// ====================================================================
// This file is part of the Endmember Induction Algorithms Toolbox for SCILAB 
// Copyright (C) Grupo de Inteligencia Computacional, Universidad del 
// País Vasco (UPV/EHU), Spain, released under the terms of the GNU 
// General Public License.
//
// Endmember Induction Algorithms Toolbox is free software: you can redistribute 
// it and/or modify it under the terms of the GNU General Public License 
// as published by the Free Software Foundation, either version 3 of the 
// License, or (at your option) any later version.
//
// Endmember Induction Algorithms Toolbox is distributed in the hope that it will
// be useful, but WITHOUT ANY WARRANTY; without even the implied warranty
// of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 
// General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with Endmember Induction Algorithms Toolbox. 
// If not, see <http://www.gnu.org/licenses/>.
// ====================================================================
function [W,M] = EIA_LAM(X,Y)
  // [W,M] = EIA_LAM(X,Y)
  // 
  // Manuel Grana <manuel.grana[AT]ehu.es>
  // Miguel Angel Veganzones <miguelangel.veganzones[AT]ehu.es>
  // Grupo de Inteligencia Computacional (GIC), Universidad del Pais Vasco /
  // Euskal Herriko Unibertsitatea (UPV/EHU)
  // http://www.ehu.es/computationalintelligence
  // 
  // Copyright (2011) Grupo de Inteligencia Computacional @ Universidad del Pais Vasco, Spain.
  //
  // The Lattice Associative Memories is a kind of associative memory working
  // over lattice operations. If X=Y then W and M are Lattice AutoAssociative
  // Memories (LAAM), otherwise they are Lattice HeteroAssociative Memories
  // (LHAM).
  // ------------------------------------------------------------------------------
  // Input:   X         : input pattern matrix [nvariables x nsamples]
  //          Y         : output pattern matrix [mvariables x nsamples]
  //
  // Output:  W         : dilative LAM [mvariables x nvariables]
  //          M         : erosive LAM [mvariables x nvariables]
  //
  // Bibliographical references:
  // [1] M. Graña, D. Chyzhyk, M. García-Sebastián, y C. Hernández, “Lattice independent component analysis for functional magnetic resonance imaging”, Information Sciences, vol. 181, nº. 10, págs. 1910-1928, May. 2011.
  
  //// Arguments
  [lhs,rhs]=argn(0);
  if lhs < 1
    error('Insuficient parameters');
  end 
  if lhs < 2
    Y = X;
  end
  [nvariables kx] = size(X);
  [mvariables ky] = size(Y);
  if (kx <> ky) | kx == 0 then
    error('Input and output dimensions missmatch or zero dimensionality');
  end
  nsamples = kx; // k is the number of samples k = kx = ky
  
  // Compute vector lattice external products
  W = zeros(mvariables,nvariables);
  M = zeros(mvariables,nvariables);
  for b = 1:mvariables
    for c = 1:nvariables
      W(b,c) = %inf;
      M(b,c) = -%inf;
    end
  end
  for a=1:nsamples
    for b = 1:mvariables
      for c = 1:nvariables
        product = Y(b,a) - X(c,a);
        W(b,c) = min(W(b,c),product);
        M(b,c) = max(M(b,c),product);
      end
    end
  end
  
endfunction