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## MATLAB Function PlotsubI

% clear workpace and command window
clear, clc
% close all figures
close all
(a) Write a MATLAB function PlotsubI that takes a value as input and executes the following:
(i) Creates vectors and , each containing 101 points ranging from to .
(ii) Produces an subplot such that for each , its subwindow is occupied by a mesh plot of vs. and , where
(iii) Labels the , and axes of each mesh plot as , and respectively.
(b) Using the function PlotsubI, write suitable MATLAB commands in order to generate subplots in separate figure windows when n = 1, 2 and 3.

## MATLAB Function Code

function PlotsubI(n)
% Creates vectors x and y, each containing 101 points ranging from -1 to 1 .
x = linspace(-1, 1, 101) ;
y = linspace(-1, 1, 101) ;
% Produces an nxn subplot such that for each k,
figure ;
set(gcf,'NumberTitle','off')
set(gcf,'Name',['n=', num2str(n)])
for k = 1:n^2
% subplots nxn
subplot(n,n, k)
% mesh grid for X and Y
[X,Y] = meshgrid(x);
% compute g(x,y) as Z
Z = exp(-k^2 * (X.^2 + Y.^2) );
mesh(X,Y,Z)
xlabel('$x$','interpreter','latex')
ylabel('$y$','interpreter','latex')
zlabel('$g(x,y)$','interpreter','latex')
title(k)
end
end
% (b) Test the function for n = 1, 2 and 3
nlist = [1 2 3];
for i = 1: numel(nlist)
n = nlist(i) ;
% calls on function for each n
PlotsubI(n)
end

## Expomat Functions that takes Vector X

Let be any 1 × m vector. The m × m expomatrix of x is a matrix denoted by

(a) Write a MATLAB function Expomat that takes a vector x as input, and computes the corresponding expomatrix A.
function A = Expomat(x)
%EXPOMAT
% Expomat(x) that takes a vector x as input, and
% computes the corresponding expomatrix A
% find length of vector x
m = length(x);
% initialize a
a= zeros(m,m) ;
for i = 1: m
for j = 1:m
a(i,j) = 2^(x(i)*x(j)) ;
end
end
% output Matrix
A = a;
end
(b) Write and execute a MATLAB script Asum that uses Expomat with input vector x = (0.5, 0.52, 0.54, ..., 1.74, 1.76) and output matrix A to calculate the sum of the first 50 entries in the 17th column of A. This calculated sum must be obtained using a �for� loop and stored as output variable S.
% Script Asum
x = [0.5:0.02:1.76];
A = Expomat(x);
S = 0; % initialize the sum
% for loop
for i= 1:50
for j = 17
S = S + A(i,j) ;
end
end
fprintf('The Sum value is: %g', S)
The Sum value is: 88.9558

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