matrix assignment in python

Nick McCullum

Software Developer & Professional Explainer

NumPy Indexing and Assignment

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In this lesson, we will explore indexing and assignment in NumPy arrays.

The Array I'll Be Using In This Lesson

As before, I will be using a specific array through this lesson. This time it will be generated using the np.random.rand method. Here's how I generated the array:

Here is the actual array:

To make this array easier to look at, I will round every element of the array to 2 decimal places using NumPy's round method:

Here's the new array:

How To Return A Specific Element From A NumPy Array

We can select (and return) a specific element from a NumPy array in the same way that we could using a normal Python list: using square brackets.

An example is below:

We can also reference multiple elements of a NumPy array using the colon operator. For example, the index [2:] selects every element from index 2 onwards. The index [:3] selects every element up to and excluding index 3. The index [2:4] returns every element from index 2 to index 4, excluding index 4. The higher endpoint is always excluded.

A few example of indexing using the colon operator are below.

Element Assignment in NumPy Arrays

We can assign new values to an element of a NumPy array using the = operator, just like regular python lists. A few examples are below (note that this is all one code block, which means that the element assignments are carried forward from step to step).

arr[2:5] = 0.5

Returns array([0. , 0. , 0.5, 0.5, 0.5])

As you can see, modifying second_new_array also changed the value of new_array .

Why is this?

By default, NumPy does not create a copy of an array when you reference the original array variable using the = assignment operator. Instead, it simply points the new variable to the old variable, which allows the second variable to make modification to the original variable - even if this is not your intention.

This may seem bizarre, but it does have a logical explanation. The purpose of array referencing is to conserve computing power. When working with large data sets, you would quickly run out of RAM if you created a new array every time you wanted to work with a slice of the array.

Fortunately, there is a workaround to array referencing. You can use the copy method to explicitly copy a NumPy array.

An example of this is below.

As you can see below, making modifications to the copied array does not alter the original.

So far in the lesson, we have only explored how to reference one-dimensional NumPy arrays. We will now explore the indexing of two-dimensional arrays.

Indexing Two-Dimensional NumPy Arrays

To start, let's create a two-dimensional NumPy array named mat :

There are two ways to index a two-dimensional NumPy array:

• mat[row, col]
• mat[row][col]

I personally prefer to index using the mat[row][col] nomenclature because it is easier to visualize in a step-by-step fashion. For example:

You can also generate sub-matrices from a two-dimensional NumPy array using this notation:

Array referencing also applies to two-dimensional arrays in NumPy, so be sure to use the copy method if you want to avoid inadvertently modifying an original array after saving a slice of it into a new variable name.

Conditional Selection Using NumPy Arrays

NumPy arrays support a feature called conditional selection , which allows you to generate a new array of boolean values that state whether each element within the array satisfies a particular if statement.

An example of this is below (I also re-created our original arr variable since its been awhile since we've seen it):

You can also generate a new array of values that satisfy this condition by passing the condition into the square brackets (just like we do for indexing).

An example of this is below:

Conditional selection can become significantly more complex than this. We will explore more examples in this section's associated practice problems.

In this lesson, we explored NumPy array indexing and assignment in thorough detail. We will solidify your knowledge of these concepts further by working through a batch of practice problems in the next section.

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• Introduction
• Introduction to NumPy
• NumPy Array Creation
• NumPy N-d Array Creation
• NumPy Data Types
• NumPy Array Attributes
• NumPy Input Output
• NumPy Array Indexing

NumPy Array Slicing

NumPy Array Reshaping

Array Operations

• NumPy Arithmetic Array Operations

NumPy Array Functions

• NumPy Comparison/Logical Operations
• NumPy Math Functions
• NumPy Constants
• NumPy Statistical Functions
• NumPy String Functions

Advance NumPy Operations

• NumPy Broadcasting
• NumPy Matrix Operations
• NumPy Set Operations
• NumPy Vectorization
• NumPy Boolean Indexing
• NumPy Fancy Indexing

Additional Topics

• NumPy Random
• NumPy Linear Algebra
• NumPy Histogram
• NumPy Interpolation
• NumPy Files
• NumPy Error Handling
• NumPy Date and Time
• NumPy Data Visualization
• NumPy Universal Function

NumPy Tutorials

• NumPy det()
• NumPy matmul()
• NumPy matrix()
• NumPy norm()
• NumPy trace()

Numpy Linear Algebra

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

The above matrix is a 3x3 (pronounced "three by three") matrix because it has 3 rows and 3 columns.

Here are some of the basic matrix operations provided by NumPy.

