scipy.optimize.curvefit() - array must not contain infs or NaNs

Question

I am trying to fit some data to a curve in Python using scipy.optimize.curve_fit. I am running into the error ValueError: array must not contain infs or NaNs.

I don't believe either my x or y data contain infs or NaNs:

>>> x_array = np.asarray_chkfinite(x_array)
>>> y_array = np.asarray_chkfinite(y_array)
>>>

To give some idea of what my x_array and y_array look like at either end (x_array is counts and y_array is quantiles):

>>> type(x_array)
<type 'numpy.ndarray'>
>>> type(y_array)
<type 'numpy.ndarray'>
>>> x_array[:5]
array([0, 0, 0, 0, 0])
>>> x_array[-5:]
array([2919, 2965, 3154, 3218, 3461])
>>> y_array[:5]
array([ 0.9999582,  0.9999163,  0.9998745,  0.9998326,  0.9997908])
>>> y_array[-5:]
array([  1.67399000e-04,   1.25549300e-04,   8.36995200e-05,
     4.18497600e-05,  -2.22044600e-16])

And my function:

>>> def func(x,alpha,beta,b):
...    return ((x/1)**(-alpha) * ((x+1*b)/(1+1*b))**(alpha-beta))
...

Which I am executing with:

>>> popt, pcov = curve_fit(func, x_array, y_array)

resulting in the error stack trace:

Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "/usr/lib/python2.7/dist-packages/scipy/optimize/minpack.py", line 426, in curve_fit
res = leastsq(func, p0, args=args, full_output=1, **kw)
File "/usr/lib/python2.7/dist-packages/scipy/optimize/minpack.py", line 338, in leastsq
cov_x = inv(dot(transpose(R),R))
File "/usr/lib/python2.7/dist-packages/scipy/linalg/basic.py", line 285, in inv
a1 = asarray_chkfinite(a)
File "/usr/lib/python2.7/dist-packages/numpy/lib/function_base.py", line 590, in asarray_chkfinite
"array must not contain infs or NaNs")
ValueError: array must not contain infs or NaNs

I'm guessing the error might not be with respect to my arrays, but rather an array created by scipy in an intermediate step? I've had a bit of a dig through the relevant scipy source files, but things get hairy pretty quickly debugging the problem that way. Is there something obvious I'm doing wrong here? I've seen casually mentioned in other questions that sometimes certain initial parameter guesses (of which I currently don't have any explicit) might result in these kind of errors, but even if this is the case, it would be good to know a) why that is and b) how to avoid it.

Answer 1

Why it is failing

Not your input arrays are entailing nans or infs, but evaluation of your objective function at some X points and for some values of the parameters results in nans or infs: in other words, the array with values func(x,alpha,beta,b) for some x, alpha, beta and b is giving nans or infs over the optimization routine.

Scipy.optimize curve fitting function uses Levenberg-Marquardt algorithm. It is also called damped least square optimization. It is an iterative procedure, and a new estimate for the optimal function parameters is computed at each iteration. Also, at some point during optimization, algorithm is exploring some region of the parameters space where your function is not defined.

How to fix

1/Initial guess

Initial guess for parameters is decisive for the convergence. If initial guess is far from optimal solution, you are more likely to explore some regions where objective function is undefined. So, if you can have a better clue of what your optimal parameters are, and feed your algorithm with this initial guess, error while proceeding might be avoided.

2/Model

Also, you could modify your model, so that it is not returning nans. For those values of the parameters, params where original function func is not defined, you wish that objective function takes huge values, or in other words that func(params) is far from Y values to be fitted.

Also, at points where your objective function is not defined, you may return a big float, for instance AVG(Y)*10e5 with AVG the average (so that you make sure to be much bigger than average of Y values to be fitted).

Link

You could have a look at this post: Fitting data to an equation in python vs gnuplot