Differentiate symbolic sum of vectors

Hello,

I'm certainly not the first to ask such kind of question, but I can't find appropriate answer...

I'm trying to make a sum of vector elements with symbolic indexes. The sum will then be differentiated in order to find the maximum of it. Here is the "code":

function kd = est(y, p, D) 
   K0 = size(p,2);
   Kp = (size(y,2) - K0)/2;

   syms m;

   som = 0;
   for k=1:Kp-D
        val = y(k+m+D+K0)*conj(y(k+m+D+K0))*conj(p(k+D))*p(k);
        som = som+val;
    end;

    Rd(m) = abs(1/(Kp-D)*som);

    kd = solve(diff(Rd(m)));
  end

y and p are known vectors and D is a scalar. For the moment, the error occurs in the for-loop, stating that "Indexing input must be numeric, logical or ':'."

If I try using the function_handle syntax, then the error occurs when assigning Rd(m)...

Any suggestion would be appreciated.

Answer 1

[ata]

Thanks for replying!

I needed this summation from the formula I was writing there (something for frame synchronisation with pilot symbols). But I found the solution in the meantime, although not really elegant... I made a loop for the values of 'm', since we can determine limits for this variable with the size of vector y.

Then I don't need to differentiate the expression, indeed.

Answer 2

[Azzi Abdelmalek]

y=[1 2 3]; 
syms m
y(m)

Error using sym/subsindex  
Indexing input must be numeric, logical or ':'.

That means you can't use a symbolic index. You should assign a positive integer value to m before using it as an index

Answer 3

[Walter Roberson]

      Rd = abs(1/(Kp-D)*som);

      kd = solve(diff(Rd), m);

I have to guess that you want to differentiate with respect to "m", as there are no other variables in your expression.

I do not know how you intend to find a maximum by differentiating: differentiation requires that the function be continuous, but everything you are working with is discrete -- you are passing in vectors for y and p, not functions, and your m is being used as an index, not as a continuous variable.

If you wish to find the largest term, then do not do a summation, just find max() of the sequence of values.