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Finding Max value on peak point of graph (logistics growth model)

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Is there a method in matlab where i can find the value of the point in the graph (red arrow) before it plateues. I was thinking of using the gradient function. But unable to get any. Some help please !
  2 Comments
dpb
dpb on 27 Mar 2021
Have more success if attach the data file, probably, so folks have something to work from.
save the variable and attach the .mat file
Nirmal Kishore Janakiraman
Edited: Nirmal Kishore Janakiraman on 30 Mar 2021
Thank you sir. I have attached below and what is it that im trying to find.

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Accepted Answer

Ananya Tewari
Ananya Tewari on 30 Mar 2021
I understand you want the coordinates of the point after which the graph plateaus. Assuming you are having the data points of the graph, using movmax we can get the desired result.
maxi = movmax(data,[0 2]); % Taking 3 values at a time and finding maximum of them
idx = 0; % this will capture the index after which the graph plateaus
for k = 1:n % where n is number of data points
% when the middle value of the 3 elements is the largest we break the loop
if(maxi(k) == data(k+1))
idx = k;
break;
end
end
  3 Comments
Ananya Tewari
Ananya Tewari on 31 Mar 2021
Hi Nirmal,
The ischange() finds abrupt changes in a given data and this function can be leveraged to find the approximate point after which the graph plateaus.A possible workaround is as follows:
data = biomass_conc(1,:) %data-points
x=1:5000
% Find change points
changeIndices = ischange(biomass_conc,'linear','MaxNumChanges',20,...
'SamplePoints',x);
% Display results
clf
plot(x,biomass_conc,'Color',[109 185 226]/255,'DisplayName','Input data')
hold on
% Plot change points
x2 = repelem(x(changeIndices),3);
y = repmat([ylim(gca) NaN]',nnz(changeIndices),1);
plot(x2,y,'Color',[51 160 44]/255,'LineWidth',1,'DisplayName','Change points')
title(['Number of change points: ' num2str(nnz(changeIndices))])
hold off
% The last value of x2 contains the approximate x-coordinate after which
% the graph plateaus
x_dash = x2(end) % x-coordinate
y_dash = biomass_conc(x_dash) % corresponding y-coordinate
Nirmal Kishore Janakiraman
Dear Ananya,
Thank you very much for your assistance on this. Appreciate it a lot!

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