fit_exp_decay_log

mdtools.functions.fit_exp_decay_log(xdata, ydata, ysd=None, return_valid=False, **kwargs)[source]

Fit an exponential decay function to ydata using scipy.optimize.curve_fit().

Instead of fitting the data directly with an exponential decay function \(e^{-kt}\), the logarithm of the y-data is fitted by

\[f(t) = -k \cdot t\]

Parameters:

xdata (array_like) – The independent variable where the data is measured.
ydata (array_like) – The dependent data. Must have the same shape as xdata. Only data points with 0 < ydata <= 1 will be considered. NaN’s and infinite values will not be considered, either.
ysd (array_like, optional) – The standard deviation of ydata. Must have the same shape as ydata.
return_valid (bool, optional) – If True, return a boolean array of the same shape as ydata that indicates which elements of ydata meet the requirements given above.
kwargs (dict, optional) – Additional keyword arguments (besides xdata, ydata and sigma) to parse to scipy.optimize.curve_fit(). See there for possible options. By default, absolute_sigma is set to True, p0 is set to 1 / (len(ydata) * np.mean(ydata)) and bounds is set to (0, np.inf).

Returns:

popt (numpy.ndarray) – Optimal values for the parameters so that the sum of the squared residuals is minimized. The first and only element of popt is the optimal \(k\) value.
perr (numpy.ndarray) – Standard deviation of the optimal parameters.
valid (numpy.ndarray) – Boolean array of the same shape as ydata indicating, which elements of ydata were used for the fit. Only returned if return_valid is True.