# Python Scipy Special Module With Examples

This Python tutorial will learn about the “Python Scipy Special” where we will calculate the factorial, combinations, and softmax of the given numbers or array of integers. Additionally, cover the following topics:

• Python Scipy Special
• Python Scipy Special Factorial
• Python Scipy Special Softmax
• Python Scipy Special Legendre
• Python Scipy Special Comb
• Python Scipy Special Logit
• Python Scipy Special Gamma
• Python Scipy Special Binom
• Python Scipy Special Erf
• Python Scipy Special Beta

## Python Scipy Special

The Python Scipy module `scipy.special` that has the definition of several unique functions of mathematical physics is the major part of the `scipy.special module`. Elliptic, Airy, vessel, beta, hypergeometric, Mathieu, parabolic cylinder, kelvin, Struve, gamma, and spheroidal wave are some of the available functions.

There are also specific low-level stats functions that are not intended for public use because the stats module provides a more user-friendly interface to these functions.

The majority of these functions can accept array parameters and return array results using the same broadcasting principles as other Numerical Python math functions.

## Python Scipy Special Factorial

The Python SciPy has a method `factorial` within module `scipy.special` that get the factorial of a number or a set of numbers.

The syntax is given below.

``scipy.special.factorial(n, exact=True)``

Where parameters are:

• n(array_data, integer): Values for input, If n is less than zero, the result is 0.
• exact(boolean): If True, use long integer arithmetic to calculate the answer. If False, the gamma function is used to swiftly approximate the result in a floating point.

The method `factorial` returns the `nf`( which is the factorial of integer of array of numbers) of type int, array, or float.

Let’s understand with an example by following the below steps:

Import the required libraries using the below python code.

``````import numpy as np
from scipy import special``````

Create an array containing numbers and pass this array to a method `factorial()` to compute the factorial of all the numbers with the array using the below code.

``````array_num = np.array([5, 3, 4])
special.factorial(array_num,exact= False)``````

Again compute the factorial of the same array with parameter `exact` equal to `True` using the below code.

``special.factorial(array_num,exact= True)``

Look at the output, how the factorial is different when we change the value `False` ( for false it shows the result in float) to `True` (for true, the result is only in integer) of parameter `exact`.

This is how to compute the factorial of a given number or set of numbers using the method `factorial()` of Python Scipy.

## Python Scipy Special Softmax

The Python Scipy module `scipy.special` contains a method `softmax()` that changes each item of an array by calculating each item’s exponential divided by the total of all the items’ exponentials.

The syntax is given below.

``scipy.special.softmax(x, axis=0)``

Where parameters are:

• x(array_data): It is the array of data as input.
• axis(None, int): Calculate values along the specified axis.

The method `softmax()` returns `s` (An array with the same dimensions as x. Along the selected axis, the outcome will equal one) of type ndarray.

Let’s understand with an example by following the below steps:

Import the required libraries using the below python code.

``````from scipy import special
import numpy as np``````

Create an array of numbers using the below code.

``````array_num = np.array([[3, 0.2, 0.5, 1],
[3,  7,   1, -1],
[13,  3,  2, 12]])``````

Apply the softmax function on the whole array to transform each value of the array using the below code.

``special.softmax(array_num)``

Look at the returned output that contains the values which are transformed by the method `softmax()`.

This is how to compute the softmax of the given array.

## Python Scipy Special Legendre

The module `scipy.special` of Python SciPy contains a method `legendre()` to calculate the Legendre polynomial.

The syntax is given below.

``scipy.special.legendre(n, monic=True``

Where parameters are:

• n(int): To specify the polynomial degree.
• monic(boolean): If this is the true case, the leading coefficient should be scaled to one.

The method `legendre()` returns `P` which is orthoploy1d.

Let’s take an example by following the below steps:

Import the required libraries and create the Legendre polynomial of 4th order using the below code.

``````from scipy import special
special.legendre(4)``````

This is how to generate the Legendre polynomial using the method `legendre()` of Python SciPy.

## Python Scipy Special Comb

The method `comb()` is used to compute the combination that is the number of different combinations of N different things that can be done k at a time. This method exists in the module `scipy.special` of Python SciPy.

The syntax is given below.

``scipy.special.comb(N, k, repetition=True, exact=True)``

Where parameters are:

• N(ndarray, int): It is used to define the number of things.
• k(ndarray, int): The number of elements that were taken.
• repetition(boolean): If the value repetition is true, the number of combinations with repetition is calculated.
• exact(boolean): If exact is false, floating-point precision is employed; otherwise, a large integer is computed with exact precision.

The method returns `val` (which is the number of possible combinations in total) of types ndarray, int, and float.

Let’s take an example by following the below steps:

Import the required libraries using the below python code.

