How does lmfit's exponential model work when approximating a (negative) exponential function?
The following tried to follow https://lmfit.github.io/lmfit-py/model.html, but failed to provide the right results:
mod = lmfit.models.ExponentialModel()
pars = mod.guess([1, 0.5], x=[0, 1])
out = mod.fit([1, 0.5], pars, x=[0, 1])
out.eval(x=0) # result is 0.74999998273811308, should be 1
out.eval(x=1) # result is 0.75000001066995159, should be 0.5
You'll need more than two data points to fit the two-parameter exponential model to data. Lmfit Models are designed to do data fitting. Something like this will work:
import numpy as np
import lmfit
xdat = np.linspace(0, 2.0, 11)
ydat = 2.1 * np.exp(-xdat /0.88) + np.random.normal(size=len(xdat), scale=0.06)
mod = lmfit.models.ExponentialModel()
pars = mod.guess(ydat, x=xdat)
out = mod.fit(ydat, pars, x=xdat)
print(out.fit_report())
Instead, you're getting amplitude = 0.75 and decay > 1e6.