check quadratic formulation in symmetric Q

make_quad.m

function [y,x] = make_quad(Q)
  n=size(Q,1);
  x=sym('x', [n 1]);
  assume(x,'real');
  y=simplify(1/2 * x' * Q * x);
end

usage.lst

>> % Consider f(x) = x1^2 + 3x1x2 + x2^2. We want to express this as 1/2 * x' * Q * x.
>> % I think this Q should be right:
>> Q=[2 3;3 2]

Q =

     2     3
     3     2

>> % Let's verify:
>> [y,x]=make_quad(Q)

y =

x1^2 + 3*x1*x2 + x2^2


x =

 x1
 x2

>> % Guess I was right!
>> % It should work on larger problems too:
>> Q=[  1   0  3/2
        0   0  5/2
      3/2 5/2   10];
>> [y,x]=check_Q(Q)

y =

x1^2/2 + (3*x1*x3)/2 + 5*x3^2 + (5*x2*x3)/2


x =

 x1
 x2
 x3