How to calculate the integral of the complicated functions of function handles in a cell?

Hi, I stuck for two days. I don't know how to calculate the integral of the sum of function handles in a cell. Please see the below examples:

f{1} = @(x) x;

f{2} = @(x) x^2;

g = @(x) sum(cellfun(@(y) y(x), f));

integral(@(x) g, -3,3);

Error: Input function must return 'double' or 'single' values. Found 'function_handle'.

PS: please don't change the formula, because this is just an example. My real problem is far more complicated than this. It has log and exp of this sum (integral(log(sum), -inf, inf)). So I can't break them up to do the integral individually and sum the integrals.I need to use sum(cellfun). Thank you.

Version: Matlab R2012a

Can anyone help me? Really appreciate.

[Patrik Ek]

integral(f{1}+f{2}) = integral(f{1}) + integral(f{2}). This is a fundamental theorem of mathematics.

[smashing]

Hi Patrik,

Thanks for the tip. As I said, my problem is comlicated than this example. It is not a sum, it has log and exp. So I can't break them up to do the integral individually and sum the integrals.

Answer 1

[Azzi Abdelmalek]

f{1} = @(x) x;
f{2} = @(x) x.^2;
g=@(x) f{1}(x)+f{2}(x)
integral(@(x) g(x), -3,3)

[smashing]

Thank you Azzi, is there any way that you can work it out using sum? Because in my real problem, the sun-function has dynamic range, i.e., f{1},...f{i}... It depends on another input.

[Azzi Abdelmalek]

Maybe there is better. for the moment I have one solution using eval

f{1} = @(x) x;
f{2} = @(x) x.^2;
n=numel(f)
d=['g=@(x)' sprintf('f{%d}(x)+',1:n)]
d(end)=[]
eval(d)
integral(@(x) g(x), -3,3)

[smashing]

This is great! I think this is the solution I am looking for. Thanks Azzi.

Answer 2

[Sean de Wolski]

Here's a method that scales:

f{1} = @(x) x;
f{2} = @(x) x.^2;
f{3} = @(x) exp(x)-log(x);
I = sum(cellfun(@(fun)integral(fun,-3,3),f))

Instead of using cellfun to evaluate the functions, use it to evaluate the integral and sum the integrals as Patrik suggested above.

Note you need to vectorize the functions (. before /*^)

[smashing]

Hi Sean,

Thanks for the tip. As I said, my problem is comlicated than this example. It is not a sum, it has log and exp. So I can't break them up to do the integral individually and sum the integrals.

[Sean de Wolski]

Huh?

cellfun(@(fun)integral(fun,-3,3),f)

Evaluates the integral over the range for each function in funs. Do with this info as you wish!

[Azzi Abdelmalek]

Smashing, you have to be clear, your question was about the sum. If there is something else, please edit your question and make it precise.