why result is zero?

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

[Habib]

Thank you for your answer.

I read it, but i couldn't understand what is wrong. Now, what must I do? how i can fixed it?

[Torsten]

x = -3:.1:3; 
y = -5:.1:5; 
[X,Y] = meshgrid(x,y); 
F = X.^2 + Y.^2;
I = trapz(y,trapz(x,F,2));

integrates the function f(x,y)=x^2+y^2 over the rectangle [-3:3]x[-5:5].

Now insert your function and your domain of integration.

Best wishes

Torsten.

Answer 1

[Torsten]

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.