ROL
ROL_Beale.hpp
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49#ifndef USE_HESSVEC
50#define USE_HESSVEC 1
51#endif
52
53#ifndef ROL_BEALE_HPP
54#define ROL_BEALE_HPP
55
57#include "ROL_TestProblem.hpp"
58
59namespace ROL {
60namespace ZOO {
61
64 template<class Real>
65 class Objective_Beale : public Objective<Real> {
66 private:
67 std::vector<Real> y_;
68
69 public:
71 y_.clear();
72 y_.push_back(static_cast<Real>(1.5));
73 y_.push_back(static_cast<Real>(2.25));
74 y_.push_back(static_cast<Real>(2.625));
75 }
76
77 Real value( const Vector<Real> &x, Real &tol ) {
78 Ptr<const std::vector<Real> > ex
79 = dynamic_cast<const StdVector<Real>&>(x).getVector();
80
81 Real f1 = static_cast<Real>(1.5)-(*ex)[0]*(static_cast<Real>(1)-(*ex)[1]);
82 Real f2 = static_cast<Real>(2.25)-(*ex)[0]*(static_cast<Real>(1)-pow((*ex)[1],2));
83 Real f3 = static_cast<Real>(2.625)-(*ex)[0]*(static_cast<Real>(1)-pow((*ex)[1],3));
84
85 return pow(f1,2)+pow(f2,2)+pow(f3,2);
86 }
87
88 void gradient( Vector<Real> &g, const Vector<Real> &x, Real &tol ) {
89 Ptr<std::vector<Real> > eg
90 = dynamic_cast<StdVector<Real>&>(g).getVector();
91 Ptr<const std::vector<Real> > ex
92 = dynamic_cast<const StdVector<Real>&>(x).getVector();
93
94 Real f1 = static_cast<Real>(1.5)-(*ex)[0]*(static_cast<Real>(1)-(*ex)[1]);
95 Real f2 = static_cast<Real>(2.25)-(*ex)[0]*(static_cast<Real>(1)-pow((*ex)[1],2));
96 Real f3 = static_cast<Real>(2.625)-(*ex)[0]*(static_cast<Real>(1)-pow((*ex)[1],3));
97 Real df1dx = -(static_cast<Real>(1)-(*ex)[1]);
98 Real df1dy = (*ex)[0];
99 Real df2dx = -(static_cast<Real>(1)-pow((*ex)[1],2));
100 Real df2dy = static_cast<Real>(2)*(*ex)[0]*(*ex)[1];
101 Real df3dx = -(static_cast<Real>(1)-pow((*ex)[1],3));
102 Real df3dy = static_cast<Real>(3)*(*ex)[0]*pow((*ex)[1],2);
103
104 (*eg)[0] = static_cast<Real>(2)*df1dx*f1+static_cast<Real>(2)*df2dx*f2+static_cast<Real>(2)*df3dx*f3;
105 (*eg)[1] = static_cast<Real>(2)*df1dy*f1+static_cast<Real>(2)*df2dy*f2+static_cast<Real>(2)*df3dy*f3;
106 }
107#if USE_HESSVEC
108 void hessVec( Vector<Real> &hv, const Vector<Real> &v, const Vector<Real> &x, Real &tol ) {
109 Ptr<std::vector<Real> > ehv
110 = dynamic_cast<StdVector<Real>&>(hv).getVector();
111 Ptr<const std::vector<Real> > ev
112 = dynamic_cast<const StdVector<Real>&>(v).getVector();
113 Ptr<const std::vector<Real> > ex
114 = dynamic_cast<const StdVector<Real>&>(x).getVector();
115
116 Real f1 = static_cast<Real>(1.5)-(*ex)[0]*(static_cast<Real>(1)-(*ex)[1]);
117 Real f2 = static_cast<Real>(2.25)-(*ex)[0]*(static_cast<Real>(1)-pow((*ex)[1],2));
118 Real f3 = static_cast<Real>(2.625)-(*ex)[0]*(static_cast<Real>(1)-pow((*ex)[1],3));
119 Real df1dx = -(static_cast<Real>(1)-(*ex)[1]);
120 Real df1dy = (*ex)[0];
121 Real df2dx = -(static_cast<Real>(1)-pow((*ex)[1],2));
