Intrepid2_IntegratedLegendreBasis_HGRAD_LINE.hpp

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// @HEADER
// *****************************************************************************
//                           Intrepid2 Package
//
// Copyright 2007 NTESS and the Intrepid2 contributors.
// SPDX-License-Identifier: BSD-3-Clause
// *****************************************************************************
// @HEADER
 
#ifndef Intrepid2_IntegratedLegendreBasis_HGRAD_LINE_h
#define Intrepid2_IntegratedLegendreBasis_HGRAD_LINE_h
 
#include <Kokkos_DynRankView.hpp>
 
#include <Intrepid2_config.h>
 
#include "Intrepid2_Basis.hpp"
#include "Intrepid2_Polynomials.hpp"
#include "Intrepid2_Utils.hpp"
 
namespace Intrepid2
{
  template<class DeviceType, class OutputScalar, class PointScalar,
           class OutputFieldType, class InputPointsType>
  struct Hierarchical_HGRAD_LINE_Functor
  {
    using ExecutionSpace     = typename DeviceType::execution_space;
    using ScratchSpace       = typename ExecutionSpace::scratch_memory_space;
    using OutputScratchView  = Kokkos::View<OutputScalar*,ScratchSpace,Kokkos::MemoryTraits<Kokkos::Unmanaged>>;
    using PointScratchView   = Kokkos::View<PointScalar*, ScratchSpace,Kokkos::MemoryTraits<Kokkos::Unmanaged>>;
    
    using TeamPolicy = Kokkos::TeamPolicy<ExecutionSpace>;
    using TeamMember = typename  TeamPolicy::member_type;
    
    EOperator opType_; // OPERATOR_VALUE or OPERATOR_GRAD
    
    OutputFieldType  output_;      // F,P
    InputPointsType  inputPoints_; // P,D
    
    int polyOrder_;
    bool defineVertexFunctions_;
    int numFields_, numPoints_;
    
    size_t fad_size_output_;
    
    Hierarchical_HGRAD_LINE_Functor(EOperator opType, OutputFieldType output, InputPointsType inputPoints,
                                    int polyOrder, bool defineVertexFunctions)
    : opType_(opType), output_(output), inputPoints_(inputPoints),
      polyOrder_(polyOrder), defineVertexFunctions_(defineVertexFunctions),
      fad_size_output_(getScalarDimensionForView(output))
    {
      numFields_ = output.extent_int(0);
      numPoints_ = output.extent_int(1);
      INTREPID2_TEST_FOR_EXCEPTION(numPoints_ != inputPoints.extent_int(0), std::invalid_argument, "point counts need to match!");
      INTREPID2_TEST_FOR_EXCEPTION(numFields_ != polyOrder_+1, std::invalid_argument, "output field size does not match basis cardinality");
    }
    
    KOKKOS_INLINE_FUNCTION
    void operator()( const TeamMember & teamMember ) const
    {
      auto pointOrdinal = teamMember.league_rank();
      OutputScratchView field_values_at_point;
      if (fad_size_output_ > 0) {
        field_values_at_point = OutputScratchView(teamMember.team_shmem(), numFields_, fad_size_output_);
      }
      else {
        field_values_at_point = OutputScratchView(teamMember.team_shmem(), numFields_);
      }
      
      const auto & input_x = inputPoints_(pointOrdinal,0);
      const bool taking_derivative = (opType_ != OPERATOR_VALUE);
      const bool callingShiftedScaledLegendre = (opType_ == OPERATOR_VALUE) || (opType_ == OPERATOR_GRAD) || (opType_ == OPERATOR_D1);
      
