Reference documentation for deal.II version 9.5.0
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polynomials_integrated_legendre_sz.cc
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1// ---------------------------------------------------------------------
2//
3// Copyright (C) 2015 - 2021 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
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.
13//
14// ---------------------------------------------------------------------
15
16
18
20
22 : Polynomials::Polynomial<double>(get_coefficients(k))
23{}
24
25
26
27const std::vector<double>
29{
30 std::vector<double> coefficients(k + 1);
31
32 // first two polynomials are hard-coded:
33 if (k == 0)
34 {
35 coefficients[0] = -1.;
36 return coefficients;
37 }
38 else if (k == 1)
39 {
40 coefficients[0] = 0.;
41 coefficients[1] = 1.;
42 return coefficients;
43 }
44
45 // General formula is:
46 // k*L_{k}(x) = (2*k-3)*x*L_{k-1} - (k-3)*L_{k-2}.
47 std::vector<double> coefficients_km2 = get_coefficients(k - 2);
48 std::vector<double> coefficients_km1 = get_coefficients(k - 1);
49
50 const double a = 1.0 / k;
51 const double b = 2.0 * k - 3.0;
52 const double c = k - 3.0;
53
54 // To maintain stability, delay the division (multiplication by a) until the
55 // end.
56 for (unsigned int i = 1; i <= k - 2; ++i)
57 {
58 coefficients[i] = b * coefficients_km1[i - 1] - c * coefficients_km2[i];
59 }
60
61 coefficients[0] = -c * coefficients_km2[0];
62 coefficients[k] = b * coefficients_km1[k - 1];
63 coefficients[k - 1] = b * coefficients_km1[k - 2];
64
65 for (double &coefficient : coefficients)
66 {
67 coefficient *= a;
68 }
69
70 return coefficients;
71}
72
73
74
75std::vector<Polynomials::Polynomial<double>>
77{
78 std::vector<Polynomials::Polynomial<double>> v;
79 v.reserve(degree + 1);
80 for (unsigned int i = 0; i <= degree; ++i)
81 {
82 v.push_back(IntegratedLegendreSZ(i));
83 }
84 return v;
85}
86
87
88
static std::vector< Polynomials::Polynomial< double > > generate_complete_basis(const unsigned int degree)
static const std::vector< double > get_coefficients(const unsigned int k)
std::vector< double > coefficients
Definition polynomial.h:302
unsigned int degree() const
Definition polynomial.h:800
#define DEAL_II_NAMESPACE_OPEN
Definition config.h:472
#define DEAL_II_NAMESPACE_CLOSE
Definition config.h:473