ROL
ROL_LeastSquares.hpp
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43 
49 #ifndef USE_HESSVEC
50 #define USE_HESSVEC 1
51 #endif
52 
53 #ifndef ROL_LEASTSQUARES_HPP
54 #define ROL_LEASTSQUARES_HPP
55 
56 #include "ROL_StdVector.hpp"
57 #include "ROL_Objective.hpp"
58 
59 namespace ROL {
60 namespace ZOO {
61 
64 template<class Real>
65 class Objective_LeastSquares : public Objective<Real> {
66  typedef typename std::vector<Real>::size_type uint;
67 
68 public:
69 
70  Real value( const Vector<Real> &x, Real &tol ) {
71  Teuchos::RCP<const std::vector<Real> > ex
72  = Teuchos::dyn_cast<const StdVector<Real> >(x).getVector();
73 
74  uint n = ex->size();
75  Real h = 1.0/((Real)n+1.0);
76  Real val = 0.0;
77  Real res = 0.0;
78  for (uint i=0; i<n; i++) {
79  if ( i == 0 ) {
80  res = 2.0*h*(5.0/6.0) + 1.0/h*((*ex)[i+1]-2.0*(*ex)[i]);
81  }
82  else if ( i == n-1 ) {
83  res = 2.0*h*(5.0/6.0) + 1.0/h*((*ex)[i-1]-2.0*(*ex)[i]);
84  }
85  else {
86  res = 2.0*h + 1.0/h*((*ex)[i-1]-2.0*(*ex)[i]+(*ex)[i+1]);
87  }
88  val += 0.5*res*res;
89  }
90  return val;
91  }
92 
93  void gradient( Vector<Real> &g, const Vector<Real> &x, Real &tol ) {
94  Teuchos::RCP<std::vector<Real> > eg
95  = Teuchos::dyn_cast<StdVector<Real> >(g).getVector();
96  Teuchos::RCP<const std::vector<Real> > ex
97  = Teuchos::dyn_cast<const StdVector<Real> >(x).getVector();
98 
99  uint n = ex->size();
100  Real h = 1.0/((Real)n+1.0);
101  std::vector<Real> res(n,0.0);
102  for (uint i=0; i<n; i++) {
103  if ( i == 0 ) {
104  res[i] = 2.0*h*(5.0/6.0) + 1.0/h*((*ex)[i+1]-2.0*(*ex)[i]);
105  }
106  else if ( i == n-1 ) {
107  res[i] = 2.0*h*(5.0/6.0) + 1.0/h*((*ex)[i-1]-2.0*(*ex)[i]);
108  }
109  else {
110  res[i] = 2.0*h + 1.0/h*((*ex)[i-1]-2.0*(*ex)[i]+(*ex)[i+1]);
111  }
112  }
113 
114  for (uint i=0; i<n; i++) {
115  if ( i == 0 ) {
116  (*eg)[i] = 1.0/h*(res[i+1]-2.0*res[i]);
117  }
118  else if ( i == n-1 ) {
119  (*eg)[i] = 1.0/h*(res[i-1]-2.0*res[i]);
120  }
121  else {
122  (*eg)[i] = 1.0/h*(res[i-1]-2.0*res[i]+res[i+1]);
123  }
124  }
125  }
126 #if USE_HESSVEC
127  void hessVec( Vector<Real> &hv, const Vector<Real> &v, const Vector<Real> &x, Real &tol ) {
128  Teuchos::RCP<std::vector<Real> > ehv
129  = Teuchos::dyn_cast<StdVector<Real> >(hv).getVector();
130  Teuchos::RCP<const std::vector<Real> > ev
131  = Teuchos::dyn_cast<const StdVector<Real> >(v).getVector();
132  Teuchos::RCP<const std::vector<Real> > ex
133  = Teuchos::dyn_cast<const StdVector<Real> >(x).getVector();
134 
135  uint n = ex->size();
136  Real h = 1.0/((Real)n+1.0);
137  std::vector<Real> res(n,0.0);
138  for (uint i=0; i<n; i++) {
139  if ( i == 0 ) {
140  res[i] = 1.0/h*((*ev)[i+1]-2.0*(*ev)[i]);
141  }
142  else if ( i == n-1 ) {
143  res[i] = 1.0/h*((*ev)[i-1]-2.0*(*ev)[i]);
144  }
145  else {
146  res[i] = 1.0/h*((*ev)[i-1]-2.0*(*ev)[i]+(*ev)[i+1]);
147  }
148  }
149 
150  for (uint i=0; i<n; i++) {
151  if ( i == 0 ) {
152  (*ehv)[i] = 1.0/h*(res[i+1]-2.0*res[i]);
153  }
154  else if ( i == n-1 ) {
155  (*ehv)[i] = 1.0/h*(res[i-1]-2.0*res[i]);
156  }
157  else {
158  (*ehv)[i] = 1.0/h*(res[i-1]-2.0*res[i]+res[i+1]);
159  }
160  }
161  }
162 #endif
163 };
164 
165 template<class Real>
166 void getLeastSquares( Teuchos::RCP<Objective<Real> > &obj,
167  Teuchos::RCP<Vector<Real> > &x0,
168  Teuchos::RCP<Vector<Real> > &x ) {
169  // Problem dimension
170  int n = 32;
171 
172  // Get Initial Guess
173  Teuchos::RCP<std::vector<Real> > x0p = Teuchos::rcp(new std::vector<Real>(n,0.0));
174  for ( int i = 0; i < n; i++ ) {
175  (*x0p)[i] = 0.0;
176  }
177  x0 = Teuchos::rcp(new StdVector<Real>(x0p));
178 
179  // Get Solution
180  Teuchos::RCP<std::vector<Real> > xp = Teuchos::rcp(new std::vector<Real>(n,0.0));
181  Real h = 1.0/((Real)n+1.0), pt = 0.0;
182  for( int i = 0; i < n; i++ ) {
183  pt = (Real)(i+1)*h;
184  (*xp)[i] = pt*(1.0-pt);
185  }
186  x = Teuchos::rcp(new StdVector<Real>(xp));
187 
188  // Instantiate Objective Function
189  obj = Teuchos::rcp(new Objective_LeastSquares<Real>);
190 }
191 
192 } // End ZOO Namespace
193 } // End ROL Namespace
194 
195 #endif
Provides the interface to evaluate objective functions.
std::vector< Real >::size_type uint
virtual void hessVec(Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
Apply Hessian approximation to vector.
void gradient(Vector< Real > &g, const Vector< Real > &x, Real &tol)
Compute gradient.
Defines the linear algebra or vector space interface.
Definition: ROL_Vector.hpp:74
Real value(const Vector< Real > &x, Real &tol)
Compute value.
void getLeastSquares(Teuchos::RCP< Objective< Real > > &obj, Teuchos::RCP< Vector< Real > > &x0, Teuchos::RCP< Vector< Real > > &x)