text: #ifndef Magnum_Math_Algorithms_GaussJordan_h
  #define Magnum_Math_Algorithms_GaussJordan_h
  /*
      This file is part of Magnum.
  
      Copyright © 2010, 2011, 2012, 2013, 2014
                Vladimír Vondruš <mosra@centrum.cz>
  
      Permission is hereby granted, free of charge, to any person obtaining a
      copy of this software and associated documentation files (the "Software"),
      to deal in the Software without restriction, including without limitation
      the rights to use, copy, modify, merge, publish, distribute, sublicense,
      and/or sell copies of the Software, and to permit persons to whom the
      Software is furnished to do so, subject to the following conditions:
  
      The above copyright notice and this permission notice shall be included
      in all copies or substantial portions of the Software.
  
      THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
      IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
      FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
      THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
      LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
      FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
      DEALINGS IN THE SOFTWARE.
  */
  
  /** @file
   * @brief Function @ref Magnum::Math::Algorithms::gaussJordanInPlaceTransposed(), @ref Magnum::Math::Algorithms::gaussJordanInPlace()
   */
  
  #include "Magnum/Math/RectangularMatrix.h"
  
  namespace Magnum { namespace Math { namespace Algorithms {
  
  /**
  @brief In-place Gauss-Jordan elimination on transposed matrices
  @param a     Transposed left side of augmented matrix
  @param t     Transposed right side of augmented matrix
  @return True if @p a is regular, false if @p a is singular (and thus the
      system cannot be solved).
  
  As Gauss-Jordan elimination works on rows and matrices in OpenGL are
  column-major, it is more efficient to operate on transposed matrices and treat
  columns as rows. See also @ref gaussJordanInPlace() which works with
  non-transposed matrices.
  
  The function eliminates matrix @p a and solves @p t in place. For efficiency
  reasons, only pure Gaussian elimination is done on @p a and the final
  backsubstitution is done only on @p t, as @p a would always end with identity
  matrix anyway.
  
  Based on ultra-compact Python code by Jarno Elonen,
  http://elonen.iki.fi/code/misc-notes/python-gaussj/index.html.
  */
  template<std::size_t size, std::size_t rows, class T> bool gaussJordanInPlaceTransposed(RectangularMatrix<size, size, T>& a, RectangularMatrix<size, rows, T>& t) {
      for(std::size_t row = 0; row != size; ++row) {
          /* Find max pivot */
          std::size_t rowMax = row;
          for(std::size_t row2 = row+1; row2 != size; ++row2)
              if(std::abs(a[row2][row]) > std::abs(a[rowMax][row]))
                  rowMax = row2;
  
          /* Swap the rows */
          std::swap(a[row], a[rowMax]);
          std::swap(t[row], t[rowMax]);
  
          /* Singular */
          if(TypeTraits<T>::equals(a[row][row], T(0)))
              return false;
  
          /* Eliminate column */
          for(std::size_t row2 = row+1; row2 != size; ++row2) {
              T c = a[row2][row]/a[row][row];
  
              a[row2] -= a[row]*c;
              t[row2] -= t[row]*c;
          }
      }
  
      /* Backsubstitute */
      for(std::size_t row = size; row != 0; --row) {
          T c = T(1)/a[row-1][row-1];
  
          for(std::size_t row2 = 0; row2 != row-1; ++row2)
              t[row2] -= t[row-1]*a[row2][row-1]*c;
  
          /* Normalize the row */
          t[row-1] *= c;
      }
  
      return true;
  }
  
  /**
  @brief In-place Gauss-Jordan elimination
  
  Transposes the matrices, calls @ref gaussJordanInPlaceTransposed() on them and
  then transposes them back.
  */
  template<std::size_t size, std::size_t cols, class T> bool gaussJordanInPlace(RectangularMatrix<size, size, T>& a, RectangularMatrix<cols, size, T>& t) {
      a = a.transposed();
      RectangularMatrix<size, cols, T> tTransposed = t.transposed();
  
      bool ret = gaussJordanInPlaceTransposed(a, tTransposed);
  
      a = a.transposed();
      t = tTransposed.transposed();
  
      return ret;
  }
  
  }}}
  
  #endif
  