Evaluate a function in a grid

I want to plot an isosurface of a function*_ v_*.

Problem is that v doesn't accept matrix arguments (not vectorizable function as it contains Laguerre associated polynomials)

So if I create a meshgrid for the values of x,y,l

      [r,th,l]=meshgrid(0:0.5:5,0:pi/2:2*pi,0:2);
       x=r.*cos(th);
       y=r.*sin(th);

Then I suppose to evaluate v using loops (counters) as I can not bypass x , y & l as arguments

But I'm doing something wrong, and as a consequence I'm not evaluating v in the points of the grid:

for l=0:2
k=k+1;
    for r=0:0.5:5
    i=i+1;
        for th=0:pi/2:2*pi
        j=j+1;      

fun1=@(R)4*real(exp(-r.^2-R^2+2*1i*R*l./r).*(r+1i*R).^(2*l).*...
  (mfun('L',n/2-l/2,l,r.^2+R^2)).^2);

v(i,j,k)=integral(fun1,-inf,inf);

          end
      end  
  end

does someone knows how to do the loops so I can obtain a v that matches in size with x, y, l so I can use:

isosurface(x,y,l,v) ??

or does someone knows how to obtain the mentioned isosurface v through an alternative way?

I actually need all the help I can get to do this.

Thanks, Pablo

Answer 1

[Jonathan Epperl]

Does that code run for you? I'm sure it doesn't, you should have mentioned that, along with the error messages...

Anyway, there are several problems:

• integral needs the option 'ArrayValued',true to integrate vector valued functions.
• the term 1./r in your fun1 evaluates to [Inf ...]
• you redefine l (terrible choice of a variable name btw) as your loop variable, so by the time the loop is done (once you fixed it), l will have the value 2, and not be a 3-dim array.

Fix that, see if it works, if it doesn't come back here, this time with error messages, please.

[Pablo]

No well, when you try to evaluate isosurface(x,y,l,v) it returns you the message error

Error using isosurface (line 74)
The size of X must match the size of V or the number of columns of V.

Error in proyecto3 (line 29)
fv = isosurface(x,y,z,v,0.5);

They just would have the same dimension if counters i and j didn't change during the loops that change the value of variables r and l(sorry for the name)

then, I don't know exactly how to do

thanks for your comment,

Pablo