trind.generator | R Documentation |

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.

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

`K` |
positive integer determining the size of the array. |

`ifunc` |
if |

`reverse` |
should the reverse indices be computed? Probably not if |

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.

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).

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

```
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)
```

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