ROL_MomentObjective.hpp

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#ifndef ROL_MOMENTOBJECTIVE_H
#define ROL_MOMENTOBJECTIVE_H

#include "ROL_Objective.hpp"
#include "ROL_SROMVector.hpp"
#include "ROL_Types.hpp"
#include <iostream>

namespace ROL {

template <class Real>
class MomentObjective : public Objective<Real> {
private:
  const std::vector<std::vector<std::pair<size_t, Real> > > moments_;

  Real momentValue(const size_t dim, const Real power, const Real moment, const SROMVector<Real> &x) const {
    const size_t numSamples = x.getNumSamples();
    Real val = 0., xpt = 0., xwt = 0.;
    for (size_t k = 0; k < numSamples; k++) {
      xpt = (*x.getPoint(k))[dim]; xwt = x.getWeight(k);
      val += xwt * ((power==1) ? xpt : std::pow(xpt,power));
    }
    return 0.5*std::pow((val-moment)/moment,2);
  }

  void momentGradient(std::vector<Real> &gradx, std::vector<Real> &gradp,  Real &scale,
                const size_t dim, const Real power, const Real moment, const SROMVector<Real> &x) const {
    const size_t numSamples = x.getNumSamples();
    gradx.resize(numSamples,0.); gradp.resize(numSamples,0.);
    scale = 0.;
    Real xpt = 0., xwt = 0., xpow = 0.;
    for (size_t k = 0; k < numSamples; k++) {
      xpt = (*x.getPoint(k))[dim]; xwt = x.getWeight(k);
      xpow = ((power==1) ? 1. : ((power==2) ? xpt : std::pow(xpt,power-1)));
      scale += xwt * xpow * xpt;
      gradx[k] = xwt * xpow * power;
      gradp[k] = xpow * xpt;
    }
    scale -= moment;
    scale /= std::pow(moment,2);
  }

  void momentHessVec(std::vector<Real> &hvx1, std::vector<Real> &hvx2, std::vector<Real> &hvx3,
                     std::vector<Real> &hvp1, std::vector<Real> &hvp2,
                     Real &scale1, Real &scale2, Real &scale3,
               const size_t dim, const Real power, const Real moment,
               const SROMVector<Real> &x, const SROMVector<Real> &v) const {
    const size_t numSamples = x.getNumSamples();
    hvx1.resize(numSamples,0.); hvx2.resize(numSamples,0.); hvx3.resize(numSamples,0.);
    hvp1.resize(numSamples,0.); hvp2.resize(numSamples,0.);
    scale1 = 0.; scale2 = 0.; scale3 = 0.;
    Real xpt = 0., xwt = 0., vpt = 0., vwt = 0.;
    Real xpow0 = 0., xpow1 = 0., xpow2 = 0.;
    const Real moment2 = std::pow(moment,2);
    for (size_t k = 0; k < numSamples; k++) {
      xpt = (*x.getPoint(k))[dim]; xwt = x.getWeight(k);
      vpt = (*v.getPoint(k))[dim]; vwt = v.getWeight(k);
      xpow2 = ((power==1) ? 0. : ((power==2) ? 1. : ((power==3) ?  xpt :
                std::pow(xpt,power-2))));
      xpow1 = ((power==1) ? 1. : xpow2 * xpt);
      xpow0 = xpow1 * xpt;
      scale1 += xwt * xpow1 * vpt;
      scale2 += xwt * xpow0;
      scale3 += vwt * xpow0;
      hvx1[k] = power * xwt * xpow1;
      hvx2[k] = power * (power-1.) * xwt * xpow2 * vpt;
      hvx3[k] = power * vwt * xpow1;
      hvp1[k] = xpow0;
      hvp2[k] = power * xpow1 * vpt;
    }
    scale1 *= power/moment2;
    scale2 -= moment;
    scale2 /= moment2;
    scale3 /= moment2;
  }

public:
  MomentObjective(const std::vector<std::vector<std::pair<size_t, Real> > > &moments)
    : Objective<Real>(), moments_(moments) {}

