metric_spaces.h

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/*
 * Copyright (c) 2014-2017:  G-CSC, Goethe University Frankfurt
 * Author: Arne Naegel
 *
 * This file is part of UG4.
 *
 * UG4 is free software: you can redistribute it and/or modify it under the
 * terms of the GNU Lesser General Public License version 3 (as published by the
 * Free Software Foundation) with the following additional attribution
 * requirements (according to LGPL/GPL v3 §7):
 *
 * (1) The following notice must be displayed in the Appropriate Legal Notices
 * of covered and combined works: "Based on UG4 (www.ug4.org/license)".
 *
 * (2) The following notice must be displayed at a prominent place in the
 * terminal output of covered works: "Based on UG4 (www.ug4.org/license)".
 *
 * (3) The following bibliography is recommended for citation and must be
 * preserved in all covered files:
 * "Reiter, S., Vogel, A., Heppner, I., Rupp, M., and Wittum, G. A massively
 *   parallel geometric multigrid solver on hierarchically distributed grids.
 *   Computing and visualization in science 16, 4 (2013), 151-164"
 * "Vogel, A., Reiter, S., Rupp, M., Nägel, A., and Wittum, G. UG4 -- a novel
 *   flexible software system for simulating pde based models on high performance
 *   computers. Computing and visualization in science 16, 4 (2013), 165-179"
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
 * GNU Lesser General Public License for more details.
 */
 
#ifndef __H__UG__LIB_DISC__FUNCTION_SPACE__METRIC_SPACES_H_
#define __H__UG__LIB_DISC__FUNCTION_SPACE__METRIC_SPACES_H_
 
// C++ includes
#include <vector>
#include <cmath>
 
// UG includes
#include "common/common.h"
#include "common/util/smart_pointer.h"
 
#include "lib_algebra/lib_algebra.h"
#include "lib_algebra/operator/debug_writer.h"
 
#include "lib_disc/function_spaces/integrate.h"
#include "lib_disc/function_spaces/grid_function.h"
#include "lib_disc/function_spaces/grid_function_user_data.h"
#include "lib_disc/function_spaces/integrate.h"
 
#include "lib_disc/spatial_disc/user_data/linker/darcy_velocity_linker.h"  // required for Darcy velocity linker
 
namespace ug {
template<typename TVector>
class IBanachSpace
{
 
public:
  virtual ~IBanachSpace() {}
 
  virtual double norm(TVector &x)
  { return x.norm(); }
 
  virtual double distance(TVector& x, TVector& y)
  {
    SmartPtr<TVector> delta = x.clone();
    *delta -= y;
    return norm(*delta);
  }
 
};
 
 
 
template<typename TGridFunction>
class IGridFunctionSpace  :
    public IBanachSpace<typename TGridFunction::vector_type>
{
 
public:
  typedef typename TGridFunction::vector_type vector_type;
  typedef TGridFunction grid_function_type;
 
  virtual ~IGridFunctionSpace() {}
 
  virtual double norm(TGridFunction& x) = 0;
  virtual double norm2(TGridFunction& x) = 0;
 
  // { return x.norm(); }
 
  virtual double distance(TGridFunction& x, TGridFunction& y) = 0;
  virtual double distance2(TGridFunction& x, TGridFunction& y) = 0;
  /*{
    SmartPtr<TGridFunction> delta = x.clone();
    *delta -= y;
    return norm(*delta);
  }*/
 
  virtual double norm(vector_type &x)
  {
    TGridFunction* gfX=dynamic_cast< TGridFunction*>(&x);
    UG_ASSERT(gfX!=NULL, "Huhh: GridFunction required!");
    return norm(*gfX);
  }
 
  virtual double distance(vector_type &x, vector_type &y)
  { return distance(static_cast<TGridFunction &>(x), static_cast<TGridFunction &>(y)); }
 
  virtual double scaling() const
  { return 1.0; }
 
  virtual std::string config_string() const
   { return std::string("IGridFunctionSpace"); }
};
 
template<typename TGridFunction>
class AlgebraicSpace : public IGridFunctionSpace<TGridFunction>
{
  typedef typename TGridFunction::vector_type vector_type;
  virtual ~AlgebraicSpace() {}
 
  virtual double norm(TGridFunction& x)
  {return x.norm();}
 
  virtual double norm2(TGridFunction& x)
  { double n = this->norm(x); return n*n; }
 
  virtual double distance(TGridFunction& x, TGridFunction& y)
  { SmartPtr<TGridFunction> delta = x.clone(); *delta -= y; return delta->norm(); }
 
  virtual double distance2(TGridFunction& x, TGridFunction& y)
  { double d = this->distance(x,y);; return d*d;}
};
 
