Python 花式索引 指的是利用整数数组进行索引

In [6]: arr = np.empty((8, 4))

In [7]: arr

Out[7]:

array([[3.60332862e+252, 1.28156830e+213, 1.15824202e+171,

3.60313285e+252],

[6.32384870e-310, 1.09610677e-315, 1.09585729e-315,

1.09610606e-315],

[1.09610487e-315, 1.09645989e-315, 1.09645823e-315,

1.09609301e-315],

[1.09499445e-315, 1.09610179e-315, 1.09645965e-315,

1.09611104e-315],

[1.09645918e-315, 1.04832050e-315, 1.09585159e-315,

1.09586582e-315],

[1.09586155e-315, 1.09502591e-315, 1.09646013e-315,

1.09609373e-315],

[1.04832596e-315, 1.09502425e-315, 1.09610843e-315,

1.09646155e-315],

[1.09585539e-315, 1.09586013e-315, 1.09646416e-315,

1.09645847e-315]])

In [9]: for i in range(8):

...: arr[i] = i

In [10]: arr

Out[10]:

array([[0., 0., 0., 0.],

[1., 1., 1., 1.],

[2., 2., 2., 2.],

[3., 3., 3., 3.],

[4., 4., 4., 4.],

[5., 5., 5., 5.],

[6., 6., 6., 6.],

[7., 7., 7., 7.]])

##为了以特定顺序选取行子集，只需传入一个用于指定顺序的整数列表或ndarray即可

In [11]: arr[[4, 3, 0, 6]]

Out[11]:

array([[4., 4., 4., 4.],

[3., 3., 3., 3.],

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

[6., 6., 6., 6.]])

##使用负数索引将会从末尾开始选取行

In [12]: arr[[-3, -5, -7]]

Out[12]:

array([[5., 5., 5., 5.],

[3., 3., 3., 3.],

[1., 1., 1., 1.]])

In [13]: np.arange(32)

Out[13]:

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, 24, 25, 26, 27, 28, 29, 30, 31])

In [14]: np.arange(32).reshape((8, 4))

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],

[24, 25, 26, 27],

[28, 29, 30, 31]])

In [15]: arr = np.arange(32).reshape((8, 4))

##可以一次传入多个索引数组，对应的是arr[1][0],arr[5][3],arr[7][1],arr[2][2]

In [16]: arr[[1, 5, 7, 2], [0, 3, 1, 2]]

Out[16]: array([ 4, 23, 29, 10])

##方法1：arr[1][0],arr[1][3],...arr[5][0],arr[5][3],...依次类推

In [18]: arr[[1, 5, 7, 2]][:, [0, 3, 1, 2]]

Out[18]:

array([[ 4, 7, 5, 6],

[20, 23, 21, 22],

[28, 31, 29, 30],

[ 8, 11, 9, 10]])

##方法2：使用np.ix_()函数，它可以将两个一维整数数组转换为一个用于选取方形区域的索引器

In [19]: arr[np.ix_([1, 5, 7, 2], [0, 3, 1, 2])]

Out[19]:

array([[ 4, 7, 5, 6],

[20, 23, 21, 22],

[28, 31, 29, 30],

[ 8, 11, 9, 10]])

##花式索引跟切片不一样，它总是将数据复制到新数组中

数组转置和轴对换

##转置是重塑的一种特殊形式，它返回的是源数据的视图

##数组不仅有transpose方法，还有一个特殊的T属性

In [20]: arr = np.arange(15).reshape((3, 5))

In [21]: arr

Out[21]:

array([[ 0, 1, 2, 3, 4],

[ 5, 6, 7, 8, 9],

[10, 11, 12, 13, 14]])

In [22]: arr.T

Out[22]:

array([[ 0, 5, 10],

[ 1, 6, 11],

[ 2, 7, 12],

[ 3, 8, 13],

[ 4, 9, 14]])

##在进行矩阵计算时，经常需要用到该操作，比如利用np.dot计算矩阵内积XTX:

In [23]: arr = np.random.randn(6, 3)

In [24]: arr

Out[24]:

array([[ 1.43246019, -0.89622631, -0.90893883],

[ 1.5384252 , 2.2980319 , 0.05432292],

[ 1.21427005, -1.64032306, -0.99550839],

[-0.76845128, 0.29905102, -0.57052217],

[ 0.97445692, -0.64012016, -1.43677043],

[ 0.31091144, 1.27995381, 0.38438765]])

In [25]: np.dot(arr.T, arr)

Out[25]:

array([[ 7.52989561, -0.19587687, -3.26940483],

[-0.19587687, 10.91229902, 3.81349498],

[-3.26940483, 3.81349498, 4.35771641]])

##对于高维数组，transpose需要得到一个由轴编号组成的元组才能对这些轴进行转置：

In [26]: arr = np.arange(16).reshape((2, 2, 4))

In [27]: arr

Out[27]:

array([[[ 0, 1, 2, 3],

[ 4, 5, 6, 7]],

[[ 8, 9, 10, 11],

[12, 13, 14, 15]]])

In [28]: arr.transpose((1, 0, 2))

Out[28]:

array([[[ 0, 1, 2, 3],

[ 8, 9, 10, 11]],

[[ 4, 5, 6, 7],

[12, 13, 14, 15]]])

##ndarray还有一个swapaxes方法，它需要接受一对轴编号：

In [29]: arr

Out[29]:

array([[[ 0, 1, 2, 3],

[ 4, 5, 6, 7]],

[[ 8, 9, 10, 11],

[12, 13, 14, 15]]])

In [30]: arr.swapaxes(1, 2)

Out[30]:

array([[[ 0, 4],

[ 1, 5],

[ 2, 6],

[ 3, 7]],

[[ 8, 12],

[ 9, 13],

[10, 14],

[11, 15]]])