ENH: Add option to keep index in `pd.melt`

[erfannariman]

When melting a dataframe, there's no option to keep the original index. This can be beneficial for example when users want to do different kind ravel than the deault F (Fortran style) right now. To make this more clear, see example:

df = pd.DataFrame({'A': [1, 4],
                   'B': [2, 5],
                   'C': [3, 6]})
print(df)
   A  B  C
0  1  2  3
1  4  5  6

print(df.melt())
  variable  value
0        A      1
1        A      4
2        B      2
3        B      5
4        C      3
5        C      6

But the expected output can be row wise instead:

  variable  value
0        A      1
1        B      2
2        C      3
3        A      4
4        B      5
5        C      6

Solution proposal
This could be solved by adding an ignore_index argument which is True by default, but if it is set to False, the result would come out like:

  variable  value
0        A      1
1        A      4
0        B      2
1        B      5
0        C      3
1        C      6

This way the user can sort the index themself and achieve the same result:

print(df.sort_index())
  variable  value
0        A      1
0        B      2
0        C      3
1        A      4
1        B      5
1        C      6

Also in pandas/core/reshape/melt there is an # TODO: what about the existing index? in the melt function. This might solve that TODO if I'm not mistaken.

[WillAyd]

I believe this is already being addressed in #33659

[WillAyd]

Closing as a duplicate of #17440 but lmk if overlooking something

[erfannariman]

Yes it's a dupe, thanks for closing. @WillAyd