text: //=================================================================================================
  /*!
  //  \file blaze/math/lapack/orgr2.h
  //  \brief Header file for the LAPACK functions to reconstruct Q from a RQ decomposition (orgr2)
  //
  //  Copyright (C) 2012-2020 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_ORGR2_H_
  #define _BLAZE_MATH_LAPACK_ORGR2_H_
  
  
  //*************************************************************************************************
  // Includes
  //*************************************************************************************************
  
  #include <memory>
  #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/expressions/DenseMatrix.h>
  #include <blaze/math/lapack/clapack/org2l.h>
  #include <blaze/math/lapack/clapack/orgr2.h>
  #include <blaze/util/Assert.h>
  #include <blaze/util/constraints/Builtin.h>
  #include <blaze/util/NumericCast.h>
  
  
  namespace blaze {
  
  //=================================================================================================
  //
  //  LAPACK FUNCTIONS TO RECONSTRUCT Q FROM A RQ DECOMPOSITION (ORGR2)
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*!\name LAPACK functions to reconstruct Q from a RQ decomposition (orgr2) */
  //@{
  template< typename MT, bool SO >
  void orgr2( DenseMatrix<MT,SO>& A, const ElementType_t<MT>* tau );
  //@}
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief LAPACK kernel for the reconstruction of the orthogonal matrix Q from a RQ decomposition.
  // \ingroup lapack_decomposition
  //
  // \param A The decomposed matrix.
  // \param tau Array for the scalar factors of the elementary reflectors; size >= min( \a m, \a n ).
  // \return void
  //
  // This function reconstructs the orthogonal matrix \a Q of a RQ decomposition based on the LAPACK
  // orgr2() functions from matrices that have already been RQ factorized by the gerqf() functions.
  // Note that this function can only be used for general, non-adapted matrices with \c float or
  // \c double element type. The attempt to call the function with any adapted matrix or matrices
  // of any other element type results in a compile time error!\n
  //
  // The min(\a m,\a n)-by-\a n \a Q matrix is stored within the given matrix \a A:
  
     \code
     using blaze::DynamicMatrix;
     using blaze::columnMajor;
  
     DynamicMatrix<double,columnMajor> A;
     DynamicVector<double> tau;
     // ... Resizing and initialization
  
     gerqf( A, tau.data() );  // Performing the RQ decomposition
     orgr2( A, tau.data() );  // Reconstructing the Q matrix
  
     const size_t m( A.rows() );
     const size_t n( A.columns() );
  
     const size_t row( m > n ? m - n : 0UL )
     DynamicMatrix<double,columnMajor> Q( submatrix( A, row, 0UL, min(m,n), n ) );
     \endcode
  
  // For more information on the orgr2() functions (i.e. sorgr2() and dorgr2()) 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.
  */
  template< typename MT, bool SO >
  inline void orgr2( DenseMatrix<MT,SO>& A, const ElementType_t<MT>* tau )
  {
     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> );
     BLAZE_CONSTRAINT_MUST_BE_BUILTIN_TYPE( ElementType_t<MT> );
  
     using ET = ElementType_t<MT>;
  
     blas_int_t m   ( numeric_cast<blas_int_t>( SO ? (*A).rows() : (*A).columns() ) );
     blas_int_t n   ( numeric_cast<blas_int_t>( SO ? (*A).columns() : (*A).rows() ) );
     blas_int_t k   ( min( m, n ) );
     blas_int_t lda ( numeric_cast<blas_int_t>( (*A).spacing() ) );
     blas_int_t info( 0 );
  
     if( k == 0 ) {
        return;
     }
  
     const std::unique_ptr<ET[]> work( new ET[m] );
  
     if( SO ) {
        const size_t offset( static_cast<size_t>( ( m > n )?( m - n ):( 0 ) ) );
        orgr2( k, n, k, (*A).data()+offset, lda, tau, work.get(), &info );
     }
     else {
        const size_t offset( static_cast<size_t>( ( m < n )?( n - m ):( 0 ) ) );
        org2l( m, k, k, (*A).data(offset), lda, tau, work.get(), &info );
     }
  
     BLAZE_INTERNAL_ASSERT( info == 0, "Invalid argument for Q reconstruction" );
  }
  //*************************************************************************************************
  
  } // namespace blaze
  
  #endif
  