      // shiftedScaledIntegratedLegendreValues{_dx} expects x in [0,1]
      const PointScalar x = callingShiftedScaledLegendre ? PointScalar((input_x + 1.0)/2.0) : PointScalar(input_x);
      const double legendreScaling = 1.0;
      const double outputScaling   = taking_derivative ? 0.5 : 1.0; // output scaling -- 0.5 if we take derivatives, 1.0 otherwise
      
      switch (opType_)
      {
        case OPERATOR_VALUE:
          // field values are integrated Legendre polynomials, except for the first and second field,
          // which may be 1 and x or x and 1-x, depending on whether the vertex compatibility flag is set.
          Polynomials::shiftedScaledIntegratedLegendreValues(field_values_at_point, polyOrder_, x, legendreScaling);
          
          // note that because shiftedScaledIntegratedLegendreValues determines field values recursively, there is not much
          // opportunity at that level for further parallelism
          
          if (defineVertexFunctions_)
          {
            field_values_at_point(0) = 1. - x;
            field_values_at_point(1) = x;
          }
          break;
        case OPERATOR_GRAD:
        case OPERATOR_D1:
          // field values are Legendre polynomials, except for the first and second field,
          // which may be 0 and 1 or -1 and 1, depending on whether the vertex compatibility flag is set.
          Polynomials::shiftedScaledIntegratedLegendreValues_dx(field_values_at_point, polyOrder_, x, legendreScaling);
          
          // note that because shiftedScaledIntegratedLegendreValues_dx determines field values recursively, there is not much
          // opportunity at that level for further parallelism
          
          if (defineVertexFunctions_)
          {
            field_values_at_point(0) = -1.0; // derivative of 1-x
            field_values_at_point(1) =  1.0; // derivative of x
          }
          break;
        case OPERATOR_D2:
        case OPERATOR_D3:
        case OPERATOR_D4:
        case OPERATOR_D5:
        case OPERATOR_D6:
        case OPERATOR_D7:
        case OPERATOR_D8:
        case OPERATOR_D9:
        case OPERATOR_D10:
        {
          auto derivativeOrder = getOperatorOrder(opType_) - 1;
          Polynomials::legendreDerivativeValues(field_values_at_point, polyOrder_, x, derivativeOrder);
          
          // L_i is defined in terms of an integral of P_(i-1), so we need to shift the values by 1
          if (numFields_ >= 3)
          {
            OutputScalar Pn_minus_one = field_values_at_point(1);
            for (int fieldOrdinal=2; fieldOrdinal<numFields_; fieldOrdinal++)
            {
              OutputScalar Pn = field_values_at_point(fieldOrdinal);
              field_values_at_point(fieldOrdinal) = Pn_minus_one;
              Pn_minus_one = Pn;
            }
          }
          if (numFields_ >= 1) field_values_at_point(0) = 0.0;
          if (numFields_ >= 2) field_values_at_point(1) = 0.0;
          // legendreDerivativeValues works on [-1,1], so no per-derivative scaling is necessary
          // however, there is a factor of 0.5 that comes from the scaling of the Legendre polynomials prior to integration
          // in the shiftedScaledIntegratedLegendreValues -- the first derivative of our integrated polynomials is 0.5 times the Legendre polynomial
          break;
        }
        default:
          // unsupported operator type
          device_assert(false);
      }
      
      // copy the values into the output container
      for (int fieldOrdinal=0; fieldOrdinal<numFields_; fieldOrdinal++)
      {
        // access() allows us to write one line that applies both to gradient (for which outputValues has rank 3, but third rank has only one entry) and to value (rank 2)
        output_.access(fieldOrdinal,pointOrdinal,0) = outputScaling * field_values_at_point(fieldOrdinal);
      }
    }
    