 
 
template <typename W>
class IObjectWithWeights
{
public:
  typedef W weight_type;
 
  IObjectWithWeights()
  : m_spWeight(SPNULL) {}
 
  IObjectWithWeights(ConstSmartPtr<weight_type> spW)
  : m_spWeight(spW) {}
 
  void set_weight(ConstSmartPtr<weight_type> spWeight)
  { m_spWeight = spWeight; }
 
  ConstSmartPtr<weight_type> get_weight()
  { return m_spWeight; }
 
protected:
  ConstSmartPtr<weight_type> m_spWeight;
};
 
 
/*
class ITimeData {
 
public:
  virtual ~ITimeData() {};
 
  virtual void update_time_data(number dt) = 0;
 
  virtual bool is_time_dependent() const
  { return false; }
 
};
 
*/
 
template <typename TGridFunction>
class IComponentSpace :
    public IGridFunctionSpace<TGridFunction>
{
protected:
  std::string m_fctNames;
  const char* m_ssNames;
  int m_quadorder;
 
public:
  typedef IGridFunctionSpace<TGridFunction> base_type;
  static const int dim=TGridFunction::dim;
 
  IComponentSpace(const char *fctNames)
  : m_fctNames(fctNames), m_ssNames(NULL), m_quadorder(3){}
 
  IComponentSpace(const char *fctNames, int order)
  : m_fctNames(fctNames), m_ssNames(NULL), m_quadorder(order) {}
 
  IComponentSpace(const char *fctNames, const char* ssNames, int order)
  : m_fctNames(fctNames), m_ssNames(ssNames), m_quadorder(order) {}
 
  virtual ~IComponentSpace() {};
 
  // per convention, norm must return sqrt of norm2
  virtual double norm(TGridFunction& uFine)
  { return sqrt(norm2(uFine)); }
 
  // per convention, distance must return sqrt of distance2
  virtual double distance(TGridFunction& uFine, TGridFunction& uCoarse)
  { return sqrt(distance2(uFine, uCoarse)); }
 
  virtual double norm2(TGridFunction& uFine)  = 0;
  virtual double distance2(TGridFunction& uFine, TGridFunction& uCoarse)  = 0;
 
 
public:
  virtual std::string config_string() const
  {
    std::stringstream ss;
 
    if (this->m_ssNames)
    ss << this->m_fctNames << ", " << this->m_ssNames << ", " << this->m_quadorder
      << ", type=" << std::endl;
 
    else
      ss << this->m_fctNames << ",  (no name), " << this->m_quadorder
            << ", type=" << std::endl;
    return ss.str();
  }
 
};
 
 
template <typename TGridFunction>
class GridFunctionComponentSpace
: public IComponentSpace<TGridFunction>
{
  public:
    GridFunctionComponentSpace(const char* fctNames)
    : IComponentSpace<TGridFunction>(fctNames) {}
 
    GridFunctionComponentSpace(const char* fctNames, const char* ssNames)
    : IComponentSpace<TGridFunction>(fctNames, ssNames, 1) {}
 
    virtual ~GridFunctionComponentSpace() {};
 
    virtual double norm2(TGridFunction& uFine)
    {
      ConstSmartPtr<DoFDistribution> dd = uFine.dof_distribution();
 
      // find function indices
      FunctionGroup fg(dd->function_pattern());
      try {fg.add(TokenizeTrimString(this->m_fctNames));}
      UG_CATCH_THROW("Could not convert function names to function indices.");
 
      // find subset indices
      SubsetGroup sg(dd->subset_handler());
      if (this->m_ssNames)
      {
        try {sg.add(TokenizeTrimString(this->m_ssNames));}
        UG_CATCH_THROW("Could not convert subset names to subset indices.");
      }
      else
        sg.add_all();
 
 
      // loop subsets
      number sum = 0.0;
      const size_t sgSz = sg.size();
      for (size_t i = 0; i < sgSz; ++i)
      {
        int si = sg[i];
        if (dd->max_dofs(VERTEX, si)) add_norm_values<Vertex>(sum, uFine, dd, sg[i], fg);
        if (dd->max_dofs(EDGE, si)) add_norm_values<Edge>(sum, uFine, dd, sg[i], fg);
        if (dd->max_dofs(FACE, si)) add_norm_values<Face>(sum, uFine, dd, sg[i], fg);
        if (dd->max_dofs(VOLUME, si)) add_norm_values<Volume>(sum, uFine, dd, sg[i], fg);
      }
 
