Package org.hipparchus.analysis.differentiation

Class TaylorMap

java.lang.Object

org.hipparchus.analysis.differentiation.TaylorMap

All Implemented Interfaces:

DifferentialAlgebra

public class TaylorMap
extends Object
implements DifferentialAlgebra

Container for a Taylor map.

A Taylor map is a set of n DerivativeStructure \((f_1, f_2, \ldots, f_n)\) depending on m parameters \((p_1, p_2, \ldots, p_m)\), with positive n and m.

Since:

2.2

Constructor Summary

Constructors

Constructor	Description
TaylorMap(double[] point, DerivativeStructure[] functions)	Simple constructor.
TaylorMap(int parameters, int order, int nbFunctions)	Constructor for identity map.

Method Summary

Modifier and Type	Method	Description
TaylorMap	compose(TaylorMap other)	Compose the instance with another Taylor map as \(\mathrm{this} \circ \mathrm{other}\).
int	getFreeParameters()	Get the number of free parameters.
DerivativeStructure	getFunction(int i)	Get a function from the map.
int	getNbFunctions()	Get the number of functions of the map.
int	getOrder()	Get the maximum derivation order.
double[]	getPoint()	Get the point at which map is evaluated.
TaylorMap	invert(MatrixDecomposer decomposer)	Invert the instance.
double[]	value(double... deltaP)	Evaluate Taylor expansion of the map at some offset.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

TaylorMap

public TaylorMap(double[] point,
 DerivativeStructure[] functions)

Simple constructor.

The number of number of parameters and derivation orders of all functions must match.

Parameters:

point - point at which map is evaluated

functions - functions composing the map (must contain at least one element)

TaylorMap

public TaylorMap(int parameters,
 int order,
 int nbFunctions)

Constructor for identity map.

The identity is considered to be evaluated at origin.

Parameters:

parameters - number of free parameters

order - derivation order

nbFunctions - number of functions

Method Details

getFreeParameters

public int getFreeParameters()

Get the number of free parameters.

Specified by:

getFreeParameters in interface DifferentialAlgebra

Returns:

number of free parameters

getOrder

public int getOrder()

Get the maximum derivation order.

Specified by:

getOrder in interface DifferentialAlgebra

Returns:

maximum derivation order

getNbFunctions

public int getNbFunctions()

Get the number of functions of the map.

Returns:

number of functions of the map

getPoint

public double[] getPoint()

Get the point at which map is evaluated.

Returns:

point at which map is evaluated

getFunction

public DerivativeStructure getFunction(int i)

Get a function from the map.

Parameters:

i - index of the function (must be between 0 included and getNbFunctions() excluded

Returns:

function at index i

value

public double[] value(double... deltaP)

Evaluate Taylor expansion of the map at some offset.

Parameters:

deltaP - parameters offsets \((\Delta p_1, \Delta p_2, \ldots, \Delta p_n)\)

Returns:

value of the Taylor expansion at \((p_1 + \Delta p_1, p_2 + \Delta p_2, \ldots, p_n + \Delta p_n)\)

compose

public TaylorMap compose(TaylorMap other)

Compose the instance with another Taylor map as \(\mathrm{this} \circ \mathrm{other}\).

Parameters:

other - map with which instance must be composed

Returns:

composed map \(\mathrm{this} \circ \mathrm{other}\)

invert

public TaylorMap invert(MatrixDecomposer decomposer)

Invert the instance.

Consider Taylor expansion of the map with small parameters offsets \((\Delta p_1, \Delta p_2, \ldots, \Delta p_n)\) which leads to evaluation offsets \((f_1 + df_1, f_2 + df_2, \ldots, f_n + df_n)\). The map inversion defines a Taylor map that computes \((\Delta p_1, \Delta p_2, \ldots, \Delta p_n)\) from \((df_1, df_2, \ldots, df_n)\).

The map must be square to be invertible (i.e. the number of functions and the number of parameters in the functions must match)

Parameters:

decomposer - matrix decomposer to user for inverting the linear part

Returns:

inverted map

See Also:

• chapter 2 of Advances in Imaging and Electron Physics, vol 108 by Martin Berz