• Create Matrix in NumPy

In NumPy, we use the np.array() function to create a matrix. For example,

Here, we have created two matrices: 2x2 matrix and 3x3 matrix by passing a list of lists to the np.array() function respectively.

• Perform Matrix Multiplication in NumPy

We use the np.dot() function to perform multiplication between two matrices.

Let's see an example.

In this example, we have used the np.dot(matrix1, matrix2) function to perform matrix multiplication between two matrices: matrix1 and matrix2 .

To learn more about Matrix multiplication, please visit NumPy Matrix Multiplication .

Note : We can only take a dot product of matrices when they have a common dimension size. For example, For A = (M x N) and B = (N x K) when we take a dot product of C = A . B the resulting matrix is of size C = (M x K) .

• Transpose NumPy Matrix

The transpose of a matrix is a new matrix that is obtained by exchanging the rows and columns. For 2x2 matrix,

In NumPy, we can obtain the transpose of a matrix using the np.transpose() function. For example,

Here, we have used the np.transpose(matrix1) function to obtain the transpose of matrix1 .

Note : Alternatively, we can use the .T attribute to get the transpose of a matrix. For example, if we used matrix1.T in our previous example, the result would be the same.

• Calculate Inverse of a Matrix in NumPy

In NumPy, we use the np.linalg.inv() function to calculate the inverse of the given matrix.

However, it is important to note that not all matrices have an inverse. Only square matrices that have a non-zero determinant have an inverse.

Now, let's use np.linalg.inv() to calculate the inverse of a square matrix.

Note : If we try to find the inverse of a non-square matrix, we will get an error message: numpy.linalg.linalgerror: Last 2 dimensions of the array must be square

Find Determinant of a Matrix in NumPy

We can find the determinant of a square matrix using the np.linalg.det() function to calculate the determinant of the given matrix.

Suppose we have a 2x2 matrix A :

So, the determinant of a 2x2 matrix will be:

where a, b, c, and d are the elements of the matrix.

Here, we have used the np.linalg.det(matrix1) function to find the determinant of the square matrix matrix1 .

• Flatten Matrix in NumPy

Flattening a matrix simply means converting a matrix into a 1D array.

To flatten a matrix into a 1-D array we use the array.flatten() function. Let's see an example.

Here, we have used the matrix1.flatten() function to flatten matrix1 into a 1D array, without compromising any of its elements

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Programming

5 Best Ways to Explain Python Matrix with Examples

💡 Problem Formulation: Matrices are fundamental for a multitude of operations in software development, data analysis, and scientific computing. In Python, a matrix can be represented and manipulated in various ways. This article solves the problem of how to create, modify, and perform operations on Python matrices with practical examples. Imagine you want to represent 2D data like pixel values in an image or distances between cities; such tasks require creating and managing a matrix efficiently.

Method 1: Using Nested Lists

In Python, one of the most straightforward ways to represent a matrix is using nested lists. Each inner list represents a row in the matrix, and the elements of these lists are the matrix elements. Accessing, updating, and iterating over these matrices is intuitive and requires no additional libraries.

Here’s an example:

The code snippet creates a 3×3 matrix with nested lists. It then accesses and prints the element on the second row and third column, which is the number 6. This method is easy to understand and works well without additional dependencies, but can become inefficient for large matrices or complex operations.

Method 2: Using NumPy Arrays

NumPy is a powerful library for numerical computing in Python. Its array object is more efficient and convenient for large matrices and supports a wide range of mathematical operations. NumPy arrays are homogeneous, which can lead to better performance compared to nested lists.

This example demonstrates creating a NumPy array to represent a matrix and performing an element-wise addition with another matrix. NumPy arrays offer more efficient storage and better functionality for large-scale operations than lists.

Method 3: Using pandas DataFrame

pandas is another library that’s extremely useful for data analysis, and it provides the DataFrame object which can be thought of as a matrix with more functionality like labeled rows and columns. DataFrames are great for handling tabular data and can be created from lists, dicts, or even reading from files like CSV.

This code snippet creates a 3×3 matrix as a pandas DataFrame with labeled rows and columns. It selects and prints the element from row labeled ‘Y’ and column labeled ‘B’. pandas DataFrames are ideal for complex data manipulation but may be an overkill for simple matrix operations.

Method 4: Using List Comprehensions

List comprehensions provide a concise way to create lists including matrices. They are elegant and can be used to initialize, transform, and even transpose matrices with readable and compact code. List comprehensions are a Pythonic way to operate with matrices represented by lists.

The given code uses a list comprehension to create a 3×3 identity matrix, a matrix with 1s on the diagonal and 0s elsewhere. List comprehensions are a compact and readable method to create matrices, but can become less readable for very complex operations.

