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   -> Python知识库 -> 学习NumPy全套代码【超详细】基本操作、数据类型、数组运算、复制和试图、索引、切片和迭代、形状操作、通用函数、线性代数 -> 正文阅读

[Python知识库]学习NumPy全套代码【超详细】基本操作、数据类型、数组运算、复制和试图、索引、切片和迭代、形状操作、通用函数、线性代数

大家好，我又来给大家分享新知识了，最近几篇博客（文末有链接）都致力于将以前的学习资源整理成博客的形式分享给大家，真心干货满满，希望能给大家带来收获。

那么本篇博客将会给出大家平时使用NumPy的时候经常需要用到的功能代码，同时也会给出运行结果，以帮助大家更进一步的理解。

另外，我也以注释的形式更进一步的补充说明代码的功能及其作用，需要本篇博文中用到的文档文件以及代码的朋友，也可以三连支持一下，并评论留下你的邮箱，我会在看到后的第一时间发送给你。

当然啦，你也可以把本篇博文当作一本小小的NumPy书籍，当需要用到pandas哪些知识的时候，Ctrl+F就可以搜索到啦，现在不看的话就先收藏着。

目录

一、基本操作

1.1 数组创建

import numpy as np # Shift + Enter

# 创建可以将Python，中list列表转换成NumPy数组
l = [1,2,3,4,5]

# NumPy数组
nd1 = np.array(l) # 输入一部分arr + tab（命令中自动补全，按键） 代码提示，自动补全
print(nd1)
display(nd1) # 显示

[1 2 3 4 5]



array([1, 2, 3, 4, 5])

nd2 = np.zeros(shape = (3,4),dtype = np.int16) # shift + tab提示方法的属性，使用
nd2

array([[0, 0, 0, 0],
       [0, 0, 0, 0],
       [0, 0, 0, 0]], dtype=int16)

nd3 = np.ones(shape = (3,5),dtype=np.float32)
nd3 # juppyter中执行程序，代码，最后一行，默认就是输出

array([[1., 1., 1., 1., 1.],
       [1., 1., 1., 1., 1.],
       [1., 1., 1., 1., 1.]], dtype=float32)

# 三维数组
nd4 = np.full(shape = (3,4,5),fill_value=3.1415926) # 生成任意指定的数组
nd4

array([[[3.1415926, 3.1415926, 3.1415926, 3.1415926, 3.1415926],
        [3.1415926, 3.1415926, 3.1415926, 3.1415926, 3.1415926],
        [3.1415926, 3.1415926, 3.1415926, 3.1415926, 3.1415926],
        [3.1415926, 3.1415926, 3.1415926, 3.1415926, 3.1415926]],

       [[3.1415926, 3.1415926, 3.1415926, 3.1415926, 3.1415926],
        [3.1415926, 3.1415926, 3.1415926, 3.1415926, 3.1415926],
        [3.1415926, 3.1415926, 3.1415926, 3.1415926, 3.1415926],
        [3.1415926, 3.1415926, 3.1415926, 3.1415926, 3.1415926]],

       [[3.1415926, 3.1415926, 3.1415926, 3.1415926, 3.1415926],
        [3.1415926, 3.1415926, 3.1415926, 3.1415926, 3.1415926],
        [3.1415926, 3.1415926, 3.1415926, 3.1415926, 3.1415926],
        [3.1415926, 3.1415926, 3.1415926, 3.1415926, 3.1415926]]])

nd5 = np.random.randint(0,100,size = 20) # 从0，到100，生成随机数字，int，整数
nd5

array([26, 97, 32, 88, 28, 65, 77, 74, 68, 97, 32, 35, 46, 55, 33, 83, 63,
        6, 77,  5])

nd6 = np.random.rand(3,5) # 生成0~1之间随机数
nd6

array([[0.64501117, 0.58522154, 0.90132264, 0.99409845, 0.63923959],
       [0.2164321 , 0.53874694, 0.54988461, 0.82581533, 0.42652412],
       [0.01025381, 0.49834132, 0.71353756, 0.44433708, 0.05175048]])

nd7 = np.random.randn(3,5) # 正态分布，平均值是0，标准差是1
display(nd7)

array([[-1.34974864, -0.35255807, -0.06337357, -0.39990286,  0.18276669],
       [ 0.42686337, -0.29675634, -0.66351388,  0.15499455,  0.22191029],
       [-2.24510816, -0.25372978,  0.61602861, -0.53877681,  1.8443575 ]])

nd8 = np.random.normal(loc = 175,scale = 10,size = (3,5)) # 正态分布，平均值是175，标准差是10
print(nd8)

[[154.35099611 188.63428445 178.86129064 173.99374674 173.92688007]
 [173.48768953 185.57252565 172.63843251 192.40089968 177.04776165]
 [166.25486758 198.20977267 162.28102209 167.1159521  183.41324182]]

nd9 = np.arange(1,100,step = 10) # 等差数列，左闭右开，100取不到
nd9

array([ 1, 11, 21, 31, 41, 51, 61, 71, 81, 91])

nd10 = np.linspace(1,100,num = 19) # 等差数列，左闭右闭,num表示生成等差数列长度
nd10

array([  1. ,   6.5,  12. ,  17.5,  23. ,  28.5,  34. ,  39.5,  45. ,
        50.5,  56. ,  61.5,  67. ,  72.5,  78. ,  83.5,  89. ,  94.5,
       100. ])

1.2 查看数组属性

import numpy as np

nd = np.random.randn(5,3)
nd

array([[ 0.72059556, -1.95187973, -0.56373137],
       [-1.73917205, -1.16500837,  1.42147895],
       [ 0.38178684, -1.44311435, -0.47301186],
       [-1.02896549,  0.05223197,  0.05234227],
       [ 0.21264316, -1.0635056 , -0.98622601]])

# 查看数组形状，返回了形状 shape = (5,3)
nd.shape

(5, 3)

nd.dtype # 告诉数组的数据类型 float64 位，一位占一个0或者一个1

dtype('float64')

nd.size # 尺寸，数组可以是多维的，请问，里面共有多少数据 3*5 = 15

15

nd.ndim # 数组维度 

2

nd.itemsize # 条目 尺寸长度 8 字节
# 数据类型是float64 64位 -----> 1个字节8位-----> 64/8 = 8 字节

8

1.3 文件读写

nd1 = np.random.randint(0,100,size = (3,5))
nd2 = np.random.randn(3,5)
display(nd1,nd2)

array([[17,  9, 81, 22, 35],
       [33,  3, 76, 56, 39],
       [51,  7, 98, 68, 76]])



array([[-1.00157588, -1.42826357, -0.0595288 ,  1.52754491, -0.36709515],
       [-1.27106787,  0.10364645,  0.32066376, -1.66321598, -1.25959691],
       [-1.71740637, -0.25518009, -0.81794158,  0.76914636,  1.14322894]])

np.save('./data',nd1) # 把一个数据存到文件中

np.load('./data.npy') # 默认添加npy后缀

array([[17,  9, 81, 22, 35],
       [33,  3, 76, 56, 39],
       [51,  7, 98, 68, 76]])

