Re: functions: compiled vs. uncompiled version
- To: mathgroup at smc.vnet.net
- Subject: [mg94099] Re: functions: compiled vs. uncompiled version
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Fri, 5 Dec 2008 05:28:13 -0500 (EST)
- Organization: Uni Leipzig
- References: <gh8hou$r4u$1@smc.vnet.net>
- Reply-to: kuska at informatik.uni-leipzig.de
Hi,
hmm, don't compile it ?
Regards
Jens
Diego Guadagnoli wrote:
> Hi All,
>
> I am performing mathematica calculations involving
> many nested sums of the kind
> FUN = Sum[term[i,j,k], {i,6},{j,6},{k,2} ] or similar,
> where term[__] returns a complex number.
>
> Since I have many those sums, Timing is really long.
> Therefore I thought to implement both term[__] and FUN
> as compiled functions. I noticed however than in both
> cases Timing is not improved, actually it is worse in the
> compiled version.
>
> An example of the code is reported below as plain text.
> There are a "Needed input" and a "Functions" part. In "Functions",
> an example of term[__] is provided by the VUUS function, which is
> implemented in uncompiled (VUUS[i_, j_, k_]) and compiled form (VUUSc).
> This function is then called in the repeated sum "fun" (uncompiled) or
> respectively "func" (compiled).
>
> As you can see, the Timing in func is actually worse than in fun.
>
> Any suggestion for improving my code without translating it in FORTRAN
> would be very appreciated.
>
> Cheers,
> D
>
>
> %%%%%Please copy the content below to a mathematica notebook
>
> (*NEEDED INPUT*)
>
> BR[i_] := v[1] ZR[[1, i]] - v[2] ZR[[2, i]];
>
> {g1, sW, v[1], v[2], yuRos[1], yuRos[2], yuRos[3]} =
> Table[Random[], {i, 7}];
>
> AuRos = Table[RandomComplex[], {i, 3}, {j, 3}];
>
> ZR = Table[Random[], {i, 2}, {j, 2}];
>
> ZU = Table[RandomComplex[], {i, 6}, {j, 6}];
>
> \[Mu]Ros = 300;
>
>
>
> (*FUNCTIONS*)
>
> VUUS[i_, j_,
> k_] := -(g1^2/3)*BR[k] (KroneckerDelta[i, j] + (3 - 8 sW^2)/(4 sW^2)
> Sum[Conjugate[ZU[[I, i]]] ZU[[I, j]], {I, 1, 3}]) -
> Sum[v[2] (yuRos[I])^2
> ZR[[2, k]] (Conjugate[ZU[[I, i]]] ZU[[I, j]] +
> Conjugate[ZU[[I + 3, i]]] ZU[[I + 3, j]]), {I, 1, 3}] +
> Sum[1/Sqrt[2]
> ZR[[2, k]] (Conjugate[AuRos[[I, J]]] Conjugate[ZU[[I, i]]]
> ZU[[J + 3, j]] +
> AuRos[[I, J]] ZU[[I, j]] Conjugate[ZU[[J + 3, i]]]), {I, 1,
> 3}, {J, 1, 3}] +
> Sum[1/Sqrt[2] yuRos[I]
> ZR[[1, k]] (Conjugate[\[Mu]Ros] ZU[[I, j]]
> Conjugate[ZU[[I + 3, i]]] + \[Mu]Ros Conjugate[ZU[[I, i]]]
> ZU[[I + 3, j]]), {I, 1, 3}];
>
> VUUSc = Compile[{{i, _Integer}, {j, _Integer}, {k, _Integer}},
> sum1 = 0. + 0. I;
> Do[sum1 = sum1 + Conjugate[ZU[[ii, i]]] ZU[[ii, j]], {ii, 1, 3}];
> sum2 = 0. + 0. I;
> Do[sum2 =
> sum2 + v[2] (yuRos[ii])^2
> ZR[[2, k]] (Conjugate[ZU[[ii, i]]] ZU[[ii, j]] +
> Conjugate[ZU[[ii + 3, i]]] ZU[[ii + 3, j]]), {ii, 1, 3}];
> sum3 = 0. + 0. I;
> Do[sum3 =
> sum3 + 1/Sqrt[2]
> ZR[[2, k]] (Conjugate[AuRos[[ii, J]]] Conjugate[ZU[[ii, i]]]
> ZU[[J + 3, j]] +
> AuRos[[ii, J]] ZU[[ii, j]] Conjugate[ZU[[J + 3, i]]]), {ii,
> 1, 3}, {J, 1, 3}];
> sum4 = 0. + 0. I;
> Do[sum4 =
> sum4 + 1/Sqrt[2] yuRos[ii]
> ZR[[1, k]] (Conjugate[\[Mu]Ros] ZU[[ii, j]]
> Conjugate[ZU[[ii + 3, i]]] + \[Mu]Ros Conjugate[
> ZU[[ii, i]]] ZU[[ii + 3, j]]), {ii, 1, 3}];
> -(g1^2/3)
> BR[k] (KroneckerDelta[i, j] + (3 - 8 sW^2)/(4 sW^2) sum1) -
> sum2 + sum3 + sum4,
> {{BR[_], _Real}, {ZU, _Complex,
> 6}, {v[_], _Real}, {yuRos[_], _Real}, {ZR, _Real,
> 2}, {AuRos, _Complex, 3}, {\[Mu]Ros, _Complex}}];
>
> fun = Compile[{{k, _Integer}},
> sum1 = 0. + 0. I;
> Do[sum1 = sum1 + VUUS[l, m, k], {l, 1, 6}, {m, 1, 6}];
> -sum1, {{VUUS[__], _Complex}}
> ];
>
> func = Compile[{{k, _Integer}},
> sum1 = 0. + 0. I;
> Do[sum1 = sum1 + VUUSc[l, m, k], {l, 1, 6}, {m, 1, 6}];
> -sum1, {{VUUS[__], _Complex}}
> ];
>
> VUUS[1, 1, 1] // Timing
>
> VUUSc[1, 1, 1] // Timing
>
> fun[1] // Timing
>
> func[1] // Timing
>