DOFVector.hh 40.3 KB
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#include <list>
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#include <algorithm>
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#include <math.h>
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#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 "ElementVector.h"
#include "Assembler.h"
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#include "OpenMP.h"
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#include "Operator.h"
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#include "Parameters.h"
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namespace AMDiS {

  template<typename T>
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  DOFVectorBase<T>::DOFVectorBase(const FiniteElemSpace *f, std::string n)
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    : feSpace(f),
      name(n),
      elementVector(NULL),
      boundaryManager(NULL)
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  {
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    nBasFcts = feSpace->getBasisFcts()->getNumber();
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    int dim = feSpace->getMesh()->getDim();
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    localIndices.resize(omp_get_max_threads());
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    grdPhis.resize(omp_get_max_threads());
    D2Phis.resize(omp_get_max_threads());
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    for (int i = 0; i < omp_get_max_threads(); i++) {
      localIndices[i] = GET_MEMORY(DegreeOfFreedom, this->nBasFcts);      
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      grdPhis[i] = NEW DimVec<double>(dim, DEFAULT_VALUE, 0.0);
      D2Phis[i] = NEW DimMat<double>(dim, NO_INIT);
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    }
  }
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  template<typename T>
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  DOFVectorBase<T>::~DOFVectorBase()
  {
    for (int i = 0; i < static_cast<int>(localIndices.size()); i++) {
      FREE_MEMORY(localIndices[i], DegreeOfFreedom, this->nBasFcts);
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      DELETE grdPhis[i];
      DELETE D2Phis[i];
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    }
  }
  
  template<typename T>
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  DOFVector<T>::DOFVector(const FiniteElemSpace* f, std::string n)
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    : DOFVectorBase<T>(f, n),
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      refineInter(false), 
      coarsenOperation(NO_OPERATION)
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  {
    init(f, n);
  } 

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

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

    if (this->boundaryManager) {
      DELETE this->boundaryManager;
    }
  }

  template<typename T>
  DOFVector<T> * DOFVector<T>::traverseVector = NULL;

  template<typename T>
  FastQuadrature *DOFVector<T>::quad_fast = NULL;

  template<typename T>
  double DOFVector<T>::norm = 0.0;

  template<typename T>
  int DOFVector<T>::dim = 0;

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  template<typename T>
  void DOFVectorBase<T>::addElementVector(T factor, 
					  const ElementVector &elVec, 
					  const BoundaryType *bound,
					  bool add)
  {
    FUNCNAME("DOFVector::addElementVector()");

    int n_row = elVec.getSize();

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

      if(!(condition && condition->isDirichlet())) {
	DegreeOfFreedom irow = elVec.dofIndices[i];
	(*this)[irow] = (add ? (*this)[irow] : 0.0);
	(*this)[irow] += factor * elVec[i];
      }
    }
  }

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  template<typename T>
  double DOFVector<T>::nrm2() const
  {
    FUNCNAME("DOFVector<T>::nrm2()");

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    TEST_EXIT_DBG(feSpace)("feSpace is NULL\n");
    TEST_EXIT_DBG(feSpace->getAdmin())("admin is NULL\n");
    TEST_EXIT_DBG(static_cast<int>(vec.size()) >= feSpace->getAdmin()->getUsedSize())
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      ("size = %d too small: admin->sizeUsed = %d\n", vec.size(),
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       feSpace->getAdmin()->getUsedSize());
    
    double nrm = 0.0;
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    Iterator vecIterator(dynamic_cast<DOFIndexed<T>*>(const_cast<DOFVector<T>*>(this)), USED_DOFS);
    for(vecIterator.reset(); !vecIterator.end(); ++vecIterator)
      nrm += (*vecIterator) * (*vecIterator);

    return(sqrt(nrm));
  }

  template<typename T>
  double DOFVector<T>::squareNrm2() const
  {
    FUNCNAME("DOFVector<T>::nrm2()");

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    TEST_EXIT_DBG(feSpace)("feSpace is NULL\n");
    TEST_EXIT_DBG(feSpace->getAdmin())("admin is NULL\n");
    TEST_EXIT_DBG(static_cast<int>(vec.size()) >= feSpace->getAdmin()->getUsedSize())
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      ("size = %d too small: admin->sizeUsed = %d\n", vec.size(),
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       feSpace->getAdmin()->getUsedSize());
    
    double nrm = 0.0;
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    Iterator vecIterator(dynamic_cast<DOFIndexed<T>*>(const_cast<DOFVector<T>*>(this)), USED_DOFS);
    for(vecIterator.reset(); !vecIterator.end(); ++vecIterator)
      nrm += (*vecIterator) * (*vecIterator);

    return nrm;
  }

  template<typename T>
  T DOFVector<T>::asum() const
  {
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    FUNCNAME("DOFVector<T>::asum()");
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    TEST_EXIT_DBG(feSpace)("feSpace is NULL\n");
    TEST_EXIT_DBG(feSpace->getAdmin())("admin is NULL\n");
    TEST_EXIT_DBG(static_cast<int>(vec.size()) >= feSpace->getAdmin()->getUsedSize())
      ("size = %d too small: admin->sizeUsed = %d\n", vec.size(),
       feSpace->getAdmin()->getUsedSize());
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    double nrm = 0.0;
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    Iterator vecIterator(dynamic_cast<DOFIndexed<T>*>(const_cast<DOFVector<T>*>(this)), USED_DOFS);
    for(vecIterator.reset(); !vecIterator.end(); ++vecIterator)
      nrm += abs(*vecIterator);

