How to create a nested for loop to create a mesh plot

I am trying to finish this problem for a beginner class, so it can't have too difficult of code and I can't seem to figure out what is asked and how to make it happen.

Question: Using a nested for loop,multiply the vector y1 with the decay e-at,for 1<t<100 and a=1,and create the array z. Plot z using the command “mesh”. Find the minimum value of a, for which all the values of z at time 100 are approximately zero.

My Answer So Far:

clear all;
clc;
for i=1:501;
    x(i)=(i-1)*(20/500)-10;
end;
y1=sin(2.*x)+sin(x);
if y1(y1<-1);
    y1(y1<-1)=0;
end;
if y1(y1>1);
    y1(y1>1)=0;
end;
plot(x,y1);

a=1;
for m=1:100;
    for t=1:m;
        f(t)= exp(-a*t);
    end;
    z(y1)=y1.*f;
end;

This comes back with:

"Subscript indices must either be real positive integers or logicals.

Error in SinLoopIfThen (line 20)
    z(y1)=y1.*f;

Am I even understanding the question and if so how can I fix it?

Answer 1

[Desiree Phillips]

The error comes up because your passing y1 to z as if it were an index (which must be a "real positive integer or logical"- a single constant) but it is a vector. Maybe

z(m) = y1.*f;

is what you meant. Going over all of your code, I think Matrix Indexing would be a great link for you to go over. There's a couple of things you can do to reduce the lines of code as well:

Matlab supports indexing using logical statements (e.g.: y1>1 - refer to link above), so the if statements aren't needed. Therefore,

if y1(y1<-1);
    y1(y1<-1)=0;
end;
if y1(y1>1);
    y1(y1>1)=0;
end;

can be reduced to

y1(y1<-1)=0;
y1(y1>1)=0;

As for the question you are trying to solve, checking the Mesh Plot page, you can see that mesh(z) has the requirement that z be a matrix.

The question seems to be asking you to make a z matrix where each row (or column) of z is the product of y1 and e^(-at) for each time t.

Is what you posted the exact wording of the question? It seems a bit confusing. Can you post the whole thing (sorry if its lengthy)?

Answer 2

[Ahmed A. Selman]

I'm not sure what are your conditions (in the if statements), but you used (y1) as a matrix index which cannot be made unless (y1) varies as 1, 2, 3.. (positive real integer, and larger than zero). But I think the following is what you're looking for:

clear all 
clc 
a=1;
z=zeros(501,100);
f=zeros(1,100);
x=zeros(1,501);
for i=1:501 
    x(i)=(i-1)*(20/500)-10;
 y1=sin(2.*x)+sin(x);
 if y1(y1<-1) 
    y1(y1<-1)=0;
end 
if y1(y1>1) 
    y1(y1>1)=0;
end 
   for t=1:100 
   f(t)= exp(-a*t);
  end 
z(i,:)=y1(i)*f;
f=zeros(1,100); % resetting f
end
plot(x,y1);
figure  
mesh(z)
xlabel('time');ylabel('Signal');zlabel('Amplitude');
title('Damping some signal with exponential decay function','fontWeight','bold');

And, theoretically, the value of (a) that makes (z at t=100) become zero is (infinity), since

exp(-a*t) = zero

if and only if (-at) goes to (- infinity), and since (t) is finite (t=100), so (a) must be as mentioned (I think you meant the largest value of variable a instead of the smallest). But you can assign large value to (a) that makes Matlab unable to recognize it from absolute zero, as

a=7.4200

then

min(min(z(:,100))) =  -4.0019e-322

at a=7.5000, Matlab finds that the minimum is exactly 0.