DOFVector.hh

/******************************************************************************
 *
 * AMDiS - Adaptive multidimensional simulations
 *
 * Copyright (C) 2013 Dresden University of Technology. All Rights Reserved.
 * Web: https://fusionforge.zih.tu-dresden.de/projects/amdis
 *
 * Authors: 
 * Simon Vey, Thomas Witkowski, Andreas Naumann, Simon Praetorius, et al.
 *
 * This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
 * WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
 *
 *
 * This file is part of AMDiS
 *
 * See also license.opensource.txt in the distribution.
 * 
 ******************************************************************************/


#include <list>
#include <algorithm>
#include <math.h>

#include <boost/numeric/mtl/mtl.hpp>
#include <boost/numeric/mtl/utility/tag.hpp>
#include <boost/numeric/mtl/utility/category.hpp>
#include <boost/numeric/linear_algebra/identity.hpp>

#include "FixVec.h"
#include "Boundary.h"
#include "DOFAdmin.h"
#include "ElInfo.h"
#include "Error.h"
#include "FiniteElemSpace.h"
#include "Global.h"
#include "Mesh.h"
#include "Quadrature.h"
#include "AbstractFunction.h"
#include "BoundaryManager.h"
#include "Assembler.h"
#include "Operator.h"
#include "Initfile.h"
#include "Traverse.h"
#include "DualTraverse.h"

#ifdef HAVE_PARALLEL_DOMAIN_AMDIS
#include "parallel/MpiHelper.h"
#endif

// Defining the interface for MTL4
namespace mtl {

  // Let MTL4 know that DOFVector it is a column vector
  namespace traits {
    template <typename T>
    struct category< AMDiS::DOFVector<T> > 
    {
      typedef tag::dense_col_vector type;
    };
  }

  namespace ashape {
    template <typename T>
    struct ashape< AMDiS::DOFVector<T> > 
    {
      typedef cvec<typename ashape<T>::type> type;
    };
  }

  // Modelling Collection and MutableCollection
  template <typename T>
  struct Collection< AMDiS::DOFVector<T> > 
  {
    typedef T               value_type;
    typedef const T&        const_reference;
    typedef std::size_t     size_type;
  };

  template <typename T>
  struct MutableCollection< AMDiS::DOFVector<T> > 
    : public Collection< AMDiS::DOFVector<T> > 
  {
    typedef T&              reference;
  };


} // namespace mtl



namespace AMDiS {

  template<typename T>
  DOFVectorBase<T>::DOFVectorBase(const FiniteElemSpace *f, std::string n)
    : feSpace(f),
      name(n),
      elementVector(f->getBasisFcts()->getNumber()),
      boundaryManager(NULL)
  {    
    nBasFcts = feSpace->getBasisFcts()->getNumber();
    dim = feSpace->getMesh()->getDim();
  }
  

  template<typename T>
  DOFVectorBase<T>::~DOFVectorBase()
  {}

 
  template<typename T>
  DOFVector<T>::DOFVector(const FiniteElemSpace* f, std::string n)
    : DOFVectorBase<T>(f, n),
      coarsenOperation(COARSE_INTERPOL)
  {
    vec.resize(0);
    init(f, n);
  } 


  template<typename T>
  void DOFVector<T>::init(const FiniteElemSpace* f, std::string n)
  {
    this->name = n;
    this->feSpace = f;
    if (this->feSpace && this->feSpace->getAdmin())
      (this->feSpace->getAdmin())->addDOFIndexed(this);
    this->boundaryManager = new BoundaryManager(f);
  }

  template<typename T>
  DOFVector<T>::~DOFVector()
  {
    if (this->feSpace && this->feSpace->getAdmin())
      (this->feSpace->getAdmin())->removeDOFIndexed(this);
    
    if (this->boundaryManager)
      delete this->boundaryManager;
    
    vec.clear();
  }

  template<typename T>
  void DOFVectorBase<T>::addElementVector(T factor, 
					  const ElementVector &elVec, 
					  const BoundaryType *bound,
					  ElInfo *elInfo,
					  bool add)
  {
    std::vector<DegreeOfFreedom> indices(nBasFcts);
    feSpace->getBasisFcts()->getLocalIndices(elInfo->getElement(), 
					     feSpace->getAdmin(),
					     indices);

    for (DegreeOfFreedom i = 0; i < nBasFcts; i++) {
      BoundaryCondition *condition = 
	bound ? this->getBoundaryManager()->getBoundaryCondition(bound[i]) : NULL;

      if (!(condition && condition->isDirichlet())) {
	DegreeOfFreedom irow = indices[i];

	if (add)
	  (*this)[irow] += factor * elVec[i];
	else  
	  (*this)[irow] = factor * elVec[i];
      }
    }
  }

  template<typename T>
  double DOFVector<T>::nrm2() const
  {
    checkFeSpace(this->feSpace, vec);

    double nrm = 0.0;
    Iterator vecIterator(dynamic_cast<DOFIndexed<T>*>(const_cast<DOFVector<T>*>(this)), 
			 USED_DOFS);
    for (vecIterator.reset(); !vecIterator.end(); ++vecIterator)
      nrm += (*vecIterator) * (*vecIterator);