    return(nrm);
  }

  template<typename T>
  T DOFVector<T>::sum() const
  {
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    FUNCNAME("DOFVector<T>::sum()");
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    TEST_EXIT_DBG(feSpace)("feSpace is NULL\n");
    TEST_EXIT_DBG(feSpace->getAdmin())("admin is NULL\n");
    TEST_EXIT_DBG(static_cast<int>(vec.size()) >= feSpace->getAdmin()->getUsedSize())
      ("size = %d too small: admin->sizeUsed = %d\n", vec.size(),
       feSpace->getAdmin()->getUsedSize());
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    double nrm = 0.0;    
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    Iterator vecIterator(dynamic_cast<DOFIndexed<T>*>(const_cast<DOFVector<T>*>(this)), USED_DOFS);
    for(vecIterator.reset(); !vecIterator.end(); ++vecIterator)
      nrm += *vecIterator;

    return(nrm);
  }

  template<typename T>
  void DOFVector<T>::set(T alpha)
  {
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    FUNCNAME("DOFVector<T>::set()");
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    TEST_EXIT_DBG(feSpace)("feSpace is NULL\n");
    TEST_EXIT_DBG(feSpace->getAdmin())("admin is NULL\n");
    TEST_EXIT_DBG(static_cast<int>(vec.size()) >= feSpace->getAdmin()->getUsedSize())
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      ("size = %d too small: admin->sizeUsed = %d\n", vec.size(),
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       feSpace->getAdmin()->getUsedSize());
    
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    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)
  {
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    FUNCNAME("DOFVector<T>::copy()");
    
    TEST_EXIT_DBG(feSpace && x.feSpace)
      ("feSpace is NULL: %8X, %8X\n", feSpace, x.feSpace);
    TEST_EXIT_DBG(feSpace->getAdmin() && (feSpace->getAdmin() == x.feSpace->getAdmin()))
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      ("no admin or different admins: %8X, %8X\n",
       feSpace->getAdmin(), x.feSpace->getAdmin());
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    TEST_EXIT_DBG(static_cast<int>(vec.size()) >= feSpace->getAdmin()->getUsedSize())
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      ("size = %d too small: admin->sizeUsed = %d\n", vec.size(), 
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       feSpace->getAdmin()->getUsedSize());
    TEST_EXIT_DBG(static_cast<int>(x.vec.size()) >= feSpace->getAdmin()->getUsedSize())
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      ("x.size = %d too small: admin->sizeUsed = %d\n", x.vec.size(), 
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       feSpace->getAdmin()->getUsedSize());
    
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    Iterator vecIterator(dynamic_cast<DOFIndexed<T>*>(this), USED_DOFS);
    Iterator xIterator(dynamic_cast<DOFVector<T>*>(const_cast<DOFVector<T>*>(&x)), USED_DOFS);
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    for (vecIterator.reset(), xIterator.reset();
	 !vecIterator.end();
	 ++vecIterator, ++xIterator) {
      
      *vecIterator = *xIterator; 
    };
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  }


  template<typename T>
  T DOFVector<T>::min() const
  {
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    FUNCNAME("DOFVector<T>::min()");
    
    TEST_EXIT_DBG(feSpace && feSpace->getAdmin())
      ("pointer is NULL: %8X, %8X\n", this, feSpace->getAdmin());
    TEST_EXIT_DBG((static_cast<int>(vec.size())) >= feSpace->getAdmin()->getUsedSize())
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      ("size = %d too small: admin->sizeUsed = %d\n", vec.size(), 
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       feSpace->getAdmin()->getUsedSize());

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

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    return m;
  }

  template<typename T>
  T DOFVector<T>::max() const 
  {
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    FUNCNAME("DOFVector<T>::max()");
    
    TEST_EXIT_DBG(feSpace && feSpace->getAdmin())
      ("pointer is NULL: %8X, %8X\n", this, feSpace->getAdmin());
    TEST_EXIT_DBG((static_cast<int>(vec.size())) >= feSpace->getAdmin()->getUsedSize())
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      ("size = %d too small: admin->sizeUsed = %d\n", vec.size(), 
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       feSpace->getAdmin()->getUsedSize());
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    T m;    
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    Iterator vecIterator(const_cast<DOFIndexed<T>*>(dynamic_cast<const DOFIndexed<T>*>(this)), USED_DOFS);
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    for (vecIterator.reset(), m = *vecIterator; !vecIterator.end(); ++vecIterator) {
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      m = std::max(m, *vecIterator);
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    }

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    return m;
  }

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

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  template<typename T>
  void gemv(MatrixTranspose transpose, T alpha,
	    const DOFMatrix& a, const DOFVector<T>& x,
	    T beta, DOFVector<T>& y)
  {
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    FUNCNAME("DOFVector<T>::gemv()");

