Numpy数组索引和切片
数组可以通过索引或切片的方式进行访问或修改，数组切片x[start:stop:step]，与Ptyhon内置的list标准索引和切片类似，只是数组产生的是一个非副本视图，根据条件索引的值如果修改，直接在原数组上修改，不另建立副本
一般索引
In [1]: import numpy as np
In [2]: x = np.arange(10)
In [3]: x
Out[3]: array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
#获取索引值为0的元素
In [4]: x[0]
Out[4]: 0
#获取索引值为2的元素
In [5]: x[2]
Out[5]: 2
#获取前5个元素
In [6]: x[:5]
Out[6]: array([0, 1, 2, 3, 4])
#获取索引5之后的元素
In [7]: x[5:]
Out[7]: array([5, 6, 7, 8, 9])
#获取索引[4,7)之间的元素
In [8]: x[4:7]
Out[8]: array([4, 5, 6])
#每隔一个元素获取，步长为2
In [9]: x[::2]
Out[9]: array([0, 2, 4, 6, 8])
#从索引1开始每隔一个元素获取，步长为2
In [10]: x[1::2]
Out[10]: array([1, 3, 5, 7, 9])
#获取所有元素
In [11]: x[:]
Out[11]: array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
#获取所有元素，步长为-1（负号表示逆序）
In [12]: x[::-1]
Out[12]: array([9, 8, 7, 6, 5, 4, 3, 2, 1, 0])
#从索引5开始每隔一个元素获取，步长为-2（负号表示逆序）
In [13]: x[5::-2]
Out[13]: array([5, 3, 1])
布尔索引（Boolean Indexing)
利用布尔数组作为索引。
In [1]: import numpy as np
In [2]: names = np.array(['Bob','Joe','Will','Bob','Will','Joe','Joe'])
# Return a sample (or samples) from the "standard normal" distribution.
In [3]: data = np.random.randn(7,4)
# names 为用于做布尔索引的数组
In [4]: names
Out[4]: array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe'], dtype='<U4')
# data 为用于索引的数组7*4
In [5]: data
Out[5]:
array([[ 0.25289291, -0.00816246, -0.96999809, 1.29376934],
[ 0.44550485, -0.68194628, 1.14512874, -0.29373544],
[ 0.40232255, -0.00788444, 0.63469223, -0.20523947],
[ 0.74526848, -0.72704461, -0.50133668, 0.40030561],
[ 0.54539544, -0.93755557, 0.0147922 , -1.6301914 ],
[ 1.59887252, 0.79954153, -0.48389643, -1.11492092],
[-0.93389025, 0.36513027, -0.49868663, 0.67454948]])
# 创建一个names == 'Bob' 真值数组用于索引data
In [7]: names == 'Bob'
Out[7]: array([ True, False, False, True, False, False, False])
# data数组的行与names数组元素一一对应，当条件names=='Bob'=True则返回相应行数组
In [8]: data[names=='Bob']
Out[8]:
array([[ 0.25289291, -0.00816246, -0.96999809, 1.29376934],
[ 0.74526848, -0.72704461, -0.50133668, 0.40030561]])
# data数组的行与names数组元素一一对应，当条件names=='Bob'=True则返回相应行数组，1：用于切割列数据
In [9]: data[names == 'Bob', 1:]
Out[9]:
array([[-0.00816246, -0.96999809, 1.29376934],
[-0.72704461, -0.50133668, 0.40030561]])
# data数组的行与names数组元素一一对应，当条件names=='Bob'=True则返回相应行数组，1用于切割得到第一列数据
In [10]: data[names == 'Bob', 1]
Out[10]: array([-0.00816246, -0.72704461])
# != 和 ~ 用于取非值
In [11]: data[names != 'Bob']
Out[11]:
array([[ 0.44550485, -0.68194628, 1.14512874, -0.29373544],
[ 0.40232255, -0.00788444, 0.63469223, -0.20523947],
[ 0.54539544, -0.93755557, 0.0147922 , -1.6301914 ],
[ 1.59887252, 0.79954153, -0.48389643, -1.11492092],
[-0.93389025, 0.36513027, -0.49868663, 0.67454948]])
In [12]: data[~(names == 'Bob')]
Out[12]:
array([[ 0.44550485, -0.68194628, 1.14512874, -0.29373544],
[ 0.40232255, -0.00788444, 0.63469223, -0.20523947],
[ 0.54539544, -0.93755557, 0.0147922 , -1.6301914 ],
[ 1.59887252, 0.79954153, -0.48389643, -1.11492092],
[-0.93389025, 0.36513027, -0.49868663, 0.67454948]])
# and / or 表示整个数组对象的与和或，而&和|对一个对象的内容（单个比特或字节）执行多个布尔运算，因此只能用& / | 表示数组内容的与和或
In [13]: data[(names == 'Bob') | (names == 'Will')]
Out[13]:
array([[ 0.25289291, -0.00816246, -0.96999809, 1.29376934],
[ 0.40232255, -0.00788444, 0.63469223, -0.20523947],
[ 0.74526848, -0.72704461, -0.50133668, 0.40030561],
