Reference documentation for deal.II version GIT 5dd0dfed0b 2022-12-08 21:45:02+00:00
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function.h
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3 // Copyright (C) 1998 - 2022 by the deal.II authors
4 //
5 // This file is part of the deal.II library.
6 //
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8 // it, and/or modify it under the terms of the GNU Lesser General
9 // Public License as published by the Free Software Foundation; either
10 // version 2.1 of the License, or (at your option) any later version.
11 // The full text of the license can be found in the file LICENSE.md at
12 // the top level directory of deal.II.
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15 
16 #ifndef dealii_function_h
17 #define dealii_function_h
18 
19 
20 #include <deal.II/base/config.h>
21 
24 #include <deal.II/base/point.h>
27 #include <deal.II/base/tensor.h>
28 
29 #include <functional>
30 #include <vector>
31 
33 
34 // Forward declarations
35 #ifndef DOXYGEN
36 template <typename number>
37 class Vector;
38 template <int rank, int dim, typename Number>
39 class TensorFunction;
40 #endif
41 
149 template <int dim, typename RangeNumberType = double>
150 class Function : public FunctionTime<
151  typename numbers::NumberTraits<RangeNumberType>::real_type>,
152  public Subscriptor
153 {
154 public:
159  static constexpr unsigned int dimension = dim;
160 
164  const unsigned int n_components;
165 
169  using time_type = typename FunctionTime<
171 
177  explicit Function(const unsigned int n_components = 1,
178  const time_type initial_time = 0.0);
179 
183  Function(const Function &f) = default;
184 
206  virtual ~Function() override = 0;
207 
214  Function &
215  operator=(const Function &f);
216 
223  virtual RangeNumberType
224  value(const Point<dim> &p, const unsigned int component = 0) const;
225 
233  virtual void
235 
245  virtual void
246  value_list(const std::vector<Point<dim>> &points,
247  std::vector<RangeNumberType> & values,
248  const unsigned int component = 0) const;
249 
260  virtual void
261  vector_value_list(const std::vector<Point<dim>> & points,
262  std::vector<Vector<RangeNumberType>> &values) const;
263 
272  virtual void
273  vector_values(const std::vector<Point<dim>> & points,
274  std::vector<std::vector<RangeNumberType>> &values) const;
275 
281  gradient(const Point<dim> &p, const unsigned int component = 0) const;
282 
286  virtual void
288  const Point<dim> & p,
289  std::vector<Tensor<1, dim, RangeNumberType>> &gradients) const;
290 
297  virtual void
298  gradient_list(const std::vector<Point<dim>> & points,
300  const unsigned int component = 0) const;
301 
310  virtual void
312  const std::vector<Point<dim>> & points,
313  std::vector<std::vector<Tensor<1, dim, RangeNumberType>>> &gradients) const;
314 
324  virtual void
326  const std::vector<Point<dim>> & points,
327  std::vector<std::vector<Tensor<1, dim, RangeNumberType>>> &gradients) const;
328 
332  virtual RangeNumberType
333  laplacian(const Point<dim> &p, const unsigned int component = 0) const;
334 
339  virtual void
341 
345  virtual void
346  laplacian_list(const std::vector<Point<dim>> &points,
347  std::vector<RangeNumberType> & values,
348  const unsigned int component = 0) const;
349 
353  virtual void
354  vector_laplacian_list(const std::vector<Point<dim>> & points,
355  std::vector<Vector<RangeNumberType>> &values) const;
356 
362  hessian(const Point<dim> &p, const unsigned int component = 0) const;
363 
368  virtual void
370  const Point<dim> & p,
372 
376  virtual void
377  hessian_list(const std::vector<Point<dim>> & points,
