Pandas: building a column with self-referencing past values

Question

I need to generate a column that starts with an initial value, and then is generated by a function that includes past values of that column. For example

df = pd.DataFrame({'a': [1,1,5,2,7,8,16,16,16]})
df['b'] = 0
df.ix[0, 'b'] = 1
df

    a  b
0   1  1
1   1  0
2   5  0
3   2  0
4   7  0
5   8  0
6  16  0
7  16  0
8  16  0

Now, I want to generate the rest of the column 'b' by taking the minimum of the previous row and adding two. One solution would be

for i in range(1, len(df)):
    df.ix[i, 'b'] = df.ix[i-1, :].min() + 2

Resulting in the desired output

    a   b
0   1   1
1   1   3
2   5   3
3   2   5
4   7   4
5   8   6
6  16   8
7  16  10
8  16  12

Does pandas have a 'clean' way to do this? Preferably one that would vectorize the computation?

Answer 1

pandas doesn't have a great way to handle general recursive calculations. There may be some trick to vectorize it, but if you can take the dependency, this is relatively painless and very fast with numba.

@numba.njit
def make_b(a):
    b = np.zeros_like(a)
    b[0] = 1
    for i in range(1, len(a)):
        b[i] = min(b[i-1], a[i-1]) + 2

    return b

df['b'] = make_b(df['a'].values)

df
Out[73]: 
    a   b
0   1   1
1   1   3
2   5   3
3   2   5
4   7   4
5   8   6
6  16   8
7  16  10
8  16  12