[心得] Spinski Triangle with CompilationTarget->"C"

[chungyuandye (養花種魚數月亮賞星星)]

Mathematica 較為人詬病的就是計算速度及不可編譯為執行檔。
但這在7.0及8.0之後的Compile及平行運算大致已獲得解決。

$Version

newpt[x_List] := {{x[[1]], Mean@{x[[1]], x[[2]]},
    Mean@{x[[1]], x[[3]]}}, {x[[2]], Mean@{x[[2]], x[[1]]},
    Mean@{x[[2]], x[[3]]}}, {x[[3]], Mean@{x[[3]], x[[1]]},
    Mean@{x[[3]], x[[2]]}}};

(*不編譯程式*)
Stgraph1[pt_List, n_Integer] :=
  Nest[Flatten[Map[newpt, #], 1] &, {pt}, n];

(* 編譯程式 *)
Stgraph2 =
  Compile[{{pt, _Real, 2}, {n, _Integer}},
   Nest[Flatten[
      Map[{{#[[1]], Mean@{#[[1]], #[[2]]},
          Mean@{#[[1]], #[[3]]}}, {#[[2]], Mean@{#[[2]], #[[1]]},
          Mean@{#[[2]], #[[3]]}}, {#[[3]], Mean@{#[[3]], #[[1]]},
          Mean@{#[[3]], #[[2]]}}} &, #], 1] &, {pt}, n]];

(*由 C Compiler 編譯程式*)
Stgraph3 =
  Compile[{{pt, _Real, 2}, {n, _Integer}},
   Nest[Flatten[
      Map[{{#[[1]], Mean@{#[[1]], #[[2]]},
          Mean@{#[[1]], #[[3]]}}, {#[[2]], Mean@{#[[2]], #[[1]]},
          Mean@{#[[2]], #[[3]]}}, {#[[3]], Mean@{#[[3]], #[[1]]},
          Mean@{#[[3]], #[[2]]}}} &, #], 1] &, {pt}, n],
   CompilationTarget -> "C"];

pt = {{0, 0}, {2, 0}, {1, Sqrt[3]}};

First@AbsoluteTiming@Stgraph1[pt, 8]
First@AbsoluteTiming@Stgraph2[pt, 8]
First@AbsoluteTiming@Stgraph3[pt, 8]

Graphics[{Red, Polygon /@ Stgraph3[pt, 8]}]


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養花種魚數月亮賞星星

http://chungyuandye.twbbs.org


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推 kichigop:老師來個平行運算教學吧^^...我試過但是好像沒成功