Add two series indexed by distinct but overlapping intervals

Question

Suppose I have the following series:

import pandas as pd

index1 = pd.IntervalIndex.from_tuples([(1, 3), (2.5, 4), (6, 7)])
x = pd.Series([1, 2, 3], index=index1)

index2 = pd.IntervalIndex.from_tuples([(1, 2), (5, 6.5)])
y = pd.Series([10, 20], index=index2)

z = x+y

Ideally, this is how I would like z to look:

(1.0, 2.0]    11
(2.0, 2.5]    1
(2.5, 3.0]    3
(3.0, 4.0]    2
(4.0, 5.0]    0
(5.0, 6.0]    20
(6.0, 6.5]    23
(6.5, 7.0]    3

Of course, when I do add them, I get a bunch of NaNs, because the indices don't align.

Should I upsample, and then add? (Also... is there a fancy way to downsample in pandas?)

How would I deal with one of the series having overlapping intervals inside its own index?

Context:

I'm trying to keep track of the number of students who have a class going on at a certain time.

I've scraped the class schedule, and I'm running into a problem when classes start and get out at different times.

Answer 1

This is my approach, hope it's self-explained:

# gather x and y and separate start and end time
df = (pd.concat((x,y))
        .to_frame(name='val')
        .assign(start=lambda x: x.index.left,
                end=lambda x: x.index.right)
     )

# unique time point
idx = (df.index.left.to_series()
    .append(df.index.right.to_series())
    .drop_duplicates()
    .to_frame(name='pt')
    .assign(dummy=1)
)

# cross join, query the valid entries, and sum:
(df.assign(dummy=1)
   .merge(idx, on='dummy')
   .query('start < pt <= end')
   .groupby('pt')
   .val
   .sum()
)

Output (note that pt is the end point for each interval, the start point is the previous end point).

pt
2.0    11
2.5     1
3.0     3
4.0     2
6.0    20
6.5    23
7.0     3
Name: val, dtype: int64

Answer 2

flatten all left and right values of x.index and y.index and filter by unique values. Construct new IntervalIndex from these unique values. Using listcomp on the new IntervalIndex checking and slicing on overlaps of x, y to construct final output

arr = np.unique(x.index.append(y.index).to_tuples().to_numpy().sum())

Out:
array([1. , 2. , 2.5, 3. , 4. , 5. , 6. , 6.5, 7. ])

iix = pd.IntervalIndex.from_breaks(arr)
s = pd.Series([x[x.index.overlaps(ix)].sum() + y[y.index.overlaps(ix)].sum() 
                            for ix in iix], index=iix)

Out[379]:
(1.0, 2.0]    11
(2.0, 2.5]     1
(2.5, 3.0]     3
(3.0, 4.0]     2
(4.0, 5.0]     0
(5.0, 6.0]    20
(6.0, 6.5]    23
(6.5, 7.0]     3
dtype: int64