/**
 * @file simple_tolerance_termination.hpp
 * @author Sumedh Ghaisas
 *
 * Termination policy used in AMF (Alternating Matrix Factorization).
 *
 * mlpack is free software; you may redistribute it and/or modify it under the
 * terms of the 3-clause BSD license.  You should have received a copy of the
 * 3-clause BSD license along with mlpack.  If not, see
 * http://www.opensource.org/licenses/BSD-3-Clause for more information.
 */
#ifndef _MLPACK_METHODS_AMF_SIMPLE_TOLERANCE_TERMINATION_HPP_INCLUDED
#define _MLPACK_METHODS_AMF_SIMPLE_TOLERANCE_TERMINATION_HPP_INCLUDED

#include <mlpack/prereqs.hpp>

namespace mlpack {
namespace amf {

/**
 * This class implements residue tolerance termination policy. Termination
 * criterion is met when increase in residue value drops below the given tolerance.
 * To accommodate spikes certain number of successive residue drops are accepted.
 * This upper imit on successive drops can be adjusted with reverseStepCount.
 * Secondary termination criterion terminates algorithm when iteration count
 * goes above the threshold.
 *
 * @see AMF
 */
template <class MatType>
class SimpleToleranceTermination
{
 public:
  //! empty constructor
  SimpleToleranceTermination(const double tolerance = 1e-5,
                             const size_t maxIterations = 10000,
                             const size_t reverseStepTolerance = 3)
            : tolerance(tolerance),
              maxIterations(maxIterations),
              reverseStepTolerance(reverseStepTolerance) {}

  /**
   * Initializes the termination policy before stating the factorization.
   *
   * @param V Input matrix to be factorized.
   */
  void Initialize(const MatType& V)
  {
    residueOld = DBL_MAX;
    iteration = 1;
    residue = DBL_MIN;
    reverseStepCount = 0;
    isCopy = false;

    this->V = &V;

    c_index = 0;
    c_indexOld = 0;

    reverseStepCount = 0;
  }

  /**
   * Check if termination criterio is met.
   *
   * @param W Basis matrix of output.
   * @param H Encoding matrix of output.
   */
  bool IsConverged(arma::mat& W, arma::mat& H)
  {
    arma::mat WH;

    WH = W * H;

    // compute residue
    residueOld = residue;
    size_t n = V->n_rows;
    size_t m = V->n_cols;
    double sum = 0;
    size_t count = 0;
    for (size_t i = 0; i < n; i++)
    {
        for (size_t j = 0; j < m; j++)
        {
            double temp = 0;
            if ((temp = (*V)(i, j)) != 0)
            {
                temp = (temp - WH(i, j));
                temp = temp * temp;
                sum += temp;
                count++;
            }
        }
    }
    residue = sum / count;
    residue = sqrt(residue);

    // increment iteration count
    iteration++;
    Log::Info << "Iteration " << iteration << "; residue "
        << ((residueOld - residue) / residueOld) << ".\n";

    // if residue tolerance is not satisfied
    if ((residueOld - residue) / residueOld < tolerance && iteration > 4)
    {
      // check if this is a first of successive drops
      if (reverseStepCount == 0 && isCopy == false)
      {
        // store a copy of W and H matrix
        isCopy = true;
        this->W = W;
        this->H = H;
        // store residue values
        c_index = residue;
        c_indexOld = residueOld;
      }
      // increase successive drop count
      reverseStepCount++;
    }
    // if tolerance is satisfied
    else
    {
      // initialize successive drop count
      reverseStepCount = 0;
      // if residue is droped below minimum scrap stored values
      if (residue <= c_indexOld && isCopy == true)
      {
        isCopy = false;
      }
    }

    // check if termination criterion is met
    if (reverseStepCount == reverseStepTolerance || iteration > maxIterations)
    {
      // if stored values are present replace them with current value as they
      // represent the minimum residue point
      if (isCopy)
      {
        W = this->W;
        H = this->H;
        residue = c_index;
      }
      return true;
    }
    else return false;
  }

  //! Get current value of residue
  const double& Index() const { return residue; }

  //! Get current iteration count
  const size_t& Iteration() const { return iteration; }

  //! Access upper limit of iteration count
  const size_t& MaxIterations() const { return maxIterations; }
  size_t& MaxIterations() { return maxIterations; }

  //! Access tolerance value
  const double& Tolerance() const { return tolerance; }
  double& Tolerance() { return tolerance; }

 private:
  //! tolerance
  double tolerance;
  //! iteration threshold
  size_t maxIterations;

  //! pointer to matrix being factorized
  const MatType* V;

  //! current iteration count
  size_t iteration;

  //! residue values
  double residueOld;
  double residue;
  double normOld;

  //! tolerance on successive residue drops
  size_t reverseStepTolerance;
  //! successive residue drops
  size_t reverseStepCount;

  //! indicates whether a copy of information is available which corresponds to
  //! minimum residue point
  bool isCopy;

  //! variables to store information of minimum residue poi
  arma::mat W;
  arma::mat H;
  double c_indexOld;
  double c_index;
}; // class SimpleToleranceTermination

} // namespace amf
} // namespace mlpack

#endif // _MLPACK_METHODS_AMF_SIMPLE_TOLERANCE_TERMINATION_HPP_INCLUDED