487 lines
18 KiB
C++
487 lines
18 KiB
C++
/*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*
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* Copyright 2011-2015 Danny Robson <danny@nerdcruft.net>
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*/
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#ifndef __UTIL_MATRIX_HPP
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#define __UTIL_MATRIX_HPP
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#include "point.hpp"
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#include "range.hpp"
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#include "vector.hpp"
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#include "iterator.hpp"
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#include <cstdlib>
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#include <ostream>
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namespace util {
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template <
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std::size_t Rows,
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std::size_t Cols,
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typename T
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>
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struct matrix {
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static constexpr auto rows = Rows;
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static constexpr auto cols = Cols;
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using row_t = util::vector<Cols,T>;
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///////////////////////////////////////////////////////////////////////
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constexpr matrix () noexcept = default;
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//---------------------------------------------------------------------
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constexpr matrix (const T(&_data)[Rows][Cols]) noexcept:
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values {}
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{
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static_assert (sizeof (*this) == sizeof (T) * Rows * Cols);
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for (std::size_t r = 0; r < Rows; ++r)
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for (std::size_t c = 0; c < Cols; ++c)
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values[r][c] = _data[r][c];
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}
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//---------------------------------------------------------------------
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template <std::size_t S, typename SelfT>
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constexpr matrix (const util::coord::base<S,T,SelfT> (&_data)[Rows]) noexcept
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{
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for (std::size_t r = 0; r < Rows; ++r)
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for (std::size_t c = 0; c < Cols; ++c)
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values[r][c] = _data[r][c];
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}
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///////////////////////////////////////////////////////////////////////
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// index operators return a pointer into the data array so that
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// multidimensional array syntax can be used transparently on this
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// type.
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constexpr row_t& operator[] (std::size_t idx)& { return values[idx]; }
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constexpr const row_t& operator[] (std::size_t idx) const& { return values[idx]; }
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//---------------------------------------------------------------------
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constexpr row_t*
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data (void)& noexcept
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{
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return &values[0];
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}
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//---------------------------------------------------------------------
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constexpr const row_t*
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data (void) const& noexcept
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{
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return &values[0];
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}
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//---------------------------------------------------------------------
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constexpr auto
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begin (void) const& noexcept
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{
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return data ();
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}
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//---------------------------------------------------------------------
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constexpr auto
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begin (void)& noexcept
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{
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return data ();
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}
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//---------------------------------------------------------------------
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constexpr row_t*
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end (void)& noexcept
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{
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return &values[Rows];
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}
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//---------------------------------------------------------------------
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constexpr const row_t*
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end (void) const& noexcept
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{
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return &values[Rows];
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}
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//---------------------------------------------------------------------
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constexpr auto
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cbegin (void) const& noexcept
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{
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return begin ();
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}
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//---------------------------------------------------------------------
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constexpr auto
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cend (void) const& noexcept
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{
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return end ();
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}
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///////////////////////////////////////////////////////////////////////
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T determinant (void) const;
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matrix inverse (void) const;
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matrix
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inverse_affine (void) const
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{
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// TODO: ensure we have specialisations for typical dimensions
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return inverse ();
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}
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template <typename VectorT>
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std::enable_if_t<is_coord_v<VectorT>, VectorT>
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operator* (const VectorT &rhs) const
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{
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VectorT out;
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for (std::size_t r = 0; r < Rows; ++r)
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out[r] = dot (rhs, values[r]);
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return out;
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}
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bool is_affine (void) const;
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template <typename U>
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matrix<Rows,Cols,U>
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cast (void) const noexcept
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{
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matrix out;
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std::copy (cbegin (), cend (), std::begin (out));
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return out;
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}
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// Constant matrices
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static constexpr
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matrix identity (void) noexcept
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{
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auto m = zeroes ();
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for (std::size_t i = 0; i < Rows; ++i)
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m[i][i] = 1;
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return m;
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}
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static constexpr
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matrix zeroes (void) noexcept
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{
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matrix ret {};
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std::fill (std::begin (ret), std::end (ret), row_t{0});
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return ret;
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}
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private:
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row_t values[Rows];
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};
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// Perspective matrices
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template <typename T> matrix<4,4,T> ortho (T left, T right, T bottom, T top, T near, T far);
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template <typename T> matrix<4,4,T> ortho2D (T left, T right, T bottom, T top);
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template <typename T> matrix<4,4,T> perspective (T fov, T aspect, range<T> Z);
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template <typename T> matrix<4,4,T> look_at (point<3,T> eye, point<3,T> target, vector<3,T> up);
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// Affine matrices
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template <typename T> matrix<4,4,T> translation (vector<3,T>);
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template <typename T> matrix<4,4,T> scale (vector<3,T>);
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template <typename T> matrix<4,4,T> scale (T);
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template <typename T> matrix<4,4,T> rotation (T angle, vector<3,T> about);
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///////////////////////////////////////////////////////////////////////////
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// Convert an affine rotation matrix to euler angles.
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//
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// Results are undefined if the matrix is not purely a rotation matrix,
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// or if the dimension is not 3x3 or 4x4.
