Find the mean of a sub matrix if the first column of the matrix provides the index values

Question

For a given matrix Z and assuming the first column refers to index values, is it possible to find the mean of Z(:,2:3) based on the index values in the first column Z(:,1).

Z  =  [1    3    4
       2    7    8
       1    3    9
       3    4    4
       1    5    7]

So how can I loop over Z to find the mean of corresponding rows with index value 1 (in the first column) i.e finding the mean of Z1

Z1  =    3  4
         3  9
         5  7

Please can anyone help by explaining how to do this?

Answer 1

This should do the trick:

mean(mean(Z(Z(:,1)==1,2:3)))

Answer 2

How about:

mean([accumarray(Z(:,1), Z(:,2),[],@mean), accumarray(Z(:,1), Z(:,3),[],@mean)]')'

It gives you the mean corresponding to each number. i.e. row one of the result is the mean for rows corresponding to 1, row two is for 2 etc

Answer 3

Bsxfun appproach -

Zc = [Z(:,1) mean(Z(:,[2 3]),2)]

ind1 = bsxfun(@eq,Zc(:,1),min(Zc(:,1)):max(Zc(:,1)))
mean_values = sum(bsxfun(@times,ind1,Zc(:,2)))./sum(ind1,1)

Output -

mean_values =
    5.1667    7.5000    4.0000

Answer 4

To do that for every index in column 1, all at once:

>> accumarray(repmat(Z(:,1),size(Z,2)-1,1), reshape(Z(:,2:3),[],1), [], @mean)
ans =
    5.1667
    7.5000
    4.0000