logistic.hpp

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/** \file logistic.hpp
 * \brief The logistic function
 *
 * \author Jared R. Males (jaredmales@gmail.com)
 *
 * \ingroup gen_math_files
 *
 */
 
//***********************************************************************//
// Copyright 2015, 2016, 2017 Jared R. Males (jaredmales@gmail.com)
//
// This file is part of mxlib.
//
// mxlib 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.
//
// mxlib 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 mxlib.  If not, see <http://www.gnu.org/licenses/>.
//***********************************************************************//
 
#ifndef __logistic_hpp__
#define __logistic_hpp__
 
namespace mx
{
 
namespace math
{
 
namespace func
{
 
/// Return the logistic function parameter for a specified rise time
/** The logistic function is
 * \f[
 *  f(t) = \frac{1}{1 + e^{-a(t-t_0)}}
 * \f]
 * The parameter \f$ a \f$ controls how fast the function rises.  Here it is specified by the
 * value \f$ f(t_{1/2}) = x\f$, where \f$ 0 < x < 1 \f$.
 *
 *
 * \returns the value of a
 *
 * \tparam floatT is the floating point type of the arguments and the returned value.
 *
 * \ingroup gen_math_logistic
 */
template <typename floatT>
floatT logistic_param( floatT x,    ///< [in] the value at which the rise time is specified.
                       floatT thalf ///< [in]  half the rise time, or the time after 0 when f(t) = x.
)
{
    return -log( 1.0 / x - 1 ) / thalf;
}
 
/// Return the value of the logistic function
/** The logistic function is
 * \f[
 *  f(t) = \frac{1}{1 + e^{-a(t-t_0)}}
 * \f]
 *
 * \param t [input] the argument.
 * \param t0 [input] [optional] the center of the curve, defaults to 0.
 * \param a [input] [optional] the exponent parameter, defaults to 1.
 *
 * \returns the value of the logistic function at t
 *
 * \tparam floatT is the floating point type of the arguments and the returned value.
 *
 * \ingroup gen_math_logistic
 */
template <typename floatT>
floatT logistic( floatT t, floatT t0 = 0, floatT a = 1 )
{
    return 1.0 / ( 1.0 + exp( -a * ( t - t0 ) ) );
}
 
} // namespace func
} // namespace math
} // namespace mx
 
#endif //__logistic_hpp__