How do I use of "trapz" for numerical integration?

Hi everyone. I tried to use of "Tarpz" command for numerical integration and I use of "Meshgrid" command for make a matrix.in final, when script running, I get this error: X must be a vector. so How I can use of the "Tarpz" for my work? and I do not get the mentioned error.

close all

clear all

clc

z=0.42;

wvl=1030e-9; % is wavelength k=(2*pi)/wvl;

w0=0.1;

zr=pi*w0.^2/wvl;

w=w0*sqrt(1+(z/zr));

R=z*(1+(zr/z).^2);

x_1=linspace(-1,1,1000);

x_2=linspace(-1,1,1000);

[r1, r2]=meshgrid(x_1,x_2); [r3, r4]=meshgrid(x_1,x_2);

u1=w0/w*exp(-(r1.^2+r2.^2).^2/w.^2)*exp(-1i*k*z).*exp(-1i*k*(r1.^2+r2.^2).^2/(2*R))*exp(atan(z/zr)); % guassian beam fomula

A=(1/sqrt(1i))*sqrt(2*z./(pi*k*r1.*r2))*exp(-(1i*k*r1.*r2)/z); % bessel function formula that converted to expotential form

u2=trapz(r1,A.*u1);

Answer 1

[Roger Stafford]

The quantity which you have designated as 'r1' in the call to 'trapz' is meant to represent the variable of integration, and as such it must be either a scalar giving constant increments of this variable or a vector giving its successive values. It cannot be a two-dimensional array as you have produced from 'meshgrid'. You need to carefully read the documentation for 'trapz' at:

   http://www.mathworks.com/help/matlab/ref/trapz.html

and then rethink your implementation so as to comply with this requirement.

[Added comment] It looks as though you are attempting to perform a double integration wherein there are two variables of integration. If so, you can only do that using 'trapz' by making two successive calls on it in an appropriate manner.