  Real value( const Vector<Real> &x, Real &tol ) {
    const SROMVector<Real> &ex = Teuchos::dyn_cast<const SROMVector<Real> >(x);
    size_t dimension  = ex.getDimension();
    Real val = 0.;
    std::vector<std::pair<size_t, Real> > data;
    for (size_t d = 0; d < dimension; d++) {
      data = moments_[d];
      for (size_t m = 0; m < data.size(); m++) {
        val += momentValue(d,(Real)data[m].first,data[m].second,ex);
      }
    }
    return val;
  }

  void gradient( Vector<Real> &g, const Vector<Real> &x, Real &tol ) {
    SROMVector<Real> &eg = Teuchos::dyn_cast<SROMVector<Real> >(g);
    const SROMVector<Real> &ex = Teuchos::dyn_cast<const SROMVector<Real> >(x);
    size_t dimension  = ex.getDimension();
    size_t numSamples = ex.getNumSamples();
    std::vector<Real> gradx(numSamples,0.), gradp(numSamples,0.);
    Real scale = 0.;
    std::vector<std::pair<size_t, Real> > data;
    std::vector<Real> val_wt(numSamples,0.), tmp(dimension,0.);
    std::vector<std::vector<Real> > val_pt(numSamples,tmp);
    for (size_t d = 0; d < dimension; d++) {
      data = moments_[d];
      for (size_t m = 0; m < data.size(); m++) {
        momentGradient(gradx,gradp,scale,d,(Real)data[m].first,data[m].second,ex);
        for (size_t k = 0; k < numSamples; k++) {
          (val_pt[k])[d] += scale*gradx[k];
          val_wt[k]      += scale*gradp[k];
        }
      }
    }
    for (size_t k = 0; k < numSamples; k++) {
      eg.setPoint(k,val_pt[k]);
      eg.setWeight(k,val_wt[k]);
    }
  }

  void hessVec( Vector<Real> &hv, const Vector<Real> &v, const Vector<Real> &x, Real &tol ) {
    SROMVector<Real> &ehv = Teuchos::dyn_cast<SROMVector<Real> >(hv);
    const SROMVector<Real> &ev = Teuchos::dyn_cast<const SROMVector<Real> >(v);
    const SROMVector<Real> &ex = Teuchos::dyn_cast<const SROMVector<Real> >(x);
    const size_t dimension  = ex.getDimension();
    const size_t numSamples = ex.getNumSamples();
    std::vector<Real> hvx1(numSamples,0.), hvx2(numSamples,0.), hvx3(numSamples,0.);
    std::vector<Real> hvp1(numSamples,0.), hvp2(numSamples,0.);
    Real scale1 = 0., scale2 = 0., scale3 = 0.;
    std::vector<std::pair<size_t, Real> > data;
    std::vector<Real> val_wt(numSamples,0.), tmp(dimension,0.);
    std::vector<std::vector<Real> > val_pt(numSamples,tmp);
    for (size_t d = 0; d < dimension; d++) {
      data = moments_[d];
      for (size_t m = 0; m < data.size(); m++) {
        momentHessVec(hvx1,hvx2,hvx3,hvp1,hvp2,scale1,scale2,scale3,
                      d,(Real)data[m].first,data[m].second,ex,ev);
        for (size_t k = 0; k < numSamples; k++) {
          (val_pt[k])[d] += (scale1+scale3)*hvx1[k] + scale2*(hvx2[k]+hvx3[k]);
          val_wt[k]      += (scale1+scale3)*hvp1[k] + scale2*hvp2[k];
        }
      }
    }
    for (size_t k = 0; k < numSamples; k++) {
      ehv.setPoint(k,val_pt[k]);
      ehv.setWeight(k,val_wt[k]);
    }
  }
}; // class SROMObjective

} // namespace ROL

#endif