/usr/include/trilinos/ROL_GMRES.hpp is in libtrilinos-rol-dev 12.10.1-3.
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// ************************************************************************
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// Rapid Optimization Library (ROL) Package
// Copyright (2014) Sandia Corporation
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// @HEADER
#ifndef ROL_GMRES_H
#define ROL_GMRES_H
/** \class ROL::GMRES
\brief Preconditioned GMRES solver.
*/
#include "ROL_Krylov.hpp"
#include "ROL_LinearOperator.hpp"
#include "ROL_Vector.hpp"
#include "ROL_Types.hpp"
#include "Teuchos_SerialDenseMatrix.hpp"
#include "Teuchos_SerialDenseVector.hpp"
#include "Teuchos_LAPACK.hpp"
namespace ROL {
template<class Real>
class GMRES : public Krylov<Real> {
typedef Teuchos::SerialDenseMatrix<int, Real> SDMatrix;
typedef Teuchos::SerialDenseVector<int, Real> SDVector;
private:
Teuchos::RCP<Vector<Real> > r_;
Teuchos::RCP<Vector<Real> > z_;
Teuchos::RCP<Vector<Real> > w_;
Teuchos::RCP<SDMatrix> H_; // quasi-Hessenberg matrix
Teuchos::RCP<SDVector> cs_; // Givens Rotations cosine components
Teuchos::RCP<SDVector> sn_; // Givens Rotations sine components
Teuchos::RCP<SDVector> s_;
Teuchos::RCP<SDVector> y_;
Teuchos::RCP<SDVector> cnorm_;
Teuchos::RCP<std::vector<Real> > res_;
bool isInitialized_;
bool useInexact_;
bool useInitialGuess_; // If false, inital x will be ignored and zero vec used
int maxit_;
Real absTol_;
Real relTol_;
Teuchos::LAPACK<int,Real> lapack_;
public:
GMRES( Teuchos::ParameterList &parlist ) : isInitialized_(false) {
using Teuchos::RCP;
using Teuchos::rcp;
using std::vector;
Real zero(0), oem2(1.e-2), oem4(1.e-4);
Teuchos::ParameterList &gList = parlist.sublist("General");
Teuchos::ParameterList &kList = gList.sublist("Krylov");
useInexact_ = gList.get("Inexact Hessian-Times-A-Vector",false);
maxit_ = kList.get("Iteration Limit",50);
absTol_ = kList.get("Absolute Tolerance", oem4);
relTol_ = kList.get("Relative Tolerance", oem2);
useInitialGuess_ = kList.get("Use Initial Guess",false);
H_ = rcp( new SDMatrix( maxit_+1, maxit_ ) );
cs_ = rcp( new SDVector( maxit_ ) );
sn_ = rcp( new SDVector( maxit_ ) );
s_ = rcp( new SDVector( maxit_+1 ) );
y_ = rcp( new SDVector( maxit_+1 ) );
cnorm_ = rcp( new SDVector( maxit_ ) );
res_ = rcp( new std::vector<Real>(maxit_+1,zero) );
}
void run( Vector<Real> &x, LinearOperator<Real> &A, const Vector<Real> &b,
LinearOperator<Real> &M, int &iter, int &flag ) {
using Teuchos::RCP;
flag = 0;
Real zero(0), one(1);
if ( !isInitialized_ ) {
r_ = b.clone();
w_ = b.clone();
z_ = x.clone();
isInitialized_ = true;
}
Real itol = std::sqrt(ROL_EPSILON<Real>());
// Compute initial residual
if(useInitialGuess_) {
A.apply(*r_,x,itol);
r_->scale(-one);
r_->plus(b); // r = b-Ax
}
else {
x.zero();
r_->set(b);
}
Real temp = 0;
std::vector<RCP<Vector<Real > > > V;
std::vector<RCP<Vector<Real > > > Z;
(*res_)[0] = r_->norm();
Real rtol = std::min(absTol_,relTol_*(*res_)[0]);
V.push_back(b.clone());
(V[0])->set(*r_);
(V[0])->scale(one/(*res_)[0]);
(*s_)(0) = (*res_)[0];
for( iter=0; iter<maxit_; ++iter ) {
// std::cout << (*res_)[iter] << std::endl;
if( useInexact_ ) {
itol = rtol/(maxit_*(*res_)[iter]);
}
Z.push_back(x.clone());
// Apply right preconditioner
M.applyInverse(*(Z[iter]),*(V[iter]),itol);
// Apply operator
A.apply(*w_,*(Z[iter]),itol);
// Evaluate coefficients and orthogonalize using Gram-Schmidt
for( int k=0; k<=iter; ++k ) {
(*H_)(k,iter) = w_->dot(*(V[k]));
w_->axpy( -(*H_)(k,iter), *(V[k]) );
}
(*H_)(iter+1,iter) = w_->norm();
V.push_back( b.clone() );
(V[iter+1])->set(*w_);
(V[iter+1])->scale(one/((*H_)(iter+1,iter)));
// Apply Givens rotations
for( int k=0; k<=iter-1; ++k ) {
temp = (*cs_)(k)*(*H_)(k,iter) + (*sn_)(k)*(*H_)(k+1,iter);
(*H_)(k+1,iter) = -(*sn_)(k)*(*H_)(k,iter) + (*cs_)(k)*(*H_)(k+1,iter);
(*H_)(k,iter) = temp;
}
// Form i-th rotation matrix
if( (*H_)(iter+1,iter) == zero ) {
(*cs_)(iter) = one;
(*sn_)(iter) = zero;
}
else if ( std::abs((*H_)(iter+1,iter)) > std::abs((*H_)(iter,iter)) ) {
temp = (*H_)(iter,iter) / (*H_)(iter+1,iter);
(*sn_)(iter) = one / std::sqrt( one + temp*temp );
(*cs_)(iter) = temp*(*sn_)(iter);
}
else {
temp = (*H_)(iter+1,iter) / (*H_)(iter,iter);
(*cs_)(iter) = one / std::sqrt( one + temp*temp );
(*sn_)(iter) = temp*(*cs_)(iter);
}
// Approximate residual norm
temp = (*cs_)(iter)*(*s_)(iter);
(*s_)(iter+1) = -(*sn_)(iter)*(*s_)(iter);
(*s_)(iter) = temp;
(*H_)(iter,iter) = (*cs_)(iter)*(*H_)(iter,iter) + (*sn_)(iter)*(*H_)(iter+1,iter);
(*H_)(iter+1,iter) = zero;
(*res_)[iter+1] = std::abs((*s_)(iter+1));
// Update solution approximation.
const char uplo = 'U';
const char trans = 'N';
const char diag = 'N';
const char normin = 'N';
Real scaling = zero;
int info = 0;
*y_ = *s_;
lapack_.LATRS(uplo, trans, diag, normin, iter+1, H_->values(), maxit_+1, y_->values(), &scaling, cnorm_->values(), &info);
z_->zero();
for( int k=0; k<=iter;++k ) {
z_->axpy((*y_)(k),*(Z[k]));
}
if( (*res_)[iter+1] <= rtol ) {
// Update solution vector
x.plus(*z_);
break;
}
if(iter == maxit_) {
flag = 1;
}
} // loop over iter
}
}; // class GMRES
} // namespace ROL
#endif // ROL_GMRES_H
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