dune-functions  2.8.0
bsplinebasis.hh
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1 // -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
2 // vi: set et ts=4 sw=2 sts=2:
3 #ifndef DUNE_FUNCTIONS_FUNCTIONSPACEBASES_BSPLINEBASIS_HH
4 #define DUNE_FUNCTIONS_FUNCTIONSPACEBASES_BSPLINEBASIS_HH
5 
10 #include <array>
11 #include <numeric>
12 
14 #include <dune/common/dynmatrix.hh>
15 
16 #include <dune/localfunctions/common/localbasis.hh>
17 #include <dune/common/diagonalmatrix.hh>
18 #include <dune/localfunctions/common/localkey.hh>
19 #include <dune/localfunctions/common/localfiniteelementtraits.hh>
20 #include <dune/geometry/type.hh>
24 
25 namespace Dune
26 {
27 namespace Functions {
28 
29 // A maze of dependencies between the different parts of this. We need a few forward declarations
30 template<typename GV, typename R, typename MI>
32 
33 template<typename GV, class MI>
34 class BSplinePreBasis;
35 
36 
45 template<class GV, class R, class MI>
47 {
48  friend class BSplineLocalFiniteElement<GV,R,MI>;
49 
50  typedef typename GV::ctype D;
51  enum {dim = GV::dimension};
52 public:
53 
55  typedef LocalBasisTraits<D,dim,FieldVector<D,dim>,R,1,FieldVector<R,1>,
56  FieldMatrix<R,1,dim> > Traits;
57 
64  : preBasis_(preBasis),
65  lFE_(lFE)
66  {}
67 
71  void evaluateFunction (const FieldVector<D,dim>& in,
72  std::vector<FieldVector<R,1> >& out) const
73  {
74  FieldVector<D,dim> globalIn = offset_;
75  scaling_.umv(in,globalIn);
76 
77  preBasis_.evaluateFunction(globalIn, out, lFE_.currentKnotSpan_);
78  }
79 
83  void evaluateJacobian (const FieldVector<D,dim>& in,
84  std::vector<FieldMatrix<D,1,dim> >& out) const
85  {
86  FieldVector<D,dim> globalIn = offset_;
87  scaling_.umv(in,globalIn);
88 
89  preBasis_.evaluateJacobian(globalIn, out, lFE_.currentKnotSpan_);
90 
91  for (size_t i=0; i<out.size(); i++)
92  for (int j=0; j<dim; j++)
93  out[i][0][j] *= scaling_[j][j];
94  }
95 
97  template<size_t k>
98  inline void evaluate (const typename std::array<int,k>& directions,
99  const typename Traits::DomainType& in,
100  std::vector<typename Traits::RangeType>& out) const
101  {
102  switch(k)
103  {
104  case 0:
105  evaluateFunction(in, out);
106  break;
107  case 1:
108  {
109  FieldVector<D,dim> globalIn = offset_;
110  scaling_.umv(in,globalIn);
111 
112  preBasis_.evaluate(directions, globalIn, out, lFE_.currentKnotSpan_);
113 
114  for (size_t i=0; i<out.size(); i++)
115  out[i][0] *= scaling_[directions[0]][directions[0]];
116  break;
117  }
118  case 2:
119  {
120  FieldVector<D,dim> globalIn = offset_;
121  scaling_.umv(in,globalIn);
122 
123  preBasis_.evaluate(directions, globalIn, out, lFE_.currentKnotSpan_);
124 
125  for (size_t i=0; i<out.size(); i++)
126  out[i][0] *= scaling_[directions[0]][directions[0]]*scaling_[directions[1]][directions[1]];
127  break;
128  }
129  default:
130  DUNE_THROW(NotImplemented, "B-Spline derivatives of order " << k << " not implemented yet!");
131  }
132  }
133 
141  unsigned int order () const
142  {
143  return *std::max_element(preBasis_.order_.begin(), preBasis_.order_.end());
144  }
145 
148  std::size_t size() const
149  {
150  return lFE_.size();
151  }
152 
153 private:
154  const BSplinePreBasis<GV,MI>& preBasis_;
155 
157 
158  // Coordinates in a single knot span differ from coordinates on the B-spline patch
159  // by an affine transformation. This transformation is stored in offset_ and scaling_.
160  FieldVector<D,dim> offset_;
161  DiagonalMatrix<D,dim> scaling_;
162 };
163 
177 template<int dim>
179 {
180  // Return i as a d-digit number in the (k+1)-nary system
181  std::array<unsigned int,dim> multiindex (unsigned int i) const
182  {
183  std::array<unsigned int,dim> alpha;
184  for (int j=0; j<dim; j++)
185  {
186  alpha[j] = i % sizes_[j];
187  i = i/sizes_[j];
188  }
189  return alpha;
190  }
191 
193  void setup1d(std::vector<unsigned int>& subEntity)
194  {
195  if (sizes_[0]==1)
196  {
197  subEntity[0] = 0;
198  return;
199  }
200 
201  /* edge and vertex numbering
202  0----0----1
203  */
204  unsigned lastIndex=0;
205  subEntity[lastIndex++] = 0; // corner 0
206  for (unsigned i = 0; i < sizes_[0] - 2; ++i)
207  subEntity[lastIndex++] = 0; // inner dofs of element (0)
208 
209  subEntity[lastIndex++] = 1; // corner 1
210 
211  assert(size()==lastIndex);
212  }
213 
214  void setup2d(std::vector<unsigned int>& subEntity)
215  {
216  unsigned lastIndex=0;
217 
218  // LocalKey: entity number , entity codim, dof indices within each entity
219  /* edge and vertex numbering
220  2----3----3
221  | |
222  | |
223  0 1
224  | |
225  | |
226  0----2----1
227  */
228 
229  // lower edge (2)
230  subEntity[lastIndex++] = 0; // corner 0
231  for (unsigned i = 0; i < sizes_[0]-2; ++i)
232  subEntity[lastIndex++] = 2; // inner dofs of lower edge (2)
233 
234  subEntity[lastIndex++] = 1; // corner 1
235 
236  // iterate from bottom to top over inner edge dofs
237  for (unsigned e = 0; e < sizes_[1]-2; ++e)
238  {
239  subEntity[lastIndex++] = 0; // left edge (0)
240  for (unsigned i = 0; i < sizes_[0]-2; ++i)
241  subEntity[lastIndex++] = 0; // face dofs
242  subEntity[lastIndex++] = 1; // right edge (1)
243  }
244 
245  // upper edge (3)
246  subEntity[lastIndex++] = 2; // corner 2
247  for (unsigned i = 0; i < sizes_[0]-2; ++i)
248  subEntity[lastIndex++] = 3; // inner dofs of upper edge (3)
249 
250  subEntity[lastIndex++] = 3; // corner 3
251 
252  assert(size()==lastIndex);
253  }
254 
255 
256 public:
257  void init(const std::array<unsigned,dim>& sizes)
258  {
259  sizes_ = sizes;
260 
261  li_.resize(size());
262 
263  // Set up array of codimension-per-dof-number
264  std::vector<unsigned int> codim(li_.size());
265 
266  for (std::size_t i=0; i<codim.size(); i++)
267  {
268  codim[i] = 0;
269  // Codimension gets increased by 1 for each coordinate direction
270  // where dof is on boundary
271  std::array<unsigned int,dim> mIdx = multiindex(i);
272  for (int j=0; j<dim; j++)
273  if (mIdx[j]==0 or mIdx[j]==sizes[j]-1)
274  codim[i]++;
275  }
276 
277  // Set up index vector (the index of the dof in the set of dofs of a given subentity)
278  // Algorithm: the 'index' has the same ordering as the dof number 'i'.
