Merge pairs in a list that have the same 1st element by averaging the the 2nd elements

Question

I'm trying to do interpolation on a large list of data of the format {{x1, y1}, {x2, y2}, {x3, y3}, ..., {xn, yn}} that is exported from a simulation.

Unfortunately, the exported data has some points {x_(i), y_(i)} and {x_(i + 1), y_(i + 1)} that share the same x point: x_(i) = x_(i + 1). This is just because of poor precision in the export process from the simulation.

The interpolation function doesn't like the fact that there are duplicate points that share the same x value, and gives me an error message with no output interpolation.

I want to take the duplicate points {x_(i), y_(i)} and {x_(i + 1), y_(i + 1)}, average y_(i) and y_(i + 1) and remove x_(i + 1) from the list. The final list should have no duplicates.

It should be pretty straightforward. I'm just a little slow at programming, because I don't have to do it very often.

Answer 1

When the x-values are exact duplicates, the following might work (data is the n x 2 -matrix with the data points).

KeySort@GroupBy[data, First -> Last, Mean]

This produces an association. You may obtain a list again with

Transpose[ 
 Through[{Keys, Values}[
  KeySort@GroupBy[data, First -> Last, Mean]]
  ]
 ]

Answer 2

data = {{1, 2}, {3, 4}, {5, 6}, {1, 6}};

assocs = AssociationThread @* Apply[Rule] /@ data

<|1 -> 2|>, <|3 -> 4|>, <|5 -> 6|>, <|1 -> 6|>}

means = Merge[Mean][assocs]

<|1 -> 4, 3 -> 4, 5 -> 6|>

List @@@ Normal @ means

{{1, 4}, {3, 4}, {5, 6}}

Answer 3

How about this?

data = {{1, 2}, {3, 4}, {5, 6}, {1, 2}};

data2 = Union[data, SameTest -> (#1[[1]] == #2[[1]] &)]

(* {{1,2},{3,4},{5,6}} *)

If the x values are not exact duplicates then you can use:

SameTest -> (Abs[#1[[1]] - #2[[1]]] < minDifference &)

with minDifference set to an appropriate value.