将自定义 function 应用于 pandas dataframe 依赖于可变数量的先前行

Question

I want an efficient solution to add a column to my table which calculates the sum of the absolute differences between this row's value and the values in the last N rows. eg

number	new_col_2	new_col_3	new_col_4
10	-	-	-
11	-	-	-
12	3	-	-
9	5	6	-
8	5	8	10
12	7	7	8

new_col_2 => refers to calculating this for the last 2 rows. 
(12-10) + (12-11) => 3
(11-9) + (12-9) => 5

new_col_3 => refers to calculate this for the last 3 rows
(10-9) + (11-9) + (12-9) => 6
(11-8) + (12-8) + (9-8) => 8 

and so on.

If N was a fixed number, I understand I could do this easily using:

df[new_col_N] = abs(df[number]-df[number].shift(N)) + abs(df[number]-df[number].shift(N-1)) + etc

But this assumes a fixed N. I want to write a function where I can add this column with N as an integer variable that can change.

Any idea what the most efficient way to do this is?

Edit: Answer accepted below leads to the following solution for me:

df[new_col_name] = df['number'].rolling(window=period+1).apply(lambda x: np.sum(np.abs(x[:-1]-x[-1])))

Answer 1

We can do numpy broad cast

n = 2 
a = df.number.values
df.loc[n:,'new'] = np.sum(np.abs(np.tril(np.triu(a-a[:,None],k=-n))),1)[n:]
df
Out[188]: 
   number new_col_2 new_col_3 new_col_4   new1
0      10         -         -         -    NaN
1      11         -         -         -    NaN
2      12         3         -         -    3.0
3       9         5         6         -    5.0
4       8         5         8        10    5.0
5      12         7         7         8    7.0