Generate the sparse multidimensional Gaussian quadrature grids.
Currently unused. See
GHrule() for the version
currently in use in package lme4.
GQdk(d = 1L, k = 1L) GQN
integer scalar - the dimension of the function
to be integrated with respect to the standard
integer scalar - the order of the grid. A grid
GQdk() returns a matrix with
d + 1 columns. The first
column is the weights and the remaining
d columns are the
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
the order of the quadrature.
GQN contains only the non-redundant nodes. To regenerate
the whole array of nodes, all possible permutations of
axes and all possible combinations of
must be applied to the axes. This entire array of nodes is exactly
The number of nodes gets very large very quickly with
k. See the charts at
GQdk(2,5) # 53 x 3 GQN[][] # a 14 x 4 matrix
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