# 多个数据存到一个文件中
np.savez('./data.npz',a = nd1,abc = nd2) # 保存数据是起名：a,abc,称为key，自己命名

data = np.load('./data.npz')
data

<numpy.lib.npyio.NpzFile at 0x2352497f7c8>

data['a'] # 单引号

array([[17,  9, 81, 22, 35],
       [33,  3, 76, 56, 39],
       [51,  7, 98, 68, 76]])

data['abc']

array([[-1.00157588, -1.42826357, -0.0595288 ,  1.52754491, -0.36709515],
       [-1.27106787,  0.10364645,  0.32066376, -1.66321598, -1.25959691],
       [-1.71740637, -0.25518009, -0.81794158,  0.76914636,  1.14322894]])

# data['www'] # 没有保存，无法获取

np.savez_compressed('./data2.npz',x = nd1,y = nd2)

np.load('./data2.npz')['x']

array([[0, 4, 9, 0, 8],
       [6, 2, 5, 1, 1],
       [7, 5, 2, 4, 3]])

np.savetxt(fname = './data.txt',# 文件名
           X = nd1, # 数据
           fmt='%0.2f', # 格式
           delimiter=',')# 分隔符

np.savetxt(fname = './data.cvs',# 文件名
           X = nd1, # 数据
           fmt='%d', # 格式
           delimiter=';')# 分隔符

np.loadtxt('./data.cvs',delimiter=';')

array([[0., 4., 9., 0., 8.],
       [6., 2., 5., 1., 1.],
       [7., 5., 2., 4., 3.]])

np.loadtxt('./data.txt',delimiter=',')

array([[0., 4., 9., 0., 8.],
       [6., 2., 5., 1., 1.],
       [7., 5., 2., 4., 3.]])

二、数据类型

# int8，int16，int32，int64，uint8无符号
# float16，float32，float64
# str字符串类型
# int8 表示 2**8个数字 256个 -128 ~ 127 有符号
# uint8 表示256个数字，无符号，表明只有正数：0 ~ 255

np.array([2,4,7],dtype = np.int8)

array([2, 4, 7], dtype=int8)

np.array([-3,-7,255,108,0,256],dtype = np.uint8)

array([253, 249, 255, 108,   0,   0], dtype=uint8)

np.random.randint(0,100,size = 10,dtype = 'int64')

array([ 8, 36, 88, 80, 20, 52, 83, 42, 18,  1], dtype=int64)

nd = np.random.rand(10,2)
nd

array([[0.91420288, 0.83364378],
       [0.88974876, 0.33297581],
       [0.40118288, 0.07479842],
       [0.16937616, 0.26712123],
       [0.94525666, 0.34948455],
       [0.96704048, 0.61851364],
       [0.90099123, 0.3941368 ],
       [0.58999302, 0.40133028],
       [0.95706455, 0.53783821],
       [0.19142784, 0.38579803]])

nd.dtype

dtype('float64')

np.asarray(nd,dtype = 'float16')

array([[0.914  , 0.8335 ],
       [0.8896 , 0.333  ],
       [0.4011 , 0.07477],
       [0.1694 , 0.267  ],
       [0.9453 , 0.3494 ],
       [0.967  , 0.6187 ],
       [0.901  , 0.394  ],
       [0.59   , 0.4014 ],
       [0.957  , 0.5376 ],
       [0.1914 , 0.3857 ]], dtype=float16)

nd.astype(dtype = np.float16)

array([[0.914  , 0.8335 ],
       [0.8896 , 0.333  ],
       [0.4011 , 0.07477],
       [0.1694 , 0.267  ],
       [0.9453 , 0.3494 ],
       [0.967  , 0.6187 ],
       [0.901  , 0.394  ],
       [0.59   , 0.4014 ],
       [0.957  , 0.5376 ],
       [0.1914 , 0.3857 ]], dtype=float16)

nd = np.random.randn(1000,3) # 默认数据类型是float64
np.save('./data1',nd)

np.save('./data2',nd.astype('float16'))

nd2 = np.array(list('abcdefghi'))
nd2

array(['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i'], dtype='<U1')

nd2.dtype

dtype('<U1')

三、数组运算

3.1 基本运算

# 加减乘除指数幂运算
nd1 = np.random.randint(0,10,size = 5)
nd2 = np.random.randint(0,10,size = 5)
display(nd1,nd2)

array([7, 9, 4, 6, 7])



array([0, 4, 6, 6, 0])

nd3 = nd1 - nd2 # 返回一个新对象，原来的数组，内容不变！
nd3 # nd3数组操作后，接收的对象

array([ 7,  5, -2,  0,  7])

nd1 * nd2 # 乘法

array([ 0, 36, 24, 36,  0])

nd1 / nd2 # 除法

d:\python\lib\site-packages\ipykernel_launcher.py:1: RuntimeWarning: divide by zero encountered in true_divide
  """Entry point for launching an IPython kernel.





array([       inf, 2.25      , 0.66666667, 1.        ,        inf])

nd1**nd2 # 幂运算

array([    1,  6561,  4096, 46656,     1], dtype=int32)

2**3

8

np.power(2,3) # 表示2的3次幂

8

np.power(nd1,nd2) # 表示nd1的nd2次幂，对应位置，进行计算

array([    1,  6561,  4096, 46656,     1], dtype=int32)

np.log(100) # 底数是自然底数e 2.718

4.605170185988092

np.log10(1000) # 对数运算返回结果是：3

3.0

np.log2(1024) # 返回结果就是：10

10.0

3.2 逻辑运算

display(nd1,nd2)

array([7, 9, 4, 6, 7])



array([0, 4, 6, 6, 0])

nd1 > nd2

array([ True,  True, False, False,  True])

nd1 < nd2

array([False, False,  True, False, False])

nd1 >= nd2 # 表示nd1数组中的数据，是否大于等于nd2中的对应位置的数据，如果大于等于，放回True

array([ True,  True, False,  True,  True])

nd1 == nd2 # 两个等号表示逻辑判断，问，是否相等

array([False, False, False,  True, False])

3.3 数组与标量计算

nd1

array([7, 9, 4, 6, 7])