379  const unsigned int component = 0) const;
380 
384  virtual void
386  const std::vector<Point<dim>> & points,
387  std::vector<std::vector<SymmetricTensor<2, dim, RangeNumberType>>> &values)
388  const;
389 
390 
396  virtual std::size_t
398 };
399 
400 
401 namespace Functions
402 {
409  template <int dim, typename RangeNumberType = double>
410  class ConstantFunction : public Function<dim, RangeNumberType>
411  {
412  public:
417  explicit ConstantFunction(const RangeNumberType value,
418  const unsigned int n_components = 1);
419 
425  explicit ConstantFunction(const std::vector<RangeNumberType> &values);
426 
433 
438  ConstantFunction(const RangeNumberType *begin_ptr,
439  const unsigned int n_components);
440 
441  virtual RangeNumberType
442  value(const Point<dim> &p, const unsigned int component = 0) const override;
443 
444  virtual void
446  Vector<RangeNumberType> &return_value) const override;
447 
448  virtual void
449  value_list(const std::vector<Point<dim>> &points,
450  std::vector<RangeNumberType> & return_values,
451  const unsigned int component = 0) const override;
452 
453  virtual void
455  const std::vector<Point<dim>> & points,
456  std::vector<Vector<RangeNumberType>> &return_values) const override;
457 
459  gradient(const Point<dim> & p,
460  const unsigned int component = 0) const override;
461 
462  virtual void
464  const Point<dim> & p,
465  std::vector<Tensor<1, dim, RangeNumberType>> &gradients) const override;
466 
467  virtual void
468  gradient_list(const std::vector<Point<dim>> & points,
470  const unsigned int component = 0) const override;
471 
472  virtual void
474  const std::vector<Point<dim>> & points,
475  std::vector<std::vector<Tensor<1, dim, RangeNumberType>>> &gradients)
476  const override;
477 
480  const unsigned int component = 0) const override;
481 
482  virtual RangeNumberType
484  const unsigned int component = 0) const override;
485 
486  virtual std::size_t
487  memory_consumption() const override;
488 
489  protected:
493  std::vector<RangeNumberType> function_value_vector;
494  };
495 
496 
497 
509  template <int dim, typename RangeNumberType = double>
510  class ZeroFunction : public ConstantFunction<dim, RangeNumberType>
511  {
512  public:
516  explicit ZeroFunction(const unsigned int n_components = 1);
517  };
518 
529  template <int dim, typename RangeNumberType = double>
530  class IdentityFunction : public Function<dim, RangeNumberType>
531  {
532  public:
537 
541  virtual RangeNumberType
542  value(const Point<dim> &p, const unsigned int component = 0) const override;
543 
548  gradient(const Point<dim> & p,
549  const unsigned int component = 0) const override;
550 
554  virtual RangeNumberType
556  const unsigned int component = 0) const override;
557 
562  hessian(const Point<dim> & p,
563  const unsigned int component = 0) const override;
564  };
565 } // namespace Functions
566 
580 template <int dim, typename RangeNumberType = double>
582  : public Functions::ConstantFunction<dim, RangeNumberType>
583 {
584 public:
590  ComponentSelectFunction(const unsigned int selected,
591  const RangeNumberType value,
592  const unsigned int n_components);
593 
598  ComponentSelectFunction(const unsigned int selected,
599  const unsigned int n_components);
600 
608  ComponentSelectFunction(const std::pair<unsigned int, unsigned int> &selected,
609  const unsigned int n_components);
610 
611 
625  virtual void
628 
632  virtual void
634  Vector<RangeNumberType> &return_value) const override;
635 
642  virtual void
644  const std::vector<Point<dim>> & points,
