Package org.hipparchus.analysis.differentiation

This package holds the main interfaces and basic building block classes dealing with differentiation. The core class is DerivativeStructure which holds the value and the differentials of a function. This class handles some arbitrary number of free parameters and arbitrary differentiation order. It is used both as the input and the output type for the UnivariateDifferentiableFunction interface. Any differentiable function should implement this interface.

The UnivariateDerivative1, UnivariateDerivative2 and Gradient classes are more restricted implementation of classes holding the value and the differentials of a function. These classes handle only either one free parameter (i.e. univariate functions) with derivation orders 1 or 2, or several free parameters with derivation order 1. As they arefar less general than DerivativeStructure, they have less overhead and are more efficient in their respective domains.

The UnivariateFunctionDifferentiator interface defines a way to differentiate a simple UnivariateFunction and get a UnivariateDifferentiableFunction.

Similar interfaces also exist for multivariate functions and for vector or matrix valued functions.

Interface Summary

Interface	Description
Derivative<T extends CalculusFieldElement<T>>	Interface representing both the value and the differentials of a function.
FieldDerivative<S extends CalculusFieldElement<S>,T extends FieldDerivative<S,T>>	Interface representing both the value and the differentials of a function.
MultivariateDifferentiableFunction	Extension of MultivariateFunction representing a multivariate differentiable real function.
MultivariateDifferentiableVectorFunction	Extension of MultivariateVectorFunction representing a multivariate differentiable vectorial function.
UnivariateDifferentiableFunction	Interface for univariate functions derivatives.
UnivariateDifferentiableMatrixFunction	Extension of UnivariateMatrixFunction representing a univariate differentiable matrix function.
UnivariateDifferentiableVectorFunction	Extension of UnivariateVectorFunction representing a univariate differentiable vectorial function.
UnivariateFunctionDifferentiator	Interface defining the function differentiation operation.
UnivariateMatrixFunctionDifferentiator	Interface defining the function differentiation operation.
UnivariateVectorFunctionDifferentiator	Interface defining the function differentiation operation.

Class Summary

Class	Description
DerivativeStructure	Class representing both the value and the differentials of a function.
DSCompiler	Class holding "compiled" computation rules for derivative structures.
DSFactory	Factory for DerivativeStructure.
DSFactory.DSField	Field for {link DerivativeStructure} instances.
FDSFactory<T extends CalculusFieldElement<T>>	Factory for FieldDerivativeStructure.
FDSFactory.DerivativeField<T extends CalculusFieldElement<T>>	Field for {link FieldDerivativeStructure} instances.
FieldDerivativeStructure<T extends CalculusFieldElement<T>>	Class representing both the value and the differentials of a function.
FieldGradient<T extends CalculusFieldElement<T>>	Class representing both the value and the differentials of a function.
FieldGradientField<T extends CalculusFieldElement<T>>	Field for Gradient instances.
FieldTaylorMap<T extends CalculusFieldElement<T>>	Container for a Taylor map.
FieldUnivariateDerivative<S extends CalculusFieldElement<S>,T extends FieldUnivariateDerivative<S,T>>	Abstract class representing both the value and the differentials of a function.
FieldUnivariateDerivative1<T extends CalculusFieldElement<T>>	Class representing both the value and the differentials of a function.
FieldUnivariateDerivative1Field<T extends CalculusFieldElement<T>>	Field for FieldUnivariateDerivative1 instances.
FieldUnivariateDerivative2<T extends CalculusFieldElement<T>>	Class representing both the value and the differentials of a function.
FieldUnivariateDerivative2Field<T extends CalculusFieldElement<T>>	Field for FieldUnivariateDerivative2 instances.
FiniteDifferencesDifferentiator	Univariate functions differentiator using finite differences.
Gradient	Class representing both the value and the differentials of a function.
GradientField	Field for Gradient instances.
GradientFunction	Class representing the gradient of a multivariate function.
JacobianFunction	Class representing the Jacobian of a multivariate vector function.
SparseGradient	First derivative computation with large number of variables.
TaylorMap	Container for a Taylor map.
UnivariateDerivative<T extends UnivariateDerivative<T>>	Abstract class representing both the value and the differentials of a function.
UnivariateDerivative1	Class representing both the value and the differentials of a function.
UnivariateDerivative1Field	Field for UnivariateDerivative1 instances.
UnivariateDerivative2	Class representing both the value and the differentials of a function.
UnivariateDerivative2Field	Field for UnivariateDerivative2 instances.