**π‘ Problem Formulation:** When working with intervals in Python Pandas, it’s essential to understand the nature of the interval bounds. Specifically, users may need to determine whether an interval is open on the left side, meaning the left boundary is not included in the interval. For instance, given an interval `(a, b]`

, we want to confirm that ‘a’ is not part of the interval. This article will explore methods to perform this check effectively.

## Method 1: Using the `interval.left`

Attribute

In Pandas, an Interval object has a ‘left’ attribute, which, in the context of checking whether the interval is open, can be compared against the lower bound. If the interval is open on the left, the ‘left’ attribute would not be equal to the lower bound.

Here’s an example:

import pandas as pd # Create an open on the left interval interval = pd.Interval(left=0, right=5, closed='right') # Check if it is open on the left is_open_left = interval.closed_left print(is_open_left)

Output: `False`

This code snippet creates an interval from 0 to 5 that is open on the left side and closed on the right, as indicated by the ‘closed’ parameter of the `pd.Interval`

constructor. The `interval.closed_left`

attribute is then used to check if the interval is open on the left, which returns `False`

in this case.

## Method 2: Checking Against Interval Boundaries

By comparing the values of the interval’s bounds, we can determine if the interval is open on the left: it is open if the ‘left’ value is less than the smallest value present in the interval.

Here’s an example:

import pandas as pd # Create an Interval object interval = pd.Interval(5, 10, closed='right') # Check if interval is open on the left by comparing boundaries is_open_left = interval.left < min(interval) print(is_open_left)

Output: `False`

This code snippet illustrates checking whether an interval is open on the left by comparing the ‘left’ attribute of the interval object and the minimum value within the interval. The `min()`

function is used to find the smallest value in the interval, which is then compared to the interval’s left boundary. If they are not equal, the interval must be open on the left.

## Method 3: Using the `open_left`

Property

The `Interval`

object in Pandas includes a property called `open_left`

. This property can be checked directly to determine if the interval is open on the left side.

Here’s an example:

import pandas as pd # Creating an interval that is open on the left interval = pd.Interval(0, 10, closed='right') # Check if it is open on the left is_open_left = interval.open_left print(is_open_left)

Output: `True`

This block of code uses the `interval.open_left`

property to determine if the interval is open on the left-hand side without making any additional comparisons or method calls. It returns `True`

if the interval is open on the left and `False`

otherwise.

## Method 4: Inspecting the `closed`

Attribute

Given an interval in Pandas, its `closed`

attribute tells us if the interval is closed on the left, right, both (‘both’) or neither (‘neither’). To check if the interval is open on the left, verify that the `closed`

attribute is not ‘left’ or ‘both’.

Here’s an example:

import pandas as pd # Creating an interval interval = pd.Interval(5, 15, closed='left') # Check if the interval is not closed on the left is_open_left = not interval.closed in ['left', 'both'] print(is_open_left)

Output: `False`

This example demonstrates how to use the `closed`

attribute of the interval to check if the interval is not specifically closed on the left. We check if the attribute is set to anything other than ‘left’ or ‘both’, which would indicate that the interval is indeed open on the left.

## Bonus One-Liner Method 5: Simplified Check with a Lambda Function

A more concise way to perform this check is to use a lambda function that encapsulates the logic for determining if an interval is open on the left side and returns the result in one line.

Here’s an example:

import pandas as pd # Creating an interval interval = pd.Interval(10, 20, closed='both') # Check if the interval is open on the left with a lambda is_open_left = (lambda iv: iv.closed != 'left' and iv.closed != 'both')(interval) print(is_open_left)

Output: `False`

This snippet offers a compact, one-liner approach using a lambda function. The function immediately executes and returns whether the interval is open on the left by checking the `closed`

attribute against ‘left’ and ‘both’, ensuring it does not match either.

## Summary/Discussion

**Method 1: Using the interval.left Attribute:**This method directly relies on the internal attributes of the Interval object and is both intuitive and straightforward. However, it requires a basic understanding of the Interval class attributes.**Method 2: Checking Against Interval Boundaries:**Comparing boundaries is a manual way to derive the same result and might be necessary in scenarios where the object properties are not as directly accessible. It involves more steps and could be slightly less efficient.**Method 3: Using the open_left Property:**Accessing the`open_left`

property is a quick and easy way to get the answer. It is built-in and thus should be preferred for clarity and succinctness, but newer Python developers may need time to familiarize themselves with these properties.**Method 4: Inspecting the closed Attribute:**Checking the`closed`

attribute is an explicit way to determine interval openness, providing a good balance of clarity and expressiveness. Its disadvantage lies in remembering the possible values of the ‘closed’ attribute.**Bonus One-Liner Method 5:**The lambda function provides a compact solution that could be useful for inline checks without creating extra variables. However, it sacrifices some readability, especially for those who may not be familiar with lambda functions.