maths.numerical_analysis.integration_by_simpson_approx
======================================================

.. py:module:: maths.numerical_analysis.integration_by_simpson_approx

.. autoapi-nested-parse::

   Author : Syed Faizan ( 3rd Year IIIT Pune )
   Github : faizan2700

   Purpose : You have one function f(x) which takes float integer and returns
   float you have to integrate the function in limits a to b.
   The approximation proposed by Thomas Simpson in 1743 is one way to calculate
   integration.

   ( read article : https://cp-algorithms.com/num_methods/simpson-integration.html )

   simpson_integration() takes function,lower_limit=a,upper_limit=b,precision and
   returns the integration of function in given limit.



Attributes
----------

.. autoapisummary::

   maths.numerical_analysis.integration_by_simpson_approx.N_STEPS


Functions
---------

.. autoapisummary::

   maths.numerical_analysis.integration_by_simpson_approx.f
   maths.numerical_analysis.integration_by_simpson_approx.simpson_integration


Module Contents
---------------

.. py:function:: f(x: float) -> float

.. py:function:: simpson_integration(function, a: float, b: float, precision: int = 4) -> float

   Args:
       function : the function which's integration is desired
       a : the lower limit of integration
       b : upper limit of integration
       precision : precision of the result,error required default is 4

   Returns:
       result : the value of the approximated integration of function in range a to b

   Raises:
       AssertionError: function is not callable
       AssertionError: a is not float or integer
       AssertionError: function should return float or integer
       AssertionError: b is not float or integer
       AssertionError: precision is not positive integer

   >>> simpson_integration(lambda x : x*x,1,2,3)
   2.333

   >>> simpson_integration(lambda x : x*x,'wrong_input',2,3)
   Traceback (most recent call last):
       ...
   AssertionError: a should be float or integer your input : wrong_input

   >>> simpson_integration(lambda x : x*x,1,'wrong_input',3)
   Traceback (most recent call last):
       ...
   AssertionError: b should be float or integer your input : wrong_input

   >>> simpson_integration(lambda x : x*x,1,2,'wrong_input')
   Traceback (most recent call last):
       ...
   AssertionError: precision should be positive integer your input : wrong_input
   >>> simpson_integration('wrong_input',2,3,4)
   Traceback (most recent call last):
       ...
   AssertionError: the function(object) passed should be callable your input : ...

   >>> simpson_integration(lambda x : x*x,3.45,3.2,1)
   -2.8

   >>> simpson_integration(lambda x : x*x,3.45,3.2,0)
   Traceback (most recent call last):
       ...
   AssertionError: precision should be positive integer your input : 0

   >>> simpson_integration(lambda x : x*x,3.45,3.2,-1)
   Traceback (most recent call last):
       ...
   AssertionError: precision should be positive integer your input : -1



.. py:data:: N_STEPS
   :value: 1000