Solve using python$/$jupyter notebook

Problem $1$

Emmendorfer and Dimuro $(2021)$ presented a novel point interpolation algorithm derived from a simple weighted linear regression model, resulting in a mathematical

expression sharing similarities to the Inverse Distance Weighting interpolation method. Calling their method as inverse distance weighted regression, the authors provide

their procedure in the following pseudocode:

Input: A set of values $y_1,y_2,$cdots,$y_n$ and the corresponding

coordinate vectors $x_1,x_2,$cdots,$x_n.$

Input: A coordinate vector of a point of interest $c_j,$ for which an

estimated value will be computed.

Output: The interpolated value hat$(y{)}_j^R,$ computed for the location $c_j.$

nlarr the number of input points;

for all input points iin$\{1,2,$cdots,$n\}$ do

$d_{i,j}$larr Euclidean distance between $x_i$ and $c_j$;

for all input points iin$\{1,2,$cdots,$n\}$ do

$w_{i,j}$larr$\frac{d_{i,j}^{-2}}{{\displaystyle \underset{k=1}{\overset{n}{}}}{d}_{k,j}^{-2}}$

${?}^6$hat$(y{)}_j^{\text{I}\text{D}\text{W}}$larr${\displaystyle \underset{i=1}{\overset{n}{}}}{w}_{i,j}{y}_i$

$7$hat$(y{)}_j^R$larrhat$(y{)}_j^{\text{I}\text{D}\text{W}}+n\frac{{\displaystyle \underset{i=1}{\overset{n}{}}}{y}_i-\text{n}\text{h}\text{a}\text{t}(y{)}_j^{\text{I}\text{D}\text{W}}}{n^2-{\displaystyle \underset{i=1}{\overset{n}{}}}{d}_{i,j}^{-2}{\displaystyle \underset{i=1}{\overset{n}{}}}{d}_{i,j}^2}$

return hat$(y{)}_j^R$

Note that $x_n$ represents a coordinate vector, i$.$e$.,x=x$ in $2$D or $y=f(x),$ and $x=(x_1,x_2)$ in $3$D or $y=f(x_1,x_2).$

Part B

Write a Python function IDWR$(x,x,y)$ where $x$ is the coordinate vector $x$ value whose $y$ value is to be interpolated while $x$ represents coordinate vectors

corresponding to a vector of $y$ values $Y.$ The function should return a list, tuple, or array of interpolated values.

Use your Python function to confirm the results from part A and to draw the IDWR interpolant surface for the following data set

Then graph the $3$D output.