libtrilinos-rol-dev 12.10.1-3 / usr / include / trilinos / ROL_ChebyshevKusuoka.hpp

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#ifndef ROL_CHEBYSHEVKUSUOKA_HPP
#define ROL_CHEBYSHEVKUSUOKA_HPP

#include "ROL_SpectralRisk.hpp"
#include "ROL_GaussChebyshev1Quadrature.hpp"
#include "ROL_GaussChebyshev2Quadrature.hpp"
#include "ROL_GaussChebyshev3Quadrature.hpp"

/** @ingroup risk_group
    \class ROL::ChebyshevKusuoka
    \brief Provides an interface for the Chebyshev-Kusuoka risk measure.

    The Chebyshev-Kusuoka risk measure is defined as
    \f[
       \mathcal{R}(X) = \int_{\alpha_0}^{\alpha_1} w(\alpha)
          \mathrm{CVaR}_{\alpha}(X) \,\mathrm{d}\alpha
    \f]
    where \f$0\le \alpha_0 < \alpha_1 < 1\f$ and the conditional value-at-risk
    (CVaR) with confidence level \f$0\le \alpha < 1\f$ is
    \f[
       \mathrm{CVaR}_\alpha(X) = \inf_{t\in\mathbb{R}} \left\{
         t + \frac{1}{1-\alpha} \mathbb{E}\left[(X-t)_+\right]
         \right\}, \quad (x)_+ = \max\{0,x\}.
    \f]
    There are three choices of weight functions \f$w\f$: (i) the first weight
    function generates the Chebyshev polynomials of the first kind and has
    the specific form
    \f[
       w(x) = \frac{1}{\sqrt{(x-\alpha_0)(\alpha_1-x)}};
    \f]
    (ii) the second weight function generates the Chebyshev polynomials of the
    second kind and has the specific form
    \f[
       w(x) = \sqrt{(x-\alpha_0)(\alpha_1-x)};
    \f]
    and (iii) the third weight function is related again to the Chebyshev
    polynomials of the first kind and has the specific form
    \f[
       w(x) = \sqrt{\frac{x-\alpha_0}{\alpha_1-x}}.
    \f]
    As defined, \f$\mathcal{R}\f$ is a law-invariant coherent risk measure.

    ROL implements \f$\mathcal{R}\f$ by approximating the integral with
    the appropriate Gauss-Chebyshev quadrature rule.  The corresponding
    quadrature points and weights are then used to construct a
    ROL::MixedQuantileQuadrangle risk measure.
    When using derivative-based optimization, the user can provide a smooth
    approximation of \f$(\cdot)_+\f$ using the ROL::PlusFunction class.
*/

namespace ROL {

template<class Real>
class ChebyshevKusuoka : public SpectralRisk<Real> {
private:
  Teuchos::RCP<PlusFunction<Real> > plusFunction_;

  Real lower_, upper_;
  int nQuad_; 
  int wType_;

  std::vector<Real> wts_;
  std::vector<Real> pts_;

  void checkInputs(void) const {
    TEUCHOS_TEST_FOR_EXCEPTION(lower_ > upper_, std::invalid_argument,
      ">>> ERROR (ROL::ChebyshevKusuoka): Lower bound exceeds upper!");
    TEUCHOS_TEST_FOR_EXCEPTION(lower_ < static_cast<Real>(0), std::invalid_argument,
      ">>> ERROR (ROL::ChebyshevKusuoka): Lower bound is less than zero!");
    TEUCHOS_TEST_FOR_EXCEPTION(static_cast<Real>(1) < upper_, std::invalid_argument,
      ">>> ERROR (ROL::ChebyshevKusuoka): Upper bound is greater than one!");
    TEUCHOS_TEST_FOR_EXCEPTION((wType_ < 1 || wType_ > 3), std::invalid_argument,
      ">>> ERROR (ROL::ChebyshevKusuoka): Weight must be 1, 2 or 3!");
    TEUCHOS_TEST_FOR_EXCEPTION(plusFunction_ == Teuchos::null, std::invalid_argument,
      ">>> ERROR (ROL::ChebyshevKusuoka): PlusFunction pointer is null!");
  }

  void initialize(void) {
     Teuchos::RCP<Quadrature1D<Real> > quad;
     if ( wType_ == 1 ) {
       quad = Teuchos::rcp(new GaussChebyshev1Quadrature<Real>(nQuad_));
     }
     else if ( wType_ == 2 ) {
       quad = Teuchos::rcp(new GaussChebyshev2Quadrature<Real>(nQuad_));
     }
     else if ( wType_ == 3 ) {
       quad = Teuchos::rcp(new GaussChebyshev3Quadrature<Real>(nQuad_));
     }
     // quad->test();
     quad->get(pts_,wts_);
     Real sum(0), half(0.5), one(1);
     for (int i = 0; i < nQuad_; ++i) {
       sum += wts_[i];
     }
     for (int i = 0; i < nQuad_; ++i) {
       wts_[i] /= sum;
       pts_[i] = lower_ + (upper_-lower_)*half*(pts_[i] + one);
     }
     SpectralRisk<Real>::buildMixedQuantile(pts_,wts_,plusFunction_);
  }

public:
  /** \brief Constructor.

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

      parlist should contain sublists "SOL"->"Risk Measure"->"Chebyshev-Kusuoka"
      and the "Chebyshev-Kusuoka" sublist should have the following parameters
      \li "Lower Bound" (between 0 and 1)
      \li "Upper Bound" (between 0 and 1, greater than "Lower Bound")
      \li "Weight Type" (either 1, 2, or 3)
      \li "Number of Quadrature Points"
      \li A sublist for plus function information.
  */
  ChebyshevKusuoka( Teuchos::ParameterList &parlist )
    : SpectralRisk<Real>() {
    Teuchos::ParameterList &list
      = parlist.sublist("SOL").sublist("Risk Measure").sublist("Chebyshev-Kusuoka");
    // Grab confidence level and quadrature order
    lower_ = list.get("Lower Bound",0.0);
    upper_ = list.get("Upper Bound",1.0);
    nQuad_ = list.get("Number of Quadrature Points",5);
    wType_ = list.get("Weight Type",1);
    plusFunction_ = Teuchos::rcp(new PlusFunction<Real>(list));
    // Check inputs
    checkInputs();
    initialize();
  }

  /** \brief Constructor.

      @param[in]     lower   is the lower confidence level (between 0 and 1)
      @param[in]     upper   is the upper confidence level (between 0 and 1, greater than lower)
      @param[in]     nQuad   is the number of quadrature points
      @param[in]     wType   is the weight type (either 1, 2, or 3)
      @param[in]     pf      is the plus function or an approximation
  */
  ChebyshevKusuoka(const Real lower, const Real upper,
                   const int nQuad, const int wType,
                   const Teuchos::RCP<PlusFunction<Real> > &pf)
    : RiskMeasure<Real>(), plusFunction_(pf),
      lower_(lower), upper_(upper), nQuad_(nQuad), wType_(wType) {
    // Check inputs
    checkInputs();
    initialize();
  }
};

}

#endif