ROL_MeanVariance.hpp

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#ifndef ROL_MEANVARIANCE_HPP
#define ROL_MEANVARIANCE_HPP

#include "ROL_RandVarFunctional.hpp"
#include "ROL_PositiveFunction.hpp"
#include "ROL_PlusFunction.hpp"
#include "ROL_AbsoluteValue.hpp"

#include "ROL_ParameterList.hpp"

namespace ROL {

template<class Real>
class MeanVariance : public RandVarFunctional<Real> {
  typedef typename std::vector<Real>::size_type uint;
private:
  Ptr<PositiveFunction<Real> > positiveFunction_;
  std::vector<Real> order_;
  std::vector<Real> coeff_;
  uint NumMoments_;

  Ptr<SampledScalar<Real>> values_;
  Ptr<SampledScalar<Real>> gradvecs_;
  Ptr<SampledVector<Real>> gradients_;
  Ptr<SampledVector<Real>> hessvecs_;

  using RandVarFunctional<Real>::val_;
  using RandVarFunctional<Real>::gv_;
  using RandVarFunctional<Real>::g_;
  using RandVarFunctional<Real>::hv_;
  using RandVarFunctional<Real>::dualVector_;

  using RandVarFunctional<Real>::point_;
  using RandVarFunctional<Real>::weight_;

  using RandVarFunctional<Real>::computeValue;
  using RandVarFunctional<Real>::computeGradient;
  using RandVarFunctional<Real>::computeGradVec;
  using RandVarFunctional<Real>::computeHessVec;

  void initializeMV(void) {
    values_    = makePtr<SampledScalar<Real>>();
    gradvecs_  = makePtr<SampledScalar<Real>>();
    gradients_ = makePtr<SampledVector<Real>>();
    hessvecs_  = makePtr<SampledVector<Real>>();

    RandVarFunctional<Real>::setStorage(values_,gradients_);
    RandVarFunctional<Real>::setHessVecStorage(gradvecs_,hessvecs_);
  }

  void checkInputs(void) {
    int oSize = order_.size(), cSize = coeff_.size();
    ROL_TEST_FOR_EXCEPTION((oSize!=cSize),std::invalid_argument,
      ">>> ERROR (ROL::MeanVariance): Order and coefficient arrays have different sizes!");
    Real zero(0), two(2);
    for (int i = 0; i < oSize; i++) {
      ROL_TEST_FOR_EXCEPTION((order_[i] < two), std::invalid_argument,
        ">>> ERROR (ROL::MeanVariance): Element of order array out of range!");
      ROL_TEST_FOR_EXCEPTION((coeff_[i] < zero), std::invalid_argument,
        ">>> ERROR (ROL::MeanVariance): Element of coefficient array out of range!");
    }
    ROL_TEST_FOR_EXCEPTION(positiveFunction_ == nullPtr, std::invalid_argument,
      ">>> ERROR (ROL::MeanVariance): PositiveFunction pointer is null!");
    initializeMV();
  }

public:
  MeanVariance( const Real order, const Real coeff,
                const Ptr<PositiveFunction<Real> > &pf )
    : RandVarFunctional<Real>(), positiveFunction_(pf) {
    order_.clear(); order_.push_back(order);
    coeff_.clear(); coeff_.push_back(coeff);
    checkInputs();
    NumMoments_ = order_.size();
  }

  MeanVariance( const std::vector<Real> &order,
                const std::vector<Real> &coeff, 
                const Ptr<PositiveFunction<Real> > &pf )
    : RandVarFunctional<Real>(), positiveFunction_(pf) {
    order_.clear(); coeff_.clear();
    for ( uint i = 0; i < order.size(); i++ ) {
      order_.push_back(order[i]);
    }
    for ( uint i = 0; i < coeff.size(); i++ ) {
      coeff_.push_back(coeff[i]);
    }
    checkInputs();
    NumMoments_ = order_.size();
  }

