ROL_MeanDeviation.hpp

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#ifndef ROL_MEANDEVIATION_HPP
#define ROL_MEANDEVIATION_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 MeanDeviation : 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_;

  std::vector<Real> dev0_;
  std::vector<Real> dev1_;
  std::vector<Real> dev2_;
  std::vector<Real> dev3_;
  std::vector<Real> des0_;
  std::vector<Real> des1_;
  std::vector<Real> des2_;
  std::vector<Real> des3_;
  std::vector<Real> devp_;
  std::vector<Real> gvp1_;
  std::vector<Real> gvp2_;
  std::vector<Real> gvp3_;
  std::vector<Real> gvs1_;
  std::vector<Real> gvs2_;
  std::vector<Real> gvs3_;

  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 initializeStorage(void) {
    NumMoments_ = order_.size();

    dev0_.clear(); dev1_.clear(); dev2_.clear(); dev3_.clear();
    des0_.clear(); des1_.clear(); des2_.clear(); des3_.clear();
    devp_.clear();
    gvp1_.clear(); gvp2_.clear(); gvp3_.clear();
    gvs1_.clear(); gvs2_.clear(); gvs3_.clear();

    dev0_.resize(NumMoments_); dev1_.resize(NumMoments_);
    dev2_.resize(NumMoments_); dev3_.resize(NumMoments_);
    des0_.resize(NumMoments_); des1_.resize(NumMoments_);
    des2_.resize(NumMoments_); des3_.resize(NumMoments_);
    devp_.resize(NumMoments_);
    gvp1_.resize(NumMoments_); gvp2_.resize(NumMoments_);
    gvp3_.resize(NumMoments_);
    gvs1_.resize(NumMoments_); gvs2_.resize(NumMoments_);
    gvs3_.resize(NumMoments_);

    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 clear(void) {
    const Real zero(0);
    dev0_.assign(NumMoments_,zero); dev1_.assign(NumMoments_,zero);
    dev2_.assign(NumMoments_,zero); dev3_.assign(NumMoments_,zero);
    des0_.assign(NumMoments_,zero); des1_.assign(NumMoments_,zero);
    des2_.assign(NumMoments_,zero); des3_.assign(NumMoments_,zero);
    devp_.assign(NumMoments_,zero);
    gvp1_.assign(NumMoments_,zero); gvp2_.assign(NumMoments_,zero);
    gvp3_.assign(NumMoments_,zero);
    gvs1_.assign(NumMoments_,zero); gvs2_.assign(NumMoments_,zero);
    gvs3_.assign(NumMoments_,zero);

    gradvecs_->update();
    hessvecs_->update();
  }

  void checkInputs(void) {
    int oSize = order_.size(), cSize = coeff_.size();
    ROL_TEST_FOR_EXCEPTION((oSize!=cSize),std::invalid_argument,
      ">>> ERROR (ROL::MeanDeviation): 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::MeanDeviation): Element of order array out of range!");
      ROL_TEST_FOR_EXCEPTION((coeff_[i] < zero), std::invalid_argument,
        ">>> ERROR (ROL::MeanDeviation): Element of coefficient array out of range!");
    }
    ROL_TEST_FOR_EXCEPTION(positiveFunction_ == nullPtr, std::invalid_argument,
      ">>> ERROR (ROL::MeanDeviation): PositiveFunction pointer is null!");
    initializeStorage();
  }

public:
  MeanDeviation( 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();
  }

  MeanDeviation( 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();
  }

  MeanDeviation( ROL::ParameterList &parlist )
    : RandVarFunctional<Real>() {
    ROL::ParameterList &list
      = parlist.sublist("SOL").sublist("Risk Measure").sublist("Mean Plus Deviation");

    // 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::MeanDeviation): Deviation type is not recoginized!");
    }
    // Check inputs
    checkInputs();
  }

  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 initialize(const Vector<Real> &x) {
    RandVarFunctional<Real>::initialize(x);
    clear();
  }
  
  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;
  }

  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 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_,hv);
  }

  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 diff(0), pf0(0), dev(0), one(1), 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++ ) {
        dev0_[p] += std::pow(pf0,order_[p]) * weight;
      }
    }
    sampler.sumAll(&dev0_[0],&des0_[0],NumMoments_);
    for ( uint p = 0; p < NumMoments_; p++ ) {
      dev += coeff_[p]*std::pow(des0_[p],one/order_[p]);
    }
    // Return mean plus deviation
    return ev + dev;
  }