279  // To make it consecutive we interpret 'i' in the (k+1)-adic system, omit all digits
280  // that correspond to axes where the dof is on the element boundary, and transform the
281  // rest to the (k-1)-adic system.
282  std::vector<unsigned int> index(size());
283 
284  for (std::size_t i=0; i<index.size(); i++)
285  {
286  index[i] = 0;
287 
288  std::array<unsigned int,dim> mIdx = multiindex(i);
289 
290  for (int j=dim-1; j>=0; j--)
291  if (mIdx[j]>0 and mIdx[j]<sizes[j]-1)
292  index[i] = (sizes[j]-1)*index[i] + (mIdx[j]-1);
293  }
294 
295  // Set up entity and dof numbers for each (supported) dimension separately
296  std::vector<unsigned int> subEntity(li_.size());
297 
298  if (subEntity.size() > 0)
299  {
300  if (dim==1) {
301 
302  setup1d(subEntity);
303 
304  } else if (dim==2 and sizes_[0]>1 and sizes_[1]>1) {
305 
306  setup2d(subEntity);
307 
308  }
309  }
310 
311  for (size_t i=0; i<li_.size(); i++)
312  li_[i] = LocalKey(subEntity[i], codim[i], index[i]);
313  }
314 
316  std::size_t size () const
317  {
318  return std::accumulate(sizes_.begin(), sizes_.end(), 1, std::multiplies<unsigned int>());
319  }
320 
322  const LocalKey& localKey (std::size_t i) const
323  {
324  return li_[i];
325  }
326 
327 private:
328 
329  // Number of shape functions on this element per coordinate direction
330  std::array<unsigned, dim> sizes_;
331 
332  std::vector<LocalKey> li_;
333 };
334 
339 template<int dim, class LB>
341 {
342 public:
344  template<typename F, typename C>
345  void interpolate (const F& f, std::vector<C>& out) const
346  {
347  DUNE_THROW(NotImplemented, "BSplineLocalInterpolation::interpolate");
348  }
349 
350 };
351 
362 template<class GV, class R, class MI>
364 {
365  typedef typename GV::ctype D;
366  enum {dim = GV::dimension};
367  friend class BSplineLocalBasis<GV,R,MI>;
368 public:
369 
372  typedef LocalFiniteElementTraits<BSplineLocalBasis<GV,R,MI>,
375 
379  : preBasis_(preBasis),
380  localBasis_(preBasis,*this)
381  {}
382 
386  : preBasis_(other.preBasis_),
387  localBasis_(preBasis_,*this)
388  {}
389 
396  void bind(const std::array<unsigned,dim>& elementIdx)
397  {
398  /* \todo In the long run we need to precompute a table for this */
399  for (size_t i=0; i<elementIdx.size(); i++)
400  {
401  currentKnotSpan_[i] = 0;
402 
403  // Skip over degenerate knot spans
404  while (preBasis_.knotVectors_[i][currentKnotSpan_[i]+1] < preBasis_.knotVectors_[i][currentKnotSpan_[i]]+1e-8)
405  currentKnotSpan_[i]++;
406 
407  for (size_t j=0; j<elementIdx[i]; j++)
408  {
409  currentKnotSpan_[i]++;
410 
411  // Skip over degenerate knot spans
412  while (preBasis_.knotVectors_[i][currentKnotSpan_[i]+1] < preBasis_.knotVectors_[i][currentKnotSpan_[i]]+1e-8)
413  currentKnotSpan_[i]++;
414  }
415 
416  // Compute the geometric transformation from knotspan-local to global coordinates
417  localBasis_.offset_[i] = preBasis_.knotVectors_[i][currentKnotSpan_[i]];
418  localBasis_.scaling_[i][i] = preBasis_.knotVectors_[i][currentKnotSpan_[i]+1] - preBasis_.knotVectors_[i][currentKnotSpan_[i]];
419  }
420 
421  // Set up the LocalCoefficients object
422  std::array<unsigned int, dim> sizes;
423  for (size_t i=0; i<dim; i++)
424  sizes[i] = size(i);
425  localCoefficients_.init(sizes);
426  }
427 
430  {
431  return localBasis_;
432  }
433 
436  {
437  return localCoefficients_;
438  }
439 
442  {
443  return localInterpolation_;
444  }
445 
447  unsigned size () const
448  {
449  std::size_t r = 1;
450  for (int i=0; i<dim; i++)
451  r *= size(i);
452  return r;
453  }
454 
457  GeometryType type () const
458  {
459  return GeometryTypes::cube(dim);
460  }
461 
462 //private:
463 
465  unsigned int size(int i) const
466  {
467  const auto& order = preBasis_.order_;
468  unsigned int r = order[i]+1; // The 'normal' value
469  if (currentKnotSpan_[i]<order[i]) // Less near the left end of the knot vector
470  r -= (order[i] - currentKnotSpan_[i]);
471  if ( order[i] > (preBasis_.knotVectors_[i].size() - currentKnotSpan_[i] - 2) )
472  r -= order[i] - (preBasis_.knotVectors_[i].size() - currentKnotSpan_[i] - 2);
473  return r;
474  }
475 
477 
481 
482  // The knot span we are bound to
483  std::array<unsigned,dim> currentKnotSpan_;
484 };
485 
486 
487 template<typename GV, typename MI>
488 class BSplineNode;
489 
500 template<typename GV, class MI>
502 {
503  static const int dim = GV::dimension;
504 
506  class MultiDigitCounter
507  {
508  public:
509 
513  MultiDigitCounter(const std::array<unsigned int,dim>& limits)
514  : limits_(limits)
515  {
516  std::fill(counter_.begin(), counter_.end(), 0);
517  }
518 
520  MultiDigitCounter& operator++()
521  {
522  for (int i=0; i<dim; i++)
523  {
524  ++counter_[i];
525 
526  // no overflow?
