Re: Friendly Challenge 2: sort by column

*To*: mathgroup at smc.vnet.net*Subject*: [mg35067] Re: Friendly Challenge 2: sort by column*From*: gleam at flashmail.com ("Mr. Wizard")*Date*: Thu, 20 Jun 2002 23:56:17 -0400 (EDT)*Organization*: The Math Forum*Sender*: owner-wri-mathgroup at wolfram.com

MathGroup readers and challenge participants, Now that I have let a few days go by, allowing time for those who would choose to participate to write and post their methods, I will share the function that I have been using. First, for Hartmut Wolf, who wrote: Paul, what do you mean "handling duplicates" exactly? Merely the behavior of the program when there are identical items in the sort column, possibly resulting in ambiguity. In general I prefer the Rotate solution as it more closely follows the default behavior of Sort. Of course, this is slower however. <snip> ad[[Ordering[RotateLeft[ad,{0,2}]]]]//MatrixForm And there you have it! That's all that I was after. :-) Next, to DrBob, who wrote: Another interpretation (the one I prefer) is to preserve preexisting order in case of ties. That allows us to sort by one column, then by another, and get the result we'd expect. After some experimentation, I found that hw4 and hw5 (and hence Ordering itself) preserve order already, without modification. As you will see, this is included in my function with the following syntax: positionSort[a, n] uses Rotate positionSort[a, {n}] sorts by only column n, preserving other ordering. positionSort[a, {n, o, ...} sorts secondarily by o, etc. n can be negative to give the column n from the end. A third argument can be given to specify an arbitrary sort function. Here is a variation of the function that I use. The original code uses pattern matching differently (in place of the If statement, for example), and is too verbose for posting, though it yields a small improvement in performance: Notebook[{ Cell["Array test function", "Text"], Cell[BoxData[ \(mtest = #~TensorRank~2 > 1 &\)], "Input"], Cell["Optional sort function handling", "Text"], Cell[BoxData[ \(zz = HoldPattern[ z : \(\((_Symbol | _Function | _Sequence)\) : Sequence[]\)]\)], "Input"], Cell["Handling of trivial parameters", "Text"], Cell[BoxData[{ \(positionSort[a_, 0 | {0}] := a\), "\n", \(positionSort[a_List, 1] := Sort@a\)}], "Input"], Cell["\<\ Sort by only one column (disregard the rest); arbitrary sort function\ \ \>", "Text"], Cell[BoxData[ \(positionSort[a_?mtest, {p_Integer} | \(p : {_Integer .. }\), zz] := a\[LeftDoubleBracket] a\[LeftDoubleBracket]All, p\[RightDoubleBracket]~Ordering~ z\[RightDoubleBracket]\)], "Input"], Cell["Arbitrary sort function", "Text"], Cell[BoxData[ \(positionSort[a_?mtest, p_Integer, zz] := a\[LeftDoubleBracket]a~RotateLeft~{0, If[p < 0, p, p - 1]}~ Ordering~z\[RightDoubleBracket]\)], "Input"] }] Paul