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 Copyright (C) 2015 Peter Caspers
6
7 This file is part of QuantLib, a free-software/open-source library
8 for financial quantitative analysts and developers - http://quantlib.org/
9
10 QuantLib is free software: you can redistribute it and/or modify it
11 under the terms of the QuantLib license. You should have received a
12 copy of the license along with this program; if not, please email
13 <quantlib-dev@lists.sf.net>. The license is also available online at
14 <http://quantlib.org/license.shtml>.
15
16 This program is distributed in the hope that it will be useful, but WITHOUT
17 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
18 FOR A PARTICULAR PURPOSE. See the license for more details.
19*/
20
21/*! \file segmentintegral.hpp
22 \brief Integral of a one-dimensional function using segment algorithm
23*/
24
25#ifndef quantlib_segment_integral_h
26#define quantlib_segment_integral_h
27
28#include <ql/math/integrals/integral.hpp>
29#include <ql/math/comparison.hpp>
30#include <ql/errors.hpp>
31
32namespace QuantLib {
33
34 //! Integral of a one-dimensional function
35 /*! Given a number \f$ N \f$ of intervals, the integral of
36 a function \f$ f \f$ between \f$ a \f$ and \f$ b \f$ is
37 calculated by means of the trapezoid formula
38 \f[
39 \int_{a}^{b} f \mathrm{d}x =
40 \frac{1}{2} f(x_{0}) + f(x_{1}) + f(x_{2}) + \dots
41 + f(x_{N-1}) + \frac{1}{2} f(x_{N})
42 \f]
43 where \f$ x_0 = a \f$, \f$ x_N = b \f$, and
44 \f$ x_i = a+i \Delta x \f$ with
45 \f$ \Delta x = (b-a)/N \f$.
46
47 \test the correctness of the result is tested by checking it
48 against known good values.
49 */
50 class SegmentIntegral : public Integrator {
51 public:
52 explicit SegmentIntegral(Size intervals);
53 protected:
54 Real integrate(const ext::function<Real(Real)>& f, Real a, Real b) const override;
55
56 private:
57 Size intervals_;
58 };
59
60
61 // inline and template definitions
62
63 inline Real
64 SegmentIntegral::integrate(const ext::function<Real (Real)>& f,
65 Real a,
66 Real b) const {
67 if(close_enough(x: a,y: b))
68 return 0.0;
69 Real dx = (b-a)/intervals_;
70 Real sum = 0.5*(f(a)+f(b));
71 Real end = b - 0.5*dx;
72 for (Real x = a+dx; x < end; x += dx)
73 sum += f(x);
74 return sum*dx;
75 }
76
77}
78
79#endif
80

source code of quantlib/ql/math/integrals/segmentintegral.hpp