527  if (counter_[i] < limits_[i])
528  break;
529 
530  counter_[i] = 0;
531  }
532  return *this;
533  }
534 
536  const unsigned int& operator[](int i) const
537  {
538  return counter_[i];
539  }
540 
542  unsigned int cycle() const
543  {
544  unsigned int r = 1;
545  for (int i=0; i<dim; i++)
546  r *= limits_[i];
547  return r;
548  }
549 
550  private:
551 
553  const std::array<unsigned int,dim> limits_;
554 
556  std::array<unsigned int,dim> counter_;
557 
558  };
559 
560 public:
561 
563  using GridView = GV;
564  using size_type = std::size_t;
565 
567 
569  using IndexSet = Impl::DefaultNodeIndexSet<BSplinePreBasis>;
570 
572  using MultiIndex = MI;
573 
574  using SizePrefix = Dune::ReservedVector<size_type, 1>;
575 
576  // Type used for function values
577  using R = double;
578 
598  const std::vector<double>& knotVector,
599  unsigned int order,
600  bool makeOpen = true)
602  {
603  // \todo Detection of duplicate knots
604  std::fill(elements_.begin(), elements_.end(), knotVector.size()-1);
605 
606  // Mediocre sanity check: we don't know the number of grid elements in each direction.
607  // but at least we know the total number of elements.
608  assert( std::accumulate(elements_.begin(), elements_.end(), 1, std::multiplies<unsigned>()) == gridView_.size(0) );
609 
610  for (int i=0; i<dim; i++)
611  {
612  // Prepend the correct number of additional knots to open the knot vector
614  if (makeOpen)
615  for (unsigned int j=0; j<order; j++)
616  knotVectors_[i].push_back(knotVector[0]);
617 
618  knotVectors_[i].insert(knotVectors_[i].end(), knotVector.begin(), knotVector.end());
619 
620  if (makeOpen)
621  for (unsigned int j=0; j<order; j++)
622  knotVectors_[i].push_back(knotVector.back());
623  }
624 
625  std::fill(order_.begin(), order_.end(), order);
626  }
627 
650  const FieldVector<double,dim>& lowerLeft,
651  const FieldVector<double,dim>& upperRight,
652  const std::array<unsigned int,dim>& elements,
653  unsigned int order,
654  bool makeOpen = true)
655  : elements_(elements),
657  {
658  // Mediocre sanity check: we don't know the number of grid elements in each direction.
659  // but at least we know the total number of elements.
660  assert( std::accumulate(elements_.begin(), elements_.end(), 1, std::multiplies<unsigned>()) == gridView_.size(0) );
661 
662  for (int i=0; i<dim; i++)
663  {
664  // Prepend the correct number of additional knots to open the knot vector
666  if (makeOpen)
667  for (unsigned int j=0; j<order; j++)
668  knotVectors_[i].push_back(lowerLeft[i]);
669 
670  // Construct the actual knot vector
671  for (size_t j=0; j<elements[i]+1; j++)
672  knotVectors_[i].push_back(lowerLeft[i] + j*(upperRight[i]-lowerLeft[i]) / elements[i]);
673 
674  if (makeOpen)
675  for (unsigned int j=0; j<order; j++)
676  knotVectors_[i].push_back(upperRight[i]);
677  }
678 
679  std::fill(order_.begin(), order_.end(), order);
680  }
681 
684  {}
685 
687  const GridView& gridView() const
688  {
689  return gridView_;
690  }
691 
693  void update(const GridView& gv)
694  {
695  gridView_ = gv;
696  }
697 
701  Node makeNode() const
702  {
703  return Node{this};
704  }
705 
713  [[deprecated("Warning: The IndexSet typedef and the makeIndexSet method are deprecated. "\
714  "As a replacement use the indices() method of the PreBasis directly.")]]
716  {
717  return IndexSet{*this};
718  }
719 
721  size_type size(const SizePrefix prefix) const
722  {
723  assert(prefix.size() == 0 || prefix.size() == 1);
724  return (prefix.size() == 0) ? size() : 0;
725  }
726 
729  {
730  return size();
731  }
732 
735  {
736  size_type result = 1;
737  for (int i=0; i<dim; i++)
738  result *= order_[i]+1;
739  return result;
740  }
741 
743  template<typename It>
744  It indices(const Node& node, It it) const
745  {
746  // Local degrees of freedom are arranged in a lattice.
747  // We need the lattice dimensions to be able to compute lattice coordinates from a local index
748  std::array<unsigned int, dim> localSizes;
749  for (int i=0; i<dim; i++)
750  localSizes[i] = node.finiteElement().size(i);
751  for (size_type i = 0, end = node.size() ; i < end ; ++i, ++it)
752  {
753  std::array<unsigned int,dim> localIJK = getIJK(i, localSizes);
754 
755  const auto currentKnotSpan = node.finiteElement().currentKnotSpan_;
756  const auto order = order_;
757 
758  std::array<unsigned int,dim> globalIJK;
759  for (int i=0; i<dim; i++)
760  globalIJK[i] = std::max((int)currentKnotSpan[i] - (int)order[i], 0) + localIJK[i]; // needs to be a signed type!
