Question

I have a 30-vector, x where each element of x follows a standardised normal distribution.
So in Matlab,

I have:

for i=1:30;
x(i)=randn;
end;

Now I want to create 30*30=900 elements from vector, x to make a 900-vector, C defined as follows:

I am unable to do the loop for two variables (k and l) properly. I have:

for k=1:30,l=1:30;
C(k,l)=(1/30)*symsum((x(i))*(x(i-abs(k-l))),1,30+abs(k-l));
end

It says ‘??? Undefined function or method ‘symsum’ for input arguments of type
‘double’.‘

I hope to gain from this a 900-vector, C which I will then rewrite as a matrix. The reason I have using two indices k and l instead of one is because I eventually want these indices to denote the (k,l)-entry of such a matrix so it is important that that my 900-vector will be in the form of C = [ row 1 row 2 row 3 … row 30 ] so I can use the reshape tool i.e.

C'=reshape(C,30,30)

Could anyone help me with the code for the summation and getting such a 900 vector.

Answer 1

Let’s try to make this a bit efficient.

n = 30;
x = randn(n,1);

%# preassign C for speed
C = zeros(n); 

%# fill only one half of C, since it's symmetric
for k = 2:n
   for l = 1:k-1
      %# shift the x-vector by |k-l| and sum it up
      delta = k-l; %# k is always larger than l
      C(k,l) = sum( x(1:end-delta).*x(1+delta:end) );
   end
end

%# fill in the other half of C
C = C + C';

%# add the diagonal (where delta is 0, and thus each
%# element of x is multiplied with itself
C(1:n+1:end) = sum(x.^2);