Numpy之repeat、tile用法总结

repeat函数的作用：①扩充数组元素 ②降低数组维度

numpy.repeat(a, repeats, axis=None)：若axis=None，对于多维数组而言，可以将多维数组变化为一维数组，然后再根据repeats参数扩充数组元素；若axis=M，表示数组在轴M上扩充数组元素。

下面以3维数组为例，了解下repeat函数的使用方法：

In [1]: import numpy as np

In [2]: arr = np.arange(12).reshape(1,4,3)

In [3]: arr
Out[3]:
array([[[ 0,  1,  2],
        [ 3,  4,  5],
        [ 6,  7,  8],
        [ 9, 10, 11]]])

①repeats为整数N，axis=None：数组arr首先被扁平化，然后将数组arr中的各个元素依次重复N次

In [4]: arr.repeat(2)
Out[4]:
array([ 0,  0,  1,  1,  2,  2,  3,  3,  4,  4,  5,  5,  6,  6,  7,  7,  8,
        8,  9,  9, 10, 10, 11, 11])

②repeats为整数数组rp_arr，axis=None：数组arr首先被扁平化，然后再将数组arr中元素依次重复对应rp_arr数组中元素对应次数。若rp_arr为一个值的一维数组，则数组arr中各个元素重复相同次数，否则rp_arr数组长度必须和数组arr的长度相等，否则报错

a：rp_arr为单值一维数组，进行广播

In [5]: arr.repeat([2])
Out[5]:
array([ 0,  0,  1,  1,  2,  2,  3,  3,  4,  4,  5,  5,  6,  6,  7,  7,  8,
        8,  9,  9, 10, 10, 11, 11])

b：rp_arr长度小于数组arr长度，无法进行广播，报错

In [6]: arr.repeat([2,3,4])
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-6-d3b52907284c> in <module>()
----> 1 arr.repeat([2,3,4])

ValueError: operands could not be broadcast together with shape (12,) (3,)

c：rp_arr长度和数组arr长度相等

In [7]: arr.repeat(np.arange(12))
Out[7]:
array([ 1,  2,  2,  3,  3,  3,  4,  4,  4,  4,  5,  5,  5,  5,  5,  6,  6,
        6,  6,  6,  6,  7,  7,  7,  7,  7,  7,  7,  8,  8,  8,  8,  8,  8,
        8,  8,  9,  9,  9,  9,  9,  9,  9,  9,  9, 10, 10, 10, 10, 10, 10,
       10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11])

d：rp_arr长度大于数组arr长度，也无法广播，报错

In [8]: arr.repeat(np.arange(13))
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-8-ec8454224d1b> in <module>()
----> 1 arr.repeat(np.arange(13))

ValueError: operands could not be broadcast together with shape (12,) (13,)

结论：两个数组满足广播的条件是两个数组的后缘维度(即从末尾开始算起的维度)的轴长度相等或其中一方的长度为1

③repeats为整数N，axis=M：数组arr的轴M上的每个元素重复N次，M=-1代表最后一条轴

In [9]: arr.repeat(2,axis=0)
Out[9]:
array([[[ 0,  1,  2],
        [ 3,  4,  5],
        [ 6,  7,  8],
        [ 9, 10, 11]],

       [[ 0,  1,  2],
        [ 3,  4,  5],
        [ 6,  7,  8],
        [ 9, 10, 11]]])

In [12]: arr.repeat(2,axis=-1)#arr.repeat(2,axis=-1)等同于arr.repeat(2,axis=2)
Out[12]:
array([[[ 0,  0,  1,  1,  2,  2],
        [ 3,  3,  4,  4,  5,  5],
        [ 6,  6,  7,  7,  8,  8],
        [ 9,  9, 10, 10, 11, 11]]])

④repeats为整数数组rp_arr，axis=M：把数组arr1轴M上的元素依次重复对应rp_arr数组中元素对应次数。若rp_arr为一个值的一维数组，则数组arr1轴M上的各个元素重复相同次数，否则rp_arr数组长度必须和数组arr1轴M的长度相等，否则报错

a：rp_arr长度和数组arr1轴M上长度相等

在轴0上扩充数组元素

In [13]: arr1 = np.arange(24).reshape(4,2,3)

