Running sum of complicated functions using pandas data frame values - pandas

Question

In this simplified example I have three lists of the same length, list a, list b, and list c. I want to find the following running summations
from math import exp
a = [1.3, 4.5, 7.8, 9.2, 4.1]
b = [2.1, 1.1, 1.0, 1.0, -2.0]
c = [3.1, 4.0, 5.0, 6.0, 7.0]
# This simple, but SLOW method
sum1 = 0.0
for i in range(0, 3):
sum1 += a[i] ** b[i] + 3.1 * c[i]
sum2 = 0.0
for i in range(2,4):
sum2 += (b[i] / a[i]) * exp(-c[i])
total = sum1 + sum2
print(total) # yields 52.27644
The above code works just fine; however, for examples with MUCH larger lists it runs very slow. If I were to combine the lists in a pandas data frame, is there some built-in and vectorized capability to conduct this same running summations with the data frame? Something like below.
import pandas as pd
df_dict = {'A': [1.3, 4.5, 7.8, 9.2, 4.1],
'B': [2.1, 1.1, 1.0, 1.0, -2.0],
'C': [3.1, 4.0, 5.0, 6.0, 7.0]}
df = pd.DataFrame(df_dict)
# Some version of a running summation here!

Answer 1

I do not think you need a dataframe here, just use numpy's functions :
step1 = np.power(a[:3], b[:3])
step2 = np.multiply(c[:3], 3.1)
sum1 = np.add(step1, step2).sum()
step3 = np.divide(b[2:4], a[2:4])
step4 = np.exp(np.multiply(c[2:4], -1))
sum2 = np.multiply(step3, step4).sum()
result = sum1 + sum2
result
52.27644589942484
This should be significantly faster as the list size grows; plus you can optimize it further.