vectorial.hh

#ifndef DUNE_FEM_BASISFUNCTIONSET_VECTORIAL_HH
#define DUNE_FEM_BASISFUNCTIONSET_VECTORIAL_HH
 
#include <cstddef>
#include <utility>
#include <vector>
 
#include <dune/geometry/referenceelements.hh>
#include <dune/geometry/type.hh>
 
#include <dune/fem/space/basisfunctionset/functor.hh>
#include <dune/fem/space/common/functionspace.hh>
 
namespace Dune
{
 
  namespace Fem
  {
 
    // DofAlignment
    // ------------
 
    template< class Implementation >
    class DofAlignment
    {
    public:
      typedef std::size_t GlobalDofType;
      typedef std::pair< int, std::size_t > LocalDofType;
 
    protected:
      DofAlignment () = default;
 
    public:
      GlobalDofType globalDof ( const LocalDofType &localDof ) const
      {
        return impl().globalDof( localDof );
      }
 
      LocalDofType localDof ( const GlobalDofType &globalDof ) const
      {
        return impl().localDof( globalDof );
      }
 
    protected:
      const Implementation &impl () const
      {
        return static_cast< const Implementation & >( *this );
      }
    };
 
 
 
    // HorizontalDofAlignment
    // ----------------------
 
    template< class ScalarBasisFunctionSet, class Range >
    class HorizontalDofAlignment
    : public DofAlignment< HorizontalDofAlignment< ScalarBasisFunctionSet, Range > >
    {
      typedef HorizontalDofAlignment< ScalarBasisFunctionSet, Range > ThisType;
      typedef DofAlignment< HorizontalDofAlignment< ScalarBasisFunctionSet, Range > > BaseType;
 
    public:
      typedef typename BaseType::GlobalDofType GlobalDofType;
      typedef typename BaseType::LocalDofType LocalDofType;
 
      HorizontalDofAlignment () = default;
 
      explicit HorizontalDofAlignment ( const ScalarBasisFunctionSet &scalarBasisFunctionSet )
      : scalarSize_( scalarBasisFunctionSet.size() )
      {}
 
      GlobalDofType globalDof ( const LocalDofType &localDof ) const
      {
        return GlobalDofType( localDof.first*scalarSize_ + localDof.second );
      }
 
      LocalDofType localDof ( const GlobalDofType &globalDof ) const
      {
         return LocalDofType( globalDof / scalarSize_, globalDof % scalarSize_ );
      }
 
    private:
      std::size_t scalarSize_;
    };
 
 
 
    // VerticalDofAlignment
    // --------------------
 
    template< class ScalarBasisFunctionSet, class Range >
    class VerticalDofAlignment
    : public DofAlignment< VerticalDofAlignment< ScalarBasisFunctionSet, Range > >
    {
      typedef VerticalDofAlignment< ScalarBasisFunctionSet, Range > ThisType;
      typedef DofAlignment< VerticalDofAlignment< ScalarBasisFunctionSet, Range > > BaseType;
 
      static const int dimRange = Range::dimension;
 
    public:
      typedef typename BaseType::GlobalDofType GlobalDofType;
      typedef typename BaseType::LocalDofType LocalDofType;
 
      VerticalDofAlignment () = default;
 
      explicit VerticalDofAlignment ( const ScalarBasisFunctionSet & ) {}
 
      GlobalDofType globalDof ( const LocalDofType &localDof ) const
      {
        return GlobalDofType( localDof.first + localDof.second*dimRange );
      }
 
      LocalDofType localDof ( const GlobalDofType &globalDof ) const
      {
        return LocalDofType( globalDof % dimRange, globalDof / dimRange );
      }
    };
 
 
 
    // SubDofVector
    // ------------
 
    template< class DofVector, class DofAlignment >
    class SubDofVector;
 
