text: //=================================================================================================
  /*!
  //  \file blaze/math/dense/Eigen.h
  //  \brief Header file for the dense matrix eigenvalue functions
  //
  //  Copyright (C) 2012-2018 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_DENSE_EIGEN_H_
  #define _BLAZE_MATH_DENSE_EIGEN_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/MutableDataAccess.h>
  #include <blaze/math/expressions/DenseMatrix.h>
  #include <blaze/math/expressions/DenseVector.h>
  #include <blaze/math/lapack/geev.h>
  #include <blaze/math/lapack/heevd.h>
  #include <blaze/math/lapack/syevd.h>
  #include <blaze/math/typetraits/IsContiguous.h>
  #include <blaze/math/typetraits/IsHermitian.h>
  #include <blaze/math/typetraits/IsRowMajorMatrix.h>
  #include <blaze/math/typetraits/IsSymmetric.h>
  #include <blaze/math/typetraits/RemoveAdaptor.h>
  #include <blaze/util/DisableIf.h>
  #include <blaze/util/EnableIf.h>
  #include <blaze/util/mpl/If.h>
  #include <blaze/util/typetraits/IsComplex.h>
  #include <blaze/util/typetraits/IsFloatingPoint.h>
  
  
  namespace blaze {
  
  //=================================================================================================
  //
  //  EIGENVALUE FUNCTIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*!\name Eigenvalue functions */
  //@{
  template< typename MT, bool SO, typename VT, bool TF >
  inline void eigen( const DenseMatrix<MT,SO>& A, DenseVector<VT,TF>& w );
  
  template< typename MT1, bool SO1, typename VT, bool TF, typename MT2, bool SO2 >
  inline void eigen( const DenseMatrix<MT1,SO1>& A, DenseVector<VT,TF>& w, DenseMatrix<MT2,SO2>& V );
  //@}
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Backend for the eigenvalue computation of the given dense symmetric matrix.
  // \ingroup dense_matrix
  //
  // \param A The given symmetric matrix.
  // \param w The resulting vector of eigenvalues.
  // \return void
  // \exception std::invalid_argument Invalid non-square matrix provided.
  // \exception std::invalid_argument Vector cannot be resized.
  // \exception std::runtime_error Eigenvalue computation failed.
  //
  // This function is the backend implementation for computing the eigenvalues of the given
  // dense symmetric matrix.\n
  // This function must \b NOT be called explicitly! It is used internally for the dispatch to
  // the correct LAPACK function. Calling this function explicitly might result in erroneous
  // results and/or in compilation errors. Instead of using this function use the according
  // eigen() function.
  */
  template< typename MT  // Type of the matrix A
          , bool SO      // Storage order of the matrix A
          , typename VT  // Type of the vector w
          , bool TF >    // Transpose flag of the vector w
  inline auto eigen_backend( const DenseMatrix<MT,SO>& A, DenseVector<VT,TF>& w )
     -> EnableIf_t< IsSymmetric_v<MT> && IsFloatingPoint_v< ElementType_t<MT> > >
  {
     using ATmp = ResultType_t< RemoveAdaptor_t<MT> >;
  
     BLAZE_CONSTRAINT_MUST_NOT_BE_ADAPTOR_TYPE( ATmp );
     BLAZE_CONSTRAINT_MUST_NOT_BE_COMPUTATION_TYPE( ATmp );
     BLAZE_CONSTRAINT_MUST_HAVE_MUTABLE_DATA_ACCESS( ATmp );
     BLAZE_CONSTRAINT_MUST_BE_BLAS_COMPATIBLE_TYPE( ElementType_t<ATmp> );
  
