numpy.tile用法

先说下在numpy中，个人对array的维度的比较形象的理解：
array的维度就是从最外边的[]出发（可理解为array的声明），一直找到具体数值而经过的[]的数量（含最后的数值，它是最后一维）
比如：

• （1） [1,2]的维度是(2,),因为最外层的[]仅仅是声明，穿过该[]，直接找到数值，所以是一维的，数量是2.

• （2）

  [[1,2],
  [3,4]] 的维度是（2,2），从最外层[]出发，向里走，有[1,2],[3,4]，所以第一维的数量是2，继续往里走，遇到'1,2'和'3,4'，所以第二维的数量是2

• （3）

[[[1,2],
[3,4]],
[[5,6],
[7,8]]]

的维度是（2,2,2），从最外层[]，有两个[[]],所以第一维度是2，继续往里走有两个[]，所以第二维度是2，继续走是两个数值，达到了最后一维，且最后一维的数量也是2.

import numpy as np

help(np.tile)

Help on function tile in module numpy.lib.shape_base:

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 `reps` of (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
    ----------
    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.
    
    See Also
    --------
    repeat : Repeat elements of an array.
    broadcast_to : Broadcast an array to a new shape
    
    Examples
    --------
    >>> a = np.array([0, 1, 2])
    >>> np.tile(a, 2)
    array([0, 1, 2, 0, 1, 2])
    >>> np.tile(a, (2, 2))
    array([[0, 1, 2, 0, 1, 2],
           [0, 1, 2, 0, 1, 2]])
    >>> np.tile(a, (2, 1, 2))
    array([[[0, 1, 2, 0, 1, 2]],
           [[0, 1, 2, 0, 1, 2]]])
    
    >>> b = np.array([[1, 2], [3, 4]])
    >>> np.tile(b, 2)
    array([[1, 2, 1, 2],
           [3, 4, 3, 4]])
    >>> np.tile(b, (2, 1))
    array([[1, 2],
           [3, 4],
           [1, 2],
           [3, 4]])
    
    >>> c = np.array([1,2,3,4])
    >>> np.tile(c,(4,1))
    array([[1, 2, 3, 4],
           [1, 2, 3, 4],
           [1, 2, 3, 4],
           [1, 2, 3, 4]])

​

np.tile（A,reps）就是根据reps的值，将array A在某些维度上进行复制，而产生新的array.
如果reps的长度等于A.ndim，则根据reps的值对A相应的维度进行复制。如果不相等，最后的结果取A.ndim和reps长度的较大值的维度；
如果A.ndim>len(reps)，则先对reps前置若干个'1'，使reps长度与ndim匹配，然后再进行各维度的复制；
如果A.ndim<len(reps), 则先对A的维度前置若干个'1'，使两者匹配，再进行各维度复制。

• A的维度与reps长度相等：

a=np.array([1,2,3])

a.ndim

1

np.tile(a,2)# 可见，将a在自身的维度下复制2次。

array([1, 2, 3, 1, 2, 3])

b=np.array([[1,2,3],
           [4,5,6]])

np.tile(b,(2,3))

array([[1, 2, 3, 1, 2, 3, 1, 2, 3],
       [4, 5, 6, 4, 5, 6, 4, 5, 6],
       [1, 2, 3, 1, 2, 3, 1, 2, 3],
       [4, 5, 6, 4, 5, 6, 4, 5, 6]])

可见，是先将最后一维在自己的维度复制3遍，然后在第一维复制2遍

• A的维度与reps长度不相等

A.ndim>len(reps)

np.tile(b,2)

array([[1, 2, 3, 1, 2, 3],
       [4, 5, 6, 4, 5, 6]])

将reps扩展成与b维度一样的即，等效于np.tile(b,(1,2))!

np.tile(b,(1,2)) #在最后一维复制2遍

array([[1, 2, 3, 1, 2, 3],
       [4, 5, 6, 4, 5, 6]])

A.ndim<len(reps)

np.tile(b,(3,2,2))

array([[[1, 2, 3, 1, 2, 3],
        [4, 5, 6, 4, 5, 6],
        [1, 2, 3, 1, 2, 3],
        [4, 5, 6, 4, 5, 6]],

       [[1, 2, 3, 1, 2, 3],
        [4, 5, 6, 4, 5, 6],
        [1, 2, 3, 1, 2, 3],
        [4, 5, 6, 4, 5, 6]],

       [[1, 2, 3, 1, 2, 3],
        [4, 5, 6, 4, 5, 6],
        [1, 2, 3, 1, 2, 3],
        [4, 5, 6, 4, 5, 6]]])

将A扩展成与b维度一样的,即A先升维为（1,2,3）

bb=b[np.newaxis,:]

bb

array([[[1, 2, 3],
        [4, 5, 6]]])

bb.shape

(1, 2, 3)

np.tile(bb,(3,2,2))

array([[[1, 2, 3, 1, 2, 3],
        [4, 5, 6, 4, 5, 6],
        [1, 2, 3, 1, 2, 3],
        [4, 5, 6, 4, 5, 6]],

       [[1, 2, 3, 1, 2, 3],
        [4, 5, 6, 4, 5, 6],
        [1, 2, 3, 1, 2, 3],
        [4, 5, 6, 4, 5, 6]],

       [[1, 2, 3, 1, 2, 3],
        [4, 5, 6, 4, 5, 6],
        [1, 2, 3, 1, 2, 3],
        [4, 5, 6, 4, 5, 6]]])

即先在最后一维复制2次，然后倒数第二维复制2次，最后第一维复制3次。