ROL_Gumbel.hpp

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#ifndef ROL_GUMBEL_HPP
#define ROL_GUMBEL_HPP

#include "ROL_Distribution.hpp"
#include "ROL_ParameterList.hpp"

namespace ROL {

template<class Real>
class Gumbel : public Distribution<Real> {
private:
  Real loc_;
  Real scale_;

  void checkInputs(const Real loc, const Real scale) const {
    if (scale <= static_cast<Real>(0)) {
      throw Exception::NotImplemented(">>> (Gumbel::Gumbel): Scale must be greater than zero!");
    }
  }

public: 
  Gumbel(const Real loc = 0., const Real scale = 1.)
    : loc_(loc), scale_(scale) {
    checkInputs(loc_,scale_);
  }

  Gumbel(ROL::ParameterList &parlist) {
    loc_   = parlist.sublist("SOL").sublist("Distribution").sublist("Gumbel").get("Location",0.);
    scale_ = parlist.sublist("SOL").sublist("Distribution").sublist("Gumbel").get("Scale",1.);
    checkInputs(loc_,scale_);
  }

  Real evaluatePDF(const Real input) const {
    Real z = (x-loc_)/scale_;
    return std::exp(-(z+exp(-z)))/scale_;
  }

  Real evaluateCDF(const Real input) const {
    Real z = (x-loc_)/scale_;
    return std::exp(-std::exp(-z));
  }

  Real integrateCDF(const Real input) const {
    throw Exception::NotImplemented(">>> (Gumbel::integrateCDF): Not implemented!");
    return static_cast<Real>(0);
  }

  Real invertCDF(const Real input) const {
    return loc_ - scale_*std::log(-std::log(input));
  }

  Real moment(const size_t m) const {
    Real val(0), gamma(0.57721566490153286);
    if (m==1) {
      val = loc_+scale_*gamma;
    }
    else if (m==2) {
      Real pi(M_PI), six(6);
      val = std::pow(scale_*pi,2)/six + std::pow(loc_+scale_*gamma,2);
    }
    else {
      throw Exception::NotImplemented(">>> (Gumbel::moment): Moment is only implemented for m=1,2!");
    }
    return val;
  }

  Real lowerBound(void) const {
    return ROL_NINF<Real>();
  }

  Real upperBound(void) const {
    return ROL_INF<Real>();
  }
 
  void test(std::ostream &outStream = std::cout ) const {
    size_t size = 3;
    std::vector<Real> X(size,0.);
    std::vector<int> T(size,0);
    X[0] = loc_-4.0*(Real)rand()/(Real)RAND_MAX;
    T[0] = 0;
    X[1] = loc_;
    T[1] = 1;
    X[2] = loc_+4.0*(Real)rand()/(Real)RAND_MAX;
    T[2] = 0;
    Distribution<Real>::test(X,T,outStream);
  }
};

}

#endif