/usr/include/ql/math/generallinearleastsquares.hpp is in libquantlib0-dev 1.7.1-1.
This file is owned by root:root, with mode 0o644.
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/*
Copyright (C) 2009 Dirk Eddelbuettel
Copyright (C) 2006, 2009, 2010 Klaus Spanderen
Copyright (C) 2010 Kakhkhor Abdijalilov
Copyright (C) 2010 Slava Mazur
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.
*/
/*! \file linearleastsquaresregression.hpp
\brief general linear least square regression
*/
#ifndef quantlib_general_linear_least_squares_hpp
#define quantlib_general_linear_least_squares_hpp
#include <ql/qldefines.hpp>
#include <ql/math/matrixutilities/svd.hpp>
#include <ql/math/array.hpp>
#include <ql/math/functional.hpp>
#include <boost/function.hpp>
#include <boost/type_traits.hpp>
#include <vector>
namespace QuantLib {
//! general linear least squares regression
/*! References:
"Numerical Recipes in C", 2nd edition,
Press, Teukolsky, Vetterling, Flannery,
\test the correctness of the returned values is tested by
checking their properties.
*/
class GeneralLinearLeastSquares {
public:
template <class xContainer, class yContainer, class vContainer>
GeneralLinearLeastSquares(const xContainer & x,
const yContainer &y, const vContainer & v);
template<class xIterator, class yIterator, class vIterator>
GeneralLinearLeastSquares(xIterator xBegin, xIterator xEnd,
yIterator yBegin, yIterator yEnd,
vIterator vBegin, vIterator vEnd);
const Array& coefficients() const { return a_; }
const Array& residuals() const { return residuals_; }
//! standard parameter errors as given by Excel, R etc.
const Array& standardErrors() const { return standardErrors_; }
//! modeling uncertainty as definied in Numerical Recipes
const Array& error() const { return err_;}
Size size() const { return residuals_.size(); }
Size dim() const { return a_.size(); }
protected:
Array a_, err_, residuals_, standardErrors_;
template <class xIterator, class yIterator, class vIterator>
void calculate(
xIterator xBegin, xIterator xEnd,
yIterator yBegin, yIterator yEnd,
vIterator vBegin, vIterator vEnd);
};
template <class xContainer, class yContainer, class vContainer> inline
GeneralLinearLeastSquares::GeneralLinearLeastSquares(const xContainer & x,
const yContainer &y,
const vContainer & v)
: a_(v.size(), 0.0),
err_(v.size(), 0.0),
residuals_(y.size()),
standardErrors_(v.size()) {
calculate(x.begin(), x.end(), y.begin(), y.end(), v.begin(), v.end());
}
template<class xIterator, class yIterator, class vIterator> inline
GeneralLinearLeastSquares::GeneralLinearLeastSquares(
xIterator xBegin, xIterator xEnd,
yIterator yBegin, yIterator yEnd,
vIterator vBegin, vIterator vEnd)
: a_(std::distance(vBegin, vEnd), 0.0),
err_(a_.size(), 0.0),
residuals_(std::distance(yBegin, yEnd)),
standardErrors_(a_.size()) {
calculate(xBegin, xEnd, yBegin, yEnd, vBegin, vEnd);
}
template <class xIterator, class yIterator, class vIterator>
void GeneralLinearLeastSquares::calculate(xIterator xBegin, xIterator xEnd,
yIterator yBegin, yIterator yEnd,
vIterator vBegin, vIterator vEnd) {
const Size n = residuals_.size();
const Size m = err_.size();
QL_REQUIRE( n == Size(std::distance(yBegin, yEnd)),
"sample set need to be of the same size");
QL_REQUIRE(n >= m, "sample set is too small");
Size i;
Matrix A(n, m);
for (i=0; i<m; ++i)
std::transform(xBegin, xEnd, A.column_begin(i), *vBegin++);
const SVD svd(A);
const Matrix& V = svd.V();
const Matrix& U = svd.U();
const Array& w = svd.singularValues();
const Real threshold = n*QL_EPSILON;
for (i=0; i<m; ++i) {
if (w[i] > threshold) {
const Real u = std::inner_product(U.column_begin(i),
U.column_end(i),
yBegin, 0.0)/w[i];
for (Size j=0; j<m; ++j) {
a_[j] +=u*V[j][i];
err_[j]+=V[j][i]*V[j][i]/(w[i]*w[i]);
}
}
}
err_ = Sqrt(err_);
Array tmp = A*a_;
std::transform(tmp.begin(), tmp.end(),
yBegin, residuals_.begin(), std::minus<Real>());
const Real chiSq
= std::inner_product(residuals_.begin(), residuals_.end(),
residuals_.begin(), 0.0);
std::transform(err_.begin(), err_.end(), standardErrors_.begin(),
std::bind1st(std::multiplies<Real>(),
std::sqrt(chiSq/(n-2))));
}
}
#endif
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