  MeanVariance( ROL::ParameterList &parlist )
    : RandVarFunctional<Real>() {
    ROL::ParameterList &list
      = parlist.sublist("SOL").sublist("Risk Measure").sublist("Mean Plus Variance");
    // Get data from parameter list
    order_ = ROL::getArrayFromStringParameter<double>(list,"Orders");
    coeff_ = ROL::getArrayFromStringParameter<double>(list,"Coefficients");
    // Build (approximate) positive function
    std::string type = list.get<std::string>("Deviation Type");
    if ( type == "Upper" ) {
      positiveFunction_ = makePtr<PlusFunction<Real>>(list);
    }
    else if ( type == "Absolute" ) {
      positiveFunction_ = makePtr<AbsoluteValue<Real>>(list);
    }
    else {
      ROL_TEST_FOR_EXCEPTION(true, std::invalid_argument,
        ">>> (ROL::MeanVariance): Variance type is not recoginized!");
    }
    // Check inputs
    checkInputs();
    NumMoments_ = order_.size();
  }

  void setStorage(const Ptr<SampledScalar<Real>> &value_storage,
                  const Ptr<SampledVector<Real>> &gradient_storage) {
    values_    = value_storage;
    gradients_ = gradient_storage;
    RandVarFunctional<Real>::setStorage(values_,gradients_);
  }

  void setHessVecStorage(const Ptr<SampledScalar<Real>> &gradvec_storage,
                         const Ptr<SampledVector<Real>> &hessvec_storage) {
    gradvecs_ = gradvec_storage;
    hessvecs_ = hessvec_storage;
    RandVarFunctional<Real>::setHessVecStorage(gradvecs_,hessvecs_);
  }
  
  void updateValue(Objective<Real>         &obj,
                   const Vector<Real>      &x,
                   const std::vector<Real> &xstat,
                   Real                    &tol) {
    Real val = computeValue(obj,x,tol);
    val_    += weight_ * val;
  }

  Real getValue(const Vector<Real>      &x,
                const std::vector<Real> &xstat,
                SampleGenerator<Real>   &sampler) {
    // Compute expected value
    Real ev(0);
    sampler.sumAll(&val_,&ev,1);
    // Compute deviation
    Real val(0), diff(0), pf0(0), var(0), weight(0);
    for (int i = sampler.start(); i < sampler.numMySamples(); ++i) {
      values_->get(diff,sampler.getMyPoint(i));
      weight = sampler.getMyWeight(i);
      diff  -= ev;
      pf0    = positiveFunction_->evaluate(diff,0);
      for ( uint p = 0; p < NumMoments_; p++ ) {
        val += coeff_[p] * std::pow(pf0,order_[p]) * weight;
      }
    }
    sampler.sumAll(&val,&var,1);
    // Return mean plus deviation
    return ev + var;
  }

  void updateGradient(Objective<Real>         &obj,
                      const Vector<Real>      &x,
                      const std::vector<Real> &xstat,
                      Real                    &tol) {
    Real val = computeValue(obj,x,tol);
    val_ += weight_ * val;
    computeGradient(*dualVector_,obj,x,tol);
    g_->axpy(weight_,*dualVector_);
  }

