You must supply this method to evaluate the elements

H_{i j} = \frac{\partial^{2} F}{\partial x_{i} \partial x_{j}}

of the matrix of second derivatives of

F (x)

at any point

x

. It should be tested separately before being used in conjunction with e04ly (see the E04 class).

Syntax

C#
public delegate void E04LY_HESS2( int n, double[] xc, double[] heslc, double[] hesdc )

Visual Basic
Public Delegate Sub E04LY_HESS2 ( _ n As Integer, _ xc As Double(), _ heslc As Double(), _ hesdc As Double() _ )

Visual C++
public delegate void E04LY_HESS2( int n, array<double>^ xc, array<double>^ heslc, array<double>^ hesdc )

F#
type E04LY_HESS2 = delegate of n : int * xc : float[] * heslc : float[] * hesdc : float[] -> unit

xc: Type: array<System..::..Double>[]()[][]
On entry: the point $x$ at which the derivatives are required.

heslc: Type: array<System..::..Double>[]()[][]
On exit: hess2 must place the strict lower triangle of the second derivative matrix $H$ in heslc, stored by rows, i.e., set $heslc [(i - 1) (i - 2) / 2 + j - 1] = \frac{\partial^{2} F}{\partial x_{i} \partial x_{j}}$ , for $i = 2, 3, \dots, n$ and $j = 1, 2, \dots, i - 1$ . (The upper triangle is not required because the matrix is symmetric.)

hesdc: Type: array<System..::..Double>[]()[][]
On exit: must contain the diagonal elements of the second derivative matrix, i.e., set $hesdc [j - 1] = \frac{\partial^{2} F}{\partial x_{j}^{2}}$ , for $j = 1, 2, \dots, n$ .

See Also