numpy.tile(A,reps)定义如下：
Construct an array by repeating A the number of times given by reps.
Ifrepshaslengthd,theresultwillhavedimensionofmax(d, A.ndim).
IfA.ndim < d,Aispromotedtobed-dimensionalbyprependingnewaxes.Soashape(3,)arrayispromotedto (1, 3) for 2-D replication, or shape (1, 1, 3) for 3-D replication. If this is not the desired behavior, promote Ato d-dimensions manually before calling this function.
IfA.ndim > d,repsispromotedtoA.ndimbypre-pending1’stoit.ThusforanAofshape(2,3,4,5),arepsof (2, 2) is treated as (1, 1, 2, 2).
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.
Examples
NumPy Reference, Release 1.8.0
>>> np.vsplit(x, 2)[array([[[ 0., 1.],
[ 2., 3.]]]),
array([[[ 4., 5.],
[ 6., 7.]]])]
>>> 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],
设A为数组，且A为x维。reps的长度为y，则，numpy.tile(A,reps)表示如下：
另A=(A1,A2,A3....,Ax)，reps＝(Y1,Y2,Y3,.......,Ym).
如果m<x：则reps=(1,1,.....,Y1,Y2,...,Ym)
对A从低维到高维，每个维度按照Ym,Ym-1,.......,1的倍数进行复制。其中一个中括号[]代表一个维度。
如果m>x：则
对A从低维到高维，每个维度按照Ym,Ym-1,.....,Y1的倍数进行复制。其中一个中括号[]代表一个维度。
numpy.sum(a, axis=None, dtype=None, out=None, keepdims=False)
Sum of array elements over a given axis.
设A.ndim=x，axis=y
则A.sum(axis=y)，意味着A按照（x-y）的维度进行求和。例如：
>>> p=numpy.array([[[1,2],[9,10]]])
>>> p
array([[[ 1, 2],
[ 9, 10]]])
>>> p.sum(axis=2)
array([[ 3, 19]])
>>> p.sum(axis=0)
array([[ 1, 2],
[ 9, 10]])
>>> p.sum(axis=1)
array([[10, 12]])