How to remove error Matrix dimension must agree for double integration

I am calculation the coverage probability of a heterogeneous network. At the time of integration i am getting error. I think the error is basically due to using (x^q) in the denomination of fun. The code is given below:

clear all;
close all;
R=0.5; %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 = 40;
lambdam1 = lambdas1/4;
lambdas= Es * lambdas1;
lambdam = Es* lambdam1;
u= (lambdam +(lambdas*(Ps/Pm)^(2/q)));
ga1=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)
fun1= @(x)((1/2)-((1/pi).*c(x))).*2.*pi.*lambdam.*x.* exp(-pi.*u.*x.^2);
c1 = integral(fun1, 0,Inf)

I am new in matlab. If any body have any idea. Please help. Any advice will be appreciated.

Answer 1

[Walter Roberson]

c = @(X) arrayfun(@(x) integral(@(w) fun(w,x), 0,Inf), X)

integral() calls the target function with a vector of varying length, so fun1 would be called with a vector x. That would cause c to be called with a vector x. The integral() call inside c is going to call fun with a w of varying length that will have nothing to do with the length of x. You then have problems inside fun because your x and w vectors are not the same size.

The change I show causes the inner integral() call to be processed with only one of the x values at a time.

[Shweta Rajoria]

Thank you for the suggestion sir but after using this also i am getting error. I think the error is due to (x^q) term in igamma and one more place in fun. If i replace (x^q) by x, then there is no error. But, i requires to deal with x.

[Walter Roberson]

x.^q

[Shweta Rajoria]

sir, i am using x.^q in the program, still error is coming,by mistake i have written x^q here. After using arrayfun program may be went to infinite loop , output does not come and on stopping the program, error is as follows:

Operation terminated by user during sym/privBinaryOp (line 820)

In sym/igamma (line 10)
Y = privBinaryOp(nu, Z, 'symobj::vectorizeSpecfunc', 'igamma', 'infinity');

In useSymForDouble (line 10)
  res = double(fn(args{:}));

In double/igamma (line 10)
Y = useSymForDouble(@igamma, nu, Z);

In
@(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

In @(w)fun(w,x)

In integralCalc/iterateScalarValued (line 323)
                fx = FUN(t).*w;

In integralCalc/vadapt (line 132)
            [q,errbnd] = iterateScalarValued(u,tinterval,pathlen);

In integralCalc (line 83)
        [q,errbnd] = vadapt(@AToInfInvTransform,interval);

In integral (line 88)
Q = integralCalc(fun,a,b,opstruct);

In @(x)integral(@(w)fun(w,x),0,Inf)

In @(x)arrayfun(@(x)integral(@(w)fun(w,x),0,Inf),x)

In @(x)((1/2)-((1/pi).*c(x))).*2.*pi.*lambdam.*x.*exp(-pi.*u.*x.^2)

In integralCalc/iterateScalarValued (line 314)
                fx = FUN(t);

In integralCalc/vadapt (line 132)
            [q,errbnd] = iterateScalarValued(u,tinterval,pathlen);

In integralCalc (line 83)
        [q,errbnd] = vadapt(@AToInfInvTransform,interval);

In integral (line 88)
Q = integralCalc(fun,a,b,opstruct);

In qqq (line 20)
c1 = integral(fun1, 0,Inf)

i have send the code above, after running that you will be able to get these error.

[Walter Roberson]

You have nested integrals. The calculation can take a long time.

You might want to consider switching from igamma, which calculates symbolically for higher precision, to gammainc, which calculates numerically but would be faster.