     ATmp Atmp( A );
  
     syevd( Atmp, ~w, 'N', 'L' );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Backend for the eigenvalue computation of the given dense Hermitian matrix.
  // \ingroup dense_matrix
  //
  // \param A The given Hermitian matrix.
  // \param w The resulting vector of eigenvalues.
  // \return void
  // \exception std::invalid_argument Invalid non-square matrix provided.
  // \exception std::invalid_argument Vector cannot be resized.
  // \exception std::runtime_error Eigenvalue computation failed.
  //
  // This function is the backend implementation for computing the eigenvalues of the given
  // dense Hermitian matrix.\n
  // This function must \b NOT be called explicitly! It is used internally for the dispatch to
  // the correct LAPACK function. Calling this function explicitly might result in erroneous
  // results and/or in compilation errors. Instead of using this function use the according
  // eigen() function.
  */
  template< typename MT  // Type of the matrix A
          , bool SO      // Storage order of the matrix A
          , typename VT  // Type of the vector w
          , bool TF >    // Transpose flag of the vector w
  inline auto eigen_backend( const DenseMatrix<MT,SO>& A, DenseVector<VT,TF>& w )
     -> EnableIf_t< IsHermitian_v<MT> && IsComplex_v< ElementType_t<MT> > >
  {
     using ATmp = ResultType_t< RemoveAdaptor_t<MT> >;
  
     BLAZE_CONSTRAINT_MUST_NOT_BE_ADAPTOR_TYPE( ATmp );
     BLAZE_CONSTRAINT_MUST_NOT_BE_COMPUTATION_TYPE( ATmp );
     BLAZE_CONSTRAINT_MUST_HAVE_MUTABLE_DATA_ACCESS( ATmp );
     BLAZE_CONSTRAINT_MUST_BE_BLAS_COMPATIBLE_TYPE( ElementType_t<ATmp> );
  
     ATmp Atmp( A );
  
     heevd( Atmp, ~w, 'N', 'L' );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Backend for the eigenvalue computation of the given dense general matrix.
  // \ingroup dense_matrix
  //
  // \param A The given general matrix.
  // \param w The resulting vector of eigenvalues.
  // \return void
  // \exception std::invalid_argument Invalid non-square matrix provided.
  // \exception std::invalid_argument Vector cannot be resized.
  // \exception std::runtime_error Eigenvalue computation failed.
  //
  // This function is the backend implementation for computing the eigenvalues of the given
  // dense general matrix.\n
  // This function must \b NOT be called explicitly! It is used internally for the dispatch to
  // the correct LAPACK function. Calling this function explicitly might result in erroneous
  // results and/or in compilation errors. Instead of using this function use the according
  // eigen() function.
  */
  template< typename MT  // Type of the matrix A
          , bool SO      // Storage order of the matrix A
          , typename VT  // Type of the vector w
          , bool TF >    // Transpose flag of the vector w
  inline auto eigen_backend( const DenseMatrix<MT,SO>& A, DenseVector<VT,TF>& w )
     -> DisableIf_t< ( IsSymmetric_v<MT> && IsFloatingPoint_v< ElementType_t<MT> > ) ||
                     ( IsHermitian_v<MT> && IsComplex_v< ElementType_t<MT> > ) >
  {
     using ATmp = ResultType_t< RemoveAdaptor_t<MT> >;
  
     BLAZE_CONSTRAINT_MUST_NOT_BE_ADAPTOR_TYPE( ATmp );
     BLAZE_CONSTRAINT_MUST_NOT_BE_COMPUTATION_TYPE( ATmp );
     BLAZE_CONSTRAINT_MUST_HAVE_MUTABLE_DATA_ACCESS( ATmp );
     BLAZE_CONSTRAINT_MUST_BE_BLAS_COMPATIBLE_TYPE( ElementType_t<ATmp> );
  
     ATmp Atmp( A );
  
     geev( Atmp, ~w );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief Eigenvalue computation of the given dense matrix.
  // \ingroup dense_matrix
  //
  // \param A The given general matrix.
  // \param w The resulting vector of eigenvalues.
  // \return void
  // \exception std::invalid_argument Invalid non-square matrix provided.
  // \exception std::invalid_argument Vector cannot be resized.
  // \exception std::runtime_error Eigenvalue computation failed.
  //
  // This function computes the eigenvalues of the given \a n-by-\a n matrix. The eigenvalues are
  // returned in the given vector \a w, which is resized to the correct size (if possible and
  // necessary).
  //
  // Please note that in case the given matrix is either a compile time symmetric matrix with
  // floating point elements or an Hermitian matrix with complex elements, the resulting eigenvalues
  // will be of floating point type and therefore the elements of the given eigenvalue vector are
  // expected to be of floating point type. In all other cases they are expected to be of complex
  // type. Also please note that for complex eigenvalues no order of eigenvalues can be assumed,
  // except that complex conjugate pairs of eigenvalues appear consecutively with the eigenvalue
  // having the positive imaginary part first.
  //
  // The function fails if ...
  //
  //  - ... the given matrix \a A is not a square matrix;
  //  - ... the given vector \a w is a fixed size vector and the size doesn't match;
  //  - ... the eigenvalue computation fails.
  //
  // In all failure cases an exception is thrown.
  //
  // Examples:
  