#ifdef HAVE_PARALLEL_DOMAIN_AMDIS
    double localNrm = nrm;
    MPI::COMM_WORLD.Allreduce(&localNrm, &nrm, 1, MPI_DOUBLE, MPI_SUM);
#endif

    return sqrt(nrm);
  }


  template<typename T>
  double DOFVector<T>::squareNrm2() const
  {
    checkFeSpace(this->feSpace, vec);
    
    double nrm = 0.0;
    Iterator vecIterator(dynamic_cast<DOFIndexed<T>*>(const_cast<DOFVector<T>*>(this)), 
			 USED_DOFS);
    for (vecIterator.reset(); !vecIterator.end(); ++vecIterator)
      nrm += (*vecIterator) * (*vecIterator);

#ifdef HAVE_PARALLEL_DOMAIN_AMDIS
    double localNrm = nrm;
    MPI::COMM_WORLD.Allreduce(&localNrm, &nrm, 1, MPI_DOUBLE, MPI_SUM);
#endif

    return nrm;
  }


  template<typename T>
  T DOFVector<T>::asum() const
  {
    checkFeSpace(this->feSpace, vec);

    double nrm = 0.0;
    Iterator vecIterator(dynamic_cast<DOFIndexed<T>*>(const_cast<DOFVector<T>*>(this)), 
			 USED_DOFS);
    for (vecIterator.reset(); !vecIterator.end(); ++vecIterator)
      nrm += abs(*vecIterator);

#ifdef HAVE_PARALLEL_DOMAIN_AMDIS
    double localNrm = nrm;
    MPI::COMM_WORLD.Allreduce(&localNrm, &nrm, 1, MPI_DOUBLE, MPI_SUM);
#endif

    return nrm;
  }


  template<typename T>
  T DOFVector<T>::sum() const
  {
    checkFeSpace(this->feSpace, vec);

    double nrm = 0.0;    
    Iterator vecIterator(dynamic_cast<DOFIndexed<T>*>(const_cast<DOFVector<T>*>(this)), 
			 USED_DOFS);
    for (vecIterator.reset(); !vecIterator.end(); ++vecIterator)
      nrm += *vecIterator;

#ifdef HAVE_PARALLEL_DOMAIN_AMDIS
    double localNrm = nrm;
    MPI::COMM_WORLD.Allreduce(&localNrm, &nrm, 1, MPI_DOUBLE, MPI_SUM);
#endif

    return nrm;
  }


  template<typename T>
  void DOFVector<T>::set(T alpha)
  {
    checkFeSpace(this->feSpace, vec);

    Iterator vecIterator(dynamic_cast<DOFIndexed<T>*>(this), USED_DOFS);
    for (vecIterator.reset(); !vecIterator.end(); ++vecIterator)
      *vecIterator = alpha ; 
  }


  template<typename T>
  void DOFVector<T>::copy(const DOFVector<T>& x)
  {
    FUNCNAME_DBG("DOFVector<T>::copy()");

    checkFeSpace(this->feSpace, vec);

    TEST_EXIT_DBG(static_cast<int>(x.vec.size()) >= 
		  this->feSpace->getAdmin()->getUsedSize())
      ("x.size = %d too small: admin->sizeUsed = %d\n", x.vec.size(), 
       this->feSpace->getAdmin()->getUsedSize());
    
    Iterator vecIterator(dynamic_cast<DOFIndexed<T>*>(this), USED_DOFS);
    Iterator xIterator(dynamic_cast<DOFVector<T>*>(const_cast<DOFVector<T>*>(&x)), 
		       USED_DOFS);
    for (vecIterator.reset(), xIterator.reset(); !vecIterator.end();
	 ++vecIterator, ++xIterator)      
      *vecIterator = *xIterator; 
  }


  template<typename T>
  T DOFVector<T>::min() const
  {    
    checkFeSpace(this->feSpace, vec);