Bonus One-Liner Method 5: Using zip() and * Operator

Transposing a matrix, which is flipping it over its diagonal, can be elegantly achieved in Python by using the zip() function in conjunction with the star operator * . This one-liner is very readable and takes advantage of Python’s unpacking feature.

The code takes a 3×2 matrix and transposes it to a 2×3 matrix using the zip() function. The star operator unpacks the rows of the original matrix such that they are passed as separate arguments to zip() , which pairs elements of the same index from these arguments. This is a short and efficient one-liner for transposing matrices but may be less obvious to beginners.

Summary/Discussion

• Method 1: Nested Lists. Easily understandable. Not as efficient for large or complex matrices.
• Method 2: Using NumPy Arrays. Highly efficient and versatile. Requires additional knowledge of NumPy.
• Method 3: Using pandas DataFrames. Great for complex data manipulations with labeled axes. Overly powerful for simple tasks.
• Method 4: List Comprehensions. Elegant and Pythonic. Can become unwieldy for complex operations.
• Bonus Method 5: Using zip() and * Operator. Succinct for transposing. Less intuitive for those unfamiliar with argument unpacking.

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.

How Matrix Work in Python and How to Use Them

December 29, 2021, table of contents, quick access, python: popular features of this language, how to automate the download folder with python, how to connect mongodb database with django.

Before getting into the topic of how to create an NXNXM Matrix in Python , we must define what a Matrix consists of within this popular programming language.

When we talk about Matrix in Python, we are referring to a specialized two-dimensional rectangular array of data, which is stored in rows and columns. Within this matrix, there can be data in the form of numbers, strings, symbols, expressions, etc. The matrix is ​​one of the important data structures that can be used in mathematical and scientific calculations.

How does Matrix work in Python?

The data inside the matrix looks like the one shown in this graph:

First step:

Here a 2x2 matrix is ​​shown, where two rows and two columns are observed. The data within this matrix are presented in the form of numbers, where the values ​​2, 3 are observed in row one and the values ​​4, 5 in row two. In the columns, there is column one with the values ​​3 and 4 and column two with the values ​​3 and 5.

Second step:

A slightly different 2 x 3 matrix is ​​shown with two rows and three columns. The data within the first row has values ​​2, 3, 4 and in the second row, it has values ​​5, 6, 7. The first column has values ​​2.5, the second column has values ​​3.6 and the third column has values 4.7.

Similarly, you can have your data stored inside the nxn Matrix in Python. Many operations can be performed in addition, subtraction, multiplication, etc.

Create a Python Matrix using a nested list data type

In Python, Matrix is represented by the list data type. We are going to teach you how to create a 3x3 matrix using the list.

The matrix is ​​made up of three rows and three columns.

• Row number one within the list format will have the following data: [8,14, -6]
• Row number two will be: [12,7,4]
• Row number three will be: [-11,3,21]

The matrix within a list with all rows and columns can look like this:

List = [[Row1],            [Row2],            [Row3]            ...            [RowN]]

So, according to the above array, the Matrix's direct data list type is as follows:

M1 = [[8, 14, -6], [12,7,4], [-11,3,21]]

How we can read data into a Python Matrix when using a list

We will use the previous matrix. The example will read the data, print the Matrix, display the last element in each row.

Example: to print the matrix

M1 = [[8, 14, -6],            [12,7,4],            [-11.3.21]]

#To print the matrix print (M1)

Production:

The Matrix M1 = [[8, 14, -6], [12, 7, 4], [-11, 3, 21]]

Example 2: Read the last element of each row.

matrix_length = len (M1)

#To read the last element from each row. for i in range (matrix_length):     print (M1 [i] [- 1])

-6 4 twenty-one

Example 3: to print the rows in the matrix

#To print the rows in the Matrix for i in range (matrix_length):     print (M1 [i])

[8, 14, -6] [12, 7, 4] [-11, 3, 21]

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array — Efficient arrays of numeric values ¶

This module defines an object type which can compactly represent an array of basic values: characters, integers, floating point numbers. Arrays are sequence types and behave very much like lists, except that the type of objects stored in them is constrained. The type is specified at object creation time by using a type code , which is a single character. The following type codes are defined:

It can be 16 bits or 32 bits depending on the platform.

Changed in version 3.9: array('u') now uses wchar_t as C type instead of deprecated Py_UNICODE . This change doesn’t affect its behavior because Py_UNICODE is alias of wchar_t since Python 3.3.

Deprecated since version 3.3, will be removed in version 4.0.

The actual representation of values is determined by the machine architecture (strictly speaking, by the C implementation). The actual size can be accessed through the array.itemsize attribute.

The module defines the following item:

A string with all available type codes.

