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/*!
* \file
* \brief Definition of numerical integration
* \author Tony Ottosson
*
* -------------------------------------------------------------------------
*
* IT++ - C++ library of mathematical, signal processing, speech processing,
* and communications classes and functions
*
* Copyright (C) 1995-2008 (see AUTHORS file for a list of contributors)
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* 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
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
*
* -------------------------------------------------------------------------
*/
#ifndef INTEGRATION_H
#define INTEGRATION_H
#include <limits>
namespace itpp {
/*!
\addtogroup integration
\brief Numerical integration routines
*/
//@{
/*!
1-dimensional numerical Simpson quadrature integration
Calculate the 1-dimensional integral
\f[
\int_a^b f(x) dx
\f]
Uses an adaptive Simpson quadrature method. See [Gander] for more
details. The integrand is specified as a function \code double
f(double) \endcode.
Example:
\code
#include "itpp/itbase.h"
double f(const double x)
{
return x*log(x);
}
int main()
{
double res = quad( f, 1.5, 3.5);
cout << "res = " << res << endl;
return 0;
}
\endcode
References:
[Gander] Gander, W. and W. Gautschi, "Adaptive Quadrature -
Revisited", BIT, Vol. 40, 2000, pp. 84-101.
This document is also available at http://www.inf.ethz.ch/personal/gander.
*/
double quad(double (*f)(double), double a, double b,
double tol = std::numeric_limits<double>::epsilon());
/*!
1-dimensional numerical adaptive Lobatto quadrature integration
Calculate the 1-dimensional integral
\f[
\int_a^b f(x) dx
\f]
Uses an adaptive Lobatto quadrature method. See [Gander] for more
details. The integrand is specified as a function \code double
f(double) \endcode.
Example:
\code
#include "itpp/itbase.h"
double f(const double x)
{
return x*log(x);
}
int main()
{
double res = quadl( f, 1.5, 3.5);
cout << "res = " << res << endl;
return 0;
}
\endcode
References:
[Gander] Gander, W. and W. Gautschi, "Adaptive Quadrature -
Revisited", BIT, Vol. 40, 2000, pp. 84-101.
This document is also available at http:// www.inf.ethz.ch/personal/gander.
*/
double quadl(double (*f)(double), double a, double b,
double tol = std::numeric_limits<double>::epsilon());
//@}
} // namespace itpp
#endif // #ifndef INTEGRATION_H
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