Package org.hipparchus.analysis.differentiation

Class DerivativeStructure

  • All Implemented Interfaces:
    Serializable, Derivative<DerivativeStructure>, DifferentialAlgebra, CalculusFieldElement<DerivativeStructure>, FieldElement<DerivativeStructure>
    public class DerivativeStructure
extends Object
implements Derivative<DerivativeStructure>, Serializable
    Class representing both the value and the differentials of a function.

    This class is the workhorse of the differentiation package.

    This class is an implementation of the extension to Rall's numbers described in Dan Kalman's paper Doubly Recursive Multivariate Automatic Differentiation, Mathematics Magazine, vol. 75, no. 3, June 2002. Rall's numbers are an extension to the real numbers used throughout mathematical expressions; they hold the derivative together with the value of a function. Dan Kalman's derivative structures hold all partial derivatives up to any specified order, with respect to any number of free parameters. Rall's numbers therefore can be seen as derivative structures for order one derivative and one free parameter, and real numbers can be seen as derivative structures with zero order derivative and no free parameters.

    DerivativeStructure instances can be used directly thanks to the arithmetic operators to the mathematical functions provided as methods by this class (+, -, *, /, %, sin, cos ...).

    Implementing complex expressions by hand using Derivative-based classes (or in fact any CalculusFieldElement class) is a tedious and error-prone task but has the advantage of not requiring users to compute the derivatives by themselves and allowing to switch for one derivative implementation to another as they all share the same filed API.

    Implementing complex expression can also be done by developing computation code using standard primitive double values and to use differentiators to create the DerivativeStructure-based instances. This method is simpler but may be limited in the accuracy and derivation orders and may be computationally intensive (this is typically the case for finite differences differentiator.

    Instances of this class are guaranteed to be immutable.

    See Also:
    DSCompiler, FieldDerivativeStructure, Serialized Form