I have a pandas dataframe that looks like

import pandas as pd

data = {
  "Race_ID": [2,2,2,2,2,5,5,5,5,5,5],
  "Student_ID": [1,2,3,4,5,9,10,2,3,6,5],
  "theta": [8,9,2,12,4,5,30,3,2,1,50]
}

df = pd.DataFrame(data)

and I have a function f(thetai, *theta) = thetai ** 2 + the other thetas in the same race which I want to apply to the theta column in dataframe grouped by Race_ID and create a new column called feature.

So we have

For student 1 in Race 2, the value is 8^2 + 9+2+12+4

For student 2 in Race 2, the value is 9^2 + 8+2+12+4

For student 3 in Race 2, the value is 2^2 + 8+9+12+4

etc.

I know about the groupby and apply methods but I don’t know how to apply the methods when the number of arguments can vary.

So the desired outcome looks like

data = {
  "Race_ID": [2,2,2,2,2,5,5,5,5,5,5],
  "Student_ID": [1,2,3,4,5,9,10,2,3,6,5],
  "theta": [8,9,2,12,4,5,30,3,2,1,50],
  "fearure": [91,107,37,167,47,111,961,97,93,91,2541]
}

df = pd.DataFrame(data)