text: //=================================================================================================
  /*!
  //  \file blaze/math/lapack/syevx.h
  //  \brief Header file for the LAPACK symmetric matrix eigenvalue functions (syevx)
  //
  //  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_SYEVX_H_
  #define _BLAZE_MATH_LAPACK_SYEVX_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/Exception.h>
  #include <blaze/math/expressions/DenseMatrix.h>
  #include <blaze/math/expressions/DenseVector.h>
  #include <blaze/math/lapack/clapack/syevx.h>
  #include <blaze/math/typetraits/IsRowMajorMatrix.h>
  #include <blaze/util/Assert.h>
  #include <blaze/util/constraints/Builtin.h>
  #include <blaze/util/NumericCast.h>
  #include <blaze/util/Types.h>
  #include <blaze/util/typetraits/IsFloatingPoint.h>
  
  
  namespace blaze {
  
  //=================================================================================================
  //
  //  LAPACK SYMMETRIC MATRIX EIGENVALUE FUNCTIONS (SYEVX)
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*!\name LAPACK symmetric matrix eigenvalue functions (syevx) */
  //@{
  template< typename MT, bool SO, typename VT, bool TF >
  size_t syevx( DenseMatrix<MT,SO>& A, DenseVector<VT,TF>& w, char uplo );
  
  template< typename MT, bool SO, typename VT, bool TF, typename ST >
  size_t syevx( DenseMatrix<MT,SO>& A, DenseVector<VT,TF>& w, char uplo, ST low, ST upp );
  
  template< typename MT1, bool SO1, typename VT, bool TF, typename MT2, bool SO2 >
  size_t syevx( DenseMatrix<MT1,SO1>& A, DenseVector<VT,TF>& w,
                DenseMatrix<MT2,SO2>& Z, char uplo );
  
  template< typename MT1, bool SO1, typename VT, bool TF, typename MT2, bool SO2, typename ST >
  size_t syevx( DenseMatrix<MT1,SO1>& A, DenseVector<VT,TF>& w,
                DenseMatrix<MT2,SO2>& Z, char uplo, ST low, ST upp );
  //@}
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Backend of the LAPACK heevx kernel for symmetric matrices.
  // \ingroup lapack_eigenvalue
  //
  // \param A The given symmetric matrix.
  // \param w The resulting vector of eigenvalues.
  // \param uplo \c 'L' to use the lower part of the matrix, \c 'U' to use the upper part.
  // \param range Specifies the range of eigenvalues to find (\c 'A', \c 'V', or \c 'I').
  // \param vl The lower bound of the interval to be searched for eigenvalues (\a vl < \a vu).
  // \param vu The upper bound of the interval to be searched for eigenvalues (\a vl < \a vu).
  // \param il The index of the smallest eigenvalue to be returned (0 <= \a il <= \a iu).
  // \param iu The index of the largest eigenvalue to be returned (0 <= \a il <= \a iu).
  // \return The total number of eigenvalues found.
  // \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
  // syevx() 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
          , typename ST >  // Type of the scalar boundary values
  inline size_t syevx_backend( DenseMatrix<MT,SO>& A, DenseVector<VT,TF>& w,
                               char uplo, char range, ST vl, ST vu,
                               blas_int_t il, blas_int_t iu )
  {
     BLAZE_INTERNAL_ASSERT( isSquare( ~A ), "Invalid non-square matrix detected" );
     BLAZE_INTERNAL_ASSERT( range != 'A' || (~w).size() == (~A).rows(), "Invalid vector dimension detected" );
     BLAZE_INTERNAL_ASSERT( range != 'V' || (~w).size() == (~A).rows(), "Invalid vector dimension detected" );
     BLAZE_INTERNAL_ASSERT( range != 'I' || (~w).size() == size_t( iu-il+1 ), "Invalid vector dimension detected" );
  
     using ET = ElementType_t<MT>;
  
