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  public:
67  Real value( const Vector<Real> &x, Real &tol ) {
68  StdVector<Real> & ex =
69  Teuchos::dyn_cast<StdVector<Real> >(const_cast <Vector<Real> &>(x));
70  Teuchos::RCP<const std::vector<Real> > xp = ex.getVector();
71 
72  int n = xp->size();
73  Real h = 1.0/((Real)n+1.0);
74  Real val = 0.0;
75  Real res = 0.0;
76  for (int i=0; i<n; i++) {
77  if ( i == 0 ) {
78  res = 2.0*h*(5.0/6.0) + 1.0/h*((*xp)[i+1]-2.0*(*xp)[i]);
79  }
80  else if ( i == n-1 ) {
81  res = 2.0*h*(5.0/6.0) + 1.0/h*((*xp)[i-1]-2.0*(*xp)[i]);
82  }
83  else {
84  res = 2.0*h + 1.0/h*((*xp)[i-1]-2.0*(*xp)[i]+(*xp)[i+1]);
85  }
86  val += 0.5*res*res;
87  }
88 
89  return val;
90  }
91 
92  void gradient( Vector<Real> &g, const Vector<Real> &x, Real &tol ) {
93  Teuchos::RCP<const std::vector<Real> > xp =
94  (Teuchos::dyn_cast<StdVector<Real> >(const_cast<Vector<Real> &>(x))).getVector();
95  Teuchos::RCP<std::vector<Real> > gp =
96  Teuchos::rcp_const_cast<std::vector<Real> >((Teuchos::dyn_cast<StdVector<Real> >(g)).getVector());
97 
98  int n = xp->size();
99  Real h = 1.0/((Real)n+1.0);
100  std::vector<Real> res(n,0.0);
101  for (int i=0; i<n; i++) {
102  if ( i == 0 ) {
103  res[i] = 2.0*h*(5.0/6.0) + 1.0/h*((*xp)[i+1]-2.0*(*xp)[i]);
104  }
105  else if ( i == n-1 ) {
106  res[i] = 2.0*h*(5.0/6.0) + 1.0/h*((*xp)[i-1]-2.0*(*xp)[i]);
107  }
108  else {
109  res[i] = 2.0*h + 1.0/h*((*xp)[i-1]-2.0*(*xp)[i]+(*xp)[i+1]);
110  }
111  }
112 
113  for (int i=0; i<n; i++) {
114  if ( i == 0 ) {
115  (*gp)[i] = 1.0/h*(res[i+1]-2.0*res[i]);
116  }
117  else if ( i == n-1 ) {
118  (*gp)[i] = 1.0/h*(res[i-1]-2.0*res[i]);
119  }
120  else {
121  (*gp)[i] = 1.0/h*(res[i-1]-2.0*res[i]+res[i+1]);
122  }
123  }
124  }
125 #if USE_HESSVEC
126  void hessVec( Vector<Real> &hv, const Vector<Real> &v, const Vector<Real> &x, Real &tol ) {
127  Teuchos::RCP<const std::vector<Real> > xp =
128  (Teuchos::dyn_cast<StdVector<Real> >(const_cast<Vector<Real> &>(x))).getVector();
129  Teuchos::RCP<const std::vector<Real> > vp =
130  (Teuchos::dyn_cast<StdVector<Real> >(const_cast<Vector<Real> &>(v))).getVector();
131  Teuchos::RCP<std::vector<Real> > hvp =
132  Teuchos::rcp_const_cast<std::vector<Real> >((Teuchos::dyn_cast<StdVector<Real> >(hv)).getVector());
133 
134  int n = xp->size();
135  Real h = 1.0/((Real)n+1.0);
136  std::vector<Real> res(n,0.0);
137  for (int i=0; i<n; i++) {
138  if ( i == 0 ) {
139  res[i] = 1.0/h*((*vp)[i+1]-2.0*(*vp)[i]);
140  }
141  else if ( i == n-1 ) {
142  res[i] = 1.0/h*((*vp)[i-1]-2.0*(*vp)[i]);
143  }
144  else {
145  res[i] = 1.0/h*((*vp)[i-1]-2.0*(*vp)[i]+(*vp)[i+1]);
146  }
147  }
148 
149  for (int i=0; i<n; i++) {
150  if ( i == 0 ) {
151  (*hvp)[i] = 1.0/h*(res[i+1]-2.0*res[i]);
152  }
153  else if ( i == n-1 ) {
154  (*hvp)[i] = 1.0/h*(res[i-1]-2.0*res[i]);
155  }
156  else {
157  (*hvp)[i] = 1.0/h*(res[i-1]-2.0*res[i]+res[i+1]);
158  }
159  }
160  }
161 #endif
162  };
163 
164  template<class Real>
165  void getLeastSquares( Teuchos::RCP<Objective<Real> > &obj, Vector<Real> &x0, Vector<Real> &x ) {
166  // Cast Initial Guess and Solution Vectors
167  Teuchos::RCP<std::vector<Real> > x0p =
168  Teuchos::rcp_const_cast<std::vector<Real> >((Teuchos::dyn_cast<StdVector<Real> >(x0)).getVector());
169  Teuchos::RCP<std::vector<Real> > xp =
170  Teuchos::rcp_const_cast<std::vector<Real> >((Teuchos::dyn_cast<StdVector<Real> >(x)).getVector());
171  int n = xp->size();
172  // Resize Vectors
173  n = 32;
174  x0p->resize(n);
175  xp->resize(n);
176  // Instantiate Objective Function
177  obj = Teuchos::rcp( new Objective_LeastSquares<Real> );
178  // Get Initial Guess
179  for (int i=0; i<n; i++) {
180  (*x0p)[i] = 0.0;
181  }
182  // Get Solution
183  Real h = 1.0/((Real)n+1.0);
184  Real pt = 0.0;
185  for( int i=0; i<n; i++ ) {
186  pt = (Real)(i+1)*h;
187  (*xp)[i] = pt*(1.0-pt);
188  }
189  }
190 
191 } // End ZOO Namespace
192 } // End ROL Namespace
193 
194 #endif
Provides the interface to evaluate objective functions.
Teuchos::RCP< const std::vector< Element > > getVector() const
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:72
Real value(const Vector< Real > &x, Real &tol)
Compute value.
Provides the std::vector implementation of the ROL::Vector interface.
void getLeastSquares(Teuchos::RCP< Objective< Real > > &obj, Vector< Real > &x0, Vector< Real > &x)