text: //=================================================================================================
  /*!
  //  \file blaze/math/lapack/orgrq.h
  //  \brief Header file for the LAPACK functions to reconstruct Q from a RQ decomposition (orgrq)
  //
  //  Copyright (C) 2013 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_ORGRQ_H_
  #define _BLAZE_MATH_LAPACK_ORGRQ_H_
  
  
  //*************************************************************************************************
  // Includes
  //*************************************************************************************************
  
  #include <memory>
  #include <boost/cast.hpp>
  #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/MutableDataAccess.h>
  #include <blaze/math/expressions/DenseMatrix.h>
  #include <blaze/math/lapack/clapack/orgql.h>
  #include <blaze/math/lapack/clapack/orgrq.h>
  #include <blaze/util/Assert.h>
  #include <blaze/util/constraints/Builtin.h>
  
  
  namespace blaze {
  
  //=================================================================================================
  //
  //  LAPACK FUNCTIONS TO RECONSTRUCT Q FROM A RQ DECOMPOSITION (ORGRQ)
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*!\name LAPACK functions to reconstruct Q from a RQ decomposition (orgrq) */
  //@{
  template< typename MT, bool SO >
  inline void orgrq( DenseMatrix<MT,SO>& A, const ElementType_<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
  // orgrq() 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
     orgrq( A, tau.data() );  // Reconstructing the Q matrix
  
     const int m( A.rows() );
     const int 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 orgrq() functions (i.e. sorgrq() and dorgrq()) see the LAPACK
  // online documentation browser:
  //
  //        http://www.netlib.org/lapack/explore-html/
  //
  // \note This function can only be used if the fitting LAPACK library 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 orgrq( DenseMatrix<MT,SO>& A, const ElementType_<MT>* tau )
  {
     using boost::numeric_cast;
  
     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_BLAS_COMPATIBLE_TYPE( ElementType_<MT> );
     BLAZE_CONSTRAINT_MUST_BE_BUILTIN_TYPE( ElementType_<MT> );
  
     typedef ElementType_<MT>  ET;
  
     int m   ( numeric_cast<int>( SO ? (~A).rows() : (~A).columns() ) );
     int n   ( numeric_cast<int>( SO ? (~A).columns() : (~A).rows() ) );
     int k   ( min( m, n ) );
     int lda ( numeric_cast<int>( (~A).spacing() ) );
     int info( 0 );
  
     if( k == 0 ) {
        return;
     }
  
     int lwork( k*lda );
     const std::unique_ptr<ET[]> work( new ET[lwork] );
  
     if( SO ) {
        const size_t offset( ( m > n )?( m - n ):( 0UL ) );
        orgrq( k, n, k, (~A).data()+offset, lda, tau, work.get(), lwork, &info );
     }
     else {
        const size_t offset( ( m < n )?( n - m ):( 0UL ) );
        orgql( m, k, k, (~A).data(offset), lda, tau, work.get(), lwork, &info );
     }
  
     BLAZE_INTERNAL_ASSERT( info == 0, "Invalid argument for Q reconstruction" );
  }
  //*************************************************************************************************
  
  } // namespace blaze
  
  #endif
  