     BLAZE_CONSTRAINT_MUST_BE_BUILTIN_TYPE( ET );
  
     blas_int_t n   ( numeric_cast<blas_int_t>( (~A).rows() ) );
     blas_int_t lda ( numeric_cast<blas_int_t>( (~A).spacing() ) );
     blas_int_t m   ( 0 );
     blas_int_t info( 0 );
  
     blas_int_t lwork( 12*n + 2 );
     const std::unique_ptr<ET[]>  work ( new ET[lwork] );
     const std::unique_ptr<blas_int_t[]> iwork( new blas_int_t[12*n] );
     const std::unique_ptr<blas_int_t[]> ifail( new blas_int_t[n] );
  
     syevx( 'N', range, uplo, n, (~A).data(), lda, vl, vu, il, iu, ET(0), &m,
            (~w).data(), nullptr, 1, work.get(), lwork, iwork.get(), ifail.get(), &info );
  
     const size_t num( numeric_cast<size_t>( m ) );
  
     BLAZE_INTERNAL_ASSERT( info >= 0, "Invalid argument for eigenvalue computation" );
     BLAZE_INTERNAL_ASSERT( num <= (~w).size(), "Invalid number of eigenvalues detected" );
  
     if( info > 0 ) {
        BLAZE_THROW_LAPACK_ERROR( "Eigenvalue computation failed" );
     }
  
     return num;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief LAPACK kernel for computing the eigenvalues of the given dense symmetric matrix.
  // \ingroup lapack_eigenvalue
  //
  // \param A The given symmetric matrix.
  // \param w The resulting vector of eigenvalues.
  // \param uplo \c 'L' to use the lower part of the matrix, \c 'U' to use the upper part.
  // \return The total number of eigenvalues found.
  // \exception std::invalid_argument Invalid non-square matrix provided.
  // \exception std::invalid_argument Vector cannot be resized.
  // \exception std::invalid_argument Invalid uplo argument provided.
  // \exception std::runtime_error Eigenvalue computation failed.
  //
  // This function computes all eigenvalues of a symmetric \a n-by-\a n matrix based on the
  // LAPACK syevx() functions. The real eigenvalues are returned in ascending order in the given
  // vector \a w. \a w is resized to the correct size (if possible and necessary).
  //
  // Note that this function can only be used 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 any adapted matrix or matrices of any other element type results in a compile
  // time error!
  //
  // 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 \a uplo argument is neither \c 'L' nor \c 'U';
  //  - ... 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 symmetric matrix A
     // ... Initialization
  
     DynamicVector<double,columnVector> w( 5UL );  // The vector for the real eigenvalues
  
     syevx( A, w, 'L' );
     \endcode
  
  // For more information on the syevx() functions (i.e. ssyevx() and dsyevx()) 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  // 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 size_t syevx( DenseMatrix<MT,SO>& A, DenseVector<VT,TF>& w, char uplo )
  {
     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> );
  
     BLAZE_CONSTRAINT_MUST_NOT_BE_COMPUTATION_TYPE( VT );
     BLAZE_CONSTRAINT_MUST_HAVE_MUTABLE_DATA_ACCESS( VT );
     BLAZE_CONSTRAINT_MUST_BE_CONTIGUOUS_TYPE( VT );
     BLAZE_CONSTRAINT_MUST_BE_BLAS_COMPATIBLE_TYPE( ElementType_t<VT> );
     BLAZE_CONSTRAINT_MUST_BE_BUILTIN_TYPE( ElementType_t<VT> );
  
     using ET = ElementType_t<MT>;
  
     const size_t N( (~A).rows() );
  
