Friday, 13 January 2012

Finding the diagonal of a non-square matrix with matlab.

Sometime you need to find something similar to a diagonal in a non-square matrix. For instance, in neural networks, when you have an x layer of m units to be topologically connected to an y layer of n units, you could simply fill the diagonal elements of the matrix W of weights. so that the activations given by the weighted sum W*x would be topologically spread on the y layer.

The following matlab function returns a mask with the diagonal elements (plus a given neiborourhood)  for any matrix dimentionality.

function m = gendiag(N,M,slope)
  x=1:N;  y=1:M;
  [Y X]=meshgrid(y/M,x/N);
  M = 1-abs(X-Y);
  m = exp(-(M-1).^2/(2*(slope^2)));
end


example:

octave:12> imagesc(gendiag(70,30, 0.2))

gives



while
octave:12> imagesc(gendiag(40,75, 0.05))
gives






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