gtsam 4.1.1 gtsam
gtsam::FourierBasis Class Reference

## Detailed Description

Fourier basis.

Inheritance diagram for gtsam::FourierBasis:

## 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. 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. More...

static DiffMatrix DifferentiationMatrix (size_t N)
Compute D = differentiation matrix. 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 Public Member Functions inherited from gtsam::Basis< FourierBasis >
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)

## Public Types

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

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

## ◆ 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'.

The documentation for this class was generated from the following file:
• /Users/dellaert/git/github/gtsam/basis/Fourier.h