text: //=================================================================================================
  /*!
  //  \file blaze/math/InversionFlag.h
  //  \brief Header file for the dense matrix inversion flags
  //
  //  Copyright (C) 2012-2019 Klaus Iglberger - All Rights Reserved
  //
  //  This file is part of the Blaze library. You can redistribute it and/or modify it under
  //  the terms of the New (Revised) BSD License. Redistribution and use in source and binary
  //  forms, with or without modification, are permitted provided that the following conditions
  //  are met:
  //
  //  1. Redistributions of source code must retain the above copyright notice, this list of
  //     conditions and the following disclaimer.
  //  2. Redistributions in binary form must reproduce the above copyright notice, this list
  //     of conditions and the following disclaimer in the documentation and/or other materials
  //     provided with the distribution.
  //  3. Neither the names of the Blaze development group nor the names of its contributors
  //     may be used to endorse or promote products derived from this software without specific
  //     prior written permission.
  //
  //  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
  //  EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
  //  OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT
  //  SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
  //  INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
  //  TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR
  //  BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
  //  CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
  //  ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
  //  DAMAGE.
  */
  //=================================================================================================
  
  #ifndef _BLAZE_MATH_INVERSIONFLAG_H_
  #define _BLAZE_MATH_INVERSIONFLAG_H_
  
  
  namespace blaze {
  
  //=================================================================================================
  //
  //  INVERSION FLAG VALUES
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*!\brief Inversion flag.
  // \ingroup math
  //
  // The InversionFlag type enumeration represents the different types of matrix inversion algorithms
  // that are available within the Blaze library. The following flags are available:
  //
  //  - \c byLU: The default inversion algorithm for general square matrices. It uses the LU
  //          algorithm to decompose a matrix into a lower unitriangular matrix \c L, an upper
  //          triangular matrix \c U, and a permutation matrix \c P (\f$ A = P L U \f$). If no
  //          permutations are required, \c P is the identity matrix.
  //  - \c byLDLT: The Bunch-Kaufman inversion algorithm for symmetric indefinite matrices. It
  //          decomposes the given matrix into either \f$ A = U D U^{T} \f$ or \f$ A = L D L^{T} \f$,
  //          where \c U (or \c L) is a product of permutation and unit upper (lower) triangular
  //          matrices, and \c D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal
  //          blocks.
  //  - \c byLDLH: The Bunch-Kaufman inversion algorithm for Hermitian indefinite matrices. It
  //          decomposes the given matrix into either \f$ A = U D U^{H} \f$ or \f$ A = L D L^{H} \f$,
  //          where \c U (or \c L) is a product of permutation and unit upper (lower) triangular
  //          matrices, and \c D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal
  //          blocks.
  //  - \c byLLH: The Cholesky inversion algorithm for Hermitian positive definite matrices. It
  //          decomposes a given matrix into either \f$ A = L L^H \f$, where \c L is a lower
  //          triangular matrix, or \f$ A = U^H U \f$, where \c U is an upper triangular matrix.
  //
  // Alternatively, the type of the matrix can be specified, leaving it to the Blaze library to
  // select the appropriate matrix inversion algorithm. The following flags are available:
  //
  //  - \c asGeneral: This flag selects the best suited inversion algorithm for general square
  //          matrices. In case no further compile time information is available, this will imply
  //          the use of the LU decomposition algorithm (see the \c byLU flag).
  //  - \c asSymmetric: This flag selects the most suited inversion algorithm for symmetric matrices.
  //          In case no further compile time information is available, the Bunch-Kaufman matrix
  //          decomposition algorithm will be used (see the \c byLDLT flag).
  //  - \c asHermitian: This flag selects the most suited inversion algorithm for Hermitian matrices.
  //          In case no further compile time information is available, the Bunch-Kaufman matrix
  //          decomposition algorithm will be used (see the \c byLDLH flag).
  //  - \c asLower: This flag selects the most suited inversion algorithm for lower triangular
  //          matrices. In case no further compile time information is available, the inversion will
  //          be performed by a forward substitution. No matrix decomposition will be performed.
  //  - \c asUniLower: This flag selects the most suited inversion algorithm for lower unitriangular
  //          matrices. In case no further compile time information is available, the inversion will
  //          be performed by a forward substitution. No matrix decomposition will be performed.
  //  - \c asUpper: This flag selects the most suited inversion algorithm for upper triangular
  //          matrices. In case no further compile time information is available, the inversion will
  //          be performed by a back substitution. No matrix decomposition will be performed.
  //  - \c asUniUpper: This flag selects the most suited inversion algorithm for upper unitriangular
  //          matrices. In case no further compile time information is available, the inversion will
  //          be performed by a back substitution. No matrix decomposition will be performed.
  //  - \c asDiagonal: This flag selects the most suited inversion algorithm for diagonal matrices.
  //          In case no further compile time information is available, the inversion will be
  //          performed by directly computing the reciprocal of each diagonal element. No matrix
  //          decomposition will be performed.
  */
  enum InversionFlag
  {
     byLU        =  0,  //!< Flag for the LU-based matrix inversion.
     byLDLT      =  1,  //!< Flag for the Bunch-Kaufman-based inversion for symmetric matrices.
     byLDLH      =  2,  //!< Flag for the Bunch-Kaufman-based inversion for Hermitian matrices.
     byLLH       =  3,  //!< Flag for the Cholesky-based inversion for positive-definite matrices.
  
     asGeneral   =  4,  //!< Flag for the inversion of a general matrix (same as byLU).
     asSymmetric =  5,  //!< Flag for the inversion of a symmetric matrix (same as byLDLT).
     asHermitian =  6,  //!< Flag for the inversion of a Hermitian matrix (same as byLDLH).
     asLower     =  7,  //!< Flag for the inversion of a lower triangular matrix.
     asUniLower  =  8,  //!< Flag for the inversion of a lower unitriangular matrix.
     asUpper     =  9,  //!< Flag for the inversion of a upper triangular matrix.
     asUniUpper  = 10,  //!< Flag for the inversion of a upper unitriangular matrix.
     asDiagonal  = 11   //!< Flag for the inversion of a diagonal matrix.
  };
  //*************************************************************************************************
  
  } // namespace blaze
  
  #endif
  