The module defines the following type:

A new array whose items are restricted by typecode , and initialized from the optional initializer value, which must be a bytes or bytearray object, a Unicode string, or iterable over elements of the appropriate type.

If given a bytes or bytearray object, the initializer is passed to the new array’s frombytes() method; if given a Unicode string, the initializer is passed to the fromunicode() method; otherwise, the initializer’s iterator is passed to the extend() method to add initial items to the array.

Array objects support the ordinary sequence operations of indexing, slicing, concatenation, and multiplication. When using slice assignment, the assigned value must be an array object with the same type code; in all other cases, TypeError is raised. Array objects also implement the buffer interface, and may be used wherever bytes-like objects are supported.

Raises an auditing event array.__new__ with arguments typecode , initializer .

The typecode character used to create the array.

The length in bytes of one array item in the internal representation.

Append a new item with value x to the end of the array.

Return a tuple (address, length) giving the current memory address and the length in elements of the buffer used to hold array’s contents. The size of the memory buffer in bytes can be computed as array.buffer_info()[1] * array.itemsize . This is occasionally useful when working with low-level (and inherently unsafe) I/O interfaces that require memory addresses, such as certain ioctl() operations. The returned numbers are valid as long as the array exists and no length-changing operations are applied to it.

When using array objects from code written in C or C++ (the only way to effectively make use of this information), it makes more sense to use the buffer interface supported by array objects. This method is maintained for backward compatibility and should be avoided in new code. The buffer interface is documented in Buffer Protocol .

“Byteswap” all items of the array. This is only supported for values which are 1, 2, 4, or 8 bytes in size; for other types of values, RuntimeError is raised. It is useful when reading data from a file written on a machine with a different byte order.

Return the number of occurrences of x in the array.

Append items from iterable to the end of the array. If iterable is another array, it must have exactly the same type code; if not, TypeError will be raised. If iterable is not an array, it must be iterable and its elements must be the right type to be appended to the array.

Appends items from the bytes-like object , interpreting its content as an array of machine values (as if it had been read from a file using the fromfile() method).

Added in version 3.2: fromstring() is renamed to frombytes() for clarity.

Read n items (as machine values) from the file object f and append them to the end of the array. If less than n items are available, EOFError is raised, but the items that were available are still inserted into the array.

Append items from the list. This is equivalent to for x in list: a.append(x) except that if there is a type error, the array is unchanged.

Extends this array with data from the given Unicode string. The array must have type code 'u' ; otherwise a ValueError is raised. Use array.frombytes(unicodestring.encode(enc)) to append Unicode data to an array of some other type.

Return the smallest i such that i is the index of the first occurrence of x in the array. The optional arguments start and stop can be specified to search for x within a subsection of the array. Raise ValueError if x is not found.

Changed in version 3.10: Added optional start and stop parameters.

Insert a new item with value x in the array before position i . Negative values are treated as being relative to the end of the array.

Removes the item with the index i from the array and returns it. The optional argument defaults to -1 , so that by default the last item is removed and returned.

Remove the first occurrence of x from the array.

Reverse the order of the items in the array.

Convert the array to an array of machine values and return the bytes representation (the same sequence of bytes that would be written to a file by the tofile() method.)

Added in version 3.2: tostring() is renamed to tobytes() for clarity.

Write all items (as machine values) to the file object f .

Convert the array to an ordinary list with the same items.

Convert the array to a Unicode string. The array must have a type 'u' ; otherwise a ValueError is raised. Use array.tobytes().decode(enc) to obtain a Unicode string from an array of some other type.

The string representation of array objects has the form array(typecode, initializer) . The initializer is omitted if the array is empty, otherwise it is a Unicode string if the typecode is 'u' , otherwise it is a list of numbers. The string representation is guaranteed to be able to be converted back to an array with the same type and value using eval() , so long as the array class has been imported using from array import array . Variables inf and nan must also be defined if it contains corresponding floating point values. Examples:

Packing and unpacking of heterogeneous binary data.

Packing and unpacking of External Data Representation (XDR) data as used in some remote procedure call systems.

The NumPy package defines another array type.

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Solving Assignment Problem using Linear Programming in Python

Learn how to use Python PuLP to solve Assignment problems using Linear Programming.

In earlier articles, we have seen various applications of Linear programming such as transportation, transshipment problem, Cargo Loading problem, and shift-scheduling problem. Now In this tutorial, we will focus on another model that comes under the class of linear programming model known as the Assignment problem. Its objective function is similar to transportation problems. Here we minimize the objective function time or cost of manufacturing the products by allocating one job to one machine.

