Problem with quad: how to handle a loop in the integrand function ?

I would like to integrate over a function which uses a loop. I simplified the example on purpose. This integrand function is :

      function [EU]=toy(d1,M)
           test=zeros(size(M,1),size(M,2))
           for i=1:size(M,1)
               for j=1:size(M,2)
                   test(i,j)=M(i,j)+d1;
               end
           end
EU=sum(sum(test);

When I use:

ex=quad(@(d1) toy(d1,M),0.3,0.5)

I get an error message:

??? Subscripted assignment dimension mismatch.

Error in ==> toy at 6
       test(i,j)=M(i,j)+d1;

Error in ==> @(d1)toy(d1,M)

Error in ==> quad at 76
y = f(x, varargin{:});

However, for any particular value of d1, the function yields a unique number. When I try alternative functions within the loop, I always get some kind of error. Has this to do with the way quad works ? Is there some solution ?

Thanks a lot in advance for your replies.

Best regards,

Guillaume

Answer 1

[Mike Hosea]

QUAD, and most of the other integration functions in MATLAB, is written to evaluate the integrand at more than one point at a time. So it is expects to pass a vector input and get a vector output. You can add this "vectorization" with a loop in your integrand:

function EU = toy(d1,M)
EU = zeros(size(d1));
for k = 1:numel(EU)
    test = zeros(size(M,1),size(M,2));
    for i=1:size(M,1)
        for j=1:size(M,2)
            test(i,j) = M(i,j) + d1(k);
        end
    end
    EU(k) = sum(sum(test));
end

Another way to add the outer loop (without modifying the integrand) is to use ARRAYFUN. Finally, QUAD is obsolete. We now recommend INTEGRAL. INTEGRAL expects the same kind of vectorization, but it also has the 'ArrayValued' option. If you set 'ArrayValued' to true, it will assume your function is vector-valued (doesn't matter if the vector only has one element!), so it will only call the integrand with scalar inputs. -- Mike

[Guillaume]

Thanks a lot. This is extremely helpful.