Vector length error while using built-in function quad with diff

I tried to solve integral problem with built-in function quad. But I couldn't get the solution. The simplified version of my code is given below.

F=@(x)(diff(x).*diff(x)); Q = quad(F,-1,1)

But I have got the following error message;

??? Error using ==> quad at 80 The integrand function must return an output vector of the same length as the input vector.

Error in ==> Untitled at 3 Q = quad(F,-1,1)

I know that "diff" reduces the length of a vector by one, but I couldn't find way to solve this problem.

Thanks for your time.

Answer 1

[Jan]

You can append a 0:

F = @(x)([0, diff(x) .* diff(x)]);
Q = quad(F, -1, 1)

Which effects does this have to the results?

Another idea:

F = @(x)(gradient(x) .* gradient(x));
Q = quad(F, -1, 1)

The result is slightly different.

Answer 2

[the cyclist]

I am assuming that you are using "diff" inside your function F because it represent a numerical derivative of some kind. If that is the case, I recommend some caution, because simple differencing is not a very good way of doing that. I can make two related suggestions.

First, you could use the gradient() function instead of diff().

F=@(x)(gradient(x).*gradient(x));
Q = quad(F,-1,1)

[ Carefully read the documentation for gradient, as it makes different assumptions about the spacing of "x" that I am not 100% sure are what you need. ]

This should solve your length problem as well as being more numerically stable.

The second is to read this thread that discusses some of these issues. In particular, carefully read the posts from John D'Errico, a very knowledgeable user.

http://www.mathworks.com/matlabcentral/newsreader/view_thread/275252