#ifdef UG_PARALLEL
      if (pcl::NumProcs() > 1)
      {
        pcl::ProcessCommunicator pc;
        sum = pc.allreduce(sum, PCL_RO_SUM);
      }
#endif
 
      return sum;
    }
 
    virtual double distance2(TGridFunction& uFine, TGridFunction& uCoarse)
    {
      ConstSmartPtr<DoFDistribution> dd = uFine.dof_distribution();
      UG_COND_THROW(dd != uCoarse.dof_distribution(),
        "GridFunctionComponentSpace::distance2: GF1 DoF distro is not the same as for GF2.\n"
        "This case is not implemented.");
 
      // find function indices
      FunctionGroup fg(dd->function_pattern());
      try {fg.add(TokenizeTrimString(this->m_fctNames));}
      UG_CATCH_THROW("Could not convert function names to function indices.");
 
      // find subset indices
      SubsetGroup sg(dd->subset_handler());
      if (this->m_ssNames)
      {
        try {sg.add(TokenizeTrimString(this->m_ssNames));}
        UG_CATCH_THROW("Could not convert subset names to subset indices.");
      }
      else
        sg.add_all();
 
 
      // loop subsets
      number sum = 0.0;
      const size_t sgSz = sg.size();
      for (size_t i = 0; i < sgSz; ++i)
      {
        int si = sg[i];
        if (dd->max_dofs(VERTEX, si)) add_distance_values<Vertex>(sum, uFine, uCoarse, dd, sg[i], fg);
        if (dd->max_dofs(EDGE, si)) add_distance_values<Edge>(sum, uFine, uCoarse, dd, sg[i], fg);
        if (dd->max_dofs(FACE, si)) add_distance_values<Face>(sum, uFine, uCoarse, dd, sg[i], fg);
        if (dd->max_dofs(VOLUME, si)) add_distance_values<Volume>(sum, uFine, uCoarse, dd, sg[i], fg);
      }
 
#ifdef UG_PARALLEL
      if (pcl::NumProcs() > 1)
      {
        pcl::ProcessCommunicator pc;
        sum = pc.allreduce(sum, PCL_RO_SUM);
      }
#endif
 
      return sum;
    }
 
  private:
    template <typename TBaseElem>
    void add_distance_values
    (
      number& sum,
      const TGridFunction& uFine,
      const TGridFunction& uCoarse,
      ConstSmartPtr<DoFDistribution> dd,
      int si,
      const FunctionGroup& fg
    ) const
    {
      const SurfaceView& sv = *dd->surface_view();
      const MultiGrid& mg = *dd->multi_grid();
 
      const number nFct = fg.size();
 
      // iterate all elements (including SHADOW_RIM_COPY!)
      typename DoFDistribution::traits<TBaseElem>::const_iterator iter, iterEnd;
      iter = dd->template begin<TBaseElem>(si, SurfaceView::ALL);
      iterEnd = dd->template end<TBaseElem>(si, SurfaceView::ALL);
      std::vector<DoFIndex> vInd;
      for (; iter != iterEnd; ++iter)
      {
        TBaseElem* elem = *iter;
        if (sv.is_contained(elem, dd->grid_level(), SurfaceView::SHADOW_RIM_COPY))
        {
          if (mg.num_children<TBaseElem>(elem) > 0)
          {
            TBaseElem* child = mg.get_child<TBaseElem>(elem, 0);
            if (sv.is_contained(child, dd->grid_level(), SurfaceView::SURFACE_RIM))
              continue;
          }
        }
 
        for (size_t fi = 0; fi < nFct; ++fi)
        {
          dd->inner_dof_indices(elem, fg[fi], vInd);
 
          const size_t nDof = vInd.size();
          for (size_t dof = 0; dof < nDof; ++dof)
          {
            const number tmp = DoFRef(uFine, vInd[dof]) - DoFRef(uCoarse, vInd[dof]);
            sum += tmp*tmp;
          }
        }
      }
      // note: no duplicate additions possible
    }
 
    template <typename TBaseElem>
    void add_norm_values
    (
      number& sum,
      const TGridFunction& uFine,
      ConstSmartPtr<DoFDistribution> dd,
      int si,
      const FunctionGroup& fg
    ) const
    {
      const SurfaceView& sv = *dd->surface_view();
      const MultiGrid& mg = *dd->multi_grid();
 
      const number nFct = fg.size();
 