    T m;    
    Iterator vecIterator(const_cast<DOFIndexed<T>*>(dynamic_cast<const DOFIndexed<T>*>(this)), USED_DOFS);
    for (vecIterator.reset(), m = *vecIterator; !vecIterator.end(); ++vecIterator)
      m = std::min(m, *vecIterator);

#ifdef HAVE_PARALLEL_DOMAIN_AMDIS
    double localMin = m;
    MPI::COMM_WORLD.Allreduce(&localMin, &m, 1, MPI_DOUBLE, MPI_MIN);
#endif

    return m;
  }


  template<typename T>
  T DOFVector<T>::max() const 
  {    
    checkFeSpace(this->feSpace, vec);

    T m;    
    Iterator vecIterator(const_cast<DOFIndexed<T>*>(dynamic_cast<const DOFIndexed<T>*>(this)), USED_DOFS);
    for (vecIterator.reset(), m = *vecIterator; !vecIterator.end(); ++vecIterator)
      m = std::max(m, *vecIterator);

#ifdef HAVE_PARALLEL_DOMAIN_AMDIS
    double localMax = m;
    MPI::COMM_WORLD.Allreduce(&localMax, &m, 1, MPI_DOUBLE, MPI_MAX);
#endif

    return m;
  }


  template<typename T>
  T DOFVector<T>::absMax() const
  {
    return std::max(abs(max()), abs(min()));
  }


  template<typename T>
  T DOFVector<T>::average() const
  {    
    checkFeSpace(this->feSpace, vec);

    int count = 0;
    T m = 0;
    Iterator vecIterator(const_cast<DOFIndexed<T>*>(dynamic_cast<const DOFIndexed<T>*>(this)), USED_DOFS);
    for (vecIterator.reset(); !vecIterator.end(); ++vecIterator) {
      m += *vecIterator;
      count++;
    }

#ifdef HAVE_PARALLEL_DOMAIN_AMDIS
    double localSum = m;
    int localCount = count;
    MPI::COMM_WORLD.Allreduce(&localSum, &m, 1, MPI_DOUBLE, MPI_SUM);
    MPI::COMM_WORLD.Allreduce(&localCount, &count, 1, MPI_INT, MPI_SUM);
#endif

    return m / count;
  }


  template<typename T>
  void DOFVector<T>::print() const
  {
    FUNCNAME("DOFVector<T>::print()");

    const DOFAdmin *admin = NULL;
    const char *format;

    if (this->feSpace) 
      admin = this->feSpace->getAdmin();

    MSG("Vec `%s':\n", this->name.c_str());
    int j = 0;
    if (admin) {
      if (admin->getUsedSize() > 100)
	format = "%s(%3d,%10.5le)";
      else if (admin->getUsedSize() > 10)
	format = "%s(%2d,%10.5le)";
      else
	format = "%s(%1d,%10.5le)";

      Iterator vecIterator(dynamic_cast<DOFIndexed<T>*>(const_cast<DOFVector<T>*>(this)), USED_DOFS);
      for (vecIterator.reset(); !vecIterator.end(); ++vecIterator) {
	if ((j % 3) == 0) {
	  if (j) 
	    Msg::print("\n");
	  MSG(format, "", vecIterator.getDOFIndex(), *vecIterator);
	} else {
	  Msg::print(format, " ", vecIterator.getDOFIndex(), *vecIterator);
	}
	j++;
      }
      Msg::print("\n");
    } else {
	MSG("no DOFAdmin, print whole vector.\n");
    
	for (int i = 0; i < static_cast<int>( vec.size()); i++) {
	  if ((j % 3) == 0) {
	    if (j) 
	      Msg::print("\n");
	    MSG("(%d,%10.5e)",i,vec[i]);
	  } else {
	    Msg::print(" (%d,%10.5e)",i,vec[i]);
	  }
	  j++;
	}
	Msg::print("\n");
      }
    return;
  }


  template<typename T>
  int DOFVector<T>::calcMemoryUsage() const
  {
    int result = 0;
    result += sizeof(DOFVector<T>);
    result += vec.size() * sizeof(T);

    return result;
  }


  template<typename T>
  T DOFVectorBase<T>::evalUh(const DimVec<double>& lambda, 
			     DegreeOfFreedom* dof_indices)
  {
    BasisFunction* phi = const_cast<BasisFunction*>(this->getFeSpace()->getBasisFcts());
    int nBasisFcts = phi->getNumber();
    T val = 0.0;

    for (int i = 0; i < nBasisFcts; i++)
      val += (*this)[dof_indices[i]]*(*phi->getPhi(i))(lambda);

