python 静默转置秩为 1 的数组

Question

import numpy as np
x1 = np.arange(9.0).reshape((3, 3))
print("x1\n",x1,"\n")
x2 = np.arange(3.0)
print("x2\n",x2)
print(x2.shape,"\n")
print("Here, the shape of x2 is 3 rows by 1 column ")
print("x1@x2\n",x1@x2)
print("")
print("x2@x1  should not be possible\n",x2@x1,"\n"*3)

给予

x1
 [[0. 1. 2.]
 [3. 4. 5.]
 [6. 7. 8.]] 

x2
 [0. 1. 2.]
(3,) 

Here, the shape of x2 is 3 rows by 1 column 
x1@x2 =
 [ 5. 14. 23.]

x2@x1  should not be possible, BUT
 [15. 18. 21.]

Python3 似乎默默地将 x2 转换为 (1,3) 数组，以便它可以乘以 x1。还是我缺少一些语法？

Answer 1

Numpy broadcasted 数组。

引用广播文档：

The term broadcasting describes how numpy treats arrays with different shapes during arithmetic operations. Subject to certain constraints, the smaller array is “broadcast” across the larger array so that they have compatible shapes. Broadcasting provides a means of vectorizing array operations so that looping occurs in C instead of Python. It does this without making needless copies of data and usually leads to efficient algorithm implementations. There are, however, cases where broadcasting is a bad idea because it leads to inefficient use of memory that slows computation.

将以下行添加到您的代码中，您将 x2 的形状明确设置为 (3,1)，您将收到如下错误：

import numpy as np
x1 = np.arange(9.0).reshape((3, 3))
print(x1.shape) # new line added
print("x1\n",x1,"\n")
x2 = np.arange(3.0)
x2 = x2.reshape(3, 1) # new line added
print("x2\n",x2)
print(x2.shape,"\n")
print("Here, the shape of x2 is 3 rows by 1 column ")
print("x1@x2\n",x1@x2)
print("")
print("x2@x1  should not be possible\n",x2@x1,"\n"*3)

输出

(3, 3)
x1
 [[0. 1. 2.]
 [3. 4. 5.]
 [6. 7. 8.]] 

x2
 [[0.]
 [1.]
 [2.]]
(3, 1) 

Here, the shape of x2 is 3 rows by 1 column 
x1@x2
 [[ 5.]
 [14.]
 [23.]]

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-12-c61849986c5c> in <module>
     12 print("x1@x2\n",x1@x2)
     13 print("")
---> 14 print("x2@x1  should not be possible\n",x2@x1,"\n"*3)

ValueError: matmul: Input operand 1 has a mismatch in its core dimension 0, with gufunc signature (n?,k),(k,m?)->(n?,m?) (size 3 is different from 1)

python 静默转置秩为 1 的数组

python silently transposing rank 1 arrays

python

arrays

matrix-multiplication