ROL_TruncatedMeanQuadrangle.hpp

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#ifndef ROL_TRUNCATEDMEANQUAD_HPP
#define ROL_TRUNCATEDMEANQUAD_HPP

#include "ROL_ExpectationQuad.hpp"

namespace ROL {

template<class Real>
class TruncatedMeanQuadrangle : public ExpectationQuad<Real> {
private:

  Real beta_;

public:

  TruncatedMeanQuadrangle(Real beta)
    : ExpectationQuad<Real>(), beta_(beta) {}

  Real error(Real x, int deriv = 0) {
    bool inside = ((abs_->evaluate(x,0) <= beta_) ? true : false );
    Real err    = 0.0;
    if (deriv==0) {
      err = (inside ? 0.5*std::pow(x,2.0)/beta_ : std::abs(x)-0.5*beta_);
    }
    else (deriv==1) {
      err = (inside ? x/beta_ : ((0.0 < x) - (x < 0.0)))
    }
    else {
      err = (inside ? 1.0/beta_ : 0.0);
    }
    return err;
  }

  Real regret(Real x, int deriv = 0) {
    Real X = ((deriv==0) ? x : ((deriv==1) ? 1.0 : 0.0));
    Real reg = error(x,deriv) + X;
    return reg;
  }

  void checkRegret(void) {
    ExpectationQuad<Real>::checkRegret();
    // Check v'(beta)
    Real x = beta_;
    Real vx = 0.0, vy = 0.0;
    Real dv = regret(x,1);
    Real t = 1.0;
    Real diff = 0.0;
    Real err = 0.0;
    std::cout << std::right << std::setw(20) << "CHECK REGRET: v'(beta) is correct? \n";
    std::cout << std::right << std::setw(20) << "t"
                            << std::setw(20) << "v'(x)"
                            << std::setw(20) << "(v(x+t)-v(x-t))/2t"
                            << std::setw(20) << "Error"
                            << "\n";
    for (int i = 0; i < 13; i++) {
      vy = regret(x+t,0);
      vx = regret(x-t,0);
      diff = (vy-vx)/(2.0*t);
      err = std::abs(diff-dv);
      std::cout << std::scientific << std::setprecision(11) << std::right
                << std::setw(20) << t
                << std::setw(20) << dv
                << std::setw(20) << diff
                << std::setw(20) << err
                << "\n";
      t *= 0.1;
    }
    std::cout << "\n";
    // Check v'(-beta)
    x = -beta_;
    vx = 0.0;
    vy = 0.0;
    dv = regret(x,1);
    t = 1.0;
    diff = 0.0;
    err = 0.0;
    std::cout << std::right << std::setw(20) << "CHECK REGRET: v'(-beta) is correct? \n";
    std::cout << std::right << std::setw(20) << "t"
                            << std::setw(20) << "v'(x)"
                            << std::setw(20) << "(v(x+t)-v(x-t))/2t"
                            << std::setw(20) << "Error"
                            << "\n";
    for (int i = 0; i < 13; i++) {
      vy = regret(x+t,0);
      vx = regret(x-t,0);
      diff = (vy-vx)/(2.0*t);
      err = std::abs(diff-dv);
      std::cout << std::scientific << std::setprecision(11) << std::right
                << std::setw(20) << t
                << std::setw(20) << dv
                << std::setw(20) << diff
                << std::setw(20) << err
                << "\n";
      t *= 0.1;
    }
    std::cout << "\n";
  }

};

}
#endif