     \code
     using blaze::DynamicMatrix;
     using blaze::DynamicVector;
     using blaze::rowMajor;
     using blaze::columnVector;
  
     DynamicMatrix<double,rowMajor> A( 5UL, 5UL );  // The general matrix A
     // ... Initialization
  
     DynamicVector<complex<double>,columnVector> w( 5UL );  // The vector for the complex eigenvalues
  
     eigen( A, w );
     \endcode
  
     \code
     using blaze::SymmetricMatrix;
     using blaze::DynamicMatrix;
     using blaze::DynamicVector;
     using blaze::rowMajor;
     using blaze::columnVector;
  
     SymmetricMatrix< DynamicMatrix<double,rowMajor> > A( 5UL, 5UL );  // The symmetric matrix A
     // ... Initialization
  
     DynamicVector<double,columnVector> w( 5UL );  // The vector for the real eigenvalues
  
     eigen( A, w );
     \endcode
  
     \code
     using blaze::HermitianMatrix;
     using blaze::DynamicMatrix;
     using blaze::DynamicVector;
     using blaze::rowMajor;
     using blaze::columnVector;
  
     DynamicMatrix<complex<double>,rowMajor> A( 5UL, 5UL );  // The Hermitian matrix A
     // ... Initialization
  
     DynamicVector<double,columnVector> w( 5UL );  // The vector for the real eigenvalues
  
     eigen( A, w );
     \endcode
  
  // \note This function only works for matrices with \c float, \c double, \c complex<float>, or
  // \c complex<double> element type. The attempt to call the function with matrices of any other
  // element type results in a compile time error!
  //
  // \note This function can only be used if a fitting LAPACK library is available and linked to
  // the executable. Otherwise a call to this function will result in a linker error.
  //
  // \note Further options for computing eigenvalues and eigenvectors are available via the geev(),
  // syev(), syevd(), syevx(), heev(), heevd(), and heevx() functions.
  */
  template< typename MT  // Type of the matrix A
          , bool SO      // Storage order of the matrix A
          , typename VT  // Type of the vector w
          , bool TF >    // Transpose flag of the vector w
  inline void eigen( const DenseMatrix<MT,SO>& A, DenseVector<VT,TF>& w )
  {
     BLAZE_CONSTRAINT_MUST_NOT_BE_COMPUTATION_TYPE( MT );
     BLAZE_CONSTRAINT_MUST_BE_BLAS_COMPATIBLE_TYPE( ElementType_t<MT> );
  
     BLAZE_CONSTRAINT_MUST_NOT_BE_COMPUTATION_TYPE( VT );
     BLAZE_CONSTRAINT_MUST_HAVE_MUTABLE_DATA_ACCESS( VT );
     BLAZE_CONSTRAINT_MUST_BE_BLAS_COMPATIBLE_TYPE( ElementType_t<VT> );
  
     using WTmp = If_t< IsContiguous_v<VT>, VT&, ResultType_t<VT> >;
  
     WTmp wtmp( ~w );
  
     eigen_backend( ~A, wtmp );
  
