title: Calculate Rao's quadratic entropy
body: <p>Rao QE is a weighted Euclidian distance matrix. I have the vectors for the elements of the d_ijs in a data table dt, one column per element (say there are x of them). p is the final column. nrow = S. The double sums are for the lower left (or upper right since it is symmetric) elements of the distance matrix. 
  <a href="https://i.stack.imgur.com/j0z1N.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/j0z1N.png" alt="Formula for Rao&#39;s QE"></a></p>
  
  <p>If I only needed an unweighted distance matrix I could simply do dist() over the x columns. How do I weight the d_ijs by the product of p_i and p_j?</p>
  
  <p>And example data set is at <a href="https://github.com/GeraldCNelson/nutmod/blob/master/RaoD_example.csv" rel="nofollow noreferrer">https://github.com/GeraldCNelson/nutmod/blob/master/RaoD_example.csv</a> with the ps in the column called foodQ.ratio.</p>