numpy mean is larger than max for memmap

Question

I have an array of timestamps, increasing for each row in the 2nd column of matrix X. I calculate the mean value of the timestamps and it's larger than the max value. I'm using a numpy memmap for storage. Why is this happening?

>>> self.X[:,1]
memmap([  1.45160858e+09,   1.45160858e+09,   1.45160858e+09, ...,
     1.45997146e+09,   1.45997683e+09,   1.45997939e+09], dtype=float32)
>>> np.mean(self.X[:,1])
1.4642646e+09
>>> np.max(self.X[:,1])
memmap(1459979392.0, dtype=float32)
>>> np.average(self.X[:,1])
1.4642646e+09
>>> self.X[:,1].shape
(873608,)
>>> np.sum(self.X[:,1])
memmap(1279193195216896.0, dtype=float32)
>>> np.sum(self.X[:,1]) / self.X[:,1].shape[0]
memmap(1464264515.9120522)

EDIT: I have uploaded the memmap file here. http://www.filedropper.com/x_2 This is how I load it.

filepath = ...
shape = (875422, 23)
X = np.memmap(filepath, dtype="float32", mode="r", shape=shape)

# I preprocess X by removing rows with all 0s
# note this step doesn't affect the problem
to_remove = np.where(np.all(X == 0, axis=1))[0]
X = np.delete(X, to_remove, axis=0)

Answer 1

This is not a numpy or memmap issue. The issue is with floating point, float32 to be precise. You can see the same error happening in other languages like C++.

The float32 accumulator used gets imprecise as more and more numbers are added to it.

In [26]: a = np.ones((1024,1024), dtype=np.float32)*4567

In [27]: a.min()
Out[27]: 4567.0

In [28]: a.max()
Out[28]: 4567.0

In [29]: a.mean()
Out[29]: 4596.5264

This won't happen in np.float64 type (gives some more breathing room).

In [30]: a = np.ones((1024,1024), dtype=np.float64)*4567

In [31]: a.min()
Out[31]: 4567.0

In [32]: a.mean()
Out[32]: 4567.0

You can make mean() to use a float64 buffer by specifying it explicitly.

In [12]: a = np.ones((1024,1024), dtype=np.float32)*4567

In [13]: a.mean(dtype=np.float64)
Out[13]: 4567.0