      // iterate all elements (including SHADOW_RIM_COPY!)
      typename DoFDistribution::traits<TBaseElem>::const_iterator iter, iterEnd;
      iter = dd->template begin<TBaseElem>(si, SurfaceView::ALL);
      iterEnd = dd->template end<TBaseElem>(si, SurfaceView::ALL);
      std::vector<DoFIndex> vInd;
      for (; iter != iterEnd; ++iter)
      {
        TBaseElem* elem = *iter;
        if (sv.is_contained(elem, dd->grid_level(), SurfaceView::SHADOW_RIM_COPY))
        {
          if (mg.num_children<TBaseElem>(elem) > 0)
          {
            TBaseElem* child = mg.get_child<TBaseElem>(elem, 0);
            if (sv.is_contained(child, dd->grid_level(), SurfaceView::SURFACE_RIM))
              continue;
          }
        }
 
        for (size_t fi = 0; fi < nFct; ++fi)
        {
          dd->inner_dof_indices(elem, fg[fi], vInd);
 
          const size_t nDof = vInd.size();
          for (size_t dof = 0; dof < nDof; ++dof)
          {
            const number tmp = DoFRef(uFine, vInd[dof]);
            sum += tmp*tmp;
          }
        }
      }
      // note: no duplicate additions possible
    }
};
 
 
 
template <typename TGridFunction>
class TimeDependentSpace :
    public IGridFunctionSpace<TGridFunction>
{
public:
  typedef IGridFunctionSpace<TGridFunction> base_type;
  typedef IComponentSpace<TGridFunction> comp_space_type;
 
  TimeDependentSpace(SmartPtr<comp_space_type> spSpace, number tScale)
  : m_spSpatialSpace(spSpace), m_tScale(tScale) {};
 
  virtual ~TimeDependentSpace() {};
 
  using base_type::norm;
  using base_type::distance;
  using base_type::scaling;
 
  double scaling() const
  { return (m_spSpatialSpace->scaling()*m_tScale); }
 
  void update_time_data(number tScale)
  {  m_tScale = tScale; }
 
  std::string config_string() const
  {
    std::stringstream ss;
    ss << "TimeDependentSpace for " <<  std::endl;
    ss <<  m_spSpatialSpace->config_string() << std::endl;
    return ss.str();
  }
 
protected:
  SmartPtr<comp_space_type> m_spSpatialSpace;
  number m_tScale;
};
 
 
template <typename TGridFunction>
class L2ComponentSpace :
    public IComponentSpace<TGridFunction>,
    public IObjectWithWeights<typename L2DistIntegrand<TGridFunction>::weight_type >
{
public:
  typedef IComponentSpace<TGridFunction> base_type;
  typedef typename L2DistIntegrand<TGridFunction>::weight_type weight_type;
  typedef IObjectWithWeights<weight_type> weighted_obj_type;
 
  L2ComponentSpace(const char *fctNames)
  : base_type(fctNames), weighted_obj_type(make_sp(new ConstUserNumber<TGridFunction::dim>(1.0))) {};
 
  L2ComponentSpace(const char *fctNames, int order)
  : base_type(fctNames, order), weighted_obj_type(make_sp(new ConstUserNumber<TGridFunction::dim>(1.0))) {};
 
  L2ComponentSpace(const char *fctNames,  int order, double weight, const char* ssNames=0)
  : base_type(fctNames, ssNames, order), weighted_obj_type(make_sp(new ConstUserNumber<TGridFunction::dim>(weight))) {};
 
  L2ComponentSpace(const char *fctNames, int order, ConstSmartPtr<weight_type> spWeight, const char* ssNames=0)
  : base_type(fctNames, ssNames, order), weighted_obj_type(spWeight) {};
 
  ~L2ComponentSpace() {};
 
  using IComponentSpace<TGridFunction>::norm;
  using IComponentSpace<TGridFunction>::distance;
 
  using weighted_obj_type::set_weight;
  using weighted_obj_type::get_weight;
  using weighted_obj_type::m_spWeight;
 
  double norm2(TGridFunction& uFine)
  { return L2Norm2(uFine, base_type::m_fctNames.c_str(), base_type::m_quadorder, base_type::m_ssNames, weighted_obj_type::m_spWeight); }
 
  double distance2(TGridFunction& uFine, TGridFunction& uCoarse)
  { return L2Distance2(uFine, base_type::m_fctNames.c_str(), uCoarse, base_type::m_fctNames.c_str(),
    base_type::m_quadorder, base_type::m_ssNames, weighted_obj_type::m_spWeight);}
 
 
 
};
 
template <typename TGridFunction>
class L2QuotientSpace :
    public IComponentSpace<TGridFunction>,
    public IObjectWithWeights<typename L2DistIntegrand<TGridFunction>::weight_type >
{
public:
  typedef IComponentSpace<TGridFunction> base_type;
  typedef typename L2DistIntegrand<TGridFunction>::weight_type weight_type;
  typedef IObjectWithWeights<weight_type> weighted_obj_type;
 
  L2QuotientSpace(const char *fctNames)
  : base_type(fctNames), weighted_obj_type(make_sp(new ConstUserNumber<TGridFunction::dim>(1.0))) {};
 