    // Provide the shared memory capacity.
    // This function takes the team_size as an argument,
    // which allows team_size-dependent allocations.
    size_t team_shmem_size (int team_size) const
    {
      // we want to use shared memory to create a fast buffer that we can use for basis computations
      size_t shmem_size = 0;
      if (fad_size_output_ > 0)
        shmem_size += OutputScratchView::shmem_size(numFields_, fad_size_output_);
      else
        shmem_size += OutputScratchView::shmem_size(numFields_);
      
      return shmem_size;
    }
  };
  
  template<typename DeviceType,
           typename OutputScalar = double,
           typename PointScalar  = double,
           bool defineVertexFunctions = true,            // if defineVertexFunctions is true, first and second basis functions are x and 1-x.  Otherwise, they are 1 and x.
           bool useMinusOneToOneReferenceElement = true> // if useMinusOneToOneReferenceElement is true, basis is define on [-1,1].  Otherwise, [0,1].
  class IntegratedLegendreBasis_HGRAD_LINE
  : public Basis<DeviceType,OutputScalar,PointScalar>
  {
  public:
    using BasisBase = Basis<DeviceType,OutputScalar,PointScalar>;
    using HostBasis = IntegratedLegendreBasis_HGRAD_LINE<typename Kokkos::HostSpace::device_type,OutputScalar,PointScalar,defineVertexFunctions,useMinusOneToOneReferenceElement>;
 
    using typename BasisBase::OrdinalTypeArray1DHost;
    using typename BasisBase::OrdinalTypeArray2DHost;
 
    using typename BasisBase::OutputViewType;
    using typename BasisBase::PointViewType;
    using typename BasisBase::ScalarViewType;
 
    using typename BasisBase::ExecutionSpace;
 
  protected:
    int polyOrder_; // the maximum order of the polynomial
    bool defineVertexFunctions_; // if true, first and second basis functions are x and 1-x.  Otherwise, they are 1 and x.
    EPointType pointType_;
  public:
    IntegratedLegendreBasis_HGRAD_LINE(int polyOrder, EPointType pointType=POINTTYPE_DEFAULT)
    :
    polyOrder_(polyOrder),
    pointType_(pointType)
    {
      INTREPID2_TEST_FOR_EXCEPTION(pointType!=POINTTYPE_DEFAULT,std::invalid_argument,"PointType not supported");
 
      this->basisCardinality_     = polyOrder+1;
      this->basisDegree_          = polyOrder;
      this->basisCellTopologyKey_ = shards::Line<2>::key;
      this->basisType_            = BASIS_FEM_HIERARCHICAL;
      this->basisCoordinates_     = COORDINATES_CARTESIAN;
      this->functionSpace_        = FUNCTION_SPACE_HGRAD;
      
      const int degreeLength = 1;
      this->fieldOrdinalPolynomialDegree_ = OrdinalTypeArray2DHost("Integrated Legendre H(grad) line polynomial degree lookup", this->basisCardinality_, degreeLength);
      this->fieldOrdinalH1PolynomialDegree_ = OrdinalTypeArray2DHost("Integrated Legendre H(grad) line polynomial H^1 degree lookup", this->basisCardinality_, degreeLength);
      
      for (int i=0; i<this->basisCardinality_; i++)
      {
        // for H(grad) line, if defineVertexFunctions is false, first basis member is constant, second is first-degree, etc.
        // if defineVertexFunctions is true, then the only difference is that the entry is also degree 1
        this->fieldOrdinalPolynomialDegree_  (i,0) = i;
        this->fieldOrdinalH1PolynomialDegree_(i,0) = i;
      }
      if (defineVertexFunctions)
      {
        this->fieldOrdinalPolynomialDegree_  (0,0) = 1;
        this->fieldOrdinalH1PolynomialDegree_(0,0) = 1;
      }
      
      // initialize tags
      {
        const auto & cardinality = this->basisCardinality_;
        
        // Basis-dependent initializations
        const ordinal_type tagSize  = 4;        // size of DoF tag, i.e., number of fields in the tag
        const ordinal_type posScDim = 0;        // position in the tag, counting from 0, of the subcell dim
        const ordinal_type posScOrd = 1;        // position in the tag, counting from 0, of the subcell ordinal
        const ordinal_type posDfOrd = 2;        // position in the tag, counting from 0, of DoF ordinal relative to the subcell
        