If we want to solve the maximization problem assignment problem then we subtract all the elements of the matrix from the highest element in the matrix or multiply the entire matrix by –1 and continue with the procedure. For solving the assignment problem, we use the Assignment technique or Hungarian method, or Flood’s technique.

The transportation problem is a special case of the linear programming model and the assignment problem is a special case of transportation problem, therefore it is also a special case of the linear programming problem.

In this tutorial, we are going to cover the following topics:

Assignment Problem

A problem that requires pairing two sets of items given a set of paired costs or profit in such a way that the total cost of the pairings is minimized or maximized. The assignment problem is a special case of linear programming.

For example, an operation manager needs to assign four jobs to four machines. The project manager needs to assign four projects to four staff members. Similarly, the marketing manager needs to assign the 4 salespersons to 4 territories. The manager’s goal is to minimize the total time or cost.

Problem Formulation

A manager has prepared a table that shows the cost of performing each of four jobs by each of four employees. The manager has stated his goal is to develop a set of job assignments that will minimize the total cost of getting all 4 jobs.  

Initialize LP Model

In this step, we will import all the classes and functions of pulp module and create a Minimization LP problem using LpProblem class.

Define Decision Variable

In this step, we will define the decision variables. In our problem, we have two variable lists: workers and jobs. Let’s create them using  LpVariable.dicts()  class.  LpVariable.dicts()  used with Python’s list comprehension.  LpVariable.dicts()  will take the following four values:

• First, prefix name of what this variable represents.
• Second is the list of all the variables.
• Third is the lower bound on this variable.
• Fourth variable is the upper bound.
• Fourth is essentially the type of data (discrete or continuous). The options for the fourth parameter are  LpContinuous  or  LpInteger .

Let’s first create a list route for the route between warehouse and project site and create the decision variables using LpVariable.dicts() the method.

Define Objective Function

In this step, we will define the minimum objective function by adding it to the LpProblem  object. lpSum(vector)is used here to define multiple linear expressions. It also used list comprehension to add multiple variables.

Define the Constraints

Here, we are adding two types of constraints: Each job can be assigned to only one employee constraint and Each employee can be assigned to only one job. We have added the 2 constraints defined in the problem by adding them to the LpProblem  object.

Solve Model

In this step, we will solve the LP problem by calling solve() method. We can print the final value by using the following for loop.

From the above results, we can infer that Worker-1 will be assigned to Job-1, Worker-2 will be assigned to job-3, Worker-3 will be assigned to Job-2, and Worker-4 will assign with job-4.

In this article, we have learned about Assignment problems, Problem Formulation, and implementation using the python PuLp library. We have solved the Assignment problem using a Linear programming problem in Python. Of course, this is just a simple case study, we can add more constraints to it and make it more complicated. You can also run other case studies on Cargo Loading problems , Staff scheduling problems . In upcoming articles, we will write more on different optimization problems such as transshipment problem, balanced diet problem. You can revise the basics of mathematical concepts in  this article  and learn about Linear Programming  in this article .

• Solving Blending Problem in Python using Gurobi
• Transshipment Problem in Python Using PuLP

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scipy.optimize.linear_sum_assignment ¶

Solve the linear sum assignment problem.

The linear sum assignment problem is also known as minimum weight matching in bipartite graphs. A problem instance is described by a matrix C, where each C[i,j] is the cost of matching vertex i of the first partite set (a “worker”) and vertex j of the second set (a “job”). The goal is to find a complete assignment of workers to jobs of minimal cost.

Formally, let X be a boolean matrix where \(X[i,j] = 1\) iff row i is assigned to column j. Then the optimal assignment has cost

s.t. each row is assignment to at most one column, and each column to at most one row.

This function can also solve a generalization of the classic assignment problem where the cost matrix is rectangular. If it has more rows than columns, then not every row needs to be assigned to a column, and vice versa.

The method used is the Hungarian algorithm, also known as the Munkres or Kuhn-Munkres algorithm.

New in version 0.17.0.

• http://csclab.murraystate.edu/bob.pilgrim/445/munkres.html
• Harold W. Kuhn. The Hungarian Method for the assignment problem. Naval Research Logistics Quarterly , 2:83-97, 1955.
• Harold W. Kuhn. Variants of the Hungarian method for assignment problems. Naval Research Logistics Quarterly , 3: 253-258, 1956.
• Munkres, J. Algorithms for the Assignment and Transportation Problems. J. SIAM , 5(1):32-38, March, 1957.
• https://en.wikipedia.org/wiki/Hungarian_algorithm

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Python Tutorial

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Note: Python does not have built-in support for Arrays, but Python Lists can be used instead.

Note: This page shows you how to use LISTS as ARRAYS, however, to work with arrays in Python you will have to import a library, like the NumPy library .

