Find peaks, max and min of an interpolation function?

Question

I'm new in mathematica.

I have a list of values and i don't know how to find some poitns, such as peaks, the max and min of an interpolation function.

RA = List[{0, 0.727578}, {0.4, 0.73179}, {0.8, 0.773248}, {1.2, 1.342248}, {1.6, 0.987746}, {2, 0.791317}, {2.4, 1.11788}, {2.8, 0.996614}, {3.2, 0.938749}];

f = Interpolation[RA]

InterpolatingFunction[{{0., 3.2}}, <>]

Thanks

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Chris K · Answer 1 · 2019-11-08T15:08:34.827

7

This functionality is included in the FindMaxima, FindMinima & FindExtrema functions in my EcoEvo package (the continuous part is based on this answer by @DanielLichtblau).

Import["https://raw.githubusercontent.com/cklausme/EcoEvo/master/EcoEvo/EcoEvo.m"]
(* ... or install with: *)
(* PacletInstall["https://github.com/cklausme/EcoEvo/releases/download/v1.1.0/EcoEvo-1.1.0.paclet"] *)
(* then load the package: *) 
(* <<EcoEvo` *)
(* EcoEvo Package Version 1.1.0 (October 22, 2019) *)

FindMaxima[RA]
(* {{1.2, 1.34225}, {2.4, 1.11788}} *)

FindMaxima[f]
(* {{0.171237, 0.75627}, {1.2, 1.34225}, {2.41594, 1.11823}} *)

edited Nov 08 '19 at 15:08

answered Nov 08 '19 at 14:07

Chris K

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@AntonAntonov Good idea, thanks! – Chris K Nov 08 '19 at 14:28
2

These might be a good candidate for the Wolfram Function Repository, should you wish to make it available in that way. – Daniel Lichtblau Nov 08 '19 at 15:55
@DanielLichtblau I might, but I'm mostly holding out for the Paclet Repository! – Chris K Nov 08 '19 at 17:35
The advantage of the Function Repository is that it actually exists (not to get into ontological debates or anything...) – Daniel Lichtblau Nov 09 '19 at 16:12

score 6 · Answer 2 · answered Nov 08 '19 at 13:10

Here is your list and its interpolation. I only made the interpolation smoother:

rA = List[{0, 0.727578}, {0.4, 0.73179}, {0.8, 0.773248}, {1.2, 
    1.342248}, {1.6, 0.987746}, {2, 0.791317}, {2.4, 1.11788}, {2.8, 
    0.996614}, {3.2, 0.938749}];

f = Interpolation[rA, InterpolationOrder -> 3, Method -> "Spline"];

Let us plot it:

Plot[f[x], {x, 0, 3.2}]

Now, try this:

Map[FindMaximum[f[x], {x, #}] &, {0.1, 1., 2.3}]

(*  {{0.801624, {x -> 0.169875}}, {1.35071, {x -> 
    1.24042}}, {1.13541, {x -> 2.48519}}}   *)

Map[FindMinimum[f[x], {x, #}] &, {0.6, 2.1, 2.9}]

(*  {{0.672974, {x -> 0.605239}}, {0.772641, {x -> 
    1.91542}}, {0.890775, {x -> 3.06279}}}   *)

Have fun!

Find peaks, max and min of an interpolation function?

2 Answers2