Re: [functional approach should give] an even faster way to normalize

*To*: mathgroup at smc.vnet.net*Subject*: [mg85696] Re: [functional approach should give] an even faster way to normalize*From*: Szabolcs Horvát <szhorvat at gmail.com>*Date*: Tue, 19 Feb 2008 02:04:15 -0500 (EST)*Organization*: University of Bergen*References*: <fp9945$199$1@smc.vnet.net> <47B841CA.9020908@gmail.com>

Szabolcs Horvát wrote: > congruentialuminaire at yahoo.com wrote: >> Hello UG: >> >> I have a 512x512 array of 3-tuples. I want to make any tuple with a >> value outside of 0 <--> 1, become {0.,0.,0.}. >> >> The first version has this loop: >> >> For[i = 1, i <= graphSize, i++, >> For[j = 1, j <= graphSize, j++, >> If[((sum[[i, j, 1]] < 0) || (sum[[i, j, 1]] > 1) || >> (sum[[i, j, 2]] < 0) || (sum[[i, j, 2]] > 1) || >> (sum[[i, j, 3]] < 0) || (sum[[i, j, 3]] > 1)), >> sum[[i, j]] = {0., 0., 0.} >> ] >> ] >> ]; > > Please don't use For[] for iteration. It is so ugly and unreadable. :-( > Use Do[] instead, which does exactly the same thing, and doesn't even > need to be nested. > >> >> After scratching my head for a while I came up with this (equivalent) >> Map statement. >> >> sum = Map[ >> If[#[[1]] < 0 || #[[1]] > 1 || #[[2]] < 0 || #[[2]] > 1 || #[[3]] < >> 0 || #[[3]] > 1, {0., 0., 0.}, #] &, sum, {2}]; >> >> It is faster but only by about 15%. >> >> It is unreasonable to believe some other construction can accomplish >> this with a bigger payoff? > > Try this: > > Clip[data, {0, 1}] /. 1 -> 0; // Timing > > (Note the space between /. and 1 !!) > > On my computer (which has a Pentium-M processor) the For[] version takes > 3.8 s, the Map[] version ~0.9 s, and the Clip[] version ~0.5 s. But > please understand that *any* timing less than a few seconds is > completely unreliable (especially with Mathematica's Timing[] on a > Windows platform). So all that these results tell us is that the Map[] > version is surely a few times faster than For[]. But please don't make > quantitative conclusions about the performance of the Clip[] version vs > the Map[] version. > What I forgot to mention is that the Clip[] version is really limited by ReplaceAll[] and not Clip[]. It should have been calles replace-version instead.