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/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*************************************************************************
*
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* Copyright 2000, 2010 Oracle and/or its affiliates.
*
* OpenOffice.org - a multi-platform office productivity suite
*
* This file is part of OpenOffice.org.
*
* OpenOffice.org is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License version 3
* only, as published by the Free Software Foundation.
*
* OpenOffice.org 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 Lesser General Public License version 3 for more details
* (a copy is included in the LICENSE file that accompanied this code).
*
* You should have received a copy of the GNU Lesser General Public License
* version 3 along with OpenOffice.org. If not, see
* <http://www.openoffice.org/license.html>
* for a copy of the LGPLv3 License.
*
************************************************************************/
#include <rtl/logfile.hxx>
#include "interpre.hxx"
double const fHalfMachEps = 0.5 * ::std::numeric_limits<double>::epsilon();
// The idea how this group of gamma functions is calculated, is
// based on the Cephes library
// online http://www.moshier.net/#Cephes [called 2008-02]
/** You must ensure fA>0.0 && fX>0.0
valid results only if fX > fA+1.0
uses continued fraction with odd items */
double ScInterpreter::GetGammaContFraction( double fA, double fX )
{
RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::GetGammaContFraction" );
double const fBigInv = ::std::numeric_limits<double>::epsilon();
double const fBig = 1.0/fBigInv;
double fCount = 0.0;
double fNum = 0.0; // dummy value
double fY = 1.0 - fA;
double fDenom = fX + 2.0-fA;
double fPk = 0.0; // dummy value
double fPkm1 = fX + 1.0;
double fPkm2 = 1.0;
double fQk = 1.0; // dummy value
double fQkm1 = fDenom * fX;
double fQkm2 = fX;
double fApprox = fPkm1/fQkm1;
bool bFinished = false;
double fR = 0.0; // dummy value
do
{
fCount = fCount +1.0;
fY = fY+ 1.0;
fNum = fY * fCount;
fDenom = fDenom +2.0;
fPk = fPkm1 * fDenom - fPkm2 * fNum;
fQk = fQkm1 * fDenom - fQkm2 * fNum;
if (fQk != 0.0)
{
fR = fPk/fQk;
bFinished = (fabs( (fApprox - fR)/fR ) <= fHalfMachEps);
fApprox = fR;
}
fPkm2 = fPkm1;
fPkm1 = fPk;
fQkm2 = fQkm1;
fQkm1 = fQk;
if (fabs(fPk) > fBig)
{
// reduce a fraction does not change the value
fPkm2 = fPkm2 * fBigInv;
fPkm1 = fPkm1 * fBigInv;
fQkm2 = fQkm2 * fBigInv;
fQkm1 = fQkm1 * fBigInv;
}
} while (!bFinished && fCount<10000);
// most iterations, if fX==fAlpha+1.0; approx sqrt(fAlpha) iterations then
if (!bFinished)
{
SetError(errNoConvergence);
}
return fApprox;
}
/** You must ensure fA>0.0 && fX>0.0
valid results only if fX <= fA+1.0
uses power series */
double ScInterpreter::GetGammaSeries( double fA, double fX )
{
RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::GetGammaSeries" );
double fDenomfactor = fA;
double fSummand = 1.0/fA;
double fSum = fSummand;
int nCount=1;
do
{
fDenomfactor = fDenomfactor + 1.0;
fSummand = fSummand * fX/fDenomfactor;
fSum = fSum + fSummand;
nCount = nCount+1;
} while ( fSummand/fSum > fHalfMachEps && nCount<=10000);
// large amount of iterations will be carried out for huge fAlpha, even
// if fX <= fAlpha+1.0
if (nCount>10000)
{
SetError(errNoConvergence);
}
return fSum;
}
/** You must ensure fA>0.0 && fX>0.0) */
double ScInterpreter::GetLowRegIGamma( double fA, double fX )
{
RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::GetLowRegIGamma" );
double fLnFactor = fA * log(fX) - fX - GetLogGamma(fA);
double fFactor = exp(fLnFactor); // Do we need more accuracy than exp(ln()) has?
if (fX>fA+1.0) // includes fX>1.0; 1-GetUpRegIGamma, continued fraction
return 1.0 - fFactor * GetGammaContFraction(fA,fX);
else // fX<=1.0 || fX<=fA+1.0, series
return fFactor * GetGammaSeries(fA,fX);
}
/** You must ensure fA>0.0 && fX>0.0) */
double ScInterpreter::GetUpRegIGamma( double fA, double fX )
{
RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::GetUpRegIGamma" );
double fLnFactor= fA*log(fX)-fX-GetLogGamma(fA);
double fFactor = exp(fLnFactor); //Do I need more accuracy than exp(ln()) has?;
if (fX>fA+1.0) // includes fX>1.0
return fFactor * GetGammaContFraction(fA,fX);
else //fX<=1 || fX<=fA+1, 1-GetLowRegIGamma, series
return 1.0 -fFactor * GetGammaSeries(fA,fX);
}
/** Gamma distribution, probability density function.
fLambda is "scale" parameter
You must ensure fAlpha>0.0 and fLambda>0.0 */
double ScInterpreter::GetGammaDistPDF( double fX, double fAlpha, double fLambda )
{
RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::GetGammaDistPDF" );
if (fX < 0.0)
return 0.0; // see ODFF
else if (fX == 0)
// in this case 0^0 isn't zero
{
if (fAlpha < 1.0)
{
SetError(errDivisionByZero); // should be #DIV/0
return HUGE_VAL;
}
else if (fAlpha == 1)
{
return (1.0 / fLambda);
}
else
{
return 0.0;
}
}
else
{
double fXr = fX / fLambda;
// use exp(ln()) only for large arguments because of less accuracy
if (fXr > 1.0)
{
const double fLogDblMax = log( ::std::numeric_limits<double>::max());
if (log(fXr) * (fAlpha-1.0) < fLogDblMax && fAlpha < fMaxGammaArgument)
{
return pow( fXr, fAlpha-1.0) * exp(-fXr) / fLambda / GetGamma(fAlpha);
}
else
{
return exp( (fAlpha-1.0) * log(fXr) - fXr - log(fLambda) - GetLogGamma(fAlpha));
}
}
else // fXr near to zero
{
if (fAlpha<fMaxGammaArgument)
{
return pow( fXr, fAlpha-1.0) * exp(-fXr) / fLambda / GetGamma(fAlpha);
}
else
{
return pow( fXr, fAlpha-1.0) * exp(-fXr) / fLambda / exp( GetLogGamma(fAlpha));
}
}
}
}
/** Gamma distribution, cumulative distribution function.
fLambda is "scale" parameter
You must ensure fAlpha>0.0 and fLambda>0.0 */
double ScInterpreter::GetGammaDist( double fX, double fAlpha, double fLambda )
{
RTL_LOGFILE_CONTEXT_AUTHOR( aLogger, "sc", "er", "ScInterpreter::GetGammaDist" );
if (fX <= 0.0)
return 0.0;
else
return GetLowRegIGamma( fAlpha, fX / fLambda);
}
/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
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