ROL_MoreauYosidaCVaR.hpp

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#ifndef ROL_MOREAUYOSIDACVAR_HPP
#define ROL_MOREAUYOSIDACVAR_HPP

#include "ROL_ExpectationQuad.hpp"

namespace ROL {

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

  Real prob_;
  Real eps_;

  Real omp_;
  Real ub_;

  void checkInputs(void) const {
    Real zero(0), one(1);
    TEUCHOS_TEST_FOR_EXCEPTION((prob_ <= zero) || (prob_ >= one), std::invalid_argument,
      ">>> ERROR (ROL::MoreauYosidaCVaR): Confidence level must be between 0 and 1!");
    TEUCHOS_TEST_FOR_EXCEPTION((eps_ <= zero), std::invalid_argument,
      ">>> ERROR (ROL::MoreauYosidaCVaR): Smoothing parameter must be positive!");
  }

  void setParameters(void) {
    Real one(1);
    omp_  = one-prob_;
    ub_   = eps_/omp_;
  }

public:
  MoreauYosidaCVaR(Real prob, Real eps )
    : ExpectationQuad<Real>(), prob_(prob), eps_(eps) {
    checkInputs();
    setParameters();
  }

  MoreauYosidaCVaR(Teuchos::ParameterList &parlist)
    : ExpectationQuad<Real>() {
    Teuchos::ParameterList& list
      = parlist.sublist("SOL").sublist("Risk Measure").sublist("Moreau-Yosida CVaR");
    prob_ = list.get<Real>("Confidence Level");
    eps_  = list.get<Real>("Smoothing Parameter");
    checkInputs();
    setParameters();
  }

  Real error(Real x, int deriv = 0) {
    Real zero(0), one(1);
    Real X = ((deriv==0) ? x : ((deriv==1) ? one : zero));
    return regret(x,deriv) - X;
  }

  Real regret(Real x, int deriv = 0) {
    Real zero(0), half(0.5), one(1), reg(0);
    if ( x <= zero ) {
      reg = 0;
    }
    else if ( x >= ub_ ) {
      reg  = ((deriv == 0) ? (x-half*ub_)/omp_
           : ((deriv == 1) ? one/omp_ : zero));
    }
    else {
      reg  = ((deriv == 0) ? half/eps_*x*x
           : ((deriv == 1) ? x/eps_ : one/eps_));
    }
    return reg;
  }

  void checkRegret(void) {
    ExpectationQuad<Real>::checkRegret();
    Real zero(0), one(1), two(2), p1(0.1);
    // Check v'(eps)
    Real x = eps_;
    Real vx = zero, vy = zero;
    Real dv = regret(x,1);
    Real t = one;
    Real diff = zero;
    Real err = zero;
    std::cout << std::right << std::setw(20) << "CHECK REGRET: v'(eps) 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)/(two*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 *= p1;
    }
    std::cout << "\n";
    // check v''(eps) 
    vx = zero;
    vy = zero;
    dv = regret(x,2);
    t = one;
    diff = zero;
    err = zero;
    std::cout << std::right << std::setw(20) << "CHECK REGRET: v''(eps) 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,1);
      vx = regret(x-t,1);
      diff = (vy-vx)/(two*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 *= p1;
    }
    std::cout << "\n"; 
    // Check v'(0)
    x = zero;
    vx = zero;
    vy = zero;
    dv = regret(x,1);
    t = one;
    diff = zero;
    err = zero;
    std::cout << std::right << std::setw(20) << "CHECK REGRET: v'(0) 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)/(two*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 *= p1;
    }
    std::cout << "\n";
    // check v''(eps) 
    vx = zero;
    vy = zero;
    dv = regret(x,2);
    t = one;
    diff = zero;
    err = zero;
    std::cout << std::right << std::setw(20) << "CHECK REGRET: v''(0) 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,1);
      vx = regret(x-t,1);
      diff = (vy-vx)/(two*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 *= p1;
    }
    std::cout << "\n"; 
    // Check v'(0)
    x = -eps_;
    vx = zero;
    vy = zero;
    dv = regret(x,1);
    t = one;
    diff = zero;
    err = zero;
    std::cout << std::right << std::setw(20) << "CHECK REGRET: v'(-eps) 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)/(two*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 *= p1;
    }
    std::cout << "\n";
    // check v''(eps) 
    vx = zero;
    vy = zero;
    dv = regret(x,2);
    t = one;
    diff = zero;
    err = zero;
    std::cout << std::right << std::setw(20) << "CHECK REGRET: v''(-eps) 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,1);
      vx = regret(x-t,1);
      diff = (vy-vx)/(two*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 *= p1;
    }
    std::cout << "\n"; 
  }

};

}
#endif