shifted_calculations_benchmark.py

import pandas as pd
import numpy as np
import perfplot 
import numba 
  
def with_df_loc(df):
    df.at[0, 'b'] = 5

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

    return df

@numba.njit
def func(a, b_0=5):
    n = len(a)
    b = np.full(n, b_0, dtype=np.float64)
    for i in range(1, n):
        b[i] = (b[i - 1] + a[i - 1]) / 2
    return b
    
def with_numba(df):    
    df['b'] = func(df['a'].to_numpy())
    return df

df = pd.DataFrame([1, 6, 2, 8], columns=['a'])
kernels = [with_df_loc, with_numba]

perfplot.show(
    setup=lambda n: pd.concat([df] * n, ignore_index=True),
    kernels=kernels,
    labels=[k.__name__ for k in kernels],
    n_range=[2**k for k in range(1, 12)],
    xlabel='N',
    logx=True,
    logy=True,
    equality_check=np.allclose)