Reference documentation for deal.II version 9.5.0
Searching...
No Matches
polynomials_bernstein.cc
Go to the documentation of this file.
1// ---------------------------------------------------------------------
2//
3// Copyright (C) 2004 - 2018 by the deal.II authors
4//
5// This file is part of the deal.II library.
6//
7// The deal.II library is free software; you can use it, redistribute
8// it, and/or modify it under the terms of the GNU Lesser General
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.
13//
14// ---------------------------------------------------------------------
15
17
18#include <boost/math/special_functions/binomial.hpp>
19
20#include <vector>
21
23
24namespace
25{
26 template <typename number>
27 std::vector<number>
28 get_bernstein_coefficients(const unsigned int k, const unsigned int n)
29 {
30 Assert(n > 0,
31 ExcMessage("Bernstein polynomial needs to be of degree > 0."));
32 AssertIndexRange(k, n + 1);
33 std::vector<number> coeff(n + 1, number(0.0));
34 for (unsigned int i = k; i < n + 1; ++i)
35 {
36 coeff[i] = ((i - k) % 2 == 0 ? 1 : -1) *
37 boost::math::binomial_coefficient<number>(n, i) *
38 boost::math::binomial_coefficient<number>(i, k);
39 }
40 return coeff;
41 }
42} // namespace
43
44template <typename number>
46 const unsigned int degree)
47 : Polynomials::Polynomial<number>(
48 get_bernstein_coefficients<number>(index, degree))
49{}
50
51
52#include "polynomials_bernstein.inst"
53
PolynomialsBernstein(const unsigned int index, const unsigned int degree)
#define DEAL_II_NAMESPACE_OPEN
Definition config.h:472
#define DEAL_II_NAMESPACE_CLOSE
Definition config.h:473
#define Assert(cond, exc)
#define AssertIndexRange(index, range)
static ::ExceptionBase & ExcMessage(std::string arg1)