     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" );
     }
  
     resize( ~w, N, false );
  
     if( N == 0UL ) {
        return 0;
     }
  
     return syevx_backend( ~A, ~w, uplo, 'A', ET(), ET(), 0, 0 );
  }
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief LAPACK kernel for computing the eigenvalues of the given dense symmetric matrix.
  // \ingroup lapack_eigenvalue
  //
  // \param A The given symmetric matrix.
  // \param w The resulting vector of eigenvalues.
  // \param uplo \c 'L' to use the lower part of the matrix, \c 'U' to use the upper part.
  // \param low The lower bound of the interval to be searched for eigenvalues.
  // \param upp The upper bound of the interval to be searched for eigenvalues.
  // \return The total number of eigenvalues found.
  // \exception std::invalid_argument Invalid non-square matrix provided.
  // \exception std::invalid_argument Vector cannot be resized.
  // \exception std::invalid_argument Invalid uplo argument provided.
  // \exception std::invalid_argument Invalid value range provided.
  // \exception std::invalid_argument Invalid index range provided.
  // \exception std::runtime_error Eigenvalue computation failed.
  //
  // This function computes a specific number of eigenvalues of a symmetric \a n-by-\a n matrix
  // based on the LAPACK syevx() functions. The number of eigenvalues to be computed is specified
  // by the lower bound \a low and the upper bound \a upp, which either form an integral or a
  // floating point range.
  //
  // In case \a low and \a upp are of integral type, the function computes all eigenvalues in the
  // index range \f$[low..upp]\f$. The \a num resulting real eigenvalues are stored in ascending
  // order in the given vector \a w, which is either resized (if possible) or expected to be a
  // \a num-dimensional vector.
  //
  // In case \a low and \a upp are of floating point type, the function computes all eigenvalues
  // in the half-open interval \f$(low..upp]\f$. The resulting real eigenvalues are stored in
  // ascending order in the given vector \a w, which is either resized (if possible) or expected
  // to be an \a n-dimensional vector.
  //
  // Note that this function can only be used 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 any adapted matrix or matrices of any other element type results in a compile
  // time error!
  //
  // 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 scalar values don't form a proper range;
  //  - ... the given \a uplo argument is neither \c 'L' nor \c 'U';
  //  - ... 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 symmetric matrix A
     // ... Initialization
  
     DynamicVector<double,columnVector> w( 5UL );  // The vector for the real eigenvalues
  
     syevx( A, w, 'L', 1.0, 2.0 );  // Computes all eigenvalues in the interval (1..2]
     \endcode
  
     \code
     using blaze::DynamicMatrix;
     using blaze::DynamicVector;
     using blaze::rowMajor;
     using blaze::columnVector;
  
     DynamicMatrix<double,rowMajor> A( 5UL, 5UL );  // The symmetric matrix A
     // ... Initialization
  
     DynamicVector<double,columnVector> w( 3UL );  // The vector for the real eigenvalues
  
     syevx( A, w, 'L', 0, 2 );  // Computes the first three eigenvalues
     \endcode
  
  // For more information on the syevx() functions (i.e. ssyevx() and dsyevx()) 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    // 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
          , typename ST >  // Type of the scalar boundary values
  inline size_t syevx( DenseMatrix<MT,SO>& A, DenseVector<VT,TF>& w, char uplo, ST low, ST upp )
  {
     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> );
  
     BLAZE_CONSTRAINT_MUST_NOT_BE_COMPUTATION_TYPE( VT );
     BLAZE_CONSTRAINT_MUST_HAVE_MUTABLE_DATA_ACCESS( VT );
     BLAZE_CONSTRAINT_MUST_BE_CONTIGUOUS_TYPE( VT );
     BLAZE_CONSTRAINT_MUST_BE_BLAS_COMPATIBLE_TYPE( ElementType_t<VT> );
     BLAZE_CONSTRAINT_MUST_BE_BUILTIN_TYPE( ElementType_t<VT> );
  