645  std::vector<Vector<RangeNumberType>> &values) const override;
646 
650  virtual std::size_t
651  memory_consumption() const override;
652 
653 protected:
657  const std::pair<unsigned int, unsigned int> selected_components;
658 };
659 
660 
661 
802 template <int dim, typename RangeNumberType = double>
803 class ScalarFunctionFromFunctionObject : public Function<dim, RangeNumberType>
804 {
805 public:
812  const std::function<RangeNumberType(const Point<dim> &)> &function_object);
813 
818  virtual RangeNumberType
819  value(const Point<dim> &p, const unsigned int component = 0) const override;
820 
821 private:
826  const std::function<RangeNumberType(const Point<dim> &)> function_object;
827 };
828 
829 
830 
869 template <int dim, typename RangeNumberType = double>
871  : public Function<dim, RangeNumberType>
872 {
873 public:
887  const std::function<RangeNumberType(const Point<dim> &)> &function_object,
888  const unsigned int selected_component,
889  const unsigned int n_components);
890 
895  virtual RangeNumberType
896  value(const Point<dim> &p, const unsigned int component = 0) const override;
897 
903  virtual void
905  Vector<RangeNumberType> &values) const override;
906 
907 private:
912  const std::function<RangeNumberType(const Point<dim> &)> function_object;
913 
918  const unsigned int selected_component;
919 };
920 
921 
957 template <int dim, typename RangeNumberType = double>
958 class FunctionFromFunctionObjects : public Function<dim, RangeNumberType>
959 {
960 public:
969  explicit FunctionFromFunctionObjects(const unsigned int n_components = 1,
970  const double initial_time = 0);
971 
981  const std::vector<std::function<RangeNumberType(const Point<dim> &)>>
982  & values,
983  const double initial_time = 0.0);
984 
994  const std::vector<std::function<RangeNumberType(const Point<dim> &)>>
995  &values,
996  const std::vector<
997  std::function<Tensor<1, dim, RangeNumberType>(const Point<dim> &)>>
998  & gradients,
999  const double initial_time = 0.0);
1000 
1001 
1008  virtual RangeNumberType
1009  value(const Point<dim> &p, const unsigned int component = 0) const override;
1010 
1019  const unsigned int component = 0) const override;
1020 
1026  void
1028  const std::vector<std::function<RangeNumberType(const Point<dim> &)>>
1029  &values);
1030 
1036  void
1038  const std::vector<
1039  std::function<Tensor<1, dim, RangeNumberType>(const Point<dim> &)>>
1040  &gradients);
1041 
1042 private:
1046  std::vector<std::function<RangeNumberType(const Point<dim> &)>>
1048 
1052  std::vector<
1053  std::function<Tensor<1, dim, RangeNumberType>(const Point<dim> &)>>
1055 };
1056 
1057 
1093 template <int dim, typename RangeNumberType = double>
1094 class VectorFunctionFromTensorFunction : public Function<dim, RangeNumberType>
1095 {
1096 public:
1115  const unsigned int selected_component = 0,
1116  const unsigned int n_components = dim);
1117 
1122  virtual ~VectorFunctionFromTensorFunction() override = default;
1123 
1127  virtual RangeNumberType
1128  value(const Point<dim> &p, const unsigned int component = 0) const override;
1129 
1135  virtual void
1137  Vector<RangeNumberType> &values) const override;
1138 
1146  virtual void
1148  const std::vector<Point<dim>> & points,
1149  std::vector<Vector<RangeNumberType>> &value_list) const override;
1150 
1151 private:
1157 
1164  const unsigned int selected_component;
1165 };
1166 
1167 
1168 #ifndef DOXYGEN
1169 // icc 2018 complains about an undefined reference
1170 // if we put this in the templates.h file
1171 //
1172 // The destructor is pure virtual so we can't default it
1173 // in the declaration.
