#include <Chebyshev.h>
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using | Parameters = Eigen::Matrix< double, -1, 1 > |
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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...
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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...
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static Matrix | WeightMatrix (size_t N, const Vector &X) |
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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...
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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.
◆ CalculateWeights()
static Weights gtsam::Chebyshev1Basis::CalculateWeights |
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size_t |
N, |
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double |
x, |
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double |
a = -1 , |
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double |
b = 1 |
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) |
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static |
Evaluate Chebyshev Weights on [-1,1] at x up to order N-1 (N values)
- Parameters
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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::Chebyshev1Basis::DerivativeWeights |
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size_t |
N, |
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double |
x, |
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double |
a = -1 , |
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double |
b = 1 |
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) |
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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.
- Parameters
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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]
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]
Calculate weights for all x in vector X, with interval [a,b].
- Parameters
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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.
The documentation for this struct was generated from the following file:
- /home/docs/checkouts/readthedocs.org/user_builds/gtsam-jlblanco-docs/checkouts/latest/gtsam/basis/Chebyshev.h