Create your own universal function in NumPy

NumPy ufuncs | Universal functions

Last Updated : 01 Feb, 2024

NumPy Universal functions (ufuncs in short) are simple mathematical functions that operate on ndarray (N-dimensional array) in an element-wise fashion.

It supports array broadcasting, type casting, and several other standard features. NumPy provides various universal functions like standard trigonometric functions, functions for arithmetic operations, handling complex numbers, statistical functions, etc.

Characteristics of NumPy ufuncs

These functions operate on ndarray (N-dimensional array) i.e. NumPy’s array class.
It performs fast element-wise array operations.
It supports various features like array broadcasting, type casting, etc.
Numpy universal functions are objects that belong to numpy.ufunc class.
Python functions can also be created as a universal function using the frompyfunc library function.
Some ufuncs are called automatically when the corresponding arithmetic operator is used on arrays. For example, when the addition of two arrays is performed element-wise using the ‘+’ operator then np.add() is called internally.

Why use ufuncs?

ufunc, or universal functions offer various advantages in NumPy. Some benefits of using ufuncs are:

1. Vectorized Operations

ufuncs are applied element-wise to all the elements in the ndarray.
ufuncs are more efficient than loops as they are applied simultaneously to all elements. Vectorization is very useful on large data sets.

2. Type Casting

Type casting means converting the data type of a variable to perform the necessary operation.
ufuncs automatically handle type casting and ensure compatible datatypes for calculations.
This allows code to be concise and reduces the chances of error.

3. Broadcasting

Broadcasting means to perform arithmetic operations on arrays of different size.
ufuncs automatically handle broadcasting and avoids the need for manual array shape manipulation.

Basic Universal Functions (ufunc) in NumPy

Here are some of the universal functions (ufunc) in the NumPy Python library:

Trigonometric functions

These functions work on radians, so angles need to be converted to radians by multiplying by pi/180. Only then we can call trigonometric functions. They take an array as input arguments.

It includes functions like:

ufunc’s Trigonometric Functions in NumPy
Function	Description
sin, cos, tan	compute the sine, cosine, and tangent of angles
arcsin, arccos, arctan	calculate inverse sine, cosine, and tangent
hypot	calculate the hypotenuse of the given right triangle
sinh, cosh, tanh	compute hyperbolic sine, cosine, and tangent
arcsinh, arccosh, arctanh	compute inverse hyperbolic sine, cosine, and tangent
deg2rad	convert degree into radians
rad2deg	convert radians into degree

Example: Using Trigonometric Functions

Python3

# Python code to demonstrate trigonometric function 
import numpy as np 
  
# create an array of angles 
angles = np.array([0, 30, 45, 60, 90, 180])  
  
# conversion of degree into radians 
# using deg2rad function 
radians = np.deg2rad(angles) 
  
# sine of angles 
print('Sine of angles in the array:') 
sine_value = np.sin(radians) 
print(np.sin(radians)) 
  
# inverse sine of sine values 
print('Inverse Sine of sine values:') 
print(np.rad2deg(np.arcsin(sine_value))) 
  
# hyperbolic sine of angles 
print('Sine hyperbolic of angles in the array:') 
sineh_value = np.sinh(radians) 
print(np.sinh(radians)) 
  
# inverse sine hyperbolic  
print('Inverse Sine hyperbolic:') 
print(np.sin(sineh_value))  
  
# hypot function demonstration 
base = 4
height = 3
print('hypotenuse of right triangle is:') 
print(np.hypot(base, height)) 

Output

Sine of angles in the array:
[  0.00000000e+00   5.00000000e-01   7.07106781e-01   8.66025404e-01
   1.00000000e+00   1.22464680e-16]

Inverse Sine of sine values:
[  0.00000000e+00   3.00000000e+01   4.50000000e+01   6.00000000e+01
   9.00000000e+01   7.01670930e-15]

Sine hyperbolic of angles in the array:
[  0.           0.54785347   0.86867096   1.24936705   2.3012989
  11.54873936]

Inverse Sine hyperbolic:
[ 0.          0.52085606  0.76347126  0.94878485  0.74483916 -0.85086591]

hypotenuse of right triangle is:
5.0

Statistical functions

These functions calculate the mean, median, variance, minimum, etc. of array elements.

They are used to perform statistical analysis of array elements.

