Indexing a 1D Numpy array using 2D array

Question

In Numpy, can we use a 2D array as index into a 1D array? What array array indexing rule applies to following code?

# 1D array
arr = np.arange(10)
# array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

# 2D index 
indx = np.array([[2, 4], [6, 8]])

# 2D index in 1D array
arr[indx]

# Output of above indexing is a 2D array!
array([[2, 4],[6, 8]])

Answer 1

What array array indexing rule applies to following code?

That's how numpy's advanced indexing works. The shape of result array is related to shape of index array, the array's shape and the axis you're passing the index. Here are some examples that passes a 3D array as index to the first axis of arrays with different shapes.

In [47]: a.shape
Out[47]: (2, 5)

In [48]: b = a[np.array([[[0],[1]],[[1],[1]]])]

In [49]: b.shape
Out[49]: (2, 2, 1, 5)

In [50]: arr.shape
Out[50]: (3, 3, 3)

In [51]: b = arr[np.array([[[0],[1]],[[1],[1]]])]

In [52]: b.shape
Out[52]: (2, 2, 1, 3, 3)

And here is what you get when you pass different arrays to different axises:

In [61]: b = arr[[[0],[2]],[[1],[0]]]

In [62]: b.shape
Out[62]: (2, 1, 3)

In [63]: arr.shape
Out[63]: (3, 3, 3)

In all of these indexings, Numpy will check multiple things, first off, it checks the type of the objects passed as index. Secondly, it compares the shapes of your index array with the shape of respective axis of your array. Thirdly, it checks if the result produces a valid Numpy array.

Here are some other examples:

In [64]: b = arr[[[[0],[2]]],[[1],[0]]]

In [65]: b.shape
Out[65]: (1, 2, 1, 3)

In [66]: b
Out[66]: 
array([[[[ 3,  4,  5]],

        [[18, 19, 20]]]])

In [67]: b = arr[[[[0],[2]]],[1],[0]]

In [68]: b
Out[68]: 
array([[[ 3],
        [21]]])

In [69]: b = arr[[[['a'],[2]]],[1],[0]]
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
<ipython-input-69-dba030ba9787> in <module>()
----> 1 b = arr[[[['a'],[2]]],[1],[0]]

IndexError: only integers, slices (`:`), ellipsis (`...`), numpy.newaxis (`None`) and integer or boolean arrays are valid indices

In [70]: b = arr[[[[0],[2]]],[1],0]

In [71]: b = arr[[[[0],[2]]],[5],0]
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
<ipython-input-71-0962012e570a> in <module>()
----> 1 b = arr[[[[0],[2]]],[5],0]

IndexError: index 5 is out of bounds for axis 1 with size 3

In [72]: 

In [72]: b = arr[[[[0],[[2]]]],[5],0]
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-72-9a520b0cb30e> in <module>()
----> 1 b = arr[[[[0],[[2]]]],[5],0]

ValueError: setting an array element with a sequence.

In [73]: b = arr[[[[0],[[2]]]],[5],[0]]
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-73-67187db6f452> in <module>()
----> 1 b = arr[[[[0],[[2]]]],[5],[0]]

ValueError: setting an array element with a sequence.