    int j, jcol, ysize;
    T sum, ax;
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    const DOFMatrix::MatrixRow *row;
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    TEST_EXIT_DBG(a.getRowFESpace() && 
		  a.getColFESpace() && 
		  x.getFESpace() && 
		  y.getFESpace())
      ("feSpace is NULL: %8X, %8X, %8X, %8X\n", 
       a.getRowFESpace(), a.getColFESpace(), x.getFESpace(), y.getFESpace());
    TEST_EXIT_DBG(a.getRowFESpace()->getAdmin() && 
		  a.getColFESpace()->getAdmin() && 
		  (((transpose == NoTranspose) && 
		    (a.getColFESpace()->getAdmin() == x.getFESpace()->getAdmin()) && 
		    (a.getRowFESpace()->getAdmin() == y.getFESpace()->getAdmin()))||
		   ((transpose == Transpose) && 
		    (a.getRowFESpace()->getAdmin() == x.getFESpace()->getAdmin()) && 
		    (a.getColFESpace()->getAdmin() == y.getFESpace()->getAdmin()))))
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      ("no admin or different admins: %8X, %8X, %8X, %8X\n",
       a.getRowFESpace()->getAdmin(), a.getColFESpace()->getAdmin(), 
       x.getFESpace()->getAdmin(), y.getFESpace()->getAdmin());
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    if (transpose == NoTranspose) {
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      TEST_EXIT_DBG(static_cast<int>(x.getSize()) >= a.getColFESpace()->getAdmin()->getUsedSize())
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	("x.size = %d too small: admin->sizeUsed = %d\n",
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	 x.getSize(), a.getColFESpace()->getAdmin()->getUsedSize());
      TEST_EXIT_DBG(static_cast<int>(y.getSize()) >= a.getRowFESpace()->getAdmin()->getUsedSize())
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	("y.size = %d too small: admin->sizeUsed = %d\n",
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	 y.getSize(), a.getRowFESpace()->getAdmin()->getUsedSize());
      TEST_EXIT_DBG(static_cast<int>( a.getSize()) >= a.getRowFESpace()->getAdmin()->getUsedSize())
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	("a.size = %d too small: admin->sizeUsed = %d\n",
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	a.getSize(), a.getRowFESpace()->getAdmin()->getUsedSize());
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    }
    else  if (transpose == Transpose) {
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      TEST_EXIT_DBG(static_cast<int>(x.getSize()) >= a.getRowFESpace()->getAdmin()->getUsedSize())
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	("x.size = %d too small: admin->sizeUsed = %d\n",
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	 x.getSize(), a.getRowFESpace()->getAdmin()->getUsedSize());
      TEST_EXIT_DBG(static_cast<int>(y.getSize()) >= a.getColFESpace()->getAdmin()->getUsedSize())
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	("y.size = %d too small: admin->sizeUsed = %d\n",
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	 y.getSize(), a.getColFESpace()->getAdmin()->getUsedSize());
      TEST_EXIT_DBG(static_cast<int>( a.getSize()) >= a.getRowFESpace()->getAdmin()->getUsedSize())
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	("a.size = %d too small: admin->sizeUsed = %d\n",
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	a.getSize(), a.getRowFESpace()->getAdmin()->getUsedSize());
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    }

    ysize = y.getSize();

    typename DOFVector<T>::Iterator vecIterator(dynamic_cast<DOFIndexed<T>*>(&y), FREE_DOFS);
    for(vecIterator.reset();
	!vecIterator.end(); ++vecIterator) { 
      *vecIterator = 0;
    };

    if (transpose == NoTranspose) {
      typename DOFVector<T>::Iterator vecIterator(dynamic_cast<DOFIndexed<T>*>(&y), USED_DOFS); 
      DOFMatrix::Iterator rowIterator(const_cast<DOFMatrix*>(&a), USED_DOFS);
      for(vecIterator.reset(), rowIterator.reset();
	  !rowIterator.end();
	  ++rowIterator, ++vecIterator) { 
	sum = 0;
	row = &(a[rowIterator.getDOFIndex()]);
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	for(std::vector<MatEntry>::iterator colIterator = rowIterator->begin();
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	    colIterator != rowIterator->end();
	    colIterator++) {
	  jcol = colIterator->col;
	  if (jcol >= 0) { // entry used? 
	    sum += (static_cast<T>(colIterator->entry)) * x[jcol];
	  } else {
	    if (jcol == DOFMatrix::NO_MORE_ENTRIES)
	      break;
	  }
	}
	*vecIterator *= beta;
	*vecIterator += alpha * sum;
      };
    } else if (transpose == Transpose) {
      typename DOFVector<T>::Iterator vecIterator(dynamic_cast<DOFIndexed<T>*>(&y), USED_DOFS);
      for(vecIterator.reset();
	  !vecIterator.end(); 
	  ++vecIterator) {
	*vecIterator  *= beta ; 
      };
    
      typename DOFVector<T>::Iterator xIterator(dynamic_cast<DOFIndexed<T>*>(const_cast<DOFVector<T>*>(&x)), USED_DOFS);
      DOFMatrix::Iterator rowIterator(const_cast<DOFMatrix*>(&a), USED_DOFS);
      for(xIterator.reset(), rowIterator.reset();
	  !rowIterator.end();
	  ++rowIterator, ++xIterator) { 
	ax = alpha * (*xIterator);
	row = &(a[rowIterator.getDOFIndex()]);
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	for(std::vector<MatEntry>::iterator colIterator = rowIterator->begin();
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	    colIterator != rowIterator->end();
	    colIterator++) {
	  jcol = colIterator->col;
	  if (jcol >= 0) // entry used?
	    y[jcol] += ax * (static_cast<T>(colIterator->entry));
	  else 
	    if (jcol == DOFMatrix::NO_MORE_ENTRIES) break;
	}
      }
    }
    else {
      ERROR_EXIT("transpose=%d\n", transpose);
    }
  }

  template<typename T>
  void DOFVector<T>::print() const
  {
    FUNCNAME("DOFVector<T>::print");
    int  i, j;
    const DOFAdmin *admin = NULL;
    const char     *format;

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

    MSG("Vec `%s':\n", name.c_str());
    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 (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>
  T DOFVectorBase<T>::evalUh(const DimVec<double>& lambda, 
			     DegreeOfFreedom* dof_indices)
  {
    int i;
    BasisFunction* phi = const_cast<BasisFunction*>(this->getFESpace()->getBasisFcts());
    int numberOfBasFcts = phi->getNumber();
    T val = 0.0;

