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NumPy ufuncs | Universal functions

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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

sin, cos, tancompute the sine, cosine, and tangent of angles
arcsin, arccos, arctancalculate inverse sine, cosine, and tangent
hypotcalculate the hypotenuse of the given right triangle
sinh, cosh, tanhcompute hyperbolic sine, cosine, and tangent
arcsinh, arccosh, arctanhcompute inverse hyperbolic sine, cosine, and tangent
deg2radconvert degree into radians
rad2degconvert radians into degree

Example: Using Trigonometric Functions


# 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)
# inverse sine of sine values
print('Inverse Sine of sine values:')
# hyperbolic sine of angles
print('Sine hyperbolic of angles in the array:')
sineh_value = np.sinh(radians)
# inverse sine hyperbolic 
print('Inverse Sine hyperbolic:')
# hypot function demonstration
base = 4
height = 3
print('hypotenuse of right triangle is:')
print(np.hypot(base, height))


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

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

hypotenuse of right triangle is:

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

amin, amaxreturns minimum or maximum of an array or along an axis
ptpreturns 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
mediancompute the median of data along a specified axis
meancompute the mean of data along a specified axis
stdcompute the standard deviation of data along a specified axis
varcompute the variance of data along a specified axis
averagecompute the average of data along a specified axis

Example: Using Statistical functions


# 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: ')
# percentile
print('Weight below which 70 % student fall: ')
print(np.percentile(weight, 70))
# mean 
print('Mean weight of the students: ')
# median 
print('Median weight of the students: ')
# standard deviation 
print('Standard deviation of weight of the students: ')
# variance 
print('Variance of weight of the students: ')
# average 
print('Average weight of the students: ')


Minimum and maximum weight of the students: 
45.0 73.25

Range of the weight of the students: 

Weight below which 70 % student fall: 

Mean weight of the students: 

Median weight of the students: 

Standard deviation of weight of the students: 

Variance of weight of the students: 

Average weight of the students: 

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

bitwise_andperforms bitwise and operation on two array elements
bitwies_orperforms bitwise or operation on two array elements
bitwise_xorperforms bitwise xor operation on two array elements
invertperforms bitwise inversion of an array of elements
left_shiftshift the bits of elements to the left
right_shiftshift the bits of elements to the left

Example: Using Bit-twiddling functions


# 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: ')
# 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))


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]


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.

Last Updated : 01 Feb, 2024
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