output
array([[ 0.24747071, -0.43886742],
[ -0.03916734, -0.70580089],
[ 0.00462337, -0.51431584],
...,
[ 0.15071507, -0.57029653],
[ 0.06246116, -0.33766761],
[ 0.08218585, -0.59906501]], dtype=float32)
ipdb> np.shape(output)
( 64, 2)
ipdb> np.max(output, axis= 1)[:,np.newaxis]
array([[ 0.24747071],
[ -0.03916734],
[ 0.00462337],
...,
[ 0.15071507],
[ 0.06246116],
[ 0.08218585]], dtype=float32)
ipdb> np.tile(np.max(output, axis= 1)[:,np.newaxis], [1,2]))
*** SyntaxError: invalid syntax (<stdin>, line 1)
ipdb> np.tile(np.max(output, axis= 1)[:,np.newaxis], [1,2])
array([[ 0.24747071, 0.24747071],
[ -0.03916734, -0.03916734],
[ 0.00462337, 0.00462337],
...,
[ 0.15071507, 0.15071507],
[ 0.06246116, 0.06246116],
[ 0.08218585, 0.08218585]], dtype=float32)
ipdb> output
array([[ 0.24747071, -0.43886742],
[ -0.03916734, -0.70580089],
[ 0.00462337, -0.51431584],
...,
[ 0.15071507, -0.57029653],
[ 0.06246116, -0.33766761],
[ 0.08218585, -0.59906501]], dtype=float32)
ipdb> np.max(output, axis= 1)
array([ 0.24747071, -0.03916734, 0.00462337, ..., 0.15071507,
0.06246116, 0.08218585], dtype=float32)
ipdb> np.exp(output - np.tile(np.max(output, axis= 1)[:,np.newaxis], [1,2]))
array([[ 1. , 0.50341612],
[ 1. , 0.51343411],
[ 1. , 0.59515154],
...,
[ 1. , 0.48626012],
[ 1. , 0.67023373],
[ 1. , 0.50598365]], dtype=float32)

1- np.newaxis

np.newaxis的功能是插入新维度，看下面的例子：

a=np.array([1,2,3,4,5])
print a.shape

print a

输出结果

(5,)
[1 2 3 4 5]

可以看出a是一个一维数组,

x_data=np.linspace(-1,1,300)[:,np.newaxis]
a=np.array([1,2,3,4,5])
b=a[np.newaxis,:]
print a.shape,b.shape
print a

print b

输出结果：

(5,) (1, 5)
[1 2 3 4 5]
[[1 2 3 4 5]]

x_data=np.linspace(-1,1,300)[:,np.newaxis]
a=np.array([1,2,3,4,5])
b=a[:,np.newaxis]
print a.shape,b.shape
print a
print b

输出结果

(5,) (5, 1)
[1 2 3 4 5]
[[1]
[2]
[3]
[4]
[5]]

可以看出np.newaxis分别是在行或列上增加维度，原来是（6，）的数组，在行上增加维度变成（1,6）的二维数组，在列上增加维度变为(6,1)的二维数组

2. np.tile

函数原型：numpy.tile(A,reps) #简单理解是此函数将A进行重复输出

其中A和reps都是array_like的参数，A可以是：array,list,tuple,dict,matrix以及基本数据类型int,string,float以及bool类型,reps的类型可以是tuple,list,dict,array,int,bool,但不可以是float,string,matrix类型。

计较常用的形式有两种，是将A简单进行一维重复输出，和将A进行二维重复后输出。
一维重复：

import numpy as np
a = [[ 1,2,3],[4,5,5]]
b = np.tile(a, 3)
print(b)
#输出为
#[[1 2 3 1 2 3 1 2 3]
# [4 5 5 4 5 5 4 5 5]]

二维重复：#上面的一维重复相当于 b = np.tile(a,[1,3])

import numpy as np
a = [[ 1,2,3],[4,5,5]]
b = np.tile(a,[ 2,3])
print(b)
#输出为：
#[[1 2 3 1 2 3 1 2 3]
# [4 5 5 4 5 5 4 5 5]
# [1 2 3 1 2 3 1 2 3]
# [4 5 5 4 5 5 4 5 5]]

2.1 np.tile

numpy.tile()是个什么函数呢，说白了，就是把数组沿各个方向复制

比如 a = np.array([0,1,2]), np.tile(a,(2,1))就是把a先沿x轴（就这样称呼吧）复制1倍，即没有复制，仍然是 [0,1,2]。再把结果沿y方向复制2倍，即最终得到

array([[0,1,2],

[0,1,2]])

同理：

>>> b = np.array([[1, 2], [3, 4]]) >>> np.tile(b, 2) #沿X轴复制2倍 array([[1, 2, 1, 2],  [3, 4, 3, 4]]) >>> np.tile(b, (2, 1))#沿X轴复制1倍（相当于没有复制），再沿Y轴复制2倍 array([[1, 2],  [3, 4],  [1, 2],  [3, 4]])

numpy.tile()具体细节，如下：

numpy. tile (A, reps )

Construct an array by repeating A the number of times given by reps.

If reps has length d, the result will have dimension of max(d, A.ndim).

If A.ndim < d, A is promoted to be d-dimensional by prepending new axes. So a shape (3,) array is promoted to (1, 3) for 2-D replication, or shape (1, 1, 3) for 3-D replication. If this is not the desired behavior, promote A to d-dimensions manually before calling this function.

If A.ndim > d, reps is promoted to A.ndim by pre-pending 1’s to it. Thus for an A of shape (2, 3, 4, 5), a repsof (2, 2) is treated as (1, 1, 2, 2).

Note : Although tile may be used for broadcasting, it is strongly recommended to use numpy’s broadcasting operations and functions.

Parameters:

Parameters:	A : array_like The input array. reps : array_like The number of repetitions of A along each axis.
Returns:	c : ndarray The tiled output array.

A : array_like

The input array.

reps : array_like

The number of repetitions of A along each axis.

Returns:

c : ndarray

The tiled output array.

np.tile 和np.newaxis

1- np.newaxis

2. np.tile

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