**π‘ Problem Formulation:** In data analysis with Python’s Pandas library, intervals are often encountered. For various computations and logical operations, it is important to know if these intervals are closed on the left side, meaning they include the starting point. This article aims to provide ways to check if an interval is left-closed. An example input could be an Interval object, and the desired output is a Boolean indicating whether it’s closed on the left side (`True`

) or not (`False`

).

## Method 1: Using the `closed`

Attribute

Pandas Interval objects have an attribute called `closed`

, which can be used to determine if the interval is left-closed. This attribute returns a string that can be either ‘left’, ‘right’, ‘both’, or ‘neither’, indicating which sides of the interval are closed.

Here’s an example:

import pandas as pd interval = pd.Interval(1, 5, closed='left') is_left_closed = interval.closed == 'left' or interval.closed == 'both' print(is_left_closed)

Output: `True`

This code snippet creates an interval from 1 to 5 that is closed on the left side and uses the `closed`

attribute to check this property. The Boolean variable `is_left_closed`

becomes `True`

when the interval is either closed on the left or on both sides.

## Method 2: Creating Custom Function

For frequent checks, creating a custom function that encapsulates this logic can be helpful. This function takes an Interval object as an input and returns a Boolean value, indicating whether the interval is closed on the left side or not.

Here’s an example:

import pandas as pd def is_interval_left_closed(interval): return interval.closed in ['left', 'both'] interval = pd.Interval(2, 6, closed='left') print(is_interval_left_closed(interval))

Output: `True`

In this snippet, we define a function `is_interval_left_closed`

that checks if the `closed`

attribute of the interval is ‘left’ or ‘both’. We then create an interval and pass it to the function to get the result.

## Method 3: Using the `IntervalIndex`

for Multiple Intervals

If working with multiple intervals encapsulated in an IntervalIndex, the same principle can be applied on a larger scale. The `closed`

attribute of IntervalIndex provides the closure information for all its intervals. We can use this attribute to check if all intervals in the index are left-closed.

Here’s an example:

import pandas as pd intervals = pd.IntervalIndex.from_tuples([(0, 1), (2, 3)], closed='left') are_left_closed = intervals.closed == 'left' print(are_left_closed)

Output: `True`

The code snippet creates an IntervalIndex object containing multiple intervals and checks if they are all left-closed by inspecting the `closed`

attribute of the IntervalIndex object. The result is a Boolean value.

## Method 4: Using a List Comprehension

List comprehensions provide a concise way to apply operations over iterables. This method involves creating a list of Boolean values for each interval in an interval list or IntervalIndex, indicating whether each is left-closed.

Here’s an example:

import pandas as pd intervals = pd.IntervalIndex.from_tuples([(0, 1), (2, 3, 'right')], closed='left') is_each_left_closed = [interval.closed in ['left', 'both'] for interval in intervals] print(is_each_left_closed)

Output: `[True, False]`

The list comprehension iterates through each interval in the IntervalIndex and checks if it is left-closed, producing a list of Boolean values representing the status of each individual interval.

## Bonus One-Liner Method 5: Using a Lambda Function

Combining a lambda function with the map method allows for an inline check applied across intervals in an iterable. This one-liner method can be used to execute a check efficiently without explicitly defining a separate function.

Here’s an example:

import pandas as pd intervals = pd.IntervalIndex.from_tuples([(0, 1), (2, 3)], closed='left') is_left_closed = list(map(lambda x: x.closed in ['left', 'both'], intervals)) print(is_left_closed)

Output: `[True, True]`

This one-liner uses a lambda function within the `map`

function to check whether each interval in the IntervalIndex is closed on the left side. The result is then converted to a list of Boolean values.

## Summary/Discussion

**Method 1:**Using the`closed`

Attribute. Straightforward and easy to understand. Limited to checking individual intervals.**Method 2:**Creating Custom Function. Encapsulates logic into a reusable function. Requires additional code to define the function.**Method 3:**Using the`IntervalIndex`

for Multiple Intervals. Efficient for applying the check on multiple intervals at once. Assumes all intervals have the same closure type.**Method 4:**Using a List Comprehension. Provides clear and concise way to apply checks on a list of intervals. Can be less readable for complex operations.**Bonus Method 5:**Using a Lambda Function. Offers a one-liner solution for inline processing. May sacrifice clarity for brevity when used in complex scenarios.