MaximumLikelihoodWFunctions.cpp

#include "MaximumLikelihoodWFunctions.h"

#include <QDataStream>
#include <QString>

#include <math.h>
#include <stdio.h>

#include "IException.h"
#include "IString.h"

namespace Isis {
  MaximumLikelihoodWFunctions::MaximumLikelihoodWFunctions() {
    this->setModel(Huber);
  } // choose Model and define the tweaking constant



  MaximumLikelihoodWFunctions::MaximumLikelihoodWFunctions(Model modelSelection) {
    // choose Model and define the tweaking constant
    this->setModel(modelSelection);
  }


  
  MaximumLikelihoodWFunctions::MaximumLikelihoodWFunctions(Model modelSelection, 
                                                           double tweakingConstant) {
    // choose Model and define the tweaking constant
    setModel(modelSelection, tweakingConstant);
  }

  MaximumLikelihoodWFunctions::MaximumLikelihoodWFunctions(
      const MaximumLikelihoodWFunctions &other)
      : m_model(other.m_model), 
        m_tweakingConstant(other.m_tweakingConstant) {
  }


  MaximumLikelihoodWFunctions::~MaximumLikelihoodWFunctions() {
  } // empty destructor


  MaximumLikelihoodWFunctions &MaximumLikelihoodWFunctions::operator=(
      const MaximumLikelihoodWFunctions &other) {
    m_model = other.m_model;
    m_tweakingConstant = other.m_tweakingConstant;
    return *this;
  }

  void MaximumLikelihoodWFunctions::setModel(Model modelSelection) {
    // choose Model and use default tweaking constant
    m_model = modelSelection;
    this->setTweakingConstantDefault();
  }



  void MaximumLikelihoodWFunctions::setTweakingConstantDefault() {
    // default tweaking constants for the various likelihood models
    switch (m_model) {
      case Huber:
        m_tweakingConstant = 1.345; // "95% asymptotic efficiecy on the standard normal distribution"
                                    // is obtained with this constant, 
                                    // see Zhang's "Parameter Estimation"
        break;
      case HuberModified:
        m_tweakingConstant = 1.2107;// "95% asymptotic efficiecy on the standard normal distribution"
                                    // is obtained with this constant,
                                    // see Zhang's "Parameter Estimation"
        break;
      case Welsch:
        m_tweakingConstant = 2.9846;// "95% asymptotic efficiecy on the standard normal distribution"
                                    // is obtained with this constant,
                                    // see Zhang's "Parameter Estimation"
        break;
      case Chen:
        m_tweakingConstant = 1;     // This is the constant used by Chen in his paper, 
                                    // no specific reason why is stated
        break;
      default:
        m_tweakingConstant = 1;     // default, though at the time of writing this class,
                                    // this value should never actually be used
    }
  }



  void MaximumLikelihoodWFunctions::setModel(Model modelSelection, double tweakingConstant) { 
    // choose Model and define the tweaking constant
    m_model = modelSelection;
    setTweakingConstant(tweakingConstant);
  }



  void MaximumLikelihoodWFunctions::setTweakingConstant(double tweakingConstant) { 
    // leave model type unaltered and change tweaking constant
    if (tweakingConstant <= 0.0) {
      IString msg = "Maximum likelihood estimation tweaking constants must be > 0.0";
      throw IException(IException::Programmer, msg, _FILEINFO_);
    }
    m_tweakingConstant = tweakingConstant;
  }



  double MaximumLikelihoodWFunctions::tweakingConstant() const {
    return m_tweakingConstant;
  }



  double MaximumLikelihoodWFunctions::weightScaler(double residualZScore) {  
    // this is likely the least usefull of the scaler functions but it is provided for completness.
    // This directly provides the scaler for the weight (instead of the radical weight), thus it
    // provides sqrtWeightScaler^2 
    switch(m_model) {
    case Huber:
      return this->huber(residualZScore);  
    case HuberModified:
      return this->huberModified(residualZScore);
    case Welsch:
      return this->welsch(residualZScore);  
    case Chen:
      return this->chen(residualZScore);
    default:
      return 1.0;  // default to prevent nonsense from being returned, 
                   // but the program should never reach this line
    }
  }



  double MaximumLikelihoodWFunctions::sqrtWeightScaler(double residualZScore) {
    // it is often convient to use square roots of weights when building normals, this function
    // provides the scaler for the square root of the weight directly
    double scaler = this->weightScaler(residualZScore);
    if (scaler <= 0.0) {
      return 0.0;  // <0 should never happen, but 0.0 may be quite frequent
                   //    (thus this saves some time)
    }
    return sqrt(scaler);
  }



  double MaximumLikelihoodWFunctions::huber(double residualZScore) {
    // huber weight function
    if ( fabs(residualZScore) < m_tweakingConstant) {
      return 1.0;
    }
    else {
      return m_tweakingConstant/fabs(residualZScore);
    }
  }



  double MaximumLikelihoodWFunctions::huberModified(double residualZScore) {
    // huber modified weight function
    if ( fabs(residualZScore)/m_tweakingConstant < Isis::HALFPI) {
      return m_tweakingConstant*(sin(residualZScore/m_tweakingConstant)/residualZScore);
    }
    else {
      return m_tweakingConstant / fabs(residualZScore);
    }
  }



