ROL_MeanDeviationFromTarget.hpp

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#ifndef ROL_MEANDEVIATIONFROMTARGET_HPP
#define ROL_MEANDEVIATIONFROMTARGET_HPP

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

namespace ROL {

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

  std::vector<Real> pval_; 
  std::vector<Real> pgv_; 

  std::vector<Ptr<Vector<Real> > > pg0_;
  std::vector<Ptr<Vector<Real> > > pg_;
  std::vector<Ptr<Vector<Real> > > phv_;

  bool firstResetMDT_;

  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 initializeMDT(void) {
    // Initialize additional storage
    pg_.clear(); pg0_.clear(); phv_.clear(); pval_.clear(); pgv_.clear();
    pg_.resize(NumMoments_);
    pg0_.resize(NumMoments_);
    phv_.resize(NumMoments_);
    pval_.resize(NumMoments_);
    pgv_.resize(NumMoments_);
  }

  void checkInputs(void) {
    int oSize = order_.size(), cSize = coeff_.size(), tSize = target_.size();
    ROL_TEST_FOR_EXCEPTION((oSize!=cSize),std::invalid_argument,
      ">>> ERROR (ROL::MeanDeviationFromTarget): Order and coefficient arrays have different sizes!");
    ROL_TEST_FOR_EXCEPTION((oSize!=tSize),std::invalid_argument,
      ">>> ERROR (ROL::MeanDeviationFromTarget): Order and target 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::MeanDeviationFromTarget): Element of order array out of range!");
      ROL_TEST_FOR_EXCEPTION((coeff_[i] < zero), std::invalid_argument,
        ">>> ERROR (ROL::MeanDeviationFromTarget): Element of coefficient array out of range!");
    }
    ROL_TEST_FOR_EXCEPTION(positiveFunction_ == nullPtr, std::invalid_argument,
      ">>> ERROR (ROL::MeanDeviationFromTarget): PositiveFunction pointer is null!");
    initializeMDT();
  }

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

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

  MeanDeviationFromTarget( ROL::ParameterList &parlist )
    : RandVarFunctional<Real>(), firstResetMDT_(true) {
    ROL::ParameterList &list
      = parlist.sublist("SOL").sublist("Risk Measure").sublist("Mean Plus Deviation From Target");

    // Get data from parameter list
    target_ = ROL::getArrayFromStringParameter<double>(list,"Targets");

    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::MeanDeviation): Deviation type is not recoginized!");
    }
    // Check inputs
    NumMoments_ = order_.size();
    checkInputs();
  }

  void initialize(const Vector<Real> &x) {
    RandVarFunctional<Real>::initialize(x);
    if (firstResetMDT_) {
      for ( uint p = 0; p < NumMoments_; p++ ) {
        pg0_[p] = x.dual().clone();
        pg_[p]  = x.dual().clone();
        phv_[p] = x.dual().clone();
      }
      firstResetMDT_  = false;
    }
    Real zero(0);
    for ( uint p = 0; p < NumMoments_; p++ ) {
      pg0_[p]->zero(); pg_[p]->zero(); phv_[p]->zero();
      pval_[p] = zero; pgv_[p] = zero;
    }
  }
  
  void updateValue(Objective<Real>         &obj,
                   const Vector<Real>      &x,
                   const std::vector<Real> &xstat,
                   Real                    &tol) {
    Real diff(0), pf0(0);
    Real val = computeValue(obj,x,tol);
    val_    += weight_ * val;
    for ( uint p = 0; p < NumMoments_; p++ ) {
      diff = val-target_[p];
      pf0  = positiveFunction_->evaluate(diff,0);
      pval_[p] += weight_ * std::pow(pf0,order_[p]);
    }
  }

