numpy.ndarray.ndim

Number of array dimensions.
数组维度的个数

import numpy as np
x = np.array([1, 2, 3])
y = np.array([[1, 2, 3], [4, 5, 6]])
z = np.zeros((2, 3, 4))

>>> x.ndim
1

>>> y.ndim
2

>>> z.ndim
3

numpy.ndarray.shape

Tuple of array dimensions.
数组的维度，n行m列对应的shape为(n, m)，shape的长度就是ndim

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

>>> x.shape
(3,)

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

>>> y.shape
(2, 3)

>>> z
array([[[ 0.,  0.,  0.,  0.],
        [ 0.,  0.,  0.,  0.],
        [ 0.,  0.,  0.,  0.]],

       [[ 0.,  0.,  0.,  0.],
        [ 0.,  0.,  0.,  0.],
        [ 0.,  0.,  0.,  0.]]])

>>> z.shape
(2, 3, 4)

numpy.tile

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).

1. 比较数组维度d和元组维度reps，如果d<reps，在需要时对数组补中括号 [] 来增加维度。
2. 元组数字从右到左，数组维度从最深维度到最低维度。假设元组为（a,b,c,d,e,f），则数组最深维度重复f次，然后次深维度重复e次，接着次次深维度重复d次，再然后次次次深维度重复c次…… 以此类推，直到对最低维度重复a次，结束，得到结果。
   参考python numpy-tile函数

a = np.array([0, 1, 2])
b = np.array([[1, 2], [3, 4]])
c = np.array([1, 2, 3, 4])

>>> a
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
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
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]])

numpy.argsort

argsort(a, axis=-1, kind='quicksort', order=None)
Returns the indices that would sort an array.

Perform an indirect sort along the given axis using the algorithm specified
by the `kind` keyword. It returns an array of indices of the same shape as
`a` that index data along the given axis in sorted order.

Parameters
----------
a : array_like
    Array to sort.
axis : int or None, optional
    Axis along which to sort.  The default is -1 (the last axis). If None,
    the flattened array is used.
kind : {'quicksort', 'mergesort', 'heapsort'}, optional
    Sorting algorithm.
order : str or list of str, optional
    When `a` is an array with fields defined, this argument specifies
    which fields to compare first, second, etc.  A single field can
    be specified as a string, and not all fields need be specified,
    but unspecified fields will still be used, in the order in which
    they come up in the dtype, to break ties.

返回数组的索引，升序排列。

a = np.array([3, 1, 2])
b = np.array([[0, 3], [2, 2]])
c = np.array([(1, 0), (0, 1)], dtype=[('x', '<i4'), ('y', '<i4')])

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

>>> np.argsort(a)
array([1, 2, 0])

>>> b
array([[0, 3],
       [2, 2]])

>>> np.argsort(b, axis=0)
array([[0, 1],
       [1, 0]])

>>> np.argsort(b, axis=1)
array([[0, 1],
       [0, 1]])

>>> c
array([(1, 0), (0, 1)], 
      dtype=[('x', '<i4'), ('y', '<i4')])

>>> np.argsort(c, order=('x','y'))
array([1, 0])

>>> np.argsort(c, order=('y','x'))
array([0, 1])

降序排列

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

>>> np.argsort(-a)
array([0, 2, 1])