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Sorting on multiple columns within a matrix
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| Lee Newman 2005-06-09, 9:01 am |
| Hello,
I can't come up with a solution to the following simple task:
- I have a matrix, let's M={ {"Z",2,"a"},{"A",2,"k"}, {"Z",1,"z"},
{"A",1,"a"},{"Z",3,"k"}, {"A",3,"z"} }
- I want to be able to sort the matrix row-wise, based on multiple
columns, for example sort first on column 2 (ascending) and then
secondly on column1 (ascending)
desired result:
A 1 a
Z 1 z
A 2 k
Z 2 a
A 3 z
Z 3 k
I suspect the solution involves using a pure function of some form as
the second argument in the Sort function, but I can't figure out what
this function should be.
Thanks,
Lee
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| Jens-Peer Kuska 2005-06-09, 9:01 am |
| Hi,
Sort[M, If[#1[[2]] =!= #2[[2]], #1[[2]] < #2[[2]],
#1[[1]] < #2[[1]]] &]
??
Regards
Jens
"Lee Newman" <leenewm@umich.edu> schrieb im
Newsbeitrag news:d892lm$sc6$1@smc.vnet.net...
> Hello,
>
> I can't come up with a solution to the following
> simple task:
>
> - I have a matrix, let's M={
> {"Z",2,"a"},{"A",2,"k"}, {"Z",1,"z"},
> {"A",1,"a"},{"Z",3,"k"}, {"A",3,"z"} }
> - I want to be able to sort the matrix
> row-wise, based on multiple
> columns, for example sort first on column 2
> (ascending) and then
> secondly on column1 (ascending)
>
> desired result:
> A 1 a
> Z 1 z
> A 2 k
> Z 2 a
> A 3 z
> Z 3 k
>
> I suspect the solution involves using a pure
> function of some form as
> the second argument in the Sort function, but I
> can't figure out what
> this function should be.
>
> Thanks,
> Lee
>
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| Hello Lee,
You need "Ordered" like in this example:
Sort[m, If[#1[[2]] === #2[[2]], OrderedQ[{#1[[1]], #2[[1]]}],
OrderedQ[{#1[[2]], #2[[2]]}]] &]
sincerely, Daniel
Lee Newman wrote:
> Hello,
>
> I can't come up with a solution to the following simple task:
>
> - I have a matrix, let's M={ {"Z",2,"a"},{"A",2,"k"}, {"Z",1,"z"},
> {"A",1,"a"},{"Z",3,"k"}, {"A",3,"z"} }
> - I want to be able to sort the matrix row-wise, based on multiple
> columns, for example sort first on column 2 (ascending) and then
> secondly on column1 (ascending)
>
> desired result:
> A 1 a
> Z 1 z
> A 2 k
> Z 2 a
> A 3 z
> Z 3 k
>
> I suspect the solution involves using a pure function of some form as
> the second argument in the Sort function, but I can't figure out what
> this function should be.
>
> Thanks,
> Lee
>
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| Lee Newman 2005-06-10, 9:00 am |
| dh -- thanks, your solution works, but it seems it might be awkward to
extend it to many more than two columns.
I am wondering if anyone knows a way to generalize dh's solution such
that it could be applied as a pure function to a list which contains the
columns to sort? I noodled over it but was unable to figure it out.
Something like:
Sort[matrix, puresortfunc[#] ]& /@ {1,14,2,4}
where 1,14,2,4 are the columns to use for sorting, and puresortfunc is
this tricky sorting function that would successively map # to the
elements in the list of columns to sort.
Lee
Lee Newman wrote:
> Hello,
>
> I can't come up with a solution to the following simple task:
>
> - I have a matrix, let's M={ {"Z",2,"a"},{"A",2,"k"}, {"Z",1,"z"},
> {"A",1,"a"},{"Z",3,"k"}, {"A",3,"z"} }
> - I want to be able to sort the matrix row-wise, based on multiple
> columns, for example sort first on column 2 (ascending) and then
> secondly on column1 (ascending)
>
> desired result:
> A 1 a
> Z 1 z
> A 2 k
> Z 2 a
> A 3 z
> Z 3 k
>
> I suspect the solution involves using a pure function of some form as
> the second argument in the Sort function, but I can't figure out what
> this function should be.
>
> Thanks,
> Lee
>
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On Jun 9, 2005, at 5:18 AM, Lee Newman wrote:
> Hello,
>
> I can't come up with a solution to the following simple task:
>
> - I have a matrix, let's M={ {"Z",2,"a"},{"A",2,"k"}, {"Z",1,"z"},
> {"A",1,"a"},{"Z",3,"k"}, {"A",3,"z"} }
> - I want to be able to sort the matrix row-wise, based on multiple
> columns, for example sort first on column 2 (ascending) and then
> secondly on column1 (ascending)
>
> desired result:
> A 1 a
> Z 1 z
> A 2 k
> Z 2 a
> A 3 z
> Z 3 k
>
> I suspect the solution involves using a pure function of some form as
> the second argument in the Sort function, but I can't figure out what
> this function should be.
>
> Thanks,
> Lee
>
The solution to it is in the Help under the Sort examples. Here it
is for this case:
In[1]:=
mm = {{"Z", 2, "a"},
{"A", 2, "k"}, {"Z", 1,
"z"}, {"A", 1, "a"},
{"Z", 3, "k"}, {"A", 3,
"z"}};
In[2]:=
ColumnForm[mm]
Out[2]=
{"Z", 2, "a"}
{"A", 2, "k"}
{"Z", 1, "z"}
{"A", 1, "a"}
{"Z", 3, "k"}
{"A", 3, "z"}
In[15]:=
nn = mm[[Ordering[mm[[All,
{2, 1}]]]]];
In[16]:=
ColumnForm[nn]
Out[16]=
{"A", 1, "a"}
{"Z", 1, "z"}
{"A", 2, "k"}
{"Z", 2, "a"}
{"A", 3, "z"}
{"Z", 3, "k"}
János
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| Mark Fisher 2005-06-10, 9:00 am |
| How about this?
ColumnOrderSort[matrix_List, columns_List] :=
Sort[matrix, OrderedQ[{#1[[columns]], #2[[columns]]}] &]
ColumnOrderSort[M, {2,1}]//MatrixForm
--Mark
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