Re: Timing of looping operators

*To*: mathgroup at smc.vnet.net*Subject*: [mg62426] Re: [mg62416] Timing of looping operators*From*: Sseziwa Mukasa <mukasa at jeol.com>*Date*: Thu, 24 Nov 2005 06:33:24 -0500 (EST)*References*: <200511230931.EAA20248@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On Nov 23, 2005, at 4:31 AM, dh wrote: > Hello, > The Mathematica gospel tells you that you should NOT use loops because > it is inefficient. > Well consider the following examples and their times: > > n=10^6; > d=Table[i,{i,n}]; > fun[x_]:=x; > > a) Timing[fun & /@ d;] needs 0.8 sec > b) Timing[Scan[fun, d]] needs 1 second > c) Timing[Do[f[i], {i, n}];] needs 0.7 sec > > a) applies the function and creates a new list. b) does not create > a new > list -- but it is slower! And finally c) the loop is fastest!!! > > If you change the function to: f[x_]:=x^2, the times are even more > striking: > > 0.8, 2.4, 0.7 > it seems like in a and c the function evaluation takes negliable time > compared to the loop construct, but not so in b. > > has anybody an explanation??? I don't have an explanation but a couple of observations: - When I execute expression a more than once it takes about the same amount of time as expression c after the first execution, the first execution takes longest. This behavior leads me to believe that something large is being cached which was created the first time. - These tests are not equivalent, b and c are relatively similar in that they do nothing but evaluate f. Expression a creates a list which is then be discarded, my guess is the initial time penalty is for the time to make the storage for the result. Once this memory is allocated it can be reused whenever an object of similar size is needed, which may explain the cache like behavior noted in my first point. - If you reverse the order of the timing statements so that expression c is evaluated before a, a actually executes faster than c and faster than if a is executed before c. Again this leads me to believe that what we are seeing is related to Mathematica's pattern of memory usage and is not an accurate assessment of compute time. In short, without access to the actual implementation of Mathematica it is impossible to definitively determine how compute and memory resources are actually being used by these expressions. The behavior of Scan is curious but it may mean little more than that Scan is more complicated internally than a naive implementation: Map with no storage allocation, would indicate. At any rate the behavior of the expressions and the fact that the timing is dependent on the number of times they are executed as well as the order of execution indicates that Mathematica is optimizing the expressions, most likely for memory usage, and thus one cannot infer much about their computational efficiency. I should make clear that I executed all of the Timing statements in one cell. I'm sure the behavior would be yet again different if I executed each in its own cell. Regards, Ssezi

**References**:**Timing of looping operators***From:*dh <dh@metrohm.ch>

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