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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
*
* Copyright © 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/solver_cg.hh"
#include "solver/solver_error.hh"
#include <iomanip>
#include <cmath>
#include <sstream>
namespace muSpectre {
/* ---------------------------------------------------------------------- */
template <Dim_t DimS, Dim_t DimM>
SolverCG<DimS, DimM>::SolverCG(Sys_t& sys, Real tol, Uint maxiter,
bool verbose)
:Parent(sys, tol, maxiter, verbose),
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)}
{}
/* ---------------------------------------------------------------------- */
template <Dim_t DimS, Dim_t DimM>
void SolverCG<DimS, DimM>::solve(const Field_t & rhs,
Field_t & x_f) {
x_f.eigenvec() = this-> solve(rhs.eigenvec(), x_f.eigenvec());
};
//----------------------------------------------------------------------------//
template <Dim_t DimS, Dim_t DimM>
typename SolverCG<DimS, DimM>::SolvVectorOut
SolverCG<DimS, DimM>::solve(const SolvVectorInC rhs, SolvVectorIn x_0) {
// 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 = typename Field_t::EigenMap(x_0.data(), r.rows(), r.cols());
// initialisation of algo
r = this->sys.directional_stiffness_with_copy(x);
r -= typename Field_t::ConstEigenMap(rhs.data(), r.rows(), r.cols());
p = -r;
this->converged = false;
Real rdr = (r*r).sum();
Real rhs_norm2 = rhs.squaredNorm();
Real tol2 = ipow(this->tol,2)*rhs_norm2;
size_t count_width{}; // for output formatting in verbose case
if (this->verbose) {
count_width = size_t(std::log10(this->maxiter))+1;
}
for (Uint i = 0;
i < this->maxiter && (rdr > tol2 || i == 0);
++i, ++this->counter) {
Ap = this->sys.directional_stiffness_with_copy(p);
Real alpha = rdr/(p*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 " << std::setw(count_width) << i
<< ": |r|/|b| = " << std::setw(15) << std::sqrt(rdr/rhs_norm2)
<< ", cg_tol = " << this->tol << std::endl;
}
p = -r+beta*p;
}
if (rdr < tol2) {
this->converged=true;
} else {
std::stringstream err {};
err << " After " << this->counter << " steps, the solver "
<< " FAILED with |r|/|b| = "
<< std::setw(15) << std::sqrt(rdr/rhs_norm2)
<< ", cg_tol = " << this->tol << std::endl;
throw ConvergenceError("Conjugate gradient has not converged." + err.str());
}
return x_0;
}
/* ---------------------------------------------------------------------- */
template <Dim_t DimS, Dim_t DimM>
typename SolverCG<DimS, DimM>::Tg_req_t
SolverCG<DimS, DimM>::get_tangent_req() const {
return tangent_requirement;
}
template class SolverCG<twoD, twoD>;
//template class SolverCG<twoD, threeD>;
template class SolverCG<threeD, threeD>;
} // muSpectre

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