Re: How to map a list on function

*To*: mathgroup at smc.vnet.net*Subject*: [mg97575] Re: How to map a list on function*From*: Raffy <raffy at mac.com>*Date*: Mon, 16 Mar 2009 04:22:19 -0500 (EST)*References*: <gpg18t$ceh$1@smc.vnet.net> <gpilb2$595$1@smc.vnet.net>

On Mar 15, 3:29 am, Ray Koopman <koop... at sfu.ca> wrote: > 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, so taking parts is not a good idea. > > How to use Map or similar ? > > Thanks. > > Here are five ways to do it. For lists of 1000 and 2000 4-tuples, > g4 and g5 are best and about equally fast, but for longer lists > g5 is fastest. > > list = {{10,3,5,7},{4,6,8,9},{0,8,3,6}}; > g1[list_] := Tr[Times@@({x,y,z,u}^#)& /@ list]; > g2[list_] := Tr[Inner[Power,{x,y,z,u},#,Times]& /@ list]; > g3[list_] := Tr@Inner[#2^#1&,list,{x,y,z,u},Times]; > g4[list_] := Tr[Times@@({x,y,z,u}^Transpose@list)]; > g5[list_] := Tr@Inner[Power,{x,y,z,u},Transpose@list,Times]; > SameQ @@ (#@list& /@ {g1,g2,g3,g4,g5}) > g5[list]//InputForm > > True > u^6*y^8*z^3 + u^7*x^10*y^3*z^5 + u^9*x^4*y^6*z^8 > > try[length_,reps_] := Block[{list = Table[Random[Integer,9], > {length},{4}]}, {length, First/@{Timing@Do[g1[list],{reps}], > Timing@Do[g2[list],{reps}], Timing@Do[g3[list],{reps}], > Timing@Do[g4[list],{reps}], Timing@Do[g5[list],{reps}]}/.Second->1}] > > try[1000#,64/#]&/@{1,2,4,8} > > {{1000, {1.93, 1.56, 1.50, 1.21, 1.23}}, > {2000, {2.10, 1.75, 1.73, 1.46, 1.47}}, > {4000, {2.45, 2.13, 2.16, 1.95, 1.88}}, > {8000, {2.72, 2.44, 2.42, 2.36, 2.17}}} Wow, the speed gain of Tr over Total or Plus@@ is interesting. Thanks for that tidbit!