gtsam 4.2.0
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Chebyshev2.h
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1/* ----------------------------------------------------------------------------
2
3 * GTSAM Copyright 2010, Georgia Tech Research Corporation,
4 * Atlanta, Georgia 30332-0415
5 * All Rights Reserved
6 * Authors: Frank Dellaert, et al. (see THANKS for the full author list)
7
8 * See LICENSE for the license information
9
10 * -------------------------------------------------------------------------- */
11
33#pragma once
34
35#include <gtsam/base/Manifold.h>
37#include <gtsam/basis/Basis.h>
38
39namespace gtsam {
40
46class GTSAM_EXPORT Chebyshev2 : public Basis<Chebyshev2> {
47 public:
48 EIGEN_MAKE_ALIGNED_OPERATOR_NEW
49
50 using Base = Basis<Chebyshev2>;
51 using Parameters = Eigen::Matrix<double, /*Nx1*/ -1, 1>;
52 using DiffMatrix = Eigen::Matrix<double, /*NxN*/ -1, -1>;
53
55 static double Point(size_t N, int j) {
56 assert(j >= 0 && size_t(j) < N);
57 const double dtheta = M_PI / (N > 1 ? (N - 1) : 1);
58 // We add -PI so that we get values ordered from -1 to +1
59 // sin(- M_PI_2 + dtheta*j); also works
60 return cos(-M_PI + dtheta * j);
61 }
62
64 static double Point(size_t N, int j, double a, double b) {
65 assert(j >= 0 && size_t(j) < N);
66 const double dtheta = M_PI / (N - 1);
67 // We add -PI so that we get values ordered from -1 to +1
68 return a + (b - a) * (1. + cos(-M_PI + dtheta * j)) / 2;
69 }
70
72 static Vector Points(size_t N) {
73 Vector points(N);
74 for (size_t j = 0; j < N; j++) points(j) = Point(N, j);
75 return points;
76 }
77
79 static Vector Points(size_t N, double a, double b) {
80 Vector points = Points(N);
81 const double T1 = (a + b) / 2, T2 = (b - a) / 2;
82 points = T1 + (T2 * points).array();
83 return points;
84 }
85
94 static Weights CalculateWeights(size_t N, double x, double a = -1,
95 double b = 1);
96
101 static Weights DerivativeWeights(size_t N, double x, double a = -1,
102 double b = 1);
103
108 static DiffMatrix DifferentiationMatrix(size_t N, double a = -1,
109 double b = 1);
110
129 static Weights IntegrationWeights(size_t N, double a = -1, double b = 1);
130
134 template <size_t M>
135 static Matrix matrix(std::function<Eigen::Matrix<double, M, 1>(double)> f,
136 size_t N, double a = -1, double b = 1) {
137 Matrix Xmat(M, N);
138 for (size_t j = 0; j < N; j++) {
139 Xmat.col(j) = f(Point(N, j, a, b));
140 }
141 return Xmat;
142 }
143}; // \ Chebyshev2
144
145} // namespace gtsam
Base class and basic functions for Manifold types.
Special class for optional Jacobian arguments.
Compute an interpolating basis.
Global functions in a separate testing namespace.
Definition chartTesting.h:28
CRTP Base class for function bases.
Definition Basis.h:100
Chebyshev Interpolation on Chebyshev points of the second kind Note that N here, the number of points...
Definition Chebyshev2.h:46
static double Point(size_t N, int j)
Specific Chebyshev point.
Definition Chebyshev2.h:55
static double Point(size_t N, int j, double a, double b)
Specific Chebyshev point, within [a,b] interval.
Definition Chebyshev2.h:64
static Vector Points(size_t N)
All Chebyshev points.
Definition Chebyshev2.h:72
static Vector Points(size_t N, double a, double b)
All Chebyshev points, within [a,b] interval.
Definition Chebyshev2.h:79
static Matrix matrix(std::function< Eigen::Matrix< double, M, 1 >(double)> f, size_t N, double a=-1, double b=1)
Create matrix of values at Chebyshev points given vector-valued function.
Definition Chebyshev2.h:135