     if( IsContiguous_v<VT> ) {
        (~w) = wtmp;
     }
  }
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Backend for the eigenvalue computation of the given dense symmetric matrix.
  // \ingroup dense_matrix
  //
  // \param A The given symmetric matrix.
  // \param w The resulting vector of eigenvalues.
  // \param V The resulting matrix of eigenvectors.
  // \return void
  // \exception std::invalid_argument Invalid non-square matrix provided.
  // \exception std::invalid_argument Vector cannot be resized.
  // \exception std::invalid_argument Matrix cannot be resized.
  // \exception std::runtime_error Eigenvalue computation failed.
  //
  // This function is the backend implementation for computing the eigenvalues of the given
  // dense symmetric matrix.\n
  // This function must \b NOT be called explicitly! It is used internally for the dispatch to
  // the correct LAPACK function. Calling this function explicitly might result in erroneous
  // results and/or in compilation errors. Instead of using this function use the according
  // eigen() function.
  */
  template< typename MT1  // Type of the matrix A
          , bool SO1      // Storage order of the matrix A
          , typename VT   // Type of the vector w
          , bool TF       // Transpose flag of the vector w
          , typename MT2  // Type of the matrix V
          , bool SO2 >    // Storage order of the matrix V
  inline auto eigen_backend( const DenseMatrix<MT1,SO1>& A, DenseVector<VT,TF>& w, DenseMatrix<MT2,SO2>& V )
     -> EnableIf_t< IsSymmetric_v<MT1> && IsFloatingPoint_v< ElementType_t<MT1> > >
  {
     using ATmp = ResultType_t< RemoveAdaptor_t<MT1> >;
  
     BLAZE_CONSTRAINT_MUST_NOT_BE_ADAPTOR_TYPE( ATmp );
     BLAZE_CONSTRAINT_MUST_NOT_BE_COMPUTATION_TYPE( ATmp );
     BLAZE_CONSTRAINT_MUST_HAVE_MUTABLE_DATA_ACCESS( ATmp );
     BLAZE_CONSTRAINT_MUST_BE_BLAS_COMPATIBLE_TYPE( ElementType_t<ATmp> );
  
     ATmp Atmp( A );
  
     syevd( Atmp, ~w, 'V', 'L' );
  
     (~V) = Atmp;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Backend for the eigenvalue computation of the given dense Hermitian matrix.
  // \ingroup dense_matrix
  //
  // \param A The given Hermitian matrix.
  // \param w The resulting vector of eigenvalues.
  // \param V The resulting matrix of eigenvectors.
  // \return void
  // \exception std::invalid_argument Invalid non-square matrix provided.
  // \exception std::invalid_argument Vector cannot be resized.
  // \exception std::invalid_argument Matrix cannot be resized.
  // \exception std::runtime_error Eigenvalue computation failed.
  //
  // This function is the backend implementation for computing the eigenvalues of the given
  // dense Hermitian matrix.\n
  // This function must \b NOT be called explicitly! It is used internally for the dispatch to
  // the correct LAPACK function. Calling this function explicitly might result in erroneous
  // results and/or in compilation errors. Instead of using this function use the according
  // eigen() function.
  */
  template< typename MT1  // Type of the matrix A
          , bool SO1      // Storage order of the matrix A
          , typename VT   // Type of the vector w
          , bool TF       // Transpose flag of the vector w
          , typename MT2  // Type of the matrix V
          , bool SO2 >    // Storage order of the matrix V
  inline auto eigen_backend( const DenseMatrix<MT1,SO1>& A, DenseVector<VT,TF>& w, DenseMatrix<MT2,SO2>& V )
     -> EnableIf_t< IsHermitian_v<MT1> && IsComplex_v< ElementType_t<MT1> > >
  {
     using ATmp = ResultType_t< RemoveAdaptor_t<MT1> >;
  
     BLAZE_CONSTRAINT_MUST_NOT_BE_ADAPTOR_TYPE( ATmp );
     BLAZE_CONSTRAINT_MUST_NOT_BE_COMPUTATION_TYPE( ATmp );
     BLAZE_CONSTRAINT_MUST_HAVE_MUTABLE_DATA_ACCESS( ATmp );
     BLAZE_CONSTRAINT_MUST_BE_BLAS_COMPATIBLE_TYPE( ElementType_t<ATmp> );
  
     ATmp Atmp( A );
  
     heevd( Atmp, ~w, 'V', 'L' );
  