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template <std::size_t Rows, std::size_t Cols, typename T>
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vector<3,T>
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to_euler (const matrix<Rows, Cols, T>&);
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///////////////////////////////////////////////////////////////////////////
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// logical operations
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template <std::size_t Rows, std::size_t Cols, typename T>
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constexpr
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bool
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operator== (const matrix<Rows,Cols,T> &a, const matrix<Rows,Cols,T> &b)
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{
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return std::equal (std::cbegin (a), std::cend (a), std::cbegin (b));
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}
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//-------------------------------------------------------------------------
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template <std::size_t Rows, std::size_t Cols, typename T>
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constexpr
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bool
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operator!= (const matrix<Rows,Cols,T> &a, const matrix<Rows,Cols,T> &b)
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{
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return !(a == b);
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}
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///////////////////////////////////////////////////////////////////////////
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// element operations
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template <std::size_t Rows, std::size_t Cols, typename T>
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constexpr
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matrix<Rows,Cols,T>
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operator+ (const matrix<Rows,Cols,T>&, const matrix<Rows,Cols,T>&);
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template <std::size_t Rows, std::size_t Cols, typename T>
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constexpr
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matrix<Rows,Cols,T>
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operator- (const matrix<Rows,Cols,T>&, const matrix<Rows,Cols,T>&);
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template <std::size_t Rows, std::size_t Cols, typename T>
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constexpr
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matrix<Rows,Cols,T>
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div (const matrix<Rows,Cols,T> &a, const matrix<Rows,Cols,T> &b)
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{
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matrix<Rows,Cols,T> out {};
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for (std::size_t r = 0; r < Rows; ++r)
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for (std::size_t c = 0; c < Cols; ++c)
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out[r][c] = a[r][c] / b[r][c];
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return out;
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}
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template <std::size_t Rows, std::size_t Cols, typename T>
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constexpr T
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max (const matrix<Rows,Cols,T> &m)
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{
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T val = m[0][0];
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for (std::size_t r = 0; r < Rows; ++r)
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for (std::size_t c = 0; c < Cols; ++c)
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val = max (val, m[r][c]);
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return val;
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}
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///////////////////////////////////////////////////////////////////////////
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// scalar operations
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template <std::size_t R, std::size_t C, typename T> constexpr matrix<R,C,T> operator* (const matrix<R,C,T>&, T);
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template <std::size_t R, std::size_t C, typename T> constexpr matrix<R,C,T> operator/ (const matrix<R,C,T>&, T);
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template <std::size_t R, std::size_t C, typename T> constexpr matrix<R,C,T> operator+ (const matrix<R,C,T>&, T);
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template <std::size_t R, std::size_t C, typename T> constexpr matrix<R,C,T> operator- (const matrix<R,C,T>&, T);
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template <std::size_t R, std::size_t C, typename T> constexpr matrix<R,C,T> operator* (T, const matrix<R,C,T>&);
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template <std::size_t R, std::size_t C, typename T> constexpr matrix<R,C,T> operator/ (T, const matrix<R,C,T>&);
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template <std::size_t R, std::size_t C, typename T> constexpr matrix<R,C,T> operator+ (T, const matrix<R,C,T>&);
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template <std::size_t R, std::size_t C, typename T> constexpr matrix<R,C,T> operator- (T, const matrix<R,C,T>&);
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template <std::size_t R, std::size_t C, typename T> constexpr matrix<R,C,T>& operator*= (matrix<R,C,T>&, T);
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template <std::size_t R, std::size_t C, typename T> constexpr matrix<R,C,T>& operator/= (matrix<R,C,T>&, T);
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template <std::size_t R, std::size_t C, typename T> constexpr matrix<R,C,T>& operator+= (matrix<R,C,T>&, T);
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template <std::size_t R, std::size_t C, typename T> constexpr matrix<R,C,T>& operator-= (matrix<R,C,T>&, T);
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///////////////////////////////////////////////////////////////////////////
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// matrix operations
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template <
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std::size_t R1, //int C1,
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std::size_t RC, //int R2,
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std::size_t C2,
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typename T
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>
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constexpr
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matrix<R1,C2,T>
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operator* (const matrix<R1,RC,T>&a, const matrix<RC,C2,T>&b)
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{
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matrix<R1,C2,T> res {};
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// TODO: iterating over r,c rather than c,r will cause an ICE with
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// clang#xxxx: 'X86 DAG->DAG Instruction Selection'.
