ValueError: The input contains nan values - from lmfit model despite the input not containing NaNs

Question

I'm trying to build a model using lmfit (link to docs) and I can't seems to find out why I keep getting a ValueError: The input contains nan values when I try to fit the model.

from lmfit import minimize, Minimizer, Parameters, Parameter, report_fit, Model
import numpy as np

def cde(t, Qi, at, vw, R, rhob_cb, al, d, r):
    # t (time), is the independent variable
    return Qi / (8 * np.pi * ((at * vw)/R) * t * rhob_cb * (np.sqrt(np.pi * ((al * vw)/R * t))))  * \
        np.exp(- (R * (d - (t * vw)/ R)**2) / (4 * (al * vw) * t) - (R * r**2)/ (4 * (at * vw) * t))

model_cde =  Model(cde)


# Allowed to vary
model_cde.set_param_hint('vw', value =10**-4, min=0.000001)
model_cde.set_param_hint('d', value = -0.038, min = 0.0001)
model_cde.set_param_hint('r', value = 5.637e-10)
model_cde.set_param_hint('at', value =0.1)
model_cde.set_param_hint('al', value =0.15)

# Fixed
model_cde.set_param_hint('Qi', value = 1000, vary = False)
model_cde.set_param_hint('R', value =1.7, vary = False)
model_cde.set_param_hint('rhob_cb', value =3000, vary = False)

# test data
data = [ 1.37,  1.51,  1.65,  1.79,  1.91,  2.02,  2.12,  2.2 ,
        2.27,  2.32,  2.36,  2.38,  2.4 ,  2.41,  2.42,  2.41,  2.4 ,
        2.39,  2.37,  2.35,  2.33,  2.31,  2.29,  2.26,  2.23,  2.2 ,
        2.17,  2.14,  2.11,  2.08,  2.06,  2.02,  1.99,  1.97,  1.94,
        1.91,  1.88,  1.85,  1.83,  1.8 ,  1.78,  1.75,  1.72,  1.7 ,
        1.68,  1.65,  1.63,  1.61,  1.58]

time = list(range(5,250,5))

model_cde.fit(data, t= time)

Produces the following error:

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-16-785fcc6a994b> in <module>()
----> 1 model_cde.fit(data, t= time)

/home/bprodz/.virtualenvs/phd_dev/lib/python3.5/site-packages/lmfit/model.py in fit(self, data, params, weights, method, iter_cb, scale_covar, verbose, fit_kws, **kwargs)
    539                              scale_covar=scale_covar, fcn_kws=kwargs,
    540                              **fit_kws)
--> 541         output.fit(data=data, weights=weights)
    542         output.components = self.components
    543         return output

/home/bprodz/.virtualenvs/phd_dev/lib/python3.5/site-packages/lmfit/model.py in fit(self, data, params, weights, method, **kwargs)
    745         self.init_fit    = self.model.eval(params=self.params, **self.userkws)
    746 
--> 747         _ret = self.minimize(method=self.method)
    748 
    749         for attr in dir(_ret):

/home/bprodz/.virtualenvs/phd_dev/lib/python3.5/site-packages/lmfit/minimizer.py in minimize(self, method, params, **kws)
   1240                     val.lower().startswith(user_method)):
   1241                     kwargs['method'] = val
-> 1242         return function(**kwargs)
   1243 
   1244 

/home/bprodz/.virtualenvs/phd_dev/lib/python3.5/site-packages/lmfit/minimizer.py in leastsq(self, params, **kws)
   1070         np.seterr(all='ignore')
   1071 
-> 1072         lsout = scipy_leastsq(self.__residual, vars, **lskws)
   1073         _best, _cov, infodict, errmsg, ier = lsout
   1074         result.aborted = self._abort

/home/bprodz/.virtualenvs/phd_dev/lib/python3.5/site-packages/scipy/optimize/minpack.py in leastsq(func, x0, args, Dfun, full_output, col_deriv, ftol, xtol, gtol, maxfev, epsfcn, factor, diag)
    385             maxfev = 200*(n + 1)
    386         retval = _minpack._lmdif(func, x0, args, full_output, ftol, xtol,
--> 387                                  gtol, maxfev, epsfcn, factor, diag)
    388     else:
    389         if col_deriv:

/home/bprodz/.virtualenvs/phd_dev/lib/python3.5/site-packages/lmfit/minimizer.py in __residual(self, fvars, apply_bounds_transformation)
    369 
    370         out = self.userfcn(params, *self.userargs, **self.userkws)
--> 371         out = _nan_policy(out, nan_policy=self.nan_policy)
    372 
    373         if callable(self.iter_cb):

/home/bprodz/.virtualenvs/phd_dev/lib/python3.5/site-packages/lmfit/minimizer.py in _nan_policy(a, nan_policy, handle_inf)
   1430 
   1431         if contains_nan:
-> 1432             raise ValueError("The input contains nan values")
   1433         return a
   1434 

ValueError: The input contains nan values

However the results of the following checks for NaNs confirms that there were no NaN values in my data:

print(np.any(np.isnan(data)), np.any(np.isnan(time)))
False False

So far I've tried converting 1 and/or both of data and time from lists to numpy ndarrays, removing the 0th time step (in case there was a dividing by 0 error), explicitly specifying the t as being independent and allowing all variables to vary. However these all throw the same error.

Does anyone have ideas what is causing this error to be thrown? Thanks.

Answer 1

I tried to fit my model using scipy.optimize.curve_fit and got the following error:

/home/bprodz/.virtualenvs/phd_dev/lib/python3.4/site-packages/ipykernel/__main__.py:3: RuntimeWarning: invalid value encountered in sqrt
  app.launch_new_instance()

Which suggests the problem is with my model generating some negative numbers for np.sqrt(). The default behaviour for np.sqrt() when given a negative number is to output nan as per this question. NB the np.sqrt can be set to raise an error if given a negative number be setting the following: np.seterr(all='raise') source

TIP I also asked for help in the lmfit google group and received the following helpful advice:

• Consider breaking long formulas into smaller pieces to make troubleshooting easier
• Use Model.eval() to test what certain parameters will produce when run through your model function
• np.ndarray is generally superior to python lists in these (numerical) situations