**π‘ Problem Formulation:** When working with continuous data in Python Pandas, we may often need to create intervals and retrieve specific endpoints. This article discusses how to construct an `IntervalArray`

from an array of splits and then extract the left endpoints of each resulting interval. For example, given input split points as `[1, 3, 5, 7]`

, we aim to form intervals and retrieve the left endpoints, which in this case would be `[1, 3, 5]`

.

## Method 1: Using Pandas IntervalIndex

This method consists of creating an IntervalIndex from the array of splits and then accessing the `left`

attribute to get the left endpoints. The IntervalIndex is used for indexing and data alignment purposes, making it suitable for creating intervals from split points.

Here’s an example:

import pandas as pd # Array of splits splits = [1, 3, 5, 7] # Create IntervalIndex from splits interval_index = pd.IntervalIndex.from_breaks(splits) # Access the left endpoints left_endpoints = interval_index.left print(left_endpoints)

Output:

Int64Index([1, 3, 5], dtype='int64')

In this snippet, the `from_breaks`

method of the `IntervalIndex`

class is used to convert the split points into a series of intervals. From this, we extract the left endpoints using the `left`

attribute which is made up of the left edges of each interval.

## Method 2: Using the cut function

Pandas `cut`

function can be used to segment and sort data values into bins. This function also returns an `IntervalIndex`

which contains the intervals, and we can proceed similarly to Method 1 to extract the left endpoints.

Here’s an example:

import pandas as pd import numpy as np # Array of values and splits values = np.arange(10) splits = [0, 3, 5, 7] # Use cut to bin the values binned = pd.cut(values, bins=splits) # Extract the left endpoints from the binned object's IntervalIndex left_endpoints = binned.categories.left print(left_endpoints)

Output:

Float64Index([0.0, 3.0, 5.0], dtype='float64')

Here, `cut`

is used to bin the values in the range from 0 to 9 into intervals determined by the split points. The resulting binned object contains an `IntervalIndex`

. To extract the left endpoints, we access the `categories.left`

property of this binned object.

## Method 3: List Comprehension and Manual Interval Creation

In scenarios where you need more control over interval creation, you can manually create intervals using list comprehension. This method does not rely on Pandas and instead uses basic Python functionality.

Here’s an example:

splits = [1, 3, 5, 7] # Manually create intervals and extract the left endpoints left_endpoints = [splits[i] for i in range(len(splits)-1)] print(left_endpoints)

Output:

[1, 3, 5]

The code defines a list of split points and then generates a new list containing just the left endpoints (i.e., every split point except the last one). This approach is less sophisticated but offers simplicity and full control over interval creation.

## Method 4: Using IntervalArray directly

Pandas provides the `IntervalArray`

class which is a more direct way to handle intervals. After creating an `IntervalArray`

, you can directly access its `left`

attribute to get the left endpoints.

Here’s an example:

import pandas as pd # Array of splits splits = [1, 3, 5, 7] # Create an IntervalArray from splits interval_array = pd.IntervalIndex.from_breaks(splits).to_numpy() # Access the left endpoints left_endpoints = interval_array.left print(left_endpoints)

Output:

array([1, 3, 5])

This snippet first constructs an IntervalArray from an array of splits, then retrieves the left endpoints by accessing the `left`

attribute. This is a straightforward method when working exclusively with interval operations within Pandas.

## Bonus One-Liner Method 5: Using NumPy

A one-liner solution can be crafted using NumPy, ignoring the label-based features of Pandas altogether if you only need numerical results.

Here’s an example:

import numpy as np # Array of splits splits = np.array([1, 3, 5, 7]) # Extract the left endpoints in a one-liner left_endpoints = splits[:-1] print(left_endpoints)

Output:

[1 3 5]

This line is using NumPy’s slicing functionality to discard the last element of the array, effectively collecting the left endpoints of the intervals defined by the split points. This is the simplest and fastest approach for numerical arrays.

## Summary/Discussion

**Method 1:**IntervalIndex from_breaks. Good for creating intervals from ordered splits. May be overkill if only the endpoints are needed.**Method 2:**cut function. Useful for data binning and categorization, besides extracting endpoints. Requires understanding of Pandas categorization.**Method 3:**List comprehension. Straightforward approach for simple cases. Lacks advanced Pandas features.**Method 4:**Direct IntervalArray. Pandas-centric method, provides direct access to interval features. May require additional conversions for non-Pandas uses.**Method 5:**NumPy slicing. One-liner, very efficient for numerical computations. Best when you do not need label-based indexing.