Plotting with multiple nested arrays issue with trapz() function.

clear 

%g = 1;
k = 0.2; 
no = 0; 
nm = 0; 
Del = 1; 
Ohm = -1; 
gam = 0.2; 

w = (-10:0.01:10);
g = (0:0.01:20);

xat = 1 - (1i.*(w + Del).*(2./k));
xbt = 1 - (1i.*(w - Ohm).*(2./gam));

for u=1:length(g)
    C = sqrt((4.*(g(u).^2))./(k.*gam)); 
    Ca(u) = C; %C-array

      c =  (2.*1i.*Ca(u))./(sqrt(gam).*(xat(u).*xbt(u)+(Ca(u).^2))); %power spectrum coefficient
      ca(u)= c; %c-array
      d =  (2.*xat(u))./(sqrt(gam).*(xat(u).*xbt(u)+(Ca(u).^2))); %power spectrum coefficient
      da(u) = d; %d-array

      Sbb = (abs(ca(u)).^2).*(no+(1/2))+(abs(da(u)).^2).*(nm+(1/2)); %power spectrum

      Q = ((1./(2.*pi)).*trapz(w,Sbb))-0.5; %phonon population
      Qa(u) = Q; %Q-array
  end

figure(1)
plot(Ca,Qa)

Greetings!

As you can see, I am trying to plot a graph of Qa versus Ca. But upon running, I got an error saying: ORDER contains an invalid permutation index. I suspect it's the trapz() function not recognizing my Sbb. Given how I am trying to store lots of arrays, they got nested inside the loop and I think I lost track of what I really needed to loop over. This is really important to me and I would appreciate any form of help!

Thank you very much in advance!

Answer 1

[Walter Roberson]

When you go to trapz, you have a vector of w and a scalar fractional Sbb.

trapz can be called with two arguments in a few different ways: the second argument Sbb can be an array the same size as w; Or w and Sbb can be "compatible" sizes (e.g., Sbb could be an array and w could be a vector with the same number of elements as the number of rows in Sbb); Or Sbb can be positive integer scalar that indicates the dimension number of w to work over. You are passing in a scalar so it thinks you are trying to pass a dimension number, but the dimension number you are providing is not a positive integer, so you get an error.

Perhaps you should be building an array of Sbb values, and then have your trapz after the loop ?

[Alvin]

w = (-10:0.01:10); 
g = (0:0.01:20);

xat = 1 - (1i.*(w + Del).*(2./k));
xbt = 1 - (1i.*(w - Ohm).*(2./gam));

for u=1:length(g)
    C = sqrt((4.*(g(u).^2))./(k.*gam)); %Cooperativity
    Ca(u) = C;

      c =  (2.*1i.*Ca(u))./(sqrt(gam).*(xat(u).*xbt(u)+(Ca(u).^2))); %power spectrum coefficient
      ca(u)= c; %c-array
      d =  (2.*xat(u))./(sqrt(gam).*(xat(u).*xbt(u)+(Ca(u).^2))); %power spectrum coefficient
      da(u) = d; %d-array

      Sbb = (abs(ca(u)).^2).*(no+(1/2))+(abs(da(u)).^2).*(nm+(1/2));
      Sbba(u) = Sbb; %Sbb-array
      %Qa(u) = Q;
  end

Q = ((1./(2.*pi)).*trapz(w,Sbba))-0.5; %phonon population

Hello Mr Roberson!

Firstly, thanks for your reply! I think I understand what you're saying, it appears I did not create an array of Sbb before including it into my trapz() function.

I have created an array for Sbb (called Sbba(u)) as shown above in this message while including my trapz() outside the loop. Upon computing, I encounter no errors, however my Q function has only one value instead of a 1x2001 array. This shouldn't be the case since Sbba is an array so I should be having an array of Q values (Qa(u)).

Given the circumstance, I then proceed to put Q back into the loop and defining the array Qa(u) = Q. But this leads me back to the same error as before. Namely: ORDER contains an invalid permutation index

I apologize if I'm not understanding you correctly. I hope this clarifies my progress.

Thanks!

[Walter Roberson]

Perhaps

Q = ((1./(2.*pi)).*cumtrapz(w,Sbba))-0.5; %phonon population