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
|
/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2001, 2002, 2003 Nicolas Di Césaré
Copyright (C) 2005 StatPro Italia srl
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.
*/
#include <ql/math/optimization/conjugategradient.hpp>
#include <ql/math/optimization/leastsquare.hpp>
#include <ql/math/optimization/problem.hpp>
#include <utility>
namespace QuantLib {
Real LeastSquareFunction::value(const Array & x) const {
// size of target and function to fit vectors
Array target(lsp_.size()), fct2fit(lsp_.size());
// compute its values
lsp_.targetAndValue(x, target, fct2fit);
// do the difference
Array diff = target - fct2fit;
// and compute the scalar product (square of the norm)
return DotProduct(diff, diff);
}
Array LeastSquareFunction::values(const Array& x) const {
// size of target and function to fit vectors
Array target(lsp_.size()), fct2fit(lsp_.size());
// compute its values
lsp_.targetAndValue(x, target, fct2fit);
// do the difference
Array diff = target - fct2fit;
return diff*diff;
}
void LeastSquareFunction::gradient(Array& grad_f,
const Array& x) const {
// size of target and function to fit vectors
Array target (lsp_.size ()), fct2fit (lsp_.size ());
// size of gradient matrix
Matrix grad_fct2fit (lsp_.size (), x.size ());
// compute its values
lsp_.targetValueAndGradient(x, grad_fct2fit, target, fct2fit);
// do the difference
Array diff = target - fct2fit;
// compute derivative
grad_f = -2.0*(transpose(grad_fct2fit)*diff);
}
Real LeastSquareFunction::valueAndGradient(Array& grad_f,
const Array& x) const {
// size of target and function to fit vectors
Array target(lsp_.size()), fct2fit(lsp_.size());
// size of gradient matrix
Matrix grad_fct2fit(lsp_.size(), x.size());
// compute its values
lsp_.targetValueAndGradient(x, grad_fct2fit, target, fct2fit);
// do the difference
Array diff = target - fct2fit;
// compute derivative
grad_f = -2.0*(transpose(grad_fct2fit)*diff);
// and compute the scalar product (square of the norm)
return DotProduct(diff, diff);
}
NonLinearLeastSquare::NonLinearLeastSquare(Constraint& c,
Real accuracy,
Size maxiter)
: exitFlag_(-1), accuracy_ (accuracy), maxIterations_ (maxiter),
om_ (ext::shared_ptr<OptimizationMethod>(new ConjugateGradient())),
c_(c)
{}
NonLinearLeastSquare::NonLinearLeastSquare(Constraint& c,
Real accuracy,
Size maxiter,
ext::shared_ptr<OptimizationMethod> om)
: exitFlag_(-1), accuracy_(accuracy), maxIterations_(maxiter), om_(std::move(om)), c_(c) {}
Array& NonLinearLeastSquare::perform(LeastSquareProblem& lsProblem) {
Real eps = accuracy_;
// wrap the least square problem in an optimization function
LeastSquareFunction lsf(lsProblem);
// define optimization problem
Problem P(lsf, c_, initialValue_);
// minimize
EndCriteria ec(maxIterations_,
std::min(static_cast<Size>(maxIterations_/2), static_cast<Size>(100)),
eps, eps, eps);
exitFlag_ = om_->minimize(P, ec);
// summarize results of minimization
// nbIterations_ = om_->iterationNumber();
results_ = P.currentValue();
resnorm_ = P.functionValue();
bestAccuracy_ = P.functionValue();
return results_;
}
}
|
