ROL
ROL_PointwiseCDFObjective.hpp
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43
44#ifndef ROL_POINTWISECDFOBJECTIVE_H
45#define ROL_POINTWISECDFOBJECTIVE_H
46
47#include "ROL_Objective.hpp"
48#include "ROL_BatchManager.hpp"
49#include "ROL_Vector.hpp"
50#include "ROL_Distribution.hpp"
51#include "ROL_Ptr.hpp"
52#include <math.h>
53
54namespace ROL {
55
56template <class Real>
57class PointwiseCDFObjective : public Objective<Real> {
58private:
59 std::vector<ROL::Ptr<Distribution<Real> > > dist_;
60 ROL::Ptr<BatchManager<Real> > bman_;
61 const Real scale_;
62 const Real sqrt2_;
63 const Real sqrtpi_;
64
65 Real valueCDF(const int dim, const Real loc, const SROMVector<Real> &x) const {
66 const int numSamples = x.getNumSamples();
67 Real val = 0., hs = 0., xpt = 0., xwt = 0.;
68 for (int k = 0; k < numSamples; k++) {
69 xpt = (*x.getPoint(k))[dim]; xwt = x.getWeight(k);
70 hs = 0.5 * (1. + erf((loc-xpt)/(sqrt2_*scale_)));
71 val += xwt * hs;
72 }
73 return val;
74 }
75
76 Real gradientCDF(std::vector<Real> &gradx, std::vector<Real> &gradp,
77 const int dim, const Real loc, const SROMVector<Real> &x) const {
78 const int numSamples = x.getNumSamples();
79 gradx.resize(numSamples,0.); gradp.resize(numSamples,0.);
80 Real val = 0., hs = 0., xpt = 0., xwt = 0.;
81 for (int k = 0; k < numSamples; k++) {
82 xpt = (*x.getPoint(k))[dim]; xwt = x.getWeight(k);
83 hs = 0.5 * (1. + erf((loc-xpt)/(sqrt2_*scale_)));
84 val += xwt * hs;
85 gradx[k] = -(xwt/(sqrt2_*sqrtpi_*scale_))
86 * std::exp(-std::pow((loc-xpt)/(sqrt2_*scale_),2));
87 gradp[k] = hs;
88 }
89 return val;
90 }
91
92 Real hessVecCDF(std::vector<Real> &hvx,
93 const int dim, const Real loc, const SROMVector<Real> &x, const SROMVector<Real> &v) const {
94 const int numSamples = x.getNumSamples();
95 hvx.resize(numSamples,0.);
96 Real val = 0., hs = 0., xpt = 0., xwt = 0., scale3 = std::pow(scale_,3);
97 for (int k = 0; k < numSamples; k++) {
98 xpt = (*x.getPoint(k))[dim]; xwt = x.getWeight(k);
99 hs = 0.5 * (1. + erf((loc-xpt)/(sqrt2_*scale_)));
100 val += xwt * hs;
101 hvx[k] = -(xwt/(sqrt2_*sqrtpi_*scale3))
102 * std::exp(-std::pow((loc-xpt)/(sqrt2_*scale_),2)) * (loc-xpt);
103 }
104 return val;
105 }
106
107public:
108 PointwiseCDFObjective(const std::vector<ROL::Ptr<Distribution<Real> > > &dist,
109 ROL::Ptr<BatchManager<Real> > &bman,
110 const Real scale = 1.e-2)
111 : Objective<Real>(), dist_(dist), bman_(bman), scale_(scale),
112 sqrt2_(std::sqrt(2.)), sqrtpi_(std::sqrt(ROL::ScalarTraits<Real>::pi())) {}
113
114 Real value( const Vector<Real> &x, Real &tol ) {
115 const SROMVector<Real> &ex = dynamic_cast<const SROMVector<Real>&>(x);
116 const int dimension = ex.getDimension();
117 const int numSamples = ex.getNumSamples();
118 Real val = 0., diff = 0., xpt = 0., sum = 0.;
119 for (int d = 0; d < dimension; d++) {
120 for (int k = 0; k < numSamples; k++) {
121 xpt = (*ex.getPoint(k))[d];
122 diff = (valueCDF(d,xpt,ex)-dist_[d]->evaluateCDF(xpt));
123 val += std::pow(diff,2);
124 }
125 }
126 bman_->sumAll(&val,&sum,1);
127 return 0.5*sum;
128 }
129
130 void gradient( Vector<Real> &g, const Vector<Real> &x, Real &tol ) {
131 SROMVector<Real> &eg = dynamic_cast<SROMVector<Real>&>(g);
132 const SROMVector<Real> &ex = dynamic_cast<const SROMVector<Real>&>(x);
133 const int dimension = ex.getDimension();
134 const int numSamples = ex.getNumSamples();
135 std::vector<Real> gradx(numSamples,0.), gradp(numSamples,0.);
136 Real diff = 0., xpt = 0., val = 0., sum = 0.;
137 std::vector<Real> val_wt(numSamples,0.), tmp(dimension,0.);
138 std::vector<std::vector<Real> > val_pt(numSamples,tmp);
139 for (int d = 0; d < dimension; d++) {
140 for (int k = 0; k < numSamples; k++) {
141 xpt = (*ex.getPoint(k))[d];
142 val = gradientCDF(gradx,gradp,d,xpt,ex);
143 diff = (val-dist_[d]->evaluateCDF(xpt));
144 sum = 0.;
145 for (int j = 0; j < numSamples; j++) {
146 (val_pt[j])[d] += diff * gradx[j];
147 val_wt[j] += diff * gradp[j];
148 sum -= gradx[j];
149 }
150 (val_pt[k])[d] += diff * (sum - dist_[d]->evaluatePDF(xpt));
151 }
152 }
153 for (int k = 0; k < numSamples; k++) {
154 eg.setPoint(k,val_pt[k]);
155 eg.setWeight(k,val_wt[k]);
156 }
157 }
158
159// void hessVec( Vector<Real> &hv, const Vector<Real> &v, const Vector<Real> &x, Real &tol ) {
160// }
161}; // class LinearCombinationObjective
162
163} // namespace ROL
164
165#endif
Provides the interface to evaluate objective functions.
ROL::Ptr< BatchManager< Real > > bman_
Real hessVecCDF(std::vector< Real > &hvx, const int dim, const Real loc, const SROMVector< Real > &x, const SROMVector< Real > &v) const
PointwiseCDFObjective(const std::vector< ROL::Ptr< Distribution< Real > > > &dist, ROL::Ptr< BatchManager< Real > > &bman, const Real scale=1.e-2)
Real gradientCDF(std::vector< Real > &gradx, std::vector< Real > &gradp, const int dim, const Real loc, const SROMVector< Real > &x) const
void gradient(Vector< Real > &g, const Vector< Real > &x, Real &tol)
Compute gradient.
Real value(const Vector< Real > &x, Real &tol)
Compute value.
std::vector< ROL::Ptr< Distribution< Real > > > dist_
Real valueCDF(const int dim, const Real loc, const SROMVector< Real > &x) const
Provides the std::vector implementation of the ROL::Vector interface.
Defines the linear algebra or vector space interface.
constexpr auto dim