subtracting the 'INT' column from the 'LMP' column, but only from the indexed row per unique 'ID'

I like to create a new column named 'sub' in the DataFrame and calculate its values by subtracting the 'INT' column from the 'LMP' column, but only subtracting from the latest row per unique 'ID' where the 'FM' column is set to'time0', I calculated FM as the follows but I dont know how to implement the sub column.

data = {
    'ID': [0, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2],
    'VIS': [0.0, 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0],
    'STA': [float('NaN'), 4.0, 7.0, 7.0, 7.0, 7.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0],
    'LMP': [float('NaN'), -35.0, 411.0, 773.0, 1143.0, 1506.0, float('NaN'), float('NaN'), float('NaN'), float('NaN'), float('NaN'), float('NaN')],
    'INT': [0.0, 0.0, 413.0, 777.0, 1171.0, 1509.0, 1967.0, 2310.0, 2627.0, 2970.0, 3357.0, 3768.0],
    'FM': [-1, -1, "time0", -1, -1, "time0", -1, -1, -1, -1, -1,-1]

}

sorted_data = pd.DataFrame(data)

sorted_data['FM'] = np.nan
for id in sorted_data['ID'].unique():
    filter_condition = (sorted_data['ID'] == id) & (~sorted_data['LMP'].isnull())
    if filter_condition.any():
        last_row_index = sorted_data.loc[filter_condition].index[-1]
        sorted_data.loc[last_row_index, 'FM'] = 'time0'

sorted_data['FM'] = sorted_data['FM'].fillna(-1)

Expected output should be calculated as this :

'sub': [float('NaN'), 0-411.0,413-411, 777-1509.0 , 1171.0-1509.0 ,1509-1509, 1967.0-1509, 2310.0-1509,2627.0- 1509, 2970.0-1509, 3357.0-1509,3768.0-1509] 

Here is sample code that subtracts the INT column from the LMP column at time0

data = {
    "ID": [0, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2],
    "VIS": [0.0, 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0],
    "STA": [float("NaN"), 4.0, 7.0, 7.0, 7.0, 7.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0],
    "LMP": [
        float("NaN"),
        -35.0,
        411.0,
        773.0,
        1143.0,
        1506.0,
        float("NaN"),
        float("NaN"),
        float("NaN"),
        float("NaN"),
        float("NaN"),
        float("NaN"),
    ],
    "INT": [
        0.0,
        0.0,
        413.0,
        777.0,
        1171.0,
        1509.0,
        1967.0,
        2310.0,
        2627.0,
        2970.0,
        3357.0,
        3768.0,
    ],
    "FM": [-1, -1, "time0", -1, -1, "time0", -1, -1, -1, -1, -1, -1],
}

sorted_data = pd.DataFrame(data)

lmp_at_time0 = (
    sorted_data.groupby(["ID"])
    .apply(lambda grp: grp[grp["FM"] == "time0"]["LMP"])
    .reset_index()
    .drop(columns=["level_1"])
)
lmp_at_time0.columns = ["ID", "LMP_at_time0"]
sorted_data = sorted_data.merge(lmp_at_time0, on="ID", how="left")
sorted_data["INT"] - sorted_data["LMP_at_time0"]

IIUC, you can use:

# get the last time0 value per ID
mapper = (sorted_data
.loc[sorted_data['FM'].eq('time0')]
.drop_duplicates(subset='ID', keep='last')
.set_index('ID')['LMP']
)
# map and subtract
sorted_data['sub'] = sorted_data['INT'].sub(sorted_data['ID'].map(mapper))

Output:

    ID   VIS  STA     LMP     INT     FM     sub
0    0   0.0  NaN     NaN     0.0     -1     NaN
1    1   0.0  4.0   -35.0     0.0     -1  -411.0
2    1   1.0  7.0   411.0   413.0  time0     2.0
3    2   2.0  7.0   773.0   777.0     -1  -729.0
4    2   3.0  7.0  1143.0  1171.0     -1  -335.0
5    2   4.0  7.0  1506.0  1509.0  time0     3.0
6    2   5.0  2.0     NaN  1967.0     -1   461.0
7    2   6.0  2.0     NaN  2310.0     -1   804.0
8    2   7.0  2.0     NaN  2627.0     -1  1121.0
9    2   8.0  2.0     NaN  2970.0     -1  1464.0
10   2   9.0  2.0     NaN  3357.0     -1  1851.0
11   2  10.0  2.0     NaN  3768.0     -1  2262.0