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

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smashing
smashing 2014-4-1
编辑： Image Analyst 2014-4-1
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.
  2 个评论
Patrik Ek
Patrik Ek 2014-4-1
编辑：Patrik Ek 2014-4-1
integral(f{1}+f{2}) = integral(f{1}) + integral(f{2}). This is a fundamental theorem of mathematics.
smashing
smashing 2014-4-1
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.

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采纳的回答

Azzi Abdelmalek
Azzi Abdelmalek 2014-4-1
f{1} = @(x) x;
f{2} = @(x) x.^2;
g=@(x) f{1}(x)+f{2}(x)
integral(@(x) g(x), -3,3)
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Azzi Abdelmalek
Azzi Abdelmalek 2014-4-1
编辑：Azzi Abdelmalek 2014-4-1
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)

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Sean de Wolski
Sean de Wolski 2014-4-1
编辑：Sean de Wolski 2014-4-1
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 /*^)
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Sean de Wolski
Sean de Wolski 2014-4-1
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
Azzi Abdelmalek 2014-4-1
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.

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