Numpy: Why Is Difference Of A (2,1) Array And A Vertical Matrix Slice Not A (2,1) Array

Consider the following code: >>x=np.array([1,3]).reshape(2,1) array([[1], [3]]) >>M=np.array([[1,2],[3,4]]) array([[1, 2], [3, 4]]) >>y=M[:,0] >>x-

Solution 1:

numpy.array indexes such that a single value in any position collapses that dimension, while slicing retains it, even if the slice is only one element wide. This is completely consistent, for any number of dimensions:

>> A = numpy.arange(27).reshape(3, 3, 3)
>> A[0, 0, 0].shape
()

>> A[:, 0, 0].shape
(3,)

>> A[:, :, 0].shape
(3, 3)

>> A[:1, :1, :1].shape
(1, 1, 1)

Notice that every time a single number is used, that dimension is dropped.

You can obtain the semantics you expect by using numpy.matrix, where two single indexes return a order 0 array and all other types of indexing return matrices

>> M = numpy.asmatrix(numpy.arange(9).reshape(3, 3))

>> M[0, 0].shape
()

>> M[:, 0].shape   # This is different from the array
(3, 1)

>> M[:1, :1].shape
(1, 1)

Your example works as you expect when you use numpy.matrix:

>> x = numpy.matrix([[1],[3]])
>> M = numpy.matrix([[1,2],[3,4]])
>> y = M[:, 0]
>> x - y
matrix([[0],
        [0]])

Solution 2:

Look at the shape of y. It is (2,); 1d. The source array is (2,2), but you are selecting one column. M[:,0] not only selects the column, but removes that singleton dimension.

So we have for the 2 operations, this change in shape:

M[:,0]: (2,2) => (2,)
x - y: (2,1) (2,) => (2,1), (1,2) => (2,2)

There are various ways of ensuring that y has the shape (2,1). Index with a list/vector, M[:,[0]]; index with a slice, M[:,:1]. Add a dimension, M[:,0,None].

Think also what happens when M[0,:] or M[0,0].