     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( IsFloatingPoint_v<ST> && low >= upp ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid value range provided" );
     }
  
     if( !IsFloatingPoint_v<ST> && low > upp ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid index range provided" );
     }
  
     const size_t N( (~A).rows() );
     const size_t num( IsFloatingPoint_v<ST> ? N : size_t( upp - low ) + 1UL );
  
     if( !IsFloatingPoint_v<ST> && num > N ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid index range provided" );
     }
  
     resize( ~w, num, false );
  
     if( N == 0UL ) {
        return 0;
     }
  
     const char       range( IsFloatingPoint_v<ST> ? 'V' : 'I' );
     const ST         vl   ( IsFloatingPoint_v<ST> ? low : ST() );
     const ST         vu   ( IsFloatingPoint_v<ST> ? upp : ST() );
     const blas_int_t il   ( IsFloatingPoint_v<ST> ? 0 : numeric_cast<blas_int_t>( low ) );
     const blas_int_t iu   ( IsFloatingPoint_v<ST> ? 0 : numeric_cast<blas_int_t>( upp ) );
  
     return syevx_backend( ~A, ~w, uplo, range, vl, vu, il, iu );
  }
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Backend of the LAPACK heevx kernel for symmetric matrices.
  // \ingroup lapack_eigenvalue
  //
  // \param A The given symmetric matrix.
  // \param w The resulting vector of eigenvalues.
  // \param Z The resulting matrix of eigenvectors.
  // \param uplo \c 'L' to use the lower part of the matrix, \c 'U' to use the upper part.
  // \param range Specifies the range of eigenvalues to find (\c 'A', \c 'V', or \c 'I').
  // \param vl The lower bound of the interval to be searched for eigenvalues (\a vl < \a vu).
  // \param vu The upper bound of the interval to be searched for eigenvalues (\a vl < \a vu).
  // \param il The index of the smallest eigenvalue to be returned (0 <= \a il <= \a iu).
  // \param iu The index of the largest eigenvalue to be returned (0 <= \a il <= \a iu).
  // \return The total number of eigenvalues found.
  // \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
  // syevx() 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 Z
          , bool SO2       // Storage order of the matrix Z
          , typename ST >  // Type of the scalar boundary values
  inline size_t syevx_backend( DenseMatrix<MT1,SO1>& A, DenseVector<VT,TF>& w,
                               DenseMatrix<MT2,SO2>& Z, char uplo, char range,
                               ST vl, ST vu, blas_int_t il, blas_int_t iu )
  {
     BLAZE_INTERNAL_ASSERT( isSquare( ~A ), "Invalid non-square matrix detected" );
     BLAZE_INTERNAL_ASSERT( range != 'A' || (~w).size() == (~A).rows(), "Invalid vector dimension detected" );
     BLAZE_INTERNAL_ASSERT( range != 'V' || (~w).size() == (~A).rows(), "Invalid vector dimension detected" );
     BLAZE_INTERNAL_ASSERT( range != 'I' || (~w).size() == size_t( iu-il+1 ), "Invalid vector dimension detected" );
     BLAZE_INTERNAL_ASSERT( SO2  || (~Z).rows()    == (~w).size(), "Invalid matrix dimension detected" );
     BLAZE_INTERNAL_ASSERT( SO2  || (~Z).columns() == (~A).rows(), "Invalid matrix dimension detected" );
     BLAZE_INTERNAL_ASSERT( !SO2 || (~Z).rows()    == (~A).rows(), "Invalid matrix dimension detected" );
     BLAZE_INTERNAL_ASSERT( !SO2 || (~Z).columns() == (~w).size(), "Invalid matrix dimension detected" );
  
     using ET = ElementType_t<MT1>;
  
     BLAZE_CONSTRAINT_MUST_BE_BUILTIN_TYPE( ET );
  
     blas_int_t n   ( numeric_cast<blas_int_t>( (~A).rows() ) );
     blas_int_t lda ( numeric_cast<blas_int_t>( (~A).spacing() ) );
     blas_int_t m   ( 0 );
     blas_int_t ldz ( numeric_cast<blas_int_t>( (~Z).spacing() ) );
     blas_int_t info( 0 );
  
     blas_int_t lwork( 12*n + 2 );
     const std::unique_ptr<ET[]>  work ( new ET[lwork] );
     const std::unique_ptr<blas_int_t[]> iwork( new blas_int_t[12*n] );
     const std::unique_ptr<blas_int_t[]> ifail( new blas_int_t[n] );
  
     syevx( 'N', range, uplo, n, (~A).data(), lda, vl, vu, il, iu, ET(0), &m,
            (~w).data(), (~Z).data(), ldz, work.get(), lwork, iwork.get(), ifail.get(), &info );
  
     const size_t num( numeric_cast<size_t>( m ) );
  
