text: //=================================================================================================
  /*!
  //  \file blaze/math/StaticMatrix.h
  //  \brief Header file for the complete StaticMatrix implementation
  //
  //  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_STATICMATRIX_H_
  #define _BLAZE_MATH_STATICMATRIX_H_
  
  
  //*************************************************************************************************
  // Includes
  //*************************************************************************************************
  
  #include <blaze/math/dense/StaticMatrix.h>
  #include <blaze/math/DenseMatrix.h>
  #include <blaze/math/HybridMatrix.h>
  #include <blaze/math/IdentityMatrix.h>
  #include <blaze/math/shims/Conjugate.h>
  #include <blaze/math/shims/Real.h>
  #include <blaze/math/StaticVector.h>
  #include <blaze/math/typetraits/UnderlyingBuiltin.h>
  #include <blaze/util/Assert.h>
  #include <blaze/util/constraints/Numeric.h>
  #include <blaze/util/Random.h>
  #include <blaze/util/StaticAssert.h>
  
  
  namespace blaze {
  
  //=================================================================================================
  //
  //  RAND SPECIALIZATION
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Specialization of the Rand class template for StaticMatrix.
  // \ingroup random
  //
  // This specialization of the Rand class creates random instances of StaticMatrix.
  */
  template< typename Type  // Data type of the matrix
          , size_t M       // Number of rows
          , size_t N       // Number of columns
          , bool SO >      // Storage order
  class Rand< StaticMatrix<Type,M,N,SO> >
  {
   public:
     //**Generate functions**************************************************************************
     /*!\name Generate functions */
     //@{
     inline const StaticMatrix<Type,M,N,SO> generate() const;
  
     template< typename Arg >
     inline const StaticMatrix<Type,M,N,SO> generate( const Arg& min, const Arg& max ) const;
     //@}
     //**********************************************************************************************
  
     //**Randomize functions*************************************************************************
     /*!\name Randomize functions */
     //@{
     inline void randomize( StaticMatrix<Type,M,N,SO>& matrix ) const;
  
     template< typename Arg >
     inline void randomize( StaticMatrix<Type,M,N,SO>& matrix, const Arg& min, const Arg& max ) const;
     //@}
     //**********************************************************************************************
  };
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Generation of a random StaticMatrix.
  //
  // \return The generated random matrix.
  */
  template< typename Type  // Data type of the matrix
          , size_t M       // Number of rows
          , size_t N       // Number of columns
          , bool SO >      // Storage order
  inline const StaticMatrix<Type,M,N,SO> Rand< StaticMatrix<Type,M,N,SO> >::generate() const
  {
     StaticMatrix<Type,M,N,SO> matrix;
     randomize( matrix );
     return matrix;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Generation of a random StaticMatrix.
  //
  // \param min The smallest possible value for a matrix element.
  // \param max The largest possible value for a matrix element.
  // \return The generated random matrix.
  */
  template< typename Type   // Data type of the matrix
          , size_t M        // Number of rows
          , size_t N        // Number of columns
          , bool SO >       // Storage order
  template< typename Arg >  // Min/max argument type
  inline const StaticMatrix<Type,M,N,SO>
     Rand< StaticMatrix<Type,M,N,SO> >::generate( const Arg& min, const Arg& max ) const
  {
     StaticMatrix<Type,M,N,SO> matrix;
     randomize( matrix, min, max );
     return matrix;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Randomization of a StaticMatrix.
  //
  // \param matrix The matrix to be randomized.
  // \return void
  */
  template< typename Type  // Data type of the matrix
          , size_t M       // Number of rows
          , size_t N       // Number of columns
          , bool SO >      // Storage order
  inline void Rand< StaticMatrix<Type,M,N,SO> >::randomize( StaticMatrix<Type,M,N,SO>& matrix ) const
  {
     using blaze::randomize;
  
     for( size_t i=0UL; i<M; ++i ) {
        for( size_t j=0UL; j<N; ++j ) {
           randomize( matrix(i,j) );
        }
     }
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Randomization of a StaticMatrix.
  //
  // \param matrix The matrix to be randomized.
  // \param min The smallest possible value for a matrix element.
  // \param max The largest possible value for a matrix element.
  // \return void
  */
  template< typename Type   // Data type of the matrix
          , size_t M        // Number of rows
          , size_t N        // Number of columns
          , bool SO >       // Storage order
  template< typename Arg >  // Min/max argument type
  inline void Rand< StaticMatrix<Type,M,N,SO> >::randomize( StaticMatrix<Type,M,N,SO>& matrix,
                                                            const Arg& min, const Arg& max ) const
  {
     using blaze::randomize;
  
     for( size_t i=0UL; i<M; ++i ) {
        for( size_t j=0UL; j<N; ++j ) {
           randomize( matrix(i,j), min, max );
        }
     }
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  MAKE FUNCTIONS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Setup of a random symmetric StaticMatrix.
  //
  // \param matrix The matrix to be randomized.
  // \return void
  // \exception std::invalid_argument Invalid non-square matrix provided.
  */
  template< typename Type  // Data type of the matrix
          , size_t M       // Number of rows
          , size_t N       // Number of columns
          , bool SO >      // Storage order
  void makeSymmetric( StaticMatrix<Type,M,N,SO>& matrix )
  {
     using blaze::randomize;
  
