Find possible unique combinations of 3 columns in pandas

Question

I am trying to find all possible combinations of 3 variable columns in pandas. The sample df looks as such:

          Variable_Name Variable1 Variable2 Variable3
0                  X      6.0%      8.0%     10.0%
1                  Y      3.0%      4.0%      5.0%
2                  Z      1.0%      3.0%      5.0%

These combinations must only take values from that column and not move values to other columns, eg Using 4.0% as a 'X' would be incorrect.

Tried to use itertools.combinations , itertools.product , itertools.permutation but these results give ALL possible combinations.

I would want the results to look like this, giving 27 possible combinations:

     Y      X     Z
0   3.0%   6.0%  1.0%
1   3.0%   6.0%  3.0%
2   3.0%   6.0%  5.0%
3   3.0%   8.0%  1.0%
4   3.0%   8.0%  3.0%
5   3.0%   8.0%  5.0%
6   3.0%  10.0%  1.0%
7   3.0%  10.0%  3.0%
8   3.0%  10.0%  5.0%
9   4.0%   8.0%  3.0%
10  4.0%   8.0%  1.0%
11  4.0%   8.0%  5.0%
12  4.0%   6.0%  1.0%
13  4.0%   6.0%  3.0%
14  4.0%   6.0%  5.0%
15  4.0%  10.0%  1.0%
16  4.0%  10.0%  3.0%
17  4.0%  10.0%  5.0%
18  5.0%  10.0%  5.0%
19  5.0%  10.0%  1.0%
20  5.0%  10.0%  3.0%
21  5.0%   8.0%  1.0%
22  5.0%   8.0%  3.0%
23  5.0%   8.0%  5.0%
24  5.0%   6.0%  1.0%
25  5.0%   6.0%  3.0%
26  5.0%   6.0%  5.0%

Any help will be appreciated.

Answer 1

Let's try successively cross merging each variable's values:

from functools import reduce

import pandas as pd

df = pd.DataFrame({'Variable_Name': {0: 'X', 1: 'Y', 2: 'Z'},
                   'Variable1': {0: '6.0%', 1: '3.0%', 2: '1.0%'},
                   'Variable2': {0: '8.0%', 1: '4.0%', 2: '3.0%'},
                   'Variable3': {0: '10.0%', 1: '5.0%', 2: '5.0%'}})

# Save Var Names for later
var_names = df['Variable_Name']

# Get Variables Options in Own Rows
new_df = df.set_index('Variable_Name').stack() \
    .droplevel(1, 0) \
    .reset_index()

# Get Collection of DataFrames each with its own variable
dfs = tuple(new_df[new_df['Variable_Name'].eq(v)]
            .drop(columns=['Variable_Name']) for v in var_names)
# Successive Cross Merges
new_df = reduce(lambda left, right: pd.merge(left, right, how='cross'), dfs)
# Fix Column Names
new_df.columns = var_names
# Fix Axis Names
new_df = new_df.rename_axis(None, axis=1)

# For Display
print(new_df.to_string())

Output:

        X     Y     Z
0    6.0%  3.0%  1.0%
1    6.0%  3.0%  3.0%
2    6.0%  3.0%  5.0%
3    6.0%  4.0%  1.0%
4    6.0%  4.0%  3.0%
5    6.0%  4.0%  5.0%
6    6.0%  5.0%  1.0%
7    6.0%  5.0%  3.0%
8    6.0%  5.0%  5.0%
9    8.0%  3.0%  1.0%
10   8.0%  3.0%  3.0%
11   8.0%  3.0%  5.0%
12   8.0%  4.0%  1.0%
13   8.0%  4.0%  3.0%
14   8.0%  4.0%  5.0%
15   8.0%  5.0%  1.0%
16   8.0%  5.0%  3.0%
17   8.0%  5.0%  5.0%
18  10.0%  3.0%  1.0%
19  10.0%  3.0%  3.0%
20  10.0%  3.0%  5.0%
21  10.0%  4.0%  1.0%
22  10.0%  4.0%  3.0%
23  10.0%  4.0%  5.0%
24  10.0%  5.0%  1.0%
25  10.0%  5.0%  3.0%
26  10.0%  5.0%  5.0%

Answer 2

You can use CROSS JOIN . In pandas you can use pd.merge() or pd.DataFrame.join() with parameter how='cross' . But before cross joining you need to place each variable in a dataframe with long (unpivoted) format (Your table is in a wide format (pivoted)).

df_X = df.loc[df['Variable_Name'] == 'X', ['Variable1', 'Variable2', 'Variable3']].T
df_Y = df.loc[df['Variable_Name'] == 'Y', ['Variable1', 'Variable2', 'Variable3']].T
df_Z = df.loc[df['Variable_Name'] == 'Z', ['Variable1', 'Variable2', 'Variable3']].T

cross_join_df = df_X.join(df_Y, how='cross').join(df_Z, how='cross')
cross_join_df.columns = ['X','Y','Z']

If you need to use the code in a loop, it would be like this.

variables = df['Variable_Name'].unique()
columns_to_cross = ['Variable1', 'Variable2', 'Variable3']
cross_join_df = df.loc[df['Variable_Name'] == variables[0], columns_to_cross].T
for var in variables[1:]:
    to_join_df = df.loc[df['Variable_Name'] == var, columns_to_cross].T
    cross_join_df = pd.merge(cross_join_df, to_join_df, how='cross')
cross_join_df.columns = variables