        OrdinalTypeArray1DHost tagView("tag view", cardinality*tagSize);
        
        if (defineVertexFunctions) {
          {
            const ordinal_type v0 = 0;
            tagView(v0*tagSize+0) = 0; // vertex dof
            tagView(v0*tagSize+1) = 0; // vertex id
            tagView(v0*tagSize+2) = 0; // local dof id
            tagView(v0*tagSize+3) = 1; // total number of dofs in this vertex
            
            const ordinal_type v1 = 1;
            tagView(v1*tagSize+0) = 0; // vertex dof
            tagView(v1*tagSize+1) = 1; // vertex id
            tagView(v1*tagSize+2) = 0; // local dof id
            tagView(v1*tagSize+3) = 1; // total number of dofs in this vertex
            
            const ordinal_type iend = cardinality - 2;
            for (ordinal_type i=0;i<iend;++i) {
              const auto e = i + 2;
              tagView(e*tagSize+0) = 1;    // edge dof
              tagView(e*tagSize+1) = 0;    // edge id
              tagView(e*tagSize+2) = i;    // local dof id
              tagView(e*tagSize+3) = iend; // total number of dofs in this edge
            }
          }
        } else {
          for (ordinal_type i=0;i<cardinality;++i) {
            tagView(i*tagSize+0) = 1;           // edge dof
            tagView(i*tagSize+1) = 0;           // edge id
            tagView(i*tagSize+2) = i;           // local dof id
            tagView(i*tagSize+3) = cardinality; // total number of dofs in this edge
          }
        }
        
        // Basis-independent function sets tag and enum data in tagToOrdinal_ and ordinalToTag_ arrays:
        // tags are constructed on host
        this->setOrdinalTagData(this->tagToOrdinal_,
                                this->ordinalToTag_,
                                tagView,
                                this->basisCardinality_,
                                tagSize,
                                posScDim,
                                posScOrd,
                                posDfOrd);
      }
    }
    
   const char* getName() const override {
     return "Intrepid2_IntegratedLegendreBasis_HGRAD_LINE";
   }
 
   virtual bool requireOrientation() const override {
     return false;
   }
 
    // since the getValues() below only overrides the FEM variant, we specify that
    // we use the base class's getValues(), which implements the FVD variant by throwing an exception.
    // (It's an error to use the FVD variant on this basis.)
    using BasisBase::getValues;
    
    virtual void getValues( OutputViewType outputValues, const PointViewType  inputPoints,
                           const EOperator operatorType = OPERATOR_VALUE ) const override
    {
      auto numPoints = inputPoints.extent_int(0);
      
      using FunctorType = Hierarchical_HGRAD_LINE_Functor<DeviceType, OutputScalar, PointScalar, OutputViewType, PointViewType>;
      
      FunctorType functor(operatorType, outputValues, inputPoints, polyOrder_, defineVertexFunctions);
      
      const int outputVectorSize = getVectorSizeForHierarchicalParallelism<OutputScalar>();
      const int pointVectorSize  = getVectorSizeForHierarchicalParallelism<PointScalar>();
      const int vectorSize = std::max(outputVectorSize,pointVectorSize);
      const int teamSize = 1; // because of the way the basis functions are computed, we don't have a second level of parallelism...
 
      auto policy = Kokkos::TeamPolicy<ExecutionSpace>(numPoints,teamSize,vectorSize);
      Kokkos::parallel_for("Hierarchical_HGRAD_LINE_Functor", policy, functor);
    }
    
    virtual BasisPtr<typename Kokkos::HostSpace::device_type, OutputScalar, PointScalar>
    getHostBasis() const override {
      using HostDeviceType = typename Kokkos::HostSpace::device_type;
      using HostBasisType  = IntegratedLegendreBasis_HGRAD_LINE<HostDeviceType, OutputScalar, PointScalar, defineVertexFunctions, useMinusOneToOneReferenceElement>;
      return Teuchos::rcp( new HostBasisType(polyOrder_, pointType_) );
    }
  };
} // end namespace Intrepid2
 
#endif /* Intrepid2_IntegratedLegendreBasis_HGRAD_LINE_h */