     BLAZE_INTERNAL_ASSERT( info >= 0, "Invalid argument for eigenvalue computation" );
     BLAZE_INTERNAL_ASSERT( num <= (~w).size(), "Invalid number of eigenvalues detected" );
  
     if( info > 0 ) {
        BLAZE_THROW_LAPACK_ERROR( "Eigenvalue computation failed" );
     }
  
     return num;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief LAPACK kernel for computing the eigenvalues of the given dense symmetric matrix.
  // \ingroup lapack_eigenvalue
  //
  // \param A The given symmetric matrix.
  // \param w The resulting vector of eigenvalues.
  // \param Z The resulting matrix of eigenvectors.
  // \param uplo \c 'L' to use the lower part of the matrix, \c 'U' to use the upper part.
  // \return The total number of eigenvalues found.
  // \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::invalid_argument Invalid uplo argument provided.
  // \exception std::runtime_error Eigenvalue computation failed.
  //
  // This function computes all eigenvalues of a symmetric \a n-by-\a n matrix based on the LAPACK
  // syevx() functions. Additionally, it computes all eigenvectors of \a A. The real eigenvalues
  // are returned in ascending order in the given vector \a w. The eigenvectors are returned in
  // the rows of \a Z in case \a Z is a row-major matrix and in the columns of \a Z in case \a Z
  // is a column-major matrix. Both \a w and \a Z are resized to the correct dimensions (if
  // possible and necessary).
  //
  // Note that this function can only be used 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 any adapted matrix or matrices of any other element type results in a compile
  // time error!
  //
  // 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 Z is a fixed size matrix and the dimensions don't match;
  //  - ... the given \a uplo argument is neither \c 'L' nor \c 'U';
  //  - ... 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 symmetric matrix A
     // ... Initialization
  
     DynamicVector<double,columnVector> w( 5UL );       // The vector for the real eigenvalues
     DynamicMatrix<double,rowMajor>     Z( 5UL, 5UL );  // The matrix for the real eigenvectors
  
     syevx( A, w, 'L' );
     \endcode
  
  // For more information on the syevx() functions (i.e. ssyevx() and dsyevx()) 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 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 Z
          , bool SO2 >    // Storage order of the matrix Z
  inline size_t syevx( DenseMatrix<MT1,SO1>& A, DenseVector<VT,TF>& w,
                       DenseMatrix<MT2,SO2>& Z, char uplo )
  {
     BLAZE_CONSTRAINT_MUST_NOT_BE_ADAPTOR_TYPE( MT1 );
     BLAZE_CONSTRAINT_MUST_NOT_BE_COMPUTATION_TYPE( MT1 );
     BLAZE_CONSTRAINT_MUST_HAVE_MUTABLE_DATA_ACCESS( MT1 );
     BLAZE_CONSTRAINT_MUST_BE_CONTIGUOUS_TYPE( MT1 );
     BLAZE_CONSTRAINT_MUST_BE_BLAS_COMPATIBLE_TYPE( ElementType_t<MT1> );
     BLAZE_CONSTRAINT_MUST_BE_BUILTIN_TYPE( ElementType_t<MT1> );
  