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

    return val;
  }

  template<typename T>
  void DOFVector<T>::interpol(AbstractFunction<T, WorldVector<double> > *fct)
  {
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    FUNCNAME("DOFVector<T>::interpol()");
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    TEST_EXIT_DBG(fct)("no function to interpolate\n");

    interFct = fct;
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    if (!this->getFESpace()) {
      MSG("no dof admin in vec %s, skipping interpolation\n",
	  this->getName().c_str());
      return;
    }
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    if (!(this->getFESpace()->getAdmin())) {
      MSG("no dof admin in feSpace %s, skipping interpolation\n", 
	  this->getFESpace()->getName().c_str());
      return;
    }
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    if (!(this->getFESpace()->getBasisFcts())) {
      MSG("no basis functions in admin of vec %s, skipping interpolation\n",
	  this->getName().c_str());
      return;
    }
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    if (!(fct)) {
      MSG("function that should be interpolated only pointer to NULL, ");
      Msg::print("skipping interpolation\n");
      return;
    }
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    traverseVector = this;
    this->getFESpace()->getMesh()->traverse(-1, 
					    Mesh::CALL_LEAF_EL |
					    Mesh::FILL_COORDS, 
					    interpolFct);

    return;
  }

  template<typename T>
  int DOFVector<T>::interpolFct(ElInfo* elinfo)
  {
    int i;
    const BasisFunction *basFct = traverseVector->getFESpace()->getBasisFcts();
    const DOFAdmin* admin = traverseVector->getFESpace()->getAdmin();
    const DegreeOfFreedom   *dof = 
      basFct->getLocalIndices(const_cast<Element *>(elinfo->getElement()), 
			      admin, NULL);
    const T *inter_val = 
      const_cast<BasisFunction*>(basFct)->interpol(elinfo, 
						   0, 
						   NULL,
						   traverseVector->interFct, 
						   NULL);

    int number = basFct->getNumber();
    for (i = 0; i < number; i++)
      (*traverseVector)[dof[i]] = inter_val[i];

    return 0;
  }

  // das hat Andreas eingefuegt: Integral...

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

    int deg;
    dim = mesh->getDim();

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

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

    norm = 0.0;
    traverseVector = const_cast<DOFVector<T>*>(this);

    mesh->traverse(-1, 
		   Mesh::CALL_LEAF_EL|
		   Mesh::FILL_COORDS |
		   Mesh::FILL_DET, 
		   Int_fct);

    return norm;  
  }

  template<typename T>
  int DOFVector<T>::Int_fct(ElInfo *elinfo)
  {
    double det, normT;
    const T *uh_vec;
    int iq;

    det = elinfo->getDet();
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    uh_vec = traverseVector->getVecAtQPs(elinfo, NULL, quad_fast, NULL);
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    int numPoints = quad_fast->getNumPoints();
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    for (normT = iq = 0; iq < numPoints; iq++) {
      normT += quad_fast->getWeight(iq)*(uh_vec[iq]);
    }
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    norm += det*normT;

    return 0;
  }

  // ... und die L1-Norm ...

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

    int deg;
    dim = mesh->getDim();

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

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

    norm = 0.0;
    traverseVector = const_cast<DOFVector<T>*>(this);

    mesh->traverse(-1, 
		   Mesh::CALL_LEAF_EL|
		   Mesh::FILL_COORDS |
		   Mesh::FILL_DET, 
		   L1Norm_fct);

    return norm;  
  }

  template<typename T>
  int DOFVector<T>::L1Norm_fct(ElInfo *elinfo)
  {
    double det, normT;
    const T *uh_loc, *uh_vec;
    int iq;

    det = elinfo->getDet();
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    uh_vec = traverseVector->getVecAtQPs(elinfo, NULL, quad_fast, NULL);
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    int numPoints = quad_fast->getNumPoints();
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    for (normT = iq = 0; iq < numPoints; iq++) {
      normT += quad_fast->getWeight(iq)*abs(uh_vec[iq]);
    }
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    norm += det*normT;

    return 0;
  }


  // bis hierhin gehen Andreas Ergaenzungen...

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

    int deg;
    dim = mesh->getDim();

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

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

    norm = 0.0;
    traverseVector = const_cast<DOFVector<T>*>(this);

    mesh->traverse(-1, Mesh::CALL_LEAF_EL|Mesh::FILL_COORDS|Mesh::FILL_DET, L2Norm_fct);

    return norm;  
  }

  template<typename T>
  int DOFVector<T>::L2Norm_fct(ElInfo *elinfo)
  {
    double det, normT;
    const T *uh_vec;
    int iq;

    det = elinfo->getDet();
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    uh_vec = traverseVector->getVecAtQPs(elinfo, NULL, quad_fast, NULL);
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    int numPoints = quad_fast->getNumPoints();
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    for (normT = iq = 0; iq < numPoints; iq++) {
      normT += quad_fast->getWeight(iq)*sqr(uh_vec[iq]);
    }
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    norm += det*normT;

    return 0;
  }

  template<typename T>
  int DOFVector<T>::H1Norm_fct(ElInfo *elinfo)
  {
    double norm2, normT;
    const WorldVector<T> *grduh_vec;
    int iq, j;

    double det = elinfo->getDet();

    grduh_vec = traverseVector->getGrdAtQPs(elinfo, NULL, quad_fast, NULL);

    int dimOfWorld = Global::getGeo(WORLD);

    int numPoints = quad_fast->getNumPoints();
    for (normT = iq = 0; iq < numPoints; iq++)
      {
	for (norm2 = j = 0; j < dimOfWorld; j++)
	  norm2 += sqr(grduh_vec[iq][j]);

	normT += quad_fast->getWeight(iq)*norm2;
      }
    norm += det*normT;

    return 0;
  }


  template<typename T>
  double DOFVector<T>::H1NormSquare(Quadrature *q) const
  {
    FUNCNAME("DOFVector::H1NormSquare");
    int deg;
  