761 
762  // Make one global flat index from the globalIJK tuple
763  size_type globalIdx = globalIJK[dim-1];
764 
765  for (int i=dim-2; i>=0; i--)
766  globalIdx = globalIdx * size(i) + globalIJK[i];
767 
768  *it = {{globalIdx}};
769  }
770  return it;
771  }
772 
774  unsigned int size () const
775  {
776  unsigned int result = 1;
777  for (size_t i=0; i<dim; i++)
778  result *= size(i);
779  return result;
780  }
781 
783  unsigned int size (size_t d) const
784  {
785  return knotVectors_[d].size() - order_[d] - 1;
786  }
787 
790  void evaluateFunction (const FieldVector<typename GV::ctype,dim>& in,
791  std::vector<FieldVector<R,1> >& out,
792  const std::array<unsigned,dim>& currentKnotSpan) const
793  {
794  // Evaluate
795  std::array<std::vector<R>, dim> oneDValues;
796 
797  for (size_t i=0; i<dim; i++)
798  evaluateFunction(in[i], oneDValues[i], knotVectors_[i], order_[i], currentKnotSpan[i]);
799 
800  std::array<unsigned int, dim> limits;
801  for (int i=0; i<dim; i++)
802  limits[i] = oneDValues[i].size();
803 
804  MultiDigitCounter ijkCounter(limits);
805 
806  out.resize(ijkCounter.cycle());
807 
808  for (size_t i=0; i<out.size(); i++, ++ijkCounter)
809  {
810  out[i] = R(1.0);
811  for (size_t j=0; j<dim; j++)
812  out[i] *= oneDValues[j][ijkCounter[j]];
813  }
814  }
815 
821  void evaluateJacobian (const FieldVector<typename GV::ctype,dim>& in,
822  std::vector<FieldMatrix<R,1,dim> >& out,
823  const std::array<unsigned,dim>& currentKnotSpan) const
824  {
825  // How many shape functions to we have in each coordinate direction?
826  std::array<unsigned int, dim> limits;
827  for (int i=0; i<dim; i++)
828  {
829  limits[i] = order_[i]+1; // The 'standard' value away from the boundaries of the knot vector
830  if (currentKnotSpan[i]<order_[i])
831  limits[i] -= (order_[i] - currentKnotSpan[i]);
832  if ( order_[i] > (knotVectors_[i].size() - currentKnotSpan[i] - 2) )
833  limits[i] -= order_[i] - (knotVectors_[i].size() - currentKnotSpan[i] - 2);
834  }
835 
836  // The lowest knot spans that we need values from
837  std::array<unsigned int, dim> offset;
838  for (int i=0; i<dim; i++)
839  offset[i] = std::max((int)(currentKnotSpan[i] - order_[i]),0);
840 
841  // Evaluate 1d function values (needed for the product rule)
842  std::array<std::vector<R>, dim> oneDValues;
843 
844  // Evaluate 1d function values of one order lower (needed for the derivative formula)
845  std::array<std::vector<R>, dim> lowOrderOneDValues;
846 
847  std::array<DynamicMatrix<R>, dim> values;
848 
849  for (size_t i=0; i<dim; i++)
850  {
851  evaluateFunctionFull(in[i], values[i], knotVectors_[i], order_[i], currentKnotSpan[i]);
852  oneDValues[i].resize(knotVectors_[i].size()-order_[i]-1);
853  for (size_t j=0; j<oneDValues[i].size(); j++)
854  oneDValues[i][j] = values[i][order_[i]][j];
855 
856  if (order_[i]!=0)
857  {
858  lowOrderOneDValues[i].resize(knotVectors_[i].size()-(order_[i]-1)-1);
859  for (size_t j=0; j<lowOrderOneDValues[i].size(); j++)
860  lowOrderOneDValues[i][j] = values[i][order_[i]-1][j];
861  }
862  }
863 
864 
865  // Evaluate 1d function derivatives
866  std::array<std::vector<R>, dim> oneDDerivatives;
867  for (size_t i=0; i<dim; i++)
868  {
869  oneDDerivatives[i].resize(limits[i]);
870 
871  if (order_[i]==0) // order-zero functions are piecewise constant, hence all derivatives are zero
872  std::fill(oneDDerivatives[i].begin(), oneDDerivatives[i].end(), R(0.0));
873  else
874  {
875  for (size_t j=offset[i]; j<offset[i]+limits[i]; j++)
876  {
877  R derivativeAddend1 = lowOrderOneDValues[i][j] / (knotVectors_[i][j+order_[i]]-knotVectors_[i][j]);
878  R derivativeAddend2 = lowOrderOneDValues[i][j+1] / (knotVectors_[i][j+order_[i]+1]-knotVectors_[i][j+1]);
879  // The two previous terms may evaluate as 0/0. This is to be interpreted as 0.
880  if (std::isnan(derivativeAddend1))
881  derivativeAddend1 = 0;
882  if (std::isnan(derivativeAddend2))
883  derivativeAddend2 = 0;
884  oneDDerivatives[i][j-offset[i]] = order_[i] * ( derivativeAddend1 - derivativeAddend2 );
885  }
886  }
887  }
888 
889  // Working towards computing only the parts that we really need:
890  // Let's copy them out into a separate array
891  std::array<std::vector<R>, dim> oneDValuesShort;
892 
893  for (int i=0; i<dim; i++)
894  {
895  oneDValuesShort[i].resize(limits[i]);
896 
897  for (size_t j=0; j<limits[i]; j++)
898  oneDValuesShort[i][j] = oneDValues[i][offset[i] + j];
899  }
900 
901 
902 
903  // Set up a multi-index to go from consecutive indices to integer coordinates
904  MultiDigitCounter ijkCounter(limits);
905 
906  out.resize(ijkCounter.cycle());
907 
908  // Complete Jacobian is given by the product rule
909  for (size_t i=0; i<out.size(); i++, ++ijkCounter)
910  for (int j=0; j<dim; j++)
911  {
912  out[i][0][j] = 1.0;
913  for (int k=0; k<dim; k++)
914  out[i][0][j] *= (j==k) ? oneDDerivatives[k][ijkCounter[k]]
915  : oneDValuesShort[k][ijkCounter[k]];
916  }
917 
918  }
919 
921  template <size_type k>
922  void evaluate(const typename std::array<int,k>& directions,
923  const FieldVector<typename GV::ctype,dim>& in,
924  std::vector<FieldVector<R,1> >& out,
925  const std::array<unsigned,dim>& currentKnotSpan) const
926  {
927  if (k != 1 && k != 2)
928  DUNE_THROW(RangeError, "Differentiation order greater than 2 is not supported!");
929 
930  // Evaluate 1d function values (needed for the product rule)
931  std::array<std::vector<R>, dim> oneDValues;
932  std::array<std::vector<R>, dim> oneDDerivatives;
933  std::array<std::vector<R>, dim> oneDSecondDerivatives;
934 
935  // Evaluate 1d function derivatives
936  if (k==1)
937  for (size_t i=0; i<dim; i++)
