How to use an integral inside another integral

I have the following code:

function [answer]=find_integral2(z)
F=@(y) find_integral(z-y).*find_integral(y);
answer= integral(F,-Inf,Inf);
end

function [answer]=find_integral(u)
F = @(x)normpdf(x).*normpdf(u./x); 
answer= integral(F,-Inf,Inf);
end

When I call the function find_integral2(4), I get the following error:

Error using ./ Matrix dimensions must agree.

I know I can solve this with triple integral but I want to call find_integral2 several times, i.e. , I want to again use it in another function:

F=@(y) find_integral(z-y).*find_integral2(y);answer= integral(F,-Inf,Inf);

I would appreciate if you could help me fix this error. Thank you.

Answer 1

[Mike Hosea]

Either this (find_integral is unchanged)

function [answer]=find_integral2(z)
F=@(y) arrayfun(@(y)find_integral(z-y).*find_integral(y),y);
answer= integral(F,-Inf,Inf);
end

or this

function [answer]=find_integral2(z)
F=@(y) find_integral(z-y).*find_integral(y);
answer= integral(F,-Inf,Inf,'ArrayValued',true);
end

[may]

Thanks a lot! It worked! Just a question, do you know any faster way to calculate integral with matlab? because I want to use find_integral2 recursively, and for the following function it took one hour to get the result!

function [answer]=find_integral3(z)
F=@(y) arrayfun(@(y)find_integral2(z-y).*find_integral(y),y);
answer= integral(F,-Inf,Inf);
end

[Mike Hosea]

Well, you could loosen the tolerances, say add the arguments

'AbsTol',1e-5,'RelTol',1e-3

to the integral calls.

That took about 110 seconds on my machine, which is admittedly a new workstation. For something completely different you might look into Monte Carlo or Smolyak methods. These iterated integrals just aren't that efficient as the dimension goes up. Nice set of slides here

http://people.sc.fsu.edu/~jburkardt/presentations/fsu_2010_sparse.pdf

[may]

Thank you SO MUCH! using 'AbsTol',1e-5,'RelTol',1e-3, now it takes around 1 minute!

[may]

Thanks a lot for your help again. so now using 'AbsTol',1e-5,'RelTol',1e-3, I could speed up the function find_integral3(z) (mentioned above), but now I want to again use it to calculate the following integral (this is actually the final problem I want to solve)

F = @(y)find_integral3(z)(z-y).*find_integral3(y);
answer= integral(F,-Inf,Inf,'AbsTol',1e-5,'RelTol',1e-3);

Even after around 8 hours, it did not terminate! I would appreciate if you could help me again.