Question

Question 2 We define, for a given integer m, 1 sism, h Xi = (i – 1) m-1' 1 X1 1 X2 The mx2 matrix X is defined as: X = 1 Xm [sin txi sin itx2 and the m X 1 vector Y is defined as: Y = 0.1 : [sin πm. = a) Create a function which for inputs m (a scalar) and v [v1; v2] (a column vector of 2x returns the scalar res given by res = YYT – 2vtxty + 07 XT Xv Hint: Your function must be as in this form → function res= myfunc m, v) (implement in matlab and copy your code here) b) Write a script which evaluates your function for inputs m = 20 and v = [1; 1). limplement in matlab and conv vour code horel

Answer 1

Matlab function myfunc.m for the problem

function res = myfunc(m,v)
% Input
% m: a scalar
% v: a colum vector of size 2x1
% Output
% res: a scalar
h = 1/(m-1); % Computing the value of h
i = 1:m; % crreating i vector varies from 1 to m
x = (i-1)*h; % Calculating x vector
X = [ones(m,1),x']; % Create X using x
Y = 0.1*sin(pi*x'); % Create Y using x
% Now compute the res
res = ((Y')*Y)-(2*((v')*((X')*Y)))+((v')*(((X')*X)*v));
end

Script to call the function to compute res

clc; clear; % Clearing the command window and workspace
m = 20; % setting the value of m as 20
v = [1;1]; % seting the value of v
res = myfunc(m,v); % calling the function to calculate res
% printing the result
fprintf('For m = %d and v = [%d; %d], the res = %0.4f.',m,v,res);

Screen Print of the code

1 2 3 4 5 6 function res = myfunc(mv) % Input % m: a scalar % v: a colum vector of size 2x1 % Output % res: a scalar h = 1/(m-1); % Computing the value of h i = 1:m; % crreating i vector varies from 1 to m (i-1)*h; % Calculating x vector X = [ones (m, 1),x']; % Create X using x Y = 0.1*sin(pi*x'); % Create Y using x % Now compute the res res = ((Y') *Y)-(2*((v')*((X')*Y)))+((V')*(((X') **)*v)); end 7 8 9 0 1 2 3 4 X =

1 2 - 3 clc; clear; % Clearing the command window and workspace m = 20; % setting the value of m as 20 V = [1,1]; % seting the value of v res = myfunc(mv); % calling the function to calculate res % printing the result fprintf('For m = %d and v = [%d; %d], the res %0.4f.',m, v,res); 4 5 6 7

OUTPUT of the code

COMMAND WINDOW For m = 20 and v = [1; 1], the res = 43.3166.