  Real getValue(const Vector<Real>      &x,
                const std::vector<Real> &xstat,
                SampleGenerator<Real>   &sampler) {
    const Real one(1);
    Real dev(0);
    sampler.sumAll(&val_,&dev,1);
    std::vector<Real> pval_sum(NumMoments_);
    sampler.sumAll(&pval_[0],&pval_sum[0],NumMoments_);
    for ( uint p = 0; p < NumMoments_; p++ ) {
      dev += coeff_[p] * std::pow(pval_sum[p],one/order_[p]);
    }
    return dev;
  }

  void updateGradient(Objective<Real>         &obj,
                      const Vector<Real>      &x,
                      const std::vector<Real> &xstat,
                      Real                    &tol) {
    Real diff(0), pf0(0), pf1(0), c(0), one(1);
    Real val = computeValue(obj,x,tol);
    computeGradient(*dualVector_,obj,x,tol);
    for ( uint p = 0; p < NumMoments_; p++ ) {
      diff = val-target_[p];
      pf0 = positiveFunction_->evaluate(diff,0);
      pf1 = positiveFunction_->evaluate(diff,1);
      c    = std::pow(pf0,order_[p]-one) * pf1;
      (pg_[p])->axpy(weight_ * c,*dualVector_);
      pval_[p] += weight_ * std::pow(pf0,order_[p]);
    }
    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) {
    const Real zero(0), one(1);
    sampler.sumAll(*g_,g);
    std::vector<Real> pval_sum(NumMoments_);
    sampler.sumAll(&pval_[0],&pval_sum[0],NumMoments_);
    for ( uint p = 0; p < NumMoments_; p++ ) {
      if ( pval_sum[p] > zero ) {
        dualVector_->zero();
        sampler.sumAll(*(pg_[p]),*dualVector_);
        g.axpy(coeff_[p]/std::pow(pval_sum[p],one-one/order_[p]),*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) {
    const Real one(1), two(2);
    Real diff(0), pf0(0), pf1(0), pf2(0), p0(0), p1(0), p2(0), c(0);
    Real val = computeValue(obj,x,tol);
    Real gv  = computeGradVec(*g_,obj,v,x,tol);
    computeHessVec(*dualVector_,obj,v,x,tol);
    for ( uint p = 0; p < NumMoments_; p++ ) {
      diff = val - target_[p];
      pf0 = positiveFunction_->evaluate(diff,0);
      pf1 = positiveFunction_->evaluate(diff,1);
      pf2 = positiveFunction_->evaluate(diff,2);
      p0   = std::pow(pf0,order_[p]);
      p1   = std::pow(pf0,order_[p]-one);
      p2   = std::pow(pf0,order_[p]-two);
      c    = -(order_[p]-one)*p1*pf1;
      pg0_[p]->axpy(weight_*c,*g_);
      c    = gv*((order_[p]-one)*p2*pf1*pf1 + p1*pf2);
      pg_[p]->axpy(weight_*c,*g_);
      c    = p1*pf1;
      phv_[p]->axpy(weight_*c,*dualVector_);
      pval_[p] += weight_*p0;
      pgv_[p]  += weight_*p1*pf1*gv;
    }
    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) {
    const Real zero(0), one(1), two(2);
    sampler.sumAll(*hv_,hv);
    std::vector<Real> pval_sum(NumMoments_);
    sampler.sumAll(&(pval_)[0],&pval_sum[0],NumMoments_);
    std::vector<Real> pgv_sum(NumMoments_);
    sampler.sumAll(&(pgv_)[0],&pgv_sum[0],NumMoments_);
    Real c(0);
    for ( uint p = 0; p < NumMoments_; p++ ) {
      if ( pval_sum[p] > zero ) {
        dualVector_->zero();
        sampler.sumAll(*(pg0_[p]),*dualVector_);
        c = coeff_[p]*(pgv_sum[p]/std::pow(pval_sum[p],two-one/order_[p]));
        hv.axpy(c,*dualVector_);

        dualVector_->zero();
        sampler.sumAll(*(pg_[p]),*dualVector_);
        c = coeff_[p]/std::pow(pval_sum[p],one-one/order_[p]);
        hv.axpy(c,*dualVector_);

        dualVector_->zero();
        sampler.sumAll(*(phv_[p]),*dualVector_);
        hv.axpy(c,*dualVector_);
      }
    }
  }
};

}

#endif