     BLAZE_CONSTRAINT_MUST_NOT_BE_COMPUTATION_TYPE( VT );
     BLAZE_CONSTRAINT_MUST_HAVE_MUTABLE_DATA_ACCESS( VT );
     BLAZE_CONSTRAINT_MUST_BE_CONTIGUOUS_TYPE( VT );
     BLAZE_CONSTRAINT_MUST_BE_BLAS_COMPATIBLE_TYPE( ElementType_t<VT> );
     BLAZE_CONSTRAINT_MUST_BE_BUILTIN_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_CONTIGUOUS_TYPE( MT2 );
     BLAZE_CONSTRAINT_MUST_BE_BLAS_COMPATIBLE_TYPE( ElementType_t<MT2> );
     BLAZE_CONSTRAINT_MUST_BE_BUILTIN_TYPE( ElementType_t<MT2> );
  
     using ET = ElementType_t<MT1>;
  
     const size_t N( (~A).rows() );
  
     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" );
     }
  
     resize( ~w, N, false );
     resize( ~Z, N, N, false );
  
     if( N == 0UL ) {
        return 0;
     }
  
     return syevx_backend( ~A, ~w, ~Z, uplo, 'A', ET(), ET(), 0, 0 );
  }
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief LAPACK kernel for computing the eigenvalues of the given dense symmetric matrix.
  // \ingroup lapack_eigenvalue
  //
  // \param A The given symmetric matrix.
  // \param w The resulting vector of eigenvalues.
  // \param Z The resulting matrix of eigenvectors.
  // \param uplo \c 'L' to use the lower part of the matrix, \c 'U' to use the upper part.
  // \param low The lower bound of the interval to be searched for eigenvalues.
  // \param upp The upper bound of the interval to be searched for eigenvalues.
  // \return The total number of eigenvalues found.
  // \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::invalid_argument Invalid uplo argument provided.
  // \exception std::invalid_argument Invalid value range provided.
  // \exception std::invalid_argument Invalid index range provided.
  // \exception std::runtime_error Eigenvalue computation failed.
  //
  // This function computes a specific number of eigenvalues of a symmetric \a n-by-\a n matrix
  // based on the LAPACK syevx() functions. Additionally, it computes a specific number of
  // eigenvectors of \a A. The number of eigenvalues to be computed is specified by the lower
  // bound \a low and the upper bound \a upp, which either form an integral or a floating point
  // range.
  //
  // In case \a low and \a upp are of integral type, the function computes all eigenvalues in the
  // index range \f$[low..upp]\f$. The \a num resulting real eigenvalues are stored in ascending
  // order in the given vector \a w, which is either resized (if possible) or expected to be a
  // \a num-dimensional vector. The eigenvectors are returned in the rows of \a Z in case \a Z is
  // row-major matrix and in the columns of \a Z in case \a Z is a column-major matrix. \a Z is
  // resized (if possible) or expected to be a \a num-by-\a n row-major matrix or a \a n-by-\a num
  // column-major matrix.
  //
  // In case \a low and \a upp are of floating point type, the function computes all eigenvalues
  // in the half-open interval \f$(low..upp]\f$. The resulting real eigenvalues are stored in
  // ascending order in the given vector \a w, which is either resized (if possible) or expected
  // to be an \a n-dimensional vector. The eigenvectors are returned in the rows of \a Z in case
  // \a Z is a row-major matrix and in the columns of \a Z in case \a Z is a column-major matrix.
  // \a Z is resized (if possible) or expected to be a \a n-by-\a n matrix.
  //
  // Note that this function can only be used 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 any adapted matrix or matrices of any other element type results in a compile
  // time error!
  //
  // 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 Z is a fixed size matrix and the dimensions don't match;
  //  - ... the given \a uplo argument is neither \c 'L' nor \c 'U';
  //  - ... 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 Hermitian matrix A
     // ... Initialization
  
     DynamicVector<double,columnVector> w( 5UL );       // The vector for the real eigenvalues
     DynamicMatrix<double,rowMajor>     Z( 5UL, 5UL );  // The matrix for the real eigenvectors
  
     syevx( A, w, Z, 'L', 1.0, 2.0 );  // Computes all eigenvalues in the interval (1..2]
     \endcode
  
     \code
     using blaze::DynamicMatrix;
     using blaze::DynamicVector;
     using blaze::rowMajor;
     using blaze::columnVector;
  
