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Add value in dataframe to row based on other value

I'm looking for a performant way to lookup a value in a dataframe based on another value, and add the lookup value to a column in the row with the other value.

For example, I have this dataframe:

import pandas as pd

data = {
    'role': ['primary', 'secondary', 'primary', 'secondary'],
    'serial_number': ['abc', '123', 'def', '456'],
    'primary_serial_number': ['abc', 'abc', 'def', 'def'],
    'physical_id': ['w', 'x', 'y', 'z'],
    'set_id': ['j', 'x', 'k', 'z']
}
df = pd.DataFrame(data = data)

    role    serial_number   primary_serial_number   physical_id set_id
0   primary     abc                  abc                  w       j
1   secondary   123                  abc                  x       x
2   primary     def                  def                  y       k
3   secondary   456                  def                  z       z

Secondaries always have the same physical_id and set_id. For each secondary, I'd like to have the set_id of the relevant primary in the same row as the secondary. I can look this up by matching the "primary_serial_number" for each secondary to the "serial_number" for each primary. I should then have a column labeled "primary_set_id" that has the values j, j, k, k.

I tried the following:

df['primary_set_id'] = df['primary_serial_number'].apply(
    lambda x: df['set_id'][df['serial_number'] == x])

When I run this on the above fake data, I get:

ValueError: Wrong number of items passed 2, placement implies 1

In reality, I am dealing with hundreds of thousands of rows, and this method is extremely inefficient (I have not yet let it run to completion).

I think this should do it

grps = df.groupby('role')
prim_df = grps.get_group('primary')
sec_df = grps.get_group('secondary')
primsec_df = sec_df.merge(prim_df, left_on = 'primary_serial_number', right_on = 'serial_number')
primsec_df

in column 'sec_id_y' you get what you want:

|    | role_x    |   serial_number_x | primary_serial_number_x   | physical_id_x   | set_id_x   | role_y   | serial_number_y   | primary_serial_number_y   | physical_id_y   | set_id_y   |
|---:|:----------|------------------:|:--------------------------|:----------------|:-----------|:---------|:------------------|:--------------------------|:----------------|:-----------|
|  0 | secondary |               123 | abc                       | x               | x          | primary  | abc               | abc                       | w               | j          |
|  1 | secondary |               456 | def                       | z               | z          | primary  | def               | def                       | y               | k          |

I am not sure how efficient this will be on a large df

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