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//
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// this is likely related to gold and LTO support. for the time being
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// we switch the orders because it appears to confuse the optimiser
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// sufficiently. :(
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for (std::size_t c = 0; c < C2; ++c) {
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for (std::size_t r = 0; r < R1; ++r) {
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T accum {0};
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for (std::size_t i = 0; i < RC; ++i)
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accum += a[r][i] * b[i][c];
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res[r][c] = accum;
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}
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}
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return res;
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}
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//-------------------------------------------------------------------------
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template <
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std::size_t R1, std::size_t C1,
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std::size_t R2, std::size_t C2,
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typename T
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>
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constexpr
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matrix<R1,C2,T>&
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operator*= (matrix<R1,C1,T> &a, const matrix<R2,C2,T> &b)
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{ return a = a * b; };
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///////////////////////////////////////////////////////////////////////////
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template <std::size_t Rows, std::size_t Cols, typename T>
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T
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determinant (const matrix<Rows,Cols,T>&);
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//-------------------------------------------------------------------------
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template <std::size_t Rows, std::size_t Cols, typename T>
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matrix<Rows,Cols,T>
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inverse (const matrix<Rows,Cols,T>&);
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//-------------------------------------------------------------------------
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template <std::size_t Rows, std::size_t Cols, typename T>
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matrix<Cols,Rows,T>
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transposed (const matrix<Rows,Cols,T>&);
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///////////////////////////////////////////////////////////////////////////
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template <std::size_t Rows, std::size_t Cols, typename T>
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matrix<Rows,Cols,T>
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abs (const matrix<Rows,Cols,T> &src)
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{
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matrix<Rows,Cols,T> dst;
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for (size_t r = 0; r < Rows; ++r)
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dst[r] = abs (src[r]);
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return dst;
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}
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template <std::size_t Rows, std::size_t Cols, typename T>
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constexpr T
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sum (const matrix<Rows,Cols,T> &src)
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{
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util::vector<Rows,T> accum {};
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for (size_t r = 0; r < Rows; ++r)
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accum[r] = sum (src[r]);
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return sum (accum);
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}
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///////////////////////////////////////////////////////////////////////////
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#define MATRIX_ELEMENT_OP(OP) \
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template <std::size_t Rows, std::size_t Cols, typename T> \
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constexpr \
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matrix<Rows,Cols,T> \
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operator OP ( \
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const matrix<Rows,Cols,T> &a, \
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const matrix<Rows,Cols,T> &b) \
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{ \
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matrix<Rows,Cols,T> res {}; \
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\
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for (std::size_t i = 0; i < a.rows; ++i) \
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for (std::size_t j = 0; j < a.cols; ++j) \
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res[i][j] = a[i][j] OP b[i][j]; \
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\
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return res; \
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}
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MATRIX_ELEMENT_OP(-)
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MATRIX_ELEMENT_OP(+)
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#undef MATRIX_ELEMENT_OP
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///////////////////////////////////////////////////////////////////////////
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#define MATRIX_SCALAR_OP(OP) \
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template <std::size_t Rows, std::size_t Cols, typename T> \
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constexpr \
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matrix<Rows,Cols,T> \
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operator OP (const matrix<Rows,Cols,T> &m, const T t) \
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{ \
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matrix<Rows,Cols,T> res {}; \
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\
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std::transform ( \
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std::cbegin (m), \
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std::cend (m), \
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std::begin (res), \
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[&t] (auto x) { return x OP t; } \
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); \
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\
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return res; \
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} \
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\
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\
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template <std::size_t Rows, std::size_t Cols, typename T> \
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constexpr \
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matrix<Rows,Cols,T> \
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operator OP (const T t, const matrix<Rows,Cols,T> &m) \
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{ \
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return m OP t; \
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} \
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\
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\
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template <std::size_t Rows, std::size_t Cols, typename T> \
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constexpr \
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matrix<Rows,Cols,T>& \
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operator OP##= (matrix<Rows,Cols,T> &m, T t) \
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{ \
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std::transform ( \
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std::cbegin (m), \
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std::cend (m), \
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std::begin (m), \
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[&t] (auto x) { return x OP t; } \
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); \
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\
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return m; \
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}
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MATRIX_SCALAR_OP(*)
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MATRIX_SCALAR_OP(/)
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MATRIX_SCALAR_OP(+)
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MATRIX_SCALAR_OP(-)
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#undef MATRIX_SCALAR_OP
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///////////////////////////////////////////////////////////////////////////
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template <typename T> using matrix3 = matrix<3,3,T>;
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template <typename T> using matrix4 = matrix<4,4,T>;
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template <std::size_t Rows, std::size_t Cols> using matrixf = matrix<Rows,Cols,float>;
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template <std::size_t Rows, std::size_t Cols> using matrixd = matrix<Rows,Cols,double>;
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typedef matrix<2,2,float> matrix2f;
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typedef matrix<2,2,double> matrix2d;
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typedef matrix<3,3,float> matrix3f;
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typedef matrix<3,3,double> matrix3d;
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typedef matrix<4,4,float> matrix4f;
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typedef matrix<4,4,double> matrix4d;
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///////////////////////////////////////////////////////////////////////////
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template <std::size_t Rows, std::size_t Cols, typename T>
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std::ostream&
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operator<< (std::ostream &os, const matrix<Rows,Cols,T> &m)
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{
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os << '[';
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std::copy (
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std::cbegin (m),
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std::cend (m),
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util::infix_iterator<decltype(m[0])> (os, ", ")
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);
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return os << ']';
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}
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};
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#endif
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