blaze/math/HermitianMatrix.h

//=================================================================================================
/*!
//  \file blaze/math/HermitianMatrix.h
//  \brief Header file for the complete HermitianMatrix implementation
//
//  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_HERMITIANMATRIX_H_
#define _BLAZE_MATH_HERMITIANMATRIX_H_


//*************************************************************************************************
// Includes
//*************************************************************************************************

#include <cmath>
#include <vector>
#include <blaze/math/Aliases.h>
#include <blaze/math/adaptors/DiagonalMatrix.h>
#include <blaze/math/adaptors/HermitianMatrix.h>
#include <blaze/math/constraints/DenseMatrix.h>
#include <blaze/math/constraints/Resizable.h>
#include <blaze/math/constraints/SparseMatrix.h>
#include <blaze/math/DenseMatrix.h>
#include <blaze/math/Exception.h>
#include <blaze/math/shims/Real.h>
#include <blaze/math/SparseMatrix.h>
#include <blaze/math/typetraits/IsDenseMatrix.h>
#include <blaze/math/typetraits/UnderlyingBuiltin.h>
#include <blaze/util/Assert.h>
#include <blaze/util/IntegralConstant.h>
#include <blaze/util/Random.h>
#include <blaze/util/Types.h>


namespace blaze {

//=================================================================================================
//
//  RAND SPECIALIZATION
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Specialization of the Rand class template for HermitianMatrix.
// \ingroup random
//
// This specialization of the Rand class creates random instances of HermitianMatrix.
*/
template< typename MT  // Type of the adapted matrix
        , bool SO      // Storage order of the adapted matrix
        , bool DF >    // Density flag
class Rand< HermitianMatrix<MT,SO,DF> >
{
 public:
   //**********************************************************************************************
   /*!\brief Generation of a random HermitianMatrix.
   //
   // \return The generated random matrix.
   */
   inline const HermitianMatrix<MT,SO,DF> generate() const
   {
      BLAZE_CONSTRAINT_MUST_NOT_BE_RESIZABLE_TYPE( MT );

      HermitianMatrix<MT,SO,DF> matrix;
      randomize( matrix );
      return matrix;
   }
   //**********************************************************************************************

   //**********************************************************************************************
   /*!\brief Generation of a random HermitianMatrix.
   //
   // \param n The number of rows and columns of the random matrix.
   // \return The generated random matrix.
   */
   inline const HermitianMatrix<MT,SO,DF> generate( size_t n ) const
   {
      BLAZE_CONSTRAINT_MUST_BE_RESIZABLE_TYPE( MT );

      HermitianMatrix<MT,SO,DF> matrix( n );
      randomize( matrix );
      return matrix;
   }
   //**********************************************************************************************

   //**********************************************************************************************
   /*!\brief Generation of a random HermitianMatrix.
   //
   // \param n The number of rows and columns of the random matrix.
   // \param nonzeros The number of non-zero elements of the random matrix.
   // \return The generated random matrix.
   // \exception std::invalid_argument Invalid number of non-zero elements.
   */
   inline const HermitianMatrix<MT,SO,DF> generate( size_t n, size_t nonzeros ) const
   {
      BLAZE_CONSTRAINT_MUST_BE_RESIZABLE_TYPE    ( MT );
      BLAZE_CONSTRAINT_MUST_BE_SPARSE_MATRIX_TYPE( MT );

      if( nonzeros > n*n ) {
         BLAZE_THROW_INVALID_ARGUMENT( "Invalid number of non-zero elements" );
      }

      HermitianMatrix<MT,SO,DF> matrix( n );
      randomize( matrix, nonzeros );

      return matrix;
   }
   //**********************************************************************************************

   //**********************************************************************************************
   /*!\brief Generation of a random HermitianMatrix.
   //
   // \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 Arg >  // Min/max argument type
   inline const HermitianMatrix<MT,SO,DF> generate( const Arg& min, const Arg& max ) const
   {
      BLAZE_CONSTRAINT_MUST_NOT_BE_RESIZABLE_TYPE( MT );

