text: //=================================================================================================
  /*!
  //  \file blaze/math/lapack/trtri.h
  //  \brief Header file for the LAPACK triangular matrix inversion functions (trtri)
  //
  //  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_LAPACK_TRTRI_H_
  #define _BLAZE_MATH_LAPACK_TRTRI_H_
  
  
  //*************************************************************************************************
  // Includes
  //*************************************************************************************************
  
  #include <blaze/math/Aliases.h>
  #include <blaze/math/constraints/Adaptor.h>
  #include <blaze/math/constraints/BLASCompatible.h>
  #include <blaze/math/constraints/Computation.h>
  #include <blaze/math/constraints/Contiguous.h>
  #include <blaze/math/constraints/MutableDataAccess.h>
  #include <blaze/math/Exception.h>
  #include <blaze/math/expressions/DenseMatrix.h>
  #include <blaze/math/lapack/clapack/trtri.h>
  #include <blaze/math/typetraits/IsRowMajorMatrix.h>
  #include <blaze/util/Assert.h>
  #include <blaze/util/NumericCast.h>
  
  
  namespace blaze {
  
  //=================================================================================================
  //
  //  LAPACK TRIANGULAR MATRIX INVERSION FUNCTIONS (TRTRI)
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*!\name LAPACK triangular matrix inversion functions (trtri) */
  //@{
  template< typename MT, bool SO >
  void trtri( DenseMatrix<MT,SO>& A, char uplo, char diag );
  //@}
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief LAPACK kernel for the inversion of the given dense triangular matrix.
  // \ingroup lapack_inversion
  //
  // \param A The triangular matrix to be inverted.
  // \param uplo \c 'L' in case of a lower matrix, \c 'U' in case of an upper matrix.
  // \param diag \c 'U' in case of a unitriangular matrix, \c 'N' otherwise.
  // \return void
  // \exception std::invalid_argument Invalid non-square matrix provided.
  // \exception std::invalid_argument Invalid uplo argument provided.
  // \exception std::invalid_argument Invalid diag argument provided.
  // \exception std::runtime_error Inversion of singular matrix failed.
  //
  // This function performs the dense matrix inversion based on the LAPACK trtri() functions for
  // a lower triangular (\a uplo = \c 'L') or upper triangular (\a uplo = \a 'U') matrix. Note
  // that the function only works for general, non-adapted matrices with \c float, \c double,
  // \c complex<float>, or \c complex<double> element type. The attempt to call the function with
  // adaptors or matrices of any other element type results in a compile time error!
  //
  // The function fails if ...
  //
  //  - ... the given matrix is not a square matrix;
  //  - ... the given \a uplo argument is neither \c 'L' nor \c 'U';
  //  - ... the given \a diag argument is neither \c 'U' nor \c 'N';
  //  - ... the given matrix is singular and not invertible.
  //
  // In all failure cases an exception is thrown.
  //
  // For more information on the trtri() functions (i.e. strtri(), dtrtri(), ctrtri(), and ztrtri())
  // see the LAPACK online documentation browser:
  //
  //        http://www.netlib.org/lapack/explore-html/
  //
  // \note This function can only be used if a fitting LAPACK library, which supports this function,
  // is available and linked to the executable. Otherwise a call to this function will result in a
  // linker error.
  //
  // \note This function does only provide the basic exception safety guarantee, i.e. in case of an
  // exception \a A may already have been modified.
  */
  template< typename MT  // Type of the dense matrix
          , bool SO >    // Storage order of the dense matrix
  inline void trtri( DenseMatrix<MT,SO>& A, char uplo, char diag )
  {
     BLAZE_CONSTRAINT_MUST_NOT_BE_ADAPTOR_TYPE( MT );
     BLAZE_CONSTRAINT_MUST_NOT_BE_COMPUTATION_TYPE( MT );
     BLAZE_CONSTRAINT_MUST_HAVE_MUTABLE_DATA_ACCESS( MT );
     BLAZE_CONSTRAINT_MUST_BE_CONTIGUOUS_TYPE( MT );
     BLAZE_CONSTRAINT_MUST_BE_BLAS_COMPATIBLE_TYPE( ElementType_t<MT> );
  
     if( !isSquare( ~A ) ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid non-square matrix provided" );
     }
  
     if( uplo != 'L' && uplo != 'U' ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid uplo argument provided" );
     }
  
     if( diag != 'U' && diag != 'N' ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid diag argument provided" );
     }
  
     int n   ( numeric_cast<int>( (~A).columns() ) );
     int lda ( numeric_cast<int>( (~A).spacing() ) );
     int info( 0 );
  
     if( n == 0 ) {
        return;
     }
  
     if( IsRowMajorMatrix_v<MT> ) {
        ( uplo == 'L' )?( uplo = 'U' ):( uplo = 'L' );
     }
  
     trtri( uplo, diag, n, (~A).data(), lda, &info );
  
     BLAZE_INTERNAL_ASSERT( info >= 0, "Invalid argument for matrix inversion" );
  
     if( info > 0 ) {
        BLAZE_THROW_LAPACK_ERROR( "Inversion of singular matrix failed" );
     }
  }
  //*************************************************************************************************
  
  } // namespace blaze
  
  #endif
  