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 = 4height = 3print('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]
