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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 symmetricschurdecomposition.cpp
\brief Eigenvalues / eigenvectors of a real symmetric matrix
\fullpath
ql/Math/%symmetricschurdecomposition.cpp
*/
// $Id: symmetricschurdecomposition.cpp,v 1.6 2002/01/16 14:42:29 nando Exp $
/*
Note: because of the many levels of indentation required,
only 2 spaces are used for each indentation
*/
#include <ql/Math/symmetricschurdecomposition.hpp>
namespace QuantLib {
namespace Math {
SymmetricSchurDecomposition::SymmetricSchurDecomposition(Matrix & s)
: s_(s), size_(s.rows()), diagonal_(s.rows()),
eigenVectors_(s.rows(),s.columns(),0), hasBeenComputed_(false),
maxIterations_(100), epsPrec_(1e-15) {
QL_REQUIRE(s.rows() == s.columns(),
"SymmetricSchurDecomposition: input matrix must be square");
for(int ite = 0; ite < size_; ite++){
diagonal_[ite] = s[ite][ite];
eigenVectors_[ite][ite] = 1.0;
}
}
void SymmetricSchurDecomposition::compute() const{
double threshold;
Array tmpDiag(diagonal_);
Array tmpAccumulate(size_,0);
Matrix s(s_);
bool keeplooping = true;
int ite = 1;
do{ //main loop
double sum = 0;
for (int j = 0; j < size_-1; j++) {
for (int k = j + 1; k < size_; k++){
sum += QL_FABS(s[j][k]);
}
}
if (sum == 0){
keeplooping = false;
}
else{
/*! To speed up computation a threshold is introduced to
make sure it is worthy to perform the Jacobi rotation
*/
if (ite < 5)
threshold = 0.2*sum/(size_*size_);
else
threshold = 0;
int j;
for (j = 0; j < size_-1; j++) {
for (int k = j+1; k < size_; k++) {
double sine,rho,cosin,heig,tang,beta;
double smll = QL_FABS(s[j][k]);
if( ite > 5 &&
smll < epsPrec_ * QL_FABS(diagonal_[j]) &&
smll < epsPrec_ * QL_FABS(diagonal_[k]))
s[j][k] = 0;
else if (QL_FABS(s[j][k]) > threshold) {
heig = diagonal_[k]-diagonal_[j];
if ( smll < epsPrec_ * QL_FABS(heig) )
tang = s[j][k]/heig;
else {
beta = 0.5*heig/s[j][k];
tang = 1/(QL_FABS(beta)+QL_SQRT(1+beta*beta));
if(beta < 0) tang = -tang;
}
cosin = 1/QL_SQRT(1+tang*tang);
sine = tang*cosin;
rho = sine/(1+cosin);
heig=tang*s[j][k];
tmpAccumulate[j] -= heig;
tmpAccumulate[k] += heig;
diagonal_[j] -= heig;
diagonal_[k] += heig;
s[j][k] = 0;
int l;
for (l = 0; l <= j-1; l++) {
jacobiRotate(s,rho,sine,l,j,l,k);
}
for (l = j+1; l <= k-1; l++) {
jacobiRotate(s,rho,sine,j,l,l,k);
}
for (l = k+1; l < size_; l++) {
jacobiRotate(s,rho,sine,j,l,k,l);
}
for (l = 0; l < size_; l++) {
jacobiRotate(eigenVectors_,rho,sine,l,j,l,k);
}
}
}
}
for (j = 0; j < size_; j++) {
tmpDiag[j] += tmpAccumulate[j];
diagonal_[j] = tmpDiag[j];
tmpAccumulate[j] = 0;
}
}
}while(++ite <= maxIterations_ && keeplooping);
QL_REQUIRE(ite <= maxIterations_,
"SymmetricSchurDecomposition::compute: Too many iterations reached");
hasBeenComputed_ = true;
}// end of method compute
}
}
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