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Python Matrices and NumPy Arrays

A matrix is a two-dimensional data structure where numbers are arranged into rows and columns. For example:

This matrix is a 3x4 (pronounced "three by four") matrix because it has 3 rows and 4 columns.

• Python Matrix

Python doesn't have a built-in type for matrices. However, we can treat a list of a list as a matrix. For example:

We can treat this list of a list as a matrix having 2 rows and 3 columns.

Be sure to learn about Python lists before proceed this article.

Let's see how to work with a nested list.

When we run the program, the output will be:

Here are few more examples related to Python matrices using nested lists.

• Add two matrices
• Transpose a Matrix
• Multiply two matrices

Using nested lists as a matrix works for simple computational tasks, however, there is a better way of working with matrices in Python using NumPy package.

• NumPy Array

NumPy is a package for scientific computing which has support for a powerful N-dimensional array object. Before you can use NumPy, you need to install it. For more info,

• Visit: How to install NumPy?
• If you are on Windows, download and install anaconda distribution of Python. It comes with NumPy and other several packages related to data science and machine learning.

Once NumPy is installed, you can import and use it.

NumPy provides multidimensional array of numbers (which is actually an object). Let's take an example:

As you can see, NumPy's array class is called ndarray .

How to create a NumPy array?

There are several ways to create NumPy arrays.

1. Array of integers, floats and complex Numbers

When you run the program, the output will be:

2. Array of zeros and ones

Here, we have specified dtype to 32 bits (4 bytes). Hence, this array can take values from -2 -31 to 2 -31 -1 .

3. Using arange() and shape()

Learn more about other ways of creating a NumPy array .

Matrix Operations

Above, we gave you 3 examples: addition of two matrices, multiplication of two matrices and transpose of a matrix. We used nested lists before to write those programs. Let's see how we can do the same task using NumPy array.

Addition of Two Matrices

We use + operator to add corresponding elements of two NumPy matrices.

Multiplication of Two Matrices

To multiply two matrices, we use dot() method. Learn more about how numpy.dot works.

Note: * is used for array multiplication (multiplication of corresponding elements of two arrays) not matrix multiplication.

Transpose of a Matrix

We use numpy.transpose to compute transpose of a matrix.

As you can see, NumPy made our task much easier.

Access matrix elements, rows and columns

Access matrix elements

Similar like lists, we can access matrix elements using index. Let's start with a one-dimensional NumPy array.

Now, let's see how we can access elements of a two-dimensional array (which is basically a matrix).

Access rows of a Matrix

Access columns of a Matrix

If you don't know how this above code works, read slicing of a matrix section of this article.

Slicing of a Matrix

Slicing of a one-dimensional NumPy array is similar to a list. If you don't know how slicing for a list works, visit Understanding Python's slice notation .

Let's take an example:

Now, let's see how we can slice a matrix.

As you can see, using NumPy (instead of nested lists) makes it a lot easier to work with matrices, and we haven't even scratched the basics. We suggest you to explore NumPy package in detail especially if you trying to use Python for data science/analytics.

NumPy Resources you might find helpful:

• NumPy Tutorial
• NumPy Reference

Table of Contents

• What is a matrix?
• Numbers(integers, float, complex etc.) Array
• Zeros and Ones Array
• Array Using arange() and shape()
• Multiplication
• Access elements
• Access rows
• Access columns
• Slicing of Matrix
• Useful Resources

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5 Best Ways to Find Unique Values in a Python NumPy Array

💡 Problem Formulation: When working with NumPy arrays in Python, a common task is to identify all the unique elements that exist within the array. For instance, given an input array [1, 2, 2, 3, 3, 3, 4, 5, 5, 5] , the desired output is a new array containing the unique values [1, 2, 3, 4, 5] . This article demonstrates five methods to achieve this, each with their own use-case advantages.

Method 1: Using numpy.unique()

NumPy provides a straightforward function numpy.unique() which returns the sorted unique elements of an array. It is the most commonly used method due to its simplicity and efficiency in most situations. The function can also return the indices of the input array that correspond to unique entries.

Here’s an example:

This snippet creates a NumPy array with duplicated values, and then np.unique() is called to extract an array of unique values, which is printed to the console.

Method 2: Combining numpy.unique() with return_counts

Moreover, numpy.unique() can return counts of unique values if the parameter return_counts is set to True . This enables analysis of how often each unique value appears in the array, in addition to obtaining the unique values themselves.

The code produces two arrays, one with unique elements and another with the corresponding counts of each element in the original array.

Method 3: Using numpy.unique() with Multi-dimensional Arrays

For multi-dimensional arrays, numpy.unique() can be used in combination with the axis parameter to find unique rows or columns. By specifying axis=0 or axis=1 , the function returns unique rows or unique columns respectively.

