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85 lines
3.5 KiB
85 lines
3.5 KiB
#ifndef Magnum_Math_Algorithms_GramSchmidt_h |
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#define Magnum_Math_Algorithms_GramSchmidt_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 |
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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::gramSchmidtOrthogonalizeInPlace(), @ref Magnum::Math::Algorithms::gramSchmidtOrthogonalize(), @ref Magnum::Math::Algorithms::gramSchmidtOrthonormalizeInPlace(), @ref Magnum::Math::Algorithms::gramSchmidtOrthonormalize() |
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*/ |
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#include "Magnum/Math/RectangularMatrix.h" |
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namespace Magnum { namespace Math { namespace Algorithms { |
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/** |
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@brief In-place Gram-Schmidt matrix orthogonalization |
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@param[in,out] matrix %Matrix to perform orthogonalization on |
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*/ |
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template<std::size_t cols, std::size_t rows, class T> void gramSchmidtOrthogonalizeInPlace(RectangularMatrix<cols, rows, T>& matrix) { |
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static_assert(cols <= rows, "Unsupported matrix aspect ratio"); |
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for(std::size_t i = 0; i != cols; ++i) { |
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for(std::size_t j = i+1; j != cols; ++j) |
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matrix[j] -= matrix[j].projected(matrix[i]); |
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} |
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} |
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/** |
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@brief Gram-Schmidt matrix orthogonalization |
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Unlike @ref gramSchmidtOrthogonalizeInPlace() returns the modified matrix |
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instead of performing the orthogonalization in-place. |
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*/ |
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template<std::size_t cols, std::size_t rows, class T> RectangularMatrix<cols, rows, T> gramSchmidtOrthogonalize(RectangularMatrix<cols, rows, T> matrix) { |
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gramSchmidtOrthogonalizeInPlace(matrix); |
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return matrix; |
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} |
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/** |
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@brief In-place Gram-Schmidt matrix orthonormalization |
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@param[in,out] matrix %Matrix to perform orthonormalization on |
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*/ |
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template<std::size_t cols, std::size_t rows, class T> void gramSchmidtOrthonormalizeInPlace(RectangularMatrix<cols, rows, T>& matrix) { |
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static_assert(cols <= rows, "Unsupported matrix aspect ratio"); |
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for(std::size_t i = 0; i != cols; ++i) { |
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matrix[i] = matrix[i].normalized(); |
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for(std::size_t j = i+1; j != cols; ++j) |
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matrix[j] -= matrix[j].projectedOntoNormalized(matrix[i]); |
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} |
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} |
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/** |
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@brief Gram-Schmidt matrix orthonormalization |
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Unlike @ref gramSchmidtOrthonormalizeInPlace() returns the modified matrix |
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instead of performing the orthonormalization in-place. |
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*/ |
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template<std::size_t cols, std::size_t rows, class T> RectangularMatrix<cols, rows, T> gramSchmidtOrthonormalize(RectangularMatrix<cols, rows, T> matrix) { |
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gramSchmidtOrthonormalizeInPlace(matrix); |
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return matrix; |
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} |
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}}} |
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#endif
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