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/*
Copyright (C) 2002 Ferdinando Ametrano
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 tridiagonaloperator.cpp
\brief tridiagonal operator
\fullpath
ql/FiniteDifferences/%tridiagonaloperator.cpp
*/
// $Id: tridiagonaloperator.cpp,v 1.13 2002/02/26 12:15:54 nando Exp $
#include <ql/FiniteDifferences/tridiagonaloperator.hpp>
#include <ql/dataformatters.hpp>
#include <iostream>
namespace QuantLib {
namespace FiniteDifferences {
TridiagonalOperator::TridiagonalOperator(
Size size) {
if (size>=3) {
diagonal_ = Array(size);
belowDiagonal_ = Array(size-1);
aboveDiagonal_ = Array(size-1);
} else if (size==0) {
diagonal_ = Array(0);
belowDiagonal_ = Array(0);
aboveDiagonal_ = Array(0);
} else {
throw Error("invalid size for tridiagonal operator "
"(must be null or >= 3)");
}
}
TridiagonalOperator::TridiagonalOperator(
const Array& low, const Array& mid, const Array& high)
: diagonal_(mid), belowDiagonal_(low), aboveDiagonal_(high) {
QL_ENSURE(low.size() == mid.size()-1,
"wrong size for lower diagonal vector");
QL_ENSURE(high.size() == mid.size()-1,
"wrong size for upper diagonal vector");
}
void TridiagonalOperator::setLowerBC(
const BoundaryCondition& bc) {
lowerBC_ = bc;
switch (lowerBC_.type()) {
case BoundaryCondition::None:
// does nothing
break;
case BoundaryCondition::Neumann:
setFirstRow(-1.0,1.0);
break;
case BoundaryCondition::Dirichlet:
setFirstRow(1.0,0.0);
break;
}
}
void TridiagonalOperator::setUpperBC(
const BoundaryCondition& bc) {
upperBC_ = bc;
switch (upperBC_.type()) {
case BoundaryCondition::None:
// does nothing
break;
case BoundaryCondition::Neumann:
setLastRow(-1.0,1.0);
break;
case BoundaryCondition::Dirichlet:
setLastRow(0.0,1.0);
break;
}
}
Array TridiagonalOperator::applyTo(const Array& v) const {
QL_REQUIRE(v.size()==size(),
"TridiagonalOperator::applyTo: vector of the wrong size (" +
IntegerFormatter::toString(v.size()) + "instead of " +
IntegerFormatter::toString(size()) + ")" );
Array result(size());
// matricial product
result[0] = diagonal_[0]*v[0] + aboveDiagonal_[0]*v[1];
for (Size j=1;j<=size()-2;j++)
result[j] = belowDiagonal_[j-1]*v[j-1]+ diagonal_[j]*v[j] +
aboveDiagonal_[j]*v[j+1];
result[size()-1] = belowDiagonal_[size()-2]*v[size()-2] +
diagonal_[size()-1]*v[size()-1];
// apply lower boundary condition
switch (lowerBC_.type()) {
case BoundaryCondition::None:
// does nothing
break;
case BoundaryCondition::Neumann:
result[0] = result[1] - lowerBC_.value();
break;
case BoundaryCondition::Dirichlet:
result[0] = lowerBC_.value();
break;
}
// apply upper boundary condition
switch (upperBC_.type()) {
case BoundaryCondition::None:
// does nothing
break;
case BoundaryCondition::Neumann:
result[size()-1] = result[size()-2] + upperBC_.value();
break;
case BoundaryCondition::Dirichlet:
result[size()-1] = upperBC_.value();
break;
}
return result;
}
Array TridiagonalOperator::solveFor(const Array& rhs) const {
QL_REQUIRE(rhs.size()==size(),
"TridiagonalOperator::solveFor: rhs has the wrong size");
Array bcRhs = rhs;
// apply lower boundary condition
switch (lowerBC_.type()) {
case BoundaryCondition::None:
// does nothing
break;
case BoundaryCondition::Neumann:
case BoundaryCondition::Dirichlet:
bcRhs[0] = lowerBC_.value();
break;
}
// apply upper boundary condition
switch (upperBC_.type()) {
case BoundaryCondition::None:
// does nothing
break;
case BoundaryCondition::Neumann:
case BoundaryCondition::Dirichlet:
bcRhs[size()-1] = upperBC_.value();
break;
}
// solve tridiagonal system
Array result(size()), tmp(size());
double bet=diagonal_[0];
QL_REQUIRE(bet != 0.0,
"TridiagonalOperator::solveFor: division by zero");
result[0] = bcRhs[0]/bet;
Size j;
for (j=1;j<=size()-1;j++){
tmp[j]=aboveDiagonal_[j-1]/bet;
bet=diagonal_[j]-belowDiagonal_[j-1]*tmp[j];
QL_ENSURE(bet != 0.0,
"TridiagonalOperator::solveFor: division by zero");
result[j] = (bcRhs[j]-belowDiagonal_[j-1]*result[j-1])/bet;
}
// cannot be j>=0 with Size j
for (j=size()-2;j>0;j--)
result[j] -= tmp[j+1]*result[j+1];
result[0] -= tmp[1]*result[1];
return result;
}
Array TridiagonalOperator::SOR(const Array& rhs, double tol) const {
QL_REQUIRE(rhs.size()==size(),
"TridiagonalOperator::solveFor: rhs has the wrong size");
// initial guess
Array result = rhs;
// apply lower boundary condition
switch (lowerBC_.type()) {
case BoundaryCondition::None:
// does nothing
break;
case BoundaryCondition::Neumann:
case BoundaryCondition::Dirichlet:
result[0] = lowerBC_.value();
break;
}
// apply upper boundary condition
switch (upperBC_.type()) {
case BoundaryCondition::None:
// does nothing
break;
case BoundaryCondition::Neumann:
case BoundaryCondition::Dirichlet:
result[size()-1] = upperBC_.value();
break;
}
// solve tridiagonal system with SOR technique
Size sorIteration, i;
double omega = 1.5;
double err=2.0*tol;
double temp;
for (sorIteration=0; err>tol ; sorIteration++) {
QL_REQUIRE(sorIteration<100000,
"TridiagonalOperator::SOR: tolerance ["
+ DoubleFormatter::toString(tol) +
"] not reached in "
+ IntegerFormatter::toString(sorIteration) +
" iterations. The error still is "
+ DoubleFormatter::toString(err));
err=0.0;
for (i=1; i<size()-2 ; i++) {
temp = omega * (rhs[i] -
aboveDiagonal_[i] * result[i+1]-
diagonal_[i] * result[i] -
belowDiagonal_[i-1] * result[i-1]) / diagonal_[i];
err += temp * temp;
result[i] += temp;
}
}
return result;
}
TridiagonalOperator TridiagonalOperator::identity(Size size){
return TridiagonalOperator(
Array(size-1, 0.0), // lower diagonal
Array(size, 1.0), // diagonal
Array(size-1, 0.0)); // upper diagonal
}
}
}
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