Arrays are used to store multiple values in one single variable:

Create an array containing car names:

What is an Array?

An array is a special variable, which can hold more than one value at a time.

If you have a list of items (a list of car names, for example), storing the cars in single variables could look like this:

However, what if you want to loop through the cars and find a specific one? And what if you had not 3 cars, but 300?

The solution is an array!

An array can hold many values under a single name, and you can access the values by referring to an index number.

Access the Elements of an Array

You refer to an array element by referring to the index number .

Get the value of the first array item:

Modify the value of the first array item:

The Length of an Array

Use the len() method to return the length of an array (the number of elements in an array).

Return the number of elements in the cars array:

Note: The length of an array is always one more than the highest array index.

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Looping Array Elements

You can use the for in loop to loop through all the elements of an array.

Print each item in the cars array:

Adding Array Elements

You can use the append() method to add an element to an array.

Add one more element to the cars array:

Removing Array Elements

You can use the pop() method to remove an element from the array.

Delete the second element of the cars array:

You can also use the remove() method to remove an element from the array.

Delete the element that has the value "Volvo":

Note: The list's remove() method only removes the first occurrence of the specified value.

Array Methods

Python has a set of built-in methods that you can use on lists/arrays.

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• Walrus Operator in Python 3.8
• Increment += and Decrement -= Assignment Operators in Python
• Merging and Updating Dictionary Operators in Python 3.9
• New '=' Operator in Python3.8 f-string

Python Relational Operators

• Comparison Operators in Python
• Python NOT EQUAL operator
• Difference between == and is operator in Python
• Chaining comparison operators in Python
• Python Membership and Identity Operators
• Difference between != and is not operator in Python

In Python programming, Operators in general are used to perform operations on values and variables. These are standard symbols used for logical and arithmetic operations. In this article, we will look into different types of Python operators. 

• OPERATORS: These are the special symbols. Eg- + , * , /, etc.
• OPERAND: It is the value on which the operator is applied.

Types of Operators in Python

• Arithmetic Operators
• Comparison Operators
• Logical Operators
• Bitwise Operators
• Assignment Operators
• Identity Operators and Membership Operators

Arithmetic Operators in Python

Python Arithmetic operators are used to perform basic mathematical operations like addition, subtraction, multiplication , and division .

In Python 3.x the result of division is a floating-point while in Python 2.x division of 2 integers was an integer. To obtain an integer result in Python 3.x floored (// integer) is used.

Example of Arithmetic Operators in Python

Division operators.

In Python programming language Division Operators allow you to divide two numbers and return a quotient, i.e., the first number or number at the left is divided by the second number or number at the right and returns the quotient. 

There are two types of division operators: 

Float division

• Floor division

The quotient returned by this operator is always a float number, no matter if two numbers are integers. For example:

Example: The code performs division operations and prints the results. It demonstrates that both integer and floating-point divisions return accurate results. For example, ’10/2′ results in ‘5.0’ , and ‘-10/2’ results in ‘-5.0’ .

Integer division( Floor division)

The quotient returned by this operator is dependent on the argument being passed. If any of the numbers is float, it returns output in float. It is also known as Floor division because, if any number is negative, then the output will be floored. For example:

Example: The code demonstrates integer (floor) division operations using the // in Python operators . It provides results as follows: ’10//3′ equals ‘3’ , ‘-5//2’ equals ‘-3’ , ‘ 5.0//2′ equals ‘2.0’ , and ‘-5.0//2’ equals ‘-3.0’ . Integer division returns the largest integer less than or equal to the division result.

Precedence of Arithmetic Operators in Python

The precedence of Arithmetic Operators in Python is as follows:

• P – Parentheses
• E – Exponentiation
• M – Multiplication (Multiplication and division have the same precedence)
• D – Division
• A – Addition (Addition and subtraction have the same precedence)
• S – Subtraction

The modulus of Python operators helps us extract the last digit/s of a number. For example:

• x % 10 -> yields the last digit
• x % 100 -> yield last two digits

Arithmetic Operators With Addition, Subtraction, Multiplication, Modulo and Power

Here is an example showing how different Arithmetic Operators in Python work:

Example: The code performs basic arithmetic operations with the values of ‘a’ and ‘b’ . It adds (‘+’) , subtracts (‘-‘) , multiplies (‘*’) , computes the remainder (‘%’) , and raises a to the power of ‘b (**)’ . The results of these operations are printed.

Note: Refer to Differences between / and // for some interesting facts about these two Python operators.

Comparison of Python Operators

In Python Comparison of Relational operators compares the values. It either returns True or False according to the condition.