     (~V) = Atmp;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Backend for the eigenvalue computation of the given dense general matrix.
  // \ingroup dense_matrix
  //
  // \param A The given general matrix.
  // \param w The resulting vector of eigenvalues.
  // \param V The resulting matrix of eigenvectors.
  // \return void
  // \exception std::invalid_argument Invalid non-square matrix provided.
  // \exception std::invalid_argument Vector cannot be resized.
  // \exception std::invalid_argument Matrix cannot be resized.
  // \exception std::runtime_error Eigenvalue computation failed.
  //
  // This function is the backend implementation for computing the eigenvalues of the given
  // dense general matrix.\n
  // This function must \b NOT be called explicitly! It is used internally for the dispatch to
  // the correct LAPACK function. Calling this function explicitly might result in erroneous
  // results and/or in compilation errors. Instead of using this function use the according
  // eigen() function.
  */
  template< typename MT1  // Type of the matrix A
          , bool SO1      // Storage order of the matrix A
          , typename VT   // Type of the vector w
          , bool TF       // Transpose flag of the vector w
          , typename MT2  // Type of the matrix V
          , bool SO2 >    // Storage order of the matrix V
  inline auto eigen_backend( const DenseMatrix<MT1,SO1>& A, DenseVector<VT,TF>& w, DenseMatrix<MT2,SO2>& V )
     -> DisableIf_t< ( IsSymmetric_v<MT1> && IsFloatingPoint_v< ElementType_t<MT1> > ) ||
                     ( IsHermitian_v<MT1> && IsComplex_v< ElementType_t<MT1> > ) >
  {
     using ATmp = ResultType_t< RemoveAdaptor_t<MT1> >;
  
     BLAZE_CONSTRAINT_MUST_NOT_BE_ADAPTOR_TYPE( ATmp );
     BLAZE_CONSTRAINT_MUST_NOT_BE_COMPUTATION_TYPE( ATmp );
     BLAZE_CONSTRAINT_MUST_HAVE_MUTABLE_DATA_ACCESS( ATmp );
     BLAZE_CONSTRAINT_MUST_BE_BLAS_COMPATIBLE_TYPE( ElementType_t<ATmp> );
  
     ATmp Atmp( A );
  
     if( IsRowMajorMatrix_v<MT1> )
        geev( Atmp, ~V, ~w );
     else
        geev( Atmp, ~w, ~V );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief Eigenvalue computation of the given dense matrix.
  // \ingroup dense_matrix
  //
  // \param A The given general matrix.
  // \param w The resulting vector of eigenvalues.
  // \param V The resulting matrix of eigenvectors.
  // \return void
  // \exception std::invalid_argument Invalid non-square matrix provided.
  // \exception std::invalid_argument Vector cannot be resized.
  // \exception std::invalid_argument Matrix cannot be resized.
  // \exception std::runtime_error Eigenvalue computation failed.
  //
  // This function computes the eigenvalues and eigenvectors of the given \a n-by-\a n matrix.
  // The eigenvalues are returned in the given vector \a w and the eigenvectors are returned in the
  // given matrix \a V, which are both resized to the correct dimensions (if possible and necessary).
  //
  // Please note that in case the given matrix is either a compile time symmetric matrix with
  // floating point elements or an Hermitian matrix with complex elements, the resulting eigenvalues
  // will be of floating point type and therefore the elements of the given eigenvalue vector are
  // expected to be of floating point type. In all other cases they are expected to be of complex
  // type. Also please note that for complex eigenvalues no order of eigenvalues can be assumed,
  // except that complex conjugate pairs of eigenvalues appear consecutively with the eigenvalue
  // having the positive imaginary part first.
  //
  // In case \a A is a row-major matrix, the left eigenvectors are returned in the rows of \a V,
  // in case \a A is a column-major matrix, the right eigenvectors are returned in the columns of
  // \a V. In case the given matrix is a compile time symmetric matrix with floating point elements,
  // the resulting eigenvectors will be of floating point type and therefore the elements of the
  // given eigenvector matrix are expected to be of floating point type. In all other cases they
  // are expected to be of complex type.
  //
  // The function fails if ...
  //
  //  - ... the given matrix \a A is not a square matrix;
  //  - ... the given vector \a w is a fixed size vector and the size doesn't match;
  //  - ... the given matrix \a V is a fixed size matrix and the dimensions don't match;
  //  - ... the eigenvalue computation fails.
  //
  // In all failure cases an exception is thrown.
  //
  // Examples:
  
     \code
     using blaze::DynamicMatrix;
     using blaze::DynamicVector;
     using blaze::rowMajor;
     using blaze::columnVector;
  
     DynamicMatrix<double,rowMajor> A( 5UL, 5UL );  // The general matrix A
     // ... Initialization
  