    Mesh *mesh = feSpace->getMesh();
    dim = mesh->getDim();

    if (!q)
      {
	deg = 2*feSpace->getBasisFcts()->getDegree()-2;
	q = Quadrature::provideQuadrature(dim, deg);
      }
    quad_fast = 
      FastQuadrature::provideFastQuadrature(feSpace->getBasisFcts(), 
					    *q, 
					    INIT_GRD_PHI);

    norm = 0.0;
    traverseVector = const_cast<DOFVector<T>*>(this);

    mesh->traverse(-1, Mesh::CALL_LEAF_EL | Mesh::FILL_COORDS | 
		   Mesh::FILL_DET | Mesh::FILL_GRD_LAMBDA,
		   H1Norm_fct);

    return norm;
  }

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

  template<typename T>
  ElementVector* DOFVectorBase<T>::assemble(T factor, ElInfo *elInfo,
					    const BoundaryType *bound, 
					    Operator *op)
  {
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    FUNCNAME("DOFVector::assemble()");
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    if (!(op || this->operators.size())) 
      return NULL;
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    Operator *operat = op ? op : this->operators[0];

    this->elementVector = 
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      operat->getAssembler(omp_get_thread_num())->initElementVector(this->elementVector, elInfo);
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    if (op) {
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      op->getElementVector(elInfo, this->elementVector);
    } else {
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      std::vector<Operator*>::iterator it;
      std::vector<double*>::iterator factorIt;
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      for (it = this->operators.begin(), factorIt = this->operatorFactor.begin();	
	   it != this->operators.end(); 
	   ++it, ++factorIt) {
	(*it)->getElementVector(elInfo, 
				this->elementVector, 
				*factorIt ? **factorIt : 1.0);
      }
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    }

    addElementVector(factor,
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    		     *this->elementVector, 
    		     bound);
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    return this->elementVector;
  }

  template<typename T>
  Flag DOFVectorBase<T>::getAssembleFlag()
  {
    Flag fillFlag(0);
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    std::vector<Operator*>::iterator op;
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    for(op = this->operators.begin(); op != this->operators.end(); ++op) {
      fillFlag |= (*op)->getFillFlag();
    }
    return fillFlag;
  }

  template<typename T>
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  DOFVector<T>& DOFVector<T>::operator=(const DOFVector<T>& rhs )
  {
    feSpace=rhs.feSpace;
    vec=rhs.vec;
    this->elementVector=NULL;
    interFct=rhs.interFct;
    refineInter=rhs.refineInter;
    coarsenOperation=rhs.coarsenOperation;
    this->operators=rhs.operators;
    this->operatorFactor=rhs.operatorFactor;
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    if (rhs.boundaryManager) {
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      if(this->boundaryManager) delete this->boundaryManager; 
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      this->boundaryManager = new BoundaryManager(*rhs.boundaryManager);
      //    boundaryManager->setDOFVector(this);
    }
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    else 
      this->boundaryManager=NULL;
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    return *this;
  }

  template<typename T>
  const DOFVector<T>& operator*=(DOFVector<T>& x, T scal)
  {
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    TEST_EXIT_DBG(x.getFESpace() && x.getFESpace()->getAdmin())
      ("pointer is NULL: %8X, %8X\n", x.getFESpace(), x.getFESpace()->getAdmin());
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    typename DOFVector<T>::Iterator vecIterator(dynamic_cast<DOFIndexed<T>*>(&x), USED_DOFS);
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    for (vecIterator.reset(); !vecIterator.end(); ++vecIterator) {
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      (*vecIterator) *= scal; 
    };
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    return x;
  }


  template<typename T>
  const DOFVector<T>& operator+=(DOFVector<T>& x, const DOFVector<T>& y)
  {
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    FUNCNAME("DOFVector<T>::operator+=(DOFVector<T>& x, const DOFVector<T>& y)");
    
    TEST_EXIT_DBG(x.getFESpace() && y.getFESpace())
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      ("feSpace is NULL: %8X, %8X\n", x.getFESpace(), y.getFESpace());
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    TEST_EXIT_DBG(x.getFESpace()->getAdmin() &&
	      (x.getFESpace()->getAdmin() == y.getFESpace()->getAdmin()))
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      ("no admin or different admins: %8X, %8X\n",
       x.getFESpace()->getAdmin(), y.getFESpace()->getAdmin());
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    TEST_EXIT_DBG(x.getSize() == y.getSize())("different sizes\n");
    
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    typename DOFVector<T>::Iterator xIterator(dynamic_cast<DOFIndexed<T>*>(&x), USED_DOFS);
    typename DOFVector<T>::Iterator yIterator(dynamic_cast<DOFIndexed<T>*>(const_cast<DOFVector<T>*>(&y)), USED_DOFS);
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    for (xIterator.reset(), yIterator.reset();
	 !xIterator.end();
	 ++xIterator, ++yIterator) {     
      *xIterator += *yIterator; 
    }

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    return x;
  }

  template<typename T>
  const DOFVector<T>& operator-=(DOFVector<T>& x, const DOFVector<T>& y)
  {
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    TEST_EXIT_DBG(x.getFESpace() && y.getFESpace())
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      ("feSpace is NULL: %8X, %8X\n", x.getFESpace(), y.getFESpace());
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    TEST_EXIT_DBG(x.getFESpace()->getAdmin() &&
	      (x.getFESpace()->getAdmin() == y.getFESpace()->getAdmin()))
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      ("no admin or different admins: %8X, %8X\n",
       x.getFESpace()->getAdmin(), y.getFESpace()->getAdmin());
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    TEST_EXIT_DBG(x.getSize() == y.getSize())("different sizes\n");
    
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    typename DOFVector<T>::Iterator xIterator(dynamic_cast<DOFIndexed<T>*>(&x), USED_DOFS);
    typename DOFVector<T>::Iterator yIterator(dynamic_cast<DOFIndexed<T>*>(const_cast<DOFVector<T>*>(&y)), USED_DOFS);
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    for (xIterator.reset(), yIterator.reset();
	 !xIterator.end();
	 ++xIterator, ++yIterator) {
      *xIterator -= *yIterator; 
    }
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    return x;
  }

  template<typename T>
  const DOFVector<T>& operator*=(DOFVector<T>& x, const DOFVector<T>& y)
  {
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    FUNCNAME("DOFVector<T>::operator*=(DOFVector<T>& x, const DOFVector<T>& y)");
    