     DynamicMatrix<double,rowMajor> A( 5UL, 5UL );  // The Hermitian matrix A
     // ... Initialization
  
     DynamicVector<double,columnVector> w( 3UL );       // The vector for the real eigenvalues
     DynamicMatrix<double,rowMajor>     Z( 3UL, 5UL );  // The matrix for the real eigenvectors
  
     syevx( A, w, Z, 'L', 0, 2 );  // Computes the first three eigenvalues
     \endcode
  
  // For more information on the syevx() functions (i.e. ssyevx() and dsyevx()) 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 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 Z
          , bool SO2       // Storage order of the matrix Z
          , typename ST >  // Type of the scalar boundary values
  inline size_t syevx( DenseMatrix<MT1,SO1>& A, DenseVector<VT,TF>& w,
                       DenseMatrix<MT2,SO2>& Z, char uplo, ST low, ST upp )
  {
     BLAZE_CONSTRAINT_MUST_NOT_BE_ADAPTOR_TYPE( MT1 );
     BLAZE_CONSTRAINT_MUST_NOT_BE_COMPUTATION_TYPE( MT1 );
     BLAZE_CONSTRAINT_MUST_HAVE_MUTABLE_DATA_ACCESS( MT1 );
     BLAZE_CONSTRAINT_MUST_BE_CONTIGUOUS_TYPE( MT1 );
     BLAZE_CONSTRAINT_MUST_BE_BLAS_COMPATIBLE_TYPE( ElementType_t<MT1> );
     BLAZE_CONSTRAINT_MUST_BE_BUILTIN_TYPE( ElementType_t<MT1> );
  
     BLAZE_CONSTRAINT_MUST_NOT_BE_COMPUTATION_TYPE( VT );
     BLAZE_CONSTRAINT_MUST_HAVE_MUTABLE_DATA_ACCESS( VT );
     BLAZE_CONSTRAINT_MUST_BE_CONTIGUOUS_TYPE( VT );
     BLAZE_CONSTRAINT_MUST_BE_BLAS_COMPATIBLE_TYPE( ElementType_t<VT> );
     BLAZE_CONSTRAINT_MUST_BE_BUILTIN_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_CONTIGUOUS_TYPE( MT2 );
     BLAZE_CONSTRAINT_MUST_BE_BLAS_COMPATIBLE_TYPE( ElementType_t<MT2> );
     BLAZE_CONSTRAINT_MUST_BE_BUILTIN_TYPE( ElementType_t<MT2> );
  
     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( IsFloatingPoint_v<ST> && low >= upp ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid value range provided" );
     }
  
     if( !IsFloatingPoint_v<ST> && low > upp ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid index range provided" );
     }
  
     const size_t N( (~A).rows() );
     const size_t num( IsFloatingPoint_v<ST> ? N : size_t( upp - low ) + 1UL );
  
     if( !IsFloatingPoint_v<ST> && num > N ) {
        BLAZE_THROW_INVALID_ARGUMENT( "Invalid index range provided" );
     }
  
     resize( ~w, num, false );
     resize( ~Z, ( IsRowMajorMatrix_v<MT2> ? num : N ),
             ( IsRowMajorMatrix_v<MT2> ? N : num ), false );
  
     if( N == 0UL ) {
        return 0;
     }
  
     const char       range( IsFloatingPoint_v<ST> ? 'V' : 'I' );
     const ST         vl   ( IsFloatingPoint_v<ST> ? low : ST() );
     const ST         vu   ( IsFloatingPoint_v<ST> ? upp : ST() );
     const blas_int_t il   ( IsFloatingPoint_v<ST> ? 0 : numeric_cast<blas_int_t>( low ) );
     const blas_int_t iu   ( IsFloatingPoint_v<ST> ? 0 : numeric_cast<blas_int_t>( upp ) );
  
     return syevx_backend( ~A, ~w, ~Z, uplo, range, vl, vu, il, iu );
  }
  //*************************************************************************************************
  
  } // namespace blaze
  
  #endif
  