  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);
    sampler.sumAll(&val_,&ev,1);
    // Compute deviation
    Real diff(0), pf0(0), pf1(0), c(0), one(1), zero(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);
      for ( uint p = 0; p < NumMoments_; p++ ) {
        dev0_[p] += weight * std::pow(pf0,order_[p]);
        dev1_[p] += weight * std::pow(pf0,order_[p]-one) * pf1;
      }
    }
    sampler.sumAll(&dev0_[0],&des0_[0],NumMoments_);
    sampler.sumAll(&dev1_[0],&des1_[0],NumMoments_);
    for ( uint p = 0; p < NumMoments_; p++ ) {
      dev0_[p] = std::pow(des0_[p],one-one/order_[p]);
    }
    // Compute derivative
    dualVector_->zero();
    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++ ) {
        if ( dev0_[p] > zero ) {
          c += coeff_[p]/dev0_[p] * (std::pow(pf0,order_[p]-one)*pf1 - des1_[p]);
        }
      }
      gradients_->get(*dualVector_,sampler.getMyPoint(i));
      g_->axpy(weight*c,*dualVector_);
    }
    sampler.sumAll(*g_,g);
  }

  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 = val[0], egv = val[1];
    // Compute deviation
    Real diff(0), pf0(0), pf1(0), pf2(0), zero(0), one(1), two(2);
    Real cg(0), ch(0), diff1(0), diff2(0), diff3(0), weight(0), gv(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);
      pf2  = positiveFunction_->evaluate(diff,2);
      for ( uint p = 0; p < NumMoments_; p++ ) {
        dev0_[p] += weight * std::pow(pf0,order_[p]);
        dev1_[p] += weight * std::pow(pf0,order_[p]-one) * pf1;
        dev2_[p] += weight * std::pow(pf0,order_[p]-two) * pf1 * pf1;
        dev3_[p] += weight * std::pow(pf0,order_[p]-one) * pf2;
      }
    }
    sampler.sumAll(&dev0_[0],&des0_[0],NumMoments_);
    sampler.sumAll(&dev1_[0],&des1_[0],NumMoments_);
    sampler.sumAll(&dev2_[0],&des2_[0],NumMoments_);
    sampler.sumAll(&dev3_[0],&des3_[0],NumMoments_);
    for ( uint p = 0; p < NumMoments_; p++ ) {
      devp_[p] = std::pow(des0_[p],two-one/order_[p]);
      dev0_[p] = std::pow(des0_[p],one-one/order_[p]);
    }
    for (int i = sampler.start(); i < sampler.numMySamples(); ++i) {
      values_->get(diff,sampler.getMyPoint(i));
      weight = sampler.getMyWeight(i);
      diff  -= ev;
      gradvecs_->get(gv,sampler.getMyPoint(i));
      pf0  = positiveFunction_->evaluate(diff,0);
      pf1  = positiveFunction_->evaluate(diff,1);
      pf2  = positiveFunction_->evaluate(diff,2);
      for ( uint p = 0; p < NumMoments_; p++ ) {
        gvp1_[p] += weight * (std::pow(pf0,order_[p]-one)*pf1-des1_[p]) *
                     (gv - egv);
        gvp2_[p] += weight * (std::pow(pf0,order_[p]-two)*pf1*pf1-des2_[p]) *
                     (gv - egv);
        gvp3_[p] += weight * (std::pow(pf0,order_[p]-one)*pf2-des3_[p]) *
                     (gv - egv);
      }
    }
    sampler.sumAll(&gvp1_[0],&gvs1_[0],NumMoments_);
    sampler.sumAll(&gvp2_[0],&gvs2_[0],NumMoments_);
    sampler.sumAll(&gvp3_[0],&gvs3_[0],NumMoments_);
    // Compute derivative
    dualVector_->zero();
    for (int i = sampler.start(); i < sampler.numMySamples(); ++i) {
      values_->get(diff,sampler.getMyPoint(i));
      weight = sampler.getMyWeight(i);
      diff  -= ev;
      gradvecs_->get(gv,sampler.getMyPoint(i));
      pf0  = positiveFunction_->evaluate(diff,0);
      pf1  = positiveFunction_->evaluate(diff,1);
      pf2  = positiveFunction_->evaluate(diff,2);
      cg   = one;
      ch   = zero;
      for ( uint p = 0; p < NumMoments_; p++ ) {
        if ( dev0_[p] > zero ) {
          diff1 = std::pow(pf0,order_[p]-one)*pf1-des1_[p];
          diff2 = std::pow(pf0,order_[p]-two)*pf1*pf1*(gv-egv)-gvs2_[p];
          diff3 = std::pow(pf0,order_[p]-one)*pf2*(gv-egv)-gvs3_[p];
          cg   += coeff_[p]*diff1/dev0_[p];
          ch   += coeff_[p]*(((order_[p]-one)*diff2+diff3)/dev0_[p] -
                    (order_[p]-one)*gvs1_[p]*diff1/devp_[p]);
        }
      }
      gradients_->get(*g_,sampler.getMyPoint(i));
      dualVector_->axpy(weight*ch,*g_);
      hessvecs_->get(*hv_,sampler.getMyPoint(i));
      dualVector_->axpy(weight*cg,*hv_);
    }
    sampler.sumAll(*dualVector_,hv);
  }
};

}

#endif