检查2D NumPy数组坐标的优雅方法在一定范围内

Question

So let us say we have a 2D NumPy array (denoting co-ordinates) and I want to check whether all the co-ordinates lie within a certain range. What is the most Pythonic way to do this? For example:

a = np.array([[-1,2], [1,5], [6,7], [5,2], [3,4], [0, 0], [-1,-1]])

#ALL THE COORDINATES WITHIN x-> 0 to 4 AND y-> 0 to 4 SHOULD
 BE PUT IN b (x and y ranges might not be equal)

b = #DO SOME OPERATION

>>> b
>>> [[3,4],
    [0,0]]

Answer 1

If the range is the same for both directions, x, and y, just compare them and use all :

import numpy as np

a = np.array([[-1,2], [1,5], [6,7], [5,2], [3,4], [0, 0], [-1,-1]])
a[(a >= 0).all(axis=1) & (a <= 4).all(axis=1)]
# array([[3, 4],
#        [0, 0]])

If the ranges are not the same, you can also compare to an iterable of the same size as that axis (so two here):

mins = 0, 1   # x_min, y_min
maxs = 4, 10  # x_max, y_max

a[(a >= mins).all(axis=1) & (a <= maxs).all(axis=1)]
# array([[1, 5],
#        [3, 4]])

---

To see what is happening here, let's have a look at the intermediate steps:

The comparison gives a per-element result of the comparison, with the same shape as the original array:

a >= mins
# array([[False,  True],
#        [ True,  True],
#        [ True,  True],
#        [ True,  True],
#        [ True,  True],
#        [ True, False],
#        [False, False]], dtype=bool)

Using nmpy.ndarray.all , you get if all values are truthy or not, similarly to the built-in function all :

(a >= mins).all()
# False

With the axis argument, you can restrict this to only compare values along one (or multiple) axis of the array:

(a >= mins).all(axis=1)
# array([False,  True,  True,  True,  True, False, False], dtype=bool)
(a >= mins).all(axis=0)
# array([False, False], dtype=bool)

Note that the output of this is the same shape as array, except that all dimnsions mentioned with axis have been contracted to a single True / False .

When indexing an array with a sequence of True, False values, it is cast to the right shape if possible. Since we index an array with shape (7, 2) with an (7,) = (7, 1) index, the values are implicitly repeated along the second dimension, so these values are used to select rows of the original array.