// ====================================================================
// 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 [E,C] = EIA_NFINDR(data,p,maxit)
  //// [E,C] = EIA_NFINDR(data,p,maxit)
  //
  // 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.
  // Copyright (2007) GRNPS group @ University of Extremadura, Spain. 
  //
  // N-FINDR endmembers induction algorithm.
  // ------------------------------------------------------------------------------
  // Input:   data      : column data matrix [nvariables x nsamples]
  //          p         : number of endmembers to be induced
  //          maxit     : maximum number of iterations. Default = 3*p
  //
  // Output:  E         : set of induced endmembers [nvariables x p]
  //          C         : induced endmembers indexes vector [nsamples] with {0,1} values, where '1' indicates that the corresponding sample has been identified as an endmember.
  //
  // Bibliographical references:
  // [1] Winter, M. E., «N-FINDR: an algorithm for fast autonomous spectral end-member determination in hyperspectral data», presented at the Imaging Spectrometry V, Denver, CO, USA, 1999, vol. 3753, págs. 266-275.
  
  //// Arguments
  [lhs,rhs]=argn(0);
  if lhs < 1
    error('Insuficient parameters');
  end
  if lhs < 2
    p = EIA_HFC(data,10^(-5));
  end
  if p <= 0
    p = EIA_HFC(data,10^(-5));
  end
  if maxit < 0
    maxit = 3*p;
  end
  
  //// data size
  [nvariables,nsamples] = size(data);
  
  //// Dimensionality reduction by PCA
  [pc, zscores] = princomp(data');
  data_pca = squeeze(zscores(:,1:p-1))';
  
  //// Initialization
  E = zeros(nvariables,p);
  C = zeros(1,nsamples);
  IDX = zeros(1,p);
  TestMatrix = zeros(p,p);
  TestMatrix(1,:) = 1;
  for i = 1:p
    idx = floor(rand()*nsamples) + 1;
    TestMatrix(2:p,i) = data_pca(:,idx);
    IDX(i) = idx;
  end
  actualVolume = abs(det(TestMatrix)); // instead of: volumeactual = abs(det(MatrixTest))/(factorial(p-1));
  it = 1;
  v1 = -1;
  v2 = actualVolume;
  
  //// Algorithm
  while it<=maxit & v2>v1
    for k=1:p
      for i=1:nsamples
        actualSample = TestMatrix(2:p,k);
        TestMatrix(2:p,k) = data_pca(:,i);
        volume = abs(det(TestMatrix));  // instead of: volume = abs(det(MatrixTest))/(factorial(p-1));
        if volume > actualVolume
          actualVolume = volume;
          IDX(k) = i;
        else
          TestMatrix(2:p,k) = actualSample;
        end
      end
    end
    it = it+1;
    v1 = v2;
    v2 = actualVolume;
  end
  for i = 1:p
    E(:,i) = data(:,IDX(i));
    C(IDX(i)) = 1;
  end
  
endfunction