GQdk {lme4}  R Documentation 
Sparse Gaussian / GaussHermite 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

k 
integer scalar  the order of the grid. A grid
of order 
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
nonredundant 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.
Note
GQN
contains only the nonredundant nodes. To regenerate
the whole array of nodes, all possible permutations of
axes and all possible combinations of \pm 1
must be applied to the axes. This entire array of nodes is exactly
what GQdk()
reproduces.
The number of nodes gets very large very quickly with
increasing d
and k
. See the charts at
http://www.sparsegrids.de.
Examples
GQdk(2,5) # 53 x 3
GQN[[3]][[5]] # a 14 x 4 matrix