Ok, but, these look different to me: (i. 250000 2) + reduceS 1 2 3 4 62499750001 62500000002 62499750003 62500000004 (i. 250000 2) + reduceC [ 1 2 3 4 62499750001 62500000002 3 4 (i. 250000 4) + reduceC [ 1 2 3 4 124999500001 124999750002 125000000003 125000250004
But, sure, if we only care about a description of the operation, as opposed to the results they generate, I suppose there is some kind of equivalence here. Thanks, -- Raul On Thu, Feb 25, 2016 at 7:04 PM, Pascal Jasmin <[email protected]> wrote: > all of the expressions sum 250001 rows of 4. Some of the expressions > manipulate the x side to create 4 item rows. That all of the timings are > nearly equivalent shows that such manipulations are relatively fast native > operations. Its a major improvement compared to the only way I knew how to > compute such expressions prior to today. > > > 15 timespacex '(i. 250000 ) + reduceS 1 2 3 4' > 0.0179739 1.88783e7 > > > 10 timespacex '(i. 250000 ) + reduce 1 2 3 4' > 0.125398 4.03457e7 > > 3 timespacex '(i. 250000 ) + reducE 1 2 3 4' > 0.282656 2.10458e6 > > > (i.10) + reduceS i.4 > 45 46 47 48 > > ----- Original Message ----- > From: Raul Miller <[email protected]> > To: Programming forum <[email protected]> > Sent: Thursday, February 25, 2016 6:45 PM > Subject: Re: [Jprogramming] reduce revisited > > These timings, for the most part, are not comparable. > > You have four expressions and three different results. So only two of > the four timings can be meaningfully compared. > > -- > Raul > > > On Thu, Feb 25, 2016 at 5:49 PM, Pascal Jasmin <[email protected]> wrote: >>> 5 timespacex ' +/ (i. 250000 4), 1 2 3 4' >>> 0.0200582 2.51692e7 >>> 5 timespacex '(i. 250000 2) + reduceS 1 2 3 4' >>> 0.0205952 2.51699e7 >> >> for that first expression, there are no fills, but 1m cells appended. >> >> the 2nd expression (equal speed) does 250000 row reshapes >> >> >> >>> 5 timespacex '(i. 250000 2) + reduceC [ 1 2 3 4' >> 0.0224864 2.517e7 >> >> >> this expression fills with 0s each row of x. >> >>> 5 timespacex '(i. 250000 4) + reduceC [ 1 2 3 4' >> 0.019306 2.517e7 >> >> >> equivalent to first expression. No fills needed. Should be just as fast. >> >> >> ____ >> But wouldn't timings involving reduce-with-fill depend on how much >> fill needs to get generated? >> >> Thanks, >> >> >> >> On Thu, Feb 25, 2016 at 4:51 PM, Pascal Jasmin <[email protected]> >> wrote: >>> a couple of implementations I have posted before for u/ when x items and >>> initial y are of different shape. >>> >>> reduce =: 1 : '<"_1@[ ([: u (&.>)/(>@:) ,) <@:]' >>> reducE =: 1 : (':'; 'o=. y for_i. x do. o =. i u o end.') >>> >>> reducE is explicit, and left to right. reduce boxes each side, and uses >>> the same right to >>> left order as /. reduce is 2-3x faster for + >>> >>> There's an even faster method, but before I mention it, I'd like to go over >>> how the rank 0 operators work in J >>> >>> (1 + 1 2 3 4) -: 1 1 1 1 + 1 2 3 4 >>> >>> `a scalar u"0 a_larger_shape` gets expanded to match the larger shape, and >>> its result is identical to the operation with the "pre-expanded" shape. >>> >>> 1 2 + 1 2 3 4 is rank error. >>> >>> But there are a couple of obvious expansions that would not create an error >>> >>> 1 2 1 2 + 1 2 3 4 or >>> 1 2 0 0 + 1 2 3 4 >>> >>> note that this is not an error >>> >>> 1 2 + i.2 2 but the result (with shape ommitted) is identical to >>> >>> >>> 1 1 2 2 + 0 1 2 3 >>> >>> The new reduce adverb is at its core a conjunction. Where one of its verbs >>> is how to expand the x items such that they are similar (or compatible) >>> shape to y. >>> >>> reduceC =: 2 : 'u/@:(v , ])' >>> reduceS =: reduceC ($@] $"1 _1 [) >>> >>> reduceS is an adverb that generically expands (i.2 2) + reduceS 1 2 3 4 to >>> >>> +/ 0 1 0 1 , 2 3 2 3 ,: 1 2 3 4 >>> >>> which may be better than an error, but is unusual, and so the conjunction >>> version is useful to taylor the expansion as you prefer. >>> >>> some custom applied conjunctions >>> >>> reduceC ($@] {.!._"1 _1 [) NB. take with fill set to _ to match shape of y. >>> reduceC ($@] {. 2 # [) NB. expand 1 2 to 1 1 2 2, >>> >>> NB. but make sure there are 4 items (end matches shape of y) >>> >>> 5 timespacex ' +/ (i. 250000 4), 1 2 3 4' >>> 0.0200582 2.51692e7 >>> 5 timespacex '(i. 250000 2) + reduceS 1 2 3 4' >>> 0.0205952 2.51699e7 >>> 5 timespacex '(i. 250000 2) + reduceC (2 #"1 [) 1 2 3 4' >>> 0.0231547 2.51707e7 >>> >>> 5 timespacex '(i. 250000 2) + reduce 2 2 $ 1 2 3 4' >>> 0.134078 4.66376e7 >>> >>> >>> 5 timespacex '(i. 1000000) + reduce 1 2' >>> 0.563169 1.61364e8 >>> 5 timespacex '(i. 1000000) + reduceS 1 2' >>> 0.0407191 4.1947e7 >>> >>> >>> >>> another technique that is pretty funny how its fast, but works well >>> especially when y is a string, and x is not, is to convert everything to >>> strings (using linear representations of x, lets you have x items with >>> widely varying shapes) >>> >>> NB. swaps 2 items described by x in y. >>> amV =: (0 {:: [)`(1 {:: [)`]} >>> >>> swap =: (((0 { [) ;~ ] {~ 1 { [) amV ] amV~ (1 { [) ;~ ] {~ 0 { [) >>> >>> >>> timespacex '(52 | i. 2000 2) swap reduce Alpha_j_' >>> 0.0180793 412160 >>> >>> timespacex '(":("1) 52 | i. 2000 2) (".@[ swap ])/ Alpha_j_' >>> 0.00243008 2.32998e6 >>> >>> timespacex '(52 | i. 2000 2) swap reduceC ([) i.52' >>> 0.0193757 2.2007e6 >>> >>> a [ for v argument to reduceC is same as prepending to y and letting it >>> fill. The swap function accesses x parameters by index and so it is >>> harmless to expand it. >>> ---------------------------------------------------------------------- >>> 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 > ---------------------------------------------------------------------- > 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
