numpy: what is the logic of the argmin() and argmax() functions?

Question

I can not understand the output of argmax and argmin when use with the axis parameter. For example:

>>> a = np.array([[1,2,4,7], [9,88,6,45], [9,76,3,4]])
>>> a
array([[ 1,  2,  4,  7],
       [ 9, 88,  6, 45],
       [ 9, 76,  3,  4]])
>>> a.shape
(3, 4)
>>> a.size
12
>>> np.argmax(a)
5
>>> np.argmax(a,axis=0)
array([1, 1, 1, 1])
>>> np.argmax(a,axis=1)
array([3, 1, 1])
>>> np.argmin(a)
0
>>> np.argmin(a,axis=0)
array([0, 0, 2, 2])
>>> np.argmin(a,axis=1)
array([0, 2, 2])

As you can see, the maximum value is the point (1,1) and the minimum one is the point (0,0). So in my logic when I run:

• np.argmin(a,axis=0) I expected array([0,0,0,0])
• np.argmin(a,axis=1) I expected array([0,0,0])
• np.argmax(a,axis=0) I expected array([1,1,1,1])
• np.argmax(a,axis=1) I expected array([1,1,1])

What is wrong with my understanding of things?

Answer 1

By adding the axis argument, NumPy looks at the rows and columns individually. When it's not given, the array a is flattened into a single 1D array.

axis=0 means that the operation is performed down the columns of a 2D array a in turn.

For example np.argmin(a, axis=0) returns the index of the minimum value in each of the four columns. The minimum value in each column is shown in bold below:

>>> a
array([[ 1,  2,  4,  7],  # 0
       [ 9, 88,  6, 45],  # 1
       [ 9, 76,  3,  4]]) # 2

>>> np.argmin(a, axis=0)
array([0, 0, 2, 2])

On the other hand, axis=1 means that the operation is performed across the rows of a.

That means np.argmin(a, axis=1) returns [0, 2, 2] because a has three rows. The index of the minimum value in the first row is 0, the index of the minimum value of the second and third rows is 2:

>>> a
#        0   1   2   3
array([[ 1,  2,  4,  7],
       [ 9, 88,  6, 45],
       [ 9, 76,  3,  4]])

>>> np.argmin(a, axis=1)
array([0, 2, 2])