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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 solver1d.cpp
\brief Abstract 1-D solver class
\fullpath
ql/%solver1d.cpp
*/
// $Id: solver1d.cpp,v 1.6 2002/01/16 14:43:48 nando Exp $
#include <ql/solver1d.hpp>
namespace QuantLib {
const double growthFactor = 1.6;
double Solver1D::solve(const ObjectiveFunction& f,
double xAccuracy,
double guess,
double step) const {
int flipflop = -1;
root_ = guess;
fxMax_ = f(root_);
// monotonically crescent bias, as in optionValue(volatility)
if (QL_FABS(fxMax_) <= xAccuracy)
return root_;
else if (fxMax_ > 0.0) {
xMin_ = enforceBounds_(root_ - step);
fxMin_ = f(xMin_);
xMax_ = root_;
} else {
xMin_ = root_;
fxMin_ = fxMax_;
xMax_ = enforceBounds_(root_+step);
fxMax_ = f(xMax_);
}
evaluationNumber_ = 2;
while (evaluationNumber_ <= maxEvaluations_) {
if (fxMin_*fxMax_ <= 0.0) {
if (fxMin_ == 0.0) return xMin_;
if (fxMax_ == 0.0) return xMax_;
root_ = (xMax_+xMin_)/2.0;
// check whether we really want to pass epsilon
return solve_(f, QL_MAX(QL_FABS(xAccuracy), QL_EPSILON));
}
if (QL_FABS(fxMin_) < QL_FABS(fxMax_)) {
xMin_ = enforceBounds_(xMin_+growthFactor*(xMin_ - xMax_));
fxMin_= f(xMin_);
} else if (QL_FABS(fxMin_) > QL_FABS(fxMax_)) {
xMax_ = enforceBounds_(xMax_+growthFactor*(xMax_ - xMin_));
fxMax_= f(xMax_);
} else if (flipflop == -1) {
xMin_ = enforceBounds_(xMin_+growthFactor*(xMin_ - xMax_));
fxMin_= f(xMin_);
evaluationNumber_++;
flipflop = 1;
} else if (flipflop == 1) {
xMax_ = enforceBounds_(xMax_+growthFactor*(xMax_ - xMin_));
fxMax_= f(xMax_);
flipflop = -1;
}
evaluationNumber_++;
}
throw Error("unable to bracket root in " +
IntegerFormatter::toString(maxEvaluations_) +
" function evaluations (last bracket attempt: f[" +
DoubleFormatter::toString(xMin_) +
"," + DoubleFormatter::toString(xMax_) + "] -> [" +
DoubleFormatter::toString(fxMin_) + "," +
DoubleFormatter::toString(fxMax_) + "])");
}
double Solver1D::solve(const ObjectiveFunction& f,
double xAccuracy,
double guess,
double xMin,
double xMax) const {
xMin_ = xMin;
xMax_ = xMax;
QL_REQUIRE(xMin_ < xMax_, "invalid range: xMin_ (" +
DoubleFormatter::toString(xMin_) +
") >= xMax_ (" + DoubleFormatter::toString(xMax_) + ")");
QL_REQUIRE(!lowBoundEnforced_ || xMin_ >= lowBound_, "xMin_ (" +
DoubleFormatter::toString(xMin_) + ") < enforced low bound (" +
DoubleFormatter::toString(lowBound_) + ")");
QL_REQUIRE(!hiBoundEnforced_ || xMax_ <= hiBound_, "xMax_ (" +
DoubleFormatter::toString(xMax_) +
") > enforced hi bound (" +
DoubleFormatter::toString(hiBound_) + ")");
fxMin_ = f(xMin_);
if (QL_FABS(fxMin_) < xAccuracy)
return xMin_;
fxMax_ = f(xMax_);
if (QL_FABS(fxMax_) < xAccuracy)
return xMax_;
evaluationNumber_ = 2;
QL_REQUIRE((fxMin_*fxMax_ < 0.0), "root not bracketed: f[" +
DoubleFormatter::toString(xMin_,10) + "," +
DoubleFormatter::toString(xMax_,10) + "] -> [" +
DoubleFormatter::toString(fxMin_,20) + "," +
DoubleFormatter::toString(fxMax_,20) + "]");
QL_REQUIRE(guess > xMin_, "Solver1D: guess (" +
DoubleFormatter::toString(guess) + ") < xMin_ (" +
DoubleFormatter::toString(xMin_) + ")");
QL_REQUIRE(guess < xMax_, "Solver1D: guess (" +
DoubleFormatter::toString(guess) + ") > xMax_ (" +
DoubleFormatter::toString(xMax_) + ")");
root_ = guess;
return solve_(f, QL_MAX(QL_FABS(xAccuracy), QL_EPSILON));
}
}
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