     BLAZE_STATIC_ASSERT( M == N );
  
     for( size_t i=0UL; i<N; ++i ) {
        for( size_t j=0UL; j<i; ++j ) {
           randomize( matrix(i,j) );
           matrix(j,i) = matrix(i,j);
        }
        randomize( matrix(i,i) );
     }
  
     BLAZE_INTERNAL_ASSERT( isSymmetric( matrix ), "Non-symmetric matrix detected" );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Setup of a random symmetric StaticMatrix.
  //
  // \param matrix The matrix to be randomized.
  // \param min The smallest possible value for a matrix element.
  // \param max The largest possible value for a matrix element.
  // \return void
  // \exception std::invalid_argument Invalid non-square matrix provided.
  */
  template< typename Type   // Data type of the matrix
          , size_t M        // Number of rows
          , size_t N        // Number of columns
          , bool SO         // Storage order
          , typename Arg >  // Min/max argument type
  void makeSymmetric( StaticMatrix<Type,M,N,SO>& matrix, const Arg& min, const Arg& max )
  {
     using blaze::randomize;
  
     BLAZE_STATIC_ASSERT( M == N );
  
     for( size_t i=0UL; i<N; ++i ) {
        for( size_t j=0UL; j<i; ++j ) {
           randomize( matrix(i,j), min, max );
           matrix(j,i) = matrix(i,j);
        }
        randomize( matrix(i,i), min, max );
     }
  
     BLAZE_INTERNAL_ASSERT( isSymmetric( matrix ), "Non-symmetric matrix detected" );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Setup of a random Hermitian StaticMatrix.
  //
  // \param matrix The matrix to be randomized.
  // \return void
  // \exception std::invalid_argument Invalid non-square matrix provided.
  */
  template< typename Type  // Data type of the matrix
          , size_t M       // Number of rows
          , size_t N       // Number of columns
          , bool SO >      // Storage order
  void makeHermitian( StaticMatrix<Type,M,N,SO>& matrix )
  {
     using blaze::randomize;
  
     BLAZE_STATIC_ASSERT( M == N );
     BLAZE_CONSTRAINT_MUST_BE_NUMERIC_TYPE( Type );
  
     using BT = UnderlyingBuiltin_<Type>;
  
     for( size_t i=0UL; i<N; ++i ) {
        for( size_t j=0UL; j<i; ++j ) {
           randomize( matrix(i,j) );
           matrix(j,i) = conj( matrix(i,j) );
        }
        matrix(i,i) = rand<BT>();
     }
  
     BLAZE_INTERNAL_ASSERT( isHermitian( matrix ), "Non-Hermitian matrix detected" );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Setup of a random Hermitian StaticMatrix.
  //
  // \param matrix The matrix to be randomized.
  // \param min The smallest possible value for a matrix element.
  // \param max The largest possible value for a matrix element.
  // \return void
  // \exception std::invalid_argument Invalid non-square matrix provided.
  */
  template< typename Type   // Data type of the matrix
          , size_t M        // Number of rows
          , size_t N        // Number of columns
          , bool SO         // Storage order
          , typename Arg >  // Min/max argument type
  void makeHermitian( StaticMatrix<Type,M,N,SO>& matrix, const Arg& min, const Arg& max )
  {
     using blaze::randomize;
  
     BLAZE_STATIC_ASSERT( M == N );
     BLAZE_CONSTRAINT_MUST_BE_NUMERIC_TYPE( Type );
  
     using BT = UnderlyingBuiltin_<Type>;
  
     for( size_t i=0UL; i<N; ++i ) {
        for( size_t j=0UL; j<i; ++j ) {
           randomize( matrix(i,j), min, max );
           matrix(j,i) = conj( matrix(i,j) );
        }
        matrix(i,i) = rand<BT>( real( min ), real( max ) );
     }
  
     BLAZE_INTERNAL_ASSERT( isHermitian( matrix ), "Non-Hermitian matrix detected" );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Setup of a random (Hermitian) positive definite StaticMatrix.
  //
  // \param matrix The matrix to be randomized.
  // \return void
  // \exception std::invalid_argument Invalid non-square matrix provided.
  */
  template< typename Type  // Data type of the matrix
          , size_t M       // Number of rows
          , size_t N       // Number of columns
          , bool SO >      // Storage order
  void makePositiveDefinite( StaticMatrix<Type,M,N,SO>& matrix )
  {
     using blaze::randomize;
  
     BLAZE_STATIC_ASSERT( M == N );
     BLAZE_CONSTRAINT_MUST_BE_NUMERIC_TYPE( Type );
  
     randomize( matrix );
     matrix *= ctrans( matrix );
  
     for( size_t i=0UL; i<N; ++i ) {
        matrix(i,i) += Type(N);
     }
  
     BLAZE_INTERNAL_ASSERT( isHermitian( matrix ), "Non-symmetric matrix detected" );
  }
  /*! \endcond */
  //*************************************************************************************************
  
  } // namespace blaze
  
  #endif
  