循环以在mathematica中生成矩阵的迭代行

Question

我有一个矩阵

FT= {{0, 0, 0}, {1, 1, 1}, {1, 1, 2}, {1, 1, 3}, {1, 2, 1}, {1, 2, 2}, {1,
   2, 3}, {1, 3, 1}, {1, 3, 2}, {1, 3, 3}, {2, 1, 1}, {2, 1, 2}, {2, 
  1, 3}, {2, 2, 1}, {2, 2, 2}, {2, 2, 3}, {2, 3, 1}, {2, 3, 2}, {2, 3,
   3}, {2, 4, 1}, {2, 4, 2}, {2, 4, 3}, {2, 5, 1}, {2, 5, 2}, {2, 5, 
  3}, {2, 6, 1}, {2, 6, 2}, {2, 6, 3}, {3, 1, 1}, {3, 1, 2}, {3, 1, 
  3}, {3, 2, 1}, {3, 2, 2}, {3, 2, 3}, {3, 3, 1}, {3, 3, 2}, {3, 3, 
  3}, {3, 4, 1}, {3, 4, 2}, {3, 4, 3}, {3, 5, 1}, {3, 5, 2}, {3, 5, 
  3}, {3, 6, 1}, {3, 6, 2}, {3, 6, 3}, {3, 7, 1}, {3, 7, 2}, {3, 7, 
  3}, {3, 8, 1}, {3, 8, 2}, {3, 8, 3}, {3, 9, 1}, {3, 9, 2}, {3, 9, 
  3}, {3, 10, 1}, {3, 10, 2}, {3, 10, 3}, {3, 11, 1}, {3, 11, 2}, {3, 
  11, 3}, {3, 12, 1}, {3, 12, 2}, {3, 12, 3}} 

其中每一行代表每个元素的一种地址，其第一个元素给出 G，第二个元素给出 B，第三个元素给出 M。例如对于第三个元素，G 为 1，B 为 1，M 为 2，依此类推。现在我需要为每个元素生成一个矩阵，这样每当我的 G 为 0 或 1 时，它都会给我 {0,0,0} 并且对于 G>1，它会给我 G-1、G-2 等行直到它给出 1；对于 B，它会检查 B 是否为偶数，它返回 B/2，每当 B 为奇数时，它返回 (B+1) /2 并且 M 每次都取值为 3，最后是一行 {0,0,0} .例如对于 FT= {3,12,3} 的最后一个元素，它应该给我 {{2,6,3}, {1,3,3}, {0,0,0}} 而对于 FT= {2,5,1} 它应该给我{{1,3,3}, {0,0,0}}。 你能帮我在mathematica中为此编写代码吗？ 在此先感谢:)

Answer 1

对于这个演示，小写符号用于避免与内置函数冲突，例如D、E、I、N

这个函数定义了基本操作

op[{g_, b_, m_}] := {g - 1, If[EvenQ[b], b/2, (b + 1)/2], 3}

应该重复应用，直到满足条件。 NestWhileList 对此很有用，例如

NestWhileList[op[#] &, {3, 12, 3}, First[#] > 1 &]

{{3, 12, 3}, {2, 6, 3}, {1, 3, 3}}

另一个函数使用上面的 if g > 1 :-

f[{g_, b_, m_}] := Append[
  If[g > 1, Rest@NestWhileList[op, {g, b, m}, First[#] > 1 &],
   {}], {0, 0, 0}]

例如

f[{2, 5, 1}]

{{1, 3, 3}, {0, 0, 0}}

现在f 可以映射到ft 上：-

ft = {
   {0, 0, 0}, {1, 1, 1}, {1, 1, 2}, {1, 1, 3}, {1, 2, 1},
   {1, 2, 2}, {1, 2, 3}, {1, 3, 1}, {1, 3, 2}, {1, 3, 3},
   {2, 1, 1}, {2, 1, 2}, {2, 1, 3}, {2, 2, 1}, {2, 2, 2},
   {2, 2, 3}, {2, 3, 1}, {2, 3, 2}, {2, 3, 3}, {2, 4, 1},
   {2, 4, 2}, {2, 4, 3}, {2, 5, 1}, {2, 5, 2}, {2, 5, 3},
   {2, 6, 1}, {2, 6, 2}, {2, 6, 3}, {3, 1, 1}, {3, 1, 2},
   {3, 1, 3}, {3, 2, 1}, {3, 2, 2}, {3, 2, 3}, {3, 3, 1},
   {3, 3, 2}, {3, 3, 3}, {3, 4, 1}, {3, 4, 2}, {3, 4, 3},
   {3, 5, 1}, {3, 5, 2}, {3, 5, 3}, {3, 6, 1}, {3, 6, 2},
   {3, 6, 3}, {3, 7, 1}, {3, 7, 2}, {3, 7, 3}, {3, 8, 1},
   {3, 8, 2}, {3, 8, 3}, {3, 9, 1}, {3, 9, 2}, {3, 9, 3},
   {3, 10, 1}, {3, 10, 2}, {3, 10, 3}, {3, 11, 1}, {3, 11, 2},
   {3, 11, 3}, {3, 12, 1}, {3, 12, 2}, {3, 12, 3}};    

matrix = Map[f, ft]