Re: How to map a list on function

*To*: mathgroup at smc.vnet.net*Subject*: [mg97563] Re: How to map a list on function*From*: Raffy <raffy at mac.com>*Date*: Sun, 15 Mar 2009 05:29:11 -0500 (EST)*References*: <gpg18t$ceh$1@smc.vnet.net>

On Mar 14, 3:35 am, buts <mange... at yahoo.com> wrote: > Hello, > > Could anyone explain me how to do the following: > I have a long list of integer numbers in groups of four: > > list= {{10,3,5,7},{4,6,8,9},{0,8,3,6}, ...... } > > or its Flatten version. > > How to write a fast function g[list] which does this: > > g[list] =x^10*y^3*z^5*u^7 + x^4*y^6*z^8*u^9 + y^8*z^3*u^6+ ... > > It should be done many times (say, 10^4-6) on lists with length > 1000, s= o taking parts is not a good idea. > How to use Map or similar ? > Thanks. mPowers = RandomInteger[{0, 1}, {100, 4}]; vSymbols = {x, y, z, u}; Do[r1 = Plus @@ Times @@@ Transpose[vSymbols^Transpose[mPowers]], {10000}] // Timing Do[r2 = Total[ Times @@@ Transpose[vSymbols^Transpose[mPowers]]], {10000}] // Timing Do[r3 = Plus @@ Times @@@ (Power[vSymbols, #] & /@ mPowers), {10000}] // Timing Do[r4 = Plus @@ MapThread[Times, vSymbols^Transpose[mPowers]], {10000}] // Timing If you can prebuild a function before hand: f = Evaluate[Times @@ (vSymbols^Array[Slot, Length[vSymbols]])] &; Do[r5 = Plus @@ f @@ Transpose[mPowers], {10000}] // Timing Do[r6 = Plus @@ (f @@@ mPowers), {10000}] // Timing The winner depends on the length of mPower. (Might wanna call ClearSystemCache[] for better time tests) Additionally, if the mPower vector can be Transposed before hand, you gain more speed.