This block of code demonstrates finding unique rows in a 2D array, resulting in an array that holds only the unique rows from the original array.

Method 4: Unique Values using Fancy Indexing

Fancy indexing in NumPy can also be exploited to obtain unique values by manually filtering duplicates through a combination of boolean indexing and sorting. This approach is more complex and less efficient than using numpy.unique() , but offers customizable behavior.

This code first sorts the array, and then constructs a boolean array where each element is True if it is not equal to the next element. The resulting unique array is then obtained using this boolean index.

Bonus One-Liner Method 5: Using Set Comprehension

A Pythonic way outside of NumPy to find unique elements involves using a set comprehension. This one-liner converts the array to a set, which by definition only contains unique elements, but the results will not be a NumPy array unless converted back.

The example converts the NumPy array to a set to filter out duplicate elements, then a list, and back to a NumPy array, resulting in an array of unique values.

Summary/Discussion

• Method 1: numpy.unique() . Strengths: Simple, efficient for flat arrays. Weaknesses: Not specialized for multi-dimensional arrays.
• Method 2: numpy.unique() with return_counts . Strengths: Gets unique values alongside their counts. Weaknesses: Slightly more complex if only unique values are needed.
• Method 3: numpy.unique() with multi-dimensional arrays. Strengths: Able to find unique rows/columns. Weaknesses: More computationally intensive for higher-dimensional data.
• Method 4: Fancy Indexing. Strengths: Highly customizable. Weaknesses: More complex, less efficient.
• Method 5: Set Comprehension. Strengths: Pythonic, one-liner. Weaknesses: Not a native NumPy operation, requires converting back to array.

Emily Rosemary Collins is a tech enthusiast with a strong background in computer science, always staying up-to-date with the latest trends and innovations. Apart from her love for technology, Emily enjoys exploring the great outdoors, participating in local community events, and dedicating her free time to painting and photography. Her interests and passion for personal growth make her an engaging conversationalist and a reliable source of knowledge in the ever-evolving world of technology.

Python Unique List – How to Get all the Unique Values in a List or Array

Say you have a list that contains duplicate numbers:

But you want a list of unique numbers.

There are a few ways to get a list of unique values in Python. This article will show you how.

Option 1 – Using a Set to Get Unique Elements

Using a set one way to go about it. A set is useful because it contains unique elements.

You can use a set to get the unique elements. Then, turn the set into a list.

Let’s look at two approaches that use a set and a list. The first approach is verbose, but it’s useful to see what’s happening each step of the way.

Let’s take a closer look at what’s happening. I’m given a list of numbers, numbers . I pass this list into the function, get_unique_numbers .

Inside the function, I create an empty list, which will eventually hold all of the unique numbers. Then, I use a set to get the unique numbers from the numbers list.

I have what I need: the unique numbers. Now I need to get these values into a list. To do so, I use a for loop to iterate through each number in the set.

On each iteration I add the current number to the list, list_of_unique_numbers . Finally, I return this list at the end of the program.

There’s a shorter way to use a set and list to get unique values in Python. That’s what we’ll tackle next.

A Shorter Approach with Set

All of the code written in the above example can be condensed into one line with the help of Python’s built-in functions.

Although this code looks very different from the first example, the idea is the same. Use a set to get the unique numbers. Then, turn the set into a list.

It’s helpful to think “inside out” when reading the above code. The innermost code gets evaluated first: set(numbers) . Then, the outermost code is evaluated: list(set(numbers)) .

Option 2 – Using Iteration to Identify Unique Values

Iteration is another approach to consider.

The main idea is to create an empty list that’ll hold unique numbers. Then, use a for loop iterate over each number in the given list. If the number is already in the unique list, then continue on to the next iteration. Otherwise, add the number to it.

Let's look at two ways to use iteration to get the unique values in a list, starting with the more verbose one.

Here’s what’s happening each step of the way. First, I’m given a list of numbers, numbers . I pass this list into my function, get_unique_numbers .

Inside the function, I create an empty list, unique . Eventually, this list will hold all of the unique numbers.

I use a for loop to iterate through each number in the numbers list.

The conditional inside the loop checks to see if the number of the current iteration is in the unique list. If so, the loop continues to the next iteration. Otherwise, the number gets added to this list.

Here’s the important point: only the unique numbers are added. Once the loop is complete, then I return unique which contains all of the unique numbers.

A Shorter Approach with Iteration

There’s another way to write the function in fewer lines.

The difference is the conditional. This time it’s set up to read like this: if the number is not in unique , then add it.

Otherwise, the loop will move along to the next number in the list, numbers .

The result is the same. However, it’s sometimes harder to think about and read code when the boolean is negated.

