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