unexpected Timing results

*To*: mathgroup at smc.vnet.net*Subject*: [mg115826] unexpected Timing results*From*: gleam at flashmail.com*Date*: Fri, 21 Jan 2011 04:35:57 -0500 (EST)

I experienced a couple of rather unexpected timing results today that I am hoping can be explained to me. In Mathematica 7.0.1: ragged = RandomInteger[1*^6, #] &~Array~1000; Do[PadLeft[ragged], {50}] // Timing Do[PadLeft[ragged, {1000, 1000}], {50}] // Timing Do[PadLeft[#, 1000] & /@ ragged, {50}] // Timing {4.422, Null} {4.406, Null} {0.344, Null} This difference I did not anticipate. I suppose this has something to do with packed arrays, but I do not understand why the upper two forms do not handle the task at least as well as the third one. I expected a function that can be applied at the top level to be faster that way, than when manually mapped. Now, truly baffling to me is this: padded = PadLeft[#, 1000] & /@ ragged; Do[Accumulate[padded], {800}] // Timing Do[Map[Accumulate, padded, {0}], {800}] // Timing {5.109, Null} {4.188, Null} Should not these forms be identical, other than a slight overhead for the Map function? How can Map[f, x, {0}] be faster than f[x] ? I was sure this timing was a fluke, so I restarted Mathematica and repeated it several times, and the result held. Paul