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75 lines
2.8 KiB
75 lines
2.8 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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Copyright © 2010, 2011, 2012 Vladimír Vondruš <mosra@centrum.cz> |
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This file is part of Magnum. |
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Magnum is free software: you can redistribute it and/or modify |
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it under the terms of the GNU Lesser General Public License version 3 |
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only, as published by the Free Software Foundation. |
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Magnum is distributed in the hope that it will be useful, |
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but WITHOUT ANY WARRANTY; without even the implied warranty of |
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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GNU Lesser General Public License version 3 for more details. |
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*/ |
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/** @file |
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* @brief Function Magnum::Math::Algorithms::gramSchmidtOrthogonalizeInPlace(), Magnum::Math::Algorithms::gramSchmidtOrthogonalize(), Magnum::Math::Algorithms::gramSchmidtOrthonormalizeInPlace(), Magnum::Math::Algorithms::gramSchmidtOrthonormalize() |
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*/ |
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#include "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 gramSchmidtOrthogonalizeInPlace() returns the modified matrix instead |
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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 gramSchmidtOrthonormalizeInPlace() returns the modified matrix instead |
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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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