text: // --------------------------------------------------------------------------
  //                   OpenMS -- Open-Source Mass Spectrometry
  // --------------------------------------------------------------------------
  // Copyright The OpenMS Team -- Eberhard Karls University Tuebingen,
  // ETH Zurich, and Freie Universitaet Berlin 2002-2021.
  //
  // This software is released under a three-clause BSD license:
  //  * Redistributions of source code must retain the above copyright
  //    notice, this list of conditions and the following disclaimer.
  //  * Redistributions in binary form must reproduce the above copyright
  //    notice, this list of conditions and the following disclaimer in the
  //    documentation and/or other materials provided with the distribution.
  //  * Neither the name of any author or any participating institution
  //    may be used to endorse or promote products derived from this software
  //    without specific prior written permission.
  // For a full list of authors, refer to the file AUTHORS.
  // --------------------------------------------------------------------------
  // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
  // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  // ARE DISCLAIMED. IN NO EVENT SHALL ANY OF THE AUTHORS OR THE CONTRIBUTING
  // INSTITUTIONS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
  // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
  // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS;
  // OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
  // WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
  // OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
  // ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  //
  // --------------------------------------------------------------------------
  // $Maintainer: Timo Sachsenberg $
  // $Authors: David Wojnar $
  // --------------------------------------------------------------------------
  //
  
  
  #include <unsupported/Eigen/NonLinearOptimization>
  
  #include <OpenMS/MATH/STATISTICS/GumbelDistributionFitter.h>
  
  using namespace std;
  
  // #define GUMBEL_DISTRIBUTION_FITTER_VERBOSE
  // #undef  GUMBEL_DISTRIBUTION_FITTER_VERBOSE
  
  namespace OpenMS::Math
  {
  
      double GumbelDistributionFitter::GumbelDistributionFitResult::log_eval_no_normalize(const double x) const
      {
        // -log b is a constant again
        double diff = (x - a)/b;
        return -log(b) - diff - exp(- diff);
      }
  
      GumbelDistributionFitter::GumbelDistributionFitter()
      {
        init_param_ = GumbelDistributionFitResult(0.25, 0.1);
      }
  
      GumbelDistributionFitter::~GumbelDistributionFitter() = default;
  
      void GumbelDistributionFitter::setInitialParameters(const GumbelDistributionFitResult & param)
      {
        init_param_ = param;
      }
  
      namespace // anonymous namespace to prevent name clashes with GumbleMaxLikelihoodFitter
      {
        struct GumbelDistributionFunctor
        {
          int inputs() const { return m_inputs; }
          int values() const { return m_values; }
  
          GumbelDistributionFunctor(unsigned dimensions, const std::vector<DPosition<2> >* data)
          : m_inputs(dimensions), 
            m_values(static_cast<int>(data->size())), 
            m_data(data) 
          {
          }
  
          int operator()(const Eigen::VectorXd &x, Eigen::VectorXd &fvec) const
          {
            double a = x(0); //location
            double b = x(1); //scale
  
            UInt i = 0;
            for (vector<DPosition<2> >::const_iterator it = m_data->begin(); it != m_data->end(); ++it, ++i)
            {
              double the_x = it->getX();
              double z = exp((a - the_x) / b);
              fvec(i) = (z * exp(-1 * z)) / b - it->getY();
            }
            return 0;
          }
          // compute Jacobian matrix for the different parameters
          int df(const Eigen::VectorXd &x, Eigen::MatrixXd &J) const
          {
            double a = x(0);
            double b = x(1);
            UInt i = 0;
            for (vector<DPosition<2> >::const_iterator it = m_data->begin(); it != m_data->end(); ++it, ++i)
            {
              double the_x = it->getX();
              double z = exp((a - the_x) / b);
              double f = z * exp(-1 * z);
              double part_dev_a = (f - pow(z, 2) * exp(-1 * z)) / pow(b, 2);
              J(i,0) = part_dev_a;
              double dev_z =  ((the_x - a) / pow(b, 2));
              double cum = f * dev_z;
              double part_dev_b = ((cum - z * cum) * b - f) / pow(b, 2);
              J(i,1) = part_dev_b;
            }
            return 0;
          }
  
          const int m_inputs, m_values;
          const std::vector<DPosition<2> >* m_data;
        };
      }
  
      GumbelDistributionFitter::GumbelDistributionFitResult GumbelDistributionFitter::fit(vector<DPosition<2> > & input) const
      {
  
        Eigen::VectorXd x_init (2);
        x_init(0) = init_param_.a;
        x_init(1) = init_param_.b;
        GumbelDistributionFunctor functor (2, &input);
        Eigen::LevenbergMarquardt<GumbelDistributionFunctor> lmSolver (functor);
        Eigen::LevenbergMarquardtSpace::Status status = lmSolver.minimize(x_init);
  
        //the states are poorly documented. after checking the source, we believe that
        //all states except NotStarted, Running and ImproperInputParameters are good
        //termination states.
        if (status <= Eigen::LevenbergMarquardtSpace::ImproperInputParameters)
        {
          throw Exception::UnableToFit(__FILE__, __LINE__, OPENMS_PRETTY_FUNCTION, "UnableToFit-GumbelDistributionFitter", "Could not fit the gumbel distribution to the data");
        }
  
  #ifdef GUMBEL_DISTRIBUTION_FITTER_VERBOSE
        // build a formula with the fitted parameters for gnuplot
        stringstream formula;
        formula << "f(x)=" << "(1/" << x_init(1) << ") * " << "exp(( " << x_init(0) << "- x)/" << x_init(1) << ") * exp(-exp((" << x_init(0) << " - x)/" << x_init(1) << "))";
        cout << formula.str() << endl;
  #endif
  
        return {x_init(0), x_init(1)};
      }
  
  } // namespace OpenMS   //namespace Math
  