Generates index arrays for upper triangular storage

Description

Generates index arrays for upper triangular storage up to order four. Useful when working with higher order derivatives, which generate symmetric arrays. Mainly intended for internal use.

Usage

trind.generator(K = 2, ifunc=FALSE, reverse= !ifunc)

Arguments

Details

Suppose that m=1 and you fill an array using code like for(i in 1:K) for(j in i:K) for(k in j:K) for(l in k:K) {a[,m] <- something; m <- m+1 } and do this because actually the same "something" would be stored for any permutation of the indices i,j,k,l. Clearly in storage we have the restriction l>=k>=j>=i, but for access we want no restriction on the indices. i4[i,j,k,l] produces the appropriate m for unrestricted indices. i3 and i2 do the same for 3d and 2d arrays. If ifunc==TRUE then i2, i3 and i4 are functions, so i4(i,j,k,l) returns appropriate m. For high K the function versions save storage, but are slower.

If computed, the reverse indices pick out the unique elements of a symmetric array stored redundantly. The indices refer to the location of the elements when the redundant array is accessed as its underlying vector. For example the reverse indices for a 3 by 3 symmetric matrix are 1,2,3,5,6,9.

Value

A list where the entries i1 to i4 are arrays in up to four dimensions, containing K indexes along each dimension. If ifunc==TRUE index functions are returned in place of index arrays. If reverse==TRUE reverse indices i1r to i4r are returned (always as arrays).

Author(s)

Simon N. Wood <simon.wood@r-project.org>.

Examples

library(mgcv)
A <- trind.generator(3,reverse=TRUE)

# All permutations of c(1, 2, 3) point to the same index (5)
A$i3[1, 2, 3] 
A$i3[2, 1, 3]
A$i3[2, 3, 1]
A$i3[3, 1, 2]
A$i3[1, 3, 2]

## use reverse indices to pick out unique elements
## just for illustration...
A$i2;A$i2[A$i2r]
A$i3[A$i3r]


## same again using function indices...
A <- trind.generator(3,ifunc=TRUE)
A$i3(1, 2, 3) 
A$i3(2, 1, 3)
A$i3(2, 3, 1)
A$i3(3, 1, 2)
A$i3(1, 3, 2)