1174 template <int dim, typename RangeNumberType>
1176 #endif
1177 
1178 
1180 
1181 #endif
const std::pair< unsigned int, unsigned int > selected_components
Definition: function.h:657
virtual std::size_t memory_consumption() const override
ComponentSelectFunction(const std::pair< unsigned int, unsigned int > &selected, const unsigned int n_components)
virtual void vector_value(const Point< dim > &p, Vector< RangeNumberType > &return_value) const override
virtual void vector_value_list(const std::vector< Point< dim >> &points, std::vector< Vector< RangeNumberType >> &values) const override
ComponentSelectFunction(const unsigned int selected, const unsigned int n_components)
virtual void substitute_function_value_with(const Functions::ConstantFunction< dim, RangeNumberType > &f)
ComponentSelectFunction(const unsigned int selected, const RangeNumberType value, const unsigned int n_components)
void set_function_gradients(const std::vector< std::function< Tensor< 1, dim, RangeNumberType >(const Point< dim > &)>> &gradients)
virtual Tensor< 1, dim, RangeNumberType > gradient(const Point< dim > &p, const unsigned int component=0) const override
void set_function_values(const std::vector< std::function< RangeNumberType(const Point< dim > &)>> &values)
virtual RangeNumberType value(const Point< dim > &p, const unsigned int component=0) const override
std::vector< std::function< Tensor< 1, dim, RangeNumberType >const Point< dim > &)> > function_gradients
Definition: function.h:1054
FunctionFromFunctionObjects(const std::vector< std::function< RangeNumberType(const Point< dim > &)>> &values, const double initial_time=0.0)
FunctionFromFunctionObjects(const std::vector< std::function< RangeNumberType(const Point< dim > &)>> &values, const std::vector< std::function< Tensor< 1, dim, RangeNumberType >(const Point< dim > &)>> &gradients, const double initial_time=0.0)
FunctionFromFunctionObjects(const unsigned int n_components=1, const double initial_time=0)
std::vector< std::function< RangeNumberType(const Point< dim > &)> > function_values
Definition: function.h:1047
virtual void vector_gradient_list(const std::vector< Point< dim >> &points, std::vector< std::vector< Tensor< 1, dim, RangeNumberType >>> &gradients) const
static constexpr unsigned int dimension
Definition: function.h:159
Function & operator=(const Function &f)
virtual void hessian_list(const std::vector< Point< dim >> &points, std::vector< SymmetricTensor< 2, dim, RangeNumberType >> &values, const unsigned int component=0) const
virtual void vector_laplacian(const Point< dim > &p, Vector< RangeNumberType > &values) const
typename FunctionTime< typename numbers::NumberTraits< RangeNumberType >::real_type >::time_type time_type
Definition: function.h:170
virtual std::size_t memory_consumption() const
virtual Tensor< 1, dim, RangeNumberType > gradient(const Point< dim > &p, const unsigned int component=0) const
virtual void vector_gradients(const std::vector< Point< dim >> &points, std::vector< std::vector< Tensor< 1, dim, RangeNumberType >>> &gradients) const
virtual void value_list(const std::vector< Point< dim >> &points, std::vector< RangeNumberType > &values, const unsigned int component=0) const
virtual void vector_laplacian_list(const std::vector< Point< dim >> &points, std::vector< Vector< RangeNumberType >> &values) const
const unsigned int n_components
Definition: function.h:164
virtual RangeNumberType laplacian(const Point< dim > &p, const unsigned int component=0) const
virtual ~Function() override=0
virtual SymmetricTensor< 2, dim, RangeNumberType > hessian(const Point< dim > &p, const unsigned int component=0) const
Function(const unsigned int n_components=1, const time_type initial_time=0.0)
virtual void vector_hessian(const Point< dim > &p, std::vector< SymmetricTensor< 2, dim, RangeNumberType >> &values) const
virtual void vector_value_list(const std::vector< Point< dim >> &points, std::vector< Vector< RangeNumberType >> &values) const
virtual void laplacian_list(const std::vector< Point< dim >> &points, std::vector< RangeNumberType > &values, const unsigned int component=0) const
virtual void vector_hessian_list(const std::vector< Point< dim >> &points, std::vector< std::vector< SymmetricTensor< 2, dim, RangeNumberType >>> &values) const
virtual RangeNumberType value(const Point< dim > &p, const unsigned int component=0) const
virtual void vector_values(const std::vector< Point< dim >> &points, std::vector< std::vector< RangeNumberType >> &values) const
