1 // -*- C++ -*-
2 /**
3 * @brief Chebychev polynomial factory
4 *
5 * Copyright 2005-2021 Airbus-EDF-IMACS-ONERA-Phimeca
6 *
7 * This library is free software: you can redistribute it and/or modify
8 * it under the terms of the GNU Lesser General Public License as published by
9 * the Free Software Foundation, either version 3 of the License, or
10 * (at your option) any later version.
11 *
12 * This library is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 * GNU Lesser General Public License for more details.
16 *
17 * You should have received a copy of the GNU Lesser General Public License
18 * along with this library. If not, see <http://www.gnu.org/licenses/>.
19 *
20 */
21 #include "openturns/ChebychevFactory.hxx"
22 #include "openturns/PersistentObjectFactory.hxx"
23 #include "openturns/Arcsine.hxx"
24 #include "openturns/Exception.hxx"
25
26 BEGIN_NAMESPACE_OPENTURNS
27
28 CLASSNAMEINIT(ChebychevFactory)
29
30 static const Factory<ChebychevFactory> Factory_ChebychevFactory;
31
32 /* Default constructor */
ChebychevFactory()33 ChebychevFactory::ChebychevFactory()
34 : OrthogonalUniVariatePolynomialFactory(Arcsine(-1.0, 1.0))
35 {
36 initializeCache();
37 }
38
39 /* Virtual constructor */
clone() const40 ChebychevFactory * ChebychevFactory::clone() const
41 {
42 return new ChebychevFactory(*this);
43 }
44
45
46 /* Calculate the coefficients of recurrence a0n, a1n, a2n such that
47 Pn+1(x) = (a0n * x + a1n) * Pn(x) + a2n * Pn-1(x) */
getRecurrenceCoefficients(const UnsignedInteger n) const48 ChebychevFactory::Coefficients ChebychevFactory::getRecurrenceCoefficients(const UnsignedInteger n) const
49 {
50 Coefficients recurrenceCoefficients(3, 0.0);
51 if (n == 0)
52 {
53 recurrenceCoefficients[0] = M_SQRT2;
54 return recurrenceCoefficients;
55 }
56 recurrenceCoefficients[0] = 2.0;
57 if (n == 1)
58 {
59 recurrenceCoefficients[2] = -M_SQRT2;
60 return recurrenceCoefficients;
61 }
62 recurrenceCoefficients[2] = -1.0;
63 return recurrenceCoefficients;
64 }
65
66 /* Roots of the polynomial of degree n */
getRoots(const UnsignedInteger n) const67 Point ChebychevFactory::getRoots(const UnsignedInteger n) const
68 {
69 Point roots(n);
70 for (UnsignedInteger i = 0; i < n; ++i)
71 roots[i] = std::cos((i + 0.5) * M_PI / n);
72 return roots;
73 }
74
75 /* Nodes and weights of the polynomial of degree n as the eigenvalues of the associated Jacobi matrix and the square
76 of the first component of the associated normalized eigenvectors */
getNodesAndWeights(const UnsignedInteger n,Point & weights) const77 Point ChebychevFactory::getNodesAndWeights(const UnsignedInteger n,
78 Point & weights) const
79 {
80 if (n == 0) throw InvalidArgumentException(HERE) << "Error: cannot compute the roots and weights of a constant polynomial.";
81 weights = Point(n, 1.0 / n);
82 return getRoots(n);
83 }
84
85 /* String converter */
__repr__() const86 String ChebychevFactory::__repr__() const
87 {
88 return OSS() << "class=" << getClassName()
89 << " measure=" << measure_;
90 }
91
92
93 END_NAMESPACE_OPENTURNS
94