I have a list of the form:
{{1, 0, 1}, {2, 1, 2}, {1, 0, 3}, {2, 4, 2}, {2, 1, -1}, {1, 0 ,0}}
that I would like to sort such that I calculate the sum over the third column whenever the first two columns are equal. I.e. in this case the output would be
{{1, 0, 1 + 3 + 0}, {2, 1, 2 + (-1)}, {2, 4, 2}}
or
{{1, 0, 4},{2, 1, 1},{2, 4, 2}}
Is there an elegant way to do this?
Flatten[{#[[1, {1, 2}]], Total[#[[All, 3]]]}] & /@ GatherBy[yourList, #[[{1, 2}]] &]
(* {{1, 0, 4}, {2, 1, 1}, {2, 4, 2}} *)
How this works:
GatherBy[yourList, #[[{1, 2}]] &]
this gathers elements of your list based on matching the first and second elements in each sub-list (#[[{1, 2}]] &)
Once common elements are gathered (collected) you can total/sum all the third elements by mapping them onto Total
lists = {{1, 0, 1}, {2, 1, 2}, {1, 0, 3}, {2, 4, 2}, {2, 1, -1}, {1, 0, 0}}
Reap/Sow:
Reap[Sow[#[[3]], {#[[{1, 2}]]}] & /@ lists, _, Append[#1, Total@#2] &][[2]]
ReplaceRepeated:
lists //. {a___, {x_, y_, z_}, b___, {x_, y_, w_}, c___} :> {a, {x, y, z + w}, b, c}
Cases + DeleteDuplicates:
DeleteDuplicates@Cases[lists, {w : PatternSequence[_, _], _} :>
{w, Total@(Last /@ Cases[lists, {w, _}])}]
all give
{{1, 0, 4}, {2, 1, 1}, {2, 4, 2}}
Update: In versions 10+, you can also use Merge:
KeyValueMap[Append]@Merge[Tr][Most @ # -> Last @ #& /@ lists]
{{1, 0, 4}, {2, 1, 1}, {2, 4, 2}}
Total@#/PadLeft[{1}, 3, Length@#] & /@ GatherBy[list, #[[{1, 2}]] &]
This approach is basically the same as Mike's. However, instead of summing only the last element it sums all the elements. To correct for the extra summing PadLeft[{1}, 3, Length@#] is used to divide by the number of times it was added where the {1} is included to keep the last element the same. The approach can be generalized to lists of length $n$ by replacing PadLeft[{1}, 3, Length@#] with PadLeft[{1}, Length@#[[1]], Length@#]
GroupBy, introduced in Mathemtaica 10, is applicable here and cleaner than GatherBy:
in = {{1, 0, 1}, {2, 1, 2}, {1, 0, 3}, {2, 4, 2}, {2, 1, -1}, {1, 0, 0}};
Append @@@ Normal @ GroupBy[in, Most -> Last, Tr]
{{1, 0, 4}, {2, 1, 1}, {2, 4, 2}}
See also:
Since GatherBy and Sow/Reap are already shown I'll drop back to "first principles" as it were and use more basic language.
dat = {{1, 0, 1}, {2, 1, 2}, {1, 0, 3}, {2, 4, 2}, {2, 1, -1}, {1, 0, 0}};
f[dat_] :=
Module[{key},
key[__] = 0;
key[#, #2] += #3 & @@@ dat;
Most @ DownValues @ key /. (_@_@x__ :> y_) :> {x, y}
]
f @ dat
{{1, 0, 4}, {2, 1, 1}, {2, 4, 2}}
Flattenaround the mapped function. $\endgroup$