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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2024 Klaus Spanderen
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
<https://www.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/householder.hpp>
namespace QuantLib {
HouseholderTransformation::HouseholderTransformation(Array v)
: v_(std::move(v)) {}
Array HouseholderTransformation::operator()(const Array& x) const {
return x - (2.0*DotProduct(v_, x))*v_;
}
Matrix HouseholderTransformation::getMatrix() const {
const Array y = v_ / Norm2(v_);
const Size n = y.size();
Matrix m(n, n);
for (Size i=0; i < n; ++i)
for (Size j=0; j < n; ++j)
m[i][j] = ((i == j)? 1.0: 0.0) - 2*y[i]*y[j];
return m;
}
HouseholderReflection::HouseholderReflection(Array e)
: e_(std::move(e)) {}
Array HouseholderReflection::reflectionVector(const Array& a) const {
const Real na = Norm2(a);
QL_REQUIRE(na > 0, "vector of length zero given");
const Real aDotE = DotProduct(a, e_);
const Array a1 = aDotE*e_;
const Array a2 = a - a1;
const Real eps = DotProduct(a2, a2) / (aDotE*aDotE);
if (eps < QL_EPSILON*QL_EPSILON) {
return Array(a.size(), 0.0);
}
else if (eps < 1e-4) {
const Real eps2 = eps*eps;
const Real eps3 = eps*eps2;
const Real eps4 = eps2*eps2;
const Array v =
(a2 - a1*(eps/2.0 - eps2/8.0 + eps3/16.0 - 5/128.0*eps4))
/ (aDotE*std::sqrt(eps + eps2/4.0 - eps3/8.0 + 5/64.0*eps4));
return v;
}
else {
const Array c = a - na*e_;
return c / Norm2(c);
}
}
Array HouseholderReflection::operator()(const Array& a) const {
const Array v = reflectionVector(a);
return HouseholderTransformation(v)(a);
}
}
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