  void getGradient(Vector<Real>            &g,
                   std::vector<Real>       &gstat,
                   const Vector<Real>      &x,
                   const std::vector<Real> &xstat,
                   SampleGenerator<Real>   &sampler) {
    // Compute expected value
    Real ev(0), zero(0), one(1);
    sampler.sumAll(&val_,&ev,1);
    sampler.sumAll(*g_,g);
    // Compute deviation
    g_->zero(); dualVector_->zero();
    Real diff(0), pf0(0), pf1(0), c(0), ec(0), ecs(0), weight(0);
    for (int i = sampler.start(); i < sampler.numMySamples(); ++i) {
      values_->get(diff,sampler.getMyPoint(i));
      weight = sampler.getMyWeight(i);
      diff  -= ev;
      pf0    = positiveFunction_->evaluate(diff,0);
      pf1    = positiveFunction_->evaluate(diff,1);
      c      = zero;
      for ( uint p = 0; p < NumMoments_; p++ ) {
        c += coeff_[p]*order_[p]*std::pow(pf0,order_[p]-one)*pf1;
      }
      ec += weight*c;
      gradients_->get(*dualVector_,sampler.getMyPoint(i));
      g_->axpy(weight*c,*dualVector_);
    }
    dualVector_->zero();
    sampler.sumAll(&ec,&ecs,1);
    g.scale(one-ecs);
    sampler.sumAll(*g_,*dualVector_);
    g.plus(*dualVector_);
  }

  void updateHessVec(Objective<Real>         &obj,
                     const Vector<Real>      &v,
                     const std::vector<Real> &vstat,
                     const Vector<Real>      &x,
                     const std::vector<Real> &xstat,
                     Real                    &tol) {
    Real val = computeValue(obj,x,tol);
    val_    += weight_ * val;
    Real gv  = computeGradVec(*dualVector_,obj,v,x,tol);
    gv_     += weight_ * gv;
    g_->axpy(weight_,*dualVector_);
    computeHessVec(*dualVector_,obj,v,x,tol);
    hv_->axpy(weight_,*dualVector_);
  }

  void getHessVec(Vector<Real>            &hv,
                  std::vector<Real>       &hvstat,
                  const Vector<Real>      &v,
                  const std::vector<Real> &vstat,
                  const Vector<Real>      &x,
                  const std::vector<Real> &xstat,
                  SampleGenerator<Real>   &sampler) {
    // Compute expected value
    std::vector<Real> myval(2), val(2);
    myval[0] = val_;
    myval[1] = gv_;
    sampler.sumAll(&myval[0],&val[0],2);
    Real ev = myval[0], egv = myval[1];
    dualVector_->zero();
    sampler.sumAll(*g_,*dualVector_);
    sampler.sumAll(*hv_,hv);
    // Compute deviation
    g_->zero(); hv_->zero();
    Real diff(0), pf0(0), pf1(0), pf2(0), zero(0), one(1), two(2);
    Real cg(0), ecg(0), ecgs(0), ch(0), ech(0), echs(0), weight(0), gv(0);
    for (int i = sampler.start(); i < sampler.numMySamples(); ++i) {
      values_->get(diff,sampler.getMyPoint(i));
      gradvecs_->get(gv,sampler.getMyPoint(i));
      weight = sampler.getMyWeight(i);
      diff  -= ev;
      pf0    = positiveFunction_->evaluate(diff,0);
      pf1    = positiveFunction_->evaluate(diff,1);
      pf2    = positiveFunction_->evaluate(diff,2);
      cg     = zero;
      ch     = zero;
      for ( uint p = 0; p < NumMoments_; p++ ) {
        cg += coeff_[p]*order_[p]*(gv-egv)*
                ((order_[p]-one)*std::pow(pf0,order_[p]-two)*pf1*pf1+
                std::pow(pf0,order_[p]-one)*pf2);
        ch += coeff_[p]*order_[p]*std::pow(pf0,order_[p]-one)*pf1;
      }
      ecg += weight*cg;
      ech += weight*ch;
      gradients_->get(*hv_,sampler.getMyPoint(i));
      g_->axpy(weight*cg,*hv_);
      hessvecs_->get(*hv_,sampler.getMyPoint(i));
      g_->axpy(weight*ch,*hv_);
    }
    sampler.sumAll(&ech,&echs,1);
    hv.scale(one-echs);
    sampler.sumAll(&ecg,&ecgs,1);
    hv.axpy(-ecgs,*dualVector_);
    dualVector_->zero();
    sampler.sumAll(*g_,*dualVector_);
    hv.plus(*dualVector_);
  }
};

}

#endif