Error in nested integration

I want to integrate a function and program is given below:

close all; 
clear all;
fun = @(x,y)x+(x./(y.^2));
fun1= @(y) y+ integral(@(x)fun(x,y), 0,1);
c1= integral(fun1,0,1)

In the above program if we are using 'y' instead of 'y.^2', then there is no error. But if we are using 'y.^2' error occurred matrix dimension must agree. But here we are using x, y as variable hence there should be no question of matrix dimension. If, anybody can solve the problem please help me . Any suggestions regarding this will be appreciated.

Answer 1

[Torsten]

fun1= @(y) y+ integral(@(x)fun(x,y), 0,1,'ArrayValued',true);

Note that fun is undefined at y=0. Thus c1 should come out as Inf.

Best wishes

Torsten.

[Shweta Rajoria]

Thank you sir.. Actually, the question asked above is the proto-type of my problem. The actual problem is shown below.

 clc;
clear all;
close all;
R=.01:.25:1; %bits /hz/sec
 Pm= 10; Ps=2;t=1; q=4;
M=50; S=20; k = 15; al =0.3;
mu = 1; sigma= 2;
%mean of lognormaldistribution
Es= exp((2*mu/q) + 0.5* (2*sigma/q));
lambdas1 = 10;
lambdam1 = lambdas1/4;
lambdas= Es * lambdas1;
lambdam = Es* lambdam1;
u= (lambdam +(lambdas*(Ps/Pm)^(2/q)));
for n= 1: length(R)
ga1= (S/(M-S-1)).*((2.^(R(n)./al))-1);
fun =  @(w,x) imag(exp(-2.*pi.*lambdas.*((1i.*w.*Ps).^(2/q)).*gamma(2-2/q).*gamma(2/q)./(q-2)).*exp(-1i.*w.*Pm./(ga1.*x.^q)).*exp(-pi.*lambdam.*(((gamma(1-2/q)+(2/q).*igamma(-(2/q),(-1i.*w.*Pm./x.^q)))./(-1i.*w.*Pm).^(-2/q))-x.^2)))./w;
c = @(x) integral(@(w) fun(w,x), 0,Inf,'ArrayValued',true)
fun1= @(x)((1/2)-((1/pi).*c(x))).*2.*pi.*lambdam.*x.* exp(-pi.*u.*x.^2);
c1 = integral(fun1, 0,Inf)
end

In that if i am using 'ArrayValued',true' there the program went to infinite loop and on stopping the program there is error message. Sir, please help me regard this.

[Torsten]

I guess that the division by x^q for x=0 in "fun" is the problem.

Best wishes

Torsten.

[Shweta Rajoria]

Thank you sir.. my problem is solved with your suggestion.