We can calculate the magnitude of the vector and magnitude of complex numbers in Python using Numpy. There are different functions available to calculate the magnitude of a vector. Here we are using only three different ways and abs() to calculate the magnitude of the complex number.
Using Numpy functions, it is easy to calculate the magnitude in Python. To find the magnitude of the vector, we need to calculate the length of the vector. So we can say that here we are going to calculate the length of the given vector. To find the magnitude of the complex number, we are using the “abs” method.
How to get the magnitude of a complex number?
Let us first know how to declare the complex number. There are two possible ways to declare a complex number.
a=4+3i
In the above method, 4 is a real part, and 3 is an imaginary part.
We can also declare the complex numbers in another way. By declaring it as a complex and giving real part and imaginary part as a parameter.
a=complex(4,3)
This is another method to declare complex numbers.
Here we will use the abs() function to calculate the magnitude of a given complex number.
What is abs() function?
Python abs() is a built-in function that returns an absolute value of a number. The argument may be an integer, floating number, or complex number. If we give an integer, it returns an integer. If the given is a floating number, it returns a floating number.
What are the syntax, parameter, and return type of a abs() function?
Syntax
The syntax for abs() function is
abs(value)
Parameters
The input value is given to get an absolute value.
Returns
It will return the absolute value for the given number.
| Input | Return value |
| integer | integer |
| float | float |
| complex number | the magnitude of the complex number |
Code
a=complex(5,6) print(complex)
Here we are simply assigning a complex number. A variable “a” holds the complex number. Using abs() function to get the magnitude of a complex number.
Output
7.810249675906654
How to get the magnitude of a vector in numpy?
Finding the length of the vector is known as calculating the magnitude of the vector. We can calculate the magnitude using three different functions. They are, linalg.norm(), numpy.dot(), and numpy.einsum() functions. These are useful functions to calculate the magnitude of a given vector.
What is numpy.linalg.norm()?
In Python, it contains a standard library called Numpy. The Numpy contains many functions. Among them, linalg.norm() is one of the functions used to calculate the magnitude of a vector.
What are the syntax, parameters, and return type of a linalg.norm() function?
Syntax
The syntax for linalg.norm() function is
linalg.norm(x, ord=None, axis=None, keepdims=False)
Parameters
- x : array_like.
- ord : {non-zero, int, inf, -inf, ‘fro’, ‘nuc’}
- axis : {None, int, 2-tuple of ints}
- keepdims : bool
Returns
It returns the magnitude of a given vector.
Code
import numpy as np
a=np.array([1,2,3,4])
magnitude=np.linalg.norm(a)
print("The given vector is:",a)
print("The Magnitude of the given vector is :",magnitude)
First, we need to import the library Numpy. Here we are using linalg.norm to calculate the magnitude of a given vector. A variable “a” holds an array. Using “linalg.norm()” we calculated the magnitude of a vector, and we got the output.
Output
The given vector is: [1 2 3 4] The Magnitude of the given vector is : 5.477225575051661
What is numpy.dot()?
Numpy.dot() is a function used to calculate the dot product of the vector. It is also possible to calculate the magnitude of the given vector. Here we are using numpy.dot() function to calculate the magnitude of the given vector.
What are the syntax, parameters, and return type of numpy.dot() function?
Syntax
The syntax for numpy.dot() is
numpy.dot(a, b, out=None)
Parameters
- a : array_like.
- b : array_like.
- out : ndarray, optional.
Returns
It returns the magnitude of a given array.
Code
import numpy as np
a=np.array([1,2,3,4])
magnitude=np.sqrt(a.dot(a))
print("The given vector is:",a)
print("The Magnitude of the given vector is :",magnitude)
First, we need to import the library Numpy. Here we are using numpy.dot() along with the numpy.sqrt() to calculate the magnitude of a vector. A variable “a” holds an array. Using “numpy.dot()” we calculated the magnitude of the given vector and got the output.
Output
The given vector is: [1 2 3 4] The Magnitude of the given vector is : 5.477225575051661
What is numpy.einsum()?
numpy.einsum() is used to find the Einstein summation convention. If parameters are provided, we can calculate the Einstein summation convention using this function. Here we are using this function as one possible way to calculate the magnitude of the given vector.
What are the syntax, parameters, and return type of numpy.einsum() function?
Syntax
The syntax for numpy.einsum() is
numpy.einsum(subscripts, *operands, out=None, dtype=None, order='K', casting='safe', optimize=False)
Parameters
- subscripts : str.
- operands : list of array_like.
- out ; ndarray
- dtype : {data-type, None}
- order : {‘C’, ‘F’, ‘A’, ‘K’}
- casting : {‘no’, ‘equiv’, ‘safe’, ‘same_kind’, ‘unsafe’}
- optimize : {False, True, ‘greedy’, ‘optimal’}
Returns
It returns the magnitude of a given array.
Code
import numpy as np
a=np.array([1,2,3,4])
magnitude=np.sqrt(np.einsum('i,i',a,a))
print("The given vector is:",a)
print("The Magnitude of the given vector is :",magnitude)
First, we need to import the library Numpy. Here we are using numpy.einsum() along with the numpy.sqrt() to calculate the magnitude of a vector. A variable “a” holds an array. Using “numpy.einsum()” we calculated the magnitude of the given vector and got the output.
Output
The given vector is: [1 2 3 4] The Magnitude of the given vector is : 5.477225575051661
Frequently Asked Questions Related to Numpy Magnitude
The syntax for linalg.norm() function is
linalg.norm(x, ord=None, axis=None, keepdims=False)
2.What is the syntax for numpy.dot() function?
The syntax for numpy.dot() function is
numpy.dot(a, b, out=None)
The syntax for numpy.einsum() function is
numpy.einsum(subscripts, *operands, out=None, dtype=None, order=’K’, casting=’safe’, optimize=False)
linalg.norm() function is used to find the magnitude of a given vector.
linalg.norm(), numpy.dot(), and numpy.einsum() are the functions to calculate the magnitude of the vector.
It is a built-in function available in the python library. It returns an absolute value of a given integer.
The syntax for the abs() function is
abs(value)
The abs() function returns the magnitude of a complex number.
The built-in function abs() available in the Python library is used to calculate the magnitude of a complex number.
Conclusion
We can use those three functions to calculate the magnitude of the given vector. After that, we calculated the magnitude of the given vector. We have to note in this is that all the functions gave the same output as magnitude. Because we gave the same vector as an input. The conclusion is that three functions evaluate the same result only. We can use the abs() function to calculate the magnitude of a complex number.