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sorting - Sort data after specific ordering (ascending/descending) in multiple columns


I have some data:


data={{"a", 1, 1}, {"a", 1, 2}, {"a", 1, 3}, 
{"c", 2, 1}, {"b", 2, 2}, {"b", 2, 3},
{"c", 3, 1}, {"a", 3, 2}, {"a", 3, 3}}


When I use:


Sort[data]

I get the list ordered in incremental order first with column 1 then by 2 and last by the third. Suppose I want the first column in increasing order but the second in decreasing order and the third again in increasing order. How do I do that?


I tried with Sort and SortBy but I haven't managed to make it work.


The output should be:



a 3 2


a 3 3



a 1 1


a 1 2


a 1 3


b 2 2


b 2 3


c 3 1


c 2 1




Answer





Caveat lector: Incorrect results are generated by this solution, e.g.,


sortByColumn[{{"a", 1, 1}, {"b", 2, 3}, {"a", 3, 2}}, {1, 1, -1}]


returns


{{"a", 1, 1}, {"b", 2, 3}, {"a", 3, 2}}


when the correct result is obviously


{{"a", 1, 1}, {"a", 3, 2}, {"b", 2, 3}}


I've commented on the answer to bring it to the attention of the author, however seeing as they've not been here in some time, I'm also putting this here: I think a highly upvoted and accepted answer needs to be correct. - ciao



Here is my contribution, which has the following benefits over previous answers:




  • It sorts both numbers and non-numeric structures

  • You can sort any column (not just the first, followed by the second, etc)

  • You can sort in either direction (ascending / descending)

  • Original order is kept: if you sort on the second column, the first entry will follow the order of the original list. See the example with {0,-1}

  • Edit also allow specifying the priority of the columns. So given {-1,1} for the ordering, you can specify {1,2} to give the higher priority to the second column.


The code is as follows, including my usage code for my own comments.


Clear[sortByColumn]
sortByColumn::usage =
"Arguments: [Table, Direction, Priority]. Returns the list sorted \

by the directions for each column specified in `Direction`. For \
ascending order, use `1`, and for descending order, use `-1`. For \
sorting more than one column, input `Direction` as a list. For \
example, Direction={-1,1} will sort the first column in descending \
order followed by the second column in ascending order, ignoring any \
other column. To sort on the second column, use {0,1} for the syntax.

When sorting two or more columns, you can provide the `Priority` \
for which column should be sorted first. For example, \
`sortByColumn[data,{-1,1},{1,2}]` would sort first in ascending order \

on the second column (because it has a higher priority) and then in \
descending order on the first column.";

sortByColumn[list_?MatrixQ, dir : _Integer | {__Integer}, priority_: {}] :=
Module[{l = Length@list[[1, All]], w, p, d},
w = Reverse@Range@l;
p = If[Length@priority > 0, PadRight[Flatten@{priority}, l],
p = Range@l];
w = w[[Ordering@p]];
d = PadRight[Flatten@{dir}, l];

Sort[list, NonNegative@Total[(w d MapThread[Order, {##}])] &]]

For example, using the data set provided by Mr. Wizard:


data={{"a", 1, 1}, {"a", 1, 5}, {"a", 1, 3}, 
{"c", 2, 1}, {"b", 2, 2}, {"b", 2, 3},
{"c", 3, 1}, {"a", 3, 2}, {"a", 3, 3}};
data[[All, 2]] = data[[All, 2]] /. {1 -> "q", 2 -> "r", 3 -> "s"};

Here are the results of some trial runs. First the original:


{a,q,1}

{a,q,2}
{a,q,3}
{c,r,1}
{b,r,2}
{b,r,3}
{c,s,1}
{a,s,2}
{a,s,3}

The result of sortByColumn[data,-1].



{c,r,1}
{c,s,1}
{b,r,2}
{b,r,3}
{a,q,1}
{a,q,2}
{a,q,3}
{a,s,2}
{a,s,3}


Result of sortByColumn[data,{0,-1}]


{c,s,1}
{a,s,2}
{a,s,3}
{c,r,1}
{b,r,2}
{b,r,3}
{a,q,1}
{a,q,2}
{a,q,3}


And finally, the result the OP wanted, sortByColumn[data,{1,-1,1}]


{a,s,2}
{a,s,3}
{a,q,1}
{a,q,2}
{a,q,3}
{b,r,2}
{b,r,3}
{c,s,1}

{c,r,1}

An example showing the use of the priority argument: sortByColumn[data, {-1, 1}, {1, 2}]


{a,q,1}
{a,q,5}
{a,q,3}
{c,r,1}
{b,r,2}
{b,r,3}
{c,s,1}

{a,s,2}
{a,s,3}

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