org.hipparchus.analysis.differentiation

Class FieldTaylorMap<T extends CalculusFieldElement<T>>

java.lang.Object

org.hipparchus.analysis.differentiation.FieldTaylorMap<T>

Type Parameters:

T - the type of the function parameters and value

public class FieldTaylorMap<T extends CalculusFieldElement<T>>
extends Object

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 and Description
FieldTaylorMap(Field<T> valueField, int parameters, int order, int nbFunctions) Constructor for identity map.
FieldTaylorMap(T[] point, FieldDerivativeStructure<T>[] functions) Simple constructor.

Method Summary

Modifier and Type	Method and Description
FieldTaylorMap<T>	compose(FieldTaylorMap<T> other) Compose the instance with another Taylor map as \(\mathrm{this} \circ \mathrm{other}\).
FieldDerivativeStructure<T>	getFunction(int i) Get a function from the map.
int	getNbFunctions() Get the number of functions of the map.
int	getNbParameters() Get the number of parameters of the map.
T[]	getPoint() Get the point at which map is evaluated.
FieldTaylorMap<T>	invert(FieldMatrixDecomposer<T> decomposer) Invert the instance.
T[]	value(double... deltaP) Evaluate Taylor expansion of the map at some offset.
T[]	value(T... 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 Detail

FieldTaylorMap

public FieldTaylorMap(T[] point,
                      FieldDerivativeStructure<T>[] 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)

FieldTaylorMap

public FieldTaylorMap(Field<T> valueField,
                      int parameters,
                      int order,
                      int nbFunctions)

Constructor for identity map.

The identity is considered to be evaluated at origin.

Parameters:

valueField - field for the function parameters and value

parameters - number of free parameters

order - derivation order

nbFunctions - number of functions

Method Detail

getNbParameters

public int getNbParameters()

Get the number of parameters of the map.

Returns:

number of parameters of the map

getNbFunctions

public int getNbFunctions()

Get the number of functions of the map.

Returns:

number of functions of the map

getPoint

public T[] getPoint()

Get the point at which map is evaluated.

Returns:

point at which map is evaluated

getFunction

public FieldDerivativeStructure<T> 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 T[] 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 \((p_1 + \Delta p_1, p_2 + \Delta p_2, \ldots, p_n + \Delta p_n)\)

value

public T[] value(T... 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 FieldTaylorMap<T> compose(FieldTaylorMap<T> 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 FieldTaylorMap<T> invert(FieldMatrixDecomposer<T> 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