Description

Lagrange Interpolation
i. Open the colab file shared in BUX. ii. Create a copy of that shared file. iii. Rename the colab filename using the format Name-ID-Lab Section
Lab Introduction
We know that, general form of an n degree Lagrange polynomial:

where

Now, check out the Lagrange_Polynomial class in the given code.
1. The constructor __init__(self, data_x, data_y) is written for you. (No task here)
2. The _repr__(self) function has been written for you. (No task here)
3. [Task 1] – 4 marks
You have to implement the l(self, k, x) function.
This method implements the Lagrange Basis to be used for interpolation using Lagrange Polynomials. This function would take k and x as inputs and calculate the Lagrange basis using the second Equation given above.
You will have to remove the “raise NotImplementedError()”
Hint: Set up a Loop to traverse through. Or you can use vectorized method.
4. [Task 2] – 4 marks
You have to implement the __call__(self, x_arr) function.
The function calculates the lagrange polynomial from a set of given nodes using the first equation given above.
You will have to remove the “raise NotImplementedError()”
Hint: The method to make the object callable. ‘x_arr’ is a set of given points (a numpy array). You have to use self.data_x and self.data_y to find the interpolated output of the polynomial for all elements of ‘x_arr’. Implement as you wish but your ‘total’ numpy array where the i’th element p_x_arr[i] represents the interpolated value of p(x_arr[i]). You can use nested for
loop to complete this task.
5. Plotting the polynomial (No task here)
6. [Task 3: Problem related Lagrange interpolation] – 2 marks
You will have to solve the given problem using Lagrange_Polynomial class.