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
|
/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2014 Jose Aparicio
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.
*/
#ifndef quantlib_math_multidimintegrator_hpp
#define quantlib_math_multidimintegrator_hpp
#include <ql/types.hpp>
#include <ql/errors.hpp>
#include <ql/math/integrals/integral.hpp>
#include <functional>
#include <vector>
namespace QuantLib {
/*! \brief Integrates a vector or scalar function of vector domain.
Uses a collection of arbitrary 1D integrators along each of the
dimensions. A template recursion along dimensions avoids calling depth
test or virtual functions.\par
This class generalizes to an arbitrary number of dimensions the
functionality in class TwoDimensionalIntegral
*/
class MultidimIntegral {
public:
explicit MultidimIntegral(
const std::vector<ext::shared_ptr<Integrator> >& integrators);
// scalar variant
/*! f is the integrand function; a and b are the lower and
upper integration limit domain for each dimension.
*/
Real operator()(
const std::function<Real (const std::vector<Real>&)>& f,
const std::vector<Real>& a,
const std::vector<Real>& b) const
{
QL_REQUIRE((a.size()==b.size())&&(b.size()==integrators_.size()),
"Incompatible integration problem dimensions");
return integrationLevelEntries_[integrators_.size()-1](f, a, b);
}
// to do: write std::vector<Real> operator()(...) version
private:
static const Size maxDimensions_ = 15;
/* Here is the tradeoff; this is avoiding the dimension limits checks
during integration at the price of these asignments during construction.
Explicit template instantiation is of no use, an object is needed
(notice 'this' is needed for the asignment.)
If not all the dimensions up the maximum number are used the waste goes
into storage of the functions (in fact only one is used)
*/
template<Size depth>
void spawnFcts() const;
// Splits the integration in cross-sections per dimension.
template<int T_N>
Real vectorBinder (
const std::function<Real (const std::vector<Real>&)>& f,
Real z,
const std::vector<Real>& a,
const std::vector<Real>& b) const ;
// actual integration of dimension nT
template<int nT>
Real integrate(
const std::function<Real (const std::vector<Real>&)>& f,
const std::vector<Real>& a,
const std::vector<Real>& b) const;
const std::vector<ext::shared_ptr<Integrator> > integrators_;
/* typedef (const std::function<Real
(const std::vector<Real>&arg1)>&arg2) integrableFunctType;
*/
/* vector of, functions returning reals And taking as argument:
1.- a const ref to a function taking vectors
2.- a vector, 3. another vector. typedefs eventually...
at first sight this might look like mimicking a virtual table, it isnt
that. The reason is to be able to select the correct integration
dimension at run time, this can not be done before because of the
template argument restriction to be constant known at compilation.
*/
mutable std::vector<std::function<Real (//<- members: integrate<N>
// integrable function:
const std::function<Real (const std::vector<Real>&)>&,
const std::vector<Real>&, //<- a
const std::vector<Real>&) //<- b
> >
integrationLevelEntries_;
/* One can avoid the passing around of the ct refs to a and b but the
price is to keep a copy of them (they are unknown at construction time)
On the other hand the vector integration variable has to be created.*/
mutable std::vector<Real> varBuffer_;
};
// spez last call/dimension
template<>
Real inline MultidimIntegral::vectorBinder<0> (
const std::function<Real (const std::vector<Real>&)>& f,
Real z,
const std::vector<Real>& a,
const std::vector<Real>& b) const
{
varBuffer_[0] = z;
return f(varBuffer_);
}
template<>
void inline MultidimIntegral::spawnFcts<1>() const {
integrationLevelEntries_[0] = [this](const auto& f, const auto& a, const auto& b) {
return this->integrate<0>(f, a, b);
};
}
template<int nT>
inline Real MultidimIntegral::integrate(
const std::function<Real (const std::vector<Real>&)>& f,
const std::vector<Real>& a,
const std::vector<Real>& b) const
{
return
(*integrators_[nT])([this, &f, &a, &b](auto z) {
return this->vectorBinder<nT>(f, z, a, b);
}, a[nT], b[nT]);
}
template<int T_N>
inline Real MultidimIntegral::vectorBinder (
const std::function<Real (const std::vector<Real>&)>& f,
Real z,
const std::vector<Real>& a,
const std::vector<Real>& b) const
{
varBuffer_[T_N] = z;
return integrate<T_N-1>(f, a, b);
}
template<Size depth>
void MultidimIntegral::spawnFcts() const {
integrationLevelEntries_[depth-1] = [this](const auto& f, const auto& a, const auto& b) {
return this->integrate<depth-1>(f, a, b);
};
spawnFcts<depth-1>();
}
}
#endif
|
