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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2002, 2003, 2011 Ferdinando Ametrano
Copyright (C) 2000, 2001, 2002, 2003 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
<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.
*/
#include <ql/methods/finitedifferences/tridiagonaloperator.hpp>
namespace QuantLib {
TridiagonalOperator::TridiagonalOperator(Size size) {
if (size>=2) {
n_ = size;
diagonal_ = Array(size);
lowerDiagonal_ = Array(size-1);
upperDiagonal_ = Array(size-1);
temp_ = Array(size);
} else if (size==0) {
n_ = 0;
diagonal_ = Array(0);
lowerDiagonal_ = Array(0);
upperDiagonal_ = Array(0);
temp_ = Array(0);
} else {
QL_FAIL("invalid size (" << size << ") for tridiagonal operator "
"(must be null or >= 2)");
}
}
TridiagonalOperator::TridiagonalOperator(const Array& low,
const Array& mid,
const Array& high)
: n_(mid.size()),
diagonal_(mid), lowerDiagonal_(low), upperDiagonal_(high), temp_(n_) {
QL_REQUIRE(low.size() == n_-1,
"low diagonal vector of size " << low.size() <<
" instead of " << n_-1);
QL_REQUIRE(high.size() == n_-1,
"high diagonal vector of size " << high.size() <<
" instead of " << n_-1);
}
TridiagonalOperator::TridiagonalOperator(
const Disposable<TridiagonalOperator>& from) {
swap(const_cast<Disposable<TridiagonalOperator>&>(from));
}
Disposable<Array> TridiagonalOperator::applyTo(const Array& v) const {
QL_REQUIRE(n_!=0,
"uninitialized TridiagonalOperator");
QL_REQUIRE(v.size()==n_,
"vector of the wrong size " << v.size() <<
" instead of " << n_);
Array result(n_);
std::transform(diagonal_.begin(), diagonal_.end(),
v.begin(),
result.begin(),
std::multiplies<Real>());
// matricial product
result[0] += upperDiagonal_[0]*v[1];
for (Size j=1; j<=n_-2; j++)
result[j] += lowerDiagonal_[j-1]*v[j-1]+
upperDiagonal_[j]*v[j+1];
result[n_-1] += lowerDiagonal_[n_-2]*v[n_-2];
return result;
}
Disposable<Array> TridiagonalOperator::solveFor(const Array& rhs) const {
Array result(rhs.size());
solveFor(rhs, result);
return result;
}
void TridiagonalOperator::solveFor(const Array& rhs,
Array& result) const {
QL_REQUIRE(n_!=0,
"uninitialized TridiagonalOperator");
QL_REQUIRE(rhs.size()==n_,
"rhs vector of size " << rhs.size() <<
" instead of " << n_);
Real bet = diagonal_[0];
QL_REQUIRE(!close(bet, 0.0),
"diagonal's first element (" << bet <<
") cannot be close to zero");
result[0] = rhs[0]/bet;
for (Size j=1; j<=n_-1; ++j) {
temp_[j] = upperDiagonal_[j-1]/bet;
bet = diagonal_[j]-lowerDiagonal_[j-1]*temp_[j];
QL_ENSURE(!close(bet, 0.0), "division by zero");
result[j] = (rhs[j] - lowerDiagonal_[j-1]*result[j-1])/bet;
}
// cannot be j>=0 with Size j
for (Size j=n_-2; j>0; --j)
result[j] -= temp_[j+1]*result[j+1];
result[0] -= temp_[1]*result[1];
}
Disposable<Array> TridiagonalOperator::SOR(const Array& rhs,
Real tol) const {
QL_REQUIRE(n_!=0,
"uninitialized TridiagonalOperator");
QL_REQUIRE(rhs.size()==n_,
"rhs vector of size " << rhs.size() <<
" instead of " << n_);
// initial guess
Array result = rhs;
// solve tridiagonal system with SOR technique
Real omega = 1.5;
Real err = 2.0*tol;
Real temp;
for (Size sorIteration=0; err>tol ; ++sorIteration) {
QL_REQUIRE(sorIteration<100000,
"tolerance (" << tol << ") not reached in " <<
sorIteration << " iterations. " <<
"The error still is " << err);
temp = omega * (rhs[0] -
upperDiagonal_[0] * result[1]-
diagonal_[0] * result[0])/diagonal_[0];
err = temp*temp;
result[0] += temp;
Size i;
for (i=1; i<n_-1 ; ++i) {
temp = omega *(rhs[i] -
upperDiagonal_[i] * result[i+1]-
diagonal_[i] * result[i] -
lowerDiagonal_[i-1] * result[i-1])/diagonal_[i];
err += temp * temp;
result[i] += temp;
}
temp = omega * (rhs[i] -
diagonal_[i] * result[i] -
lowerDiagonal_[i-1] * result[i-1])/diagonal_[i];
err += temp*temp;
result[i] += temp;
}
return result;
}
Disposable<TridiagonalOperator>
TridiagonalOperator::identity(Size size) {
TridiagonalOperator I(Array(size-1, 0.0), // lower diagonal
Array(size, 1.0), // diagonal
Array(size-1, 0.0)); // upper diagonal
return I;
}
}
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