Reference documentation for deal.II version GIT c415589cf0 2022-08-14 18:50:02+00:00
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polynomials_piecewise.h
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15 
16 #ifndef dealii_polynomials_piecewise_h
17 #define dealii_polynomials_piecewise_h
18 
19 
20 
21 #include <deal.II/base/config.h>
22 
24 #include <deal.II/base/point.h>
27 
28 #include <vector>
29 
31 
41 namespace Polynomials
42 {
63  template <typename number>
65  {
66  public:
78  PiecewisePolynomial(const Polynomial<number> &coefficients_on_interval,
79  const unsigned int n_intervals,
80  const unsigned int interval,
81  const bool spans_next_interval);
82 
89  PiecewisePolynomial(const std::vector<Point<1, number>> &points,
90  const unsigned int index);
91 
98  number
99  value(const number x) const;
100 
115  void
116  value(const number x, std::vector<number> &values) const;
117 
133  void
134  value(const number x,
135  const unsigned int n_derivatives,
136  number * values) const;
137 
142  unsigned int
143  degree() const;
144 
150  template <class Archive>
151  void
152  serialize(Archive &ar, const unsigned int version);
153 
157  virtual std::size_t
158  memory_consumption() const;
159 
160  protected:
166 
171  unsigned int n_intervals;
172 
177  unsigned int interval;
178 
184 
189  std::vector<number> points;
190 
195  std::vector<number> one_over_lengths;
196 
201  unsigned int index;
202  };
203 
204 
205 
211  std::vector<PiecewisePolynomial<double>>
213  const unsigned int n_subdivisions,
214  const unsigned int base_degree);
215 
220  std::vector<PiecewisePolynomial<double>>
222  const std::vector<Point<1>> &points);
223 
224 } // namespace Polynomials
225 
226 
229 /* -------------------------- inline functions --------------------- */
230 
231 namespace Polynomials
232 {
233  template <typename number>
234  inline unsigned int
236  {
237  if (points.size() > 0)
238  return 1;
239  return polynomial.degree();
240  }
241 
242 
243 
244  template <typename number>
245  inline number
247  {
248  if (points.size() > 0)
249  {
250  if (x > points[index])
251  return std::max<number>(0.0,
252  1.0 - (x - points[index]) *
253  one_over_lengths[index]);
254  else if (x < points[index])
255  return std::max<number>(0.0,
256  0.0 + (x - points[index - 1]) *
257  one_over_lengths[index - 1]);
258  else
259  return 1.0;
260  }
261 
262  AssertIndexRange(interval, n_intervals);
263  number y = x;
264  // shift polynomial if necessary
265  if (n_intervals > 1)
266  {
267  const number step = 1. / n_intervals;
268 
269  // polynomial spans over two intervals
270  if (spans_two_intervals == true)
271  {
272  const number offset = step * interval;
273  if (x < offset)
274  return 0;
275  else if (x > offset + step + step)
276  return 0;
277  else if (x < offset + step)
278  y = x - offset;
279  else
280  y = offset + step + step - x;
281  }
282  else
283  {
284  const number offset = step * interval;
285  if (x < offset || x > offset + step)
286  return 0;
287  else
288  y = x - offset;
289  }
290 
291  return polynomial.value(y);
292  }
293  else
294  return polynomial.value(x);
295  }
296 
297 
298 
299  template <typename number>
300  template <class Archive>
301  inline void
302  PiecewisePolynomial<number>::serialize(Archive &ar, const unsigned int)
303  {
304  // forward to serialization function in the base class.
305  ar &static_cast<Subscriptor &>(*this);
306  ar &polynomial;
307  ar &n_intervals;
308  ar &interval;
309  ar &spans_two_intervals;
310  ar &points;
311  ar &one_over_lengths;
312  ar &index;
313  }
314 } // namespace Polynomials
315 
317 
318 #endif
Definition: point.h:111
PiecewisePolynomial(const Polynomial< number > &coefficients_on_interval, const unsigned int n_intervals, const unsigned int interval, const bool spans_next_interval)
void serialize(Archive &ar, const unsigned int version)
number value(const number x) const
virtual std::size_t memory_consumption() const
#define DEAL_II_NAMESPACE_OPEN
Definition: config.h:442
#define DEAL_II_NAMESPACE_CLOSE
Definition: config.h:443
#define AssertIndexRange(index, range)
Definition: exceptions.h:1732
std::vector< PiecewisePolynomial< double > > generate_complete_linear_basis_on_subdivisions(const std::vector< Point< 1 >> &points)
std::vector< PiecewisePolynomial< double > > generate_complete_Lagrange_basis_on_subdivisions(const unsigned int n_subdivisions, const unsigned int base_degree)