1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
|
/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2011 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
<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 fdmndimsolver.hpp
*/
#ifndef quantlib_fdm_n_dim_solver_hpp
#define quantlib_fdm_n_dim_solver_hpp
#include <ql/patterns/lazyobject.hpp>
#include <ql/math/interpolations/multicubicspline.hpp>
#include <ql/methods/finitedifferences/finitedifferencemodel.hpp>
#include <ql/methods/finitedifferences/meshers/fdmmesher.hpp>
#include <ql/methods/finitedifferences/solvers/fdmsolverdesc.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
#include <ql/methods/finitedifferences/solvers/fdmbackwardsolver.hpp>
#include <ql/methods/finitedifferences/stepconditions/fdmsnapshotcondition.hpp>
#include <ql/methods/finitedifferences/utilities/fdminnervaluecalculator.hpp>
#include <ql/methods/finitedifferences/stepconditions/fdmstepconditioncomposite.hpp>
#include <numeric>
namespace QuantLib {
template <Size N>
class FdmNdimSolver : public LazyObject {
public:
FdmNdimSolver(const FdmSolverDesc& solverDesc,
const FdmSchemeDesc& schemeDesc,
const boost::shared_ptr<FdmLinearOpComposite>& op);
void performCalculations() const;
Real interpolateAt(const std::vector<Real>& x) const;
Real thetaAt(const std::vector<Real>& x) const;
// template meta programming
typedef typename MultiCubicSpline<N>::data_table data_table;
void static setValue(data_table& f,
const std::vector<Size>& x, Real value);
private:
const FdmSolverDesc solverDesc_;
const FdmSchemeDesc schemeDesc_;
const boost::shared_ptr<FdmLinearOpComposite> op_;
const boost::shared_ptr<FdmSnapshotCondition> thetaCondition_;
const boost::shared_ptr<FdmStepConditionComposite> conditions_;
std::vector<std::vector<Real> > x_;
std::vector<Real> initialValues_;
mutable boost::shared_ptr<data_table> f_;
mutable boost::shared_ptr<MultiCubicSpline<N> > interp_;
};
template <Size N> inline
FdmNdimSolver<N>::FdmNdimSolver(
const FdmSolverDesc& solverDesc,
const FdmSchemeDesc& schemeDesc,
const boost::shared_ptr<FdmLinearOpComposite>& op)
: solverDesc_(solverDesc),
schemeDesc_(schemeDesc),
op_(op),
thetaCondition_(new FdmSnapshotCondition(
0.99*std::min(1.0/365.0,
solverDesc.condition->stoppingTimes().empty()
? solverDesc.maturity :
solverDesc.condition->stoppingTimes().front()))),
conditions_(FdmStepConditionComposite::joinConditions(thetaCondition_,
solverDesc.condition)),
x_ (solverDesc.mesher->layout()->dim().size()),
initialValues_(solverDesc.mesher->layout()->size()) {
const boost::shared_ptr<FdmMesher> mesher = solverDesc.mesher;
const boost::shared_ptr<FdmLinearOpLayout> layout = mesher->layout();
QL_REQUIRE(layout->dim().size() == N, "solver dim " << N
<< "does not fit to layout dim " << layout->size());
for (Size i=0; i < N; ++i) {
x_[i].reserve(layout->dim()[i]);
}
const FdmLinearOpIterator endIter = layout->end();
for (FdmLinearOpIterator iter = layout->begin(); iter != endIter;
++iter) {
initialValues_[iter.index()] = solverDesc.calculator
->avgInnerValue(iter, solverDesc.maturity);
const std::vector<Size>& c = iter.coordinates();
for (Size i=0; i < N; ++i) {
if (!(std::accumulate(c.begin(), c.end(), 0)-c[i])) {
x_[i].push_back(mesher->location(iter, i));
}
}
}
f_ = boost::shared_ptr<data_table>(new data_table(x_));
}
template <Size N> inline
void FdmNdimSolver<N>::performCalculations() const {
Array rhs(initialValues_.size());
std::copy(initialValues_.begin(), initialValues_.end(), rhs.begin());
FdmBackwardSolver(op_, solverDesc_.bcSet, conditions_, schemeDesc_)
.rollback(rhs, solverDesc_.maturity, 0.0,
solverDesc_.timeSteps, solverDesc_.dampingSteps);
const boost::shared_ptr<FdmLinearOpLayout> layout
= solverDesc_.mesher->layout();
const FdmLinearOpIterator endIter = layout->end();
for (FdmLinearOpIterator iter = layout->begin(); iter != endIter;
++iter) {
setValue(*f_, iter.coordinates(), rhs[iter.index()]);
}
interp_ = boost::shared_ptr<MultiCubicSpline<N> >(
new MultiCubicSpline<N>(x_, *f_));
}
template <Size N> inline
Real FdmNdimSolver<N>::thetaAt(const std::vector<Real>& x) const {
QL_REQUIRE(conditions_->stoppingTimes().front() > 0.0,
"stopping time at zero-> can't calculate theta");
calculate();
const Array& rhs = thetaCondition_->getValues();
const boost::shared_ptr<FdmLinearOpLayout> layout
= solverDesc_.mesher->layout();
data_table f(x_);
const FdmLinearOpIterator endIter = layout->end();
for (FdmLinearOpIterator iter = layout->begin(); iter != endIter;
++iter) {
setValue(f, iter.coordinates(), rhs[iter.index()]);
}
return (MultiCubicSpline<N>(x_, f)(x)
- interpolateAt(x)) / thetaCondition_->getTime();
}
template <Size N> inline
Real FdmNdimSolver<N>::interpolateAt(const std::vector<Real>& x) const {
calculate();
return (*interp_)(x);
}
template <Size N> inline
void FdmNdimSolver<N>::setValue(data_table& f,
const std::vector<Size>& x, Real value) {
FdmNdimSolver<N-1>::setValue(f[x[x.size()-N]], x, value);
}
template <> inline
void FdmNdimSolver<1>::setValue(data_table& f,
const std::vector<Size>& x, Real value) {
f[x.back()] = value;
}
}
#endif
|