      HermitianMatrix<MT,SO,DF> matrix;
      randomize( matrix, min, max );
      return matrix;
   }
   //**********************************************************************************************

   //**********************************************************************************************
   /*!\brief Generation of a random HermitianMatrix.
   //
   // \param n The number of rows and columns of the random matrix.
   // \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 Arg >  // Min/max argument type
   inline const HermitianMatrix<MT,SO,DF> generate( size_t n, const Arg& min, const Arg& max ) const
   {
      BLAZE_CONSTRAINT_MUST_BE_RESIZABLE_TYPE( MT );

      HermitianMatrix<MT,SO,DF> matrix( n );
      randomize( matrix, min, max );
      return matrix;
   }
   //**********************************************************************************************

   //**********************************************************************************************
   /*!\brief Generation of a random HermitianMatrix.
   //
   // \param n The number of rows and columns of the random matrix.
   // \param nonzeros The number of non-zero elements of the random matrix.
   // \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.
   // \exception std::invalid_argument Invalid number of non-zero elements.
   */
   template< typename Arg >  // Min/max argument type
   inline const HermitianMatrix<MT,SO,DF> generate( size_t n, size_t nonzeros,
                                                    const Arg& min, const Arg& max ) const
   {
      BLAZE_CONSTRAINT_MUST_BE_RESIZABLE_TYPE    ( MT );
      BLAZE_CONSTRAINT_MUST_BE_SPARSE_MATRIX_TYPE( MT );

      if( nonzeros > n*n ) {
         BLAZE_THROW_INVALID_ARGUMENT( "Invalid number of non-zero elements" );
      }

      HermitianMatrix<MT,SO,DF> matrix( n );
      randomize( matrix, nonzeros, min, max );

      return matrix;
   }
   //**********************************************************************************************

   //**********************************************************************************************
   /*!\brief Randomization of a HermitianMatrix.
   //
   // \param matrix The matrix to be randomized.
   // \return void
   */
   inline void randomize( HermitianMatrix<MT,SO,DF>& matrix ) const
   {
      randomize( matrix, typename IsDenseMatrix<MT>::Type() );
   }
   //**********************************************************************************************

   //**********************************************************************************************
   /*!\brief Randomization of a sparse HermitianMatrix.
   //
   // \param matrix The matrix to be randomized.
   // \param nonzeros The number of non-zero elements of the random matrix.
   // \return void
   // \exception std::invalid_argument Invalid number of non-zero elements.
   */
   inline void randomize( HermitianMatrix<MT,SO,DF>& matrix, size_t nonzeros ) const
   {
      BLAZE_CONSTRAINT_MUST_BE_SPARSE_MATRIX_TYPE( MT );

      using ET = ElementType_t<MT>;
      using BT = UnderlyingBuiltin_t<ET>;

      const size_t n( matrix.rows() );

      if( nonzeros > n*n ) {
         BLAZE_THROW_INVALID_ARGUMENT( "Invalid number of non-zero elements" );
      }

      if( n == 0UL ) return;

      matrix.reset();
      matrix.reserve( nonzeros );

      while( matrix.nonZeros() < nonzeros )
      {
         const size_t row   ( rand<size_t>( 0UL, n-1UL ) );
         const size_t column( rand<size_t>( 0UL, n-1UL ) );

         if( row == column )
            matrix(row,column) = rand<BT>();
         else
            matrix(row,column) = rand<ET>();
      }
   }
   //**********************************************************************************************

   //**********************************************************************************************
   /*!\brief Randomization of a HermitianMatrix.
   //
   // \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 Arg >  // Min/max argument type
   inline void randomize( HermitianMatrix<MT,SO,DF>& matrix, const Arg& min, const Arg& max ) const
   {
      randomize( matrix, min, max, typename IsDenseMatrix<MT>::Type() );
   }
   //**********************************************************************************************