#ifdef HAVE_PARALLEL_DOMAIN_AMDIS
    double localVal = val;
    MPI::COMM_WORLD.Allreduce(&localVal, &val, 1, MPI_DOUBLE, MPI_SUM);
#endif

    return val;
  }


  template<typename T>
  void DOFVector<T>::interpol(AbstractFunction<T, WorldVector<double> > *fct)
  {
    FUNCNAME("DOFVector::interpol()");

    TEST_EXIT_DBG(fct)("No function to interpolate!\n");

    if (!this->getFeSpace()) {
      MSG("no dof admin in vec %s, skipping interpolation\n",
	  this->getName().c_str());
      return;
    }

    if (!(this->getFeSpace()->getAdmin())) {
      MSG("no dof admin in feSpace %s, skipping interpolation\n", 
	  this->getFeSpace()->getName().c_str());
      return;
    }
  
    if (!(this->getFeSpace()->getBasisFcts())) {
      MSG("no basis functions in admin of vec %s, skipping interpolation\n",
	  this->getName().c_str());
      return;
    }

    if (!(fct)) {
      MSG("function that should be interpolated only pointer to NULL, ");
      Msg::print("skipping interpolation\n");
      return;
    }

    const BasisFunction *basFct = this->getFeSpace()->getBasisFcts();
    const DOFAdmin* admin = this->getFeSpace()->getAdmin();
    int nBasFcts = basFct->getNumber();
    std::vector<DegreeOfFreedom> myLocalIndices(nBasFcts);
    mtl::dense_vector<T> fctInterpolValues(nBasFcts);

    TraverseStack stack;
    ElInfo *elInfo = stack.traverseFirst(this->getFeSpace()->getMesh(), -1,
					 Mesh::CALL_LEAF_EL | Mesh::FILL_COORDS);
    while (elInfo) {
      basFct->interpol(elInfo, 0, NULL, fct, fctInterpolValues);
      basFct->getLocalIndices(const_cast<Element*>(elInfo->getElement()), 
			      admin, myLocalIndices);
      for (int i = 0; i < nBasFcts; i++)
	vec[myLocalIndices[i]] = fctInterpolValues[i];

      elInfo = stack.traverseNext(elInfo);
    }
  }


  template<typename T>
  double DOFVector<T>::Int(int meshLevel, Quadrature* q) const
  {
    Mesh* mesh = this->feSpace->getMesh();

    if (!q) {
      int deg = 2 * this->feSpace->getBasisFcts()->getDegree();
      q = Quadrature::provideQuadrature(this->dim, deg);
    }

    FastQuadrature *quadFast = 
      FastQuadrature::provideFastQuadrature(this->feSpace->getBasisFcts(), *q, INIT_PHI);

    Flag flag = Mesh::FILL_COORDS | Mesh::FILL_DET;
    if (meshLevel == -1)
      flag |= Mesh::CALL_LEAF_EL;
    else
      flag |= Mesh::CALL_EL_LEVEL;

    T result; nullify(result);
    int nPoints = quadFast->getNumPoints();
    mtl::dense_vector<T> uh_vec(nPoints);
    TraverseStack stack;
    ElInfo *elInfo =  stack.traverseFirst(mesh, meshLevel, flag);
    while (elInfo) {
      double det = elInfo->getDet();
      T normT; nullify(normT);
      this->getVecAtQPs(elInfo, NULL, quadFast, uh_vec);
      for (int iq = 0; iq < nPoints; iq++)
	normT += quadFast->getWeight(iq) * (uh_vec[iq]);
      result += det * normT;

      elInfo = stack.traverseNext(elInfo);
    }

#ifdef HAVE_PARALLEL_DOMAIN_AMDIS
    Parallel::mpi::globalAdd(result);
#endif
    
    return result;
  }

  
  template<typename TOut>
  TOut integrate_Coords(const FiniteElemSpace* feSpace,
		   AbstractFunction<TOut, WorldVector<double> > *fct)
  {
    FUNCNAME("integrate_Coords()");
    
    TEST_EXIT(fct)("No function defined!\n");

    int deg = std::max(fct->getDegree(), feSpace->getBasisFcts()->getDegree());
    Quadrature* quad = 
      Quadrature::provideQuadrature(feSpace->getMesh()->getDim(), deg);
    FastQuadrature *fastQuad =
      FastQuadrature::provideFastQuadrature(feSpace->getBasisFcts(), *quad, INIT_PHI);

    WorldVector<double> coords;