     DynamicVector<complex<double>,columnVector> w( 5UL );   // The vector for the complex eigenvalues
     DynamicMatrix<complex<double>,rowMajor> V( 5UL, 5UL );  // The matrix for the left eigenvectors
  
     eigen( A, w, V );
     \endcode
  
     \code
     using blaze::SymmetricMatrix;
     using blaze::DynamicMatrix;
     using blaze::DynamicVector;
     using blaze::rowMajor;
     using blaze::columnVector;
  
     SymmetricMatrix< DynamicMatrix<double,rowMajor> > A( 5UL, 5UL );  // The symmetric matrix A
     // ... Initialization
  
     DynamicVector<double,columnVector> w( 5UL );       // The vector for the real eigenvalues
     DynamicMatrix<double,rowMajor>     V( 5UL, 5UL );  // The matrix for the left eigenvectors
  
     eigen( A, w, V );
     \endcode
  
     \code
     using blaze::HermitianMatrix;
     using blaze::DynamicMatrix;
     using blaze::DynamicVector;
     using blaze::rowMajor;
     using blaze::columnVector;
  
     HermitianMatrix< DynamicMatrix<complex<double>,rowMajor> > A( 5UL, 5UL );  // The Hermitian matrix A
     // ... Initialization
  
     DynamicVector<double,columnVector>      w( 5UL );       // The vector for the real eigenvalues
     DynamicMatrix<complex<double>,rowMajor> V( 5UL, 5UL );  // The matrix for the left eigenvectors
  
     eigen( A, w, V );
     \endcode
  
  // \note This function only works for matrices with \c float, \c double, \c complex<float>, or
  // \c complex<double> element type. The attempt to call the function with matrices of any other
  // element type results in a compile time error!
  //
  // \note This function can only be used if a fitting LAPACK library is available and linked to
  // the executable. Otherwise a call to this function will result in a linker error.
  //
  // \note Further options for computing eigenvalues and eigenvectors are available via the geev(),
  // syev(), syevd(), syevx(), heev(), heevd(), and heevx() functions.
  */
  template< typename MT1  // Type of the matrix A
          , bool SO1      // Storage order of the matrix A
          , typename VT   // Type of the vector w
          , bool TF       // Transpose flag of the vector w
          , typename MT2  // Type of the matrix V
          , bool SO2 >    // Storage order of the matrix V
  inline void eigen( const DenseMatrix<MT1,SO1>& A, DenseVector<VT,TF>& w, DenseMatrix<MT2,SO2>& V )
  {
     BLAZE_CONSTRAINT_MUST_NOT_BE_COMPUTATION_TYPE( MT1 );
     BLAZE_CONSTRAINT_MUST_BE_BLAS_COMPATIBLE_TYPE( ElementType_t<MT1> );
  
     BLAZE_CONSTRAINT_MUST_NOT_BE_COMPUTATION_TYPE( VT );
     BLAZE_CONSTRAINT_MUST_HAVE_MUTABLE_DATA_ACCESS( VT );
     BLAZE_CONSTRAINT_MUST_BE_BLAS_COMPATIBLE_TYPE( ElementType_t<VT> );
  
     BLAZE_CONSTRAINT_MUST_NOT_BE_ADAPTOR_TYPE( MT2 );
     BLAZE_CONSTRAINT_MUST_NOT_BE_COMPUTATION_TYPE( MT2 );
     BLAZE_CONSTRAINT_MUST_HAVE_MUTABLE_DATA_ACCESS( MT2 );
     BLAZE_CONSTRAINT_MUST_BE_BLAS_COMPATIBLE_TYPE( ElementType_t<MT2> );
  
     using WTmp = If_t< IsContiguous_v<VT>, VT&, ResultType_t<VT> >;
     using VTmp = If_t< IsContiguous_v<MT2>, MT2&, ResultType_t<MT2> >;
  
     WTmp wtmp( ~w );
     VTmp Vtmp( ~V );
  
     eigen_backend( ~A, wtmp, Vtmp );
  
     if( !IsContiguous_v<VT> ) {
        (~w) = wtmp;
     }
  
     if( !IsContiguous_v<MT2> ) {
        (~V) = Vtmp;
     }
  }
  //*************************************************************************************************
  
  } // namespace blaze
  
  #endif
  