ROL
ROL_GMRES.hpp
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43
44#ifndef ROL_GMRES_H
45#define ROL_GMRES_H
46
51#include "ROL_Krylov.hpp"
52#include "ROL_Types.hpp"
53#include "ROL_LAPACK.hpp"
54#include "ROL_LinearAlgebra.hpp"
55
56
57namespace ROL {
58
59template<class Real>
60class GMRES : public Krylov<Real> {
61
62 typedef LA::Matrix<Real> SDMatrix;
63 typedef LA::Vector<Real> SDVector;
64
65private:
66
67 ROL::Ptr<Vector<Real> > r_;
68 ROL::Ptr<Vector<Real> > z_;
69 ROL::Ptr<Vector<Real> > w_;
70
71 ROL::Ptr<SDMatrix> H_; // quasi-Hessenberg matrix
72 ROL::Ptr<SDVector> cs_; // Givens Rotations cosine components
73 ROL::Ptr<SDVector> sn_; // Givens Rotations sine components
74 ROL::Ptr<SDVector> s_;
75 ROL::Ptr<SDVector> y_;
76 ROL::Ptr<SDVector> cnorm_;
77
78 ROL::Ptr<std::vector<Real> > res_;
79
82 bool useInitialGuess_; // If false, inital x will be ignored and zero vec used
84 ROL::Ptr<std::ostream> outStream_;
85
86 ROL::LAPACK<int,Real> lapack_;
87
88public:
89
90 GMRES( ROL::ParameterList &parlist ) : Krylov<Real>(parlist), isInitialized_(false), printIters_(false) {
91
92 using std::vector;
93
94 Real zero(0);
95
96 ROL::ParameterList &gList = parlist.sublist("General");
97 ROL::ParameterList &kList = gList.sublist("Krylov");
98
99 useInexact_ = gList.get("Inexact Hessian-Times-A-Vector",false);
100 useInitialGuess_ = kList.get("Use Initial Guess",false);
102
103 H_ = ROL::makePtr<SDMatrix>( maxit+1, maxit );
104 cs_ = ROL::makePtr<SDVector>( maxit );
105 sn_ = ROL::makePtr<SDVector>( maxit );
106 s_ = ROL::makePtr<SDVector>( maxit+1 );
107 y_ = ROL::makePtr<SDVector>( maxit+1 );
108 cnorm_ = ROL::makePtr<SDVector>( maxit );
109 res_ = ROL::makePtr<std::vector<Real>>(maxit+1,zero);
110
111 }
112
114 LinearOperator<Real> &M, int &iter, int &flag ) {
115
119
120 flag = 0;
121
122 Real zero(0), one(1);
123
124 if ( !isInitialized_ ) {
125 r_ = b.clone();
126 w_ = b.clone();
127 z_ = x.clone();
128
129 isInitialized_ = true;
130 }
131
132 Real itol = std::sqrt(ROL_EPSILON<Real>());
133
134 // Compute initial residual
135 if(useInitialGuess_) {
136
137 A.apply(*r_,x,itol);
138 r_->scale(-one);
139 r_->plus(b); // r = b-Ax
140
141 }
142 else {
143 x.zero();
144 r_->set(b);
145 }
146
147 Real temp = 0;
148
149 std::vector<ROL::Ptr<Vector<Real > > > V;
150 std::vector<ROL::Ptr<Vector<Real > > > Z;
151
152 (*res_)[0] = r_->norm();
153
154 if (printIters_) {
155 *outStream_ << "GMRES Iteration " << 0 << ", Residual = " << (*res_)[0] << "\n";
156 }
157
158 // This should be a tolerance check
159 Real rtol = std::min(absTol,relTol*(*res_)[0]);
160 if ((*res_)[0] <= rtol) {
161 iter = 0;
162 flag = 0;
163 return (*res_)[0];
164 }
165
166 V.push_back(b.clone());
167 (V[0])->set(*r_);
168 (V[0])->scale(one/(*res_)[0]);
169
170 (*s_)(0) = (*res_)[0];
171
172 for( iter=0; iter<maxit; ++iter ) {
173
174 if( useInexact_ ) {
175 itol = rtol/(maxit*(*res_)[iter]);
176 }
177
178 Z.push_back(x.clone());
179
180 // Apply right preconditioner
181 M.applyInverse(*(Z[iter]),*(V[iter]),itol);
182
183 // Apply operator
184 A.apply(*w_,*(Z[iter]),itol);
185
186 // Evaluate coefficients and orthogonalize using Gram-Schmidt
187 for( int k=0; k<=iter; ++k ) {
188 (*H_)(k,iter) = w_->dot(*(V[k]));
189 w_->axpy( -(*H_)(k,iter), *(V[k]) );
190 }
191
192 (*H_)(iter+1,iter) = w_->norm();
193
194 V.push_back( b.clone() );
195 (V[iter+1])->set(*w_);
196 (V[iter+1])->scale(one/((*H_)(iter+1,iter)));
197
198 // Apply Givens rotations
199 for( int k=0; k<=iter-1; ++k ) {
200 temp = (*cs_)(k)*(*H_)(k,iter) + (*sn_)(k)*(*H_)(k+1,iter);
201 (*H_)(k+1,iter) = -(*sn_)(k)*(*H_)(k,iter) + (*cs_)(k)*(*H_)(k+1,iter);
202 (*H_)(k,iter) = temp;
203 }
204
205 // Form i-th rotation matrix
206 if( (*H_)(iter+1,iter) == zero ) {
207 (*cs_)(iter) = one;
208 (*sn_)(iter) = zero;
209 }
210 else if ( std::abs((*H_)(iter+1,iter)) > std::abs((*H_)(iter,iter)) ) {
211 temp = (*H_)(iter,iter) / (*H_)(iter+1,iter);
212 (*sn_)(iter) = one / std::sqrt( one + temp*temp );
213 (*cs_)(iter) = temp*(*sn_)(iter);
214 }
215 else {
216 temp = (*H_)(iter+1,iter) / (*H_)(iter,iter);
217 (*cs_)(iter) = one / std::sqrt( one + temp*temp );
218 (*sn_)(iter) = temp*(*cs_)(iter);
219 }
220
221 // Approximate residual norm
222 temp = (*cs_)(iter)*(*s_)(iter);
223 (*s_)(iter+1) = -(*sn_)(iter)*(*s_)(iter);
224 (*s_)(iter) = temp;
225 (*H_)(iter,iter) = (*cs_)(iter)*(*H_)(iter,iter) + (*sn_)(iter)*(*H_)(iter+1,iter);
226 (*H_)(iter+1,iter) = zero;
227 (*res_)[iter+1] = std::abs((*s_)(iter+1));
228
229 if (printIters_) {
230 *outStream_ << "GMRES Iteration " << iter+1 << ", Residual = " << (*res_)[iter+1] << "\n";
231 }
232
233 // Update solution approximation.
