Package 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

All Implemented Interfaces:

DifferentialAlgebra

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

Container for a Taylor map.

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

Since:

2.2

Constructor Summary

Constructors

Constructor	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	Description
FieldTaylorMap<T>	compose(FieldTaylorMap<T> other)	Compose the instance with another Taylor map as $\mathrm{this}\circ \mathrm{other}$.
int	getFreeParameters()	Get the number of free parameters.
FieldDerivativeStructure<T>	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.
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 Details

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 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 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 $(\mathrm{\Delta }{p}_1,\mathrm{\Delta }{p}_2,\dots ,\mathrm{\Delta }{p}_n)$

Returns:

value of the Taylor expansion at $(p_1+\mathrm{\Delta }{p}_1,p_2+\mathrm{\Delta }{p}_2,\dots ,p_n+\mathrm{\Delta }{p}_n)$

value

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

Evaluate Taylor expansion of the map at some offset.

Parameters:

deltaP - parameters offsets $(\mathrm{\Delta }{p}_1,\mathrm{\Delta }{p}_2,\dots ,\mathrm{\Delta }{p}_n)$

Returns:

value of the Taylor expansion at $(p_1+\mathrm{\Delta }{p}_1,p_2+\mathrm{\Delta }{p}_2,\dots ,p_n+\mathrm{\Delta }{p}_n)$

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 $(\mathrm{\Delta }{p}_1,\mathrm{\Delta }{p}_2,\dots ,\mathrm{\Delta }{p}_n)$ which leads to evaluation offsets $(f_1+d{f}_1,f_2+d{f}_2,\dots ,f_n+d{f}_n)$. The map inversion defines a Taylor map that computes $(\mathrm{\Delta }{p}_1,\mathrm{\Delta }{p}_2,\dots ,\mathrm{\Delta }{p}_n)$ from $(d{f}_1,d{f}_2,\dots ,d{f}_n)$.

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