# Anonymous functions and integration

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I want to integrate an anonymous function but be able to manipulate it first. For example

f = @(x) [x -x sin(x)];

r = integral (f'*f, 0, 1, 'ArrayValued', true);

This isn't possible. I would have to define a new function but this isn't flexible. Any alternatives to directly manipulate f?

##### 1 Comment

Cedric Wannaz
on 22 Apr 2013

Edited: Cedric Wannaz
on 22 Apr 2013

Either

r = integral (@(x)f(x)'*f(x), 0, 1, 'ArrayValued', true);

or

g = @(x)f(x)'*f(x) ;

r = integral (g, 0, 1, 'ArrayValued', true);

but that's what you call defining a new function I guess.

### Accepted Answer

Kye Taylor
on 22 Apr 2013

Try

r = integral (@(x)f(x)'*f(x), 0, 1, 'ArrayValued', true);

##### 2 Comments

Kye Taylor
on 22 Apr 2013

Edited: Kye Taylor
on 22 Apr 2013

Well, the integral function actually evaluates the function handle many times!

But, to answer your question, each time the function handle g = @(x)f(x)'*f(x) is evaluated by the integral function, the function handle f will be evaluated twice, though this will hardly affect performance.

If you're unconvinced, you could instead define the entire outer product:

g = @(x)[x^2 -x^2 x*sin(x);-x^2 x^2 -x*sin(x);x*sin(x) -x*sin(x) sin(x)^2]

then integrate

integral (g, 0, 1, 'ArrayValued', true);

### More Answers (1)

Mike Hosea
on 22 Apr 2013

MATLAB files can be flexible when they are combined with the use of anonymous functions. Anonymous functions can also be supplied as parameters to anonymous functions. The example given can be handled with simple nesting:

f1 = @(x)[x -x sin(x)]

f2 = @(x)x'*x;

g = @(x)f2(f1(x));

r = integral (g, 0, 1, 'ArrayValued', true);

More cleverness may be required in some cases, I guess. You can extend f2 to accept multiple inputs based on x or nest deeper, constructing what amounts to an evaluation tree to minimize redundant computations. -- Mike

##### 2 Comments

Mike Hosea
on 22 Apr 2013

Edited: Mike Hosea
on 22 Apr 2013

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