MATLAB: Why result is zero

trapz

Hi everybody. In second "for" nesting loop, I want to use Trapz command (numerical integration) for integration from an N*N matrix (u_2) but I got zero answer? What is wrong? I hope one give an answer.
 clc
 clear all
 close all
 aa=3e-2;
 E0=10000;
 z=0.42;
 L=z;
 N=100;
 lambda=1030e-9;
 k=2*pi/lambda;
 w0=0.0001;
 zr=pi*w0^2/lambda;
 R=z*(1+(zr/z)^2);
 w=w0*sqrt(1+(z/zr)^2);
 D1=linspace(-aa/2,aa/2,N);
 [x,y]=meshgrid(D1,D1);
 b=(lambda*L)/(N*aa);
 D2=linspace(-b/2,b/2,N);
 [xx,yy]=meshgrid(D2,D2);
 RR=1.5;
 u1=ones(size(x));
 u_2=u1;
 u2=ones(size(xx));
 [teta,r]=cart2pol(x,y);
 [teta1,rr] = cart2pol(xx,yy);
 for i=1:N
     for j=1:N
         u1(i,j)=E0*(r(i,j)/w)*exp(-(r(i,j)/w).^2);
     end
 end
 for i=1:N
     for j=1:N
         u_2(i,j)=u1(i,j)*besselj(1,-k*r(i,j)*rr(i,j))*exp(-1i*k*rr(i,j)^2/(L*w^2))*cos(teta1(i,j));
         u2(i,j)=trapz(u_2(i,j));
     end
 end

Best Answer

Take a look at the chapter "Multiple numerical integrations" under
http://de.mathworks.com/help/matlab/ref/trapz.html
to see what is wrong with your call to trapz.
Best wishes
Torsten.
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