    TOut value; nullify(value);
    Flag traverseFlag = Mesh::CALL_LEAF_EL | Mesh::FILL_COORDS | Mesh::FILL_DET;      
    TraverseStack stack;    
    ElInfo *elInfo = stack.traverseFirst(feSpace->getMesh(), -1, traverseFlag);
    while (elInfo) {
    TOut tmp; nullify(tmp);
      for (int iq = 0; iq < fastQuad->getNumPoints(); iq++) {
	elInfo->coordToWorld(fastQuad->getLambda(iq), coords);
 	tmp += fastQuad->getWeight(iq) * (*fct)(coords);
      }

      value += tmp * elInfo->getDet();
      
      elInfo = stack.traverseNext(elInfo);
    }

#ifdef HAVE_PARALLEL_DOMAIN_AMDIS
    Parallel::mpi::globalAdd(value);
#endif

    return value;
  }

  
  template<typename TOut, typename T>
  TOut integrate_Vec(const DOFVector<T> &vec,
		  AbstractFunction<TOut, T> *fct)
  {
    FUNCNAME("integrate_Vec()");

    TEST_EXIT(fct)("No function defined!\n");

    int deg = std::max(fct->getDegree(),
		       2 * vec.getFeSpace()->getBasisFcts()->getDegree());
    Quadrature* quad =
      Quadrature::provideQuadrature(vec.getFeSpace()->getMesh()->getDim(), deg);
    FastQuadrature *fastQuad =
      FastQuadrature::provideFastQuadrature(vec.getFeSpace()->getBasisFcts(), *quad, INIT_PHI);

    mtl::dense_vector<T> qp(fastQuad->getNumPoints());

    TOut value; nullify(value);

    Flag traverseFlag = Mesh::CALL_LEAF_EL | Mesh::FILL_COORDS | Mesh::FILL_DET;
    TraverseStack stack;
    ElInfo *elInfo = stack.traverseFirst(vec.getFeSpace()->getMesh(), -1, traverseFlag);
    while (elInfo) {
      vec.getVecAtQPs(elInfo, quad, fastQuad, qp);
      TOut tmp; nullify(tmp);
      for (int iq = 0; iq < fastQuad->getNumPoints(); iq++) {
 	tmp += fastQuad->getWeight(iq) * (*fct)(qp[iq]);
      }
      value += tmp * elInfo->getDet();

      elInfo = stack.traverseNext(elInfo);
    }

#ifdef HAVE_PARALLEL_DOMAIN_AMDIS
    Parallel::mpi::globalAdd(value);
#endif

    return value;
  }
  
  
  template<typename TOut, typename T1, typename T2>
  TOut integrate_Vec2(const DOFVector<T1> &vec1,
		   const DOFVector<T2> &vec2,
		   BinaryAbstractFunction<TOut, T1, T2> *fct)
  {
    if (vec1.getFeSpace()->getMesh() == vec2.getFeSpace()->getMesh())
      return int_Vec2_SingleMesh(vec1, vec2, fct);
    else
      return int_Vec2_DualMesh(vec1, vec2, fct);
  }


  template<typename TOut, typename T1, typename T2>
  TOut int_Vec2_SingleMesh(const DOFVector<T1> &vec1,
		   const DOFVector<T2> &vec2,
		   BinaryAbstractFunction<TOut, T1, T2> *fct)
  {
    FUNCNAME("intDualmesh()");
    
    TEST_EXIT(fct)("No function defined!\n");

    int deg = std::max(fct->getDegree(), 
		       2 * vec1.getFeSpace()->getBasisFcts()->getDegree());
    Quadrature* quad = 
      Quadrature::provideQuadrature(vec1.getFeSpace()->getMesh()->getDim(), deg);
    FastQuadrature *fastQuad =
      FastQuadrature::provideFastQuadrature(vec1.getFeSpace()->getBasisFcts(), *quad, INIT_PHI);

    mtl::dense_vector<T1> qp1(fastQuad->getNumPoints());
    mtl::dense_vector<T2> qp2(fastQuad->getNumPoints());

    TOut value; nullify(value);
    Flag traverseFlag = Mesh::CALL_LEAF_EL | Mesh::FILL_COORDS | Mesh::FILL_DET;      
    TraverseStack stack;    
    ElInfo *elInfo = stack.traverseFirst(vec1.getFeSpace()->getMesh(), -1, traverseFlag);
    while (elInfo) {
      vec1.getVecAtQPs(elInfo, quad, fastQuad, qp1);
      vec2.getVecAtQPs(elInfo, quad, fastQuad, qp2);

