double integral infinite limits

is there any idea how can i calculate the integral of this function with infinite limits -00,+00

function Fr = int_frustration_function2(x,Kt,i)

Fr = dblquad(@(v,u)fun2(v,u,x,Kt,i),-Inf,Inf,-Inf,Inf);

end

where for fun2

function fun2 = fun2(v,u,x,Kt,i)

global SNR sigma_a q

k= 1./(sqrt(2.*pi.*((sigma_a./q).^(2))));

temp1=((log(v)+((sigma_a./q).^(2))).^(2)); temp2=(2.*((sigma_a./q).^(2))); temp3=exp(-temp1./temp2);

temp4=((B1N(Kt,0,u,i).*SNR.*x)./4);

fun2 = k.*exp(-(u.^2)).*(besseli(0,0).*exp(-temp4.*(v.^(2))).*temp3);%

end

please help!!!

Answer 1

[Mike Hosea]

This is easy to modify if you want c and/or d to be a function handle, like for QUAD2D. Also, it should be easy to add tolerances or whatever options you would like.

function y = mydblquad(fun,a,b,c,d)
% Double integral using QUADGK.
innerintegral = @(x)arrayfun( ...
    @(xi,y1i,y2i)quadgk(@(y)fun(xi*ones(size(y)),y),y1i,y2i), ...
    x,c*ones(size(x)),d*ones(size(x)));
y = quadgk(innerintegral,a,b);  

>> mydblquad(@(x,y)1./(1+x.^4+y.^4),-inf,inf,-inf,inf)
  ans =
     5.824747385361142

[kostas]

my function is fun2(v,u,x,Kt,i) and i want to integrate it for the variables v,u from -Inf,Inf both of them..

How can i do it in the way you've sai above..Its a bit complicated for me because i 'm beginner..

[Walter Roberson]

Use Mike's mydblquad function, and call it as

mydblquad(@(v,u) fun2(v,u,x,Kt,i),-inf,inf,-inf,inf)

[kostas]

thanks a lot! in case i want to calculate the integral only inegrationg the variable v from -inf,Inf???

could you suggest me the best way???

thanks

[Walter Roberson]

If u appears in the calculation of fun2(v,u,x,Kt,i) then integrating only along v would require an expression in u as the output. That would require symbolic integration rather than numeric integration. Symbolic integration is possible with the Symbolic Toolbox using the int() function.

[Gautam]

This was a very helpful post as I was wondering how I would achieve a double integration where the limits could be Inf. Following on Mike's post, I just wanted to confirm that the following modification to Mike's code to handle the case where the upper limit of the inner integral (the integration variable being y) is a function of x:

function y = mydblquad(fun,a,b,c,d) innerintegral = @(x) arrayfun(... @(xi,yli,y2i)quadgk(@(y)fun(xi*ones(size(y)),y),yli,y2i),... x,c*ones(size(x)),feval(d,x)); y = quadgk(innerintegral,a,b);

I tried the above and it seems to work fine. Any comments would be appreciated.

- Gautam

[Mike Hosea]

One can indeed extend that method to use arbitrary lower and upper limit functions on the inner integral. I should note that the answer I gave above is somewhat old now. If you have the 2012a release of MATLAB you can use INTEGRAL2 "out of the box".

Answer 2

[the cyclist]

There is some discussion here that may help you:

http://www.mathworks.com/matlabcentral/answers/13616-double-integration-problem

Be sure to look at the comments, too, particular the ones from Walter.