    TEST_EXIT_DBG(x.getFESpace() && y.getFESpace())
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      ("feSpace is NULL: %8X, %8X\n", x.getFESpace(), y.getFESpace());
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    TEST_EXIT_DBG(x.getFESpace()->getAdmin() &&
	      (x.getFESpace()->getAdmin() == y.getFESpace()->getAdmin()))
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      ("no admin or different admins: %8X, %8X\n",
       x.getFESpace()->getAdmin(), y.getFESpace()->getAdmin());
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    TEST_EXIT_DBG(x.getSize() == y.getSize())("different sizes\n");
    
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    typename DOFVector<T>::Iterator xIterator(dynamic_cast<DOFIndexed<T>*>(&x), USED_DOFS);
    typename DOFVector<T>::Iterator yIterator(dynamic_cast<DOFIndexed<T>*>(const_cast<DOFVector<T>*>(&y)), USED_DOFS);
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    for (xIterator.reset(), yIterator.reset();
	 !xIterator.end();
	 ++xIterator, ++yIterator) {
      *xIterator *= *yIterator; 
    }
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    return x;
  }

  template<typename T>
  T operator*(DOFVector<T>& x, DOFVector<T>& y)
  {
    FUNCNAME("DOFVector<T>::operator*(DOFVector<T>& x, DOFVector<T>& y)");

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    TEST_EXIT_DBG(x.getFESpace() && y.getFESpace())
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      ("feSpace is NULL: %8X, %8X\n", x.getFESpace(), y.getFESpace());
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    TEST_EXIT_DBG(x.getFESpace()->getAdmin() && 
	      (x.getFESpace()->getAdmin() == y.getFESpace()->getAdmin()))
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      ("no admin or different admins: %8X, %8X\n",
       x.getFESpace()->getAdmin(), y.getFESpace()->getAdmin());
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    TEST_EXIT_DBG(x.getSize() == y.getSize())("different sizes\n");
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    T dot = 0;    
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    typename DOFVector<T>::Iterator xIterator(dynamic_cast<DOFIndexed<T>*>(&x), USED_DOFS);
    typename DOFVector<T>::Iterator yIterator(dynamic_cast<DOFIndexed<T>*>(&y), USED_DOFS);
    for (xIterator.reset(), yIterator.reset();
	 !xIterator.end();
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	 ++xIterator, ++yIterator) {
      dot += (*xIterator) * (*yIterator);
    };
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    return(dot);
  }

  template<typename T>
  void mv(MatrixTranspose transpose,
	  const DOFMatrix &a, 
	  const DOFVector<T>&x,
	  DOFVector<T> &result,
	  bool add)
  {
    FUNCNAME("DOFVector<T>::mv()");

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    TEST_EXIT_DBG(a.getRowFESpace() && a.getColFESpace() && x.getFESpace() && result.getFESpace())
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      ("getFESpace() is NULL: %8X, %8X, %8X, %8X\n", 
       a.getRowFESpace(), a.getColFESpace(), x.getFESpace(), result.getFESpace());
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    TEST_EXIT_DBG((a.getRowFESpace()->getAdmin() && a.getColFESpace()->getAdmin()) && 
	      (((transpose == NoTranspose) && 
		(a.getColFESpace()->getAdmin() == x.getFESpace()->getAdmin()) && 
		(a.getRowFESpace()->getAdmin() == result.getFESpace()->getAdmin())) ||
	       ((transpose == Transpose) && 
		(a.getRowFESpace()->getAdmin() == x.getFESpace()->getAdmin()) && 
		(a.getColFESpace()->getAdmin() == result.getFESpace()->getAdmin()))))
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      ("no admin or different admins: %8X, %8X, %8X, %8X\n",
       a.getRowFESpace()->getAdmin(), a.getColFESpace()->getAdmin(), 
       x.getFESpace()->getAdmin(), result.getFESpace()->getAdmin());
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    if (transpose == NoTranspose) {
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      TEST_EXIT_DBG(static_cast<int>(x.getSize()) >= a.getColFESpace()->getAdmin()->getUsedSize())
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	("x.size = %d too small: admin->sizeUsed = %d\n",
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	 x.getSize(), a.getColFESpace()->getAdmin()->getUsedSize());
      TEST_EXIT_DBG(static_cast<int>( result.getSize()) >= a.getRowFESpace()->getAdmin()->getUsedSize())
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	("size = %d too small: admin->sizeUsed = %d\n",
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	 result.getSize(), a.getRowFESpace()->getAdmin()->getUsedSize());
      TEST_EXIT_DBG(static_cast<int>( a.getSize()) >= a.getRowFESpace()->getAdmin()->getUsedSize())
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	("a.size = %d too small: admin->sizeUsed = %d\n",
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	 a.getSize(), a.getRowFESpace()->getAdmin()->getUsedSize());
      
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      typename DOFVector<T>::Iterator vecIterator(dynamic_cast<DOFIndexed<T>*>(&result), USED_DOFS); 
      DOFMatrix::Iterator rowIterator(const_cast<DOFMatrix*>(&a), USED_DOFS);
      for(vecIterator.reset(), rowIterator.reset();
      	  !rowIterator.end();
      	  ++rowIterator, ++vecIterator) { 
      	
	double sum = 0;
      	if (!add) 
	  *vecIterator = 0.0;
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      	for(std::vector<MatEntry>::iterator colIterator = rowIterator->begin();
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      	    colIterator != rowIterator->end();
      	    colIterator++) {
      	  
	  int jcol = colIterator->col;
      	  if (jcol >= 0) { // entry used? 
      	    sum += (static_cast<double>(colIterator->entry)) * x[jcol];
      	  } else {
      	    if (jcol == DOFMatrix::NO_MORE_ENTRIES)
      	      break;
      	  }
      	}
      	*vecIterator += sum;
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      }

