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[?] Find first local minima?

M.A. Ghorbani

M.A. Ghorbani, University of Tabriz

Posted 6 years ago

Dear All, I have a list as following (for example) data = {10,8,7,6,5,3,4,5,2,3,2,1,0} The first local minima is 3. How can I find this value in Mathematica ? Thank so much for your help.

POSTED BY: M.A. Ghorbani

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Hans Dolhaine

Hans Dolhaine, retired

Posted 6 years ago

What about an "old fashioned" way without sophisticated "modern" functions? data = {10, 8, 7, 6, 5, 3, 4, 5, 2, 3, 2, 1, 0}; min = data[[1]]; Catch[ Do[ If[data[[i]] < min, min = data[[i]], Throw[{i - 1, min}]], {i, 2, Length[data]}]] {6, 3}

POSTED BY: Hans Dolhaine

Marco Thiel

Marco Thiel, University of Aberdeen - Dept. of Physics/Mathematics

Posted 6 years ago

I agree that the Position function is a viable option, but keep in mind that FindPeaks gives the x-position of the maxima by default. so something like: sol = {1, -1}FindPeaks[-m, 0, 0, -Infinity][[1]] would give you x and y position of the first minimum. If you use sol = {1, -1}# & /@ FindPeaks[-m, 0, 0, -Infinity] you get the same for all minima. Using Mariusz' notation: ListPlot[CorrelationFunction[data, {100}], TicksStyle -> {{FontSize -> 16, Orange}, {FontSize -> 22, Green}}, PlotRange -> All, AxesLabel -> {Style[x, Large], Style[y, Large]}, Epilog -> {PointSize[0.01], Red, Point /@ sol}] gives: Cheers, Marco

I agree that the Position function is a viable option, but keep in mind that FindPeaks gives the x-position of the maxima by default. so something like:

sol = {1, -1}*FindPeaks[-m, 0, 0, -Infinity][[1]]

would give you x and y position of the first minimum. If you use

sol = {1, -1}*# & /@ FindPeaks[-m, 0, 0, -Infinity]

you get the same for all minima. Using Mariusz' notation:

ListPlot[CorrelationFunction[data, {100}], 
 TicksStyle -> {{FontSize -> 16, Orange}, {FontSize -> 22, Green}}, 
 PlotRange -> All, AxesLabel -> {Style[x, Large], Style[y, Large]}, 
 Epilog -> {PointSize[0.01], Red, Point /@ sol}]

gives:

enter image description here

Cheers,

Marco

POSTED BY: Marco Thiel

M.A. Ghorbani

M.A. Ghorbani, University of Tabriz

Posted 6 years ago

Dear Marco, Mariusz Thanks again. I used your solution for my real data. Unfortunately the result shows { }. Please see the attached file. Regards, Attachments:

POSTED BY: M.A. Ghorbani

Mariusz Iwaniuk

Mariusz Iwaniuk, engineer, math hobbyist.

Posted 6 years ago

You need write a pattern using Condition to force searching based on numerical equality: See here (Position->Possible Issues) for more information. Regards, Mariusz Attachments: