numpy max vs amax vs maximum

np.max is just an alias for np.amax. This function only works on a single input array and finds the value of maximum element in that entire array (returning a scalar). Alternatively, it takes an axis argument and will find the maximum value along an axis of the input array (returning a new array).

>>> a = np.array([[0, 1, 6],
                  [2, 4, 1]])
>>> np.max(a)
6
>>> np.max(a, axis=0) # max of each column
array([2, 4, 6])

The default behaviour of np.maximum is to take two arrays and compute their element-wise maximum. Here, ‘compatible’ means that one array can be broadcast to the other. For example:

>>> b = np.array([3, 6, 1])
>>> c = np.array([4, 2, 9])
>>> np.maximum(b, c)
array([4, 6, 9])

But np.maximum is also a universal function which means that it has other features and methods which come in useful when working with multidimensional arrays. For example you can compute the cumulative maximum over an array (or a particular axis of the array):

>>> d = np.array([2, 0, 3, -4, -2, 7, 9])
>>> np.maximum.accumulate(d)
array([2, 2, 3, 3, 3, 7, 9])

This is not possible with np.max.

You can make np.maximum imitate np.max to a certain extent when using np.maximum.reduce:

>>> np.maximum.reduce(d)
9
>>> np.max(d)
9

Basic testing suggests the two approaches are comparable in performance; and they should be, as np.max() actually calls np.maximum.reduce to do the computation.