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.

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 N1 (N values) More...


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) 
 Calculate weights for all x in vector X. More...


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...


static double  Derivative (double x, const Vector &p, OptionalJacobian< 1, 1 > H=boost::none) 


using  Parameters = Eigen::Matrix< double, 1, 1 > 

◆ 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 N1 (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()
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 premultiplied to the polynomial Parameters.
From Wikipedia we have D[T_n(x),x] = n*U_{n1}(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 N1 Note that it has one less weight.
The Parameters pertain to 1st kind chebs up to order N1 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
The documentation for this struct was generated from the following files: