Numpy ufunc | Universal functions

Universal functions in Numpy are simple mathematical functions. It is just a term that we gave to mathematical functions in the Numpy library. Numpy provides various universal functions that cover a wide variety of operations. 
These functions include standard trigonometric functions, functions for arithmetic operations, handling complex numbers, statistical functions, etc. Universal functions have various characteristics which are as follows- 

• These functions operates 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 those belongs to numpy.ufunc class.
• Python functions can also be created as a universal function using frompyfunc library function.
• Some ufuncs are called automatically when the corresponding arithmetic operator is used on arrays. For example when addition of two array is performed element-wise using ‘+’ operator then np.add() is called internally.

Some of the basic universal functions in Numpy are-

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-

Function	Description
sin, cos, tan	compute sine, cosine and tangent of angles
arcsin, arccos, arctan	calculate inverse sine, cosine and tangent
hypot	calculate hypotenuse of 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

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 are used to calculate mean, median, variance, minimum of array elements. It includes functions like-

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 pth percentile of array or along specified axis
median	compute median of data along specified axis
mean	compute mean of data along specified axis
std	compute standard deviation of data along specified axis
var	compute variance of data along specified axis
average	compute average of data along specified axis

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 include functions like-

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 elements
left_shift	shift the bits of elements to left
right_shift	shift the bits of elements to left

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]