  L2QuotientSpace(const char *fctNames, int order)
  : base_type(fctNames, order), weighted_obj_type(make_sp(new ConstUserNumber<TGridFunction::dim>(1.0))) {};
 
  L2QuotientSpace(const char *fctNames,  int order, double weight, const char* ssNames=0)
  : base_type(fctNames, ssNames, order), weighted_obj_type(make_sp(new ConstUserNumber<TGridFunction::dim>(weight))) {};
 
  L2QuotientSpace(const char *fctNames, int order, ConstSmartPtr<weight_type> spWeight, const char* ssNames=0)
  : base_type(fctNames, ssNames, order), weighted_obj_type(spWeight) {};
 
  ~L2QuotientSpace() {};
 
  using IComponentSpace<TGridFunction>::norm;
  using IComponentSpace<TGridFunction>::distance;
 
  using weighted_obj_type::set_weight;
  using weighted_obj_type::get_weight;
  using weighted_obj_type::m_spWeight;
 
  double norm2(TGridFunction& u)
  {
    typedef ConstUserNumber<TGridFunction::dim> MyConstUserData;
    typedef SmartPtr<UserData<number, TGridFunction::dim> > SPUserData;
 
    SPUserData spConst= make_sp(new MyConstUserData(1.0));
    number Meas = Integral(spConst, u, base_type::m_ssNames, 0.0, 1, "best");
    number uAvg = Integral(u,  base_type::m_fctNames.c_str(), base_type::m_ssNames, base_type::m_quadorder);
 
    std::cerr << "Average:=" << uAvg <<"/" << Meas << " = " << uAvg/Meas << std::endl;
    SPUserData spAvg = make_sp(new MyConstUserData(uAvg/Meas));
    double qnorm = L2Error(spAvg, u, base_type::m_fctNames.c_str(), 0.0, base_type::m_quadorder, base_type::m_ssNames);
 
    return qnorm*qnorm;
  }
 
  double distance2(TGridFunction& uFine, TGridFunction& uCoarse)
  {
    typedef ConstUserNumber<TGridFunction::dim> MyConstUserData;
    typedef SmartPtr<UserData<number, TGridFunction::dim> > SPUserData;
 
    SPUserData spConst= make_sp(new MyConstUserData(1.0));
    number Meas = Integral(spConst, uFine, base_type::m_ssNames, 0.0, 1, "best");
    number avgFine = Integral(uFine, base_type::m_fctNames.c_str(), base_type::m_ssNames, base_type::m_quadorder);
    number avgCoarse = Integral(uCoarse, base_type::m_fctNames.c_str(), base_type::m_ssNames, base_type::m_quadorder);
 
    std::cerr << "Average:=(" << avgFine << "-" << avgCoarse<<")/" << Meas << " = " << (avgFine-avgCoarse)/Meas << std::endl;
    return L2Distance2(uFine, base_type::m_fctNames.c_str(),
              uCoarse, base_type::m_fctNames.c_str(),
              base_type::m_quadorder, base_type::m_ssNames, weighted_obj_type::m_spWeight,
              (avgFine-avgCoarse)/Meas);
  }
 
 
 
};
 
 
template <typename TGridFunction>
class H1SemiComponentSpace
: public IComponentSpace<TGridFunction>,
  public IObjectWithWeights<typename H1SemiDistIntegrand<TGridFunction>::weight_type >
{
public:
  typedef IComponentSpace<TGridFunction> base_type;
  typedef typename H1SemiDistIntegrand<TGridFunction>::weight_type weight_type;
  typedef IObjectWithWeights<weight_type> weighted_obj_type;
 
 
  H1SemiComponentSpace(const char *fctNames)
  : base_type(fctNames), weighted_obj_type(make_sp(new ConstUserMatrix<TGridFunction::dim>(1.0))) {};
 
  H1SemiComponentSpace(const char *fctNames, int order)
  : base_type(fctNames, order), weighted_obj_type(make_sp(new ConstUserMatrix<TGridFunction::dim>(1.0))) {};
 
  H1SemiComponentSpace(const char *fctNames, int order, number weight, const char* ssNames=0)
  : base_type(fctNames, ssNames, order), weighted_obj_type(make_sp(new ConstUserMatrix<TGridFunction::dim>(weight)))  {};
 
  H1SemiComponentSpace(const char *fctNames, int order, ConstSmartPtr<weight_type> spWeight, const char* ssNames=0)
  : base_type(fctNames, ssNames, order), weighted_obj_type(spWeight) {};
 
  H1SemiComponentSpace(const char *fctNames, int order, const char* ssNames, ConstSmartPtr<weight_type> spWeight)
  : base_type(fctNames, ssNames, order), weighted_obj_type(spWeight) {};
 
