Public Types | Static Public Member Functions | Public Attributes | List of all members
gtsam::Chebyshev1Basis Struct Reference

#include <Chebyshev.h>

Inheritance diagram for gtsam::Chebyshev1Basis:
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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

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
NDegree of the polynomial.
xPoint to evaluate polynomial at.
aLower limit of polynomial (default=-1).
bUpper 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
NDegree of the polynomial.
xPoint to evaluate polynomial at.
aLower limit of polynomial (default=-1).
bUpper 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:


gtsam
Author(s):
autogenerated on Fri Nov 1 2024 03:51:13