Introduction to Mathematical Software Assignment Help

% 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.

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

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