In [14]: arr1
Out[14]:
array([[[ 0,  1,  2],
        [ 3,  4,  5]],

       [[ 6,  7,  8],
        [ 9, 10, 11]],

       [[12, 13, 14],
        [15, 16, 17]],

       [[18, 19, 20],
        [21, 22, 23]]])

In [15]: arr1.repeat((1,2,3,4),axis=0)
Out[15]:
array([[[ 0,  1,  2],
        [ 3,  4,  5]],

       [[ 6,  7,  8],
        [ 9, 10, 11]],

       [[ 6,  7,  8],
        [ 9, 10, 11]],

       [[12, 13, 14],
        [15, 16, 17]],

       [[12, 13, 14],
        [15, 16, 17]],

       [[12, 13, 14],
        [15, 16, 17]],

       [[18, 19, 20],
        [21, 22, 23]],

       [[18, 19, 20],
        [21, 22, 23]],

       [[18, 19, 20],
        [21, 22, 23]],

       [[18, 19, 20],
        [21, 22, 23]]])

在轴1上扩充数组元素

In [19]: arr1.repeat([1,2],axis=1)
Out[19]:
array([[[ 0,  1,  2],
        [ 3,  4,  5],
        [ 3,  4,  5]],

       [[ 6,  7,  8],
        [ 9, 10, 11],
        [ 9, 10, 11]],

       [[12, 13, 14],
        [15, 16, 17],
        [15, 16, 17]],

       [[18, 19, 20],
        [21, 22, 23],
        [21, 22, 23]]])

b：rp_arr为单值数组时，进行广播

In [20]: arr1.repeat([2],axis=0)
Out[20]:
array([[[ 0,  1,  2],
        [ 3,  4,  5]],

       [[ 0,  1,  2],
        [ 3,  4,  5]],

       [[ 6,  7,  8],
        [ 9, 10, 11]],

       [[ 6,  7,  8],
        [ 9, 10, 11]],

       [[12, 13, 14],
        [15, 16, 17]],

       [[12, 13, 14],
        [15, 16, 17]],

       [[18, 19, 20],
        [21, 22, 23]],

       [[18, 19, 20],
        [21, 22, 23]]])

c：rp_arr和数组arr1某轴不满足广播条件，则报错

In [21]: arr1.repeat((1,2,3),axis=0)
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-21-8ae4dc97e410> in <module>()
----> 1 arr1.repeat((1,2,3),axis=0)

ValueError: operands could not be broadcast together with shape (4,) (3,)

tile函数两个作用：①扩充数组元素 ②提升数组维度
numpy.tile(A, reps):根据reps中元素扩充数组A中对应轴上的元素

①reps为整数N：可以把整数N理解成含一个元素N的序列reps,若数组.ndim大于reps序列的长度，则需在reps序列的索引为0的位置开始添加元素1，直到reps的长度和数组的维度数相等，然后数组各轴上的元素依次重复reps序列中元素对应的次数

对于一维数组而言：是整体数组重复N次，从数组的最后一位置开始重复，注意与repeat函数的区别

In [26]: arr3 = np.arange(4)

In [27]: arr3
Out[27]: array([0, 1, 2, 3])

In [28]: np.tile(arr3,2)
Out[28]: array([0, 1, 2, 3, 0, 1, 2, 3])

对多维数组而言：arr2.ndim=3,，reps=[2,]，可以看出数组的长度大于序列reps的长度，因此需要向reps中添加元素，变成reps=[1,1,2]，然后arr2数组再根据reps中的元素重复其对应轴上的元素，reps=[1,1,2]代表数组arr2在轴0上各个元素重复1次，在轴1上的各个元素重复1次，在轴1上的各个元素重复2次

In [29]: arr2 = np.arange(24).reshape(4,2,3)

In [30]: arr2
Out[30]:
array([[[ 0,  1,  2],
        [ 3,  4,  5]],

       [[ 6,  7,  8],
        [ 9, 10, 11]],

       [[12, 13, 14],
        [15, 16, 17]],

       [[18, 19, 20],
        [21, 22, 23]]])

