ROL
ROL_Zakharov.hpp
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79#ifndef USE_HESSVEC
80#define USE_HESSVEC 1
81#endif
82
83#ifndef ROL_ZAKHAROV_HPP
84#define ROL_ZAKHAROV_HPP
85
86#include "ROL_TestProblem.hpp"
87#include "ROL_StdVector.hpp"
88
89
90namespace ROL {
91namespace ZOO {
92
95template<class Real>
96class Objective_Zakharov : public Objective<Real> {
97private:
98 ROL::Ptr<Vector<Real> > k_;
99
100public:
101
102 // Create using a ROL::Vector containing 1,2,3,...,n
103 Objective_Zakharov(const ROL::Ptr<Vector<Real> > k) : k_(k) {}
104
105 Real value( const Vector<Real> &x, Real &tol ) {
106
107 Real xdotx = x.dot(x);
108 Real kdotx = x.dot(*k_);
109
110 Real val = xdotx + pow(kdotx,2)/4.0 + pow(kdotx,4)/16.0;
111
112 return val;
113 }
114
115 void gradient( Vector<Real> &g, const Vector<Real> &x, Real &tol ) {
116
117 Real kdotx = x.dot(*k_);
118 Real coeff = 0.25*(2.0*kdotx+pow(kdotx,3.0));
119
120 g.set(x);
121 g.scale(2.0);
122 g.axpy(coeff,*k_);
123 }
124
125 Real dirDeriv( const Vector<Real> &x, const Vector<Real> &d, Real &tol ) {
126
127 Real kdotd = d.dot(*k_);
128 Real kdotx = x.dot(*k_);
129 Real xdotd = x.dot(d);
130
131 Real coeff = 0.25*(2.0*kdotx+pow(kdotx,3.0));
132
133 Real deriv = 2*xdotd + coeff*kdotd;
134
135 return deriv;
136
137 }
138
139#if USE_HESSVEC
140 void hessVec( Vector<Real> &hv, const Vector<Real> &v, const Vector<Real> &x, Real &tol ) {
141
142 Real kdotx = x.dot(*k_);
143 Real kdotv = v.dot(*k_);
144 Real coeff = 0.25*(2.0+3.0*pow(kdotx,2.0))*kdotv;
145
146 hv.set(v);
147 hv.scale(2.0);
148 hv.axpy(coeff,*k_);
149 }
150#endif
151 void invHessVec( Vector<Real> &ihv, const Vector<Real> &v, const Vector<Real> &x, Real &tol ) {
152
153 Real kdotv = v.dot(*k_);
154 Real kdotx = x.dot(*k_);
155 Real kdotk = (*k_).dot(*k_);
156 Real coeff = -kdotv/(2.0*kdotk+16.0/(2.0+3.0*pow(kdotx,2.0)));
157
158 ihv.set(v);
159 ihv.scale(0.5);
160 ihv.axpy(coeff,*k_);
161 }
162};
163
164
165
166template<class Real>
167class getZakharov : public TestProblem<Real> {
168public:
169 getZakharov(void) {}
170
171 Ptr<Objective<Real>> getObjective(void) const {
172 // Problem dimension
173 int n = 10;
174 // Instantiate Objective Function
175 ROL::Ptr<std::vector<Real> > k_ptr = ROL::makePtr<std::vector<Real>>(n,0.0);
176 for ( int i = 0; i < n; i++ ) {
177 (*k_ptr)[i] = i+1.0;
178 }
179 ROL::Ptr<Vector<Real> > k = ROL::makePtr<StdVector<Real>>(k_ptr);
180 return ROL::makePtr<Objective_Zakharov<Real>>(k);
181 }
182
183 Ptr<Vector<Real>> getInitialGuess(void) const {
184 // Problem dimension
185 int n = 10;
186 // Get Initial Guess
187 ROL::Ptr<std::vector<Real> > x0p = ROL::makePtr<std::vector<Real>>(n,3.0);
188 return ROL::makePtr<StdVector<Real>>(x0p);
189 }
190
191 Ptr<Vector<Real>> getSolution(const int i = 0) const {
192 // Problem dimension
193 int n = 10;
194 // Get Solution
195 ROL::Ptr<std::vector<Real> > xp = ROL::makePtr<std::vector<Real>>(n,0.0);
196 return ROL::makePtr<StdVector<Real>>(xp);
197 }
198};
199
200
201}// End ZOO Namespace
202}// End ROL Namespace
203
204#endif
Contains definitions of test objective functions.
Provides the interface to evaluate objective functions.
virtual void hessVec(Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
Apply Hessian approximation to vector.
Defines the linear algebra or vector space interface.
Definition: ROL_Vector.hpp:84
virtual void set(const Vector &x)
Set where .
Definition: ROL_Vector.hpp:209
virtual void scale(const Real alpha)=0
Compute where .
virtual void axpy(const Real alpha, const Vector &x)
Compute where .
Definition: ROL_Vector.hpp:153
virtual Real dot(const Vector &x) const =0
Compute where .
Real value(const Vector< Real > &x, Real &tol)
Compute value.
ROL::Ptr< Vector< Real > > k_
Real dirDeriv(const Vector< Real > &x, const Vector< Real > &d, Real &tol)
Compute directional derivative.
void invHessVec(Vector< Real > &ihv, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
Apply inverse Hessian approximation to vector.
void gradient(Vector< Real > &g, const Vector< Real > &x, Real &tol)
Compute gradient.
Objective_Zakharov(const ROL::Ptr< Vector< Real > > k)
Ptr< Objective< Real > > getObjective(void) const
Ptr< Vector< Real > > getSolution(const int i=0) const
Ptr< Vector< Real > > getInitialGuess(void) const