Numpy dimension, shape, axeses

First:

By convention, in Python world, the shortcut for numpy is np, so:

In [1]: import numpy as np

In [2]: a = np.array([[1,2],[3,4]])

Second：

In Numpy, dimension, axis/axes, shape are related and sometimes similar concepts:

dimension

In Mathematics/Physics, dimension or dimensionality is informally defined as the minimum number of coordinates needed to specify any point within a space. But in Numpy, according to the numpy doc, it's the same as axis/axes:

In Numpy dimensions are called axes. The number of axes is rank.

In [3]: a.ndim  # num of dimensions/axes, *Mathematics definition of dimension*

Out[3]: 2

axis/axes

the nth coordinate to index an array in Numpy. And multidimensional arrays can have one index per axis.

In [4]: a[1,0]  # to index `a`, we specific 1 at the first axis and 0 at the second axis.

Out[4]: 3  # which results in 3 (locate at the row 1 and column 0, 0-based index)

First:

By convention, in Python world, the shortcut for numpy is np, so:

In [1]: import numpy as np

In [2]: a = np.array([[1,2],[3,4]])

Second：

In Numpy, dimension, axis/axes, shape are related and sometimes similar concepts:

dimension

In Mathematics/Physics, dimension or dimensionality is informally defined as the minimum number of coordinates needed to specify any point within a space. But in Numpy, according to the numpy doc, it's the same as axis/axes:

In Numpy dimensions are called axes. The number of axes is rank.

In [3]: a.ndim  # num of dimensions/axes, *Mathematics definition of dimension*

Out[3]: 2

axis/axes

the nth coordinate to index an array in Numpy. And multidimensional arrays can have one index per axis.

In [4]: a[1,0]  # to index `a`, we specific 1 at the first axis and 0 at the second axis.

Out[4]: 3  # which results in 3 (locate at the row 1 and column 0, 0-based index)

shape

describes how many data (or the range) along each available axis.

In [5]: a.shape

Out[5]: (2, 2)  # both the first and second axis have 2 (columns/rows/pages/blocks/...) data

import numpy as np   

>>> np.shape(a)

(2,2)

Also works if the input is not a numpy array but a list of lists

>>> a = [[1,2],[1,2]]

>>> np.shape(a)

(2,2)

Or a tuple of tuples

>>> a = ((1,2),(1,2))

>>> np.shape(a)

(2,2)

np.shape first turns its argument into an array if it doesn't have the shape attribute, That's why it works on the list and tuple examples. 

References:

https://stackoverflow.com/questions/3061761/numpy-array-dimensions