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//##########################################################################
//# #
//# CCLIB #
//# #
//# This program is free software; you can redistribute it and/or modify #
//# it under the terms of the GNU Library General Public License as #
//# published by the Free Software Foundation; version 2 or later of the #
//# License. #
//# #
//# 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. #
//# #
//# COPYRIGHT: EDF R&D / TELECOM ParisTech (ENST-TSI) #
//# #
//##########################################################################
#ifndef ERROR_FUNCTION_HEADER
#define ERROR_FUNCTION_HEADER
//Local
#include "CCCoreLib.h"
#include "MathTools.h"
namespace CCLib
{
//! Relative error for Error Function computation
/** You can adjust it to trade off between accuracy and speed
but don't ask for more than 15 figures (assuming usual 52 bit mantissa
in a double). Example: 1E-12 <--> calculate 12 significant figures
**/
static const double c_erfRelativeError = 1e-12;
//! A class to compute the Error function (erf)
/** See for example http://mathworld.wolfram.com/Erf.html.
Most of the code comes from "erf.cpp" by Steve Strand
(29-Jan-04).
**/
class CC_CORE_LIB_API ErrorFunction : MathTools
{
public:
//! Computes erfc(x)
/** erfc(x) = 2/sqrt(pi)*integral(exp(-t^2),t,x,inf)
= exp(-x^2)/sqrt(pi) * [1/x+ (1/2)/x+ (2/2)/x+ (3/2)/x+ (4/2)/x+ ...]
= 1-erf(x)
(expression inside [] is a continued fraction so '+' means add to denominator
only).
\param x a real variable
\return erfc(x)
**/
static double erfc(double x);
//! Computes erf(x)
/** erf(x) = 2/sqrt(pi)*integral(exp(-t^2),t,0,x)
= 2/sqrt(pi)*[x - x^3/3 + x^5/5*2! - x^7/7*3! + ...]
= 1-erfc(x)
\param x a real variable
\return erf(x)
**/
static double erf(double x);
};
}
#endif //ERROR_FUNCTION_HEADER
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