There are other ways to find unique values in a Python list. But you’ll probably find yourself reaching for one of the approaches covered in this article.

I write about learning to program, and the best ways to go about it on amymhaddad.com . Follow me on Twitter: @amymhaddad .

Programmer and writer | howtolearneffectively.com | dailyskillplanner.com

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• Data Structures
• Linked List
• Binary Tree
• Binary Search Tree
• Segment Tree
• Disjoint Set Union
• Fenwick Tree
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• Advanced Data Structures
• Matrix Data Structure
• Introduction to Matrix or Grid Data Structure - Two Dimensional Array
• Row-wise vs column-wise traversal of matrix
• Applications of Matrices and Determinants

Basic Operations on Matrix

• Traverse a given Matrix using Recursion
• Rotate Matrix Elements
• Sort the given matrix
• Search element in a sorted matrix
• Program to find transpose of a matrix
• Adjoint and Inverse of a Matrix
• Determinant of a Matrix

Easy problems on Matrix

• Print matrix in zig-zag fashion
• Program for scalar multiplication of a matrix
• Print a given matrix in spiral form
• Find distinct elements common to all rows of a matrix

Find unique elements in a matrix

• Find maximum element of each row in a matrix
• Shift matrix elements row-wise by k
• Swap major and minor diagonals of a square matrix
• Squares of Matrix Diagonal Elements
• Sum of middle row and column in Matrix
• Program to check idempotent matrix
• Program to check diagonal matrix and scalar matrix
• Program for Identity Matrix
• Mirror of matrix across diagonal
• Program for addition of two matrices
• Program for subtraction of matrices

Intermediate problems on Matrix

• Program for Conway's Game Of Life
• Program to multiply two matrices
• Rotate a matrix by 90 degree without using any extra space | Set 2
• Check if all rows of a matrix are circular rotations of each other
• Given a matrix of 'O' and 'X', find the largest subsquare surrounded by 'X'
• Count zeros in a row wise and column wise sorted matrix
• Queries in a Matrix
• Find pairs with given sum such that elements of pair are in different rows
• Find all permuted rows of a given row in a matrix
• Find number of transformation to make two Matrix Equal
• Inplace (Fixed space) M x N size matrix transpose
• Minimum flip required to make Binary Matrix symmetric
• Magic Square | ODD Order

Hard problems on Matrix

• Find the number of islands using DFS
• A Boolean Matrix Question
• Matrix Chain Multiplication | DP-8
• Maximum size rectangle binary sub-matrix with all 1s
• Construct Ancestor Matrix from a Given Binary Tree
• Print K'th element in spiral form of matrix
• Find size of the largest '+' formed by all ones in a binary matrix
• Shortest path in a Binary Maze
• Print maximum sum square sub-matrix of given size
• Validity of a given Tic-Tac-Toe board configuration
• Minimum Initial Points to Reach Destination
• Program for Sudoku Generator

Given a matrix mat[][] having n rows and m columns. We need to find unique elements in matrix i.e, those elements which are not repeated in the matrix or those elements whose frequency is 1. 

Examples:  

Follow these steps to find a unique element: 

• Create an empty hash table or dictionary. 
• Traverse through all the elements of the matrix 
• If element is present in the dictionary, then increment its count 
• Otherwise insert element with value = 1. 

Implementation:

Complexity Analysis:

• Time Complexity: O(m*n) where m is the number of rows & n is the number of columns.
• Auxiliary Space: O(max(matrix)). 

Method – 2: Using HashMap

This approach uses a hashmap instead of creating a hashtable of size max element + 1.

Implementation

Time Complexity : O(R*C) Auxiliary Space: O(R*C)

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The Unique Matrix In Python Assignment Expert Secret Sauce? Using the Common Python Secret Sauce, You Can Write Simple Code Like This A brief explanation of the Unique Matrix in Python Training One of Python’s awesome features is that it doesn’t have a single unit of it (you actually have twelve); this way, you can keep your program isolated from the rest of the company. One other great feature of Python is the ability to extend some Python code to do other things, such as drawing, using more vectors, and so on. Instead of 1,012 lines, so be careful. People have quite a lot of material involved, and there are countless pages to learn about each one of them, but very little makes sense: some point out some fundamental concepts, create and manipulate abstract object graphs, and so on. Not all of these things are really code, and the way you write these things depends on many factors, like how common they are.

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Answer to Question #210070 in Python for sudheer

Given an MxN matrix filled with

X's and O's, find the largest square containing only X's and return its area. If there are no Xs in the entire matrix print 0.Input

The first line of input will be containing two space-separated integers, denoting M and N.

The next M lines will contain N space-separated integers, denoting the elements of the matrix.

The output should be a single line containing the area of the maximum square.

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