= is an assignment operator and == comparison operator.

Precedence of Comparison Operators in Python

In Python, the comparison operators have lower precedence than the arithmetic operators. All the operators within comparison operators have the same precedence order.

Example of Comparison Operators in Python

Let’s see an example of Comparison Operators in Python.

Example: The code compares the values of ‘a’ and ‘b’ using various comparison Python operators and prints the results. It checks if ‘a’ is greater than, less than, equal to, not equal to, greater than, or equal to, and less than or equal to ‘b’ .

Logical Operators in Python

Python Logical operators perform Logical AND , Logical OR , and Logical NOT operations. It is used to combine conditional statements.

Precedence of Logical Operators in Python

The precedence of Logical Operators in Python is as follows:

• Logical not
• logical and

Example of Logical Operators in Python

The following code shows how to implement Logical Operators in Python:

Example: The code performs logical operations with Boolean values. It checks if both ‘a’ and ‘b’ are true ( ‘and’ ), if at least one of them is true ( ‘or’ ), and negates the value of ‘a’ using ‘not’ . The results are printed accordingly.

Bitwise Operators in Python

Python Bitwise operators act on bits and perform bit-by-bit operations. These are used to operate on binary numbers.

Precedence of Bitwise Operators in Python

The precedence of Bitwise Operators in Python is as follows:

• Bitwise NOT
• Bitwise Shift
• Bitwise AND
• Bitwise XOR

Here is an example showing how Bitwise Operators in Python work:

Example: The code demonstrates various bitwise operations with the values of ‘a’ and ‘b’ . It performs bitwise AND (&) , OR (|) , NOT (~) , XOR (^) , right shift (>>) , and left shift (<<) operations and prints the results. These operations manipulate the binary representations of the numbers.

Python Assignment operators are used to assign values to the variables.

Let’s see an example of Assignment Operators in Python.

Example: The code starts with ‘a’ and ‘b’ both having the value 10. It then performs a series of operations: addition, subtraction, multiplication, and a left shift operation on ‘b’ . The results of each operation are printed, showing the impact of these operations on the value of ‘b’ .

Identity Operators in Python

In Python, is and is not are the identity operators both are used to check if two values are located on the same part of the memory. Two variables that are equal do not imply that they are identical. 

Example Identity Operators in Python

Let’s see an example of Identity Operators in Python.

Example: The code uses identity operators to compare variables in Python. It checks if ‘a’ is not the same object as ‘b’ (which is true because they have different values) and if ‘a’ is the same object as ‘c’ (which is true because ‘c’ was assigned the value of ‘a’ ).

Membership Operators in Python

In Python, in and not in are the membership operators that are used to test whether a value or variable is in a sequence.

Examples of Membership Operators in Python

The following code shows how to implement Membership Operators in Python:

Example: The code checks for the presence of values ‘x’ and ‘y’ in the list. It prints whether or not each value is present in the list. ‘x’ is not in the list, and ‘y’ is present, as indicated by the printed messages. The code uses the ‘in’ and ‘not in’ Python operators to perform these checks.

in Python, Ternary operators also known as conditional expressions are operators that evaluate something based on a condition being true or false. It was added to Python in version 2.5. 

It simply allows testing a condition in a single line replacing the multiline if-else making the code compact.

Syntax :   [on_true] if [expression] else [on_false] 

Examples of Ternary Operator in Python

The code assigns values to variables ‘a’ and ‘b’ (10 and 20, respectively). It then uses a conditional assignment to determine the smaller of the two values and assigns it to the variable ‘min’ . Finally, it prints the value of ‘min’ , which is 10 in this case.

In Python, Operator precedence and associativity determine the priorities of the operator.

Operator Precedence in Python

This is used in an expression with more than one operator with different precedence to determine which operation to perform first.

Let’s see an example of how Operator Precedence in Python works:

Example: The code first calculates and prints the value of the expression 10 + 20 * 30 , which is 610. Then, it checks a condition based on the values of the ‘name’ and ‘age’ variables. Since the name is “ Alex” and the condition is satisfied using the or operator, it prints “Hello! Welcome.”

Operator Associativity in Python

If an expression contains two or more operators with the same precedence then Operator Associativity is used to determine. It can either be Left to Right or from Right to Left.

The following code shows how Operator Associativity in Python works:

Example: The code showcases various mathematical operations. It calculates and prints the results of division and multiplication, addition and subtraction, subtraction within parentheses, and exponentiation. The code illustrates different mathematical calculations and their outcomes.

To try your knowledge of Python Operators, you can take out the quiz on Operators in Python . 

