Pandastic way of growing a dataframe - numpy

Question

So, I have a year-indexed dataframe that I would like to increment by some logic beyond the end year (2013), say, grow the last value by n percent for 10 years, but the logic could also be to just add a constant, or slightly growing number. I will leave that to a function and just stuff the logic there.
I can't think of a neat vectorized way to do that with arbitrary length of time and logic, leaving a longer dataframe with the extra increments added, and would prefer not to loop it.

Answer 1

The particular calculation matters. In general you would have to compute the values in a loop. Some NumPy ufuncs (such as np.add, np.multiply, np.minimum, np.maximum) have an accumulate method, however, which may be useful depending on the calculation.
For example, to calculate values given a constant growth rate, you could use np.multiply.accumulate (or cumprod):
import numpy as np
import pandas as pd
N = 10
index = pd.date_range(end='2013-12-31', periods=N, freq='D')
df = pd.DataFrame({'val':np.arange(N)}, index=index)
last = df['val'][-1]
# val
# 2013-12-22 0
# 2013-12-23 1
# 2013-12-24 2
# 2013-12-25 3
# 2013-12-26 4
# 2013-12-27 5
# 2013-12-28 6
# 2013-12-29 7
# 2013-12-30 8
# 2013-12-31 9
# expand df
index = pd.date_range(start='2014-1-1', periods=N, freq='D')
df = df.reindex(df.index.union(index))
# compute new values
rate = 1.1
df['val'][-N:] = last*np.multiply.accumulate(np.full(N, fill_value=rate))
yields
val
2013-12-22 0.000000
2013-12-23 1.000000
2013-12-24 2.000000
2013-12-25 3.000000
2013-12-26 4.000000
2013-12-27 5.000000
2013-12-28 6.000000
2013-12-29 7.000000
2013-12-30 8.000000
2013-12-31 9.000000
2014-01-01 9.900000
2014-01-02 10.890000
2014-01-03 11.979000
2014-01-04 13.176900
2014-01-05 14.494590
2014-01-06 15.944049
2014-01-07 17.538454
2014-01-08 19.292299
2014-01-09 21.221529
2014-01-10 23.343682
To increment by a constant value you could simply use np.arange:
step=2
df['val'][-N:] = np.arange(last+step, last+(N+1)*step, step)
or cumsum:
step=2
df['val'][-N:] = last + np.full(N, fill_value=step).cumsum()
Some linear recurrence relations can be expressed using scipy.signal.lfilter. See for example,
Trying to vectorize iterative calculation with numpy and Recursive definitions in Pandas