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/*
Copyright (C) 2000, 2001, 2002 RiskMap srl
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it under the
terms of the QuantLib license. You should have received a copy of the
license along with this program; if not, please email ferdinando@ametrano.net
The license is also available online at http://quantlib.org/html/license.html
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 license for more details.
*/
/*! \file valueatcenter.cpp
\brief compute value, first, and second derivatives at grid center
\fullpath
ql/FiniteDifferences/%valueatcenter.cpp
*/
// $Id: valueatcenter.cpp,v 1.9 2002/01/16 14:43:25 nando Exp $
#include <ql/array.hpp>
namespace QuantLib {
namespace FiniteDifferences {
double valueAtCenter(const Array& a) {
Size jmid = a.size()/2;
if (a.size() % 2 == 1)
return a[jmid];
else
return (a[jmid]+a[jmid-1])/2.0;
}
double firstDerivativeAtCenter(const Array& a, const Array& g) {
QL_REQUIRE(a.size()==g.size(),
"firstDerivativeAtCenter: "
"a and g must be of the same size");
QL_REQUIRE(a.size()>=3,
"firstDerivativeAtCenter: "
"the size of the two vectors must be at least 3");
Size jmid = a.size()/2;
if(a.size() % 2 == 1)
return (a[jmid+1]-a[jmid-1])/(g[jmid+1]-g[jmid-1]);
else
return (a[jmid]-a[jmid-1])/(g[jmid]-g[jmid-1]);
}
double secondDerivativeAtCenter(const Array& a, const Array& g) {
QL_REQUIRE(a.size()==g.size(),
"secondDerivativeAtCenter: "
"a and g must be of the same size");
QL_REQUIRE(a.size()>=4,
"secondDerivativeAtCenter: "
"the size of the two vectors must be at least 4");
Size jmid = a.size()/2;
if(a.size() % 2 == 1){
double deltaPlus = (a[jmid+1]-a[jmid])/(g[jmid+1]-g[jmid]);
double deltaMinus = (a[jmid]-a[jmid-1])/(g[jmid]-g[jmid-1]);
double dS = (g[jmid+1]-g[jmid-1])/2.0;
return (deltaPlus-deltaMinus)/dS;
}
else{
double deltaPlus = (a[jmid+1]-a[jmid-1])/(g[jmid+1]-g[jmid-1]);
double deltaMinus = (a[jmid]-a[jmid-2])/(g[jmid]-g[jmid-2]);
return (deltaPlus-deltaMinus)/(g[jmid]-g[jmid-1]);
}
}
}
}
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