numpy-np.ix_函数的使用

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博客围绕Numpy的np.ix_函数展开，给出官方文档链接，虽表示对用法和操作代码不太懂，但通过参考链接分析得出，该函数第一个参数返回行索引，第二个返回列索引等。还举例说明了二维和三维array使用该函数获取元素的情况。

官方文档：https://numpy.org/doc/stable/reference/generated/numpy.ix_.html#numpy.ix_，给出的用法是：

numpy.ix_(*args)
'''
Construct an open mesh from multiple sequences.

This function takes N 1-D sequences and returns N outputs with N dimensions each, such that the shape is 1 in all but one dimension and the dimension with the non-unit shape value cycles through all N dimensions.

Using ix_ one can quickly construct index arrays that will index the cross product. a[np.ix_([1,3],[2,5])] returns the array [[a[1,2] a[1,5]], [a[3,2] a[3,5]]].
'''

看不太懂，操作代码也是不懂：

a = np.arange(10).reshape(2, 5)
print(a)
ixgrid = np.ix_([0, 1], [2, 4])
print("-" * 10)
print(ixgrid)
print("-" * 10)
print(a[ixgrid])
'''
输出：
[[0 1 2 3 4]
 [5 6 7 8 9]]
----------
(array([[0],
       [1]]), array([[2, 4]]))
----------
[[2 4]
 [7 9]]
'''

参考链接中给出的：

'''
Its main use is to create an open mesh to select specific indices from an array (specific sub-array). 
An easy example to understand it is: Say you have an array of shape (5,5), 
and you would like to select the sub-array that is constructed from selecting 
rows 1 and 3 and columns 0 and 3. 
You can use np.ix_ to create such (index) mesh to be able to select sub-array as follows:
'''
a = np.arange(5*5).reshape(5,5)
print(a)
print("-" * 10)
sub_indices = np.ix_([1,3],[0,3])
print(sub_indices)
print("-" * 10)
print(a[sub_indices])
'''
输出：
[[ 0  1  2  3  4]
 [ 5  6  7  8  9]
 [10 11 12 13 14]
 [15 16 17 18 19]
 [20 21 22 23 24]]
----------
(array([[1],
       [3]]), array([[0, 3]]))
----------
[[ 5  8]
 [15 18]]
'''

通过上面的操作，得到的是'a'中行索引为1、3和列索引为0、3的元素：即'a[1, 0], a[1, 3], a[3, 0], a[3, 3]'。

col 0    col 3
   |        |
   v        v
[[ 0  1  2  3  4]   
 [ 5  6  7  8  9]   <- row 1
 [10 11 12 13 14]
 [15 16 17 18 19]   <- row 3
 [20 21 22 23 24]]

从np.ix_返回的结果看，函数第一个参数返回‘行的索引’，第二个参数返回‘列的索引’，第三个参数返回‘深度的索引’，以此类推。

当索引三维array时：

b = np.arange(5*5*5).reshape(5, 5, 5)
print(b)
print("-" * 10)
sub_indices = np.ix_([1,3],[0,3],[1,3])
print(sub_indices)
print("-" * 10)
print(b[sub_indices])
'''
输出：
[[[  0   1   2   3   4]
  [  5   6   7   8   9]
  [ 10  11  12  13  14]
  [ 15  16  17  18  19]
  [ 20  21  22  23  24]]

 [[ 25  26  27  28  29]
  [ 30  31  32  33  34]
  [ 35  36  37  38  39]
  [ 40  41  42  43  44]
  [ 45  46  47  48  49]]

 [[ 50  51  52  53  54]
  [ 55  56  57  58  59]
  [ 60  61  62  63  64]
  [ 65  66  67  68  69]
  [ 70  71  72  73  74]]

 [[ 75  76  77  78  79]
  [ 80  81  82  83  84]
  [ 85  86  87  88  89]
  [ 90  91  92  93  94]
  [ 95  96  97  98  99]]

 [[100 101 102 103 104]
  [105 106 107 108 109]
  [110 111 112 113 114]
  [115 116 117 118 119]
  [120 121 122 123 124]]]
----------
(array([[[1]],

       [[3]]]), array([[[0],
        [3]]]), array([[[1, 3]]]))
----------
[[[26 28]
  [41 43]]

 [[76 78]
  [91 93]]]
'''

通过上面的操作，得到的是'b'中'b[1, 0, 1], b[1, 0, 3], b[1, 3, 1], b[1, 3, 3],b[3, 0, 1], b[3, 0, 3], b[3, 3, 1], b[3, 3, 3]'。

参考：

https://stackoverflow.com/questions/62505046/what-does-numpy-ix-function-do-and-what-is-the-output-used-for