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 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

    • getNbParameters

      @Deprecated 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 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: