It's pretty efficient though.
Here's the result of a crude 13 : tacitisation, resulting from replacing
all (i.x) by y, and assuming the single argument is n :
RDM1 =: (([: |. >:/~) #&(,/) ] + (1 j. ] =/ -~/~) #"1"_1 -~/~ ) @:
i. @ <:
|: RDM1 4
0 0 0 0 0 0
0 1 1 1 1 1
1 0 2 1 2 2
2 2 0 2 1 2
ts'RDM1 10'
0.000420082 216064
ts'rgfMD/9 10'
0.00145139 27264
The main overhead in mine for k=n-1 appears to be in the
makeinsert routine, even with a somewhat more efficient
use of it than in the listing I posted yesterday.I might
special-case it...
Thanks for using 1j1 in the left arg of # - if I'd ever seen
that, I'd certainly forgotten it! V useful.
Perhaps best to leave k=3, n-2, etc, to the existing codes.
I phorgot phumbs... phrom my laptop,
Mike
On 23/11/2017 09:59, Raul Miller wrote:
Well.. hmm...
Here's the heart of that k=n-1 expression:
(i.x)=/-~/~i.x)
For example:
(i.4)=/-~/~i.4
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
0 1 0 0
0 0 1 0
0 0 0 1
0 0 0 0
0 0 1 0
0 0 0 1
0 0 0 0
0 0 0 0
0 0 0 1
0 0 0 0
0 0 0 0
0 0 0 0
(As you can see, it's not incredibly efficient. It might make sense to
transform one of those dimensions into index values to gain an order
of magnitude in compactness. You do not have to worry much about index
values all 0 rows because those get compressed out later. But the
problem you would have to solve is: what do you replace the rightmost
# operation with, when working with indices? It will probably be
something like an index and ravel and then another transformation to
get the partition control list. On the positive side, this should
eliminate the need to subtrace/add the rows - which is how I am
inserting non-zero values into the final rows with that # operation.)
Anyways...
In principle you could use a similar expression with a rank-4 bit
array which a triangular plane slicing it in a similar fashion (or,
ok, maybe map that to a rank 3 array of indices). But of course, you
lose an additional order of magnitude in efficiency from the
additional array rank - though sparse arrays might help here,
depending on how the expressions work. But I've not thought up any
good expressions for constructing that array.
Thanks,
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