how to generate random numbers that can be summed to a specific value? - pandas

Question

I have 2 dataframe as follows:
import pandas as pd
import numpy as np
# Create data set.
dataSet1 = {'id': ['A', 'B', 'C'],
'value' : [9,20,20]}
dataSet2 = {'id' : ['A', 'A','A','B','B','B','C'],
'id_2': [1, 2, 3, 2,3,4,1]}
# Create dataframe with data set and named columns.
df_map1 = pd.DataFrame(dataSet1, columns= ['id', 'value'])
df_map2 = pd.DataFrame(dataSet2, columns= ['id','id_2'])
df_map1
id value
0 A 9
1 B 20
2 C 20
df_map2
id id_2
0 A 1
1 A 2
2 A 3
3 B 2
4 B 3
5 B 4
6 C 1
where id_2 can have dups of id. (namely id_2 is subset of id)
#doing a quick merge, based on id.
df = df_map1.merge(df_map2 ,on=['id'])
id value id_2
0 A 9 1
1 A 9 2
2 A 9 3
3 B 20 2
4 B 20 3
5 B 20 4
6 C 20 1
I can represent what's the relationship between id and id_2 as follows
id_ref = df.groupby('id')['id_2'].apply(list).to_dict()
{'A': [1, 2, 3], 'B': [2, 3, 4], 'C': [1]}
Now, I would like to generate random integer say 0 to 3 put the list (5 elements for exmaple) into the pandas df and explode.
import numpy as np
import random
df['random_value'] = df.apply(lambda _: np.random.randint(0,3, 5), axis=1)
id value id_2 random_value
0 A 9 1 [0, 0, 0, 0, 1]
1 A 9 2 [0, 2, 1, 2, 1]
2 A 9 3 [0, 1, 2, 2, 1]
3 B 20 2 [2, 1, 1, 2, 2]
4 B 20 3 [0, 0, 0, 0, 0]
5 B 20 4 [1, 0, 0, 1, 0]
6 C 20 1 [1, 2, 2, 2, 1]
The condition for generating this random_value list, is that sum of the list has to be equal to 9.
That means, for id : A, if we sum all the elements inside the list, we have total of 13 shown the description below, but what we want is 9:
and same concept for id B and C.. and so on....
is there anyway to achieve this?
# i was looking into multinomial from np.random function... seems this should be the solution but im not sure how to apply this with pandas.
np.random.multinomial(9, np.ones(5)/5, size = 1)[0]
=> array([2,3,3,0,1])
2+3+3+0+1 = 9
ATTEMPT/IDEA ...
given that we have list of id_2. ie) id: A has 3 distinct elements [1,2,3].
so id A is mapped to 3 different elements. so we can get
3 * 5 = 15 ( which will be our long list )
3: length of list
5: create 5 elements of list
hence
list_A = np.random.multinomial(9,np.ones(3*5)/(3*5) ,size = 1)[0]
and then we evenly distribute/split the list.
using this list comprehension:
[list_A [i:i + n] for i in range(0, len(list_A ), n)]
but I am still unsure how to do this dynamically.

Answer 1

The core idea is as you said (about getting 3*5=15 numbers), plus reshaping it into a 2D array with the same number of rows as that id has in the dataframe. The following function does that,
def generate_random_numbers(df):
value = df['value'].iloc[0]
list_len = 5
num_rows = len(df)
num_rand = list_len*num_rows
return pd.Series(
map(list, np.random.multinomial(value, np.ones(num_rand)/num_rand).reshape(num_rows, -1)),
df.index
)
And apply it:
df['random_value'] = df.groupby(['id', 'value'], as_index=False).apply(generate_random_numbers).droplevel(0)