      TOut tmp; nullify(tmp);
      for (int iq = 0; iq < fastQuad->getNumPoints(); iq++)
 	tmp += fastQuad->getWeight(iq) * (*fct)(qp1[iq], qp2[iq]);     
      value += tmp * elInfo->getDet();
      
      elInfo = stack.traverseNext(elInfo);
    }

#ifdef HAVE_PARALLEL_DOMAIN_AMDIS
    Parallel::mpi::globalAdd(value);
#endif
    
    return value;
  }


  template<typename TOut, typename T1, typename T2>
  TOut int_Vec2_DualMesh(const DOFVector<T1> &vec1,
		   const DOFVector<T2> &vec2,
		   BinaryAbstractFunction<TOut, T1, T2> *fct)
  {
    FUNCNAME("intDualmesh()");
    
    TEST_EXIT(fct)("No function defined!\n");

    int deg = std::max(fct->getDegree(), 
		       2 * vec1.getFeSpace()->getBasisFcts()->getDegree());
    Quadrature* quad = 
      Quadrature::provideQuadrature(vec1.getFeSpace()->getMesh()->getDim(), deg);
    FastQuadrature *fastQuad =
      FastQuadrature::provideFastQuadrature(vec1.getFeSpace()->getBasisFcts(), *quad, INIT_PHI);

    mtl::dense_vector<T1> qp1(fastQuad->getNumPoints());
    mtl::dense_vector<T2> qp2(fastQuad->getNumPoints());

    TOut value; nullify(value);
    Flag traverseFlag = Mesh::CALL_LEAF_EL | Mesh::FILL_COORDS | Mesh::FILL_DET;      
    DualTraverse dualTraverse;    
    DualElInfo dualElInfo;
    bool cont = dualTraverse.traverseFirst(vec1.getFeSpace()->getMesh(),
					   vec2.getFeSpace()->getMesh(),
					   -1, -1, traverseFlag, traverseFlag,
					   dualElInfo);
    while (cont) {
      vec1.getVecAtQPs(dualElInfo.smallElInfo, dualElInfo.largeElInfo, quad, NULL, qp1);
      vec2.getVecAtQPs(dualElInfo.smallElInfo, dualElInfo.largeElInfo, quad, NULL, qp2);

      TOut tmp; nullify(tmp);
      for (int iq = 0; iq < quad->getNumPoints(); iq++)
 	tmp += quad->getWeight(iq) * (*fct)(qp1[iq], qp2[iq]);      
      value += tmp * dualElInfo.smallElInfo->getDet();
      
      cont = dualTraverse.traverseNext(dualElInfo);
    }

#ifdef HAVE_PARALLEL_DOMAIN_AMDIS
    Parallel::mpi::globalAdd(value);
#endif

    return value;
  }
  
  
  template<typename T1, typename T2>
  typename ProductType<T1,T2>::type integrate_VecTimesCoords(const DOFVector<T1> &vec,
		   AbstractFunction<T2, WorldVector<double> > *fct)
  {
    FUNCNAME("integrate_VecTimesCoords()");
    
    TEST_EXIT(fct)("No function defined!\n");
    
    typedef typename ProductType<T1,T2>::type TOut;

    const FiniteElemSpace *feSpace = vec.getFeSpace();
    Mesh *mesh = feSpace->getMesh();

    int deg = std::max(fct->getDegree(), 2 * feSpace->getBasisFcts()->getDegree());
    Quadrature* quad = Quadrature::provideQuadrature(mesh->getDim(), deg);
    FastQuadrature *fastQuad =
      FastQuadrature::provideFastQuadrature(feSpace->getBasisFcts(), *quad, INIT_PHI);

    mtl::dense_vector<T1> qp(fastQuad->getNumPoints());
    WorldVector<double> coords;

    TOut value; nullify(value);
    Flag traverseFlag = Mesh::CALL_LEAF_EL | Mesh::FILL_COORDS | Mesh::FILL_DET;      
    TraverseStack stack;    
    ElInfo *elInfo = stack.traverseFirst(mesh, -1, traverseFlag);
    while (elInfo) {
      vec.getVecAtQPs(elInfo, quad, fastQuad, qp);

      TOut tmp; nullify(tmp);
      for (int iq = 0; iq < fastQuad->getNumPoints(); iq++) {
	elInfo->coordToWorld(fastQuad->getLambda(iq), coords);
 	tmp += fastQuad->getWeight(iq) * (qp[iq] * (*fct)(coords));
      }

      value += tmp * elInfo->getDet();
      
      elInfo = stack.traverseNext(elInfo);
    }

#ifdef HAVE_PARALLEL_DOMAIN_AMDIS
    Parallel::mpi::globalAdd(value);
#endif

    return value;
  }

  
  template<typename TOut, typename T>
  TOut integrate_VecAndCoords(const DOFVector<T> &vec,
			   BinaryAbstractFunction<TOut, T, WorldVector<double> > *fct)
  {
    FUNCNAME("integrate_VecAndCoords()");