938  evaluateAll(in[i], oneDValues[i], true, oneDDerivatives[i], false, oneDSecondDerivatives[i], knotVectors_[i], order_[i], currentKnotSpan[i]);
939  else
940  for (size_t i=0; i<dim; i++)
941  evaluateAll(in[i], oneDValues[i], true, oneDDerivatives[i], true, oneDSecondDerivatives[i], knotVectors_[i], order_[i], currentKnotSpan[i]);
942 
943  // The lowest knot spans that we need values from
944  std::array<unsigned int, dim> offset;
945  for (int i=0; i<dim; i++)
946  offset[i] = std::max((int)(currentKnotSpan[i] - order_[i]),0);
947 
948  // Set up a multi-index to go from consecutive indices to integer coordinates
949  std::array<unsigned int, dim> limits;
950  for (int i=0; i<dim; i++)
951  {
952  // In a proper implementation, the following line would do
953  //limits[i] = oneDValues[i].size();
954  limits[i] = order_[i]+1; // The 'standard' value away from the boundaries of the knot vector
955  if (currentKnotSpan[i]<order_[i])
956  limits[i] -= (order_[i] - currentKnotSpan[i]);
957  if ( order_[i] > (knotVectors_[i].size() - currentKnotSpan[i] - 2) )
958  limits[i] -= order_[i] - (knotVectors_[i].size() - currentKnotSpan[i] - 2);
959  }
960 
961  // Working towards computing only the parts that we really need:
962  // Let's copy them out into a separate array
963  std::array<std::vector<R>, dim> oneDValuesShort;
964 
965  for (int i=0; i<dim; i++)
966  {
967  oneDValuesShort[i].resize(limits[i]);
968 
969  for (size_t j=0; j<limits[i]; j++)
970  oneDValuesShort[i][j] = oneDValues[i][offset[i] + j];
971  }
972 
973 
974  MultiDigitCounter ijkCounter(limits);
975 
976  out.resize(ijkCounter.cycle());
977 
978  if (k == 1)
979  {
980  // Complete Jacobian is given by the product rule
981  for (size_t i=0; i<out.size(); i++, ++ijkCounter)
982  {
983  out[i][0] = 1.0;
984  for (int l=0; l<dim; l++)
985  out[i][0] *= (directions[0]==l) ? oneDDerivatives[l][ijkCounter[l]]
986  : oneDValuesShort[l][ijkCounter[l]];
987  }
988  }
989 
990  if (k == 2)
991  {
992  // Complete derivation by deriving the tensor product
993  for (size_t i=0; i<out.size(); i++, ++ijkCounter)
994  {
995  out[i][0] = 1.0;
996  for (int j=0; j<dim; j++)
997  {
998  if (directions[0] != directions[1]) //derivation in two different variables
999  if (directions[0] == j || directions[1] == j) //the spline has to be derived (once) in this direction
1000  out[i][0] *= oneDDerivatives[j][ijkCounter[j]];
1001  else //no derivation in this direction
1002  out[i][0] *= oneDValuesShort[j][ijkCounter[j]];
1003  else //spline is derived two times in the same direction
1004  if (directions[0] == j) //the spline is derived two times in this direction
1005  out[i][0] *= oneDSecondDerivatives[j][ijkCounter[j]];
1006  else //no derivation in this direction
1007  out[i][0] *= oneDValuesShort[j][ijkCounter[j]];
1008  }
1009  }
1010  }
1011  }
1012 
1013 
1018  static std::array<unsigned int,dim> getIJK(typename GridView::IndexSet::IndexType idx, std::array<unsigned int,dim> elements)
1019  {
1020  std::array<unsigned,dim> result;
1021  for (int i=0; i<dim; i++)
1022  {
1023  result[i] = idx%elements[i];
1024  idx /= elements[i];
1025  }
1026  return result;
1027  }
1028 
1037  static void evaluateFunction (const typename GV::ctype& in, std::vector<R>& out,
1038  const std::vector<R>& knotVector,
1039  unsigned int order,
1040  unsigned int currentKnotSpan)
1041  {
1042  std::size_t outSize = order+1; // The 'standard' value away from the boundaries of the knot vector
1043  if (currentKnotSpan<order) // Less near the left end of the knot vector
1044  outSize -= (order - currentKnotSpan);
1045  if ( order > (knotVector.size() - currentKnotSpan - 2) )
1046  outSize -= order - (knotVector.size() - currentKnotSpan - 2);
1047  out.resize(outSize);
1048 
1049  // It's not really a matrix that is needed here, a plain 2d array would do
1050  DynamicMatrix<R> N(order+1, knotVector.size()-1);
1051 
1052  // The text books on splines use the following geometric condition here to fill the array N
1053  // (see for example Cottrell, Hughes, Bazilevs, Formula (2.1). However, this condition
1054  // only works if splines are never evaluated exactly on the knots.
1055  //
1056  // for (size_t i=0; i<knotVector.size()-1; i++)
1057  // N[0][i] = (knotVector[i] <= in) and (in < knotVector[i+1]);
1058  for (size_t i=0; i<knotVector.size()-1; i++)
1059  N[0][i] = (i == currentKnotSpan);
1060 
1061  for (size_t r=1; r<=order; r++)
1062  for (size_t i=0; i<knotVector.size()-r-1; i++)
1063  {
1064  R factor1 = ((knotVector[i+r] - knotVector[i]) > 1e-10)
1065  ? (in - knotVector[i]) / (knotVector[i+r] - knotVector[i])
1066  : 0;
1067  R factor2 = ((knotVector[i+r+1] - knotVector[i+1]) > 1e-10)
1068  ? (knotVector[i+r+1] - in) / (knotVector[i+r+1] - knotVector[i+1])
1069  : 0;
1070  N[r][i] = factor1 * N[r-1][i] + factor2 * N[r-1][i+1];
1071  }
1072 
1077  for (size_t i=0; i<out.size(); i++) {
1078  out[i] = N[order][std::max((int)(currentKnotSpan - order),0) + i];
1079  }
1080  }
1081 
1094  static void evaluateFunctionFull(const typename GV::ctype& in,
1095  DynamicMatrix<R>& out,
1096  const std::vector<R>& knotVector,
1097  unsigned int order,
1098  unsigned int currentKnotSpan)
1099  {
1100  // It's not really a matrix that is needed here, a plain 2d array would do
1101  DynamicMatrix<R>& N = out;
1102 
1103  N.resize(order+1, knotVector.size()-1);
1104 
1105  // The text books on splines use the following geometric condition here to fill the array N
1106  // (see for example Cottrell, Hughes, Bazilevs, Formula (2.1). However, this condition
1107  // only works if splines are never evaluated exactly on the knots.
