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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 matrix.cpp
\brief matrix used in linear algebra.
\fullpath
ql/Math/%matrix.cpp
*/
// $Id: matrix.cpp,v 1.8 2002/01/16 14:42:29 nando Exp $
#include <ql/Math/symmetricschurdecomposition.hpp>
#include <ql/dataformatters.hpp>
namespace QuantLib {
namespace Math {
Matrix matrixSqrt(const Matrix &realSymmMatrix) {
//! eigenvalues smaller than tolerance are considered zero
const double tolerance = 1e-15;
Matrix inputMatrix(realSymmMatrix);
Size size = inputMatrix.rows();
QL_REQUIRE(size == inputMatrix.columns(),
"sqrt input matrix must be square");
SymmetricSchurDecomposition jd(inputMatrix);
Matrix evectors(jd.eigenvectors());
Array evalues(jd.eigenvalues());
double maxEv=0;
Size i;
for(i = 0; i < size;i++)
if(evalues[i] >= maxEv)
maxEv = evalues[i];
Matrix diagonal(size,size,0);
for(i = 0; i < size;i++){
if(QL_FABS(evalues[i]) <= tolerance*maxEv)
evalues[i] = 0;
QL_ENSURE(evalues[i] >=0,
"sqrt: some eigenvalues("+
IntegerFormatter::toString(i) + ") = " +
DoubleFormatter::toString(evalues[i]) +
" are negative!");
diagonal[i][i] = QL_SQRT(evalues[i]);
}
Matrix result(evectors * diagonal * transpose(evectors));
return result;
}
}
}
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