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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2009 Ralph Schreyer
Copyright (C) 2009 Klaus Spanderen
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 bicgstab.cpp
\brief bi-conjugated gradient stableized algorithm
*/
#include <ql/math/matrixutilities/bicgstab.hpp>
namespace QuantLib {
BiCGstab::BiCGstab(const BiCGstab::MatrixMult& A,
Size maxIter, Real relTol,
const BiCGstab::MatrixMult& preConditioner)
: A_(A), M_(preConditioner),
maxIter_(maxIter), relTol_(relTol) {
}
BiCGStabResult BiCGstab::solve(const Array& b, const Array& x0) const {
Real bnorm2 = norm2(b);
if (bnorm2 == 0.0) {
BiCGStabResult result = { 0, 0.0, b};
return result;
}
Array x = ((!x0.empty()) ? x0 : Array(b.size(), 0.0));
Array r = b - A_(x);
Array rTld = r;
Array p, pTld, v, s, sTld, t;
Real omega = 1.0;
Real rho, rhoTld=1.0;
Real alpha=0.0, beta;
Real error=Null<Real>();
Size i;
for (i=0; i < maxIter_ && error >= relTol_; ++i) {
rho = DotProduct(rTld, r);
if (rho == 0.0 || omega == 0.0)
break;
if (i) {
beta = (rho/rhoTld)*(alpha/omega);
p = r + beta*(p - omega*v);
}
else {
p = r;
}
pTld = ((M_)? M_(p) : p);
v = A_(pTld);
alpha = rho/DotProduct(rTld, v);
s = r-alpha*v;
if (norm2(s) < relTol_*bnorm2) {
x += alpha*pTld;
error = norm2(s)/bnorm2;
break;
}
sTld = ((M_) ? M_(s) : s);
t = A_(sTld);
omega = DotProduct(t,s)/DotProduct(t,t);
x += alpha*pTld + omega*sTld;
r = s - omega*t;
error = norm2(r)/bnorm2;
rhoTld = rho;
}
QL_REQUIRE(i < maxIter_, "max number of iterations exceeded");
QL_REQUIRE(error < relTol_, "could not converge");
BiCGStabResult result = { i, error, x};
return result;
}
Real BiCGstab::norm2(const Array& a) const {
return std::sqrt(DotProduct(a, a));
}
}
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