Fzero: finding optimal integration limit between to areas

Given are measured datapoints, concentration vs time (t_0 to t_end). I do not have the exact function.

I'd like to find the specific time t_opt, where the area under the function (calculated using trapz) from t_0 to t_opt is equal to the area above the function from t_opt to t_end. Hopefully the drawing attached explains this more clearly.

My unsuccesful attempt is attached. Would really appreciate some help.

Answer 1

[Star Strider]

Without your data, this is just an hypothetical approach.

At least for a first approximation, I would use cumtrapz, not trapz. The part between ‘t0’ and ‘t_opt’ is simply the cumtrapz(t,c) result. The entire area under ‘c_max’ (the unlabeled upper asymptote) is ‘c_max*(te-t0)’, so the area between your curve and ‘c_max’ would appear to be ‘c_max*(te-t0)-cumtrapz(t,c)’. Equating these, with a bit of algebra, suggests my approach.

See if this works:

c_int = cumtrapz(t,c);
t_opt = interp1(c_int, t, c_max*(te-t0)/2, 'linear');

Note — This is obviously UNTESTED CODE.

Answer 2

[zhaoj]

Thanks for the help. Didn't work exactly but the function cumtrapz helped me figure it out.

[Star Strider]

My pleasure.