    // note: DofVector can be also const DofVector
    template< class DofVector, class ScalarBasisFunctionSet, class Range >
    class SubDofVector< DofVector, HorizontalDofAlignment< ScalarBasisFunctionSet, Range > >
    {
      typedef SubDofVector< DofVector, HorizontalDofAlignment< ScalarBasisFunctionSet, Range > > ThisType;
 
      typedef typename Range::value_type RangeFieldType;
 
      typedef HorizontalDofAlignment< ScalarBasisFunctionSet, Range > DofAlignmentType;
      typedef typename DofAlignmentType::LocalDofType LocalDofType;
 
      // extract correct RangeFieldType for const or non-const version
      typedef typename std::conditional<
         std::is_const< DofVector > :: value,
         const RangeFieldType,
         RangeFieldType > :: type DofType;
 
    public:
      typedef RangeFieldType value_type;
 
      SubDofVector( DofVector &dofs, int coordinate, const DofAlignmentType &dofAlignment )
      : dofs_( &(dofs[ dofAlignment.globalDof( LocalDofType( coordinate, 0 ) ) ] ) )
      {}
 
      DofType &operator[] ( std::size_t i )
      {
        return dofs_[ i ];
      }
 
      // const RFT& leads to problem with returning reference to temporary
      // with dofs_ = PetscDF::LocalFunction::DofVector
      RangeFieldType operator[] ( std::size_t i ) const
      {
        return dofs_[ i ];
      }
 
    private:
      DofType *dofs_;
    };
 
    // note: DofVector can be also const DofVector
    template< class DofVector, class ScalarBasisFunctionSet, class Range >
    class SubDofVector< DofVector, VerticalDofAlignment< ScalarBasisFunctionSet, Range > >
    {
      typedef SubDofVector< DofVector, VerticalDofAlignment< ScalarBasisFunctionSet, Range > > ThisType;
 
      typedef typename Range::value_type RangeFieldType;
 
      typedef VerticalDofAlignment< ScalarBasisFunctionSet, Range > DofAlignmentType;
      typedef typename DofAlignmentType::LocalDofType LocalDofType;
 
      // extract correct RangeFieldType for const or non-const version
      typedef typename std::conditional<
         std::is_const< DofVector > :: value,
         const RangeFieldType,
         RangeFieldType > :: type DofType;
 
    public:
      typedef RangeFieldType value_type;
 
      SubDofVector( DofVector &dofs, int coordinate, const DofAlignmentType &dofAlignment )
      : dofs_( dofs ),
        coordinate_( coordinate ),
        dofAlignment_( dofAlignment )
      {}
 
      DofType &operator[] ( std::size_t i )
      {
        return dofs_[ dofAlignment_.globalDof( LocalDofType( coordinate_, i ) ) ];
      }
 
      // const RFT& leads to problem with returning reference to temporary
      // with dofs_ = PetscDF::LocalFunction::DofVector
      RangeFieldType operator[] ( std::size_t i ) const
      {
        return dofs_[ dofAlignment_.globalDof( LocalDofType( coordinate_, i ) ) ];
      }
 
    private:
      DofVector &dofs_;
      int coordinate_;
      DofAlignmentType dofAlignment_;
    };
 
 
 
    // VectorialBasisFunctionSet
    // -------------------------
 
    template< class ScalarBasisFunctionSet, class Range, template< class, class > class DofAlignment = VerticalDofAlignment >
    class VectorialBasisFunctionSet
    {
      typedef VectorialBasisFunctionSet< ScalarBasisFunctionSet, Range, DofAlignment > ThisType;
 
    public:
      typedef ScalarBasisFunctionSet ScalarBasisFunctionSetType;
 
      typedef typename ScalarBasisFunctionSetType::EntityType EntityType;
      typedef typename ScalarBasisFunctionSetType::ReferenceElementType ReferenceElementType;
 
    private:
      typedef typename ScalarBasisFunctionSetType::FunctionSpaceType ScalarFunctionSpaceType;
      static const int dimRange = Range::dimension;
 
    public:
      typedef typename ToNewDimRangeFunctionSpace< ScalarFunctionSpaceType, dimRange >::Type FunctionSpaceType;
 
      typedef typename FunctionSpaceType::DomainType DomainType;
      typedef typename FunctionSpaceType::RangeType RangeType;
      typedef typename FunctionSpaceType::JacobianRangeType JacobianRangeType;
      typedef typename FunctionSpaceType::HessianRangeType HessianRangeType;
 
