generateGrid2: Generate grid points for Hessians

In pnd: Parallel Numerical Derivatives, Gradients, Jacobians, and Hessians of Arbitrary Accuracy Order

Generate grid points for Hessians

Description

Creates a list of unique evaluation points for second derivatives: both diagonal (\partial^2 / \partial x_i^2) and cross (\partial^2 / \partial x_i \partial x_j).

Usage

generateGrid2(x, side, acc.order, h)

Arguments

x	Numeric vector or scalar: the point(s) at which the derivative is estimated. FUN(x) must be finite.
side	Integer scalar or vector indicating the type of finite difference: 0 for central, 1 for forward, and -1 for backward differences. Central differences are recommended unless computational cost is prohibitive.
acc.order	Integer or vector of integers specifying the desired accuracy order for each element of x. The final error will be of the order O(h^{\mathrm{acc.order}}).
h	Numeric or character specifying the step size(s) for the numerical difference or a method of automatic step determination ("CR", "CRm", "DV", or "SW" to be used in gradstep()). The default value is described in ?GenD.

Value

A list with elements:

• xlist: a list of unique coordinate shifts,

• w: the finite-difference weights (one per point),

• i1, i2: integer vectors giving partial-derivative indices.

The length of each vector matches xlist.

See Also

GenD(), Hessian().

Examples

generateGrid2(1:4, side = rep(0, 4), acc.order = c(2, 6, 4, 2),
              h = c(1e-5, 1e-4, 2e-5, 1e-6))

pnd documentation built on Sept. 9, 2025, 5:44 p.m.