如何根据计算的同一列中的先前值计算 pandas 列？

Question

I want to achieve the following table, where the values in "md" needs to be calculated:

   msotc   md
0      0    0
1      1    1
2      2    3
3      3    7
4      4   15
5      5   31
6      6   63
7      7  127

Given:

• The total rows is based on a given value (msotc + 1)
• The first value in column "md" needs to be 0
• The value for row[1] to row[-1] are calculate based in formula: (prev_md * soss) + sopd

Solutions (I think):

• Create a new column with a formula
• Create an empty column "md" with the value 0 on index[0] and calculate the other rows

import pandas as pd
import numpy as np

msotc = 7
sopd = 1 # (= not fixed, could be eg. 0.5)
soss = 2 # (= not fixed, could be eg. 1.05)

arr = [np.NaN] * (msotc + 1)
arr[0] = 0

data = {
    "msotc": range(0, msotc + 1, 1),
    "md": arr
}

df = pd.DataFrame(
    data=data
)

# df["md"] = (df["md"].shift(1) * soss) + sopd <- This doesn't work

Answer 1

You can use math to convert your formula into a geometric series.

md[n] = md[n-1]*soss + sopd

expressed in terms of md[0] and using the formula for the sum of powers:

md[n] = md[0]*soss**(n-1) + sopd * (soss**n - 1)/(soss-1)

Thus no need to loop, you can vectorize:

msotc = 7
sopd = 1
soss = 2
md0 = 0

n = np.arange(msotc+1)
df = pd.DataFrame({'msotc': n, 'md': md0*soss**np.clip(n-1, 0, np.inf) + sopd*(soss**n-1)/(soss-1)})

output:

   msotc     md
0      0    0.0
1      1    1.0
2      2    3.0
3      3    7.0
4      4   15.0
5      5   31.0
6      6   63.0
7      7  127.0

Answer 2

This should work fine. It is quite easy to understand, just a simple loop.

arr = [0] * (msotc + 1)
for i in range(msotc + 1):
    if i == 0:
        continue
    arr[i] = (arr[i - 1] * soss) + sopd

Answer 3

Try this:

import pandas as pd

msotc = 7
sopd = 1
soss = 2

msotc_vals = []
arr = [0]
for val in range(msotc + 1):
    msotc_vals += [val]
    arr += [arr[-1] * soss + sopd]

data = {"msotc": msotc_vals, "md": arr[:-1]}

df = pd.DataFrame(data=data)