[curve fitting] dependence between coefficients
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Dear all -
I need to fit my experimental data (x_data, y_data) with a biexponential decay model:
% define fit options
fo_ = fitoptions('method','NonlinearLeastSquares','Lower',lower,'Upper',upper);
% define fittype
ft_ = fittype('offset+a*exp(-(x-x0)/b)+c*exp(-(x-x0)/d)',...
'dependent',{'y'},'independent',{'x'},...
'coefficients',{ 'offset', 'x0', 'a', 'b', 'c', 'd'});
% perform fit
[cf_, gof, output] = fit(x_data,y_data,ft_,fo_);
offset = y-offset
x0 = x-offset
a and c = amplitudes (weighing factors)
b and d = decay constants
As my experimental data are normalised, i.e. the decay occurs from 1 to 0, I would like to implement the following condition in my fitting routine: a + c = 1
How can I do this?
I appreciate your help!
Sebastian
采纳的回答
Matt J
2013-5-31
Replace occurrences of c in your model with 1-a. Then fit the remaining parameters.
ft_ = fittype('offset+a*exp(-(x-x0)/b)+(1-a)*exp(-(x-x0)/d)',...
'dependent',{'y'},'independent',{'x'},...
'coefficients',{ 'offset', 'x0', 'a', 'b', 'd'});
3 个评论
Sebastian König
2013-5-31
You could do the same thing.
amp1 = 1 - amp2 - amp3
The equation always allows one variable to be eliminated, no matter how many terms you have.
Sebastian König
2013-6-6
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2013-5-31
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