sum of function handle

Dear all, i have the following function:

 sum_{1<=i<j<=n}(X_i-X_j)

and i need to write it as function handle. Can anyone help me please. Best regards.

[Adam]

Write it as a function first, then the function handle part is trivial.

Trying to go straight from what you have there to a function handle is probably an unnecessarily complicated step unless for some reason you aren't allowed to create actual functions.

[Heborvi]

Thank you for your comment. I try to write this function but it gives me an error on X (Undefined function X):

function [f]=Target_Distribution(n,q,D)
S=0;
for i=1:n
    for j=i+1:n
        for k=1:q
        S=S+X(i,k)-X(j,k)^2;
        end
        somme(t)=sqrt(S)-D(i,j);
        t=t+1;
        S=0;
    end
end
Sum_Tot=sum(somme);
f=@(X) Sum_Tot;

[Guillaume]

Your function does not appear to be the same thing at all as the expression you wrote in your question. Why is there a third iterator k, why is there a square ^2 and later a square root sqrt ?

[Heborvi]

X is a matrix (n x q), each X_i is a vector in R^q. My function is the following:

 sum_{1<=i<j<=n} abs( (sqrt(sum_{k=1}^{q} (X(i,k)-X(j,k))^2)-D(i,j)) )

In the first question, i have introduced a simple problem to show how the summation of function handle works.

Answer 1

[Guillaume]

"I need to write it as function handle". Why do you need it? As Adam says, work it out as a normal function.

Anyway:

sumdiff = @(x) sum(diff(x(nchoosek(1:numel(x), 2)), [], 2));  %assume x is a vector

The way this works:

• nchoosek returns all the possible combinations of i and j that satisfy 1<=i<j<=n
• these combinations are use to index the original array as two columns, x(i) in the first column, x(j) in the second
• diff calculates the difference between the 2nd and 1st column
• sum sum all the differences

[Heborvi]

Thank you for your answer. In fact the matrix X is unknown therefore i need to write the fuction as function handle.

[Guillaume]

The matrix x may be unknown, that does not preclude writing the function as a regular function.

 function s = sumdiff(x)
    s = sum(reshape(triu(bsxfun(@minus, x(:), x(:).'), 1), [], 1)); %Matt's answer is more efficient than mine
 end

[Heborvi]

If X is a matrix, this function works? it is possible to include a loop in an handle function? (my algorithm take the fuction as handle function )

[Adam]

You can include anything you like in a handle function if it isn't an anonymous function.

You literally just define your function and then use function handle syntax to create a handle to it. The function could be 5000 lines long if you really want (obviously not advisable!), e.g.

function s = sumdiff(x)
   ...
end

f = @(x) sumdiff(x)
s = f(x);

Answer 2

[Matt J]

   f=@(X) sum( reshape( triu( bsxfun(@minus, X(:),X(:).'),1), [],1) )

Answer 3

[Matt J]

g=@(X) (length(X):-1:1)*X(:) - sum(cumsum(flip(X)))

[Heborvi]

if X is a matrix, flip(X) works?

[Adam]

doc flip

[Matt J]

if X is a matrix, flip(X) works?

I've been assuming -- as your original post assumes -- that X is a vector.