In [31]: np.tile(arr2,2)
Out[31]:
array([[[ 0,  1,  2,  0,  1,  2],
        [ 3,  4,  5,  3,  4,  5]],

       [[ 6,  7,  8,  6,  7,  8],
        [ 9, 10, 11,  9, 10, 11]],

       [[12, 13, 14, 12, 13, 14],
        [15, 16, 17, 15, 16, 17]],

       [[18, 19, 20, 18, 19, 20],
        [21, 22, 23, 21, 22, 23]]])

②reps为整数序列rp_arr：若数组.ndim大于rp_arr长度，方法同①相同，若数组ndim小于rp_arr长度，则需在数组的首缘维添加新轴，直到数组的维度数和rp_arr长度相等，然后数组各轴上的元素依次重复reps序列中元素对应的次数

a：数组维度大于rp_arr长度：需rp_arr提升为(1,2,3)

In [33]: arr2 = np.arange(24).reshape(4,2,3)

In [34]: arr2
Out[34]:
array([[[ 0,  1,  2],
        [ 3,  4,  5]],

       [[ 6,  7,  8],
        [ 9, 10, 11]],

       [[12, 13, 14],
        [15, 16, 17]],

       [[18, 19, 20],
        [21, 22, 23]]])

In [35]: np.tile(arr2,(2,3))
Out[35]:
array([[[ 0,  1,  2,  0,  1,  2,  0,  1,  2],
        [ 3,  4,  5,  3,  4,  5,  3,  4,  5],
        [ 0,  1,  2,  0,  1,  2,  0,  1,  2],
        [ 3,  4,  5,  3,  4,  5,  3,  4,  5]],

       [[ 6,  7,  8,  6,  7,  8,  6,  7,  8],
        [ 9, 10, 11,  9, 10, 11,  9, 10, 11],
        [ 6,  7,  8,  6,  7,  8,  6,  7,  8],
        [ 9, 10, 11,  9, 10, 11,  9, 10, 11]],

       [[12, 13, 14, 12, 13, 14, 12, 13, 14],
        [15, 16, 17, 15, 16, 17, 15, 16, 17],
        [12, 13, 14, 12, 13, 14, 12, 13, 14],
        [15, 16, 17, 15, 16, 17, 15, 16, 17]],

       [[18, 19, 20, 18, 19, 20, 18, 19, 20],
        [21, 22, 23, 21, 22, 23, 21, 22, 23],
        [18, 19, 20, 18, 19, 20, 18, 19, 20],
        [21, 22, 23, 21, 22, 23, 21, 22, 23]]])

b：数组的维度小于rp_arr的长度：需在数组的首缘维度新增加一条轴，使其shape变为(1,4,2,3)

In [36]: np.tile(arr2,(2,1,1,3))
Out[36]:
array([[[[ 0,  1,  2,  0,  1,  2,  0,  1,  2],
         [ 3,  4,  5,  3,  4,  5,  3,  4,  5]],

        [[ 6,  7,  8,  6,  7,  8,  6,  7,  8],
         [ 9, 10, 11,  9, 10, 11,  9, 10, 11]],

        [[12, 13, 14, 12, 13, 14, 12, 13, 14],
         [15, 16, 17, 15, 16, 17, 15, 16, 17]],

        [[18, 19, 20, 18, 19, 20, 18, 19, 20],
         [21, 22, 23, 21, 22, 23, 21, 22, 23]]],


       [[[ 0,  1,  2,  0,  1,  2,  0,  1,  2],
         [ 3,  4,  5,  3,  4,  5,  3,  4,  5]],

        [[ 6,  7,  8,  6,  7,  8,  6,  7,  8],
         [ 9, 10, 11,  9, 10, 11,  9, 10, 11]],

        [[12, 13, 14, 12, 13, 14, 12, 13, 14],
         [15, 16, 17, 15, 16, 17, 15, 16, 17]],

        [[18, 19, 20, 18, 19, 20, 18, 19, 20],
         [21, 22, 23, 21, 22, 23, 21, 22, 23]]]])