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1/*!
2 * \file
3 * \brief Definition of numerical integration
4 * \author Tony Ottosson
5 *
6 * -------------------------------------------------------------------------
7 *
8 * IT++ - C++ library of mathematical, signal processing, speech processing,
9 *        and communications classes and functions
10 *
11 * Copyright (C) 1995-2007  (see AUTHORS file for a list of contributors)
12 *
13 * This program is free software; you can redistribute it and/or modify
14 * it under the terms of the GNU General Public License as published by
15 * the Free Software Foundation; either version 2 of the License, or
16 * (at your option) any later version.
17 *
18 * This program is distributed in the hope that it will be useful,
19 * but WITHOUT ANY WARRANTY; without even the implied warranty of
20 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
21 * GNU General Public License for more details.
22 *
23 * You should have received a copy of the GNU General Public License
24 * along with this program; if not, write to the Free Software
25 * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
26 *
27 * -------------------------------------------------------------------------
28 */
29
30#ifndef INTEGRATION_H
31#define INTEGRATION_H
32
33#include <limits>
34
35
36namespace itpp {
37
38  /*!
39    \addtogroup integration
40    \brief Numerical integration routines
41  */
42
43  //@{
44
45  /*!
46    1-dimensional numerical Simpson quadrature integration
47
48    Calculate the 1-dimensional integral
49    \f[
50    \int_a^b f(x) dx
51    \f]
52
53    Uses an adaptive Simpson quadrature method. See [Gander] for more
54    details. The integrand is specified as a function \code double
55    f(double) \endcode.
56
57    Example:
58    \code
59    #include "itpp/itbase.h"
60
61    double f(const double x)
62    {
63      return x*log(x);
64    }
65
66    int main()
67    {
68      double res = quad( f, 1.5, 3.5);
69      cout << "res = " << res << endl;
70
71      return 0;
72    }
73    \endcode
74
75    References:
76
77    [Gander] Gander, W. and W. Gautschi, "Adaptive Quadrature -
78    Revisited", BIT, Vol. 40, 2000, pp. 84-101.
79                This document is also available at http://www.inf.ethz.ch/personal/gander.
80  */
81  double quad(double (*f)(double), double a, double b,
82              double tol = std::numeric_limits<double>::epsilon());
83
84  /*!
85    1-dimensional numerical adaptive Lobatto quadrature integration
86
87    Calculate the 1-dimensional integral
88    \f[
89    \int_a^b f(x) dx
90    \f]
91
92    Uses an adaptive Lobatto quadrature method. See [Gander] for more
93    details. The integrand is specified as a function \code double
94    f(double) \endcode.
95
96    Example:
97    \code
98    #include "itpp/itbase.h"
99
100    double f(const double x)
101    {
102      return x*log(x);
103    }
104
105    int main()
106    {
107      double res = quadl( f, 1.5, 3.5);
108      cout << "res = " << res << endl;
109
110      return 0;
111    }
112    \endcode
113
114    References:
115
116    [Gander] Gander, W. and W. Gautschi, "Adaptive Quadrature -
117    Revisited", BIT, Vol. 40, 2000, pp. 84-101.
118        This document is also available at http:// www.inf.ethz.ch/personal/gander.
119  */
120  double quadl(double (*f)(double), double a, double b,
121               double tol = std::numeric_limits<double>::epsilon());
122
123  //@}
124
125} // namespace itpp
126
127#endif // #ifndef INTEGRATION_H
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