Public Types | Static Public Member Functions | List of all members
gtsam::FourierBasis Class Reference

Fourier basis. More...

#include <Fourier.h>

Inheritance diagram for gtsam::FourierBasis:
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Public Types

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

Static Public Member Functions

static Weights CalculateWeights (size_t N, double x)
 Evaluate Real Fourier Weights of size N in interval [a, b], e.g. N=5 yields bases: 1, cos(x), sin(x), cos(2*x), sin(2*x) More...
 
static Weights CalculateWeights (size_t N, double x, double a, double b)
 Evaluate Real Fourier Weights of size N in interval [a, b], e.g. N=5 yields bases: 1, cos(x), sin(x), cos(2*x), sin(2*x) More...
 
static Weights DerivativeWeights (size_t N, double x)
 Get weights at a given x that calculate the derivative. More...
 
static Weights DerivativeWeights (size_t N, double x, double a, double b)
 Get derivative weights at a given x that calculate the derivative, in the interval [a, b]. More...
 
static DiffMatrix DifferentiationMatrix (size_t N)
 
- Static Public Member Functions inherited from gtsam::Basis< FourierBasis >
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

Fourier basis.

Definition at line 27 of file Fourier.h.

Member Typedef Documentation

◆ DiffMatrix

Definition at line 30 of file Fourier.h.

◆ Parameters

Definition at line 29 of file Fourier.h.

Member Function Documentation

◆ CalculateWeights() [1/2]

static Weights gtsam::FourierBasis::CalculateWeights ( size_t  N,
double  x 
)
inlinestatic

Evaluate Real Fourier Weights of size N in interval [a, b], e.g. N=5 yields bases: 1, cos(x), sin(x), cos(2*x), sin(2*x)

Parameters
NThe degree of the polynomial to use.
xThe point at which to compute the derivaive weights.
Returns
Weights

Definition at line 40 of file Fourier.h.

◆ CalculateWeights() [2/2]

static Weights gtsam::FourierBasis::CalculateWeights ( size_t  N,
double  x,
double  a,
double  b 
)
inlinestatic

Evaluate Real Fourier Weights of size N in interval [a, b], e.g. N=5 yields bases: 1, cos(x), sin(x), cos(2*x), sin(2*x)

Parameters
NThe degree of the polynomial to use.
xThe point at which to compute the weights.
aLower bound of interval.
bUpper bound of interval.
Returns
Weights

Definition at line 64 of file Fourier.h.

◆ DerivativeWeights() [1/2]

static Weights gtsam::FourierBasis::DerivativeWeights ( size_t  N,
double  x 
)
inlinestatic

Get weights at a given x that calculate the derivative.

Parameters
NThe degree of the polynomial to use.
xThe point at which to compute the derivaive weights.
Returns
Weights

Definition at line 92 of file Fourier.h.

◆ DerivativeWeights() [2/2]

static Weights gtsam::FourierBasis::DerivativeWeights ( size_t  N,
double  x,
double  a,
double  b 
)
inlinestatic

Get derivative weights at a given x that calculate the derivative, in the interval [a, b].

Parameters
NThe degree of the polynomial to use.
xThe point at which to compute the derivaive weights.
aLower bound of interval.
bUpper bound of interval.
Returns
Weights

Definition at line 106 of file Fourier.h.

◆ DifferentiationMatrix()

static DiffMatrix gtsam::FourierBasis::DifferentiationMatrix ( size_t  N)
inlinestatic

Compute D = differentiation matrix. Given coefficients c of a Fourier series c, D*c are the values of c'.

Definition at line 73 of file Fourier.h.


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


gtsam
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autogenerated on Tue Jul 4 2023 02:46:19