Efficient way to sum all possible pairs

Question

I have a dataframe that looks like this:

from random import randint
import pandas as pd

df = pd.DataFrame({"ID": ["a", "b", "c", "d", "e", "f", "g"], 
                   "Size": [randint(0,9) for i in range(0,7)]})

df

  ID  Size
0  a     4
1  b     3
2  c     0
3  d     2
4  e     9
5  f     5
6  g     3

And what I would like to obtain is this (could be a matrix as well):

sums_df

      a     b    c     d     e     f     g
a   8.0   7.0  4.0   6.0  13.0   9.0   7.0
b   7.0   6.0  3.0   5.0  12.0   8.0   6.0
c   4.0   3.0  0.0   2.0   9.0   5.0   3.0
d   6.0   5.0  2.0   4.0  11.0   7.0   5.0
e  13.0  12.0  9.0  11.0  18.0  14.0  12.0
f   9.0   8.0  5.0   7.0  14.0  10.0   8.0
g   7.0   6.0  3.0   5.0  12.0   8.0   6.0

That is, the sum of Size values for all possible pairs in ID.

For now I have this simple but unefficient code:

sums_df = pd.DataFrame()

for i in range(len(df)):
    for j in range(len(df)):
        sums_df.loc[i,j] = df.Size[i] + df.Size[j]

sums_df.index = list(df.ID)
sums_df.columns = list(df.ID)

It works fine for small examples like this, but for my actual data it gets too long and I am sure it is possible to avoid the nested for loops. Can you think of a better way to do this ?

Thanks for any help !

Answer 1

use np.add.outer():

In [65]: pd.DataFrame(np.add.outer(df['Size'], df['Size']),
                      columns=df['ID'].values,
                      index=df['ID'].values)
Out[65]:
    a   b  c   d   e   f   g
a   8   7  4   6  13   9   7
b   7   6  3   5  12   8   6
c   4   3  0   2   9   5   3
d   6   5  2   4  11   7   5
e  13  12  9  11  18  14  12
f   9   8  5   7  14  10   8
g   7   6  3   5  12   8   6

UPDATE: memory-saving (Pandas Multi-Index) approach (NOTE: this approach is much slower, compared to the previous one):

In [33]: r = pd.DataFrame(np.array(list(combinations(df['Size'], 2))).sum(axis=1),
    ...:                  index=pd.MultiIndex.from_tuples(list(combinations(df['ID'], 2))),
    ...:                  columns=['TotalSize']
    ...: )

In [34]: r
Out[34]:
     TotalSize
a b          7
  c          4
  d          6
  e         13
  f          9
  g          7
b c          3
  d          5
  e         12
  f          8
  g          6
c d          2
  e          9
  f          5
  g          3
d e         11
  f          7
  g          5
e f         14
  g         12
f g          8

It can be accessed as follows:

In [41]: r.loc[('a','b')]
Out[41]:
TotalSize    7
Name: (a, b), dtype: int32

In [42]: r.loc[('a','b'), 'TotalSize']
Out[42]: 7

In [44]: r.loc[[('a','b'), ('c','d')], 'TotalSize']
Out[44]:
a  b    7
c  d    2
Name: TotalSize, dtype: int32

In [43]: r.at[('a','b'), 'TotalSize']
Out[43]: 7

Memory usage comparison (DF shape: 7000x3):

In [65]: df = pd.concat([df] * 1000, ignore_index=True)

In [66]: df.shape
Out[66]: (7000, 2)

In [67]: r1 = pd.DataFrame(np.add.outer(df['Size'], df['Size']),
    ...:                       columns=df['ID'].values,
    ...:                       index=df['ID'].values)
    ...:

In [68]: r2 = pd.DataFrame(np.array(list(combinations(df['Size'], 2))).sum(axis=1),
    ...:                  index=pd.MultiIndex.from_tuples(list(combinations(df['ID'], 2))),
    ...:                  columns=['TotalSize'])
    ...:

In [69]: r1.memory_usage().sum()/r2.memory_usage().sum()
Out[69]: 2.6685407829018244

Speed comparison (DF shape: 7000x3):

In [70]: %%timeit
    ...: r1 = pd.DataFrame(np.add.outer(df['Size'], df['Size']),
    ...:                       columns=df['ID'].values,
    ...:                       index=df['ID'].values)
    ...:
180 ms ± 2.99 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)

In [71]: %%timeit
    ...: r2 = pd.DataFrame(np.array(list(combinations(df['Size'], 2))).sum(axis=1),
    ...:                  index=pd.MultiIndex.from_tuples(list(combinations(df['ID'], 2))),
    ...:                  columns=['TotalSize'])
    ...:
17 s ± 325 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

Answer 2

Use Numpy's broadcasting

size = df.Size.values
ids = df.ID.values

pd.DataFrame(
    size[:, None] + size,
    ids, ids
)

    a   b  c   d   e   f   g
a   8   7  4   6  13   9   7
b   7   6  3   5  12   8   6
c   4   3  0   2   9   5   3
d   6   5  2   4  11   7   5
e  13  12  9  11  18  14  12
f   9   8  5   7  14  10   8
g   7   6  3   5  12   8   6