> 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
