The shape of the array can also be changed using the resize() method. If the specified dimension is larger than the actual array, The extra spaces in the new array will be filled with repeated copies of the original array.
The expand_dims() function is used to expand the shape of an array. Insert a new axis that will appear at the axis position in the expanded array shape. Syntax: numpy.expand_dims(a, axis)
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.
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.
Example:
# 1D array
In [7]: arr = np.arange(4)
In [8]: arr.shape
Out[8]: (4,)
# make it as row vector by inserting an axis along first dimension
In [9]: row_vec = arr[np.newaxis, :] # arr[None, :]
In [10]: row_vec.shape
Out[10]: (1, 4)
# make it as column vector by inserting an axis along second dimension
In [11]: col_vec = arr[:, np.newaxis] # arr[:, None]
In [12]: col_vec.shape
Out[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.
Example:
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 + x2
Out[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_new
Out[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).
Example:
In [124]: arr = np.arange(5*5).reshape(5,5)
In [125]: arr.shape
Out[125]: (5, 5)
# promoting 2D array to a 5D array
In [126]: arr_5D = arr[np.newaxis, ..., np.newaxis, np.newaxis] # arr[None, ..., None, None]
In [127]: arr_5D.shape
Out[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 array
In [131]: newaxes = (0, 3, -1)
In [132]: arr_5D = np.expand_dims(arr, axis=newaxes)
In [133]: arr_5D.shape
Out[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).
Example
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 None
Out[13]: True
P.S. Also see this great answer: newaxis vs reshape to add dimensions
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 None
True
It's just more descriptive if you read code that uses np.newaxis
instead of None
.
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)
>>> a
array([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 output
array([[[0],
[1],
[2],
[3],
[4],
[5],
[6],
[7],
[8],
[9]]])
>>> a[np.newaxis, :, np.newaxis].shape
(1, 10, 1)
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 1
s 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.
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] + b array([[ 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.
newaxis
object in the selection tuple serves to expand the dimensions of the resulting selection by one unit-length dimension.
It is not just conversion of row matrix to column matrix.
Consider the example below:
In [1]:x1 = np.arange(1,10).reshape(3,3)
print(x1)
Out[1]: array([[1, 2, 3],
[4, 5, 6],
[7, 8, 9]])
Now lets add new dimension to our data,
In [2]:x1_new = x1[:,np.newaxis]
print(x1_new)
Out[2]:array([[[1, 2, 3]],
[[4, 5, 6]],
[[7, 8, 9]]])
You can see that newaxis
added the extra dimension here, x1 had dimension (3,3) and X1_new has dimension (3,1,3).
How our new dimension enables us to different operations:
In [3]:x2 = np.arange(11,20).reshape(3,3)
print(x2)
Out[3]:array([[11, 12, 13],
[14, 15, 16],
[17, 18, 19]])
Adding x1_new and x2, we get:
In [4]:x1_new+x2
Out[4]:array([[[12, 14, 16],
[15, 17, 19],
[18, 20, 22]],
[[15, 17, 19],
[18, 20, 22],
[21, 23, 25]],
[[18, 20, 22],
[21, 23, 25],
[24, 26, 28]]])
Thus, newaxis
is not just conversion of row to column matrix. It increases the dimension of matrix, thus enabling us to do more operations on it.
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