Axis problem in contour plotting

I have plotted this equation by this :

clear all
close all
a=1000;
b=1000;
v0=100;
V=zeros(1000);
V(:,1000)=0;
V(:,1)=0;
V(1,:)=0;
V(1000,:)=100;
[X,Y]=meshgrid(0.01:0.01:10, 0.005:0.005:5);
for x=1:1000
  for y=1:1000
      sum=0;
   for k=1:111
       n=(2*k)-1;
       s=((sin(n.*pi.*x./a)).*(sinh(n.*pi.*y./a)))./(n.*sinh(n.*pi.*(b./a)));
       sum=sum+s;
       
   end
   V(x,y)=(4.*v0./pi).*sum; %here
  end
end
figure
[C,h]=contourf(V);
clabel(C,h)
grid on;
axis('square')

The problem is after running I get this sort of plot:

I am supposed to get something like this :

If I swap V(x,y) with V(y,x) [commented in the code], then I get the right axis. What is happening? Are my x,y values getting interchanged or something? How to resolve this issue? Kindly help!

Thanks!

Answer 1

[Star Strider]

If you use the meshgrid outputs (with one additional argument, so one additional matrix) you get the result you want. It also avoids the loops and is likely much faster:

a=1000;
b=1000;
v0=100;
[X,Y,K]=meshgrid(1:1000, 1:1000, 1:111);
N = 2*K-1;
s = @(x,y,n) ((sin(n.*pi.*x./a)).*(sinh(n.*pi.*y./a)))./(n.*sinh(n.*pi.*(b./a)));
V = 4*v0/pi*sum(s(X,Y,N),3);

figure
[C,h]=contourf(V);
clabel(C,h)
grid on;
axis('square')

I won’t post the plot image here, because it is the one you are supposed to get, and posting it would be redundant.

[John Doe]

Thanks for the reply.

The sum function is useful, but I am curious to know why it is happening like that in "for loop" and is there any solution for it keeping the for loop.

[Star Strider]

As always, my pleasure.

In your loop, you are incrementing ‘k’ first, then ‘y’, then ‘x’, since the inner loops complete before the outer loops, then saving them in the essentially opposite order. The meshgrid function creates matrices that are transposes of the one your loop creates (that is just how meshgrid works), however the ndgrid function (if you want to experiment with it) would re-create the result of your loop (although much faster), and would produce a result that is the transpose of the meshgrid result.

So the matrix created essentially relies on the indexing order (or the meshgrid or ndgrid function) you choose. [Note that some MATLAB functions (I don’t rmemember just now which ones) actually require meshgrid and will throw an error if you use ndgrid to calculate the matrices.]

Since the ‘problem’ (if it can be called such) is the indexing order, the solution would either be to reverse the indices, or transpose the 2D matrices that result.

[John Doe]

This makes so much sense now! I wish I could upvote you 1000x. Truly a MVP of this community. Thank you!

[Star Strider]

I very much appreciate your compliment!

As always, my pleasure!

[Adam Danz]

"Truly a MVP of this community"

@John Doe, I +1'd for ya ;)

[Star Strider]

Thank you!