How can I find inflection points of a data set?

Question

My codes finds inflection points and locations of them, but some points are missing. Is there any way to find correct points on MATLAB?

My data set is at the link: https://ctrlv.it/id/17947/243681442

Answer 1

There is a solution here :

findinflections.m

% function [datapeaks datavalleys] = findinflections(plotswitch,datain)
% This program finds peaks
% Arguments: 
%   ploswitch: 0 or 1 : disable or enable plots (for debugging)
%   datain: 1D variable
% Dependencies:
% 
% Copyright (c) 2011, Arun Ramakrishnan
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function [datapeaks datavalleys] = findinflections(plotswitch,datain)
% datain = gconv;
datad1=[diff(datain)];
mp = find(datad1>0);
mn = find(datad1<=0);

datapeaks = [];
for pindex = 1:length(mp)
    [maxvalue, maxindex] = max(datain(mp(pindex):mn(min(find(mn>mp(pindex))))));
    if ~isempty(maxindex)
        datapeaks = cat(1,datapeaks, floor(mean(maxindex))+mp(pindex)-1);
    end
end
datapeaks= unique(datapeaks);

datavalleys = [];
for pindex = 1:length(mn)
    [minvalue, minindex] = min(datain(mn(pindex):mp(min(find(mp>mn(pindex))))));
    if ~isempty(minindex)
        datavalleys = cat(1,datavalleys, floor(mean(minindex))+mn(pindex)-1);
    end
end
datavalleys= unique(datavalleys);

if (plotswitch) 
    plot(1:length(datain),datain,'k-',mp,datain(mp),'b.',mn,datain(mn),'r.',datapeaks,datain(datapeaks),'g.',datavalleys,datain(datavalleys),'c.');
end

Call it (Array A is your points):

[datapeaks, datavalleys]=findinflections(1,A);

Output :