   //**********************************************************************************************
   /*!\brief Randomization of a sparse HermitianMatrix.
   //
   // \param matrix The matrix to be randomized.
   // \param nonzeros The number of non-zero elements of the random matrix.
   // \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 number of non-zero elements.
   */
   template< typename Arg >  // Min/max argument type
   inline void randomize( HermitianMatrix<MT,SO,DF>& matrix,
                          size_t nonzeros, const Arg& min, const Arg& max ) const
   {
      BLAZE_CONSTRAINT_MUST_BE_SPARSE_MATRIX_TYPE( MT );

      using ET = ElementType_t<MT>;
      using BT = UnderlyingBuiltin_t<ET>;

      const size_t n( matrix.rows() );

      if( nonzeros > n*n ) {
         BLAZE_THROW_INVALID_ARGUMENT( "Invalid number of non-zero elements" );
      }

      if( n == 0UL ) return;

      std::vector<size_t> dist( n );
      std::vector<bool> structure( n*n );
      size_t nz( 0UL );

      while( nz < nonzeros )
      {
         const size_t row = rand<size_t>( 0UL, n-1UL );
         const size_t col = rand<size_t>( 0UL, n-1UL );

         if( structure[row*n+col] ) continue;

         ++dist[row];
         structure[row*n+col] = true;
         ++nz;

         if( row != col ) {
            ++dist[col];
            structure[col*n+row] = true;
            ++nz;
         }
      }

      matrix.reset();
      matrix.reserve( nz );

      for( size_t i=0UL; i<n; ++i ) {
         matrix.reserve( i, dist[i] );
      }

      for( size_t i=0UL; i<n; ++i ) {
         for( size_t j=i; j<n; ++j ) {
            if( structure[i*n+j] ) {
               if( i == j )
                  matrix.append( i, j, rand<BT>( real( min ), real( max ) ) );
               else
                  matrix.append( i, j, rand<ET>( min, max ) );
            }
         }
      }
   }
   //**********************************************************************************************

 private:
   //**********************************************************************************************
   /*!\brief Randomization of a dense HermitianMatrix.
   //
   // \param matrix The matrix to be randomized.
   // \return void
   */
   inline void randomize( HermitianMatrix<MT,SO,DF>& matrix, TrueType ) const
   {
      BLAZE_CONSTRAINT_MUST_BE_DENSE_MATRIX_TYPE( MT );

      using ET = ElementType_t<MT>;
      using BT = UnderlyingBuiltin_t<ET>;

      const size_t n( matrix.rows() );

      for( size_t i=0UL; i<n; ++i ) {
         for( size_t j=0UL; j<i; ++j ) {
            matrix(i,j) = rand<ET>();
         }
         matrix(i,i) = rand<BT>();
      }
   }
   //**********************************************************************************************

   //**********************************************************************************************
   /*!\brief Randomization of a sparse HermitianMatrix.
   //
   // \param matrix The matrix to be randomized.
   // \return void
   */
   inline void randomize( HermitianMatrix<MT,SO,DF>& matrix, FalseType ) const
   {
      BLAZE_CONSTRAINT_MUST_BE_SPARSE_MATRIX_TYPE( MT );

      const size_t n( matrix.rows() );

      if( n == 0UL ) return;

      const size_t nonzeros( rand<size_t>( 1UL, std::ceil( 0.5*n*n ) ) );

      randomize( matrix, nonzeros );
   }
   //**********************************************************************************************

   //**********************************************************************************************
   /*!\brief Randomization of a dense HermitianMatrix.
   //
   // \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 Arg >  // Min/max argument type
   inline void randomize( HermitianMatrix<MT,SO,DF>& matrix,
                          const Arg& min, const Arg& max, TrueType ) const
   {
      BLAZE_CONSTRAINT_MUST_BE_DENSE_MATRIX_TYPE( MT );

      using ET = ElementType_t<MT>;
      using BT = UnderlyingBuiltin_t<ET>;

      const size_t n( matrix.rows() );

      for( size_t i=0UL; i<n; ++i ) {
         for( size_t j=0UL; j<i; ++j ) {
            matrix(i,j) = rand<ET>( min, max );
         }
         matrix(i,i) = rand<BT>( real( min ), real( max ) );
      }
   }
   //**********************************************************************************************