      typedef DofAlignment< ScalarBasisFunctionSet, Range > DofAlignmentType;
 
      typedef typename DofAlignmentType::GlobalDofType GlobalDofType;
      typedef typename DofAlignmentType::LocalDofType LocalDofType;
 
      typedef typename FunctionSpaceType::DomainFieldType DomainFieldType;
      typedef typename FunctionSpaceType::RangeFieldType RangeFieldType;
 
    private:
      struct EvaluateAll;
      struct JacobianAll;
      struct HessianAll;
 
    public:
      VectorialBasisFunctionSet () {}
 
      explicit VectorialBasisFunctionSet ( const ScalarBasisFunctionSetType &scalarBasisFunctionSet )
      : scalarBasisFunctionSet_( scalarBasisFunctionSet ),
        dofAlignment_( scalarBasisFunctionSet_ )
      {}
 
      int order () const { return scalarBasisFunctionSet().order(); }
 
      std::size_t size () const { return dimRange*scalarBasisFunctionSet().size(); }
 
      const ReferenceElementType &referenceElement () const { return scalarBasisFunctionSet().referenceElement(); }
 
      template< class Point, class DofVector >
      void axpy ( const Point &x, const RangeType &valueFactor, DofVector &dofs ) const
      {
        axpy< EvaluateAll >( x, valueFactor, dofs );
      }
 
      template< class Point, class DofVector >
      void axpy ( const Point &x, const JacobianRangeType &jacobianFactor, DofVector &dofs ) const
      {
        axpy< JacobianAll >( x, jacobianFactor, dofs );
      }
 
      template< class Point, class DofVector >
      void axpy ( const Point &x, const HessianRangeType &hessianFactor, DofVector &dofs ) const
      {
        axpyH( x, hessianFactor, dofs );
      }
 
      template< class Point, class DofVector >
      void axpy ( const Point &x, const RangeType &valueFactor, const JacobianRangeType &jacobianFactor,
                  DofVector &dofs ) const
      {
        axpy( x, valueFactor, dofs );
        axpy( x, jacobianFactor, dofs );
      }
 
      template< class Quadrature, class Vector, class DofVector >
      void axpy ( const Quadrature &quad, const Vector &values, DofVector & dofs ) const
      {
        const unsigned int nop = quad.nop();
        for( unsigned int qp = 0; qp < nop ; ++qp )
          axpy( quad[ qp ], values[ qp ], dofs );
      }
 
      template< class Quadrature, class VectorA, class VectorB, class DofVector >
      void axpy ( const Quadrature &quad, const VectorA &valuesA, const VectorB &valuesB, DofVector & dofs ) const
      {
        const unsigned int nop = quad.nop();
        for( unsigned int qp = 0; qp < nop ; ++qp )
        {
          axpy( quad[ qp ], valuesA[ qp ], dofs );
          axpy( quad[ qp ], valuesB[ qp ], dofs );
        }
      }
 
      template< class Point, class DofVector >
      void evaluateAll ( const Point &x, const DofVector &dofs, RangeType &value ) const
      {
        evaluateAll< EvaluateAll >( x, dofs, value );
      }
 
      template< class Point, class RangeArray >
      void evaluateAll ( const Point &x, RangeArray &values ) const
      {
        evaluateAll< EvaluateAll >( x, values );
      }
 
      template< class Quadrature, class DofVector, class RangeArray >
      void evaluateAll ( const Quadrature &quad, const DofVector &dofs, RangeArray &ranges ) const
      {
        const unsigned int nop = quad.nop();
        for( unsigned int qp = 0; qp < nop ; ++qp )
          evaluateAll( quad[ qp ], dofs, ranges[ qp ] );
      }
 
      template< class Point, class DofVector >
      void jacobianAll ( const Point &x, const DofVector &dofs, JacobianRangeType &jacobian ) const
      {
        evaluateAll< JacobianAll >( x, dofs, jacobian );
      }
 