122 Real df2dy = static_cast<Real>(2)*(*ex)[0]*(*ex)[1];
123 Real df3dx = -(static_cast<Real>(1)-pow((*ex)[1],3));
124 Real df3dy = static_cast<Real>(3)*(*ex)[0]*pow((*ex)[1],2);
125 Real d2f1dx2 = static_cast<Real>(0);
126 Real d2f1dy2 = static_cast<Real>(0);
127 Real d2f1dxdy = static_cast<Real>(1);
128 Real d2f2dx2 = static_cast<Real>(0);
129 Real d2f2dy2 = static_cast<Real>(2)*(*ex)[0];
130 Real d2f2dxdy = static_cast<Real>(2)*(*ex)[1];
131 Real d2f3dx2 = static_cast<Real>(0);
132 Real d2f3dy2 = static_cast<Real>(6)*(*ex)[0]*(*ex)[1];
133 Real d2f3dxdy = static_cast<Real>(3)*pow((*ex)[1],2);
134
135 Real H11 = static_cast<Real>(2)*(d2f1dx2*f1+df1dx*df1dx)+static_cast<Real>(2)*(d2f2dx2*f2+df2dx*df2dx)
136 +static_cast<Real>(2)*(d2f3dx2*f3+df3dx*df3dx);
137 Real H22 = static_cast<Real>(2)*(d2f1dy2*f1+df1dy*df1dy)+static_cast<Real>(2)*(d2f2dy2*f2+df2dy*df2dy)
138 +static_cast<Real>(2)*(d2f3dy2*f3+df3dy*df3dy);
139 Real H12 = static_cast<Real>(2)*(d2f1dxdy*f1 + df1dx*df1dy)+static_cast<Real>(2)*(d2f2dxdy*f2 + df2dx*df2dy)
140 +static_cast<Real>(2)*(d2f3dxdy*f3 + df3dx*df3dy);
141
142 (*ehv)[0] = H11*(*ev)[0]+H12*(*ev)[1];
143 (*ehv)[1] = H12*(*ev)[0]+H22*(*ev)[1];
144 }
145#endif
146 void invHessVec( Vector<Real> &hv, const Vector<Real> &v, const Vector<Real> &x, Real &tol ) {
147 Ptr<std::vector<Real> > ehv
148 = dynamic_cast<StdVector<Real>&>(hv).getVector();
149 Ptr<const std::vector<Real> > ev
150 = dynamic_cast<const StdVector<Real>&>(v).getVector();
151 Ptr<const std::vector<Real> > ex
152 = dynamic_cast<const StdVector<Real>&>(x).getVector();
153
154 Real f1 = static_cast<Real>(1.5)-(*ex)[0]*(static_cast<Real>(1)-(*ex)[1]);
155 Real f2 = static_cast<Real>(2.25)-(*ex)[0]*(static_cast<Real>(1)-pow((*ex)[1],2));
156 Real f3 = static_cast<Real>(2.625)-(*ex)[0]*(static_cast<Real>(1)-pow((*ex)[1],3));
157 Real df1dx = -(static_cast<Real>(1)-(*ex)[1]);
158 Real df1dy = (*ex)[0];
159 Real df2dx = -(static_cast<Real>(1)-pow((*ex)[1],2));
160 Real df2dy = static_cast<Real>(2)*(*ex)[0]*(*ex)[1];
161 Real df3dx = -(static_cast<Real>(1)-pow((*ex)[1],3));
162 Real df3dy = static_cast<Real>(3)*(*ex)[0]*pow((*ex)[1],2);
163 Real d2f1dx2 = static_cast<Real>(0);
164 Real d2f1dy2 = static_cast<Real>(0);
165 Real d2f1dxdy = static_cast<Real>(1);
166 Real d2f2dx2 = static_cast<Real>(0);
167 Real d2f2dy2 = static_cast<Real>(2)*(*ex)[0];
168 Real d2f2dxdy = static_cast<Real>(2)*(*ex)[1];
169 Real d2f3dx2 = static_cast<Real>(0);
170 Real d2f3dy2 = static_cast<Real>(6)*(*ex)[0]*(*ex)[1];
171 Real d2f3dxdy = static_cast<Real>(3)*pow((*ex)[1],2);
172
173 Real H11 = static_cast<Real>(2)*(d2f1dx2*f1+df1dx*df1dx)+static_cast<Real>(2)*(d2f2dx2*f2+df2dx*df2dx)
174 +static_cast<Real>(2)*(d2f3dx2*f3+df3dx*df3dx);