  ~H1SemiComponentSpace() {};
 
 
  using IComponentSpace<TGridFunction>::norm;
  using IComponentSpace<TGridFunction>::distance;
 
  double norm2(TGridFunction& uFine)
  { return H1SemiNorm2<TGridFunction>(uFine, base_type::m_fctNames.c_str(), base_type::m_quadorder, NULL, weighted_obj_type::m_spWeight); }
 
  double distance2(TGridFunction& uFine, TGridFunction& uCoarse)
  { return H1SemiDistance2<TGridFunction>(uFine, base_type::m_fctNames.c_str(), uCoarse, base_type::m_fctNames.c_str(), base_type::m_quadorder, m_spWeight); }
 
  using weighted_obj_type::set_weight;
  using weighted_obj_type::get_weight;
  using weighted_obj_type::m_spWeight;
 
};
 
 
 
/*
template <typename TGridFunction>
class KineticEnergyComponentSpace
: public IComponentSpace<TGridFunction>,
  public IObjectWithWeights<typename L2Integrand<TGridFunction>::weight_type >
{
public:
  typedef IComponentSpace<TGridFunction> base_type;
  typedef typename L2Integrand<TGridFunction>::weight_type weight_type;
  typedef IObjectWithWeights<weight_type> weighted_obj_type;
  typedef DarcyVelocityLinker<TGridFunction::dim> velocity_type;
 
 
  KineticEnergyComponentSpace(SmartPtr<velocity_type> spVelocity, const char *fctNames)
  : base_type(fctNames), weighted_obj_type(make_sp(new ConstUserNumber<TGridFunction::dim>(1.0))), m_spVelocity(spVelocity) {};
 
  KineticEnergyComponentSpace(SmartPtr<velocity_type> spVelocity, const char *fctNames, int order)
  : base_type(fctNames, order), weighted_obj_type(make_sp(new ConstUserNumber<TGridFunction::dim>(1.0))), m_spVelocity(spVelocity)  {};
 
  KineticEnergyComponentSpace(SmartPtr<velocity_type> spVelocity, const char *fctNames, int order, number weight, const char* ssNames=0)
  : base_type(fctNames, ssNames, order), weighted_obj_type(make_sp(new ConstUserNumber<TGridFunction::dim>(weight))), m_spVelocity(spVelocity)   {};
 
  KineticEnergyComponentSpace(SmartPtr<velocity_type> spVelocity, const char *fctNames, int order, ConstSmartPtr<weight_type> spWeight, const char* ssNames=0)
  : base_type(fctNames, ssNames, order), weighted_obj_type(spWeight), m_spVelocity(spVelocity)  {};
 
  KineticEnergyComponentSpace(SmartPtr<velocity_type> spVelocity, const char *fctNames, int order, const char* ssNames, ConstSmartPtr<weight_type> spWeight)
  : base_type(fctNames, ssNames, order), weighted_obj_type(spWeight), m_spVelocity(spVelocity) {};
 
  ~KineticEnergyComponentSpace() {};
 
 
  using IComponentSpace<TGridFunction>::m_quadorder;
  using IComponentSpace<TGridFunction>::norm;
  using IComponentSpace<TGridFunction>::distance;
 
  double norm2(TGridFunction& u)
  {
    const char* subsets = NULL;
    UserDataIntegrandSq<MathVector<TGridFunction::dim>, TGridFunction> integrand2(m_spVelocity, &u, 0.0);
    return IntegrateSubsets(integrand2, u, subsets, m_quadorder);
  }
 
  double distance2(TGridFunction& uFine, TGridFunction& uCoarse)
  {
    // UG_THROW("Not implemented!");
    const char* subsets = NULL;
    UserDataDistIntegrandSq<MathVector<TGridFunction::dim>, TGridFunction> integrand2(m_spVelocity, uFine, 0, uCoarse, 0);
    return IntegrateSubsets(integrand2, uFine, subsets, m_quadorder);
  }
 
  using weighted_obj_type::set_weight;
  using weighted_obj_type::get_weight;
  using weighted_obj_type::m_spWeight;
 
  void set_velocity(SmartPtr<velocity_type> spVelocity)
  { m_spVelocity = spVelocity;}
 
protected:
  SmartPtr<velocity_type> m_spVelocity;
 
};
*/
 
 
template <typename TGridFunction>
class H1EnergyComponentSpace
: public IComponentSpace<TGridFunction>,
  public IObjectWithWeights<typename H1EnergyDistIntegrand<TGridFunction>::weight_type >
{
public:
  typedef IComponentSpace<TGridFunction> base_type;
  typedef typename H1SemiDistIntegrand<TGridFunction>::weight_type weight_type;
  typedef IObjectWithWeights<weight_type> weighted_obj_type;
  // typedef DarcyVelocityLinker<TGridFunction::dim> velocity_type;
  static const int dim = TGridFunction::dim;
  typedef UserData<MathVector<dim>, dim> velocity_type;
 
