MATLAB: Plotting from a for loop

for loopplot

Hi, I have a code (given below) where I calculate the trace distance between two matrices and take the output which I have called td2(t) where I have a for loop for values of t. I am able to make td2 into a matrix of all outputs of t and plot for when x and t go from 0 to 5. However when I try to change these values to a different amount, i.e. changing to x=0:1:100 (being sure to change this wherever it comes up in the code) I get an error saying the vectors must be the same length. I'm not sure which part isn't changing correctly. Any help would be appreciated!
A1=0.0023;
A6=12.5/3000;
we1=0;
we5=1.0674245;
r=0;
rhoE=[0.5 + 0.115047, 0.564418 - 0.0959956*1i; 0.564418 - 0.0959956*1i, 0.5 - 0.115047];
rhoN=[0 0; 0 1];
rhoEN=kron(rhoE,rhoN);
rhoSB=tp([0.5 0.5*r; 0.5*r 0.5],4);
rhoin=kron(rhoEN,rhoSB);
PauliX=[0 1; 1 0];
PauliY=[0 -1i; 1i 0];
PauliZ=[1 0; 0 -1];
td1=zeros(0:1:5);
for t=0:1:5;
  H1=we1*kron(PauliX,eye(2))+A1*(kron(PauliX,PauliX)+kron(PauliY,PauliY)+kron(PauliZ,PauliZ));
  H5=we5*megakron(PauliX,eye(2),eye(2),eye(2),eye(2),eye(2))+ ...
      A6*(megakron(PauliX,PauliX,eye(2),eye(2),eye(2),eye(2))+ ...
          megakron(PauliX,eye(2),PauliX,eye(2),eye(2),eye(2))+ ...
          megakron(PauliX,eye(2),eye(2),PauliX,eye(2),eye(2))+ ...
          megakron(PauliX,eye(2),eye(2),eye(2),PauliX,eye(2))+ ...
          megakron(PauliX,eye(2),eye(2),eye(2),eye(2),PauliX)+ ...
          megakron(PauliY,PauliY,eye(2),eye(2),eye(2),eye(2))+ ...
          megakron(PauliY,eye(2),PauliY,eye(2),eye(2),eye(2))+ ...
          megakron(PauliY,eye(2),eye(2),PauliY,eye(2),eye(2))+ ...
          megakron(PauliY,eye(2),eye(2),eye(2),PauliY,eye(2))+ ...
          megakron(PauliY,eye(2),eye(2),eye(2),eye(2),PauliY)+ ...
          megakron(PauliZ,PauliZ,eye(2),eye(2),eye(2),eye(2))+ ...
          megakron(PauliZ,eye(2),PauliZ,eye(2),eye(2),eye(2))+ ...
          megakron(PauliZ,eye(2),eye(2),PauliZ,eye(2),eye(2))+ ...
          megakron(PauliZ,eye(2),eye(2),eye(2),PauliZ,eye(2))+ ...
          megakron(PauliZ,eye(2),eye(2),eye(2),eye(2),PauliZ));
    U1=expm(-1i*H1*t);
    U5=expm(-1i*H5*t);
    rhoout=U5*rhoin*U5';
    rhoENout=U1*rhoEN*U1';
    pt=PartialTrace(rhoout,[3,4,5,6],[2,2,2,2,2,2]);
    td1=(pt-rhoENout)^2;
    td2(t+1)=sqrt(sum(td1(:)));
    x=0:1:5;
    plot(x,td2)
end

Best Answer

 td1=zeros(0:1:5);
 for t=0:1:5;
   ...      
   pt=PartialTrace(rhoout,[3,4,5,6],[2,2,2,2,2,2]);
   td1=(pt-rhoENout)^2;
   td2(t+1)=sqrt(sum(td1(:)));
   x=0:1:5;
   plot(x,td2)
  end
There's no point in redefining x over and over as a constant...move it out of the loop. Then, having "magic numbers" buried in the code is error prone and painful to have to edit as you've already learned so make a parameter that only need to change it (or use a functional form instead of script and make it an argument of the function).
N=5;                % upper limit on t vector
t=0:N;              % define t
td1=zeros(size(t)); % preallocate output to match
for i=1:length(t)   % iterate over elements of x
  ...   
  U1=expm(-1i*H1*t(i));  % now use element of t array...
  U5=expm(-1i*H5*t(i));
  ... 
  pt=PartialTrace(rhoout,[3,4,5,6],[2,2,2,2,2,2]);
  td1=(pt-rhoENout)^2;
  td2(i)=sqrt(sum(td1(:)));   % store output
end
plot(t,td2)   % move plot until done then plot the arrays
The above uses 1:length of array as the indexing to avoid the "plus one" issue in avoiding the zero-th illegal array indexing and then plots the whole arrays when accumulated. This has the side effect of also allowing other than integer-valued t values if that's eventually desired.
On changing N to other sizes, the above should automagically take care of that, too...
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