175 Real H22 = static_cast<Real>(2)*(d2f1dy2*f1+df1dy*df1dy)+static_cast<Real>(2)*(d2f2dy2*f2+df2dy*df2dy)
176 +static_cast<Real>(2)*(d2f3dy2*f3+df3dy*df3dy);
177 Real H12 = static_cast<Real>(2)*(d2f1dxdy*f1 + df1dx*df1dy)+static_cast<Real>(2)*(d2f2dxdy*f2 + df2dx*df2dy)
178 +static_cast<Real>(2)*(d2f3dxdy*f3 + df3dx*df3dy);
179
180 (*ehv)[0] = (static_cast<Real>(1)/(H11*H22-H12*H12))*( H22*(*ev)[0] - H12*(*ev)[1]);
181 (*ehv)[1] = (static_cast<Real>(1)/(H11*H22-H12*H12))*(-H12*(*ev)[0] + H11*(*ev)[1]);
182 }
183 };
184
185 template<class Real>
186 class getBeale : public TestProblem<Real> {
187 public:
188 getBeale(void) {}
189
190 Ptr<Objective<Real>> getObjective(void) const {
191 return makePtr<Objective_Beale<Real>>();
192 }
193
194 Ptr<Vector<Real>> getInitialGuess(void) const {
195 int n = 2;
196 // Build scale
197 Ptr<std::vector<Real> > scale = makePtr<std::vector<Real>>(n,static_cast<Real>(0));
198 (*scale)[0] = static_cast<Real>(1.e-1);
199 (*scale)[1] = static_cast<Real>(1.e1);
200
201 // Get Initial Guess
202 Ptr<std::vector<Real> > x0p = makePtr<std::vector<Real>>(n,static_cast<Real>(0));
203 (*x0p)[0] = static_cast<Real>(1);
204 (*x0p)[1] = static_cast<Real>(1);
205
206 return makePtr<PrimalScaledStdVector<Real>>(x0p,scale);
207 }
208
209 Ptr<Vector<Real>> getSolution(const int i = 0) const {
210 int n = 2;
211 // Build scale
212 Ptr<std::vector<Real> > scale = makePtr<std::vector<Real>>(n,static_cast<Real>(0));
213 (*scale)[0] = static_cast<Real>(1.e-1);
214 (*scale)[1] = static_cast<Real>(1.e1);
215
216 // Get Solution
217 Ptr<std::vector<Real> > xp = makePtr<std::vector<Real>>(n,static_cast<Real>(0));
218 (*xp)[0] = static_cast<Real>(3);
219 (*xp)[1] = static_cast<Real>(0.5);
220
221 return makePtr<PrimalScaledStdVector<Real>>(xp,scale);
222 }
223 };
224
225}// End ZOO Namespace
226}// End ROL Namespace
227
228#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.
Provides the ROL::Vector interface for scalar values, to be used, for example, with scalar constraint...
Defines the linear algebra or vector space interface.
Definition: ROL_Vector.hpp:84
Beale's function.
Definition: ROL_Beale.hpp:65
void gradient(Vector< Real > &g, const Vector< Real > &x, Real &tol)
Compute gradient.
Definition: ROL_Beale.hpp:88
void invHessVec(Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
Apply inverse Hessian approximation to vector.
Definition: ROL_Beale.hpp:146
Real value(const Vector< Real > &x, Real &tol)
Compute value.
Definition: ROL_Beale.hpp:77
std::vector< Real > y_
Definition: ROL_Beale.hpp:67
Ptr< Vector< Real > > getSolution(const int i=0) const
Definition: ROL_Beale.hpp:209
Ptr< Vector< Real > > getInitialGuess(void) const
Definition: ROL_Beale.hpp:194
Ptr< Objective< Real > > getObjective(void) const
Definition: ROL_Beale.hpp:190