Class FieldTaylorMap<T extends CalculusFieldElement<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 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