# 数字3，4，5……都是标量
nd1 + 10 # 所有的位置都加了10，广播

array([17, 19, 14, 16, 17])

nd1 - 1024

array([-1017, -1015, -1020, -1018, -1017])

nd1 * 256

array([1792, 2304, 1024, 1536, 1792])

nd1 / 1024

array([0.00683594, 0.00878906, 0.00390625, 0.00585938, 0.00683594])

# 数组可以做分母，注意不能有0
1/nd1

array([0.14285714, 0.11111111, 0.25      , 0.16666667, 0.14285714])

1/np.array([1,3,0,5]) # 0不能作为分母计算结果：inf 

d:\python\lib\site-packages\ipykernel_launcher.py:1: RuntimeWarning: divide by zero encountered in true_divide
  """Entry point for launching an IPython kernel.





array([1.        , 0.33333333,        inf, 0.2       ])

3.4 -= += *=直接改变原数组

display(nd1,nd2) # 没变化

array([7, 9, 4, 6, 7])



array([0, 4, 6, 6, 0])

nd1 -= 100 # 没有打印输出，说明，改变了原来的数组

nd1

array([-93, -91, -96, -94, -93])

nd2 +=100
nd2

array([100, 104, 106, 106, 100])

nd1 *= 3
nd1

array([-279, -273, -288, -282, -279])

# nd1 /= 10 数组不支持 /=

四、复制和视图

4.1 完全没有复制

a = np.random.randint(0,10,size = 5)
b = a # 赋值操作
display(a,b)

array([7, 9, 3, 2, 9])



array([7, 9, 3, 2, 9])

a is b # 返回True说明，赋值操作，a和b一回事

True

a[0] = 1024 # 改变a那么b也发生了变化
display(a,b)

array([1024,    9,    3,    2,    9])



array([1024,    9,    3,    2,    9])

4.2 视图、查看或者浅拷贝

a = np.random.randint(0,100,size = 5)
b = a.view() # 视图，查看，浅拷贝
display(a,b)

array([69, 16, 91,  6, 96])



array([69, 16, 91,  6, 96])

a is b # 说明a和b不一样

False

a.flags.owndata # a数组数据是自己的

True

b.flags.owndata # b是浅拷贝a的数据，也就是b并不拥有自己的数据

False

a[0] = 1024
b[1] = 2048 # 无论修改谁，最终结果两个数组都发生了变化
display(a,b)

array([1024, 2048,   91,    6,   96])



array([1024, 2048,   91,    6,   96])

4.3 深拷贝

a = np.random.randint(-100,0,size = 10)
b = a.copy() # 深拷贝，此时，a和b没有关系了
display(a,b)

array([-99,  -5, -16,  -5, -11, -72, -57, -69, -66, -96])



array([-99,  -5, -16,  -5, -11, -72, -57, -69, -66, -96])

display(a is b)
display(a.flags.owndata)
display(b.flags.owndata) # b 对象拥有自己的数据

False



True



True

a[0] = 1024
b[2] = 2048 # 井水不犯河水
display(a,b)

array([1024,   -5,  -16,   -5,  -11,  -72,  -57,  -69,  -66,  -96])



array([ -99,   -5, 2048,   -5,  -11,  -72,  -57,  -69,  -66,  -96])

a = np.arange(1e8) # 0 ~ 1亿，数据量非常多的
a

array([0.0000000e+00, 1.0000000e+00, 2.0000000e+00, ..., 9.9999997e+07,
       9.9999998e+07, 9.9999999e+07])

b = a[[1,3,5,7,9,99]].copy() # 取出一部分数据，原来的数组，没有了，但是占内存特别大
del a # 删除原来的数组，内存优化

b

array([ 1.,  3.,  5.,  7.,  9., 99.])

五、索引、切片和迭代

5.1 基本索引和切片

a = np.random.randint(0,30,size = 10)
a

array([28, 19,  9, 26, 28,  4, 14, 24,  8,  3])

a[3] # 取一个
a[[1,3,5]] # 取多个 

array([19, 26,  4])

a[0:3] # 左闭右开

array([28, 19,  9])

a[:3] # 如果冒号前面不写，默认从0开始

array([28, 19,  9])

a[5:9] # 从某个索引开始切片

array([ 4, 14, 24,  8])

a[5:] # 冒号后面不写内容，那么默认就是到左后

array([ 4, 14, 24,  8,  3])

a[::2] # 两个中取一个

array([28,  9, 28, 14,  8])

a[3::3] # 从索引3开始，每三个数中，取一个

array([26, 14,  3])

a[::-1] # 倒着数，数组进行了颠倒

array([ 3,  8, 24, 14,  4, 28, 26,  9, 19, 28])

a

array([28, 19,  9, 26, 28,  4, 14, 24,  8,  3])

a[::-2] # 颠倒，两个中取一个

array([ 3, 24,  4, 26, 19])

a[5::-3]

array([4, 9])

a[1:7:2] # 从索引1开始到7结束，每两个中取一个

array([19, 26,  4])

b = np.random.randint(0,30,size = (10,10))
b # 二维数组，多维数据索引和切片和上面的规律一样

array([[25, 23, 13, 28, 17, 13,  8, 16, 25,  3],
       [20,  7,  6, 26, 26, 13, 24,  0, 20, 18],
       [ 1, 24, 10, 25, 24, 21, 16,  4, 26, 29],
       [12,  0, 18, 20,  9, 16, 14, 19, 19, 20],
       [28, 18, 29,  7,  7, 15,  5, 13, 13,  7],
       [28, 28, 25, 13,  7,  8,  5, 16,  8,  2],
       [27,  9,  2, 25, 14,  7, 26,  5, 14, 11],
       [ 6, 14, 10, 20, 24, 28, 10,  0, 24, 12],
       [ 8, 21, 22, 21, 24,  6, 25, 21, 12, 26],
       [ 0, 19,  8,  5, 20,  1,  3,  3, 15, 27]])

b[1]

array([20,  7,  6, 26, 26, 13, 24,  0, 20, 18])

b[[0,3,5]]

array([[25, 23, 13, 28, 17, 13,  8, 16, 25,  3],
       [12,  0, 18, 20,  9, 16, 14, 19, 19, 20],
       [28, 28, 25, 13,  7,  8,  5, 16,  8,  2]])

b[1,6]

24

b[3,[2,5,6]] # 多维数组，不怕，我们可以用逗号，分割

array([18, 16, 14])

b[2:7,1::3] # 行：从2到索引7。列：从1开始，每3个中取一个数字

array([[24, 24,  4],
       [ 0,  9, 19],
       [18,  7, 13],
       [28,  7, 16],
       [ 9, 14,  5]])

b[-1,-1] # 给-1表示倒着数

27

b[-2,[-2,-3,-4]]

array([12, 21, 25])

