lme4 (version 1.1-21)

GQdk: Sparse Gaussian / Gauss-Hermite Quadrature grid

Description

Generate the sparse multidimensional Gaussian quadrature grids.

Currently unused. See GHrule() for the version currently in use in package lme4.

Usage

GQdk(d = 1L, k = 1L)
  GQN

Arguments

d

integer scalar - the dimension of the function to be integrated with respect to the standard d-dimensional Gaussian density.

k

integer scalar - the order of the grid. A grid of order k provides an exact result for a polynomial of total order of 2k - 1 or less.

Value

GQdk() returns a matrix with d + 1 columns. The first column is the weights and the remaining d columns are the node coordinates.

GQN is a list of lists, containing the non-redundant quadrature nodes and weights for integration of a scalar function of a d-dimensional argument with respect to the density function of the d-dimensional Gaussian density function. The outer list is indexed by the dimension, d, in the range of 1 to 20. The inner list is indexed by k, the order of the quadrature.

Examples

# NOT RUN {
GQdk(2,5) # 53 x 3

GQN[[3]][[5]] # a 14 x 4 matrix
# }