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#ifndef ROL_LOGEXPONENTIALQUAD_HPP
#define ROL_LOGEXPONENTIALQUAD_HPP

#include "ROL_ExpectationQuad.hpp"

/** @ingroup risk_group
    \class ROL::LogExponentialQuadrangle
    \brief Provides an interface for the entropic risk using the expectation
           risk quadrangle.

    The entropic risk measure (also called the exponential utility and the
    log-exponential risk measure) is
    \f[
       \mathcal{R}(X) = \lambda
       \log\mathbb{E}\left[\exp\left(\frac{X}{\lambda}\right)\right]
    \f]
    for \f$\lambda > 0\f$.  The entropic risk is convex, translation
    equivariant and monotonic.

    This class defines the entropic risk measure using the framework of the
    expectation risk quadrangle.  In this case, the scalar regret function
    is
    \f[
       v(x) = \lambda(\exp\left(\frac{x}{\lambda}\right)-1).
    \f]
    The entropic risk measure is then implemented as
    \f[
       \mathcal{R}(X) = \inf_{t\in\mathbb{R}}\left\{
           t + \mathbb{E}[v(X-t)] \right\}.
    \f]
    ROL implements this by augmenting the optimization vector \f$x_0\f$ with
    the parameter \f$t\f$, then minimizes jointly for \f$(x_0,t)\f$.
*/

namespace ROL {

template<class Real>
class LogExponentialQuadrangle : public ExpectationQuad<Real> {
private:
  Real coeff_;

  void parseParameterList(ROL::ParameterList &parlist) {
    std::string type = parlist.sublist("SOL").get("Stochastic Component Type","Risk Averse");
    ROL::ParameterList list;
    if (type == "Risk Averse") {
      list = parlist.sublist("SOL").sublist("Risk Measure").sublist("Entropic Risk");
    }
    else if (type == "Error") {
      list = parlist.sublist("SOL").sublist("Error Measure").sublist("Exponential");
    }
    else if (type == "Deviation") {
      list = parlist.sublist("SOL").sublist("Deviation Measure").sublist("Entropic");
    }
    else if (type == "Regret") {
      list = parlist.sublist("SOL").sublist("Regret Measure").sublist("Exponential");
    }
    coeff_ = list.get<Real>("Rate");
  }

  void checkInputs(void) const {
    Real zero(0);
    ROL_TEST_FOR_EXCEPTION((coeff_ <= zero), std::invalid_argument,
      ">>> ERROR (ROL::LogExponentialQuadrangle): Rate must be positive!");
  }

public:
  /** \brief Constructor.

      @param[in]     coeff    is the scale parameter \f$\lambda\f$
  */
  LogExponentialQuadrangle(const Real coeff = 1)
    : ExpectationQuad<Real>(), coeff_(coeff) {
    checkInputs();
  }

  /** \brief Constructor.

      @param[in]     parlist is a parameter list specifying inputs

      parlist should contain sublists "SOL"->"Risk Measures"->"Log-Exponential Quadrangle"
      and withing the "Log-Exponential Quadrangle" sublist should have
      \li "Rate" (greater than 0). 
  */
  LogExponentialQuadrangle(ROL::ParameterList &parlist)
    : ExpectationQuad<Real>() {
    parseParameterList(parlist);
    checkInputs();
  }

  Real error(Real x, int deriv = 0) {
    Real err(0), one(1), cx = coeff_*x;
    if (deriv==0) {
      err = (std::exp(cx) - cx - one)/coeff_;
    }
    else if (deriv==1) {
      err = std::exp(cx) - one;
    }
    else {
      err = coeff_*std::exp(cx);
    }
    return err;
  }

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

};

}
#endif