    TEST_EXIT(fct)("No function defined!\n");

    int deg = std::max(fct->getDegree(),
		       2 * vec.getFeSpace()->getBasisFcts()->getDegree());
    Quadrature* quad =
      Quadrature::provideQuadrature(vec.getFeSpace()->getMesh()->getDim(), deg);
    FastQuadrature *fastQuad =
      FastQuadrature::provideFastQuadrature(vec.getFeSpace()->getBasisFcts(), *quad, INIT_PHI);

    mtl::dense_vector<T> qp(fastQuad->getNumPoints());
    WorldVector<double> coordsAtQP;

    TOut value; nullify(value);
    
    Flag traverseFlag = Mesh::CALL_LEAF_EL | Mesh::FILL_COORDS | Mesh::FILL_DET;
    TraverseStack stack;
    ElInfo *elInfo = stack.traverseFirst(vec.getFeSpace()->getMesh(), -1, traverseFlag);
    while (elInfo) {
      vec.getVecAtQPs(elInfo, quad, fastQuad, qp);
      TOut tmp; nullify(tmp);
      for (int iq = 0; iq < fastQuad->getNumPoints(); iq++) {
	elInfo->coordToWorld(fastQuad->getLambda(iq), coordsAtQP);
 	tmp += fastQuad->getWeight(iq) * (*fct)(qp[iq], coordsAtQP);
      }
      value += tmp * elInfo->getDet();

      elInfo = stack.traverseNext(elInfo);
    }

#ifdef HAVE_PARALLEL_DOMAIN_AMDIS
    Parallel::mpi::globalAdd(value);
#endif

    return value;
  }

  
  template<typename T>
  double DOFVector<T>::L1Norm(Quadrature* q) const
  {  
    Mesh* mesh = this->feSpace->getMesh();

    if (!q) {
      int deg = 2 * this->feSpace->getBasisFcts()->getDegree();
      q = Quadrature::provideQuadrature(this->dim, deg);
    }

    FastQuadrature *quadFast = 
      FastQuadrature::provideFastQuadrature(this->feSpace->getBasisFcts(), *q, INIT_PHI);

    double result = 0.0;
    int nPoints = quadFast->getNumPoints();
    mtl::dense_vector<T> uh_vec(nPoints);
    TraverseStack stack;
    ElInfo *elInfo = 
      stack.traverseFirst(mesh, -1, 
			  Mesh::CALL_LEAF_EL | Mesh::FILL_COORDS | Mesh::FILL_DET);
    while (elInfo) {
      double det = elInfo->getDet();
      double normT = 0.0;
      this->getVecAtQPs(elInfo, NULL, quadFast, uh_vec);
      for (int iq = 0; iq < nPoints; iq++)
	normT += quadFast->getWeight(iq) * abs(uh_vec[iq]);
      result += det * normT;

      elInfo = stack.traverseNext(elInfo);
    }

#ifdef HAVE_PARALLEL_DOMAIN_AMDIS
    double localResult = result;
    MPI::COMM_WORLD.Allreduce(&localResult, &result, 1, MPI_DOUBLE, MPI_SUM);
#endif
    
    return result;
  }


  template<typename T>
  double DOFVector<T>::L2NormSquare(Quadrature* q) const
  {
    Mesh* mesh = this->feSpace->getMesh();

    if (!q) {
      int deg = 2 * this->feSpace->getBasisFcts()->getDegree();
      q = Quadrature::provideQuadrature(this->dim, deg);
    }

    FastQuadrature *quadFast = 
      FastQuadrature::provideFastQuadrature(this->feSpace->getBasisFcts(), *q, INIT_PHI);

    double result = 0.0;
    int nPoints = quadFast->getNumPoints();
    mtl::dense_vector<T> uh_vec(nPoints);
    TraverseStack stack;
    ElInfo *elInfo = 
      stack.traverseFirst(mesh, -1, 
			  Mesh::CALL_LEAF_EL | Mesh::FILL_COORDS | Mesh::FILL_DET);
    while (elInfo) {
      double det = elInfo->getDet();
      double normT = 0.0;
      this->getVecAtQPs(elInfo, NULL, quadFast, uh_vec);
      for (int iq = 0; iq < nPoints; iq++)
	normT += quadFast->getWeight(iq) * sqr(uh_vec[iq]);
      result += det * normT;