      template< class Point, class JacobianRangeArray >
      void jacobianAll ( const Point &x, JacobianRangeArray &jacobians ) const
      {
        evaluateAll< JacobianAll >( x, jacobians );
      }
 
      template< class Quadrature, class DofVector, class JacobianArray >
      void jacobianAll ( const Quadrature &quad, const DofVector &dofs, JacobianArray &jacobians ) const
      {
        const unsigned int nop = quad.nop();
        for( unsigned int qp = 0; qp < nop ; ++qp )
          jacobianAll( quad[ qp ], dofs, jacobians[ qp ] );
      }
 
      template< class Point, class DofVector >
      void hessianAll ( const Point &x, const DofVector &dofs, HessianRangeType &hessian ) const
      {
        evaluateAll< HessianAll >( x, dofs, hessian );
      }
 
      template< class Point, class HessianRangeArray >
      void hessianAll ( const Point &x, HessianRangeArray &hessians ) const
      {
        evaluateAll< HessianAll >( x, hessians );
      }
 
      template< class Quadrature, class DofVector, class HessianArray >
      void hessianAll ( const Quadrature &quad, const DofVector &dofs, HessianArray &hessians ) const
      {
        const unsigned int nop = quad.nop();
        for( unsigned int qp = 0; qp < nop ; ++qp )
          hessianAll( quad[ qp ], dofs, hessians[ qp ] );
      }
 
      const EntityType &entity () const { return scalarBasisFunctionSet().entity(); }
      bool valid () const { return scalarBasisFunctionSet().valid(); }
 
      DofAlignmentType dofAlignment () const { return dofAlignment_ ; }
 
      const ScalarBasisFunctionSetType &scalarBasisFunctionSet () const
      {
        return scalarBasisFunctionSet_;
      }
 
    private:
      template< class Evaluate, class Point, class DofVector >
      void axpy ( const Point &x, const typename Evaluate::Vector &factor, DofVector &dofs ) const
      {
        const std::size_t size = scalarBasisFunctionSet().size();
        std::vector< typename Evaluate::Scalar > scalars( size );
        Evaluate::apply( scalarBasisFunctionSet(), x, scalars );
 
        for( int r = 0; r < dimRange; ++r )
        {
          for( std::size_t i = 0; i < size; ++i )
          {
            const GlobalDofType globalDof = dofAlignment_.globalDof( LocalDofType( r, i ) );
            dofs[ globalDof ] += factor[ r ] * scalars[ i ][ 0 ];
          }
        }
      }
      template< class Point, class DofVector >
      void axpyH ( const Point &x, const HessianRangeType &factor, DofVector &dofs ) const
      {
        const std::size_t size = scalarBasisFunctionSet().size();
        std::vector< typename HessianAll::Scalar > scalars( size );
        HessianAll::apply( scalarBasisFunctionSet(), x, scalars );
 
        const int xSize = DomainType::dimension;
        for( int r = 0; r < dimRange; ++r )
        {
          for( std::size_t i = 0; i < size; ++i )
          {
            const GlobalDofType globalDof = dofAlignment_.globalDof( LocalDofType( r, i ) );
            for ( int j = 0; j < xSize; ++j )
              dofs[ globalDof ] += factor[ r ][ j ] * scalars[ i ][ 0 ][ j ];
          }
        }
      }
 
      template< class Evaluate, class Point, class DofVector >
      void evaluateAll ( const Point &x, const DofVector &dofs, typename Evaluate::Vector &vector ) const
      {
        typename Evaluate::Scalar scalar;
        for( int r = 0; r < dimRange; ++r )
        {
          SubDofVector< const DofVector, DofAlignmentType > subDofs( dofs, r, dofAlignment_ );
          Evaluate::apply( scalarBasisFunctionSet(), x, subDofs, scalar );
          vector[ r ] = scalar[ 0 ];
        }
      }
 
      template< class Evaluate, class Point, class VectorArray >
      void evaluateAll ( const Point &x, VectorArray &vectorials ) const
      {
        const std::size_t size = scalarBasisFunctionSet().size();
        std::vector< typename Evaluate::Scalar > scalars( size );
        Evaluate::apply( scalarBasisFunctionSet(), x, scalars );
 
        typedef typename Evaluate::Vector Vector;
 
        for( int r = 0; r < dimRange; ++r )
        {
          for( std::size_t i = 0; i < size; ++i )
          {
            const GlobalDofType globalDof = dofAlignment_.globalDof( LocalDofType( r, i ) );
            Vector &vector = vectorials[ globalDof ];
            vector = Vector( typename Vector::value_type( 0 ) );
            vector[ r ] = scalars[ i ][ 0 ];
          }
        }
      }
 
