/usr/include/ql/methods/finitedifferences/trbdf2.hpp is in libquantlib0-dev 1.7.1-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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/*
Copyright (C) 2011 Fabien Le Floc'h
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
<http://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.
*/
/*! \file trbdf2.hpp
\brief TR-BDF2 scheme for finite difference methods
*/
#ifndef quantlib_trbdf2_hpp
#define quantlib_trbdf2_hpp
#include <ql/methods/finitedifferences/finitedifferencemodel.hpp>
namespace QuantLib {
//! TR-BDF2 scheme for finite difference methods
/*! See <http://ssrn.com/abstract=1648878> for details.
In this implementation, the passed operator must be derived
from either TimeConstantOperator or TimeDependentOperator.
Also, it must implement at least the following interface:
\code
typedef ... array_type;
// copy constructor/assignment
// (these will be provided by the compiler if none is defined)
Operator(const Operator&);
Operator& operator=(const Operator&);
// inspectors
Size size();
// modifiers
void setTime(Time t);
// operator interface
array_type applyTo(const array_type&);
array_type solveFor(const array_type&);
static Operator identity(Size size);
// operator algebra
Operator operator*(Real, const Operator&);
Operator operator+(const Operator&, const Operator&);
Operator operator+(const Operator&, const Operator&);
\endcode
\warning The differential operator must be linear for
this evolver to work.
\ingroup findiff
*/
// NOTE: There is room for performance improvement especially in
// the array manipulation
template <class Operator>
class TRBDF2 {
public:
// typedefs
typedef OperatorTraits<Operator> traits;
typedef typename traits::operator_type operator_type;
typedef typename traits::array_type array_type;
typedef typename traits::bc_set bc_set;
typedef typename traits::condition_type condition_type;
// constructors
TRBDF2(const operator_type& L,
const bc_set& bcs)
: L_(L), I_(operator_type::identity(L.size())),
dt_(0.0), bcs_(bcs), alpha_(2.0-sqrt(2.0)) {}
void step(array_type& a,
Time t);
void setStep(Time dt) {
dt_ = dt;
implicitPart_ = I_ + 0.5*alpha_*dt_*L_;
explicitTrapezoidalPart_ = I_ - 0.5*alpha_*dt_*L_;
explicitBDF2PartFull_ =
-(1.0-alpha_)*(1.0-alpha_)/(alpha_*(2.0-alpha_))*I_;
explicitBDF2PartMid_ = 1.0/(alpha_*(2.0-alpha_))*I_;
}
private:
Real alpha_;
operator_type L_, I_, explicitTrapezoidalPart_,
explicitBDF2PartFull_,explicitBDF2PartMid_, implicitPart_;
Time dt_;
bc_set bcs_;
array_type aInit_;
};
// inline definitions
template <class Operator>
inline void TRBDF2<Operator>::step(array_type& a, Time t) {
Size i;
Array aInit(a.size());
for (i=0; i<a.size();i++) {
aInit[i] = a[i];
}
aInit_ = aInit;
for (i=0; i<bcs_.size(); i++)
bcs_[i]->setTime(t);
//trapezoidal explicit part
if (L_.isTimeDependent()) {
L_.setTime(t);
explicitTrapezoidalPart_ = I_ - 0.5*alpha_*dt_*L_;
}
for (i=0; i<bcs_.size(); i++)
bcs_[i]->applyBeforeApplying(explicitTrapezoidalPart_);
a = explicitTrapezoidalPart_.applyTo(a);
for (i=0; i<bcs_.size(); i++)
bcs_[i]->applyAfterApplying(a);
// trapezoidal implicit part
if (L_.isTimeDependent()) {
L_.setTime(t-dt_);
implicitPart_ = I_ + 0.5*alpha_*dt_*L_;
}
for (i=0; i<bcs_.size(); i++)
bcs_[i]->applyBeforeSolving(implicitPart_,a);
a = implicitPart_.solveFor(a);
for (i=0; i<bcs_.size(); i++)
bcs_[i]->applyAfterSolving(a);
// BDF2 explicit part
if (L_.isTimeDependent()) {
L_.setTime(t);
}
for (i=0; i<bcs_.size(); i++) {
bcs_[i]->applyBeforeApplying(explicitBDF2PartFull_);
}
array_type b0 = explicitBDF2PartFull_.applyTo(aInit_);
for (i=0; i<bcs_.size(); i++)
bcs_[i]->applyAfterApplying(b0);
for (i=0; i<bcs_.size(); i++) {
bcs_[i]->applyBeforeApplying(explicitBDF2PartMid_);
}
array_type b1 = explicitBDF2PartMid_.applyTo(a);
for (i=0; i<bcs_.size(); i++)
bcs_[i]->applyAfterApplying(b1);
a = b0+b1;
// reuse implicit part - works only for alpha=2-sqrt(2)
for (i=0; i<bcs_.size(); i++)
bcs_[i]->applyBeforeSolving(implicitPart_,a);
a = implicitPart_.solveFor(a);
for (i=0; i<bcs_.size(); i++)
bcs_[i]->applyAfterSolving(a);
}
}
#endif
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