    } else if (transpose == Transpose) {
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      TEST_EXIT_DBG(static_cast<int>(x.getSize()) >= a.getRowFESpace()->getAdmin()->getUsedSize())
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	("x.size = %d too small: admin->sizeUsed = %d\n",
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	 x.getSize(), a.getRowFESpace()->getAdmin()->getUsedSize());
      TEST_EXIT_DBG(static_cast<int>( result.getSize()) >= a.getColFESpace()->getAdmin()->getUsedSize())
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	("size = %d too small: admin->sizeUsed = %d\n",
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	 result.getSize(), a.getColFESpace()->getAdmin()->getUsedSize());
      TEST_EXIT_DBG(static_cast<int>( a.getSize()) >= a.getRowFESpace()->getAdmin()->getUsedSize())
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	("a.size = %d too small: admin->sizeUsed = %d\n",
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	 a.getSize(), a.getRowFESpace()->getAdmin()->getUsedSize());
      
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      if(!add) {
	typename DOFVector<T>::Iterator vecIterator(dynamic_cast<DOFIndexed<T>*>(&result), USED_DOFS);
	for(vecIterator.reset();
	    !vecIterator.end(); ++vecIterator) {
	  *vecIterator = 0; 
	};
      }

      typename DOFVector<T>::Iterator xIterator(const_cast<DOFIndexed<T>*>(dynamic_cast<const DOFIndexed<T>*>(&x)), USED_DOFS);
      DOFMatrix::Iterator rowIterator(const_cast<DOFMatrix*>(&a), USED_DOFS);
      for(xIterator.reset(), rowIterator.reset();
	  !rowIterator.end();
	  ++rowIterator, ++xIterator) { 
	T ax = (*xIterator);
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	for (std::vector<MatEntry>::iterator colIterator = rowIterator->begin();
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	    colIterator != rowIterator->end();
	    colIterator++) {
	  int jcol = colIterator->col;
	  if (jcol >= 0) // entry used?
	    result[jcol] += (static_cast<double>(colIterator->entry)) * ax;
	  else 
	    if (jcol == DOFMatrix::NO_MORE_ENTRIES) break;
	}
      }
    } else {
      ERROR_EXIT("transpose = %d\n", transpose);
    }
  }

  template<typename T>
  void axpy(double alpha, 
	    const DOFVector<T>& x, 
	    DOFVector<T>& y)
  {
    FUNCNAME("DOFVector<T>::axpy()");

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    TEST_EXIT_DBG(x.getFESpace() && y.getFESpace())
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      ("feSpace is NULL: %8X, %8X\n", x.getFESpace(), y.getFESpace());

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    TEST_EXIT_DBG(x.getFESpace()->getAdmin() && 
	      (x.getFESpace()->getAdmin() == y.getFESpace()->getAdmin()))
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      ("no admin or different admins: %8X, %8X\n",
       x.getFESpace()->getAdmin(), y.getFESpace()->getAdmin());
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       x.getFESpace()->getAdmin()->getUsedSize());
    TEST_EXIT_DBG(static_cast<int>(y.getSize()) >= x.getFESpace()->getAdmin()->getUsedSize())
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       x.getFESpace()->getAdmin()->getUsedSize());
    
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    typename DOFVector<T>::Iterator xIterator(dynamic_cast<DOFIndexed<T>*>(const_cast<DOFVector<T>*>(&x)), USED_DOFS);
    typename DOFVector<T>::Iterator yIterator(dynamic_cast<DOFIndexed<T>*>(&y), USED_DOFS);
    for (xIterator.reset(), yIterator.reset();
	 !xIterator.end();
	 ++xIterator, ++yIterator) {
      *yIterator += alpha * (*xIterator); 
    };
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  }

  template<typename T>
  const DOFVector<T>& operator*(const DOFVector<T>& v, double d)
  {
    static DOFVector<T> result;
    return mult(d, v, result);
  }

  template<typename T>
  const DOFVector<T>& operator*(double d, const DOFVector<T>& v)
  {
    static DOFVector<T> result;
    return mult(d, v, result);
  }

  template<typename T>
  const DOFVector<T>& operator+(const DOFVector<T> &v1 , const DOFVector<T> &v2)
  {
    static DOFVector<T> result;
    return add(v1, v2, result);
  }


  template<typename T>
  void xpay(double alpha, 
	    const DOFVector<T>& x, 
	    DOFVector<T>& y)
  {
    FUNCNAME("DOFVector<T>::xpay()");

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      ("feSpace is NULL: %8X, %8X\n", x.getFESpace(), y.getFESpace());

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    TEST_EXIT_DBG(x.getFESpace()->getAdmin() && 
	      (x.getFESpace()->getAdmin() == y.getFESpace()->getAdmin()))
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      ("no admin or different admins: %8X, %8X\n",
       x.getFESpace()->getAdmin(), y.getFESpace()->getAdmin());
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    TEST_EXIT_DBG(static_cast<int>(x.getSize()) >= x.getFESpace()->getAdmin()->getUsedSize())
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       x.getFESpace()->getAdmin()->getUsedSize());
    TEST_EXIT_DBG(static_cast<int>(y.getSize()) >= x.getFESpace()->getAdmin()->getUsedSize())
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       x.getFESpace()->getAdmin()->getUsedSize());
    