5.2 花式索引和索引技巧

a = np.arange(20)
a

array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
       17, 18, 19])

b = a[3:7] # 切片时，返回的数据，不是深拷贝
b

array([3, 4, 5, 6])

b[0] = 1024
display(a,b)

array([   0,    1,    2, 1024,    4,    5,    6,    7,    8,    9,   10,
         11,   12,   13,   14,   15,   16,   17,   18,   19])



array([1024,    4,    5,    6])

a = np.arange(20)
# 花式索引返回的深拷贝的数据
b = a[[3,4,5,6]] # 花式索引：就是在索引是，给了一个数组
display(a,b)

array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
       17, 18, 19])



array([3, 4, 5, 6])

b[0] = 1024
display(a,b)

array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
       17, 18, 19])



array([1024,    4,    5,    6])

a = np.random.randint(0,151,size = (100,3)) # 100名学生，参加了3门考试:Python、Math、En
a

array([[100, 128, 122],
       [110,   1,   6],
       [120, 100, 108],
       [ 57, 112, 145],
       [ 46, 121, 130],
       [141,  20,  25],
       [  7,  98,  15],
       [141, 145, 121],
       [  1,  29, 117],
       [ 94,  62,  46],
       [ 35, 135, 101],
       [ 96,  38, 137],
       [ 97, 114,  60],
       [121, 113,  38],
       [  4,  85, 107],
       [ 13,  79,  12],
       [129,  92, 150],
       [ 54,  38,  34],
       [109,  55,  88],
       [  1,  52,  23],
       [ 16,  80, 146],
       [122,  72, 126],
       [ 39,  76,  52],
       [144,  68,  69],
       [121, 141, 147],
       [141,  71, 110],
       [100,  40, 108],
       [ 91, 121,  65],
       [  3,  44, 105],
       [ 79,  61,  75],
       [117, 146,  88],
       [  3,   2,  71],
       [ 78,  24,  86],
       [125,  62,  93],
       [ 53,  88, 132],
       [ 96,  75,  36],
       [102, 119,  97],
       [ 24,  48,  78],
       [104,  21, 150],
       [  8,  34,  30],
       [108,  56,  58],
       [ 22, 144, 100],
       [ 53, 115,  94],
       [ 52, 104,   9],
       [ 59,   2,   4],
       [ 85,  48, 138],
       [119,  21,  73],
       [  9,  31,  77],
       [ 21,   3, 132],
       [ 43, 113,  39],
       [ 51,   5, 134],
       [ 37,  97, 123],
       [  0,  92,  73],
       [ 37,  86,  13],
       [ 48,  78, 128],
       [ 74,  56,  48],
       [138, 105,  68],
       [129, 129, 103],
       [ 48,  42,  14],
       [ 50, 102, 123],
       [  6,  97,  16],
       [ 22,  88, 122],
       [ 98,  23, 137],
       [ 95,  74,  20],
       [ 20, 111, 132],
       [ 67,   9,  28],
       [ 74,   1,  79],
       [ 62,   8,  27],
       [ 24,  12,  22],
       [ 58, 111, 130],
       [ 29,  23,  28],
       [ 10,  30,  38],
       [113,  62, 122],
       [ 70, 141,  97],
       [137, 106,  53],
       [ 76,  91, 101],
       [128,  22, 101],
       [134,  75, 100],
       [114,  92,  79],
       [103,  20, 145],
       [105,  26,  51],
       [ 34,  51,  18],
       [117, 115,  31],
       [  7, 119,  75],
       [ 23,  74, 149],
       [ 56,  15,  11],
       [143,  73, 148],
       [ 11,  22,  26],
       [ 18, 113, 120],
       [ 37, 150,  21],
       [115,  89,  13],
       [134, 108,  98],
       [115,  58,   4],
       [114,  58,  29],
       [ 26, 135,  10],
       [ 82, 147, 147],
       [ 56,  13,  39],
       [ 21, 125, 134],
       [120,  71,  32],
       [143,  46, 124]])

cond = a >= 120 # 逻辑运算
# 根据条件，筛选数据，只要大于120，返回，一门大于120，就会返回这一门
a[cond]

array([128, 122, 120, 145, 121, 130, 141, 141, 145, 121, 135, 137, 121,
       129, 150, 146, 122, 126, 144, 121, 141, 147, 141, 121, 146, 125,
       132, 150, 144, 138, 132, 134, 123, 128, 138, 129, 129, 123, 122,
       137, 132, 130, 122, 141, 137, 128, 134, 145, 149, 143, 148, 120,
       150, 134, 135, 147, 147, 125, 134, 120, 143, 124])

# boolean True = 1;False = 0
# 三门科目的条件进行相乘
# 三个科目都是 大于120的同学
cond2 = cond[:,0]*cond[:,1]*cond[:,2]
a[cond2]

array([[141, 145, 121],
       [121, 141, 147]])

# 大于等于120，小于等于30找到
cond1 = a >=120
cond2 = a <= 30
a[cond2[:,0]*cond2[:,1]*cond2[:,2]]

array([[24, 12, 22],
       [29, 23, 28],
       [11, 22, 26]])

六、形状操作

6.1 数组变形

a = np.random.randint(0,10,size = (3,5))
a

array([[0, 2, 3, 7, 1],
       [2, 1, 9, 3, 0],
       [3, 3, 8, 7, 1]])

a.reshape(5,3) # 只是改变形状

array([[0, 2, 3],
       [7, 1, 2],
       [1, 9, 3],
       [0, 3, 3],
       [8, 7, 1]])

a.reshape(15,1,1)

array([[[0]],

       [[2]],

       [[3]],

       [[7]],

       [[1]],

       [[2]],

       [[1]],

       [[9]],

       [[3]],

       [[0]],

       [[3]],

       [[3]],

       [[8]],

       [[7]],

       [[1]]])

a.reshape(-1,3) # -1表示数据，3自动计算-1 = 5

array([[0, 2, 3],
       [7, 1, 2],
       [1, 9, 3],
       [0, 3, 3],
       [8, 7, 1]])

6.2 数组转置

# 转置，行变列，列变行
a.T # 矩阵 shape = (5,3)

array([[0, 2, 3],
       [2, 1, 3],
       [3, 9, 8],
       [7, 3, 7],
       [1, 0, 1]])

np.transpose(a,(1,0)) # 行0，列1。默认情况下(0,1)----->调整(1,0)

array([[0, 2, 3],
       [2, 1, 3],
       [3, 9, 8],
       [7, 3, 7],
       [1, 0, 1]])

b = np.random.randint(0,10,size = (3,5,7)) # shape = (0,1,2)
b

array([[[3, 0, 4, 0, 4, 8, 0],
        [6, 2, 2, 1, 6, 0, 4],
        [9, 5, 2, 8, 8, 6, 2],
        [0, 6, 2, 8, 0, 0, 5],
        [4, 3, 2, 3, 4, 0, 0]],