  H1EnergyComponentSpace(const char *fctNames)
  : base_type(fctNames), weighted_obj_type(make_sp(new ConstUserMatrix<TGridFunction::dim>(1.0))), m_spVelocity(SPNULL) {};
 
  H1EnergyComponentSpace(const char *fctNames, int order)
  : base_type(fctNames, order), weighted_obj_type(make_sp(new ConstUserMatrix<TGridFunction::dim>(1.0))), m_spVelocity(SPNULL) {};
 
  H1EnergyComponentSpace(const char *fctNames, int order, number weight, const char* ssNames=0)
  : base_type(fctNames, ssNames, order), weighted_obj_type(make_sp(new ConstUserMatrix<TGridFunction::dim>(weight))), m_spVelocity(SPNULL)  {};
 
  H1EnergyComponentSpace(const char *fctNames, int order, ConstSmartPtr<weight_type> spWeight, const char* ssNames=0)
  : base_type(fctNames, ssNames, order), weighted_obj_type(spWeight), m_spVelocity(SPNULL) {};
 
  /*H1EnergyComponentSpace(const char *fctNames, int order, const char* ssNames, ConstSmartPtr<weight_type> spWeight)
  : base_type(fctNames, ssNames, order), weighted_obj_type(spWeight), m_spVelocity(SPNULL) {};*/
 
  ~H1EnergyComponentSpace() {};
 
 
  using IComponentSpace<TGridFunction>::norm;
  using IComponentSpace<TGridFunction>::distance;
 
  double norm2(TGridFunction& uFine)
  {
    if (m_spVelocity.valid()) {
      //const char* subsets = NULL; // [q^2]
      UserDataIntegrandSq<MathVector<TGridFunction::dim>, TGridFunction> integrand2(m_spVelocity, &uFine, 0.0);
      return IntegrateSubsets(integrand2, uFine, base_type::m_ssNames, base_type::m_quadorder);
    } else {
      return H1EnergyNorm2<TGridFunction>(uFine, base_type::m_fctNames.c_str(), base_type::m_quadorder, base_type::m_ssNames, weighted_obj_type::m_spWeight);
    }
  }
 
  double distance2(TGridFunction& uFine, TGridFunction& uCoarse)
  { return H1EnergyDistance2<TGridFunction>(uFine, base_type::m_fctNames.c_str(), uCoarse, base_type::m_fctNames.c_str(), base_type::m_quadorder,base_type::m_ssNames, weighted_obj_type::m_spWeight); }
 
  using weighted_obj_type::set_weight;
  using weighted_obj_type::get_weight;
 
  void set_velocity(SmartPtr<velocity_type> spVelocity)
  { m_spVelocity = spVelocity;}
 
protected:
    SmartPtr<velocity_type> m_spVelocity;
 
};
 
template <typename TGridFunction>
class H1ComponentSpace :
    public IComponentSpace<TGridFunction>
{
public:
  typedef IComponentSpace<TGridFunction> base_type;
 
  H1ComponentSpace(const char *fctNames) : base_type(fctNames) {};
  H1ComponentSpace(const char *fctNames, int order) : base_type(fctNames, order) {};
  H1ComponentSpace(const char *fctNames,  const char* ssNames, int order) : base_type(fctNames, ssNames, order) {};
  ~H1ComponentSpace() {};
 
  using IComponentSpace<TGridFunction>::norm;
  using IComponentSpace<TGridFunction>::distance;
 
  double norm2(TGridFunction& uFine)
  { return H1Norm2<TGridFunction>(uFine, base_type::m_fctNames.c_str(), base_type::m_quadorder, base_type::m_ssNames); }
 
  double distance2(TGridFunction& uFine, TGridFunction& uCoarse)
  { return H1Distance2<TGridFunction>(uFine, base_type::m_fctNames.c_str(), uCoarse, base_type::m_fctNames.c_str(), base_type::m_quadorder, base_type::m_ssNames); }
 
};
 
 
 
 
template <typename TGridFunction>
class CompositeSpace : public IGridFunctionSpace<TGridFunction>
{
public:
  typedef IGridFunctionSpace<TGridFunction> base_type;
  typedef IComponentSpace<TGridFunction> obj_type;
  typedef TimeDependentSpace<TGridFunction> time_dependent_obj_type;
  typedef std::pair<SmartPtr<obj_type>, number> weighted_obj_type;
 