It includes functions like:

ufunc’s Statistical Functions in NumPy
Function	Description
amin, amax	returns minimum or maximum of an array or along an axis
ptp	returns range of values (maximum-minimum) of an array or along an axis
percentile(a, p, axis)	calculate the pth percentile of the array or along a specified axis
median	compute the median of data along a specified axis
mean	compute the mean of data along a specified axis
std	compute the standard deviation of data along a specified axis
var	compute the variance of data along a specified axis
average	compute the average of data along a specified axis

Example: Using Statistical functions

Python3

# Python code demonstrate statistical function 
import numpy as np 
  
# construct a weight array 
weight = np.array([50.7, 52.5, 50, 58, 55.63, 73.25, 49.5, 45]) 
  
# minimum and maximum  
print('Minimum and maximum weight of the students: ') 
print(np.amin(weight), np.amax(weight)) 
  
# range of weight i.e. max weight-min weight 
print('Range of the weight of the students: ') 
print(np.ptp(weight)) 
  
# percentile 
print('Weight below which 70 % student fall: ') 
print(np.percentile(weight, 70)) 
   
# mean  
print('Mean weight of the students: ') 
print(np.mean(weight)) 
  
# median  
print('Median weight of the students: ') 
print(np.median(weight)) 
  
# standard deviation  
print('Standard deviation of weight of the students: ') 
print(np.std(weight)) 
  
# variance  
print('Variance of weight of the students: ') 
print(np.var(weight)) 
  
# average  
print('Average weight of the students: ') 
print(np.average(weight)) 

Output

Minimum and maximum weight of the students: 
45.0 73.25

Range of the weight of the students: 
28.25

Weight below which 70 % student fall: 
55.317

Mean weight of the students: 
54.3225

Median weight of the students: 
51.6

Standard deviation of weight of the students: 
8.05277397857

Variance of weight of the students: 
64.84716875

Average weight of the students: 
54.3225

Bit-twiddling functions

These functions accept integer values as input arguments and perform bitwise operations on binary representations of those integers.

It includes functions like:

ufunc’s Bit-twiddling functions in NumPy
Function	Description
bitwise_and	performs bitwise and operation on two array elements
bitwies_or	performs bitwise or operation on two array elements
bitwise_xor	performs bitwise xor operation on two array elements
invert	performs bitwise inversion of an array of elements
left_shift	shift the bits of elements to the left
right_shift	shift the bits of elements to the left

Example: Using Bit-twiddling functions

Python3

# Python code to demonstrate bitwise-function 
import numpy as np 
  
# construct an array of even and odd numbers 
even = np.array([0, 2, 4, 6, 8, 16, 32]) 
odd = np.array([1, 3, 5, 7, 9, 17, 33]) 
  
# bitwise_and 
print('bitwise_and of two arrays: ') 
print(np.bitwise_and(even, odd)) 
  
# bitwise_or 
print('bitwise_or of two arrays: ') 
print(np.bitwise_or(even, odd)) 
  
# bitwise_xor 
print('bitwise_xor of two arrays: ') 
print(np.bitwise_xor(even, odd)) 
   
# invert or not 
print('inversion of even no. array: ') 
print(np.invert(even)) 
  
# left_shift  
print('left_shift of even no. array: ') 
print(np.left_shift(even, 1)) 
  
# right_shift  
print('right_shift of even no. array: ') 
print(np.right_shift(even, 1)) 

Output

bitwise_and of two arrays: 
[ 0  2  4  6  8 16 32]

bitwise_or of two arrays: 
[ 1  3  5  7  9 17 33]

bitwise_xor of two arrays: 
[1 1 1 1 1 1 1]

inversion of even no. array: 
[ -1  -3  -5  -7  -9 -17 -33]

left_shift of even no. array: 
[ 0  4  8 12 16 32 64]

right_shift of even no. array: 
[ 0  1  2  3  4  8 16]

Conclusion

NumPy ufuncs are also called universal functions in Python. They are very useful for performing operations on ndarray. They offer benefits like automatic vectorization, broadcasting, and type casting.

In this tutorial, we have covered what are ufuncs, their characteristics, and benefits, and also showed some ufuncs with examples. This guide explains ufuncs in easy language, and you can easily use ufuncs in your own Python projects.

Create your own universal function in NumPy

Tanvi_Garg

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Practice Tags :

python

NumPy ufuncs | Universal functions

Characteristics of NumPy ufuncs

Why use ufuncs?

1. Vectorized Operations

2. Type Casting

3. Broadcasting

Basic Universal Functions (ufunc) in NumPy

Trigonometric functions

Example: Using Trigonometric Functions

Python3

Statistical functions

Example: Using Statistical functions

Python3

Bit-twiddling functions

Example: Using Bit-twiddling functions

Python3

Conclusion

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Introduction

Creating NumPy Array

NumPy Array Manipulation

Matrix in NumPy

Operations on NumPy Array

Reshaping NumPy Array

Indexing NumPy Array

Arithmetic operations on NumPyArray

Linear Algebra in NumPy Array

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