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muSpectre/src/solver/solver_cg.cc
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solver_cg.cc
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/**
* file solver_cg.cc
*
* @author Till Junge <till.junge@epfl.ch>
*
* @date 20 Dec 2017
*
* @brief Implementation of cg solver
*
* @section LICENCE
*
* Copyright (C) 2017 Till Junge
*
* µSpectre is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License as
* published by the Free Software Foundation, either version 3, or (at
* your option) any later version.
*
* µSpectre is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with GNU Emacs; see the file COPYING. If not, write to the
* Free Software Foundation, Inc., 59 Temple Place - Suite 330,
* Boston, MA 02111-1307, USA.
*/
#include "solver_cg.hh"
namespace muSpectre {
/* ---------------------------------------------------------------------- */
template <Dim_t DimS, Dim_t DimM>
SolverCG<DimS, DimM>::SolverCG(Ccoord resolutions, Real tol, Uint maxiter,
bool verbose)
:Parent(resolutions),
r_k{make_field<Field_t>("residual r_k", this->collection)},
p_k{make_field<Field_t>("search direction r_k", this->collection)},
Ap_k{make_field<Field_t>("Effect of tangent A*p_k", this->collection)},
tol{tol}, maxiter{maxiter}, verbose{verbose}
{}
/* ---------------------------------------------------------------------- */
template <Dim_t DimS, Dim_t DimM>
void SolverCG<DimS, DimM>::solve(Fun_t& tangent_effect, const Field_t & rhs,
Field_t & x_f) {
// Following implementation of algorithm 5.2 in Nocedal's Numerical Optimization (p. 112)
auto r = this->r_k.eigen();
auto p = this->p_k.eigen();
auto Ap = this->Ap_k.eigen();
auto x = x_f.eigen();
// initialisation of algo
tangent_effect(this->r_k, x_f);
r = rhs.eigen();
p = -r;
this->converged = false;
Real rdr = (r*r).sum();
for (Uint i = 0; i < this->maxiter && rdr > this->tol; ++i) {
tangent_effect(this->Ap_k, this->p_k);
Real alpha = rdr/(r*Ap).sum();
x += alpha * p;
r += alpha * Ap;
Real new_rdr = (r*r).sum();
Real beta = new_rdr/rdr;
rdr = new_rdr;
if (this->verbose) {
std::cout << "at CG step " << i << ": |r| = " << std::sqrt(rdr)
<< ", cg_tol = " << this->tol << std::endl;
}
p = -r+beta*p;
}
if (rdr < this->tol) {
this->converged=true;
}
}
template class SolverCG<twoD, twoD>;
template class SolverCG<twoD, threeD>;
template class SolverCG<threeD, threeD>;
} // muSpectre
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