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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2009 Ralph Schreyer
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
<quantlib-dev@lists.sf.net>. The license is also available online at
<http://quantlib.org/license.shtml>.
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 concentrating1dmesher.cpp
\brief One-dimensional grid mesher concentrating around critical points
*/
#include <ql/errors.hpp>
#include <ql/utilities/null.hpp>
#include <ql/methods/finitedifferences/meshers/concentrating1dmesher.hpp>
#include <ql/math/interpolations/linearinterpolation.hpp>
#include <cmath>
// asinh is missing in WIN32 (and possibly on other compilers)
#if !defined(QL_HAVE_ASINH)
#define asinh(x) std::log(x + std::sqrt(x * x + 1))
#endif
namespace QuantLib {
Concentrating1dMesher::Concentrating1dMesher(
Real start, Real end, Size size, const std::pair<Real, Real>& cPoints,
const bool requireCPoint)
: Fdm1dMesher(size) {
QL_REQUIRE(end > start, "end must be larger than start");
const Real cPoint = cPoints.first;
const Real density = cPoints.second == Null<Real>() ?
Null<Real>() : cPoints.second*(end-start);
QL_REQUIRE( cPoint == Null<Real>()
|| (cPoint >= start && cPoint <= end),
"cPoint must be between start and end");
QL_REQUIRE(density == Null<Real>() || density > 0.0,
"density > 0 required" );
const Real dx = 1.0/(size-1);
if(cPoint != Null<Real>()) {
boost::shared_ptr<Interpolation> transform;
const Real c1 = asinh((start-cPoint)/density);
const Real c2 = asinh((end-cPoint)/density);
if(requireCPoint) {
const Real z0 = - c1 / (c2-c1);
const Real u0 = static_cast<int>(z0*(size-1)+0.5) / ((Real)(size-1));
std::vector<Real> u, z;
u.push_back(0.0); u.push_back(u0); u.push_back(1.0);
z.push_back(0.0); z.push_back(z0); z.push_back(1.0);
transform = boost::shared_ptr<Interpolation>(
new LinearInterpolation(u.begin(), u.end(), z.begin()));
}
for (Size i=1; i < size-1; ++i) {
const Real li = requireCPoint ? (*transform)(i*dx) : i*dx;
locations_[i] = cPoint
+ density*std::sinh(c1*(1.0-li)+c2*li);
}
}
else {
for (Size i=1; i < size-1; ++i) {
locations_[i] = start + i*dx*(end-start);
}
}
locations_.front() = start;
locations_.back() = end;
for (Size i=0; i < size-1; ++i) {
dplus_[i] = dminus_[i+1] = locations_[i+1] - locations_[i];
}
dplus_.back() = dminus_.front() = Null<Real>();
}
}
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