DXDsvd.m

% adapted from the original implementation of Gardner et al. (EMNLP 2015).
function DXDsvd(r, input_mat_filename, temp1_filename, temp2_filename, output_mat_filename, varargin)
  r = str2num(r)

  lam = 1;

  % the matrix D is written only once for all languages
  load(input_mat_filename)
  D2 = D;
  D1 = D;

  % the matrix X is written separately for each language. The filename suffix for all languages are given as a variable-length argument in this function.
  nVarargs = length(varargin);
  fprintf('Number of languages: %d.\n',nVarargs)
  for k = 1:nVarargs
	    cooccurence_filename = sprintf('%s.%s.mat', input_mat_filename, varargin{k})
	    load(cooccurence_filename)
	    if exist('total','var')
	      total = total + X;
	    else
              total = X;
            end
  end

  % done reading all cooccurence matrices
  X = total;

  [ m, n ] = size(X);
  nnzX = nnz(X);
  nnzD1 = nnz(D1);
  nnzD2 = nnz(D2);
  P1 = speye(m) + lam*D1; P2 = speye(n) + lam*D2; 
  clear D1 D2;

  opts.issym = 1;
  opts.isreal= 1;
  tic
  disp(isscalar(2*r))
  [ Q, D ] = eigs( @(u)DXDu( u, X, P1, P2, m, n ), m+n, 2*r, 'LM', opts );

  Ss = D(1:r,1:r);
  Vs = sqrt(2)*Q(1:n,1:r);
  Us = sqrt(2)*Q(n+1:n+m,1:r);
  t = toc;
  %save(temp2_filename, 'nnzX', 'nnzD1', 'nnzD2', 't');
  save(temp1_filename, 'Us', 'Ss', 'Vs', 'lam');

  % We actually only use 'Us' and scipy/octave handle structs badly
  % so save 'Us' separately as ascii to be loaded with np.loadtxt
  save('-ascii', output_mat_filename, 'Us')
exit;
end

function output = DXDu( u, X, P1, P2, m, n )
  u1 = u(1:n); u2 = u(n+1:m+n);
  uu1 = P2* ( X'* (P1'*u2) );
  uu2 = P1* ( X * (P2'*u1) );
  output = [ uu1; uu2 ];
end