234 const char uplo = 'U';
235 const char trans = 'N';
236 const char diag = 'N';
237 const char normin = 'N';
238 Real scaling = zero;
239 int info = 0;
240 *y_ = *s_;
241 lapack_.LATRS(uplo, trans, diag, normin, iter+1, H_->values(), maxit+1, y_->values(), &scaling, cnorm_->values(), &info);
242
243 z_->zero();
244
245 for( int k=0; k<=iter;++k ) {
246 z_->axpy((*y_)(k),*(Z[k]));
247 }
248
249 if( (*res_)[iter+1] <= rtol ) {
250 // Update solution vector
251 x.plus(*z_);
252 break;
253 }
254
255 } // loop over iter
256
257 if(iter == maxit) {
258 flag = 1;
259 x.plus(*z_);
260 return (*res_)[iter];
261 }
262
263 return (*res_)[iter+1];
264 }
265
266 void enableOutput(std::ostream & outStream) {
267 printIters_ = true;
268 outStream_ = ROL::makePtrFromRef(outStream);;
269 }
270
271 void disableOutput() {printIters_ = false;}
272
273}; // class GMRES
274
275} // namespace ROL
276
277#endif // ROL_GMRES_H
278
Vector< Real > V
Objective_SerialSimOpt(const Ptr< Obj > &obj, const V &ui) z0 zero)()
Contains definitions of custom data types in ROL.
Preconditioned GMRES solver.
Definition ROL_GMRES.hpp:60
LA::Vector< Real > SDVector
Definition ROL_GMRES.hpp:63
ROL::LAPACK< int, Real > lapack_
Definition ROL_GMRES.hpp:86
ROL::Ptr< Vector< Real > > r_
Definition ROL_GMRES.hpp:67
ROL::Ptr< std::ostream > outStream_
Definition ROL_GMRES.hpp:84
ROL::Ptr< SDVector > cnorm_
Definition ROL_GMRES.hpp:76
ROL::Ptr< Vector< Real > > w_
Definition ROL_GMRES.hpp:69
ROL::Ptr< SDVector > sn_
Definition ROL_GMRES.hpp:73
ROL::Ptr< SDMatrix > H_
Definition ROL_GMRES.hpp:71
void enableOutput(std::ostream &outStream)
ROL::Ptr< SDVector > cs_
Definition ROL_GMRES.hpp:72
ROL::Ptr< SDVector > y_
Definition ROL_GMRES.hpp:75
bool useInitialGuess_
Definition ROL_GMRES.hpp:82
bool useInexact_
Definition ROL_GMRES.hpp:81
void disableOutput()
ROL::Ptr< std::vector< Real > > res_
Definition ROL_GMRES.hpp:78
LA::Matrix< Real > SDMatrix
Definition ROL_GMRES.hpp:62
ROL::Ptr< SDVector > s_
Definition ROL_GMRES.hpp:74
bool isInitialized_
Definition ROL_GMRES.hpp:80
GMRES(ROL::ParameterList &parlist)
Definition ROL_GMRES.hpp:90
Real run(Vector< Real > &x, LinearOperator< Real > &A, const Vector< Real > &b, LinearOperator< Real > &M, int &iter, int &flag)
bool printIters_
Definition ROL_GMRES.hpp:83
ROL::Ptr< Vector< Real > > z_
Definition ROL_GMRES.hpp:68
Provides definitions for Krylov solvers.
unsigned getMaximumIteration(void) const
Real getAbsoluteTolerance(void) const
Real getRelativeTolerance(void) const
Provides the interface to apply a linear operator.
virtual void apply(Vector< Real > &Hv, const Vector< Real > &v, Real &tol) const =0
Apply linear operator.
virtual void applyInverse(Vector< Real > &Hv, const Vector< Real > &v, Real &tol) const
Apply inverse of linear operator.
Defines the linear algebra or vector space interface.
virtual void plus(const Vector &x)=0
Compute , where .
virtual void zero()
Set to zero vector.
virtual ROL::Ptr< Vector > clone() const =0
Clone to make a new (uninitialized) vector.