Commit c218dd6d authored by Jakub Klinkovský's avatar Jakub Klinkovský
Browse files

Added preconditioning to the CG solver

parent ca5b9f96

src/TNL/Solvers/Linear/CG.h

+1 −1
Original line number Diff line number Diff line
@@ -37,7 +37,7 @@ public: 
protected:

   void setSize( IndexType size );



   Containers::Vector< RealType, DeviceType, IndexType >  r, new_r, p, Ap;

   Containers::Vector< RealType, DeviceType, IndexType >  r, p, Ap, z;

};



} // namespace Linear

src/TNL/Solvers/Linear/CG_impl.h

+64 −45
Original line number Diff line number Diff line
@@ -33,81 +33,100 @@ solve( ConstVectorViewType b, VectorViewType x ) 
   this->resetIterations();



   RealType alpha, beta, s1, s2;

   RealType bNorm = b.lpNorm( ( RealType ) 2.0 );



   // initialize the norm of the preconditioned right-hand-side

   RealType normb;

   if( this->preconditioner ) {

      this->preconditioner->solve( b, r );

      normb = r.lpNorm( 2.0 );

   }

   else

      normb = b.lpNorm( 2.0 );

   if( normb == 0.0 )

      normb = 1.0;



   /****

    * r_0 = b - A x_0, p_0 = r_0

    */

   this->matrix->vectorProduct( x, r );

   r.addVector( b, 1.0, -1.0 );

   p = r;



   if( this->preconditioner ) {

      // z_0 = M^{-1} r_0

      this->preconditioner->solve( r, z );

      // p_0 = z_0

      p = z;

      // s1 = (r_0, z_0)

      s1 = r.scalarProduct( z );

   }

   else {

      // p_0 = r_0

      p = r;

      // s1 = (r_0, r_0)

      s1 = r.scalarProduct( r );

   // TODO

   //this->setResidue( std::sqrt(s1) / bNorm );

   this->setResidue( std::sqrt(s1) );

   }



   this->setResidue( std::sqrt(s1) / normb );



   while( this->nextIteration() )

   {

      /****

       * 1. alpha_j = ( r_j, r_j ) / ( A * p_j, p_j )

       */

      // s2 = (A * p_j, p_j)

      this->matrix->vectorProduct( p, Ap );

      s2 = Ap.scalarProduct( p );



      /****

       * if s2 = 0 => p = 0 => r = 0 => we have the solution (provided A != 0)

       */

      if( s2 == 0.0 ) break;

      else alpha = s1 / s2;

      // if s2 = 0 => p = 0 => r = 0 => we have the solution (provided A != 0)

      if( s2 == 0.0 ) {

         this->setResidue( 0.0 );

         break;

      }



      /****

       * 2. x_{j+1} = x_j + \alpha_j p_j

       */

      // alpha_j = (r_j, z_j) / (A * p_j, p_j)

      alpha = s1 / s2;



      // x_{j+1} = x_j + alpha_j p_j

      x.addVector( p, alpha );



      /****

       * 3. r_{j+1} = r_j - \alpha_j A * p_j

       */

      new_r.addVectors( r, 1, Ap, -alpha, 0 );

      // r_{j+1} = r_j - alpha_j A * p_j

      r.addVector( Ap, -alpha );



      /****

       * 4. beta_j = ( r_{j+1}, r_{j+1} ) / ( r_j, r_j )

       */

      if( this->preconditioner ) {

         // z_{j+1} = M^{-1} * r_{j+1}

         this->preconditioner->solve( r, z );

         // beta_j = (r_{j+1}, z_{j+1}) / (r_j, z_j)

         s2 = s1;

      s1 = new_r.scalarProduct( new_r );

         s1 = r.scalarProduct( z );

      }

      else {

         // beta_j = (r_{j+1}, r_{j+1}) / (r_j, r_j)

         s2 = s1;

         s1 = r.scalarProduct( r );

      }



      /****

       * if s2 = 0 => r = 0 => we have the solution

       */

      // if s2 = 0 => r = 0 => we have the solution

      if( s2 == 0.0 ) beta = 0.0;

      else beta = s1 / s2;



      /****

       * 5. p_{j+1} = r_{j+1} + beta_j * p_j

       */

      p.addVector( new_r, 1.0, beta );



      /****

       * 6. r_{j+1} = new_r

       */

      new_r.swap( r );

      if( this->preconditioner )

         // p_{j+1} = z_{j+1} + beta_j * p_j

         p.addVector( z, 1.0, beta );

      else

         // p_{j+1} = r_{j+1} + beta_j * p_j

         p.addVector( r, 1.0, beta );



      // TODO

      //this->setResidue( std::sqrt(s1) / bNorm );

      this->setResidue( std::sqrt(s1) );

      this->setResidue( std::sqrt(s1) / normb );

   }

   this->refreshSolverMonitor( true );

   return this->checkConvergence();

}



template< typename Matrix >

void CG< Matrix > :: setSize( IndexType size )

void CG< Matrix >::

setSize( IndexType size )

{

   r.setSize( size );

   new_r.setSize( size );

   p.setSize( size );

   Ap.setSize( size );

   z.setSize( size );

}



} // namespace Linear