Multidimensional integration in matlab

I would like to integrate a multivariate function such as

over . Is there a built in function in matlab to do this? Expanding it to a function of , the components of x will be really tedious if the dimension is higher.

Answer 1

[Bjorn Gustavsson]

Have a look at the help and documentation for integral2. That should be the function to do 2-D integrals, that sounds like the function you're looking for.

HTH

[Shunan Sheng]

Thanks, I tried the integral2, but there are some problems. Here is the code:

clear all;
A=diag(ones(2,1));
func = @(x, y)(quadratic_form(x, y, A));
integral_value = integral2(func, -1,1,-1,1);

function value = quadratic_form(x, y, A)
    x=reshape(x,[],1);
    y=reshape(y,[],1);
    mat = [x,y];
    disp(size(mat));
    value = diag(mat * A * mat');
    disp(size(value))
end

In particular, we have error

Error using integral2Calc>integral2t/tensor (line 241)
Integrand output size does not match the input size.

[Bjorn Gustavsson]

That is because your function is array-valued, and as far as I know integral2 doesn't handle that. You might have to evaluate the integral for each component separately.