1108  //
1109  // for (size_t i=0; i<knotVector.size()-1; i++)
1110  // N[0][i] = (knotVector[i] <= in) and (in < knotVector[i+1]);
1111  for (size_t i=0; i<knotVector.size()-1; i++)
1112  N[0][i] = (i == currentKnotSpan);
1113 
1114  for (size_t r=1; r<=order; r++)
1115  for (size_t i=0; i<knotVector.size()-r-1; i++)
1116  {
1117  R factor1 = ((knotVector[i+r] - knotVector[i]) > 1e-10)
1118  ? (in - knotVector[i]) / (knotVector[i+r] - knotVector[i])
1119  : 0;
1120  R factor2 = ((knotVector[i+r+1] - knotVector[i+1]) > 1e-10)
1121  ? (knotVector[i+r+1] - in) / (knotVector[i+r+1] - knotVector[i+1])
1122  : 0;
1123  N[r][i] = factor1 * N[r-1][i] + factor2 * N[r-1][i+1];
1124  }
1125  }
1126 
1127 
1137  static void evaluateAll(const typename GV::ctype& in,
1138  std::vector<R>& out,
1139  bool evaluateJacobian, std::vector<R>& outJac,
1140  bool evaluateHessian, std::vector<R>& outHess,
1141  const std::vector<R>& knotVector,
1142  unsigned int order,
1143  unsigned int currentKnotSpan)
1144  {
1145  // How many shape functions to we have in each coordinate direction?
1146  unsigned int limit;
1147  limit = order+1; // The 'standard' value away from the boundaries of the knot vector
1148  if (currentKnotSpan<order)
1149  limit -= (order - currentKnotSpan);
1150  if ( order > (knotVector.size() - currentKnotSpan - 2) )
1151  limit -= order - (knotVector.size() - currentKnotSpan - 2);
1152 
1153  // The lowest knot spans that we need values from
1154  unsigned int offset;
1155  offset = std::max((int)(currentKnotSpan - order),0);
1156 
1157  // Evaluate 1d function values (needed for the product rule)
1158  DynamicMatrix<R> values;
1159 
1160  evaluateFunctionFull(in, values, knotVector, order, currentKnotSpan);
1161 
1162  out.resize(knotVector.size()-order-1);
1163  for (size_t j=0; j<out.size(); j++)
1164  out[j] = values[order][j];
1165 
1166  // Evaluate 1d function values of one order lower (needed for the derivative formula)
1167  std::vector<R> lowOrderOneDValues;
1168 
1169  if (order!=0)
1170  {
1171  lowOrderOneDValues.resize(knotVector.size()-(order-1)-1);
1172  for (size_t j=0; j<lowOrderOneDValues.size(); j++)
1173  lowOrderOneDValues[j] = values[order-1][j];
1174  }
1175 
1176  // Evaluate 1d function values of two order lower (needed for the (second) derivative formula)
1177  std::vector<R> lowOrderTwoDValues;
1178 
1179  if (order>1 && evaluateHessian)
1180  {
1181  lowOrderTwoDValues.resize(knotVector.size()-(order-2)-1);
1182  for (size_t j=0; j<lowOrderTwoDValues.size(); j++)
1183  lowOrderTwoDValues[j] = values[order-2][j];
1184  }
1185 
1186  // Evaluate 1d function derivatives
1187  if (evaluateJacobian)
1188  {
1189  outJac.resize(limit);
1190 
1191  if (order==0) // order-zero functions are piecewise constant, hence all derivatives are zero
1192  std::fill(outJac.begin(), outJac.end(), R(0.0));
1193  else
1194  {
1195  for (size_t j=offset; j<offset+limit; j++)
1196  {
1197  R derivativeAddend1 = lowOrderOneDValues[j] / (knotVector[j+order]-knotVector[j]);
1198  R derivativeAddend2 = lowOrderOneDValues[j+1] / (knotVector[j+order+1]-knotVector[j+1]);
1199  // The two previous terms may evaluate as 0/0. This is to be interpreted as 0.
1200  if (std::isnan(derivativeAddend1))
1201  derivativeAddend1 = 0;
1202  if (std::isnan(derivativeAddend2))
1203  derivativeAddend2 = 0;
1204  outJac[j-offset] = order * ( derivativeAddend1 - derivativeAddend2 );
1205  }
1206  }
1207  }
1208 
1209  // Evaluate 1d function second derivatives
1210  if (evaluateHessian)
1211  {
1212  outHess.resize(limit);
1213 
1214  if (order<2) // order-zero functions are piecewise constant, hence all derivatives are zero
1215  std::fill(outHess.begin(), outHess.end(), R(0.0));
1216  else
1217  {
1218  for (size_t j=offset; j<offset+limit; j++)
1219  {
1220  assert(j+2 < lowOrderTwoDValues.size());
1221  R derivativeAddend1 = lowOrderTwoDValues[j] / (knotVector[j+order]-knotVector[j]) / (knotVector[j+order-1]-knotVector[j]);
1222  R derivativeAddend2 = lowOrderTwoDValues[j+1] / (knotVector[j+order]-knotVector[j]) / (knotVector[j+order]-knotVector[j+1]);
1223  R derivativeAddend3 = lowOrderTwoDValues[j+1] / (knotVector[j+order+1]-knotVector[j+1]) / (knotVector[j+order]-knotVector[j+1]);
1224  R derivativeAddend4 = lowOrderTwoDValues[j+2] / (knotVector[j+order+1]-knotVector[j+1]) / (knotVector[j+1+order]-knotVector[j+2]);
1225  // The two previous terms may evaluate as 0/0. This is to be interpreted as 0.
