# 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 $$(f_1, f_2, \ldots, f_n)$$ depending on m parameters $$(p_1, p_2, \ldots, p_m)$$, with positive n and m.

Since:
2.2
• ## Constructor Summary

Constructors
Constructor
Description
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
getNbParameters()
Deprecated.
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
• ### getNbParameters

public int getNbParameters()
Deprecated.
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  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  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  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