how to create a sliding window and apply functions in pandas dataframes

Question

I have the following dataframe :

Time      A

1         1
2         1
3         1
4         1
5         2
6         2
7         3
8         3
9         2
10        1
11        1
12        1
13        3
14        3
15        3

need to create a sliding window with length of 3 which slides 2 steps over time column and apply some costume function to column A ( for the sake of this examplelet's say mean and max)

the r equivalent for it would be

 dat %>% dplyr::mutate(SMA_A=rollapplyr(A, 3, mean ,by = 2,align ="center", partial=TRUE, fill=NA),
                  Max_A =rollapplyr(A, 3, max ,by=2, align ="center", partial=TRUE,fill=NA)
                 ) 

expected output :

    Time  A     SMA_A    Max_A
      1   1    1.000000     1
      2   1       NA        NA
      3   1 1.000000        1
      4   1       NA        NA
      5   2 1.666667        2
      6   2       NA        NA
      7   3 2.666667         3
      8   3       NA        NA
      9   2 2.000000        3
      10  1       NA        NA
      11  1 1.000000        1
      12  1       NA        NA
      13  3 2.333333        3
      14  3       NA        NA
      15  3 3.000000        3

or without NAs

Answer 1

You can do the following:

1. Calculate rolling mean and max with DataFrame.rolling
2. Assign them as new columns
3. Get every 2nd index row by checking if the remainder == 1 which means it's an uneven number
4. For every index in step3, assign NaN with .loc

df['A'] = df.rolling(3, center=True)['A'].mean().bfill().ffill()
df['Max_A'] = df.rolling(3, center=True)['A'].max().bfill().ffill()

mask_idx = df.index%2 == 1

df.loc[mask_idx, ['A', 'Max_A']] = np.NaN

output

    Time         A  Max_A
0      1  1.000000    1.0
1      2       NaN    NaN
2      3  1.000000    1.0
3      4       NaN    NaN
4      5  1.666667    2.0
5      6       NaN    NaN
6      7  2.666667    3.0
7      8       NaN    NaN
8      9  2.000000    3.0
9     10       NaN    NaN
10    11  1.000000    1.0
11    12       NaN    NaN
12    13  2.333333    3.0
13    14       NaN    NaN
14    15  3.000000    3.0