      ScalarBasisFunctionSetType scalarBasisFunctionSet_;
      DofAlignmentType dofAlignment_;
    };
 
 
 
    // VectorialBasisFunctionSet< ScalarBasisFunctionSet, Range >::EvaluateAll
    // -----------------------------------------------------------------------
 
    template< class ScalarBasisFunctionSet, class Range, template< class, class > class DofAlignment >
    struct VectorialBasisFunctionSet< ScalarBasisFunctionSet, Range, DofAlignment >::EvaluateAll
    {
      typedef typename ScalarFunctionSpaceType::RangeType Scalar;
      typedef RangeType Vector;
 
      template< class Point, class SubDofVector >
      static void apply ( const ScalarBasisFunctionSetType &scalarBasisFunctionSet,
                          const Point &x, const SubDofVector &dofs, Scalar &scalar )
      {
        scalarBasisFunctionSet.evaluateAll( x, dofs, scalar );
      }
 
      template< class Point, class ScalarArray >
      static void apply ( const ScalarBasisFunctionSetType &scalarBasisFunctionSet,
                          const Point &x, ScalarArray &scalars )
      {
        scalarBasisFunctionSet.evaluateAll( x, scalars );
      }
    };
 
 
 
    // VectorialBasisFunctionSet< ScalarBasisFunctionSet, Range >::JacobianAll
    // -----------------------------------------------------------------------
 
    template< class ScalarBasisFunctionSet, class Range, template< class, class > class DofAlignment >
    struct VectorialBasisFunctionSet< ScalarBasisFunctionSet, Range, DofAlignment >::JacobianAll
    {
      typedef typename ScalarFunctionSpaceType::JacobianRangeType Scalar;
      typedef JacobianRangeType Vector;
 
      template< class Point, class SubDofVector >
      static void apply ( const ScalarBasisFunctionSetType &scalarBasisFunctionSet,
                          const Point &x, const SubDofVector &dofs, Scalar &scalar )
      {
        scalarBasisFunctionSet.jacobianAll( x, dofs, scalar );
      }
 
      template< class Point, class ScalarArray >
      static void apply ( const ScalarBasisFunctionSetType &scalarBasisFunctionSet,
                          const Point &x, ScalarArray &scalars )
      {
        scalarBasisFunctionSet.jacobianAll( x, scalars );
      }
    };
 
 
 
    // VectorialBasisFunctionSet< ScalarBasisFunctionSet, Range >::HessianAll
    // ----------------------------------------------------------------------
 
    template< class ScalarBasisFunctionSet, class Range, template< class, class > class DofAlignment >
    struct VectorialBasisFunctionSet< ScalarBasisFunctionSet, Range, DofAlignment >::HessianAll
    {
      typedef typename ScalarFunctionSpaceType::HessianRangeType Scalar;
      typedef HessianRangeType Vector;
 
      template< class Point, class SubDofVector >
      static void apply ( const ScalarBasisFunctionSetType &scalarBasisFunctionSet,
                          const Point &x, const SubDofVector &dofs, Scalar &scalar )
      {
        scalarBasisFunctionSet.hessianAll( x, dofs, scalar );
      }
 
      template< class Point, class ScalarArray >
      static void apply ( const ScalarBasisFunctionSetType &scalarBasisFunctionSet,
                          const Point &x, ScalarArray &scalars )
      {
        scalarBasisFunctionSet.hessianAll( x, scalars );
      }
    };
 
  } // namespace Fem
 
} // namespace Dune
 
#endif // #ifndef DUNE_FEM_BASISFUNCTIONSET_VECTORIAL_HH