1226 
1227  if (std::isnan(derivativeAddend1))
1228  derivativeAddend1 = 0;
1229  if (std::isnan(derivativeAddend2))
1230  derivativeAddend2 = 0;
1231  if (std::isnan(derivativeAddend3))
1232  derivativeAddend3 = 0;
1233  if (std::isnan(derivativeAddend4))
1234  derivativeAddend4 = 0;
1235  outHess[j-offset] = order * (order-1) * ( derivativeAddend1 - derivativeAddend2 -derivativeAddend3 + derivativeAddend4 );
1236  }
1237  }
1238  }
1239  }
1240 
1241 
1243  std::array<unsigned int, dim> order_;
1244 
1246  std::array<std::vector<double>, dim> knotVectors_;
1247 
1249  std::array<unsigned,dim> elements_;
1250 
1252 };
1253 
1254 
1255 
1256 template<typename GV, typename MI>
1258  public LeafBasisNode
1259 {
1260  static const int dim = GV::dimension;
1261 
1262 public:
1263 
1264  using size_type = std::size_t;
1265  using Element = typename GV::template Codim<0>::Entity;
1267 
1269  preBasis_(preBasis),
1270  finiteElement_(*preBasis)
1271  {}
1272 
1274  const Element& element() const
1275  {
1276  return element_;
1277  }
1278 
1284  {
1285  return finiteElement_;
1286  }
1287 
1289  void bind(const Element& e)
1290  {
1291  element_ = e;
1292  auto elementIndex = preBasis_->gridView().indexSet().index(e);
1293  finiteElement_.bind(preBasis_->getIJK(elementIndex,preBasis_->elements_));
1294  this->setSize(finiteElement_.size());
1295  }
1296 
1297 protected:
1298 
1300 
1303 };
1304 
1305 
1306 
1307 namespace BasisFactory {
1308 
1309 namespace Imp {
1310 
1311 class BSplinePreBasisFactory
1312 {
1313 public:
1314  static const std::size_t requiredMultiIndexSize=1;
1315 
1316  BSplinePreBasisFactory(const std::vector<double>& knotVector,
1317  unsigned int order,
1318  bool makeOpen = true)
1319  : knotVector_(knotVector),
1320  order_(order),
1321  makeOpen_(makeOpen)
1322  {}
1323 
1324  template<class MultiIndex, class GridView>
1325  auto makePreBasis(const GridView& gridView) const
1326  {
1327  return BSplinePreBasis<GridView, MultiIndex>(gridView, knotVector_, order_, makeOpen_);
1328  }
1329 
1330 private:
1331  const std::vector<double>& knotVector_;
1332  unsigned int order_;
1333  bool makeOpen_;
1334 };
1335 
1336 } // end namespace BasisFactory::Imp
1337 
1344 auto bSpline(const std::vector<double>& knotVector,
1345  unsigned int order,
1346  bool makeOpen = true)
1347 {
1348  return Imp::BSplinePreBasisFactory(knotVector, order, makeOpen);
1349 }
1350 
1351 } // end namespace BasisFactory
1352 
1353 // *****************************************************************************
1354 // This is the actual global basis implementation based on the reusable parts.
1355 // *****************************************************************************
1356 
1363 template<typename GV>
1365 
1366 
1367 } // namespace Functions
1368 
1369 } // namespace Dune
1370 
1371 #endif // DUNE_FUNCTIONS_FUNCTIONSPACEBASES_BSPLINEBASIS_HH
auto bSpline(const std::vector< double > &knotVector, unsigned int order, bool makeOpen=true)
Create a pre-basis factory that can create a B-spline pre-basis.
Definition: bsplinebasis.hh:1344
Definition: polynomial.hh:10
LocalFiniteElement in the sense of dune-localfunctions, for the B-spline basis on tensor-product grid...
Definition: bsplinebasis.hh:364
const BSplinePreBasis< GV, MI > & preBasis_
Definition: bsplinebasis.hh:476
unsigned size() const
Number of shape functions in this finite element.
Definition: bsplinebasis.hh:447
std::array< unsigned, dim > currentKnotSpan_
Definition: bsplinebasis.hh:483
GeometryType type() const
Return the reference element that the local finite element is defined on (here, a hypercube)
Definition: bsplinebasis.hh:457
BSplineLocalInterpolation< dim, BSplineLocalBasis< GV, R, MI > > localInterpolation_
Definition: bsplinebasis.hh:480
void bind(const std::array< unsigned, dim > &elementIdx)
Bind LocalFiniteElement to a specific knot span of the spline patch.
Definition: bsplinebasis.hh:396
LocalFiniteElementTraits< BSplineLocalBasis< GV, R, MI >, BSplineLocalCoefficients< dim >, BSplineLocalInterpolation< dim, BSplineLocalBasis< GV, R, MI > > > Traits
Export various types related to this LocalFiniteElement.
Definition: bsplinebasis.hh:374
const BSplineLocalInterpolation< dim, BSplineLocalBasis< GV, R, MI > > & localInterpolation() const
Hand out a LocalInterpolation object.
Definition: bsplinebasis.hh:441
const BSplineLocalBasis< GV, R, MI > & localBasis() const
Hand out a LocalBasis object.
Definition: bsplinebasis.hh:429
BSplineLocalBasis< GV, R, MI > localBasis_
Definition: bsplinebasis.hh:478
BSplineLocalFiniteElement(const BSplineLocalFiniteElement &other)
Copy constructor.
Definition: bsplinebasis.hh:385
BSplineLocalFiniteElement(const BSplinePreBasis< GV, MI > &preBasis)
Constructor with a given B-spline basis.
Definition: bsplinebasis.hh:378
unsigned int size(int i) const
Number of degrees of freedom for one coordinate direction.
Definition: bsplinebasis.hh:465
const BSplineLocalCoefficients< dim > & localCoefficients() const
Hand out a LocalCoefficients object.
Definition: bsplinebasis.hh:435
BSplineLocalCoefficients< dim > localCoefficients_
Definition: bsplinebasis.hh:479
Pre-basis for B-spline basis.
Definition: bsplinebasis.hh:502
double R
Definition: bsplinebasis.hh:577
GV GridView
The grid view that the FE space is defined on.
Definition: bsplinebasis.hh:563
unsigned int size(size_t d) const
Number of shape functions in one direction.
Definition: bsplinebasis.hh:783
size_type dimension() const
Get the total dimension of the space spanned by this basis.
Definition: bsplinebasis.hh:728
void update(const GridView &gv)
Update the stored grid view, to be called if the grid has changed.
Definition: bsplinebasis.hh:693
void evaluateJacobian(const FieldVector< typename GV::ctype, dim > &in, std::vector< FieldMatrix< R, 1, dim > > &out, const std::array< unsigned, dim > &currentKnotSpan) const
Evaluate Jacobian of all B-spline basis functions.
Definition: bsplinebasis.hh:821
static void evaluateFunction(const typename GV::ctype &in, std::vector< R > &out, const std::vector< R > &knotVector, unsigned int order, unsigned int currentKnotSpan)
Evaluate all one-dimensional B-spline functions for a given coordinate direction.
Definition: bsplinebasis.hh:1037
std::size_t size_type
Definition: bsplinebasis.hh:564
BSplinePreBasis(const GridView &gridView, const std::vector< double > &knotVector, unsigned int order, bool makeOpen=true)
Construct a B-spline basis for a given grid view and set of knot vectors.
Definition: bsplinebasis.hh:597
unsigned int size() const
Total number of B-spline basis functions.
Definition: bsplinebasis.hh:774
size_type size(const SizePrefix prefix) const
Return number of possible values for next position in multi index.
