For loops indexing in Matlab

Question

I am trying to use for loops to calculate the following formula:

However, since the number of elements for 't' and 'tau' are different, I'm not sure how to properly index the code.

This is what I have done so far:

t = [0:0.1:15];
tau = [0:2:10];
dtau = tau(2)-tau(1);

BB = 4*tau;
u = 2*t;
B = zeros(1,length(t));

for ii = 1:length(t)
    for jj = 1:length(tau)
        B(ii) = B(ii) + BB(jj)*u(ii-jj+1)*dtau;
    end
end

To elaborate a bit more - the upper integration limit is the 't' in this case, so for every B(t) I would like to integrate from tau(0) to tau=t. Any suggestions? Thank you.

Answer 1

You are doing convolution so just use Matlab's built-in functions if you can i.e. conv. But here is a loopy version for your understanding:

using your data

t = [0:0.1:15];
tau = [0:2:10];
dtau = tau(2)-tau(1);

BB = 4*tau;
u = 2*t;
B = zeros(1,length(t));

We flip u and then slide it over `BB'. It's easiest to just pad BB with zeros so you don't have to deal with edges:

U = fliplr(u);
BB = [zeros(1,length(u)-1), BB, zeros(1,length(u)-1)];

for ii = 1:length(t)   %//This should actually go to 21, I don't feel like working out why right now
    B(ii) = sum(U.*BB(ii:(ii+length(u)-1)));
end

Answer 2

To answer your question:

If you want to do it like that, you only have to define tau inside the for ii = 1:length(t) loop, that's all.

So it would look something like this:

t = [0:0.1:15];

u = 2*t;
B = zeros(1,length(t));

for ii = 1:length(t)

    tau = [0:0.2*ii:ii]
    dtau = tau(2)-tau(1);
    BB = 4*tau;    

    for jj = 1:length(tau)
        B(ii) = B(ii) + BB(jj)*u(ii-jj+1)*dtau;
    end
end

That being said, I think Dan's comment is on spot: unless you want to play with the parameters by yourself, you are performing a simple convolution there.