Understanding argmax

Question

Let say I have the matrix

import numpy as np    
A = np.matrix([[1,2,3,33],[4,5,6,66],[7,8,9,99]])

I am trying to understand the function a

Answer 1

In my first steps in python i have tested this function. And the result with this example clarified me how works argmax.

Example:

# Generating 2D array for input 
array = np.arange(20).reshape(4, 5) 
array[1][2] = 25

print("The input array: \n", array) 

# without axis
print("\nThe max element: ", np.argmax(array))
# with axis
print("\nThe indices of max element: ", np.argmax(array, axis=0)) 
print("\nThe indices of max element: ", np.argmax(array, axis=1)) 

Result Example:

The input array: 
[[ 0  1  2  3  4]
[ 5  6 25  8  9]
[10 11 12 13 14]
[15 16 17 18 19]]

The max element:  7

The indices of max element:  [3 3 1 3 3]

The indices of max element:  [4 2 4 4]

In that result we can see 3 results.

1. The highest element in all array is in position 7.
2. The highest element in every column is in the last row which index is 3, except on third column where the highest value is in row number two which index is 1.
3. The highest element in every row is in the last column which index is 4, except on second row where the highest value is in third columen which index is 2.

Reference: https://www.crazygeeks.org/numpy-argmax-in-python/

I hope that it helps.

Answer 2

No argmax returns the position of the largest value. max returns the largest value.

import numpy as np    
A = np.matrix([[1,2,3,33],[4,5,6,66],[7,8,9,99]])

np.argmax(A)  # 11, which is the position of 99

np.argmax(A[:,:])  # 11, which is the position of 99

np.argmax(A[:1])  # 3, which is the position of 33

np.argmax(A[:,2])  # 2, which is the position of 9

np.argmax(A[1:,2])  # 1, which is the position of 9

Answer 3

argmax is a function which gives the index of the greatest number in the given row or column and the row or column can be decided using axis attribute of argmax funcion. If we give axis=0 then it will give the index from columns and if we give axis=1 then it will give the index from rows.

In your given example A[1:, 2] it will first fetch the values from 1st row on wards and the only 2nd column value from those rows, then it will find the index of max value from into the resulted matrix.

Answer 4

It took me a while to figure this function out. Basically argmax returns you the index of the maximum value in the array. Now the array can be 1 dimensional or multiple dimensions. Following are some examples.

1 dimensional

a = [[1,2,3,4,5]]
np.argmax(a)
>>4

The array is 1 dimensional so the function simply returns the index of the maximum value(5) in the array, which is 4.

Multiple dimensions

a = [[1,2,3],[4,5,6]]
np.argmax(a)
>>5

In this example the array is 2 dimensional, with shape (2,3). Since no axis parameter is specified in the function, the numpy library flattens the array to a 1 dimensional array and then returns the index of the maximum value. In this case the array is transformed to [[1,2,3,4,5,6]] and then returns the index of 6, which is 5.

When parameter is axis = 0

a = [[1,2,3],[4,5,6]]
np.argmax(a, axis=0)
>>array([1, 1, 1])

The result here was a bit confusing to me at first. Since the axis is defined to be 0, the function will now try to find the maximum value along the rows of the matrix. The maximum value,6, is in the second row of the matrix. The index of the second row is 1. According to the documentation https://docs.scipy.org/doc/numpy-1.15.0/reference/generated/numpy.argmax.html the dimension specified in the axis parameter will be removed. Since the shape of the original matrix was (2,3) and axis specified as 0, the returned matrix will have a shape of(3,) instead, since the 2 in the original shape(2,3) is removed.The row in which the maximum value was found is now repeated for the same number of elements as the columns in the original matrix i.e. 3.

When parameter is axis = 1

a = [[1,2,3],[4,5,6]]
np.argmax(a, axis=1)
>>array([2, 2])

Same concept as above but now index of the column is returned at which the maximum value is available. In this example the maximum value 6 is in the 3rd column, index 2. The column of the original matrix with shape (2,3) will be removed, transforming to (2,) and so the return array will display two elements, each showing the index of the column in which the maximum value was found.