``````from scipy import special
import numpy as np``````

Define several N things and elements chosen using the below code.

``````chosen_k = np.array([5, 6])
n_things = np.array([15, 15])``````

Calculate the combination using the below code.

``special.comb(n_things, chosen_k, exact=False)``

This is how to compute the combination using the method `comb()` of Python SciPy.

## Python Scipy Special Logit

The logit function is the standard logistic distribution’s quantile function. The Python Scipy module `scipy.special` contains a method `logit()` to compute the logit of a given ndarrays. Logit is the universal function.

The syntax is given below.

``scipy.special.logit(x)``

Where a parameter `x` is the ndarray to which logit should be applied element-by-element.

The method `logit()` returns `out`( A similar-shaped ndarray to x. Its elements are logit versions of the relevant x entry) of type ndarray.

Let’s compute the logit of ndarray using the below code.

``````from scipy import special
special.logit([0, 0.30, 0.6, 0.90, 0.99])``````

In the above code, we have created and passed the array containing the float values to a method `logit()` to find the logit of the values within an array.

This is how to compute the logit of a given ndarray using the method `logit()` of Python SciPy.

## Python Scipy Special Gamma

The Python Scipy has a method `gamma()` within the module `scipy.special` that calculates the gamma of the given array. The generalized factorial function is what the gamma function is known as.

The syntax is given below.

``scipy.special.gamma(z)``

Where a parameter `z` is an argument with a real or complex value of type array.

The method `gamma()` returns the gamma function’s values of type ndarray or scalar.

Let’s take an example by following the below steps:

Import the libraries using the below python code.

``from scipy import special``

Create an array of data and pass the array to a method `gamma()` as shown below the code.

``special.gamma([5,1,0.5,1])``

Define a complex number and compute the gamma of that number using the below code.

``special.gamma(1.6 + 2j)``

As we can see in the above output, we have calculated the gamma values of the array and complex numbers.

This is how to compute the gamma value of the given array or complex number using the method `gamma()` of Python SciPy.

## Python Scipy Special Binom

Binom stands for the `Binomial Coefficient` , Python SciPy has a method `binom()` that exists in a module `scipy.special`. This method performs the same operation as the method `comb()` that we have learned in the above sub-section. To know more about it, please refer to the above section “Python Scipy Comb”.

The syntax is given below.

``scipy.special.binom(n, k)``

Where parameters are:

N(ndarray, int): It is used to define the number of things.
k(ndarray, int): The number of elements that were taken.

Let’s take an example by following the below steps:

Import the required libraries using the below python code.

``````from scipy import special
import numpy as np``````

Define several N things and elements chosen using the below code.

``````chosen_k = np.array([9, 11])
n_things = np.array([20, 20])``````

Calculate the combination using the below code.

``special.binom(n_things, chosen_k)``

This is how to compute the combination using the method `binom()` of Python SciPy.

## Python Scipy Special Erf

The Erf stands for `error function` which is the method `erf()` in module `scipy.special` that returns the complicated argument’s error function.

The syntax is given below.

``scipy.special.erf(z)``

Where the parameter `z` the array of data as input.

The method `erf()` returns `res`(the error function’s values at the specified x locations) of type ndarray.

Let’s take an example by following the below steps:

Import the necessary libraries using the below python code.

``````import matplotlib.pyplot as plt
from scipy.special import erf
import numpy as np
%matplotlib inline``````

Generate an array of data using the below code.

``array_data = np.linspace(-5,5)``

Compute the error function of the array using the below code.

``````error_f = erf(array_data)
error_f[0::3]``````

Plot the graph of the error function using the below code.

``````plt.plot(array_data, error_f)
plt.xlabel('\$arraydata\$')
plt.ylabel('\$eror_function(array_data)\$')
plt.show()``````

This is how to compute the error function of the given data using the method `erf()` of Python SciPy.

## Python Scipy Special Beta

Beta functions, commonly known as the Euler integral of the first kind, are a special sort of function. The Python SciPy has a method `beta()` within the module `scipy.special` that is applied to an array containing real values to get the values. The beta function follows a symmetrical pattern.

The syntax is given below.

``scipy.special.beta(a, b, out=None)``

Where parameters are:

• a,b(array_data): It is arguments with real value as input.
• out(ndarray): The function result can have an optional output array.

The method `beta()` returns the beta function’s value of type ndarray.

Let’s take an example by following the below steps:

Import the necessary libraries using the below python code.

``from scipy import special``

Apply the beta function to the values using the below code.

``special.bet(4,8)``

Now perform the below steps to see the symmetrical pattern of the beta function.

``````print(special.beta(6,3))
print(special.beta(3,6))``````

In line 8, we have passed the two values to a method `beta()` by swapping the places of value in a function. The result is the same as shown in the above output. This is the symmetrical nature of the function `beta()`.

This is how to use the function `beta()` of Python SciPy.

Also, take a look at some more Python Scipy tutorials.

So, in this tutorial, we have learned about the “Python Scipy Special” and covered the following topics.

• Python Scipy Special
• Python Scipy Special Factorial
• Python Scipy Special Softmax
• Python Scipy Special Legendre
• Python Scipy Special Comb
• Python Scipy Special Logit
• Python Scipy Special Gamma
• Python Scipy Special Binom
• Python Scipy Special Erf
• Python Scipy Special Beta