gtsam::FourierBasis Class Reference

Fourier basis. More...

#include <Fourier.h>

Inheritance diagram for gtsam::FourierBasis:

Collaboration diagram for gtsam::FourierBasis:

Public Types
using	Parameters = Eigen::Matrix< double, -1, 1 >
using	DiffMatrix = 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 DiffMatrix	DifferentiationMatrix (size_t N)
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 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.

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

N	The degree of the polynomial to use.
x	The point at which to compute the derivaive weights.

Returns

Weights

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

N	The degree of the polynomial to use.
x	The point at which to compute the weights.
a	Lower bound of interval.
b	Upper bound of interval.

Returns

Weights

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

N	The degree of the polynomial to use.
x	The point at which to compute the derivaive weights.

Returns

Weights

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

N	The degree of the polynomial to use.
x	The point at which to compute the derivaive weights.
a	Lower bound of interval.
b	Upper bound of interval.

Returns

Weights

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'.

WeightMatrix() [1/2]

static Matrix gtsam::Basis< FourierBasis >::WeightMatrix ( size_t  N, const Vector &  X  )

inlinestaticinherited

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]

static Matrix gtsam::Basis< FourierBasis >::WeightMatrix ( size_t  N, const Vector &  X, double  a, double  b  )

inlinestaticinherited

Calculate weights for all x in vector X, with interval [a,b].

Parameters

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.

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

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