Subhypercubes of magic hypercubes
Extracts all subhypercubes from an n-dimensional hypercube.
allsubhypercubes(a)
a |
The magic hypercube whose subhypercubes are computed |
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...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.
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.
Robin K. S. Hankin
a <- magichypercube.4n(1,d=4) allsubhypercubes(a)
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