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    typename DOFVector<T>::Iterator xIterator(dynamic_cast<DOFIndexed<T>*>(const_cast<DOFVector<T>*>(&x)), USED_DOFS);
    typename DOFVector<T>::Iterator yIterator(dynamic_cast<DOFIndexed<T>*>(&y), USED_DOFS);
    for (xIterator.reset(), yIterator.reset();
	 !xIterator.end();
	 ++xIterator, ++yIterator) {
      *yIterator = alpha *(*yIterator)+ (*xIterator); 
    };
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  }

  template<typename T>
  inline const DOFVector<T>& mult(double scal,
				  const DOFVector<T>& v,
				  DOFVector<T>& result)
  {
    typename DOFVector<T>::Iterator vIterator(dynamic_cast<DOFIndexed<T>*>(const_cast<DOFVector<T>*>(&v)), USED_DOFS);
    typename DOFVector<T>::Iterator rIterator(dynamic_cast<DOFIndexed<T>*>(&result), USED_DOFS);
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    for (vIterator.reset(), rIterator.reset();
	 !vIterator.end();
	 ++vIterator, ++rIterator) {
      *rIterator = scal * (*vIterator);
    };
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    return result;
  }

  template<typename T>
  inline const DOFVector<T>& add(const DOFVector<T>& v,
				 double scal,
				 DOFVector<T>& result)
  {
    typename DOFVector<T>::Iterator vIterator(dynamic_cast<DOFIndexed<T>*>(const_cast<DOFVector<T>*>(&v)), USED_DOFS);
    typename DOFVector<T>::Iterator rIterator(dynamic_cast<DOFIndexed<T>*>(&result), USED_DOFS);
    for(vIterator.reset(), rIterator.reset();
	!vIterator.end();
	++vIterator, ++rIterator) 
      {  
	*rIterator = (*vIterator) + scal;
      };
    return result;
  }

  template<typename T>
  inline const DOFVector<T>& add(const DOFVector<T>& v1,
				 const DOFVector<T>& v2,
				 DOFVector<T>& result)
  {
    typename DOFVector<T>::Iterator v1Iterator(dynamic_cast<DOFIndexed<T>*>(const_cast<DOFVector<T>*>(&v1)), USED_DOFS);
    typename DOFVector<T>::Iterator v2Iterator(dynamic_cast<DOFIndexed<T>*>(const_cast<DOFVector<T>*>(&v2)), USED_DOFS);
    typename DOFVector<T>::Iterator rIterator(dynamic_cast<DOFIndexed<T>*>(&result), USED_DOFS);
    for(v1Iterator.reset(), v2Iterator.reset(), rIterator.reset();
	!v1Iterator.end();
	++v1Iterator, ++v2Iterator, ++rIterator) 
      {  
	*rIterator = (*v1Iterator) + (*v2Iterator);
      };
    return result;
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  }

  template<typename T>
  inline const DOFVector<T>& mod(const DOFVector<T>& v,
				 DOFVector<T>& result)
  {
    typename DOFVector<T>::Iterator vIterator(dynamic_cast<DOFIndexed<T>*>(const_cast<DOFVector<T>*>(&v)), USED_DOFS);
    typename DOFVector<T>::Iterator rIterator(dynamic_cast<DOFIndexed<T>*>(&result), USED_DOFS);
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    for (vIterator.reset(), rIterator.reset();
	 !vIterator.end();
	 ++vIterator, ++rIterator) {
      *rIterator = fmod((*vIterator), 1.0);
    }

    return result;
  }

  template<typename T>
  inline const DOFVector<T>& Tanh(const DOFVector<T>& v,
				  DOFVector<T>& result)
  {
    typename DOFVector<T>::Iterator vIterator(dynamic_cast<DOFIndexed<T>*>(const_cast<DOFVector<T>*>(&v)), USED_DOFS);
    typename DOFVector<T>::Iterator rIterator(dynamic_cast<DOFIndexed<T>*>(&result), USED_DOFS);

    double eps;
    GET_PARAMETER(1, "vecphase->epsilon", "%f", &eps);
    for (vIterator.reset(), rIterator.reset();
	 !vIterator.end();
	 ++vIterator, ++rIterator) {
      *rIterator = 0.5 * (1.0 - tanh(3.0 * (*vIterator) / eps));
    }

    return result;
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  }

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  template<typename T>
  const T *DOFVectorBase<T>::getLocalVector(const Element *el, T *d) const
  {
    static T* localVec = NULL;
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    T *result;   
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    if (d) {
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      result = d;
    } else {
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      if (localVec) 
	delete [] localVec;
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      localVec = new T[nBasFcts]; 
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      result = localVec;     
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    }
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    DegreeOfFreedom *myLocalIndices = localIndices[omp_get_thread_num()];
    feSpace->getBasisFcts()->getLocalIndices(el, feSpace->getAdmin(), 
					     myLocalIndices);
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    for (int i = 0; i < nBasFcts; i++) {
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      result[i] = (*this)[myLocalIndices[i]];
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    }
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    return result;
  }

  template<typename T>
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  const T *DOFVectorBase<T>::getVecAtQPs(const ElInfo *elInfo, 
					 const Quadrature *quad,
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					 const FastQuadrature *quadFast,
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					 T *vecAtQPs) const
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  {
    FUNCNAME("DOFVector<T>::getVecAtQPs()");
  
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    TEST_EXIT_DBG(quad || quadFast)("neither quad nor quadFast defined\n");
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    if (quad && quadFast) {
      TEST_EXIT_DBG(quad == quadFast->getQuadrature())
      	("quad != quadFast->quadrature\n");
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    }

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    TEST_EXIT_DBG(!quadFast || quadFast->getBasisFunctions() == feSpace->getBasisFcts())
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      ("invalid basis functions");

    Element *el = elInfo->getElement();

    const Quadrature *quadrature = quadFast ? quadFast->getQuadrature() : quad;
    const BasisFunction *basFcts = feSpace->getBasisFcts();

    int numPoints = quadrature->getNumPoints();

    static T *localvec = NULL;

    T *result;

    if (vecAtQPs) {
      result = vecAtQPs;
    } else {
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      if (localvec) 
	delete [] localvec;
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      localvec = new T[numPoints];
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      for (int i = 0; i < numPoints; i++) {
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	localvec[i] = 0.0;
      }
      result = localvec;
    }
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    T *localVec = new T[nBasFcts];
    getLocalVector(el, localVec);
    
    for (int i = 0; i < numPoints; i++) {
      result[i] = 0.0;
      for (int j = 0; j < nBasFcts; j++) {
	result[i] += localVec[j] *