[ 0.54539544, -0.93755557, 0.0147922 , -1.6301914 ]])
# 根据data[条件] 修改值，直接在原数组上修改，不另建立副本
In [14]: data
Out[14]:
array([[ 0.25289291, -0.00816246, -0.96999809, 1.29376934],
[ 0.44550485, -0.68194628, 1.14512874, -0.29373544],
[ 0.40232255, -0.00788444, 0.63469223, -0.20523947],
[ 0.74526848, -0.72704461, -0.50133668, 0.40030561],
[ 0.54539544, -0.93755557, 0.0147922 , -1.6301914 ],
[ 1.59887252, 0.79954153, -0.48389643, -1.11492092],
[-0.93389025, 0.36513027, -0.49868663, 0.67454948]])
#把 data < 0 的值修改为 0
In [15]: data[data < 0] = 0
In [16]: data
Out[16]:
array([[0.25289291, 0. , 0. , 1.29376934],
[0.44550485, 0. , 1.14512874, 0. ],
[0.40232255, 0. , 0.63469223, 0. ],
[0.74526848, 0. , 0. , 0.40030561],
[0.54539544, 0. , 0.0147922 , 0. ],
[1.59887252, 0.79954153, 0. , 0. ],
[0. , 0.36513027, 0. , 0.67454948]])
#把 names != 'Joe' 的行值都修改为 7
In [17]: names
Out[17]: array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe'], dtype='<U4')
In [18]: data[names != 'Joe'] = 7
In [19]: data
Out[19]:
array([[7. , 7. , 7. , 7. ],
[0.44550485, 0. , 1.14512874, 0. ],
[7. , 7. , 7. , 7. ],
[7. , 7. , 7. , 7. ],
[7. , 7. , 7. , 7. ],
[1.59887252, 0.79954153, 0. , 0. ],
[0. , 0.36513027, 0. , 0.67454948]])
花哨索引（Fancy Indexing)
传递一个索引数组或切片形式进行索引。
In [1]: import numpy as np
#创建一个空数组
In [2]: arr = np.empty((8,4))
In [3]: arr
Out[3]:
array([[2.59345432e+161, 1.68813881e+195, 6.01347002e-154,
6.01347002e-154],
[6.01347002e-154, 8.90389719e+252, 1.96086583e+243,
1.75631032e-152],
[5.49257737e+241, 1.08298236e-153, 4.78210140e+180,
6.01347002e-154],
[6.01347002e-154, 9.77795611e+024, 2.32160957e-152,
4.83245960e+276],
[3.09394663e+169, 9.08367217e+223, 5.56218818e+180,
6.79031368e+199],
[6.01347002e-154, 6.01347002e-154, 6.01347002e-154,
7.22247388e+159],
[4.89915603e+252, 8.88968974e+228, 2.52303419e-258,
7.49232572e+247],
[6.01347002e-154, 6.01347002e-154, 2.47379808e-091,
1.95132487e+227]])
# 往数组填充数据
In [4]: for i in range(8):
...: arr[i] = i
...:
In [5]: arr
Out[5]:
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.]])
# 选取数组索引为2、4、6的行
In [7]: arr[[2,4,6]]
Out[7]:
array([[2., 2., 2., 2.],
[4., 4., 4., 4.],
[6., 6., 6., 6.]])
# 选取数组索引为-1、-2、-8的行
In [8]: arr[[-1,-2,-8]]
Out[8]:
array([[7., 7., 7., 7.],
[6., 6., 6., 6.],
[0., 0., 0., 0.]])
# 从0~32中生成一个8*4的数组
In [9]: arr = np.arange(32).reshape((8,4))
In [10]: arr
Out[10]:
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]])
#[3,4,6]表示行索引，[1,2,1]表示列索引，返回(行，列)为(3,1),(4,2),(6,1)位置的数
In [11]: arr[[3,5,6],[1,2,1]]
Out[11]: array([13, 22, 25])
#[1,4,6]表示行索引，冒号(:)表示该行所有的数，[0,3,2,1]表示列排序-索引1的列与3的列对换
In [15]: arr[[1,4,6]][:,[0,3,2,1]]
Out[15]:
array([[ 4, 7, 6, 5],
[16, 19, 18, 17],
[24, 27, 26, 25]])
#利用花哨索引修改值
In [20]: x = np.arange(10)
In [21]: x
Out[21]: array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
#创建一个花哨索引数组
In [22]: i = np.array([0,2,4,6,8])
In [23]: x[i] = x[i]*2
In [24]: x
Out[24]: array([ 0, 1, 4, 3, 8, 5, 12, 7, 16, 9])
#实现累加
In [25]: x = np.zeros(10)
In [26]: i = np.array([1,3,5,7,9])
In [27]: np.add.at(x,i,1)
In [28]: x
Out[28]: array([0., 1., 0., 1., 0., 1., 0., 1., 0., 1.])
#j=[1,3,3,7,7]分别实现索引1累加1次，索引3累加2次，索引7累加2次
In [29]: j = np.array([1,3,3,7,7])
In [30]: np.add.at(x,j,1)
In [31]: x
Out[31]: array([0., 2., 0., 3., 0., 1., 0., 3., 0., 1.])
