Python/numpy issue with array/vector with empty second dimension

Question

I have what seems to be an easy question.

Observe the code:

In : x=np.array([0, 6])
Out: array([0, 6])
In : x.shape
Out: (2L,)

Which shows that the array has no second dimension, and therefore x is no differnet from x.T.

How can I make x have dimension (2L,1L)? The real motivation for this question is that I have an array y of shape [3L,4L], and I want y.sum(1) to be a vector that can be transposed, etc.

Answer 1

While you can reshape arrays, and add dimensions with [:,np.newaxis], you should be familiar with the most basic nested brackets, or list, notation. Note how it matches the display.

In [230]: np.array([[0],[6]])
Out[230]: 
array([[0],
       [6]])
In [231]: _.shape
Out[231]: (2, 1)

np.array also takes a ndmin parameter, though it add extra dimensions at the start (the default location for numpy.)

In [232]: np.array([0,6],ndmin=2)
Out[232]: array([[0, 6]])
In [233]: _.shape
Out[233]: (1, 2)

A classic way of making something 2d - reshape:

In [234]: y=np.arange(12).reshape(3,4)
In [235]: y
Out[235]: 
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])

sum (and related functions) has a keepdims parameter. Read the docs.

In [236]: y.sum(axis=1,keepdims=True)
Out[236]: 
array([[ 6],
       [22],
       [38]])
In [237]: _.shape
Out[237]: (3, 1)

empty 2nd dimension isn't quite the terminology. More like a nonexistent 2nd dimension.

A dimension can have 0 terms:

In [238]: np.ones((2,0))
Out[238]: array([], shape=(2, 0), dtype=float64)

If you are more familiar with MATLAB, which has a minimum of 2d, you might like the np.matrix subclass. It takes steps to ensure that most operations return another 2d matrix:

In [247]: ym=np.matrix(y)
In [248]: ym.sum(axis=1)
Out[248]: 
matrix([[ 6],
        [22],
        [38]])

The matrix sum does:

np.ndarray.sum(self, axis, dtype, out, keepdims=True)._collapse(axis)

The _collapse bit lets it return a scalar for ym.sum().

Answer 2

There is another point to keep dimension info:

In [42]: X
Out[42]: 
array([[0, 0],
       [0, 1],
       [1, 0],
       [1, 1]])

In [43]: X[1].shape
Out[43]: (2,)

In [44]: X[1:2].shape
Out[44]: (1, 2)

In [45]: X[1]
Out[45]: array([0, 1])

In [46]: X[1:2]  # this way will keep dimension
Out[46]: array([[0, 1]])