Understanding Matrix Notation/Arithmetic

I am a Matlab newbie, so please be gentle.

I am attempting to port some Matlab code to C++ and am not following some of the syntax.

Here is the code I am porting:

[ndata, dimx] = size(x);
[ncentres, dimc] = size(c);
if dimx ~= dimc
  error('Data dimension does not match dimension of centres')
end

n2 = (ones(ncentres, 1) * sum((x.^2)', 1))' + ...
      ones(ndata, 1) * sum((c.^2)',1) - ...
      2.*(x*(c'));

In this code, x and c are both two dimensional matrices, each with two columns and many rows.

I am getting lost on the n2 line.

Focusing on the clause: "sum((x.^2)',1))'".

I believe that squares every element in the x matrix.

Then transpose the matrix (resulting in a 2xN matrix).

Then sum each column of the matrix (resulting in a 1xN matrix).

Then transpose again (resulting in a Nx1 matrix).

Is this correct?

Thanks for any help.

Answer 1

[Jan]

Almost. You need the first part also:

(ones(ncentres, 1) * sum((x.^2)', 1))'

sum((x.^2)', 1) this is: square elements, transpose, sum over 1st dimension.

Then it is mutliplied with a [M x 1] matrix consisting of 1s from the right and transposed afterwards. Shorter (and faster):

sum(x.^2, 2) * ones(1, ncentres)

The multiplication repeates the columns only, so this is equivalent to:

repmat(sum(x.^2, 2), 1, ncentres)