Confusion in size of a numpy array

Question

Python numpy array 'size' confuses me a lot

a = np.array([1,2,3])
a.size = (3, )
------------------------
b = np.array([[2,1,3,5],
             [2,2,5,1],
             [3,6,99,5]])
b.size = (3,4)

'b' makes sense since it has 3 rows and 4 columns in each But how is 'a' size = (3, ) ? Shouldn't it be (1,3) since its 1 row and 3 columns?

Answer 1

No, a numpy.ndarray with shape (1, 3) would look like:

np.array([[1,2,3]])

Think about how the shape corresponds to indexing:

arr[0, ...]  #First row

I still have three more options, namely:

arr[0,0]
arr[0,1]
arr[0,2]

Try doing that with a 1 dimensional array

Answer 2

You should resist the urge to think of numpy arrays as having rows and columns, but instead consider them as having dimensions and shape. This is an important point which differentiates np.array and np.matrix:

x = np.array([1, 2, 3])
print(x.ndim, x.shape)  # 1 (3,)

y = np.matrix([1, 2, 3])
print(y.ndim, y.shape)  # 2 (1, 3)

An n-D array can only use n integer(s) to represent its shape. Therefore, a 1-D array only uses 1 integer to specify its shape.

In practice, combining calculations between 1-D and 2-D arrays is not a problem for numpy, and syntactically clean since @ matrix operation was introduced in Python 3.5. Therefore, there is rarely a need to resort to np.matrix in order to satisfy the urge to see expected row and column counts.

In the rare instances where 2 dimensions are required, you can still use numpy.array with some manipulation:

a = np.array([1, 2, 3])[:, None]  # equivalent to np.array([[1], [2], [3]])
print(a.ndim, a.shape)  # 2 (3, 1)

b = np.array([[1, 2, 3]])  # equivalent to np.array([1, 2, 3])[:, None].T
print(b.ndim, b.shape)  # 2 (1, 3)

Answer 3

I think you meant ndarray.shape. In that case, there's no need for confusion. Quoting the documentation from ndarray.shape:

Tuple of array dimensions.

ndarray.shape simply returns a shape tuple.

In [21]: a.shape
Out[21]: (3,)

This simply means that a is an 1D array with 3 entries.

If the shape tuple returns it as (1,3) then a would become a 2D array. For that you need to use:

In [23]: a = a[np.newaxis, :]

In [24]: a.shape
Out[24]: (1, 3)

Since array b is 2D, the shape tuple has two entries.

In [22]: b.shape
Out[22]: (3, 4)