clear all;
close all;


mat =  [ 50,4.5, -23,  12,  1,  0, -1,  0;
    	 1,  2,   3,   4,  5, 1, 0, 0;
         2,  4,   6,   8, 10, 2, 0, 0];
     
% To compute the pseudoinverse in matlab I don't need to tranpose mat,
% because matlab can do the SVD decomposition of matrices with more columns
% than rows

[U,S,V] = svd(mat);


% pseudoinv = V * inv(S) * transpose(U);
n_col = length(S(:,1));
n_fil = length(S(1,:));
max = n_fil;
if (n_col < n_fil)
    max = n_col;
end

% As S is diagonal, que can compute its inverse by dividing inverting its
% diagonal values
for i = 1:max
   if (S(i,i) > 0.0000000001)
       S(i,i) = 1/S(i,i);
   else
       S(i,i) = 0;
   end
end
invS = transpose(S);

pseudoinv = V * invS * transpose(U)