       [[6, 7, 8, 5, 5, 4, 9],
        [3, 0, 5, 6, 8, 6, 4],
        [9, 3, 5, 5, 6, 4, 6],
        [3, 0, 5, 9, 2, 7, 4],
        [5, 5, 4, 7, 8, 2, 9]],

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

c = np.transpose(b,(2,1,0)) # 就是调整维度结构2和0维度数据对调
c.shape

(7, 5, 3)

6.3 数据堆叠合并

nd1 = np.random.randint(0,10,size = (3,5))
nd2 = np.random.randint(0,10,size = (3,5))
display(nd1,nd2)

array([[5, 1, 3, 3, 4],
       [3, 0, 9, 3, 7],
       [2, 9, 3, 8, 4]])



array([[1, 9, 9, 0, 7],
       [7, 8, 8, 0, 8],
       [6, 0, 9, 3, 3]])

np.concatenate([nd1,nd2]) # 默认合并行增加

array([[5, 1, 3, 3, 4],
       [3, 0, 9, 3, 7],
       [2, 9, 3, 8, 4],
       [1, 9, 9, 0, 7],
       [7, 8, 8, 0, 8],
       [6, 0, 9, 3, 3]])

# 修改axis参数调整数据合并方向
np.concatenate([nd1,nd2],axis = 1) # axis 轴，方向 0 = 行，1 = 列

array([[5, 1, 3, 3, 4, 1, 9, 9, 0, 7],
       [3, 0, 9, 3, 7, 7, 8, 8, 0, 8],
       [2, 9, 3, 8, 4, 6, 0, 9, 3, 3]])

np.hstack((nd1,nd2)) # 堆叠，摞起来，增多，合并 h表示水平，列增多

array([[5, 1, 3, 3, 4, 1, 9, 9, 0, 7],
       [3, 0, 9, 3, 7, 7, 8, 8, 0, 8],
       [2, 9, 3, 8, 4, 6, 0, 9, 3, 3]])

np.vstack((nd1,nd2,nd2,nd2,nd1)) # v 竖直，行增加

array([[5, 1, 3, 3, 4],
       [3, 0, 9, 3, 7],
       [2, 9, 3, 8, 4],
       [1, 9, 9, 0, 7],
       [7, 8, 8, 0, 8],
       [6, 0, 9, 3, 3],
       [1, 9, 9, 0, 7],
       [7, 8, 8, 0, 8],
       [6, 0, 9, 3, 3],
       [1, 9, 9, 0, 7],
       [7, 8, 8, 0, 8],
       [6, 0, 9, 3, 3],
       [5, 1, 3, 3, 4],
       [3, 0, 9, 3, 7],
       [2, 9, 3, 8, 4]])

a = np.random.randint(0,10,size = (3,5))
b = np.random.randint(0,10,size = (3,6))
display(a,b)
np.concatenate([a,b]) # 报错

array([[2, 5, 3, 6, 8],
       [0, 8, 1, 2, 3],
       [6, 0, 7, 1, 2]])



array([[0, 9, 6, 2, 4, 8],
       [3, 0, 0, 0, 8, 3],
       [7, 3, 1, 3, 7, 0]])



---------------------------------------------------------------------------

ValueError                                Traceback (most recent call last)

<ipython-input-205-16b2fe89e6c7> in <module>
      2 b = np.random.randint(0,10,size = (3,6))
      3 display(a,b)
----> 4 np.concatenate([a,b]) # 报错


<__array_function__ internals> in concatenate(*args, **kwargs)


ValueError: all the input array dimensions for the concatenation axis must match exactly, but along dimension 1, the array at index 0 has size 5 and the array at index 1 has size 6

np.concatenate([a,b],axis =1)   # 报错

---------------------------------------------------------------------------

ValueError                                Traceback (most recent call last)

<ipython-input-242-9acf5d5d319b> in <module>
----> 1 np.concatenate([a,b],axis =1)


<__array_function__ internals> in concatenate(*args, **kwargs)


ValueError: all the input arrays must have same number of dimensions, but the array at index 0 has 2 dimension(s) and the array at index 1 has 1 dimension(s)

6.4 数组拆分

a = np.random.randint(0,100,size = (15,10))
a

array([[73, 62, 19,  9, 90, 98, 38, 91, 14, 72],
       [64, 34, 80, 81, 77, 83, 69, 84,  5, 42],
       [29, 79, 49, 87, 15,  9, 98, 68, 33, 72],
       [ 0, 89, 36, 54, 11, 12, 27, 39, 14, 11],
       [26, 84, 21, 94, 18, 32, 64, 31, 64, 39],
       [45,  0, 61, 18, 16, 29, 77, 34, 18, 86],
       [10, 63, 81, 38, 44, 47, 28, 96, 54, 53],
       [67, 50, 24, 15, 42, 10, 18, 92, 41, 42],
       [61,  0, 67, 41, 13, 87, 82, 57, 54, 50],
       [32, 69, 72, 33, 56, 12, 12, 66, 55, 94],
       [49, 45, 68, 15, 24, 51, 18, 18, 59, 47],
       [77, 58, 93, 79, 89, 63, 41, 82,  8, 20],
       [70, 84, 75, 67, 39, 53, 32, 31, 20, 37],
       [20, 51, 54, 30,  5, 71, 59, 51, 96, 68],
       [52, 31, 73, 56, 60,  3, 81,  2,  7, 69]])

np.split(a,indices_or_sections=5) # 给数字，表示平均分成多少分

[array([[73, 62, 19,  9, 90, 98, 38, 91, 14, 72],
        [64, 34, 80, 81, 77, 83, 69, 84,  5, 42],
        [29, 79, 49, 87, 15,  9, 98, 68, 33, 72]]),
 array([[ 0, 89, 36, 54, 11, 12, 27, 39, 14, 11],
        [26, 84, 21, 94, 18, 32, 64, 31, 64, 39],
        [45,  0, 61, 18, 16, 29, 77, 34, 18, 86]]),
 array([[10, 63, 81, 38, 44, 47, 28, 96, 54, 53],
        [67, 50, 24, 15, 42, 10, 18, 92, 41, 42],
        [61,  0, 67, 41, 13, 87, 82, 57, 54, 50]]),
 array([[32, 69, 72, 33, 56, 12, 12, 66, 55, 94],
        [49, 45, 68, 15, 24, 51, 18, 18, 59, 47],
        [77, 58, 93, 79, 89, 63, 41, 82,  8, 20]]),
 array([[70, 84, 75, 67, 39, 53, 32, 31, 20, 37],
        [20, 51, 54, 30,  5, 71, 59, 51, 96, 68],
        [52, 31, 73, 56, 60,  3, 81,  2,  7, 69]])]

