**π‘ Problem Formulation:** In data processing, we often encounter the task of refining datasets to include only records that meet certain criteria. Specifically, this article tackles filtering rows within a matrix or array where all elements are multiples of a specified value `k`

. If our input is a 2D list where each nested list represents a row, we aim to output a new list with only the rows composed entirely of multiples of `k`

.

## Method 1: Using List Comprehensions with all()

List comprehensions provide a concise way to create lists in Python. This method takes advantage of the `all()`

function which returns `True`

when all elements in the given iterable are true. Here, we apply a list comprehension to filter rows, checking if all elements within a row are multiples of `k`

.

Here’s an example:

matrix = [[2, 4, 6], [3, 9, 12], [8, 16, 24]] k = 4 filtered_matrix = [row for row in matrix if all(x % k == 0 for x in row)] print(filtered_matrix)

Output:

[[8, 16, 24]]

This code snippet creates a new list called `filtered_matrix`

which will only contain rows from the original `matrix`

where every element is a multiple of `k`

. The inner comprehension checks whether each number `x`

in a row is divisible by `k`

without a remainder, effectively filtering out rows that do not satisfy our criteria.

## Method 2: Using filter() Function and a Lambda

The `filter()`

function constructs an iterator from elements of an iterable for which a function returns true. In combination with a lambda function, we can use it to filter rows in a matrix based on our specific condition.

Here’s an example:

matrix = [[2, 4, 6], [3, 9, 12], [8, 16, 24]] k = 4 filtered_matrix = list(filter(lambda row: all(x % k == 0 for x in row), matrix)) print(filtered_matrix)

Output:

[[8, 16, 24]]

In this example, we define a lambda function that checks if all elements in a row are multiples of `k`

. We pass this lambda function to `filter()`

along with the original matrix. This method efficiently discards any row that doesn’t fully satisfy the condition, returning a filtered list of rows.

## Method 3: Using NumPy Library

Python’s NumPy library is highly optimized for numerical computations and can be used to effectively handle multidimensional arrays. We can use the `np.all()`

function and Boolean indexing to filter rows in a NumPy array.

Here’s an example:

import numpy as np matrix = np.array([[2, 4, 6], [3, 9, 12], [8, 16, 24]]) k = 4 filtered_matrix = matrix[np.all(matrix % k == 0, axis=1)] print(filtered_matrix)

Output:

[[ 8 16 24]]

By using NumPy’s `np.all()`

function together with modulus operation, we generate a Boolean array that represents if rows are composed entirely of multiples of `k`

. We then use this Boolean array for indexing our original matrix to yield only the rows that match our criteria.

## Method 4: Using pandas DataFrame

If working with larger datasets, using pandas to manipulate data becomes beneficial. pandas DataFrames offer a convenient structure to apply filtering operations on columnar data. We can use Boolean indexing in pandas to achieve our objective.

Here’s an example:

import pandas as pd df = pd.DataFrame([[2, 4, 6], [3, 9, 12], [8, 16, 24]]) k = 4 filtered_df = df[df.apply(lambda row: all(row % k == 0), axis=1)] print(filtered_df)

Output:

0 1 2 2 8 16 24

Here, we use the `apply()`

method to apply a lambda function across each row. The lambda function utilizes our multiples of `k`

condition, and the resulting Boolean series is then used as a mask to filter the DataFrame, extracting rows that fit our criteria.

## Bonus One-Liner Method 5: The itertools.compress Method

Python’s itertools module provides a `compress()`

function which filters elements from an iterable based on corresponding boolean values in a selectors iterable. We can combine this with a comprehension to filter our rows.

Here’s an example:

from itertools import compress matrix = [[2, 4, 6], [3, 9, 12], [8, 16, 24]] k = 4 selectors = [all(item % k == 0 for item in row) for row in matrix] filtered_matrix = list(compress(matrix, selectors)) print(filtered_matrix)

Output:

[[8, 16, 24]]

This snippet uses list comprehension to create a list of boolean values, `selectors`

, which indicates whether each row meets our filter condition. `itertools.compress()`

uses this list to filter the original `matrix`

, returning rows that are entirely composed of multiples of `k`

.

## Summary/Discussion

**Method 1: List Comprehensions with all()**. Strengths: Readable and Pythonic. Weaknesses: Might not be as fast as NumPy for large datasets.**Method 2: filter() Function with a Lambda**. Strengths: Functional programming approach, lazily evaluated. Weaknesses: Needs conversion to a list, less intuitive than a list comprehension.**Method 3: Using NumPy Library**. Strengths: Fast operation on large datasets, concise syntax. Weaknesses: Additional dependency required, overhead for small datasets.**Method 4: Using pandas DataFrame**. Strengths: Ideal for tabular data, integrates with pandas’ ecosystem. Weaknesses: Overhead for learning pandas, not necessary for simple tasks.**Bonus Method 5: itertools.compress Method**. Strengths: Combines iterator-based filtering with list comprehensions’ expressiveness. Weaknesses: Somewhat obscure, not commonly used for this purpose.