  double MaximumLikelihoodWFunctions::welsch(double residualZScore) {
    // welsch weight function
    double weightFactor = residualZScore / m_tweakingConstant;
    return exp(-(weightFactor)*(weightFactor));
  }



  double MaximumLikelihoodWFunctions::chen(double residualZScore) {
    // chen weight function
    if ( fabs(residualZScore) <= m_tweakingConstant) {
      double weightFactor = m_tweakingConstant * m_tweakingConstant 
                            - residualZScore * residualZScore;
      return 6 * weightFactor * weightFactor;  // use of weight factor variable reduces number of
                                               // operations from 7 to 4 
    }
    else {
      return 0.0;
    }
  }



  double MaximumLikelihoodWFunctions::tweakingConstantQuantile() {  
    // returns which quantile of the sqaured residuals is recommended to use as the tweaking 
    // constants, this varies as a function of the model being employed desired quantiles for
    // various models,  these parameters are estimated based on inspection of the fucntions and
    // should be tested and revised with experience
    switch(m_model) {
    case Huber:
      return 0.5;  // In this model m_tweakingConstant determines the point at which residuals stop having
                   // increased influence on the solution, so after the median all the measures will
                   // have the same effect on the solution regardless of magnitude
    case HuberModified:
      return 0.4; // In this model after residualZScore >= m_tweakingConstant*Isis::HALFPI the residuals have the same
                  // influence on the solution, 
    case Welsch:
      return 0.7; // at about double m_tweakingConstant the residuals have very little influence
    case Chen:
      return 0.98; // after r > m_tweakingConstant residuals have no influence
    default:
      return 0.5; // default, though at the time of writing this should never actually be used
    }
  }



  QString MaximumLikelihoodWFunctions::modelToString(MaximumLikelihoodWFunctions::Model model) {
    if (model == MaximumLikelihoodWFunctions::Huber)              return "Huber";
    else if (model == MaximumLikelihoodWFunctions::HuberModified) return "HuberModified";
    else if (model == MaximumLikelihoodWFunctions::Welsch)        return "Welsch";
    else if (model == MaximumLikelihoodWFunctions::Chen)          return "Chen";
    else throw IException(IException::Programmer,
                          "Unknown estimation model enum [" + toString(model) + "].",
                          _FILEINFO_);
  }



  MaximumLikelihoodWFunctions::Model MaximumLikelihoodWFunctions::stringToModel(QString modelName) {
    if (modelName.compare("HUBER", Qt::CaseInsensitive) == 0) {
      return Huber;
    }
    else if (modelName.compare("HUBER_MODIFIED", Qt::CaseInsensitive) == 0 ||
             modelName.compare("HUBERMODIFIED", Qt::CaseInsensitive) == 0 ||
             modelName.compare("HUBER MODIFIED", Qt::CaseInsensitive) == 0) {
      return HuberModified;
    }
    else if (modelName.compare("WELSCH", Qt::CaseInsensitive) == 0) {
      return Welsch;
    }
    else if (modelName.compare("CHEN", Qt::CaseInsensitive) == 0) {
      return Chen;
    }
    else {
      throw IException(IException::Programmer,
                       "Unknown maximum likelihood model name " + modelName + ".",
                       _FILEINFO_);
    }
  }



  QString MaximumLikelihoodWFunctions::weightedResidualCutoff() {
    if (m_model == Huber || m_model == HuberModified) return "N/A";
    else if (m_model == Welsch) return toString(m_tweakingConstant * 1.5);
    else if (m_model == Chen) return toString(m_tweakingConstant);
    else throw IException(IException::Programmer, "Estimation model has not been set.", _FILEINFO_);
  }



  MaximumLikelihoodWFunctions::Model MaximumLikelihoodWFunctions::model() const {
    return m_model;
  }



  QDataStream &MaximumLikelihoodWFunctions::write(QDataStream &stream) const {
    stream << (qint32)m_model
           << m_tweakingConstant;
    return stream;
  }



  QDataStream &MaximumLikelihoodWFunctions::read(QDataStream &stream) {
    qint32 model;
    stream >> model >> m_tweakingConstant;
    m_model = (MaximumLikelihoodWFunctions::Model)model;
    return stream;
  }



  QDataStream &operator<<(QDataStream &stream, const MaximumLikelihoodWFunctions &mlwf) {
    return mlwf.write(stream);
  }



  QDataStream &operator>>(QDataStream &stream,  MaximumLikelihoodWFunctions &mlwf) {
    return mlwf.read(stream);
  }



  QDataStream &operator<<(QDataStream &stream, const MaximumLikelihoodWFunctions::Model &modelEnum) {
    stream << (qint32)modelEnum;
    return stream;
  }



  QDataStream &operator>>(QDataStream &stream, MaximumLikelihoodWFunctions::Model &modelEnum) {
    qint32 modelInteger;
    stream >> modelInteger;
    modelEnum = (MaximumLikelihoodWFunctions::Model)modelInteger;
    return stream;
  }

}// end namespace Isis