How does numpy.newaxis work and when to use it? How does numpy.newaxis work and when to use it? python python

How does numpy.newaxis work and when to use it?

Simply put, numpy.newaxis is used to increase the dimension of the existing array by one more dimension, when used once. Thus,

  • 1D array will become 2D array

  • 2D array will become 3D array

  • 3D array will become 4D array

  • 4D array will become 5D array

and so on..

Here is a visual illustration which depicts promotion of 1D array to 2D arrays.

newaxis canva visualization

Scenario-1: np.newaxis might come in handy when you want to explicitly convert a 1D array to either a row vector or a column vector, as depicted in the above picture.


# 1D arrayIn [7]: arr = np.arange(4)In [8]: arr.shapeOut[8]: (4,)# make it as row vector by inserting an axis along first dimensionIn [9]: row_vec = arr[np.newaxis, :]     # arr[None, :]In [10]: row_vec.shapeOut[10]: (1, 4)# make it as column vector by inserting an axis along second dimensionIn [11]: col_vec = arr[:, np.newaxis]     # arr[:, None]In [12]: col_vec.shapeOut[12]: (4, 1)

Scenario-2: When we want to make use of numpy broadcasting as part of some operation, for instance while doing addition of some arrays.


Let's say you want to add the following two arrays:

 x1 = np.array([1, 2, 3, 4, 5]) x2 = np.array([5, 4, 3])

If you try to add these just like that, NumPy will raise the following ValueError :

ValueError: operands could not be broadcast together with shapes (5,) (3,)

In this situation, you can use np.newaxis to increase the dimension of one of the arrays so that NumPy can broadcast.

In [2]: x1_new = x1[:, np.newaxis]    # x1[:, None]# now, the shape of x1_new is (5, 1)# array([[1],#        [2],#        [3],#        [4],#        [5]])

Now, add:

In [3]: x1_new + x2Out[3]:array([[ 6,  5,  4],       [ 7,  6,  5],       [ 8,  7,  6],       [ 9,  8,  7],       [10,  9,  8]])

Alternatively, you can also add new axis to the array x2:

In [6]: x2_new = x2[:, np.newaxis]    # x2[:, None]In [7]: x2_new     # shape is (3, 1)Out[7]: array([[5],       [4],       [3]])

Now, add:

In [8]: x1 + x2_newOut[8]: array([[ 6,  7,  8,  9, 10],       [ 5,  6,  7,  8,  9],       [ 4,  5,  6,  7,  8]])

Note: Observe that we get the same result in both cases (but one being the transpose of the other).

Scenario-3: This is similar to scenario-1. But, you can use np.newaxis more than once to promote the array to higher dimensions. Such an operation is sometimes needed for higher order arrays (i.e. Tensors).


In [124]: arr = np.arange(5*5).reshape(5,5)In [125]: arr.shapeOut[125]: (5, 5)# promoting 2D array to a 5D arrayIn [126]: arr_5D = arr[np.newaxis, ..., np.newaxis, np.newaxis]    # arr[None, ..., None, None]In [127]: arr_5D.shapeOut[127]: (1, 5, 5, 1, 1)

As an alternative, you can use numpy.expand_dims that has an intuitive axis kwarg.

# adding new axes at 1st, 4th, and last dimension of the resulting arrayIn [131]: newaxes = (0, 3, -1)In [132]: arr_5D = np.expand_dims(arr, axis=newaxes)In [133]: arr_5D.shapeOut[133]: (1, 5, 5, 1, 1)

More background on np.newaxis vs np.reshape

newaxis is also called as a pseudo-index that allows the temporary addition of an axis into a multiarray.

np.newaxis uses the slicing operator to recreate the array while numpy.reshape reshapes the array to the desired layout (assuming that the dimensions match; And this is must for a reshape to happen).


In [13]: A = np.ones((3,4,5,6))In [14]: B = np.ones((4,6))In [15]: (A + B[:, np.newaxis, :]).shape     # B[:, None, :]Out[15]: (3, 4, 5, 6)

In the above example, we inserted a temporary axis between the first and second axes of B (to use broadcasting). A missing axis is filled-in here using np.newaxis to make the broadcasting operation work.

General Tip: You can also use None in place of np.newaxis; These are in fact the same objects.

In [13]: np.newaxis is NoneOut[13]: True

P.S. Also see this great answer: newaxis vs reshape to add dimensions

What is np.newaxis?

The np.newaxis is just an alias for the Python constant None, which means that wherever you use np.newaxis you could also use None:

>>> np.newaxis is NoneTrue

It's just more descriptive if you read code that uses np.newaxis instead of None.

How to use np.newaxis?

The np.newaxis is generally used with slicing. It indicates that you want to add an additional dimension to the array. The position of the np.newaxis represents where I want to add dimensions.

>>> import numpy as np>>> a = np.arange(10)>>> aarray([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])>>> a.shape(10,)

In the first example I use all elements from the first dimension and add a second dimension:

>>> a[:, np.newaxis]array([[0],       [1],       [2],       [3],       [4],       [5],       [6],       [7],       [8],       [9]])>>> a[:, np.newaxis].shape(10, 1)

The second example adds a dimension as first dimension and then uses all elements from the first dimension of the original array as elements in the second dimension of the result array:

>>> a[np.newaxis, :]  # The output has 2 [] pairs!array([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]])>>> a[np.newaxis, :].shape(1, 10)

Similarly you can use multiple np.newaxis to add multiple dimensions:

>>> a[np.newaxis, :, np.newaxis]  # note the 3 [] pairs in the outputarray([[[0],        [1],        [2],        [3],        [4],        [5],        [6],        [7],        [8],        [9]]])>>> a[np.newaxis, :, np.newaxis].shape(1, 10, 1)

Are there alternatives to np.newaxis?

There is another very similar functionality in NumPy: np.expand_dims, which can also be used to insert one dimension:

>>> np.expand_dims(a, 1)  # like a[:, np.newaxis]>>> np.expand_dims(a, 0)  # like a[np.newaxis, :]

But given that it just inserts 1s in the shape you could also reshape the array to add these dimensions:

>>> a.reshape(a.shape + (1,))  # like a[:, np.newaxis]>>> a.reshape((1,) + a.shape)  # like a[np.newaxis, :]

Most of the times np.newaxis is the easiest way to add dimensions, but it's good to know the alternatives.

When to use np.newaxis?

In several contexts is adding dimensions useful:

  • If the data should have a specified number of dimensions. For example if you want to use matplotlib.pyplot.imshow to display a 1D array.

  • If you want NumPy to broadcast arrays. By adding a dimension you could for example get the difference between all elements of one array: a - a[:, np.newaxis]. This works because NumPy operations broadcast starting with the last dimension 1.

  • To add a necessary dimension so that NumPy can broadcast arrays. This works because each length-1 dimension is simply broadcast to the length of the corresponding1 dimension of the other array.

1 If you want to read more about the broadcasting rules the NumPy documentation on that subject is very good. It also includes an example with np.newaxis:

>>> a = np.array([0.0, 10.0, 20.0, 30.0])>>> b = np.array([1.0, 2.0, 3.0])>>> a[:, np.newaxis] + barray([[  1.,   2.,   3.],       [ 11.,  12.,  13.],       [ 21.,  22.,  23.],       [ 31.,  32.,  33.]])

You started with a one-dimensional list of numbers. Once you used numpy.newaxis, you turned it into a two-dimensional matrix, consisting of four rows of one column each.

You could then use that matrix for matrix multiplication, or involve it in the construction of a larger 4 x n matrix.