# 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

 `# Python code to demonstrate trignometric 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

 `# 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

 `# 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]
```

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