沿给定轴将numpy ndarray与1d数组相乘

Question

看来我迷失于潜在的愚蠢之举。我有一个n维的numpy数组，我想将其与沿某个维度（可以改变！）的向量（1d数组）相乘。例如，假设我要沿着第一个数组的轴0将2d数组乘以1d数组，我可以执行以下操作：

a=np.arange(20).reshape((5,4))
b=np.ones(5)
c=a*b[:,np.newaxis]

容易，但我想将此概念扩展到n维（对于a，而b始终为1d）和任何轴。换句话说，我想知道如何在正确的位置使用np.newaxis生成切片。假设a是3d，并且我想沿axis
= 1进行乘法，那么我想生成一个可以正确给出的切片：

c=a*b[np.newaxis,:,np.newaxis]

即给定a的维数（例如3），以及要沿其相乘的轴（例如axis = 1），如何生成和传递切片：

np.newaxis,:,np.newaxis

谢谢。

Answer 1

解决方案代码-

import numpy as np

# Given axis along which elementwise multiplication with broadcasting 
# is to be performed
given_axis = 1

# Create an array which would be used to reshape 1D array, b to have 
# singleton dimensions except for the given axis where we would put -1 
# signifying to use the entire length of elements along that axis  
dim_array = np.ones((1,a.ndim),int).ravel()
dim_array[given_axis] = -1

# Reshape b with dim_array and perform elementwise multiplication with 
# broadcasting along the singleton dimensions for the final output
b_reshaped = b.reshape(dim_array)
mult_out = a*b_reshaped

运行示例以演示步骤-

In [149]: import numpy as np

In [150]: a = np.random.randint(0,9,(4,2,3))

In [151]: b = np.random.randint(0,9,(2,1)).ravel()

In [152]: whos
Variable   Type       Data/Info
-------------------------------
a          ndarray    4x2x3: 24 elems, type `int32`, 96 bytes
b          ndarray    2: 2 elems, type `int32`, 8 bytes

In [153]: given_axis = 1

现在，我们要沿进行元素乘法given axis = 1。让我们来创建dim_array：

In [154]: dim_array = np.ones((1,a.ndim),int).ravel()
     ...: dim_array[given_axis] = -1
     ...:

In [155]: dim_array
Out[155]: array([ 1, -1,  1])

最后，重塑b形状并执行逐元素乘法：

In [156]: b_reshaped = b.reshape(dim_array)
     ...: mult_out = a*b_reshaped
     ...:

whos再次查看信息，并特别注意b_reshaped＆mult_out：

In [157]: whos
Variable     Type       Data/Info
---------------------------------
a            ndarray    4x2x3: 24 elems, type `int32`, 96 bytes
b            ndarray    2: 2 elems, type `int32`, 8 bytes
b_reshaped   ndarray    1x2x1: 2 elems, type `int32`, 8 bytes
dim_array    ndarray    3: 3 elems, type `int32`, 12 bytes
given_axis   int        1
mult_out     ndarray    4x2x3: 24 elems, type `int32`, 96 bytes