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Find the positions of the local minima and local maxima in a list?

Laurens Wachters, retired
Posted 4 years ago

How do I find the positions of the elements in a list that are smaller (or greater) than both the previous and the next element in that list. So for instance, suppose I have the list data={2,4,1,3,4,5,3,2,1,5}. In this list the third and nineth element are smallerr than the elements right before and right after them. They are the local minima in the list. How do I find their positions? I suppose with Position[data,....&]. But what criteria should I use in this expression? The same question goes for the local maxima.
POSTED BY: Laurens Wachters
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Thank you Daniel, Hans and Henrik. Your methods work nicely.
POSTED BY: Laurens Wachters

Here is one more :)

data = {2, 4, 1, 3, 4, 5, 3, 2, 1, 5};
Last /@ SequencePosition[Sign@Differences[data], {-1, 1}]
POSTED BY: Henrik Schachner

I think this what you are looking for

data = {2, 4, 1, 3, 4, 5, 3, 2, 1, 5}
d1 = Partition[data, 3, 1]
d2 = Select[d1, #[[1]] > #[[2]] < #[[3]] &]
pp = Position[d1, #] & /@ d2
p1=1 + Flatten[pp]
POSTED BY: Hans Dolhaine

Partition into triples. Example:

ll = RandomInteger[{1, 10}, 30]

(* Out[1]= {3, 3, 8, 3, 5, 1, 1, 10, 9, 1, 8, 1, 7, 10, 2, 7, 4, 5, 6, \
4, 4, 1, 5, 1, 5, 9, 5, 4, 5, 5} *)

Get local maxima:

Flatten@
  Position[Partition[ll, 3, 1], {a_, b_, c_} /; b > a && b > c] + 1

(* Out[4]= {3, 5, 8, 11, 14, 16, 19, 23, 26} *)
POSTED BY: Daniel Lichtblau
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