#include <Chebyshev.h>

Inheritance diagram for gtsam::Chebyshev1Basis:

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

static Weights	DerivativeWeights (size_t N, double x, double a=-1, double b=1)
	Evaluate Chebyshev derivative at x. The derivative weights are pre-multiplied to the polynomial Parameters. More...

Static Public Member Functions inherited from gtsam::Basis< Chebyshev1Basis >
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...

Public Attributes
Parameters	parameters_

Detailed Description

Basis of Chebyshev polynomials of the first kind https://en.wikipedia.org/wiki/Chebyshev_polynomials#First_kind These are typically denoted with the symbol T_n, where n is the degree. The parameter N is the number of coefficients, i.e., N = n+1.

Definition at line 32 of file Chebyshev.h.

Member Typedef Documentation

◆ Parameters

using gtsam::Chebyshev1Basis::Parameters = Eigen::Matrix<double, -1, 1 >

Definition at line 33 of file Chebyshev.h.

Member Function Documentation

◆ CalculateWeights()

Weights gtsam::Chebyshev1Basis::CalculateWeights	(	size_t	N,
		double	x,
		double	a = `-1`,
		double	b = `1`
	)

static

Evaluate Chebyshev Weights on [-1,1] at 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 39 of file Chebyshev.cpp.

◆ DerivativeWeights()

Weights gtsam::Chebyshev1Basis::DerivativeWeights	(	size_t	N,
		double	x,
		double	a = `-1`,
		double	b = `1`
	)

static

Evaluate Chebyshev derivative at x. The derivative weights are pre-multiplied to the polynomial Parameters.

From Wikipedia we have D[T_n(x),x] = n*U_{n-1}(x) I.e. the derivative fo a first kind cheb is just a second kind cheb So, we define a second kind basis here of order N-1 Note that it has one less weight.

The Parameters pertain to 1st kind chebs up to order N-1 But of course the first one (order 0) is constant, so omit that weight.

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 54 of file Chebyshev.cpp.

Member Data Documentation

◆ parameters_

Parameters gtsam::Chebyshev1Basis::parameters_

Definition at line 35 of file Chebyshev.h.

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

Public Types

Static Public Member Functions

Public Attributes