Your solution is very elegant.
Perhaps the following is (a bit) more efficient (untested).
tA =: (3 2,:3 2)<;._3 A
tB =: (2 3,:2 3)<;._3 B
tA (([:,:~ {.@[ , {:@] )&(_2{. $@:>) <;.3 (+/ . *)&([:;,.L:0/"1)) tB
+--------------+--------------+
| 330 345 360| 375 390 405|
| 870 921 972|1023 1074 1125|
|1410 1497 1584|1671 1758 1845|
+--------------+--------------+
|1950 2073 2196|2319 2442 2565|
|2490 2649 2808|2967 3126 3285|
|3030 3225 3420|3615 3810 4005|
+--------------+--------------+
R.E. Boss
-----Oorspronkelijk bericht-----
Van: [email protected]
[mailto:[email protected]] Namens Marshall Lochbaum
Verzonden: dinsdag 8 november 2011 0:11
Aan: Programming forum
Onderwerp: Re: [Jprogramming] matrix multiplication (modeling in CUDA for a GPU)
If we look at the block matrices, what we want is a matrix product on
these, but with the operations of matrix addition and multiplication
instead of the regular + and * . Thus, we can replace + and * in +/ .* with
the corresponding +&.> and +/ .*&.> for boxed matrices, so
mp =. +/ .*
blockmp =. +&.>/ . (+/ .*&.>)
B=:A =: i.6 6
B mp A
330 345 360 375 390 405
870 921 972 1023 1074 1125
1410 1497 1584 1671 1758 1845
1950 2073 2196 2319 2442 2565
2490 2649 2808 2967 3126 3285
3030 3225 3420 3615 3810 4005
tA =: (2 2,:2 2)<;._3 A
tB =: (2 2,:2 2)<;._3 B
tA blockmp tB
┌─────────┬─────────┬─────────┐
│330 345 │360 375 │ 390 405│
│870 921 │972 1023 │1074 1125│
├─────────┼─────────┼─────────┤
│1410 1497│1584 1671│1758 1845│
│1950 2073│2196 2319│2442 2565│
├─────────┼─────────┼─────────┤
│2490 2649│2808 2967│3126 3285│
│3030 3225│3420 3615│3810 4005│
└─────────┴─────────┴─────────┘
tA =: (2 6,:2 6)<;._3 A
tB =: (6 2,:6 2)<;._3 B
tA blockmp tB
┌─────────┬─────────┬─────────┐
│330 345 │360 375 │ 390 405│
│870 921 │972 1023 │1074 1125│
├─────────┼─────────┼─────────┤
│1410 1497│1584 1671│1758 1845│
│1950 2073│2196 2319│2442 2565│
├─────────┼─────────┼─────────┤
│2490 2649│2808 2967│3126 3285│
│3030 3225│3420 3615│3810 4005│
└─────────┴─────────┴─────────┘
tA =: (3 2,:3 2)<;._3 A
tB =: (2 3,:2 3)<;._3 B
tA blockmp tB
┌──────────────┬──────────────┐
│ 330 345 360│ 375 390 405│
│ 870 921 972│1023 1074 1125│
│1410 1497 1584│1671 1758 1845│
├──────────────┼──────────────┤
│1950 2073 2196│2319 2442 2565│
│2490 2649 2808│2967 3126 3285│
│3030 3225 3420│3615 3810 4005│
└──────────────┴──────────────┘
All give the same product.
Marshall
On Mon, Nov 7, 2011 at 6:01 PM, Ric Sherlock <[email protected]> wrote:
> Basically the ( , ) is getting around the issue that Raul has nicely
> described - we want to turn the shape of the boxes into a simple list
>
> u&v applies the verb v to x and y before running x u y
> i.e. x u&v y <==> (v x) u (v y)
>
> where u =: +/ .*&.>/
> and v =: ,
>
> The last ( / ) is the dyadic form - Table [1] and applies each cell of
> x to the whole of y
> An alternative formulation that does the same thing is:
> (,tA) +/ .*&.>"0 _ (,tB)
>
> [1] http://www.jsoftware.com/docs/help701/dictionary/d420.htm
>
> On Tue, Nov 8, 2011 at 11:17 AM, Jan Jacobs <[email protected]>
> wrote:
> > Wow, that is exactly what I wanted, it is "equivalent" with +/ . *
> > applied the unpartitioned matrices A and B.
> > Can you explain why you've added /&, ?
> > Thanks for the help!
> >
> > On Mon, Nov 7, 2011 at 9:50 PM, Ric Sherlock <[email protected]> wrote:
> >> or did you want
> >> tA +/ .*&.>/&, tB
> >> ┌─────────┬─────────┬─────────┐
> >> │330 345 │360 375 │ 390 405│
> >> │870 921 │972 1023 │1074 1125│
> >> ├─────────┼─────────┼─────────┤
> >> │1410 1497│1584 1671│1758 1845│
> >> │1950 2073│2196 2319│2442 2565│
> >> ├─────────┼─────────┼─────────┤
> >> │2490 2649│2808 2967│3126 3285│
> >> │3030 3225│3420 3615│3810 4005│
> >> └─────────┴─────────┴─────────┘
> >>
> >>
> >> On Tue, Nov 8, 2011 at 9:40 AM, Ric Sherlock <[email protected]> wrote:
> >>> (,tA) +/ .*&.> (,tB)
> >>>
> >>> On Tue, Nov 8, 2011 at 9:09 AM, Jan Jacobs <[email protected]>
> wrote:
> >>>> ls,
> >>>> for educational purposes I want to breakdown a CUDA matrix
> >>>> multiplication in smaller parts.
> >>>> What I do not understand is that for B=:A =: i.6 6
> >>>> tA =: (2 2,:2 2)<;._3 A
> >>>> tB =: (2 2,:2 2)<;._3 B
> >>>> tA (+/ . *)&.> tB
> >>>> works fine, but
> >>>> tA =: (2 6,:2 6)<;._3 A
> >>>> tB =: (6 2,:6 2)<;._3 B
> >>>> tA (+/ . *)&.> tB
> >>>> does not:
> >>>> |length error
> >>>> | tA (+/ .*)"1&.>tB
> >>>>
> >>>> The shapes of the various boxes are as expected.
> >>>> What is going wrong?
> >>>> Thanks in advance for the help.
> >>>> Jan.
> >>>>
> >>>>
> >>>> --
> >>>> Jan Jacobs
> >>>> Esdoornstraat 33
> >>>> 5995AN Kessel
> >>>> W: www.sommaps.com
> >>>> T: +31 77 462 1887
> >>>> M: +31 6 23 82 55 21
> >>>> E: [email protected]
> >>>> ----------------------------------------------------------------------
> >>>> For information about J forums see
> http://www.jsoftware.com/forums.htm
> >>>>
> >>>
> >> ----------------------------------------------------------------------
> >> For information about J forums see http://www.jsoftware.com/forums.htm
> >
> >
> >
> > --
> > Jan Jacobs
> > Esdoornstraat 33
> > 5995AN Kessel
> > W: www.sommaps.com
> > T: +31 77 462 1887
> > M: +31 6 23 82 55 21
> > E: [email protected]
> > ----------------------------------------------------------------------
> > For information about J forums see http://www.jsoftware.com/forums.htm
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
>
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