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}