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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2009 Andreas Gaida
Copyright (C) 2009 Ralph Schreyer
Copyright (C) 2009, 2017 Klaus Spanderen
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it
under the terms of the QuantLib license. You should have received a
copy of the license along with this program; if not, please email
<quantlib-dev@lists.sf.net>. The license is also available online at
<https://www.quantlib.org/license.shtml>.
This program 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 license for more details.
*/
#include <ql/math/matrixutilities/bicgstab.hpp>
#include <ql/math/matrixutilities/gmres.hpp>
#include <ql/methods/finitedifferences/schemes/impliciteulerscheme.hpp>
#include <functional>
#include <utility>
namespace QuantLib {
ImplicitEulerScheme::ImplicitEulerScheme(ext::shared_ptr<FdmLinearOpComposite> map,
const bc_set& bcSet,
Real relTol,
SolverType solverType)
: dt_(Null<Real>()), iterations_(ext::make_shared<Size>(0U)), relTol_(relTol),
map_(std::move(map)), bcSet_(bcSet), solverType_(solverType) {}
Array ImplicitEulerScheme::apply(const Array& r, Real theta) const {
return r - (theta*dt_)*map_->apply(r);
}
void ImplicitEulerScheme::step(array_type& a, Time t) {
step(a, t, 1.0);
}
void ImplicitEulerScheme::step(array_type& a, Time t, Real theta) {
QL_REQUIRE(t-dt_ > -1e-8, "a step towards negative time given");
map_->setTime(std::max(0.0, t-dt_), t);
bcSet_.setTime(std::max(0.0, t-dt_));
bcSet_.applyBeforeSolving(*map_, a);
if (map_->size() == 1) {
a = map_->solve_splitting(0, a, -theta*dt_);
}
else {
auto preconditioner = [&](const Array& _a){ return map_->preconditioner(_a, -theta*dt_); };
auto applyF = [&](const Array& _a){ return apply(_a, theta); };
if (solverType_ == BiCGstab) {
const BiCGStabResult result =
QuantLib::BiCGstab(applyF, std::max(Size(10), a.size()),
relTol_, preconditioner).solve(a, a);
(*iterations_) += result.iterations;
a = result.x;
}
else if (solverType_ == GMRES) {
const GMRESResult result =
QuantLib::GMRES(applyF, std::max(Size(10), a.size() / 10U), relTol_,
preconditioner)
.solve(a, a);
(*iterations_) += result.errors.size();
a = result.x;
}
else
QL_FAIL("unknown/illegal solver type");
}
bcSet_.applyAfterSolving(a);
}
void ImplicitEulerScheme::setStep(Time dt) {
dt_=dt;
}
Size ImplicitEulerScheme::numberOfIterations() const {
return *iterations_;
}
}
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