      elInfo = stack.traverseNext(elInfo);
    }

#ifdef HAVE_PARALLEL_DOMAIN_AMDIS
    double localResult = result;
    MPI::COMM_WORLD.Allreduce(&localResult, &result, 1, MPI_DOUBLE, MPI_SUM);
#endif
    
    return result;
  }


  template<typename T>  
  double DOFVector<T>::H1NormSquare(Quadrature *q) const
  {
    Mesh* mesh = this->feSpace->getMesh();

    if (!q) {
      int deg = 2 * this->feSpace->getBasisFcts()->getDegree() - 2;
      q = Quadrature::provideQuadrature(this->dim, deg);
    }

    FastQuadrature *quadFast = 
      FastQuadrature::provideFastQuadrature(this->feSpace->getBasisFcts(), *q, INIT_GRD_PHI);

    double result = 0.0;
    int nPoints = quadFast->getNumPoints();
    int dimOfWorld = Global::getGeo(WORLD);
    mtl::dense_vector<WorldVector<T> > grduh_vec(nPoints);
    TraverseStack stack;
    ElInfo *elInfo = 
      stack.traverseFirst(mesh, -1, 
			  Mesh::CALL_LEAF_EL | Mesh::FILL_COORDS | 
			  Mesh::FILL_DET | Mesh::FILL_GRD_LAMBDA);
    while (elInfo) {
      double det = elInfo->getDet();
      double normT = 0.0;
      this->getGrdAtQPs(elInfo, NULL, quadFast, grduh_vec);

      for (int iq = 0; iq < nPoints; iq++) {
	double norm2 = 0.0;
	for (int j = 0; j < dimOfWorld; j++)
	  norm2 += sqr(grduh_vec[iq][j]);
	normT += quadFast->getWeight(iq) * norm2;
      }

      result += det * normT;

      elInfo = stack.traverseNext(elInfo);
    }

#ifdef HAVE_PARALLEL_DOMAIN_AMDIS
    double localResult = result;
    MPI::COMM_WORLD.Allreduce(&localResult, &result, 1, MPI_DOUBLE, MPI_SUM);
#endif
    
    return result;
  }



  template<typename T>
  bool DOFVector<T>::getDofIdxAtPoint(WorldVector<double> &p, 
					    DegreeOfFreedom &idx, 
					    ElInfo *oldElInfo, 
					    bool useOldElInfo) const
  { 
    Mesh *mesh = this->feSpace->getMesh();
    const BasisFunction *basFcts = this->feSpace->getBasisFcts();

    int dim = mesh->getDim();
    int numBasFcts = basFcts->getNumber();

    std::vector<DegreeOfFreedom> localIndices(numBasFcts);
    DimVec<double> lambda(dim, NO_INIT);

    ElInfo *elInfo = mesh->createNewElInfo();
    idx = 0;
    bool inside = false;

    if (oldElInfo && useOldElInfo && oldElInfo->getMacroElement()) {
      inside = mesh->findElInfoAtPoint(p, elInfo, lambda, oldElInfo->getMacroElement(), NULL, NULL);
      delete oldElInfo;
    } else {
      inside = mesh->findElInfoAtPoint(p, elInfo, lambda, NULL, NULL, NULL);
    }
    
    if (oldElInfo)
      oldElInfo = elInfo;
    
    if (!inside)
      return false;
    
    basFcts->getLocalIndices(elInfo->getElement(), this->feSpace->getAdmin(), localIndices);
    
    WorldVector<double> coord;
    int minIdx = -1;
    double minDist = 1.e15;
    
    for (int i = 0; i < numBasFcts; i++) {
      elInfo->coordToWorld(*(basFcts->getCoords(i)), coord);
      WorldVector<double> dist = coord - p;
      double newDist = norm(dist);
      if (newDist < minDist) {
	minIdx = i;
	minDist = newDist;
	if (minDist < 1.e-10)
	  break;
      }
    }
    
    if (minIdx >= 0)
      idx = localIndices[minIdx];
    
    if(!oldElInfo) delete elInfo;
    return inside;
  }


  template<typename T>
  void DOFVector<T>::compressDOFIndexed(int first, int last, 
					std::vector<DegreeOfFreedom> &newDOF)
  {
    for (int i = first; i <= last; i++)
      if (newDOF[i] >= 0)
	vec[newDOF[i]] = vec[i];
  }


  template<typename T>