#include <Chebyshev.h>
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_ |
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.
using gtsam::Chebyshev1Basis::Parameters = Eigen::Matrix<double, -1, 1 > |
Definition at line 33 of file Chebyshev.h.
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static |
Evaluate Chebyshev Weights on [-1,1] at x up to order N-1 (N values)
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.
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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.
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 54 of file Chebyshev.cpp.
Parameters gtsam::Chebyshev1Basis::parameters_ |
Definition at line 35 of file Chebyshev.h.