np.split(a,indices_or_sections=2,axis =1) # axis = 1 表示列，平均分成两份

[array([[73, 62, 19,  9, 90],
        [64, 34, 80, 81, 77],
        [29, 79, 49, 87, 15],
        [ 0, 89, 36, 54, 11],
        [26, 84, 21, 94, 18],
        [45,  0, 61, 18, 16],
        [10, 63, 81, 38, 44],
        [67, 50, 24, 15, 42],
        [61,  0, 67, 41, 13],
        [32, 69, 72, 33, 56],
        [49, 45, 68, 15, 24],
        [77, 58, 93, 79, 89],
        [70, 84, 75, 67, 39],
        [20, 51, 54, 30,  5],
        [52, 31, 73, 56, 60]]),
 array([[98, 38, 91, 14, 72],
        [83, 69, 84,  5, 42],
        [ 9, 98, 68, 33, 72],
        [12, 27, 39, 14, 11],
        [32, 64, 31, 64, 39],
        [29, 77, 34, 18, 86],
        [47, 28, 96, 54, 53],
        [10, 18, 92, 41, 42],
        [87, 82, 57, 54, 50],
        [12, 12, 66, 55, 94],
        [51, 18, 18, 59, 47],
        [63, 41, 82,  8, 20],
        [53, 32, 31, 20, 37],
        [71, 59, 51, 96, 68],
        [ 3, 81,  2,  7, 69]])]

# 参数给列表，根据列表中的索引，进行切片
np.split(a,indices_or_sections=[1,5,9]) # 0~1,1~5,5~9,9~

[array([[73, 62, 19,  9, 90, 98, 38, 91, 14, 72]]),
 array([[64, 34, 80, 81, 77, 83, 69, 84,  5, 42],
        [29, 79, 49, 87, 15,  9, 98, 68, 33, 72],
        [ 0, 89, 36, 54, 11, 12, 27, 39, 14, 11],
        [26, 84, 21, 94, 18, 32, 64, 31, 64, 39]]),
 array([[45,  0, 61, 18, 16, 29, 77, 34, 18, 86],
        [10, 63, 81, 38, 44, 47, 28, 96, 54, 53],
        [67, 50, 24, 15, 42, 10, 18, 92, 41, 42],
        [61,  0, 67, 41, 13, 87, 82, 57, 54, 50]]),
 array([[32, 69, 72, 33, 56, 12, 12, 66, 55, 94],
        [49, 45, 68, 15, 24, 51, 18, 18, 59, 47],
        [77, 58, 93, 79, 89, 63, 41, 82,  8, 20],
        [70, 84, 75, 67, 39, 53, 32, 31, 20, 37],
        [20, 51, 54, 30,  5, 71, 59, 51, 96, 68],
        [52, 31, 73, 56, 60,  3, 81,  2,  7, 69]])]

np.hsplit(a,indices_or_sections=2) # h水平，列方向上分割成了两份

[array([[73, 62, 19,  9, 90],
        [64, 34, 80, 81, 77],
        [29, 79, 49, 87, 15],
        [ 0, 89, 36, 54, 11],
        [26, 84, 21, 94, 18],
        [45,  0, 61, 18, 16],
        [10, 63, 81, 38, 44],
        [67, 50, 24, 15, 42],
        [61,  0, 67, 41, 13],
        [32, 69, 72, 33, 56],
        [49, 45, 68, 15, 24],
        [77, 58, 93, 79, 89],
        [70, 84, 75, 67, 39],
        [20, 51, 54, 30,  5],
        [52, 31, 73, 56, 60]]),
 array([[98, 38, 91, 14, 72],
        [83, 69, 84,  5, 42],
        [ 9, 98, 68, 33, 72],
        [12, 27, 39, 14, 11],
        [32, 64, 31, 64, 39],
        [29, 77, 34, 18, 86],
        [47, 28, 96, 54, 53],
        [10, 18, 92, 41, 42],
        [87, 82, 57, 54, 50],
        [12, 12, 66, 55, 94],
        [51, 18, 18, 59, 47],
        [63, 41, 82,  8, 20],
        [53, 32, 31, 20, 37],
        [71, 59, 51, 96, 68],
        [ 3, 81,  2,  7, 69]])]

np.vsplit(a,indices_or_sections=[3,7,11]) # v表示竖直，行切片，行分割

[array([[73, 62, 19,  9, 90, 98, 38, 91, 14, 72],
        [64, 34, 80, 81, 77, 83, 69, 84,  5, 42],
        [29, 79, 49, 87, 15,  9, 98, 68, 33, 72]]),
 array([[ 0, 89, 36, 54, 11, 12, 27, 39, 14, 11],
        [26, 84, 21, 94, 18, 32, 64, 31, 64, 39],
        [45,  0, 61, 18, 16, 29, 77, 34, 18, 86],
        [10, 63, 81, 38, 44, 47, 28, 96, 54, 53]]),
 array([[67, 50, 24, 15, 42, 10, 18, 92, 41, 42],
        [61,  0, 67, 41, 13, 87, 82, 57, 54, 50],
        [32, 69, 72, 33, 56, 12, 12, 66, 55, 94],
        [49, 45, 68, 15, 24, 51, 18, 18, 59, 47]]),
 array([[77, 58, 93, 79, 89, 63, 41, 82,  8, 20],
        [70, 84, 75, 67, 39, 53, 32, 31, 20, 37],
        [20, 51, 54, 30,  5, 71, 59, 51, 96, 68],
        [52, 31, 73, 56, 60,  3, 81,  2,  7, 69]])]

七、广播机制

arr1 = np.array([0,1,2,3]*3)
arr1.sort() # 排序，从小到大
arr1 = arr1.reshape(4,3)
arr1

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

arr2 = np.array([1,2,3])
display(arr1,arr2) # 形状不对应，依然可以进行运算：NumPy底层，为我们进行了广播

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



array([1, 2, 3])

# 行不够，广播行
arr1 + arr2 # arr2 和arr1 中每一行，进行相加：广播机制 

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

arr3 = np.array([[1],[2],[3],[4]])
display(arr1,arr3)

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



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

# 列不够，广播列
arr1 + arr3 # 广播，arr2和arr1中每一列，进行相加：广播

array([[1, 1, 1],
       [3, 3, 3],
       [5, 5, 5],
       [7, 7, 7]])

