maths.numerical_analysis.nevilles_method
========================================

.. py:module:: maths.numerical_analysis.nevilles_method

.. autoapi-nested-parse::

   Python program to show how to interpolate and evaluate a polynomial
   using Neville's method.
   Neville's method evaluates a polynomial that passes through a
   given set of x and y points for a particular x value (x0) using the
   Newton polynomial form.
   Reference:
       https://rpubs.com/aaronsc32/nevilles-method-polynomial-interpolation



Functions
---------

.. autoapisummary::

   maths.numerical_analysis.nevilles_method.neville_interpolate


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

.. py:function:: neville_interpolate(x_points: list, y_points: list, x0: int) -> list

      Interpolate and evaluate a polynomial using Neville's method.
      Arguments:
          x_points, y_points: Iterables of x and corresponding y points through
           which the polynomial passes.
          x0: The value of x to evaluate the polynomial for.
      Return Value: A list of the approximated value and the Neville iterations
          table respectively.
   >>> import pprint
   >>> neville_interpolate((1,2,3,4,6), (6,7,8,9,11), 5)[0]
   10.0
   >>> pprint.pprint(neville_interpolate((1,2,3,4,6), (6,7,8,9,11), 99)[1])
   [[0, 6, 0, 0, 0],
    [0, 7, 0, 0, 0],
    [0, 8, 104.0, 0, 0],
    [0, 9, 104.0, 104.0, 0],
    [0, 11, 104.0, 104.0, 104.0]]
   >>> neville_interpolate((1,2,3,4,6), (6,7,8,9,11), 99)[0]
   104.0
   >>> neville_interpolate((1,2,3,4,6), (6,7,8,9,11), '')
   Traceback (most recent call last):
       ...
   TypeError: unsupported operand type(s) for -: 'str' and 'int'