Python Operator Exercise Questions

Below are two Exercise Questions on Python Operators. We have covered arithmetic operators and comparison operators in these exercise questions. For more exercises on Python Operators visit the page mentioned below.

Q1. Code to implement basic arithmetic operations on integers

Q2. Code to implement Comparison operations on integers

Explore more Exercises: Practice Exercise on Operators in Python

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When we build features with AI models on the web, we often rely on server-side solutions for larger models. This is especially true for generative AI, where even the smallest models are about thousand times bigger than the median web page size . It's also true for other AI use cases, where models can range from 10s to 100s of megabytes.

Since these models aren't shared across websites , each site has to download them on page load. This is an impractical solution for developers and users

While server-side AI is a great option for large models, on-device and hybrid approaches have their own compelling upsides . To make these approaches viable, we need to address model size and model delivery.

That's why we're developing web platform APIs and browser features designed to integrate AI models, including large language models (LLMs), directly into the browser. This includes Gemini Nano , the most efficient version of the Gemini family of LLMs, designed to run locally on most modern desktop and laptop computers. With built-in AI, your website or web application can perform AI-powered tasks without needing to deploy or manage its own AI models.

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Benefits of built-in AI for web developers

With built-in AI, your browser provides and manages foundation and expert models.

As compared to do it yourself on-device AI, built-in AI offers the following benefits:

• Ease of deployment : As the browser distributes the models, it takes into account the capability of the device and manages updates to the model. This means you aren't responsible for downloading or updating large models over a network. You don't have to solve for storage eviction, runtime memory budget, serving costs, and other challenges.
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Benefits of running on-device

With a built-in AI approach, it becomes trivial to perform AI tasks on-device, which in turn offers the following upsides:

• Local processing of sensitive data : On-device AI can improve your privacy story. For example, if you work with sensitive data, you can offer AI features to users with end-to-end encryption.
• Snappy user experience : In some cases, ditching the round trip to the server means you can offer near-instant results. On-device AI can be the difference between a viable feature and a sub-optimal user experience.
• Greater access to AI : Your users' devices can shoulder some of the processing load in exchange for more access to features. For example, if you offer premium AI features, you could preview these features with on-device AI so that potential customers can see the benefits of your product, without additional cost to you. This hybrid approach can also help you manage inference costs especially on frequently used user flows.
• Offline AI usage : Your users can access AI features even when there is no internet connection. This means your sites and web apps can work as expected offline or with variable connectivity.

Hybrid AI: On-device and server-side

While on-device AI can handle a large array of use cases, there are certain use cases which require server-side support.

For example, you may need to use larger models or support a wider range of platforms and devices.

You may consider hybrid approaches, dependent on:

• Complexity: Specific, approachable use cases are easier to support with on-device AI. For complex use cases, consider server-side implementation.
• Resiliency : Use server-side by default, and use on-device when the device is offline or on a spotty connection.
• Graceful fallback : Adoption of browsers with built-in AI will take time, some models may be unavailable, and older or less powerful devices may not meet the hardware requirements for running all models optimally. Offer server-side AI for those users.

For Gemini models, you can use backend integration (with Python , Go , Node.js , or REST ) or implement in your web application with the new Google AI client SDK for Web .

Browser architecture and APIs

To support built-in AI in Chrome, we created infrastructure to access foundation and expert models for on-device execution. This infrastructure is already powering innovative browser features, such as Help me write , and will soon power APIs for on-device AI.

You'll access built-in AI capabilities primarily with task APIs, such as a translation API or a summarization API. Task APIs are designed to run inference against the best model for the assignment.

In Chrome, these APIs are built to run inference against Gemini Nano with fine-tuning or an expert model. Designed to run locally on most modern devices, Gemini Nano is best for language-related use cases, such as summarization, rephrasing, or categorization.

Also, we intend to provide exploratory APIs, so that you can experiment locally and share additional use cases.

For example, we may provide:

• Prompt API : Send an arbitrary task, expressed in natural language, to the built-in Large Language Model (Gemini Nano in Chrome).
• Fine-tuning (LoRA) API : Improve the built-in LLM's performance on a task by adjusting the model's weights with Low-Rank Adaptation fine tuning.

When to use built-in AI

Here are a few ways we expect built-in AI can benefit you and your users:

• AI-enhanced content consumption : Including summarization, translation , answering questions about some content, categorization, and characterizing.
• AI-supported content creation : Such as writing assistance, proofreading, grammar correction, and rephrasing.

What's next

Join our early preview program to experiment with early-stage built-in AI APIs.

In the meantime, you can learn how to use Gemini Pro on Google's servers with your websites and web apps in our quickstart for the Google AI JavaScript SDK .

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Last updated 2024-05-14 UTC.