numbaFor recursive calculations which are not vectorisable, numba, which uses JIT-compilation and works with lower level objects, often yields large performance improvements. You need only define a regular for loop and use the decorator @njit or (for older versions) @jit(nopython=True):
For a reasonable size dataframe, this gives a ~30x performance improvement versus a regular for loop:
from numba import jit
@jit(nopython=True)
def calculator_nb(a, b, d):
res = np.empty(d.shape)
res[0] = d[0]
for i in range(1, res.shape[0]):
res[i] = res[i-1] * a[i] + b[i]
return res
df['C'] = calculator_nb(*df[list('ABD')].values.T)
n = 10**5
df = pd.concat([df]*n, ignore_index=True)
# benchmarking on Python 3.6.0, Pandas 0.19.2, NumPy 1.11.3, Numba 0.30.1
# calculator() is same as calculator_nb() but without @jit decorator
%timeit calculator_nb(*df[list('ABD')].values.T) # 14.1 ms per loop
%timeit calculator(*df[list('ABD')].values.T) # 444 ms per loop