   //**********************************************************************************************
   /*!\brief Randomization of a sparse HermitianMatrix.
   //
   // \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 Arg >  // Min/max argument type
   inline void randomize( HermitianMatrix<MT,SO,DF>& matrix,
                          const Arg& min, const Arg& max, FalseType ) const
   {
      BLAZE_CONSTRAINT_MUST_BE_SPARSE_MATRIX_TYPE( MT );

      const size_t n( matrix.rows() );

      if( n == 0UL ) return;

      const size_t nonzeros( rand<size_t>( 1UL, std::ceil( 0.5*n*n ) ) );

      randomize( matrix, nonzeros, min, max );
   }
   //**********************************************************************************************
};
/*! \endcond */
//*************************************************************************************************


//=================================================================================================
//
//  MAKE FUNCTIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Setup of a random symmetric HermitianMatrix.
//
// \param matrix The matrix to be randomized.
// \return void
*/
template< typename MT  // Type of the adapted matrix
        , bool SO      // Storage order of the adapted matrix
        , bool DF >    // Density flag
void makeSymmetric( HermitianMatrix<MT,SO,DF>& matrix )
{
   using BT = UnderlyingBuiltin_t< ElementType_t<MT> >;

   const size_t n( matrix.rows() );

   for( size_t i=0UL; i<n; ++i ) {
      for( size_t j=0UL; j<=i; ++j ) {
         matrix(i,j) = rand<BT>();
      }
   }

   BLAZE_INTERNAL_ASSERT( isSymmetric( matrix ), "Non-symmetric matrix detected" );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Setup of a random symmetric HermitianMatrix.
//
// \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 MT     // Type of the adapted matrix
        , bool SO         // Storage order of the adapted matrix
        , bool DF         // Density flag
        , typename Arg >  // Min/max argument type
void makeSymmetric( HermitianMatrix<MT,SO,DF>& matrix, const Arg& min, const Arg& max )
{
   using BT = UnderlyingBuiltin_t< ElementType_t<MT> >;

   const size_t n( matrix.rows() );

   for( size_t i=0UL; i<n; ++i ) {
      for( size_t j=0UL; j<=i; ++j ) {
         matrix(i,j) = rand<BT>( real( min ), real( max ) );
      }
   }

   BLAZE_INTERNAL_ASSERT( isSymmetric( matrix ), "Non-symmetric matrix detected" );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Setup of a random Hermitian HermitianMatrix.
//
// \param matrix The matrix to be randomized.
// \return void
*/
template< typename MT  // Type of the adapted matrix
        , bool SO      // Storage order of the adapted matrix
        , bool DF >    // Density flag
void makeHermitian( HermitianMatrix<MT,SO,DF>& matrix )
{
   using blaze::randomize;

   randomize( matrix );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Setup of a random Hermitian HermitianMatrix.
//
// \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 MT     // Type of the adapted matrix
        , bool SO         // Storage order of the adapted matrix
        , bool DF         // Density flag
        , typename Arg >  // Min/max argument type
void makeHermitian( HermitianMatrix<MT,SO,DF>& matrix, const Arg& min, const Arg& max )
{
   using blaze::randomize;

   randomize( matrix, min, max );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Setup of a random (Hermitian) positive definite HermitianMatrix.
//
// \param matrix The matrix to be randomized.
// \return void
*/
template< typename MT  // Type of the adapted matrix
        , bool SO      // Storage order of the adapted matrix
        , bool DF >    // Density flag
void makePositiveDefinite( HermitianMatrix<MT,SO,DF>& matrix )
{
   using blaze::randomize;

   using BT = UnderlyingBuiltin_t< ElementType_t<MT> >;

   const size_t n( matrix.rows() );

   randomize( matrix );
   matrix *= matrix;

   for( size_t i=0UL; i<n; ++i ) {
      matrix(i,i) += BT(n);
   }
}
/*! \endcond */
//*************************************************************************************************

} // namespace blaze

#endif