allsubhypercubes {magic}

Subhypercubes of magic hypercubes

Description

Extracts all subhypercubes from an n-dimensional hypercube.

Usage

allsubhypercubes(a)

Arguments

a

The magic hypercube whose subhypercubes are computed

Value

Returns a list, each element of which is a subhypercube of a. Note that major diagonals are also returned (as n-by-1 arrays).

The names of the list are the extracted subhypercubes. Consider a <- magichypercube.4n(1,d=4) (so n=4) and if jj <- allsubhypercubes(a), consider jj[9]. The name of jj[9] is "n-i+1,i,i,"; its value is a square matrix. The columns of jj[9] may be recovered by a[n-i+1,i,i,] with i=1\ldots n (NB: that is, jj[[9]] == cbind(a[n-1+1,1,1,], a[n-2+1,2,2,], a[n-3+1,3,3,], a[n-4+1,4,4,]) where n=4).

The list does not include the whole array.

Note

This function is a dog's dinner. It's complicated, convoluted, and needs an absurd use of the eval(parse(text=...)) construction. Basically it sucks big time.

BUT... I cannot for the life of me see a better way that gives the same results, without loops, on hypercubes of arbitrary dimension.

On my 256MB Linuxbox, allsubhypercubes() cannot cope with d as high as 5, for n=4. Heigh ho.

The term “subhypercube” does not include diagonally oriented entities at is.magichypercube. But it does here.

Author(s)

Robin K. S. Hankin

See Also

is.perfect

Examples

  a <- magichypercube.4n(1,d=4)
  allsubhypercubes(a)