trind.generator 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)

Arguments

K	positive integer determining the size of the array.

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.

Value

A list where the entries i1 to i4 are arrays in up to four dimensions, containing K indexes along each dimension.

Author(s)

Simon N. Wood <[email protected]>.

Examples

library(mgcv)
A <- trind.generator(3)

# 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]