/usr/include/itpp/base/math/integration.h is in libitpp-dev 4.2-4.
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* \file
* \brief Definition of numerical integration
* \author Tony Ottosson
*
* -------------------------------------------------------------------------
*
* Copyright (C) 1995-2010 (see AUTHORS file for a list of contributors)
*
* This file is part of IT++ - a C++ library of mathematical, signal
* processing, speech processing, and communications classes and functions.
*
* IT++ 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 3 of the License, or (at your option) any
* later version.
*
* IT++ 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 IT++. If not, see <http://www.gnu.org/licenses/>.
*
* -------------------------------------------------------------------------
*/
#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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