Python Functions

by | Dec 18, 2021 | Python

Let’s say we are given a list of numbers and we want to find out whether the numbers are prime numbers. We can check the primality of a number n easily. We can take all numbers from 1 to n and divide n with the number. In other words, we can find out all the factors of the number n. If n has only two factors 1 and n, then n is a prime number.

n = 21
for i in range(2, n):
        if n % i == 0:
            print(“The number is a composite number”)
        else:
            continue
else:
    print(“The number is a prime number”)

Here, n is a given number. The for loop iterates through 2 to (n – 1). If any number between 2 to (n – 1) divides n, then that number is a factor of n and hence, n is a composite number. If the number does not divide n, then we are using the continue statement to stop the current iteration and continue with the next iteration. If no number from 2 to (n – 1) divides n, then the loop completes execution, and the else statement is executed and the program prints the number is a prime number.

Now, let’s say we are given several numbers and we need to check the primality of each number from different parts of the code. One way to do it is to write repeated loops. But, that will not be very convenient and we need to make a program modular also. So, the best option is to use a Python function.

We can write a block of code within a Python function and then call the function. The block of code will be executed each time the function is called. We can also call a function with different arguments each time. For example, in the above example, we can write a Python function with the above piece of code and call the function each time with a different value of n.

Facebooktwitterredditpinterestlinkedinmail

Calculate the pseudoinverse of a matrix using Python

What is the pseudoinverse of a matrix? We know that if A is a square matrix with full rank, then A-1 is said to be the inverse of A if the following condition holds: $latex AA^{-1}=A^{-1}A=I $ The pseudoinverse or the Moore-Penrose inverse of a matrix is a...

Cholesky decomposition using Python

What is Cholesky decomposition? A square matrix A is said to have Cholesky decomposition if it can be written as a product of a lower triangular matrix and its conjugate transpose. $latex A=LL^{*} $ If all the entries of A are real numbers, then the conjugate...

Tensor Hadamard Product using Python

In one of our previous articles, we already discussed what the Hadamard product in linear algebra is. We discussed that if A and B are two matrices of size mxn, then the Hadamard product of A and B is another mxn matrix C such that: $latex H_{i,j}=A_{i,j} \times...

Perform tensor addition and subtraction using Python

We can use numpy nd-array to create a tensor in Python. We can use the following Python code to perform tensor addition and subtraction. import numpy A = numpy.random.randint(low=1, high=10, size=(3, 3, 3)) B = numpy.random.randint(low=1, high=10, size=(3, 3, 3)) C =...

How to create a tensor using Python?

What is a tensor? A tensor is a generalization of vectors and matrices. It is easily understood as a multidimensional array. For example, in machine learning, we can organize data in an m-way array and refer it as a data tensor. Data related to images, sounds, movies,...

How to combine NumPy arrays using horizontal stack?

We can use the hstack() function from the numpy module to combine two or more NumPy arrays horizontally. For example, we can use the following Python code to combine three NumPy arrays horizontally. import numpy A = numpy.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) B =...

How to combine NumPy arrays using vertical stack?

Let’s say we have two or more NumPy arrays. We can combine these NumPy arrays vertically using the vstack() function from the numpy module. For example, we can use the following Python code to combine three NumPy arrays vertically. import numpy A = numpy.array([[1, 2,...

Singular Value Decomposition (SVD) using Python

What is Singular Value Decomposition (SVD)? Let A be an mxn rectangular matrix. Using Singular Value Decomposition (SVD), we can decompose the matrix A in the following way: $latex A_{m \times n}=U_{m \times m}S_{m \times n}V_{n \times n}^T $ Here, U is an mxm matrix....

Eigen decomposition of a square matrix using Python

Let A be a square matrix. Let’s say A has k eigenvalues λ1, λ2, ... λk. And the corresponding eigenvectors are X1, X2, ... Xk. $latex X_1=\begin{bmatrix} x_{11} \\ x_{21} \\ x_{31} \\ ... \\ x_{k1} \end{bmatrix} \\ X_2=\begin{bmatrix} x_{12} \\ x_{22} \\ x_{32} \\ ......

How to calculate eigenvalues and eigenvectors using Python?

In our previous article, we discussed what eigen values and eigenvectors of a square matrix are and how we can calculate the eigenvalues and eigenvectors of a square matrix mathematically. We discussed that if A is a square matrix, then $latex (A- \lambda I) \vec{u}=0...

Amrita Mitra

Author

Ms. Amrita Mitra is an author, who has authored the books “Cryptography And Public Key Infrastructure“, “Web Application Vulnerabilities And Prevention“, “A Guide To Cyber Security” and “Phishing: Detection, Analysis And Prevention“. She is also the founder of Asigosec Technologies, the company that owns The Security Buddy.

0 Comments

Submit a Comment

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Not a premium member yet?

Please follow the link below to buy The Security Buddy Premium Membership.

Featured Posts

Translate »