Finding matching interval(s) in pandas Intervalindex

Question

There's this interesting API called Intervalindex new in 0.20 that lets you create an index of intervals.

Given some sample data:

data = [(893.1516130000001, 903.9187099999999),
 (882.384516, 893.1516130000001),
 (817.781935, 828.549032)]

You can create the index like this:

idx = pd.IntervalIndex.from_tuples(data)

print(idx)
IntervalIndex([(893.151613, 903.91871], (882.384516, 893.151613], (817.781935, 828.549032]]
              closed='right',
              dtype='interval[float64]')

An interesting property of Intervals is that you can perform interval checks with in:

print(y[-1])
Interval(817.78193499999998, 828.54903200000001, closed='right')

print(820 in y[-1])
True

print(1000 in y[-1])
False

I would like to know how to apply this operation to the entire index. For example, given some number 900, how could I retrieve a boolean mask of intervals for which this number fits in?

I can think of:

m = [900 in y for y in idx]
print(m)
[True, False, False]

Are there better ways to do this?

Answer 1

If you are interested in performance, an IntervalIndex is optimized for searching. using .get_loc or .get_indexer uses an internally built IntervalTree (like a binary tree), which is constructed on first use.

In [29]: idx = pd.IntervalIndex.from_tuples(data*10000)

In [30]: %timeit -n 1 -r 1 idx.map(lambda x: 900 in x)
92.8 ms ± 0 ns per loop (mean ± std. dev. of 1 run, 1 loop each)

In [40]: %timeit -n 1 -r 1 idx.map(lambda x: 900 in x)
42.7 ms ± 0 ns per loop (mean ± std. dev. of 1 run, 1 loop each)

# construct tree and search
In [31]: %timeit -n 1 -r 1 idx.get_loc(900)
4.55 ms ± 0 ns per loop (mean ± std. dev. of 1 run, 1 loop each)

# subsequently
In [32]: %timeit -n 1 -r 1 idx.get_loc(900)
137 µs ± 0 ns per loop (mean ± std. dev. of 1 run, 1 loop each)

# for a single indexer you can do even better (note that this is
# dipping into the impl a bit
In [27]: %timeit np.arange(len(idx))[(900 > idx.left) & (900 <= idx.right)]
203 µs ± 1.55 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

Note that .get_loc() returns an indexer (which is actually more useful than a boolean array, but they are convertible to each other).

In [38]: idx.map(lambda x: 900 in x)
    ...: 
Out[38]: 
Index([ True, False, False,  True, False, False,  True, False, False,  True,
       ...
       False,  True, False, False,  True, False, False,  True, False, False], dtype='object', length=30000)

In [39]: idx.get_loc(900)
    ...: 
Out[39]: array([29997,  9987, 10008, ..., 19992, 19989,     0])

Returning a boolean array is converted to an array of indexers

In [5]: np.arange(len(idx))[idx.map(lambda x: 900 in x).values.astype(bool)]
Out[5]: array([    0,     3,     6, ..., 29991, 29994, 29997])

This is what .get_loc() and .get_indexer() return:

In [6]: np.sort(idx.get_loc(900))
Out[6]: array([    0,     3,     6, ..., 29991, 29994, 29997])

Answer 2

If you're looking for speed, you can use left and right of idx i.e getting lower bound and upper bound from the range then check if number falls between the bounds i.e

list(lower <= 900 <= upper for (lower, upper) in zip(idx.left,idx.right))

Or

[(900 > idx.left) & (900 <= idx.right)]

[True, False, False]

For small data

%%timeit
list(lower <= 900 <= upper for (lower, upper) in zip(idx.left,idx.right))
100000 loops, best of 3: 11.26 µs per loop

%%timeit
[900 in y for y in idx]
100000 loops, best of 3: 9.26 µs per loop

For large data

idx = pd.IntervalIndex.from_tuples(data*10000)

%%timeit
list(lower <= 900 <= upper for (lower, upper) in zip(idx.left,idx.right))
10 loops, best of 3: 29.2 ms per loop

%%timeit
[900 in y for y in idx]
10 loops, best of 3: 64.6 ms per loop

This method beats your solution for large data.

Answer 3

You can use map:

idx.map(lambda x: 900 in x)
#Index([True, False, False], dtype='object')

Timings:

%timeit [900 in y for y in idx]
#100000 loops, best of 3: 3.76 µs per loop

%timeit idx.map(lambda x: 900 in x)
#10000 loops, best of 3: 48.7 µs per loop

%timeit map(lambda x: 900 in x, idx)
#100000 loops, best of 3: 4.95 µs per loop

Obviously, comprehension is the fastest but builtin map doesn't fall too far behind.

Results even out when we introduce more data, to be precise 10K times more data:

%timeit [900 in y for y in idx]
#10 loops, best of 3: 26.8 ms per loop

%timeit idx.map(lambda x: 900 in x)
#10 loops, best of 3: 30 ms per loop

%timeit map(lambda x: 900 in x, idx)
#10 loops, best of 3: 29.5 ms per loop

As we see, builtin map comes very close to .map() so - lets see what happens with 10 times even more data:

%timeit [900 in y for y in idx]
#1 loop, best of 3: 270 ms per loop

%timeit idx.map(lambda x: 900 in x)
#1 loop, best of 3: 299 ms per loop

%timeit map(lambda x: 900 in x, idx)
#1 loop, best of 3: 291 ms per loop

Conclusion:

comprehension is the winner but not so distinct on larger amounts of data.

Answer 4

using NumPy

import numpy as np
data = [(893.1516130000001, 903.9187099999999),
         (882.384516, 893.1516130000001),
         (817.781935, 828.549032)]    
q = 900
# The next line broadcast q and tell if q is within the intervals/ranges defined in data (using numpy)
np.logical_xor(*(np.array(data) - q > 0).transpose())