标签归档:array-broadcasting

numpy.newaxis如何工作以及何时使用?

问题:numpy.newaxis如何工作以及何时使用?

当我尝试

numpy.newaxis

结果为我提供了一个x轴从0到1 numpy.newaxis的二维绘图框。但是,当我尝试使用对向量进行切片时,

vector[0:4,]
[ 0.04965172  0.04979645  0.04994022  0.05008303]
vector[:, np.newaxis][0:4,]
[[ 0.04965172]
[ 0.04979645]
[ 0.04994022]
[ 0.05008303]]

除了将行向量更改为列向量之外,是否一样?

通常,的用途是什么numpy.newaxis,我们应该在什么情况下使用它?

When I try

numpy.newaxis

the result gives me a 2-d plot frame with x-axis from 0 to 1. However, when I try using numpy.newaxis to slice a vector,

vector[0:4,]
[ 0.04965172  0.04979645  0.04994022  0.05008303]
vector[:, np.newaxis][0:4,]
[[ 0.04965172]
[ 0.04979645]
[ 0.04994022]
[ 0.05008303]]

Is it the same thing except that it changes a row vector to a column vector?

Generally, what is the use of numpy.newaxis, and in which circumstances should we use it?


回答 0

简而言之,当使用一次时,用于将现有数组的尺寸numpy.newaxis增加一维。从而,

  • 一维阵列将变为二维阵列

  • 2D阵列将变为3D阵列

  • 3D阵列将变成4D阵列

  • 4D阵列将变为5D阵列

等等..

这里是一个视觉说明描绘促进 1D阵列以二维阵列。


方案1:如上图所示,np.newaxis当您想将一维数组显式转换为行向量列向量时,可能会派上用场。

例:

# 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)

场景2:当我们想将numpy广播用作某些操作的一部分时,例如在添加一些数组时。

例:

假设您要添加以下两个数组:

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

如果您尝试像这样添加它们,NumPy将引发以下内容ValueError

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

在这种情况下,您可以np.newaxis用来增加数组之一的尺寸,以便NumPy可以广播

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

现在,添加:

In [3]: x1_new + x2
Out[3]:
array([[ 6,  5,  4],
       [ 7,  6,  5],
       [ 8,  7,  6],
       [ 9,  8,  7],
       [10,  9,  8]])

另外,您也可以向数组添加新轴x2

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

现在,添加:

In [8]: x1 + x2_new
Out[8]: 
array([[ 6,  7,  8,  9, 10],
       [ 5,  6,  7,  8,  9],
       [ 4,  5,  6,  7,  8]])

注意请注意,在两种情况下我们都得到相同的结果(但一种是另一种的转置)。


方案3:这类似于方案1。但是,你可以使用np.newaxis不止一次地促进阵列更高的层面。有时对于高阶数组(即Tensors)需要这样的操作。

例:

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)

关于np.newaxisnp.reshape的更多背景

newaxis 也称为伪索引,它允许将轴临时添加到多数组中。

np.newaxis使用切片运算符来重新创建阵列而np.reshape重塑阵列所需的布局(假设尺寸匹配;这是必须reshape发生)。

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)

在上面的示例中,我们在B(使用广播)的第一和第二轴之间插入了一个临时轴。此处使用缺失轴来填充,np.newaxis以使广播操作正常进行。


一般提示:您也可以None代替使用np.newaxis;这些实际上是相同的对象

In [13]: np.newaxis is None
Out[13]: True

PS也看到了一个很好的答案:newaxis vs reshape添加尺寸

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


回答 1

什么np.newaxis

np.newaxis仅仅是Python的常量的别名None,这意味着无论你使用np.newaxis,你也可以使用None

>>> np.newaxis is None
True

如果您阅读使用而不是的代码,则更具描述np.newaxisNone

如何使用np.newaxis

np.newaxis,通常使用与切片。它表示您要向数组添加其他维度。的位置np.newaxis代表我要添加尺寸的位置。

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

在第一个示例中,我使用第一个维度中的所有元素并添加第二个维度:

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

第二个示例将一个维添加为第一维,然后将原始数组的第一维中的所有元素用作结果数组的第二维中的元素:

>>> 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)

同样,您可以使用多个np.newaxis添加多个尺寸:

>>> 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)

有替代品np.newaxis吗?

NumPy:还有另一种非常相似的功能,np.expand_dims也可以用于插入一个尺寸:

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

但是考虑到它只是在中插入1s,shape您也可以reshape在数组中添加以下尺寸:

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

大多数情况下np.newaxis,添加尺寸是最简单的方法,但是最好知道替代方法。

什么时候使用np.newaxis

在某些情况下,添加尺寸很有用:

  • 数据是否应具有指定的维数。例如,如果要matplotlib.pyplot.imshow用于显示一维数组。

  • 如果您想让NumPy广播数组。通过添加维度,您可以例如获取一个数组的所有元素之间的差:a - a[:, np.newaxis]。之所以可行,是因为NumPy操作从最后一个维度1开始广播。

  • 添加必要的尺寸,以便NumPy 可以广播数组。这是可行的,因为每个length-1维仅被广播到另一个数组的对应1维的长度。


1如果您想了解有关广播规则的更多信息,关于该主题NumPy文档非常好。它还包括一个示例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.]])

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 None
True

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)
>>> 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)

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] + b
array([[  1.,   2.,   3.],
       [ 11.,  12.,  13.],
       [ 21.,  22.,  23.],
       [ 31.,  32.,  33.]])

回答 2

您从一维数字列表开始。使用完后numpy.newaxis,您将其转换为二维矩阵,每个矩阵由四行组成。

然后,您可以使用该矩阵进行矩阵乘法,或者将其用于构建更大的4 xn矩阵。

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.


回答 3

newaxis选择元组中的object对象用于将结果选择的尺寸扩展一个单位长度尺寸。

这不仅仅是行矩阵到列矩阵的转换。

考虑下面的示例:

In [1]:x1 = np.arange(1,10).reshape(3,3)
       print(x1)
Out[1]: array([[1, 2, 3],
               [4, 5, 6],
               [7, 8, 9]])

现在让我们为数据添加新维度,

In [2]:x1_new = x1[:,np.newaxis]
       print(x1_new)
Out[2]:array([[[1, 2, 3]],

              [[4, 5, 6]],

              [[7, 8, 9]]])

您可以newaxis在此处看到添加了额外的维度,x1的维度为(3,3),X1_new的维度为(3,1,3)。

我们的新维度如何使我们能够进行不同的操作:

In [3]:x2 = np.arange(11,20).reshape(3,3)
       print(x2)
Out[3]:array([[11, 12, 13],
              [14, 15, 16],
              [17, 18, 19]]) 

将x1_new和x2相加,我们得到:

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]]])

因此,newaxis不仅仅是行到列矩阵的转换。它增加了矩阵的维数,从而使我们能够对其进行更多操作。

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.