Optimise a reference that cuts my curve into 2 equal sections

Hello,

I am collecting data from excel, then basic idea is that i want to determine a constant value line that cuts my curve into 2 eqaual sections (area above the line and the curve = area under).

The objective is to determine the value of the red line.

Answer 1

[Matt J]

 %t= time, X=consumption, x=unknown midline
 
 tc=t-t(1);
 Xc=cumtrapz(t,X);
 
 x=optimvar('x');

 sol=solve( optimproblem('Objective',x,'Constraints',Xc-x*tc<=90,'ObjectiveSense','minimize') );
 lb=sol.x; %lower bound
 sol=solve( optimproblem('Objective',x,'Constraints',10<=Xc-x*tc,'ObjectiveSense','maximize') );
 ub=sol.x; %upper bound
 
 if lb>ub
  disp 'Problem is infeasible'
 else
     
  xunc=trapz(t,X)/(t(end)-t(1)); %unconstrained solution
  
  x=min(max(xunc,lb),ub); %constrained solution
  
 end

[fadi awar]

Thank you for the help,

I got an error:

Error using norm

First argument must be single or double.

[Matt J]

You probably need to upgrade your Matlab version.

If you cannot upgrade, you can try my revised version.

[fadi awar]

Yeah, this one worked.

Thank you for your help!

Answer 2

[William Rose]

@fadi awar,

If you mean that the area between the red line and the blue curve abve the line equals the area between the red line and the blue curve below the line, then the height of the red line is simply the mean value of the blue line data.

[fadi awar]

yeah right, in this case but I have other constrains to take into consideration but I am not sure how to explain my case correcctly. The area should never exceed a proper value all along the 48 data in the x axis. That means, I have an initial value x, x + area below the red line before the first intersection is limited to a value. Then x+x area below (previously calculated) - x area above is limited to a value.

It continue until reaching the end (so i need to slelect the red line while taking into consideration those constrains).

Is it possible to be done graphically? if yes using which library.

Thank you

[Matt J]

@fadi awar

It is counterproductive for you to omit details about the constraints from your post. You will simply get answers that ignore them.

[fadi awar]

So i have an initial value of X, ex X0=50. The constrains of X are : 10<X<95.

So whenever the curve crosses the red line (to determine its value), I want to calculate Xnew=X0+ brown area.

Then Xnew=Xbefore - orange area.

Then Xnew= Xbefore + red area.

All thos Xnew should meet my constrains.

Finally I will be able to get the value of the red line

[dpb]

Attach the data as a .mat file.

Just looking at the graph, I'd venture it isn't possible to meet the constraints that the integral of the area be <95 when the magnitudes of the integrand are in the thousands. Just by a very crude approximation of the leftmost area (brown?) as roughly a rectangle of height ~(2800-1800) and a duration of 12, the integral would be roughly 1000*12 --> 12,000. Unless there's a very small scaling factor to be applied, it "just ain't a-gonna' happen".

[fadi awar]

Kindly find attached the files.

I am to get the result according to my limits even if in this case of chosen data it wont matter a lot.

But Future wise I will be chaniging the data.

Thank you

Answer 3

[Catalytic]

midline = trapz(x,y)/(max(x)-min(x))