Search code examples
selectduplicatesunionwolfram-mathematica

Selecting duplicate points on a list of data

I'm trying to drop some elements of a list of data in Mathematica, but I don't understand how Select and Union work. For example, suppose I have the following list

list = {{0.10,0.20},{1.10,0.20},{0.70,0.80},{0.20,1.10},
    {1.20,1.20},{0.12,0.18},{0.68,0.76}}

and only want elements in (0,1)x(0,1) considering that points within a distance radius of 0.05 are duplicates. In the example,

list1 ={{0.10,0.20},{0.70,0.80}}

I don't care which element represents the equivalence class. I'm doing the following:

list1 = Select[list, 0 < Part[#,1] <1 &];Select[list,0 < Part[#,2] <1 &]

which gives the points in (0,1)x(0,1), but if I try to use Union, such as

Union[list1, SameTest -> (Abs[#1-#2] < 0.05 &)]

I get slot errors.

Can someone explain to me how to do it neatly?

---EDIT---

Using

DeleteDuplicates[list1, Abs[Part[#1, 1] - Part[#2, 1]] < 10^-6 &]

does the trick, but I wonder why I can't work with a list of lists.

Solution

  • There are several ways of approaching this. One way to do it, that I think is the neatest, since you require your elements to be in certain intervals, is to use IntervalMemberQ with Select.

    For example, to narrow down your list to those points in (0,1)x(0,1):

    list01 = Select[list, And @@ IntervalMemberQ[Interval[{0, 1}], #] &]

Out[1]= {{0.1, 0.2}, {0.7, 0.8}, {0.12, 0.18}, {0.68, 0.76}}

    Secondly, to eliminate duplicates, use DeleteDuplicates, which is the perfect tool for this task. You can use the same test using IntervalMemberQ:

    DeleteDuplicates[list01, 
 And @@ IntervalMemberQ[Interval[{0, 0.5}], Abs[#1 - #2]] &]

Out[2]= {{0.1, 0.2}, {0.7, 0.8}}