MATLAB: Nonlinear fit to multiple data sets with shared parameters

nonlinear curve fitting

Hello all,

I need to fit a nonlinear model to several data sets simultaneously. The model has the same functional form for all sets, and the values of some model parameters are the same for all sets, but the value of at least one parameter is different for each set. For example, three exponential decay curves might have the same decay constant but a different amplitude for each data set. The global fit to all three curves would produce one decay constant and three amplitudes.

What is the best way to do this in MatLab? (Apologizing in advance for a novice question!)

ELELAB

Best Answer

Take a look at this example of a function that partitions the parameters into a set sharing values across all datasets and a set taking different values for different datasets. You may be able to modify this for your purposes.

function sharedparams
t = (0:10)';
T = [t; t; t];
Y = 3 + [exp(-t/2); 2*exp(-t/2); 3*exp(-t/2)] + randn(33,1)/10;
dsid = [ones(11,1); 2*ones(11,1); 3*ones(11,1)];
gscatter(T,Y,dsid)
X = [T dsid];
b = nlinfit(X,Y,@subfun,ones(1,5))
line(t,b(1)+b(2)*exp(-t/b(5)),'color','r')
line(t,b(1)+b(3)*exp(-t/b(5)),'color','g')
line(t,b(1)+b(4)*exp(-t/b(5)),'color','b')
function yfit = subfun(params,X)
T = X(:,1);        % time
dsid = X(:,2);     % dataset id
A0 = params(1);    % same A0 for all datasets
A1 = params(2:4)'; % different A1 for each dataset
tau = params(5);   % same tau
yfit = A0 + A1(dsid).*exp(-T/tau);

This uses nlinfit from the Statistics Toolbox, but you could use other fitting routines instead.

Related Solutions

MATLAB: How to perform nonlinear regression accross multiple datasets

Hi Jack,

The following post on MATLAB Answers discusses a similar case:

http://www.mathworks.com/matlabcentral/answers/1056-nonlinear-fit-to-multiple-data-sets-with-shared-parameters.

In that question , there were 2 unknown shared parameters and 1 parameter was different for all the dataset but was also unknown. In this question we have 3 unknown shared parameters and 1 known parameters whose value will be different for each dataset.So I modified that to illustrate that :

function sharedparams
t = (0:10)';
T = [t; t; t;t];
Y = 3 + [exp(-t/2); 2*exp(-t/2); 3*exp(-t/2);4*exp(-t/2)] + randn(44,1)/10;
dsid = [ones(11,1); 2*ones(11,1); 3*ones(11,1);4*ones(11,1)];
gscatter(T,Y,dsid)
X = [T dsid];
A3 = [-5;1;3;4];
b = nlinfit(X,Y,@subfun,ones(1,3))
 line(t,b(1)+b(2)+b(3)*t+A3(1),'color','r');
 line(t,b(1)+b(2)+b(3)*t+A3(2),'color','g');
 line(t,b(1)+b(2)+b(3)*t+A3(3),'color','b');
 line(t,b(1)+b(2)+b(3)*t+A3(4),'color','c');
function yfit = subfun(param,X)
T = X(:,1);        % time
dsid = X(:,2);     % dataset id
A0 = param(1);
A1 = param(2);
A2 = param(3);
A3 = [-5;1;3;4]; %known paramter 
yfit = A0 + A1+ A2*T + A3(dsid);

MATLAB: Simultaneously fit multiple data sets — with one of the fit parameters common between all data sets.

I don't think you're far off. If you have m fits of n parameters each, with one parameter the same across all m fits, then you have a total of 1 + m*(n-1) parameters. So in the example you posted, x0 should have 1 + 2*(8-1) = 15 elements. You should modify fitfun slightly, too

x2 = x([9 2 10 11 12 13 14 15]);

otherwise the 10th element is left out of the fit entirely.

To keep yourself sane as you extend to 5 fits, it might help to reorder/renumber the parameters. I'd even be tempted to change voigt1 to be a function of two inputs v (scalar) and x (7-element vector). Then fitfun would look something like

    function error = fitfun(x)
        v  = x(1);
        x1 = x(2:8);
        x2 = x(9:15);
        y1 = voigt1(v,x1);
        y2 = voigt1(v,x2);
        error = sum((ydata1-y1).^2 + (ydata2-y2).^2);
    end

This would be more easily adapted to 5 (or whatever) fits.

It looks like there might be an issue with passing xdata and ydata into the functions. You can use anonymous function handles to help with that, by making the function file accept an extra input, then making an anonymous function handle with the extra input fixed:

   function error = fitfun(x,ydata1,ydata2)
     ...
   end
   x0 = ...
   ydata1 = ...
   ydata2 = ...
   f = @(x) fitfun(x,ydata1,ydata2)  % ydata1 and ydata2 are defined in the local workspace
   fminsearch(f,x0)

Best Answer

Related Solutions

MATLAB: How to perform nonlinear regression accross multiple datasets

MATLAB: Simultaneously fit multiple data sets — with one of the fit parameters common between all data sets.

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