also, I don't understand yet what groupby() is doing, could someone explain its function in more detail?

---

df

np.random.seed([3,14159])
df = pd.DataFrame(
    np.random.randint(10, size=(3, 3, 5)).tolist(),
    list('XYZ'), list('ABC')
).applymap(np.array)

df.loc['X', 'B'] = np.nan
df.loc['Z', 'A'] = np.nan

element_wise_mean

df2               = df.stack().groupby(level=1)
element_wise_mean = df2.apply(np.mean, axis=0)

element_wise_sd

element_wise_sd   = df2.apply(np.std, axis=0)
TypeError: setting an array element with a sequence.

Answer 1

Applying np.std using lambda with converting to numpy array is working for me :

element_wise_std = df2.apply(lambda x: np.std(np.array(x), 0))
#axis=0 is by default, so can be omit
#element_wise_std = df2.apply(lambda x: np.std(np.array(x)))
print (element_wise_std)
A                            [0.0, 2.5, 1.5, 0.0, 2.0]
B                            [4.0, 0.5, 1.0, 2.5, 0.0]
C    [2.62466929134, 2.16024689947, 2.94392028878, ...
dtype: object

Or solution from comment:

element_wise_std = df2.apply(lambda x: np.std(x.values, 0))
print (element_wise_std)
A                            [0.0, 2.5, 1.5, 0.0, 2.0]
B                            [4.0, 0.5, 1.0, 2.5, 0.0]
C    [2.62466929134, 2.16024689947, 2.94392028878, ...
dtype: object

I try explain more:

First reshape by stack - columns are added to index and Multiindex is created.

print (df.stack())
X  A    [4, 8, 1, 1, 9]
   C    [8, 2, 8, 4, 9]
Y  A    [4, 3, 4, 1, 5]
   B    [1, 2, 6, 2, 7]
   C    [7, 1, 1, 7, 8]
Z  B    [9, 3, 8, 7, 7]
   C    [2, 6, 3, 1, 9]
dtype: object

Then groupby(level=1) means group by first level of Multiindex - (by values A, B, C) and apply some function. Here it is np.std.

Pandas not working with arrays or lists very nice, so converting is necessary. (It looks like bug)

Answer 2

Jezrael beat me to this:

To answer your question about .groupby(), try .apply(print). You'll see what is returned, and made to be used in apply functions:

df2 = df.stack().groupby(axis=1) #groups by the second index of df.stack()
df2.apply(print)
X  A    [4, 8, 1, 1, 9]
Y  A    [4, 3, 4, 1, 5]
Name: A, dtype: object
Y  B    [1, 2, 6, 2, 7]
Z  B    [9, 3, 8, 7, 7]
Name: B, dtype: object
X  C    [8, 2, 8, 4, 9]
Y  C    [7, 1, 1, 7, 8]
Z  C    [2, 6, 3, 1, 9]
Name: C, dtype: object

Conversely, try:

df3 = df.stack().groupby(level=0) #this will group by the first index of df.stack()
df3.apply(print)
X  A    [4, 8, 1, 1, 9]
   C    [8, 2, 8, 4, 9]
Name: X, dtype: object
Y  A    [4, 3, 4, 1, 5]
   B    [1, 2, 6, 2, 7]
   C    [7, 1, 1, 7, 8]
Name: Y, dtype: object
Z  B    [9, 3, 8, 7, 7]
   C    [2, 6, 3, 1, 9]
Name: Z, dtype: object