I forgot, to remove the boxes one can use:
rb=. >@:(,.&.>/)@:(,&.>/) rb A tsp B 1 2 4 7 8 14 3 12 21 4 5 16 28 20 35 6 24 42 2 4 5 8 10 16 6 15 24 8 10 20 32 25 40 12 30 48 3 6 6 9 12 18 9 18 27 12 15 24 36 30 45 18 36 54 7 8 28 49 32 56 9 36 63 14 16 35 56 40 64 18 45 72 21 24 42 63 48 72 27 54 81 (See, the same reference). On Thu, May 1, 2014 at 3:00 PM, Jose Mario Quintana < [email protected]> wrote: > This is yet another way to define the products using an idea from Victor > Cerovski (see, http://www.jsoftware.com/jwiki/Essays/Kronecker%20Product): > > u Block=. (,./^:2)@: > ,./^:2@:u > > ( kp=. */ Block ) NB. Kronecker > ,./^:2@:(*/) > ( krp=. */Block &.> ) NB. Khatri-Rao > ,./^:2@:(*/)&.> > ( tsp=. (1 0 3 |: */)Block&.>/Block ) NB. Tracy-Singh > ,./^:2@:(,./^:2@:(1 0 3 |: */)&.>/) > > A krp B > ┌─────┬─────┐ > │1 2 │12 21│ > │4 5 │24 42│ > ├─────┼─────┤ > │14 16│45 72│ > │21 24│54 81│ > └─────┴─────┘ > > A tsp B > ┌─────┬───────────┬──┬─────┐ > │1 2 │ 4 7 8 14│3 │12 21│ > │4 5 │16 28 20 35│6 │24 42│ > ├─────┼───────────┼──┼─────┤ > │ 2 4│ 5 8 10 16│ 6│15 24│ > │ 8 10│20 32 25 40│12│30 48│ > │ 3 6│ 6 9 12 18│ 9│18 27│ > │12 15│24 36 30 45│18│36 54│ > ├─────┼───────────┼──┼─────┤ > │7 8 │28 49 32 56│9 │36 63│ > ├─────┼───────────┼──┼─────┤ > │14 16│35 56 40 64│18│45 72│ > │21 24│42 63 48 72│27│54 81│ > └─────┴───────────┴──┴─────┘ > > > The Khatri-Rao and the Tracy-Singh sums do not seem difficult to implement > but I would rather wait to see concrete, inputs and outputs, examples > before trying to code them. > > > On Tue, Apr 29, 2014 at 7:03 PM, Jose Mario Quintana < > [email protected]> wrote: > >> Your definitions reproduce the examples in >> http://en.wikipedia.org/wiki/Khatri-Rao_product#Khatri-Rao_product : >> >> >> >> ( A=. (;~1 0 1) <;.1 (1+i.3 3) ) >> ┌───┬─┐ >> │1 2│3│ >> │4 5│6│ >> ├───┼─┤ >> │7 8│9│ >> └───┴─┘ >> ( B=. (;~1 1 0) <;.1 (|: 1+i.3 3) ) >> ┌─┬───┐ >> │1│4 7│ >> ├─┼───┤ >> │2│5 8│ >> │3│6 9│ >> └─┴───┘ >> krp=. */block &.> NB. Khatri-Rao product >> A krp B >> ┌─────┬─────┐ >> │1 2 │12 21│ >> │4 5 │24 42│ >> ├─────┼─────┤ >> │14 16│45 72│ >> │21 24│54 81│ >> └─────┴─────┘ >> tsp=. (1 0 3 |: */)block&.>/block NB. Tracy-Singh product >> A tsp B >> ┌─────┬───────────┬──┬─────┐ >> │1 2 │ 4 7 8 14│3 │12 21│ >> │4 5 │16 28 20 35│6 │24 42│ >> ├─────┼───────────┼──┼─────┤ >> │ 2 4│ 5 8 10 16│ 6│15 24│ >> │ 8 10│20 32 25 40│12│30 48│ >> │ 3 6│ 6 9 12 18│ 9│18 27│ >> │12 15│24 36 30 45│18│36 54│ >> ├─────┼───────────┼──┼─────┤ >> │7 8 │28 49 32 56│9 │36 63│ >> ├─────┼───────────┼──┼─────┤ >> │14 16│35 56 40 64│18│45 72│ >> │21 24│42 63 48 72│27│54 81│ >> └─────┴───────────┴──┴─────┘ >> >> >> >> They are impressive! >> >> >> On Tue, Apr 29, 2014 at 4:32 PM, Raul Miller <[email protected]>wrote: >> >>> If I understand properly: >>> >>> Hadamard product is * >>> >>> Kroneker product is ([:,/[:,./"3*/) >>> >>> Or, >>> >>> block=: 1 : '[:,/[:,./"3 u' >>> */ block >>> >>> There are of course other ways of defining this. >>> >>> Khatri-Rao product is A */block &.> B and works on a matrix of boxed >>> matrices >>> >>> Tracy-Sigh product is (1 0 3 |: */)block&.>/block and also works on a >>> matrix of boxed matrices >>> >>> Vector cross product gets interesting because it is typically defined on >>> 3 >>> element vectors and there are at least two very distinct ways of >>> generalizing that to vectors of other lengths. >>> >>> Anyways, the paper sounds interesting, and I'd like a copy if it's not >>> too >>> much trouble. >>> >>> Thanks, >>> >>> -- >>> Raul >>> >>> On Tue, Apr 29, 2014 at 3:17 PM, mikel paternain <[email protected] >>> >wrote: >>> >>> > In a excellet review paper (see below [1]) Shuangzhe Liu & Götz >>> Trenkler >>> > show some results on matrix products: >>> > >>> > - Hadamard product >>> > - Kroneker product >>> > - Khatri-Rao product >>> > - Tracy-Sigh product >>> > - Khatri-Rao sum >>> > - Tracy-Sigh sum >>> > - Vector cross productSchur complement, etc. >>> > >>> > With this thread, we intend to create a collaborative work to find the >>> > J-expressions that meet these products and sums. >>> > If you want to collaborate, these will be published in next issue of >>> > Journal of J (deadline May-31) >>> > Thanks in advance, >>> > Mikel >>> > JoJ >>> > >>> > >>> ----------------------------------------------------------------------------------------------------------------- >>> > [1] There is a free version on the webif you can not find it, we can >>> send >>> > you a copy >>> > >>> > HADAMARD, KHATRI-RAO, KRONECKER AND OTHER MATRIX PRODUCTS >>> > Shuangzhe Liu & Götz Trenkler >>> > International Journal of Infornation ans Systems Sciences >>> > Vol. 4, N. 1, 160-177 >>> > >>> > >>> > ---------------------------------------------------------------------- >>> > For information about J forums see http://www.jsoftware.com/forums.htm >>> > >>> ---------------------------------------------------------------------- >>> For information about J forums see http://www.jsoftware.com/forums.htm >>> >> >> > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
