LSQCURVEFIT simultaniously on 4 datasets and 2 functions

I have 4 data sets, two of which comply to a fit function f1, and two of which comply to a fit function f2. These fit functions are of the form:

f1 = @(A,t_1, t_2,t) A*(1+4/5*exp(-t/t_1))*exp(-t/t_2)
f2 = @(A,t_1, t_2,t) A*(1-2/5*exp(-t/t_1))*exp(-t/t_2)

where t is the data. I need to fit these two functions to the four dataset simultaneously, because the t_1 and t_2 parameters should be equal for all data. The A parameter differs though. I can match the A parameter already for two datasets by looking at the tails of the set ( where the first exponential vanishes, the other two are impossible because they are shorter, yet more detailed) so this gives me 5 parameters:

• A_1
• A_2
• A_34 (is already matched for data set 3 and 4)
• t_1
• t_2

How would I do this?

I've tried using

% P = [A_34, A_1, A_2, t_1, t_2];
errf = @(P)   sum( (f_1( P(1), P(4), P(5), x_3) - y_3).^2 + ...
              sum( (f_2( P(1), P(4), P(5), x_4) - y_4).^2 + ...
              sum( (f_1( P(2), P(4), P(5), x_1) - y_1).^2 + ...
              sum( (f_2( P(3), P(4), P(5), x_2) - y_2).^2;
 P0 = [1000, 1000, 1000, 0.05, 5];
  P = fminsearch(errf,P);

Notice the the set 3 belongs to f_1 and set 4 to f_2, yet I can determine their relative scale by looking at the tail (where the first exponential vanishes).

This give me bad fits though. Is there a way I can do this better? I can fit each dataset using LSQCURVEFIT, but I don't see how to use it on multiple datasets/functions.

I hope this is a clear explanation.

[Renee]

Did you ever find a solution? I'm trying to do this also

[Torsten]

Take a look at my answer under

http://www.mathworks.com/matlabcentral/answers/178867-how-do-i-fit-two-equations-that-explain-two-parts-of-a-curve

Best wishes

Torsten.

Answer 1

[Matt J]

The curve function that you fit using lsqcurvefit is allowed to be vector-valued. Define the curve function to have a 2x1 vector-valued output [f1;f2] and use lsqcurvefit as normal.

Similarly, there is no need to treat t1 and t2 as separate. Just concatenate them t=[t1,t2] and feed to lsqcurvefit in the usual way. Inside the definition of the curve function, you can split t into parts and use those subsets where appropriate.

[Yingbo Li]

can you take his problem and make an example? I have trouble following your comments. you are a level 10, and most people are level 1 . :-)