Definition: bsplinebasis.hh:721
MI MultiIndex
Type used for global numbering of the basis vectors.
Definition: bsplinebasis.hh:572
size_type maxNodeSize() const
Get the maximal number of DOFs associated to node for any element.
Definition: bsplinebasis.hh:734
void initializeIndices()
Initialize the global indices.
Definition: bsplinebasis.hh:683
std::array< unsigned, dim > elements_
Number of grid elements in the different coordinate directions.
Definition: bsplinebasis.hh:1249
GridView gridView_
Definition: bsplinebasis.hh:1251
It indices(const Node &node, It it) const
Maps from subtree index set [0..size-1] to a globally unique multi index in global basis.
Definition: bsplinebasis.hh:744
static void evaluateAll(const typename GV::ctype &in, std::vector< R > &out, bool evaluateJacobian, std::vector< R > &outJac, bool evaluateHessian, std::vector< R > &outHess, const std::vector< R > &knotVector, unsigned int order, unsigned int currentKnotSpan)
Evaluate the second derivatives of all one-dimensional B-spline functions for a given coordinate dire...
Definition: bsplinebasis.hh:1137
const GridView & gridView() const
Obtain the grid view that the basis is defined on.
Definition: bsplinebasis.hh:687
void evaluateFunction(const FieldVector< typename GV::ctype, dim > &in, std::vector< FieldVector< R, 1 > > &out, const std::array< unsigned, dim > &currentKnotSpan) const
Evaluate all B-spline basis functions at a given point.
Definition: bsplinebasis.hh:790
Dune::ReservedVector< size_type, 1 > SizePrefix
Definition: bsplinebasis.hh:574
BSplinePreBasis(const GridView &gridView, const FieldVector< double, dim > &lowerLeft, const FieldVector< double, dim > &upperRight, const std::array< unsigned int, dim > &elements, unsigned int order, bool makeOpen=true)
Construct a B-spline basis for a given grid view with uniform knot vectors.
Definition: bsplinebasis.hh:649
Impl::DefaultNodeIndexSet< BSplinePreBasis > IndexSet
Type of created tree node index set.
Definition: bsplinebasis.hh:569
static void evaluateFunctionFull(const typename GV::ctype &in, DynamicMatrix< R > &out, const std::vector< R > &knotVector, unsigned int order, unsigned int currentKnotSpan)
Evaluate all one-dimensional B-spline functions for a given coordinate direction.
Definition: bsplinebasis.hh:1094
IndexSet makeIndexSet() const
Create tree node index set.
Definition: bsplinebasis.hh:715
void evaluate(const typename std::array< int, k > &directions, const FieldVector< typename GV::ctype, dim > &in, std::vector< FieldVector< R, 1 > > &out, const std::array< unsigned, dim > &currentKnotSpan) const
Evaluate Derivatives of all B-spline basis functions.
Definition: bsplinebasis.hh:922
static std::array< unsigned int, dim > getIJK(typename GridView::IndexSet::IndexType idx, std::array< unsigned int, dim > elements)
Compute integer element coordinates from the element index.
Definition: bsplinebasis.hh:1018
Node makeNode() const
Create tree node.
Definition: bsplinebasis.hh:701
std::array< std::vector< double >, dim > knotVectors_
The knot vectors, one for each space dimension.
Definition: bsplinebasis.hh:1246
std::array< unsigned int, dim > order_
Order of the B-spline for each space dimension.
Definition: bsplinebasis.hh:1243
LocalBasis class in the sense of dune-localfunctions, presenting the restriction of a B-spline patch ...
Definition: bsplinebasis.hh:47
LocalBasisTraits< D, dim, FieldVector< D, dim >, R, 1, FieldVector< R, 1 >, FieldMatrix< R, 1, dim > > Traits
export type traits for function signature
Definition: bsplinebasis.hh:56
BSplineLocalBasis(const BSplinePreBasis< GV, MI > &preBasis, const BSplineLocalFiniteElement< GV, R, MI > &lFE)
Constructor with a given B-spline patch.
Definition: bsplinebasis.hh:62
void evaluateFunction(const FieldVector< D, dim > &in, std::vector< FieldVector< R, 1 > > &out) const
Evaluate all shape functions.
Definition: bsplinebasis.hh:71
void evaluate(const typename std::array< int, k > &directions, const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions and derivatives of any order.
Definition: bsplinebasis.hh:98
unsigned int order() const
Polynomial order of the shape functions.
Definition: bsplinebasis.hh:141
void evaluateJacobian(const FieldVector< D, dim > &in, std::vector< FieldMatrix< D, 1, dim > > &out) const
Evaluate Jacobian of all shape functions.
Definition: bsplinebasis.hh:83
std::size_t size() const
Return the number of basis functions on the current knot span.
Definition: bsplinebasis.hh:148
Attaches a shape function to an entity.
Definition: bsplinebasis.hh:179
const LocalKey & localKey(std::size_t i) const
get i'th index
Definition: bsplinebasis.hh:322
void init(const std::array< unsigned, dim > &sizes)
Definition: bsplinebasis.hh:257
std::size_t size() const
number of coefficients
Definition: bsplinebasis.hh:316
Local interpolation in the sense of dune-localfunctions, for the B-spline basis on tensor-product gri...
Definition: bsplinebasis.hh:341
void interpolate(const F &f, std::vector< C > &out) const
Local interpolation of a function.
Definition: bsplinebasis.hh:345
Definition: bsplinebasis.hh:1259
const FiniteElement & finiteElement() const
Return the LocalFiniteElement for the element we are bound to.
Definition: bsplinebasis.hh:1283
BSplineNode(const BSplinePreBasis< GV, MI > *preBasis)
Definition: bsplinebasis.hh:1268
void bind(const Element &e)
Bind to element.
Definition: bsplinebasis.hh:1289
const Element & element() const
Return current element, throw if unbound.
Definition: bsplinebasis.hh:1274
std::size_t size_type
Definition: bsplinebasis.hh:1264
const BSplinePreBasis< GV, MI > * preBasis_
Definition: bsplinebasis.hh:1299
FiniteElement finiteElement_
Definition: bsplinebasis.hh:1301
Element element_
Definition: bsplinebasis.hh:1302
typename GV::template Codim< 0 >::Entity Element
Definition: bsplinebasis.hh:1265
Global basis for given pre-basis.
Definition: defaultglobalbasis.hh:47
size_type size() const
Definition: nodes.hh:140
void setSize(const size_type size)
Definition: nodes.hh:162
Definition: nodes.hh:184