ROL_Arcsine.hpp

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#ifndef ROL_ARCSINE_HPP
#define ROL_ARCSINE_HPP

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

namespace ROL {

template<class Real>
class Arcsine : public Distribution<Real> {
private:
  Real a_;
  Real b_;

public: 
  Arcsine(const Real a = 0., const Real b = 1.)
    : a_(std::min(a,b)), b_(std::max(a,b)) {}

  Arcsine(ROL::ParameterList &parlist) {
    a_ = parlist.sublist("SOL").sublist("Distribution").sublist("Arcsine").get("Lower Bound",0.);
    b_ = parlist.sublist("SOL").sublist("Distribution").sublist("Arcsine").get("Upper Bound",1.);
    Real tmp = a_;
    a_ = std::min(a_,b_);
    b_ = std::max(b_,tmp);
  }

  Real evaluatePDF(const Real input) const {
    return ((input <= a_) ? 0. : ((input >= b_) ? 0. : 
             1./(ROL::ScalarTraits<Real>::pi()*std::sqrt((input-a_)*(b_-input)))));
  }

  Real evaluateCDF(const Real input) const {
    return ((input <= a_) ? 0. : ((input >= b_) ? 1. : 
             2./ROL::ScalarTraits<Real>::pi() * asin(std::sqrt((input-a_)/(b_-a_)))));
  }
  Real integrateCDF(const Real input) const {
    ROL_TEST_FOR_EXCEPTION( true, std::invalid_argument,
      ">>> ERROR (ROL::Arcsine): Arcsine integrateCDF not implemented!");
  }

  Real invertCDF(const Real input) const {
    Real x = std::pow(std::sin(0.5*ROL::ScalarTraits<Real>::pi()*input),2);
    return x*(b_-a_) + a_;
  }

  Real moment(const size_t m) const {
    Real mean  = 0.5*(a_+b_);
    Real val   = 0.0;
    switch(m) {
      case 1: val = mean;                             break;
      case 2: val = std::pow(b_-a_,2)/8. + mean*mean; break;
      default:
        ROL_TEST_FOR_EXCEPTION( true, std::invalid_argument,
          ">>> ERROR (ROL::Arcsine): Arcsine moment not implemented for m > 2!");
    }
    return val;
  }

  Real lowerBound(void) const {
    return a_;
  }

  Real upperBound(void) const {
    return b_;
  }
 
  void test(std::ostream &outStream = std::cout ) const {
    size_t size = 5;
    std::vector<Real> X(size,0.);
    std::vector<int> T(size,0);
    X[0] = a_-4.*(Real)rand()/(Real)RAND_MAX; 
    T[0] = 0;
    X[1] = a_; 
    T[1] = 1;
    X[2] = (b_-a_)*(Real)rand()/(Real)RAND_MAX + a_; 
    T[2] = 0;
    X[3] = b_; 
    T[3] = 1;
    X[4] = b_+4.*(Real)rand()/(Real)RAND_MAX; 
    T[4] = 0;
    Distribution<Real>::test(X,T,outStream);
  }
};

}

#endif