# 广播，和复制，意思有点近似

a = np.array([0,1,2,3,4,5,6,7]*3).reshape(3,4,2)
a

array([[[0, 1],
        [2, 3],
        [4, 5],
        [6, 7]],

       [[0, 1],
        [2, 3],
        [4, 5],
        [6, 7]],

       [[0, 1],
        [2, 3],
        [4, 5],
        [6, 7]]])

b = np.array([0,1,2,3,4,5,6,7]).reshape(4,2)
b

array([[0, 1],
       [2, 3],
       [4, 5],
       [6, 7]])

display(a.shape,b.shape)

(3, 4, 2)



(4, 2)

a * b # b形状(4，2),b 广播了三份

array([[[ 0,  1],
        [ 4,  9],
        [16, 25],
        [36, 49]],

       [[ 0,  1],
        [ 4,  9],
        [16, 25],
        [36, 49]],

       [[ 0,  1],
        [ 4,  9],
        [16, 25],
        [36, 49]]])

八、通用函数

8.1 元素级数字级别的方法

# abs、sqrt、square、exp、log、sin、cos、tan，maxinmum、minimum、
# all、any、inner、clip、round、trace、ceil、floor

a = np.array([-1,-3,-5,1,5,8,9])
c = np.random.randint(-5,10,size = 7)
display(a,c)

array([-1, -3, -5,  1,  5,  8,  9])



array([ 2, -3, -4,  7,  7,  7, -2])

np.abs(a) # 求绝对值

array([1, 3, 5, 1, 5, 8, 9])

b = np.array([1,4,9,16,36,49])
b

array([ 1,  4,  9, 16, 36, 49])

np.sqrt(b) # 开平发

array([1., 2., 3., 4., 6., 7.])

np.square(b) # 平方
np.exp(3) # 自然底数e的多少次幂
np.log(20.085536) # 自然底数e对数求解
np.sin(np.pi/2) # 90度sin正弦值
np.cos(0) # 余弦值
np.tan(np.pi/6) # 正切,30度正切值
# 给两个数组，从中选取大的，或者选取小的
np.maximum(a,c) # 从a和c中选取最大的值
np.minimum(a,c) # 选取最小的值

array([-1, -3, -5,  1,  5,  7, -2])

nd1 = np.array([1,3,0]) # 出现0那么对应False，非零True
nd2 = np.array([-1,-3,4,8])
display(nd1,nd2)

array([1, 3, 0])



array([-1, -3,  4,  8])

nd1.any() # 只要有一个True，返回True

True

nd1.all() # 所有True，返回True

False

nd2.all() # 所有的都是True，返回True

True

a = np.array([1,2,3,4,5])
b = np.array([1,2,3,4,6])
np.inner(a,b) # 1*1 + 2*2 + 3*3 + 4*4 + 5*6 = 60
# 返回的是两个数组的内积，对应位置相乘加和

60

nd1 = np.random.randint(0,100,size = 30)
nd1

array([61, 15, 31, 92, 91, 24, 20, 59,  6, 41, 46,  8, 30, 37, 53, 70, 59,
       24, 66, 43, 36, 95, 14,  7, 67, 86, 53, 26, 70, 62])

np.clip(nd1,10,80) # 数据裁剪，将小于10变成10，将大于80的变成80

array([61, 15, 31, 80, 80, 24, 20, 59, 10, 41, 46, 10, 30, 37, 53, 70, 59,
       24, 66, 43, 36, 80, 14, 10, 67, 80, 53, 26, 70, 62])

nd2  = np.random.randn(20)
nd2

array([ 0.5020347 , -0.60462332, -1.17663827, -0.37269518, -1.42816971,
        0.023136  ,  0.782975  ,  0.30537136, -0.43498012, -1.08404953,
        0.85617269,  1.16387006, -0.01622137,  1.21683923, -0.29338921,
       -2.78006002,  0.07321195,  1.11264868, -0.70013613, -1.2466278 ])

nd2.round(2)

array([ 0.5 , -0.6 , -1.18, -0.37, -1.43,  0.02,  0.78,  0.31, -0.43,
       -1.08,  0.86,  1.16, -0.02,  1.22, -0.29, -2.78,  0.07,  1.11,
       -0.7 , -1.25])

np.ceil(np.array([2.7,2.1,2.05])) # 天花板，向上取整

array([3., 3., 3.])

np.floor(np.array([2.99,2.9999,2.1])) # 向下取整

array([2., 2., 2.])

a = np.random.randint(0,10,size = (3,3))
a

array([[6, 5, 1],
       [7, 3, 6],
       [9, 1, 3]])

np.trace(a) # 就算对角线上的和

12

8.2 where函数

import numpy as np
nd1 = np.array([1,3,5,7,9])
nd2 = np.array([2,4,6,8,10])
cond = np.array([True,False,False,True,True])

np.where(cond,nd1,nd2) # 条件如果是True，那么返回nd1中数据，如果Flase返回nd2中数据

array([1, 4, 6, 7, 9])

a = np.random.randint(0,100,size = 50)
display(a) # 数据展示
np.where(a > 50,a,a + 20) # 大于50，返回多少；不然返回-100

array([86, 27, 93, 30, 55, 13, 37, 60,  1,  6, 44, 77, 74, 11, 71, 95, 45,
       32,  0, 40, 13, 23, 38,  4, 36, 96, 81, 10, 79, 90, 13, 19, 15, 50,
       90, 20, 51, 56, 56, 42, 86, 41, 35, 33, 33, 46, 69, 35, 50, 15])





array([86, 47, 93, 50, 55, 33, 57, 60, 21, 26, 64, 77, 74, 31, 71, 95, 65,
       52, 20, 60, 33, 43, 58, 24, 56, 96, 81, 30, 79, 90, 33, 39, 35, 70,
       90, 40, 51, 56, 56, 62, 86, 61, 55, 53, 53, 66, 69, 55, 70, 35])

# 如果分数50~59分之间，自动加10分
a = np.random.randint(0,100,size = 50)
a

array([39, 55, 20, 11, 12,  5, 46, 55, 37, 90, 93, 33, 24, 53, 91, 82, 82,
       64, 25, 12, 74, 64, 73, 10, 50, 35, 87, 81, 59, 62, 85,  0, 53,  0,
       49, 99, 54, 82, 26, 52, 28, 66, 63, 79, 57, 70, 82, 38, 95, 58])

cond = (a >=50) & (a < 60) # 与运算
np.where(cond,a + 10,a)

array([39, 65, 20, 11, 12,  5, 46, 65, 37, 90, 93, 33, 24, 63, 91, 82, 82,
       64, 25, 12, 74, 64, 73, 10, 60, 35, 87, 81, 69, 62, 85,  0, 63,  0,
       49, 99, 64, 82, 26, 62, 28, 66, 63, 79, 67, 70, 82, 38, 95, 68])

