How to fit two data sets, y1 and y2, to different functions with shared parameters.

The two data vectors, y1(x) and y2(x), have a common x vector (dimension ~30) and common fit parameters, a=[a1,a2,a3,a4] The two fitting equations are biexponentials:

y1 = a1+[a2*exp(-x/a3)] + [(1-a2)*exp(-x/a4)] and

y2 = a1+[a2*exp(-x/a4)] + [(1-a2)*exp(-x/a3)].

Answer 1

[Star Strider]

This problems requires lsqcurvefit since the fit is to a matrix and not vector dependent variables:

y1 = rand(10,1);                                                        % Create Data
y2 = rand(10,1);                                                        % Create Data
x = 0:9;                                                                % Create Data

objfcn = @(a,x) [a(1)+a(2).*exp(-x./a(3)) + (1-a(2)).*exp(-x./a(4));
                 a(1)+a(2).*exp(-x./a(4)) + (1-a(2)).*exp(-x./a(3))];

a0 = rand(4,1);                                                         % Use Appropriate Initial Parameter Estimates
B = lsqcurvefit(objfcn, a0, x(:).', [y1(:) y2(:)].');                   % Forced Column Vectors & Transpositions Force Data To Conform To Objective Function Size

It does not matter of the data are row or column variables, since the code forces them to fit the ‘objfcn’ dimensions.