  CompositeSpace() {};
  // virtual ~CompositeSpace() {};
 
  using base_type::norm;
  using base_type::distance;
 
  double norm(TGridFunction& uFine)
  { return(sqrt(norm2(uFine))); }
 
  double norm2(TGridFunction& uFine)
  {
    number unorm2 = 0.0;
    for (typename std::vector<weighted_obj_type>::iterator it = m_spWeightedSubspaces.begin();
        it!= m_spWeightedSubspaces.end(); ++it)
    {
      double snorm2 = it->first->norm2(uFine);
      unorm2 += it->second * snorm2;            // scaling
      UG_LOG("composite-norm2:\t" << snorm2 << "\t*\t" << it->second
          << "\t=\t" << it->second * snorm2 << std::endl);
    }
    UG_LOG("composite-norm2-final:\t" << unorm2 << std::endl);
    return unorm2;
  }
 
  double distance2(TGridFunction& uFine, TGridFunction& uCoarse)
  {
    number unorm2 = 0.0;
    for (typename std::vector<weighted_obj_type>::iterator it = m_spWeightedSubspaces.begin();
          it!= m_spWeightedSubspaces.end(); ++it)
    {
      double sdist2 = it->first->distance2(uFine, uCoarse);
      unorm2 += it->second * sdist2; // scaling
      UG_LOG("composite-dist2:\t" << sdist2 << "\t*\t" << it->second
          << "\t=\t" << it->second * sdist2 << std::endl);
    }
    UG_LOG("composite-dist2-final:\t" << unorm2 << std::endl);
    return unorm2;
  }
 
  double distance(TGridFunction& uFine, TGridFunction& uCoarse)
  { return sqrt(distance2(uFine, uCoarse)); }
 
  void add(SmartPtr<obj_type> spSubSpace)
  { m_spWeightedSubspaces.push_back(std::make_pair(spSubSpace, 1.0)); }
 
  void add(SmartPtr<obj_type> spSubSpace, number sigma)
  { m_spWeightedSubspaces.push_back(std::make_pair(spSubSpace, sigma)); }
 
  std::string config_string() const
  {
      std::stringstream ss;
      ss << "CompositeSpace:" << std::endl;
 
      for (typename std::vector<weighted_obj_type>::const_iterator it = m_spWeightedSubspaces.begin();
          it!= m_spWeightedSubspaces.end(); ++it)
      { ss << it->first->config_string(); }
 
      return ss.str();
  }
 
 
  void update_time_data(number t)
  {
    for (typename std::vector<weighted_obj_type>::iterator it = m_spWeightedSubspaces.begin();
      it!= m_spWeightedSubspaces.end(); ++it)
    {
      SmartPtr<time_dependent_obj_type> spSpaceT = it->first.template cast_dynamic<time_dependent_obj_type> ();
      if (spSpaceT.valid()) spSpaceT->update_time_data(t);
    }
  }
 
  bool is_time_dependent() const
  {
    for (typename std::vector<weighted_obj_type>::const_iterator it = m_spWeightedSubspaces.begin();
        it!= m_spWeightedSubspaces.end(); ++it)
    {
      SmartPtr<time_dependent_obj_type> spSpaceT = it->first.template cast_dynamic<time_dependent_obj_type>();
      if (spSpaceT.valid()) return true;
    }
    return false;
  }
 
  const std::vector<weighted_obj_type> &get_subspaces() const
  { return m_spWeightedSubspaces; }
 
protected:
  std::vector<weighted_obj_type> m_spWeightedSubspaces;
 
};
 
/*
template <typename TGridFunction>
class TimeDependentCompositeSpace
  : public CompositeSpace<TGridFunction>, public ITimeDependentSpace<TGridFunction>
{
protected:
  using CompositeSpace<TGridFunction>::m_spSubspaces;
 
public:
  typedef typename IComponentSpace<TGridFunction> obj_type;
 
 
  void add(SmartPtr<obj_type> spSubSpace)
  { m_spSubspaces.push_back(make_sp(new ITimeDependentSpace(spSubSpace))); }
 
  void update_time_data(number t)
  {
    for (typename std::vector<SmartPtr<obj_type> >::iterator it = m_spSubspaces.begin();
      it!= m_spSubspaces.end(); ++it)
    { if ((*it)->is_time_dependent()) (*it)->update_time_data(t); }
  }
 
  bool is_time_dependent() const
  {
    for (typename std::vector<SmartPtr<obj_type> >::const_iterator it = m_spSubspaces.begin();
        it!= m_spSubspaces.end(); ++it)
    { if ((*it)->is_time_dependent()) return true; }
    return false;
  }
};
 
 */
 
} // namespace ug
#endif