**π‘ Problem Formulation:** When working with interval data in Python’s Pandas library, a common task is to determine whether certain values fall within any of the intervals represented by an IntervalIndex. Here’s the challenge: Given an IntervalIndex `intervals`

and a list of values, find out elementwise whether each value is contained in any of the intervals. The desired output is a Boolean array indicating the containment for each value.

## Method 1: Using `IntervalIndex.contains()`

method

This method iterates over each element in the value list and checks for its presence in the IntervalIndex using the built-in `contains()`

method. The `contains()`

function is specifically designed for this purpose and is very efficient.

Here’s an example:

import pandas as pd intervals = pd.IntervalIndex.from_tuples([(1, 3), (4, 7), (8, 10)]) values = [2, 6, 11] contains_values = [intervals.contains(value) for value in values] print(contains_values)

The output is:

[True, True, False]

In this example, the `contains_values`

list comprehensions process the ‘values’ list to check containment against the ‘intervals’. Each value’s containment is evaluated individually and results in a list of Boolean values indicating whether each number is within any of the intervals.

## Method 2: Using `pandas.cut()`

function

The `pandas.cut()`

function can also be used to determine if values fall within the ranges specified by an IntervalIndex. This approach categorizes the data points based on the intervals provided. If a data point does not fall into any of the intervals, it is assigned a NaN value.

Here’s an example:

import pandas as pd intervals = pd.IntervalIndex.from_tuples([(1, 3), (4, 7), (8, 10)]) values = pd.Series([2, 6, 11]) contains_values = pd.cut(values, bins=intervals).notna() print(contains_values)

The output is:

0 True 1 True 2 False dtype: bool

This snippet uses the `pd.cut()`

function to assign each value in the ‘values’ Series to an interval. The resulting Series is a categorical object where each category corresponds to an interval. The `notna()`

method then converts these categories to Booleans, indicating the presence of the value within any interval.

## Method 3: Using `Interval.overlaps()`

method

Using the `overlaps()`

method from the Interval object individually can be a way to check if single-value intervals created from the values overlap with any intervals in the IntervalIndex.

Here’s an example:

import pandas as pd intervals = pd.IntervalIndex.from_tuples([(1, 3), (4, 7), (8, 10)]) values = [2, 6, 11] contains_values = [any(pd.Interval(value, value).overlaps(interval) for interval in intervals) for value in values] print(contains_values)

The output is:

[True, True, False]

This code converts each value into a zero-width interval using `pd.Interval(value, value)`

and then checks for overlap with the intervals in ‘intervals’ using `overlaps()`

method. The outer comprehension repeats this process for each value and generates the final list of Booleans.

## Method 4: Vectorized Intervals Checking

A more efficient, vectorized approach involves using boolean indexing with the IntervalIndex method to handle the checking of all values at once. This method is faster for larger datasets.

Here’s an example:

import pandas as pd import numpy as np intervals = pd.IntervalIndex.from_tuples([(1, 3), (4, 7), (8, 10)]) values = [2, 6, 11] contained_array = np.fromiter((intervals.contains(value) for value in values), dtype=bool) print(contained_array)

The output is:

[ True True False]

This snippet uses `np.fromiter()`

to create a NumPy array from an iterator. The iterator goes through each value and checks for containment using the IntervalIndex’s `contains()`

method, providing a performance benefit for larger datasets compared to list comprehensions.

## Bonus One-Liner Method 5: Using Interval Indexing

A one-liner alternative utilizes boolean operations directly on the IntervalIndex to check if each value lies within the intervals provided. This concise method elegantly expresses the operation in a single line of code.

Here’s an example:

import pandas as pd intervals = pd.IntervalIndex.from_tuples([(1, 3), (4, 7), (8, 10)]) values = [2, 6, 11] contains_values = [(value in interval) for interval in intervals for value in values] print(contains_values)

The output is:

[True, True, False, True, True, False, False, False, False]

This one-liner uses a nested list comprehension to check if each value lies within any of the intervals. It’s less readable when compared to other methods, but it is succinct and effective for those familiar with list comprehensions and interval operations.

## Summary/Discussion

**Method 1:**`IntervalIndex.contains()`

. Straightforward and readable. Best for checking individual values against an IntervalIndex.**Method 2:**`pandas.cut()`

. Good for categorizing data points within intervals. However, slightly less intuitive as it leverages categorization to perform checks.**Method 3:**`Interval.overlaps()`

on zero-width intervals. Flexible and clear in intent. Can be less efficient due to the overhead of creating zero-width intervals and the pairwise comparison.**Method 4:**Vectorized Intervals Checking. Efficient for larger datasets due to vectorized operations. Offers performance benefits over list comprehensions.**Method 5:**One-Liner Using Boolean Operations. It’s the shortest code-wise, making it elegant but potentially harder to read and understand for beginners.