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60 lines
2.0 KiB
60 lines
2.0 KiB
10 years ago
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#ifndef Magnum_Math_Algorithms_Qr_h
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#define Magnum_Math_Algorithms_Qr_h
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/*
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This file is part of Magnum.
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Copyright © 2010, 2011, 2012, 2013, 2014, 2015, 2016
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Vladimír Vondruš <mosra@centrum.cz>
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Permission is hereby granted, free of charge, to any person obtaining a
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copy of this software and associated documentation files (the "Software"),
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to deal in the Software without restriction, including without limitation
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the rights to use, copy, modify, merge, publish, distribute, sublicense,
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and/or sell copies of the Software, and to permit persons to whom the
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Software is furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included
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in all copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
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THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
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DEALINGS IN THE SOFTWARE.
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*/
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/** @file
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* @brief Function @ref Magnum::Math::Algorithms::qr()
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*/
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#include "Magnum/Math/Matrix.h"
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namespace Magnum { namespace Math { namespace Algorithms {
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/**
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@brief QR decomposition
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Calculated using classic Gram-Schmidt process.
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*/
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template<std::size_t size, class T> std::pair<Matrix<size, T>, Matrix<size, T>> qr(const Matrix<size, T>& matrix) {
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Matrix<size, T> q, r;
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for(std::size_t k = 0; k != size; ++k) {
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Vector<size, T> p = matrix[k];
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for(std::size_t j = 0; j != k; ++j) {
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r[k][j] = Math::dot(p, q[j]);
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p -= q[j]*r[k][j];
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}
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r[k][k] = p.length();
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q[k] = p/r[k][k];
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}
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return {q, r};
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}
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}}}
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#endif
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