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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2007, 2008 Mark Joshi
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/math/matrixutilities/basisincompleteordered.hpp>
#include <algorithm>
namespace QuantLib {
BasisIncompleteOrdered::BasisIncompleteOrdered(Size euclideanDimension)
: euclideanDimension_(euclideanDimension) {}
bool BasisIncompleteOrdered::addVector(const Array& newVector1) {
QL_REQUIRE(newVector1.size() == euclideanDimension_,
"missized vector passed to "
"BasisIncompleteOrdered::addVector");
newVector_ = newVector1;
if (currentBasis_.size()==euclideanDimension_)
return false;
for (Size j=0; j<currentBasis_.size(); ++j) {
Real innerProd = std::inner_product(newVector_.begin(),
newVector_.end(),
currentBasis_[j].begin(), 0.0);
for (Size k=0; k<euclideanDimension_; ++k)
newVector_[k] -=innerProd*currentBasis_[j][k];
}
Real norm = std::sqrt(std::inner_product(newVector_.begin(),
newVector_.end(),
newVector_.begin(), 0.0));
if (norm<1e-12) // maybe this should be a tolerance
return false;
for (Size l=0; l<euclideanDimension_; ++l)
newVector_[l]/=norm;
currentBasis_.push_back(newVector_);
return true;
}
Size BasisIncompleteOrdered::basisSize() const {
return currentBasis_.size();
}
Size BasisIncompleteOrdered::euclideanDimension() const {
return euclideanDimension_;
}
Matrix BasisIncompleteOrdered::getBasisAsRowsInMatrix() const {
Matrix basis(currentBasis_.size(), euclideanDimension_);
for (Size i=0; i<basis.rows(); ++i)
for (Size j=0; j<basis.columns(); ++j)
basis[i][j] = currentBasis_[i][j];
return basis;
}
namespace
{
Real normSquared(const Matrix& v, Size row)
{
Real x=0.0;
for (Size i=0; i < v.columns(); ++i)
x += v[row][i]*v[row][i];
return x;
}
Real norm(const Matrix& v, Size row)
{
return std::sqrt(normSquared( v, row));
}
Real innerProduct(const Matrix& v, Size row1, const Matrix& w, Size row2)
{
Real x=0.0;
for (Size i=0; i < v.columns(); ++i)
x += v[row1][i]*w[row2][i];
return x;
}
}
OrthogonalProjections::OrthogonalProjections(const Matrix& originalVectors,
Real multiplierCutoff,
Real tolerance)
: originalVectors_(originalVectors),
multiplierCutoff_(multiplierCutoff),
numberVectors_(originalVectors.rows()),
dimension_(originalVectors.columns()),
validVectors_(true,originalVectors.rows()), // opposite way round from vector constructor
orthoNormalizedVectors_(originalVectors.rows(),
originalVectors.columns())
{
std::vector<Real> currentVector(dimension_);
for (Size j=0; j < numberVectors_; ++j)
{
if (validVectors_[j])
{
for (Size k=0; k< numberVectors_; ++k) // create an orthormal basis not containing j
{
for (Size m=0; m < dimension_; ++m)
orthoNormalizedVectors_[k][m] = originalVectors_[k][m];
if ( k !=j && validVectors_[k])
{
for (Size l=0; l < k; ++l)
{
if (validVectors_[l] && l !=j)
{
Real dotProduct = innerProduct(orthoNormalizedVectors_, k, orthoNormalizedVectors_,l);
for (Size n=0; n < dimension_; ++n)
orthoNormalizedVectors_[k][n] -= dotProduct*orthoNormalizedVectors_[l][n];
}
}
Real normBeforeScaling= norm(orthoNormalizedVectors_,k);
if (normBeforeScaling < tolerance)
{
validVectors_[k] = false;
}
else
{
Real normBeforeScalingRecip = 1.0/normBeforeScaling;
for (Size m=0; m < dimension_; ++m)
orthoNormalizedVectors_[k][m] *= normBeforeScalingRecip;
} // end of else (norm < tolerance)
} // end of if k !=j && validVectors_[k])
}// end of for (Size k=0; k< numberVectors_; ++k)
// we now have an o.n. basis for everything except j
Real prevNormSquared = normSquared(originalVectors_, j);
for (Size r=0; r < numberVectors_; ++r)
if (validVectors_[r] && r != j)
{
Real dotProduct = innerProduct(orthoNormalizedVectors_, j, orthoNormalizedVectors_,r);
for (Size s=0; s < dimension_; ++s)
orthoNormalizedVectors_[j][s] -= dotProduct*orthoNormalizedVectors_[r][s];
}
Real projectionOnOriginalDirection = innerProduct(originalVectors_,j,orthoNormalizedVectors_,j);
Real sizeMultiplier = prevNormSquared/projectionOnOriginalDirection;
if (std::fabs(sizeMultiplier) < multiplierCutoff_)
{
for (Size t=0; t < dimension_; ++t)
currentVector[t] = orthoNormalizedVectors_[j][t]*sizeMultiplier;
}
else
validVectors_[j] = false;
} // end of if (validVectors_[j])
projectedVectors_.push_back(currentVector);
} //end of j loop
numberValidVectors_ =0;
for (Size i=0; i < numberVectors_; ++i)
numberValidVectors_ += validVectors_[i] ? 1 : 0;
} // end of constructor
const std::valarray<bool>& OrthogonalProjections::validVectors() const
{
return validVectors_;
}
const std::vector<Real>& OrthogonalProjections::GetVector(Size index) const
{
return projectedVectors_[index];
}
Size OrthogonalProjections::numberValidVectors() const
{
return numberValidVectors_;
}
}
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