virtual void vector_value(const Point< dim > &p, Vector< RangeNumberType > &values) const
virtual void vector_gradient(const Point< dim > &p, std::vector< Tensor< 1, dim, RangeNumberType >> &gradients) const
Function(const Function &f)=default
virtual void gradient_list(const std::vector< Point< dim >> &points, std::vector< Tensor< 1, dim, RangeNumberType >> &gradients, const unsigned int component=0) const
virtual std::size_t memory_consumption() const override
virtual void vector_value_list(const std::vector< Point< dim >> &points, std::vector< Vector< RangeNumberType >> &return_values) const override
virtual void vector_gradient_list(const std::vector< Point< dim >> &points, std::vector< std::vector< Tensor< 1, dim, RangeNumberType >>> &gradients) const override
ConstantFunction(const RangeNumberType *begin_ptr, const unsigned int n_components)
virtual RangeNumberType laplacian(const Point< dim > &point, const unsigned int component=0) const override
virtual void gradient_list(const std::vector< Point< dim >> &points, std::vector< Tensor< 1, dim, RangeNumberType >> &gradients, const unsigned int component=0) const override
virtual void value_list(const std::vector< Point< dim >> &points, std::vector< RangeNumberType > &return_values, const unsigned int component=0) const override
virtual void vector_gradient(const Point< dim > &p, std::vector< Tensor< 1, dim, RangeNumberType >> &gradients) const override
ConstantFunction(const RangeNumberType value, const unsigned int n_components=1)
virtual RangeNumberType value(const Point< dim > &p, const unsigned int component=0) const override
virtual Tensor< 1, dim, RangeNumberType > gradient(const Point< dim > &p, const unsigned int component=0) const override
ConstantFunction(const std::vector< RangeNumberType > &values)
std::vector< RangeNumberType > function_value_vector
Definition: function.h:493
ConstantFunction(const Vector< RangeNumberType > &values)
virtual SymmetricTensor< 2, dim, RangeNumberType > hessian(const Point< dim > &point, const unsigned int component=0) const override
virtual void vector_value(const Point< dim > &p, Vector< RangeNumberType > &return_value) const override
virtual SymmetricTensor< 2, dim, RangeNumberType > hessian(const Point< dim > &p, const unsigned int component=0) const override
virtual RangeNumberType value(const Point< dim > &p, const unsigned int component=0) const override
virtual RangeNumberType laplacian(const Point< dim > &p, const unsigned int component=0) const override
virtual Tensor< 1, dim, RangeNumberType > gradient(const Point< dim > &p, const unsigned int component=0) const override
ZeroFunction(const unsigned int n_components=1)
Definition: point.h:111
virtual RangeNumberType value(const Point< dim > &p, const unsigned int component=0) const override
const std::function< RangeNumberType(const Point< dim > &)> function_object
Definition: function.h:826
ScalarFunctionFromFunctionObject(const std::function< RangeNumberType(const Point< dim > &)> &function_object)
Definition: tensor.h:503
const std::function< RangeNumberType(const Point< dim > &)> function_object
Definition: function.h:912
const unsigned int selected_component
Definition: function.h:918
virtual void vector_value(const Point< dim > &p, Vector< RangeNumberType > &values) const override
virtual RangeNumberType value(const Point< dim > &p, const unsigned int component=0) const override
VectorFunctionFromScalarFunctionObject(const std::function< RangeNumberType(const Point< dim > &)> &function_object, const unsigned int selected_component, const unsigned int n_components)
virtual void vector_value_list(const std::vector< Point< dim >> &points, std::vector< Vector< RangeNumberType >> &value_list) const override
virtual RangeNumberType value(const Point< dim > &p, const unsigned int component=0) const override
const TensorFunction< 1, dim, RangeNumberType > & tensor_function
Definition: function.h:1156
VectorFunctionFromTensorFunction(const TensorFunction< 1, dim, RangeNumberType > &tensor_function, const unsigned int selected_component=0, const unsigned int n_components=dim)
virtual ~VectorFunctionFromTensorFunction() override=default
virtual void vector_value(const Point< dim > &p, Vector< RangeNumberType > &values) const override
const unsigned int selected_component
Definition: function.h:1164
Definition: vector.h:109
#define DEAL_II_NAMESPACE_OPEN
Definition: config.h:458
#define DEAL_II_NAMESPACE_CLOSE
Definition: config.h:459
Point< spacedim > point(const gp_Pnt &p, const double tolerance=1e-10)
Definition: utilities.cc:189