gtsam::Chebyshev2Basis Struct Reference

#include <Chebyshev.h>

Inheritance diagram for gtsam::Chebyshev2Basis:

Collaboration 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 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.

Member Function Documentation

CalculateWeights()

static 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).

DerivativeWeights()

static 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

WeightMatrix() [1/2]

static Matrix gtsam::Basis< Chebyshev2Basis >::WeightMatrix ( size_t  N, const Vector &  X  )

inlinestaticinherited

Calculate weights for all x in vector X. Returns M*N matrix where M is the size of the vector X, and N is the number of basis functions.

WeightMatrix() [2/2]

static Matrix gtsam::Basis< Chebyshev2Basis >::WeightMatrix ( size_t  N, const Vector &  X, double  a, double  b  )

inlinestaticinherited

Calculate weights for all x in vector X, with interval [a,b].

Parameters

N	The number of basis functions.
X	The vector for which to compute the weights.
a	The lower bound for the interval range.
b	The upper bound for the interval range.

Returns

Returns M*N matrix where M is the size of the vector X.

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

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