8.3 排序

a = np.random.randint(0,100,size = 20)
a

array([45, 66, 26, 25, 69, 35, 31, 24, 73,  3, 14, 82, 21, 86, 56,  7, 36,
       39,  9, 28])

b = np.sort(a) # 打印输出，那么，原数组，没有改变
b

array([ 3,  7,  9, 14, 21, 24, 25, 26, 28, 31, 35, 36, 39, 45, 56, 66, 69,
       73, 82, 86])

a.sort() # 没有输出，说明，原数组上进行了排序

a

array([ 3,  7,  9, 14, 21, 24, 25, 26, 28, 31, 35, 36, 39, 45, 56, 66, 69,
       73, 82, 86])

index = a.argsort() # 返回排序的索引
display(index)

array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
       17, 18, 19], dtype=int64)

# 根据索引，花式索引
a[index][::-1]

array([86, 82, 73, 69, 66, 56, 45, 39, 36, 35, 31, 28, 26, 25, 24, 21, 14,
        9,  7,  3])

8.4 集合操作

a = np.random.randint(0,30,size = 15)
b = np.random.randint(0,30,size = 15)
display(a,b)

array([28,  9, 20, 24, 10,  7, 18, 23,  6, 28,  4, 13, 14,  6,  6])



array([16, 25,  4, 23, 23,  4, 24, 26,  0,  8, 15,  6,  5, 23, 11])

np.intersect1d(a,b) # 交集：a和b中都有

array([ 4,  6, 23, 24])

np.union1d(a,b) # 并集:a和b中的所有，合并

array([ 0,  4,  5,  6,  7,  8,  9, 10, 11, 13, 14, 15, 16, 18, 20, 23, 24,
       25, 26, 28])

np.setdiff1d(a,b) # 差集，a中有，b中没有

array([ 7,  9, 10, 13, 14, 18, 20, 28])

8.5 数学和统计函数

min、max、mean、median、sum、std、var、cumsum、cumprod、argmin、argmax、argwhere、cov、corrcoef

a = np.random.randint(0,100,size = (3,5))
a

array([[30, 38, 14, 95, 19],
       [11, 32, 55, 94, 33],
       [59, 64, 41, 12,  1]])

a.min()

1

a.max(axis = 0) # axis 轴，方向。axis = 0 行，axis = 1列

array([59, 64, 55, 95, 33])

a.max(axis = 1)

array([95, 94, 64])

a.mean() # 平均值

39.86666666666667

np.median(a) # 中位数

33.0

a.sum() # 求和

598

a.std() # 标准差

27.789366471528076

a.var() # 方差，数据内部波动

772.2488888888888

a.cumsum() # 累计和

array([ 30,  68,  82, 177, 196, 207, 239, 294, 388, 421, 480, 544, 585,
       597, 598], dtype=int32)

b = np.array([1,2,3,4,5,6,7])
b.cumprod() # 累乘和

array([   1,    2,    6,   24,  120,  720, 5040], dtype=int32)

a.argmin() # 返回最小值的索引

14

a.argmax() # 返回最大值的索引

3

a

array([[30, 38, 14, 95, 19],
       [11, 32, 55, 94, 33],
       [59, 64, 41, 12,  1]])

index = np.argwhere((a > 50) | (a < 20)) # 返回就是符合条件的索引
index

array([[0, 2],
       [0, 3],
       [0, 4],
       [1, 0],
       [1, 2],
       [1, 3],
       [2, 0],
       [2, 1],
       [2, 3],
       [2, 4]], dtype=int64)

for i,j in index:
    print(a[i,j])

14
95
19
11
55
94
59
64
12
1

# cov 协方差（属性之间进行计算），方差概念类似（数据内部，属性内部计算）
# 举例子：一个男生受女生欢迎程度，和这名男生萎缩程度，是否成正比，什么关系
np.cov(a)

array([[1060.7 ,  763.25, -250.85],
       [ 763.25,  992.5 , -463.  ],
       [-250.85, -463.  ,  784.3 ]])

np.corrcoef(a) # 相关性系数，1（正相关） ~ -1（负相关）
# 0 表示，没有关系

array([[ 1.        ,  0.74388409, -0.27502788],
       [ 0.74388409,  1.        , -0.5247768 ],
       [-0.27502788, -0.5247768 ,  1.        ]])

九、线性代数

A = np.random.randint(0,10,size = (3,3))

B = np.random.randint(0,10,size = (3,4))
display(A,B) # A矩阵行长度必须和B列长度一致，不然报错

array([[3, 1, 2],
       [5, 4, 8],
       [8, 6, 5]])



array([[3, 6, 2, 0],
       [6, 2, 8, 2],
       [0, 1, 4, 5]])

A.dot(B) # dot矩阵乘法 ，点乘

array([[15, 22, 22, 12],
       [39, 46, 74, 48],
       [60, 65, 84, 37]])

np.dot(A,B) # 模块提供的方法

array([[15, 22, 22, 12],
       [39, 46, 74, 48],
       [60, 65, 84, 37]])

A @ B # 邮件中@符号，表示矩阵运算

array([[15, 22, 22, 12],
       [39, 46, 74, 48],
       [60, 65, 84, 37]])

C = np.random.randint(0,10,size = (4,5))
C

array([[1, 3, 1, 5, 7],
       [0, 0, 1, 1, 3],
       [9, 2, 3, 4, 5],
       [2, 7, 3, 6, 2]])

A.dot(C) # 形状不对应，无法进行矩阵乘法

---------------------------------------------------------------------------

ValueError                                Traceback (most recent call last)

<ipython-input-384-f96e5078725a> in <module>
----> 1 A.dot(C) # 形状不对应，无法进行矩阵乘法


ValueError: shapes (3,3) and (4,5) not aligned: 3 (dim 1) != 4 (dim 0)

# B.shape = (3,4);C.shape = (4,5)
B.dot(C)

array([[21, 13, 15, 29, 49],
       [82, 48, 38, 76, 92],
       [46, 43, 28, 47, 33]])

# C.shape = (4,5);B.shape = (3,4)
C.dot(B) # 矩阵乘法不满足交换律！！！

---------------------------------------------------------------------------

ValueError                                Traceback (most recent call last)

<ipython-input-386-0ff241fbe642> in <module>
      1 # C.shape = (4,5);B.shape = (3,4)
----> 2 C.dot(B) # 矩阵乘法不满足交换律！！！


ValueError: shapes (4,5) and (3,4) not aligned: 5 (dim 1) != 3 (dim 0)

结束语

本篇博文的代码是在jupyter上运行的，不过具体在哪运行都没什么大的区别。

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