Fit time series Q(t) to a logistic function.
Inputs (vectors of same size): t (time) & Q
Outputs: Qpre (logistic model fit to data) and three independent parameters: thalf, Qinf, and a, describing the logistic
Q(t) = Qinf/(1 + exp(-a*(t-thalf)))
Qinf is value as t --> infinity
thalf is time of symmetric inflection point
a is time decay constant
Written by James Conder, Southern Illinois University, Oct. 2010
Cleaned up for publishing May 16, 2013
James Conder (2023). fit_logistic(t,Q) (https://www.mathworks.com/matlabcentral/fileexchange/41781-fit_logistic-t-q), MATLAB Central File Exchange. Retrieved .
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Added confidence limits for parameters.
1) condensed output of three individual parameters: thalf, Qinf, and alpha into one 3 element vector, p
Added a check to avoid the flatlining (Qpre goes to the mean) that has occasionally occurred.
Fixed bug for reversing time when fitting a decreasing logistic.
accidentally included debugging code in last update. update is debugged AND cleaned version
Fixed instability for short or long time frames
Fixed signs of coefficients for decreasing logistic and added screenshot
Fixed signs of coefficients for decreasing logistic.