MtxIntDiff.NumericGradRichardson Function

Numerical gradient by high precision numerical differentiation.

Pascal

procedure NumericGradRichardson(Fun: TRealFunction; const Pars: TVec; const Consts: TVec; const ObjConst: Array of TObject; const Grad: TVec);

File

MtxIntDiff

Parameters

Parameters	Description
Fun	Real function of several variables.
Pars	Function variables.
Consts	Array of additional constants which can be used in math formula.
ObjConst	Array of additional constants (pointers) which can be used in math formula.
Grad	Returns calculated gradient. If needed, Grad Length and Complex properties are adjusted automatically.

Description

Calculates the numerical gradient by high precision numerical differentiation. The algorithm uses Richardson extrapolation of three values of the symmetric difference quotient. The gradient step size is defined by GradStepSize global variable. Normally the optimal stepsize depends on seventh partial derivatives of the function. Since they are not available, the initial value for GradientStepSize is Exp(Ln(EPS)/7)*0.25, as suggested by Spellucci.