Optimizationhessian Method

ILNumerics Ultimate VS Documentation

ILNumerics - Technical Application Development

Numerical approximation of the hessian of func at position x through Ridders' method of polynomial extrapolation and a finite differences algorithm

[ILNumerics Optimization Toolbox]

Namespace: ILNumerics.Toolboxes
Assembly: ILNumerics.Toolboxes.Optimization (in ILNumerics.Toolboxes.Optimization.dll) Version: 5.5.0.0 (5.5.7503.3146)

Syntax

Copy

public static RetArray<double> hessian(
	OptimizationObjectiveFunction<double> func,
	InArray<double> x,
	InArray<double> fx = null
)

Public Shared Function hessian ( 
	func As OptimizationObjectiveFunction(Of Double),
	x As InArray(Of Double),
	Optional fx As InArray(Of Double) = Nothing
) As RetArray(Of Double)

Dim func As OptimizationObjectiveFunction(Of Double)
Dim x As InArray(Of Double)
Dim fx As InArray(Of Double)
Dim returnValue As RetArray(Of Double)

returnValue = Optimization.hessian(func, 
	x, fx)

Parameters

func: Type: ILNumerics.ToolboxesOptimizationObjectiveFunctionDouble
Scalar function defined from Rⁿ to R
x: Type: ILNumericsInArrayDouble
Vector giving the position of evaluation in Rⁿ
fx (Optional): Type: ILNumericsInArrayDouble
[optional] Result of evaluating func at x, default: null

Return Value

Type: RetArrayDouble
An array of dimension x.Length X x.Length

Exceptions

Exception	Condition
ArgumentNullException	If x is null
ArgumentOutOfRangeException	If f is not defined at x or if f has values in R ⁿ, for n>1

Remarks

If one of the input arrays is empty, an empty array will be returned. This is better for C² functions

[ILNumerics Optimization Toolbox]

Examples

Copy

ObjectiveFunction<double> polynom = x => norm(x, 1) + 1;
Array<double> C = Optimization.hessian(polynom, ones<double>(2, 1));

Reference

Optimization Class

ILNumerics.Toolboxes Namespace

Other Resources

http://ilnumerics.net/ilnumerics-optimization-toolbox.html

OptimizationAddLanguageSpecificTextSet("LSTD93C25F8_0?cpp=::|nu=.");hessian Method

Parameters

Return Value

Reference

Other Resources

Optimizationhessian Method