I'd like to dynamically construct a function that can then be referred to with a function handle for later use in Matlab functions such as integral(fun,a,b).
As an example imagine a function with terms:
(x-A)/(D-A) * (x-B)/(D-B) * (x-C)/(D-C)
where x is a variable and A,B,C,D are constants from a vector (call it K=[A,B,C,D]' as an example) generated by a different function.
I could do:
fun = @(x) (x-A)/(D-A) * (x-B)/(D-B) * (x-C)/(D-C)
However, this restricts me to three terms. I'd like to be able to take an arbitrary length vector of constants and generate a function of similar form to the one above. Normally this is easy in Matlab, but it seems like function handles expect 'x' to be a scalar, so something like:
prod( (x - K(1:3)) ./ K(4)-K(1:3) )
returns an error.
It's not true that
function handles expect 'x' to be a scalar
The problem is not the function handle, nor the fact that the function is anoymous. The problem is simply the operation you use to define that function: you can't do
prod( (x - K(1:3)) ./ K(4)-K(1:3) )
when both x and K are vectors with arbitrary sizes. As a side note, you have a pair of brackets missing in the denominator.
What you want (if I understand correctly) can be done using bsxfun twice. Assuming both x and K are column vectors, use
prod(bsxfun(@rdivide, bsxfun(@minus, x.', K(1:end-1)), K(end)-K(1:end-1)))
to compute your function.
So: first define K and then you can define the anonymous function and its handle as
fun = @(x) prod(bsxfun(@rdivide,bsxfun(@minus,x.',K(1:end-1)),K(end)-K(1:end-1)))
Note that the value of K is "hardwired" into the anonymous function when you define the latter. The function won't change if you later modify K (unless of course you define the function again with the new K).
Example:
>> K = [3 4 5 6].';
>> fun = @(x)prod(bsxfun(@rdivide,bsxfun(@minus,x.',K(1:end-1)),K(end)-K(1:end-1)));
>> x = [1 2].';
>> fun(x)
ans =
-4 -1
Check:
>> prod( (x(1) - K(1:3)) ./ (K(4)-K(1:3)) )
ans =
-4
>> prod( (x(2) - K(1:3)) ./ (K(4)-K(1:3)) )
ans =
-1