how to understand empty dimension in python numpy array?

Question

In python numpy package, I am having trouble understanding the situation where an ndarray has the 2nd dimension being empty. Here is an example:

    In[1]: d2 = np.random.rand(10)
    In[2]: d2.shape = (-1, 1)

    In[3]: print d2.shape
    In[4]: print(d2)

    In[5]: print d2[::2, 0].shape
    In[6]: print d2[::2, 0]

    Out[3]:(10, 1)
    Out[4]:
[[ 0.12362278]
 [ 0.26365227]
 [ 0.33939172]
 [ 0.91501369]
 [ 0.97008342]
 [ 0.95294087]
 [ 0.38906367]
 [ 0.1012371 ]
 [ 0.67842086]
 [ 0.23711077]]

    Out[5]: (5,)
    Out[6]: [ 0.12362278  0.33939172  0.97008342  0.38906367  0.67842086]

My understanding is that d2 is a 10 rows by 1 column ndarray. Out[6] is obviously a 1 by 5 array, how can the dimensions be (5,) ? What does the empty 2nd dimension mean?

Answer 1

Let me just give you one example that illustrate one important difference.

d1 = np.array([1,2,3,4,5]) # array([1, 2, 3, 4, 5])
d1.shape -> (5,) # row array.    
d1.size -> 5
# Note: d1.T is the same as d1.

d2 = d1[np.newaxis] # array([[1, 2, 3, 4, 5]]). Note extra []
d2.shape -> (1,5) 
d2.size -> 5
# Note: d2.T will give a column array
array([[1],
       [2],
       [3],
       [4],
       [5]])
d2.T.shape -> (5,1)