numpy - python difference between the two form of matrix x[i,j] and x[i][j]

Question

i want to understand the difference between x[i,j] and x[i][j] where x is a matrix

x = np.zeros((N,M))

The answer that i found while doing the research is always about array with 2D dimension but in my case i have a matrix with two index to work with i and j and i need to manipulate the matrix according the index with a for loop.

    for i in range(1,N+1):
        for j in range(1,M+1):
            x[i-1][j-1]=random.uniform(5,10)

so can you help me understand the difference between x[i,j] and x[i][j]and to be more clear for each i(base station) there is a number of j (users)

Answer 1

For simple indexing of a 2d array both forms work:

In [28]: x = np.arange(6).reshape(2,3)
In [29]: x
Out[29]: 
array([[0, 1, 2],
       [3, 4, 5]])
In [30]: x[1,2]
Out[30]: 5
In [31]: x[1][2]
Out[31]: 5

For np.matrix (which you probably shouldn't be using anyways) they aren't:

In [32]: X = np.matrix(x)
In [33]: X
Out[33]: 
matrix([[0, 1, 2],
        [3, 4, 5]])
In [34]: X[1,2]
Out[34]: 5
In [35]: X[1][2]
...
IndexError: index 2 is out of bounds for axis 0 with size 1

The two forms are not syntactically the same. [1][2] first indexes with 1, and then indexes the result with 2. That's not the same as indexing once with both parameters.

In [36]: x[1]
Out[36]: array([3, 4, 5])      # (3,) shape
In [37]: X[1]
Out[37]: matrix([[3, 4, 5]])   # (1,3) shape

The error arises because np.matrix returns another np.matrix. So the next [2] indexing will again be indexing the first dimension.

x[1] is really short for x[1,:], that is, index the first dimension, and slice all the rest (or X[1,...] to allow for 3d and higher). So x[1][2] is really

temp = x[1,:]
temp[2]

or for the matrix case:

temp = X[1,:]
temp[2,:]

In other words, it is 2 indexing operations. It's a Python expression, not a specific numpy usage.

When we index with lists or slices, the difference between the two forms becomes more significant, especially when setting values.

I encourage beginners to use the x[i,j] form. Don't use x[1][2] unless you really understand what is going on.

If needed I could get into how indexing is translated into calls to __setitem__ and __getitem__.