Scipy expit: Unexpected behavour. NaNs

Question

Noticed some nan's were appearing unexpectedly, in my data. (and expanding out and naning everything they touched) Did some careful investigation and produced a minimal working example: ``` >>> import numpy >>> from scipy.special import expit >>> expit(709) 1.0 >>> expit(710) nan ``` Expit is the inverse logit. Scipy documentation here. Which tells us: `expit(x) = 1/(1+exp(-x))` So `1+exp(-709)==1.0` so that `expit(709)=1.0` Seems fairly reasonable, rounding `exp(-709)==0`. However, what is going on with `expit(710)`? `expit(710)==nan` implies that `1+exp(-710)==0`, which implies: `exp(-710)=-1` which is not right at all. What is going on? I am fixing it with: ``` def sane_expit(x): x = np.minimum(x,700*np.ones_like(x)) #Cap it at 700 to avoid overflow return expit(x) ``` But this is going to be a bit slower, because extra op, and the python overhead. I am using numpy 1.8.-0, and scipy 0.13.2

Accepted Answer

What is going on?

The function is evidently not coded to deal with such large inputs, and encounters an overflow during the internal calculations.

The significance of the number 710 is that `math.exp(709)` can be represented as `float`, whereas `math.exp(710)` cannot:

```
In [27]: import math

In [28]: math.exp(709)
Out[28]: 8.218407461554972e+307

In [29]: math.exp(710)
---------------------------------------------------------------------------
OverflowError                             Traceback (most recent call last)
----> 1 math.exp(710)

OverflowError: math range error
```

Might be worth filing a bug against SciPy.

Scipy expit: Unexpected behavour. NaNs

Solution

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