Multiply elements in second column according to labels in the first

Question

I'm working in Matlab. I have a two-dimensional matrix with two columns. Lets consider elements in the first column as labels. Labels may be repeated.

How to multiply all elements in the second column for every label?

Example:

matrix = [1,3,3,1,5; 2,3,7,8,3]'

I need to get:

a = [1,3,5; 16,21,3]'

Can you help me with doing it without for-while cycles?

Answer 1

I would use accumarray. The preprocessing with unique assigns integer indices 1:n to the values in the first row, which allow accumarray to work without creating unnecessary bins for 2 and 4. It also enables the support for negative numbers and floats.

[ulable,~,uindex]=unique(matrix(:,1))
r=accumarray(uindex,matrix(:,2),[],@prod)
r=[ulable,r]

/You can also use splitapply:

[ulable,~,uindex]=unique(matrix(:,1))
r=splitapply(@prod,matrix(:,2),uindex)
r=[ulable,r]

Answer 2

You can do it without loops using accumarray and the prod function:

clear
clc


matrix = [1,3,3,1,5; 2,3,7,8,3]';

A = unique(matrix,'rows');

group = A(:,1);

data = A(:,2);

indices = [group ones(size(group))];

prods = accumarray(indices, data,[],@prod); %// As mentionned by @Daniel. My previous answer had a function handle but there is no need for that here since prod is already defined in Matlab.

a = nonzeros(prods)

Out = [unique(group) a]

Out =

     1    16
     3    21
     5     3

Check Lauren blog's post here, accumarray is quite interesting and powerful!