QuantLib: a free/open-source library for quantitative finance
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dplusdminus.hpp
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1/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
2
3/*
4 Copyright (C) 2000, 2001, 2002, 2003 RiskMap srl
5
6 This file is part of QuantLib, a free-software/open-source library
7 for financial quantitative analysts and developers - http://quantlib.org/
8
9 QuantLib is free software: you can redistribute it and/or modify it
10 under the terms of the QuantLib license. You should have received a
11 copy of the license along with this program; if not, please email
12 <quantlib-dev@lists.sf.net>. The license is also available online at
13 <http://quantlib.org/license.shtml>.
14
15 This program is distributed in the hope that it will be useful, but WITHOUT
16 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
17 FOR A PARTICULAR PURPOSE. See the license for more details.
18*/
19
20/*! \file dplusdminus.hpp
21 \brief \f$ D_{+}D_{-} \f$ matricial representation
22*/
23
24#ifndef quantlib_d_plus_d_minus_h
25#define quantlib_d_plus_d_minus_h
26
28
29namespace QuantLib {
30
31 //! \f$ D_{+}D_{-} \f$ matricial representation
32 /*! The differential operator \f$ D_{+}D_{-} \f$ discretizes the
33 second derivative with the second-order formula
34 \f[ \frac{\partial^2 u_{i}}{\partial x^2} \approx
35 \frac{u_{i+1}-2u_{i}+u_{i-1}}{h^2} = D_{+}D_{-} u_{i}
36 \f]
37
38 \ingroup findiff
39
40 \test the correctness of the returned values is tested by
41 checking them against numerical calculations.
42 */
44 public:
45 DPlusDMinus(Size gridPoints, Real h);
46 };
47
48
49 // inline definitions
50
51 inline DPlusDMinus::DPlusDMinus(Size gridPoints, Real h)
52 : TridiagonalOperator(gridPoints) {
53 setFirstRow(0.0,0.0); // linear extrapolation
54 setMidRows(1/(h*h),-2/(h*h),1/(h*h));
55 setLastRow(0.0,0.0); // linear extrapolation
56 }
57
58}
59
60
61#endif
matricial representation
Definition: dplusdminus.hpp:43
DPlusDMinus(Size gridPoints, Real h)
Definition: dplusdminus.hpp:51
Base implementation for tridiagonal operator.
QL_REAL Real
real number
Definition: types.hpp:50
std::size_t Size
size of a container
Definition: types.hpp:58
Definition: any.hpp:35
tridiagonal operator