#include <Chebyshev.h>

Inheritance diagram for gtsam::Chebyshev2Basis:

Public Types
using	Parameters = Eigen::Matrix< double, -1, 1 >

Static Public Member Functions
static Weights	CalculateWeights (size_t N, double x, double a=-1, double b=1)

static Weights	DerivativeWeights (size_t N, double x, double a=-1, double b=1)
	Evaluate Chebyshev derivative at x. More...

Static Public Member Functions inherited from gtsam::Basis< Chebyshev2Basis >
static Matrix	WeightMatrix (size_t N, const Vector &X)

static Matrix	WeightMatrix (size_t N, const Vector &X, double a, double b)
	Calculate weights for all x in vector X, with interval [a,b]. More...

Detailed Description

Basis of Chebyshev polynomials of the second kind. https://en.wikipedia.org/wiki/Chebyshev_polynomials#Second_kind These are typically denoted with the symbol U_n, where n is the degree. The parameter N is the number of coefficients, i.e., N = n+1. In contrast to the templates in Chebyshev2, the classes below specify basis functions, weighted combinations of which are used to approximate functions. In this sense, they are like the sines and cosines of the Fourier basis.

Definition at line 80 of file Chebyshev.h.

Member Typedef Documentation

◆ Parameters

using gtsam::Chebyshev2Basis::Parameters = Eigen::Matrix<double, -1, 1 >

Definition at line 81 of file Chebyshev.h.

Member Function Documentation

◆ CalculateWeights()

Weights gtsam::Chebyshev2Basis::CalculateWeights	(	size_t	N,
		double	x,
		double	a = `-1`,
		double	b = `1`
	)

static

Evaluate Chebyshev Weights on [-1,1] at any x up to order N-1 (N values).

Parameters

N	Degree of the polynomial.
x	Point to evaluate polynomial at.
a	Lower limit of polynomial (default=-1).
b	Upper limit of polynomial (default=1).

Definition at line 64 of file Chebyshev.cpp.

◆ DerivativeWeights()

Weights gtsam::Chebyshev2Basis::DerivativeWeights	(	size_t	N,
		double	x,
		double	a = `-1`,
		double	b = `1`
	)

static

Evaluate Chebyshev derivative at x.

Parameters

N	Degree of the polynomial.
x	Point to evaluate polynomial at.
a	Lower limit of polynomial (default=-1).
b	Upper limit of polynomial (default=1).

Returns: Weights

Definition at line 79 of file Chebyshev.cpp.

The documentation for this struct was generated from the following files: