No.0.0.2 numpy全总结

import numpy as np

arr=np.array([1,2,3,4,5])
arr

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

arr=np.array(['a','b',3,4,5])
arr

array(['a', 'b', '3', '4', '5'], dtype=' 
list_1=[i for i in range(100)]
np.array(list_1)

 
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, 32, 33,
       34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50,
       51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67,
       68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84,
       85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99])
 
第一部分 
1数组内部函数创建 
#1.全1数组
arr_1=np.ones(5)
arr_1
 
array([1., 1., 1., 1., 1.])
 
#2.全0数组
arr_0=np.zeros(5)
arr_0
 
array([0., 0., 0., 0., 0.])
 
#3.全为fill_value s的数组

arr_full=np.full(shape=[2,3],fill_value=123)
arr_full
 
array([[123, 123, 123],
       [123, 123, 123]])
 
#4.等查数列（步长跳跃）
arr_arange=np.arange(start=0,stop=10,step=3)
arr_arange
 
array([0, 3, 6, 9])
 
#5.等分位函数arr_linspace=np.linspace(start=0,stop=9,num=11)arr_linspace
 
array([0. , 0.9, 1.8, 2.7, 3.6, 4.5, 5.4, 6.3, 7.2, 8.1, 9. ])
 
#6.随机整数 arr_random_int=np.random.randint(0,100,size=10)arr_random_int
 
array([35, 83, 71, 28, 30, 15, 15, 56, 13, 56])
 
#7.正态分布数arr_random_θ=np.random.randn(20)arr_random_θ
 
array([-0.26125824, -1.10471905,  0.47196747, -0.45830774, -0.77667846,       -0.19228595, -0.88741877,  0.78935227,  0.38761409,  0.11356884,       -0.79957499, -0.42100158,  1.31760935,  0.83588336,  0.70025361,        0.96548828, -0.05750231,  1.00665188, -0.58256791, -1.06221666])
 
#8.随机数float 01范围arr_random_float=np.random.random([2,3])arr_random_float
 
array([[0.4602639 , 0.723614  , 0.75192543],       [0.1464745 , 0.96532921, 0.86107633]])
 
#9.随机数float 任意范围
arr_random_float_2=np.random.uniform(5,10,5)
arr_random_float_2
 
array([6.41475055, 7.90246005, 6.81719872, 9.80708543, 7.85627567])
 
2.查看操作 
#1.2.1 轴数，维度
arr=np.random.randint(0,100,size=(4,2))
arr.ndim
 
2
 
#1.2.2 形状尺寸arr=np.random.randint(0,100,size=(4,2,5))arr.shape
 
(4, 2, 5)
 
#1.2.3数组元素个数 sizearr=np.random.randint(0,100,size=(3,4,5))arr.size
 
60
 
#1.2.4数据类型arr=np.random.randint(0,100,size=(3,4,5),dtype='int64')arr.dtype
 
dtype('int64')
 
#1.2.5数组中每个元素大小
arr=np.random.randint(0,100,size=(3,4,5),dtype='int32')
arr.itemsize
 
4
 
3.文件io操作 
#1.3.1保存数组
x=np.random.randn(5)
y=np.arange(0,10,1)
z=np.linspace(0,100,80)
np.save("x_arr",x)#默认 .npy
np.savez("all_arr",xarr=x,yarr=y,zarr=z)

 
#1.3.2读取保存数组
np.load("x_arr.npy")
 
array([-2.48913545,  0.00585772,  2.21861779,  0.48855107, -0.90451461])
 
np.load("all_arr.npz")['yarr']
 
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
 
#1.3.3读取保存数组arr =np.random.randint(0,10,size=(3,4))
 
np.savetxt("arr.csv",arr,delimiter=",")np.loadtxt("arr.csv",delimiter=",",dtype=np.int32)
 
array([[5, 3, 0, 2],       [2, 6, 0, 5],       [4, 6, 7, 5]])
 
第二部分 数据类型 
ndarray的数据类型： 
int: int8、uint8、int16、int32、int64
float: float16、float32、float64
str
 
# 2.1创建指定数据类型np.array(np.arange(1,10,2),dtype='int8')
 
array([1, 3, 5, 7, 9], dtype=int8)
 
# 2.2转换时指定数据类型arr =list(range(20))np.asarray(arr,dtype='float32')
 
array([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10., 11., 12.,       13., 14., 15., 16., 17., 18., 19.], dtype=float32)
 
# 2.3转换时指定数据类型
arr=np.random.randint(0,10,5,dtype='int32')
arr.dtype
 
dtype('int32')
 
arr=arr.astype('float64')
arr.dtype
 
dtype('float64')
 
第三部分 数组运算 
3.1加减乘除幂运算 
arr1=np.array(list(range(1,5)))
arr2=np.array(list(range(2,6)))
 
arr1-arr2
 
array([-1, -1, -1, -1])
 
arr1+arr2
 
array([3, 5, 7, 9])
 
arr2/arr1
 
array([2.        , 1.5       , 1.33333333, 1.25      ])
 
arr2*arr1
 
array([ 2,  6, 12, 20])
 
arr2**arr1
 
array([  2,   9,  64, 625], dtype=int32)
 
3.2逻辑运算 > 、<、=、>=、<= 
arr1<5
 
array([ True,  True,  True,  True])
 
arr1>5
 
array([False, False, False, False])
 
arr1==4
 
array([False, False, False,  True])
 
arr1==arr2
 
array([False, False, False, False])
 
3.3数组与标量计算 
arr1=np.array([5,5,5,5])
 
arr2=np.array(list(range(5)))
 
arr1+=5
 
arr1-=5
 
arr1*=5
 
# arr1/=5 没有除等
 
第四部分 复制和视图 
4.1 拷贝复制 完全没有复制 
在操作数组时，有时会将其数据复制到新数组中，有时不复制。 
对于初学者来说，这通常会引起混乱。有以下三种情况 
a=np.random.randint(0,100,[4,5])b=a
 
a is b # 返回True a和b是两个不同名字对应同⼀个内存对象
 
True
 
b[0,0]=1024 #a与b位置相同，同时被修改print(a[0,0],b[0,0])
 
1024 1024
 
display(a,b)
 
array([[1024,   31,   42,   19,   68],
       [  69,   67,   22,    7,   93],
       [  77,   62,   20,   15,   25],
       [   4,   46,   88,   67,   80]])



array([[1024,   31,   42,   19,   68],
       [  69,   67,   22,    7,   93],
       [  77,   62,   20,   15,   25],
       [   4,   46,   88,   67,   80]])
 
4.2 查看或浅拷贝 
a=np.random.randint(0,100,[4,5])
b=a.view()  # 使⽤a中的数据创建⼀个新数组对象
 
a is b# 返回False a和b是两个不同名字对应同⼀个内存对象
 
False
 
b.base is a   # 返回False a和b是两个不同名字对应同⼀个内存对象
 
True
 
b.flags.owndata # 返回False b中的数据不是其⾃⼰的
 
False
 
a.flags.owndata # 返回True a中的数据是其⾃⼰的
 
True
 
a[0,0]=1024
 
b[0,0]
 
1024
 
display(a,b)
 
array([[1024,   86,   36,   96,   66],       [  17,   68,   11,   88,   26],       [  89,   39,   14,   21,   90],       [  49,   82,   46,   98,    3]])



array([[1024,   86,   36,   96,   66],       [  17,   68,   11,   88,   26],       [  89,   39,   14,   21,   90],       [  49,   82,   46,   98,    3]])
 
4.3 深拷贝 
a=np.random.randint(0,100,[4,5])b=a.copy()  
 
b is a
 
False
 
b.base is a
 
False
 
b.flags.owndata
 
True
 
a.flags.owndata
 
True
 
b[0,0]=1024
 
a[0,0]
 
52
 
display(a,b)
 
array([[52, 60, 16, 93, 64],       [67, 36, 75, 82, 42],       [86, 58, 17, 54, 22],       [72, 14, 85, 92, 17]])



array([[1024,   60,   16,   93,   64],       [  67,   36,   75,   82,   42],       [  86,   58,   17,   54,   22],       [  72,   14,   85,   92,   17]])
 
copy应该在不再需要原来的数组情况下，切⽚后调⽤。例如，假设a是⼀个巨⼤的中间结果，⽽最终结果b仅包含的⼀⼩部分a，则在b使⽤切⽚进⾏构造时应制作⼀个深拷⻉：
 
a=np.arange(1e8)b=a[::1000000]del ab.shape
 
(100,)
 
第五部分 索引 切片 迭代 
5.1基本索引与切片 
## 5.1基本索引与切片arr=np.arange(10)arr
 
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
 
arr[5]
 
5
 
arr[5:8]
 
array([5, 6, 7])
 
arr[5::2]
 
array([5, 7, 9])
 
arr[::2]
 
array([0, 2, 4, 6, 8])
 
arr[:7:2]
 
array([0, 2, 4, 6])
 
arr[::-2] # 倒序取
 
array([9, 7, 5, 3, 1])
 
arr[::-1] 
 
array([9, 8, 7, 6, 5, 4, 3, 2, 1, 0])
 
arr[0:3]=999
arr
 
array([999, 999, 999,   3,   4,   5,   6,   7,   8,   9])
 
temp=arr[5:8]
temp[1]=1034
arr
 
array([ 999,  999,  999,    3,    4,    5, 1034,    7,    8,    9])
 
5.2高维索引与切片 
对于⼆维数组或者⾼维数组，我们可以按照之前的知识来索引，当然也可以传⼊⼀个以逗号隔开的索引
列表来选区单个或多个元素
 
arr2d=np.array(list(range(12)))arr2d.shape=(3,4)arr2d
 
array([[ 0,  1,  2,  3],       [ 4,  5,  6,  7],       [ 8,  9, 10, 11]])
 
arr2d[0,-1]# 第一位表示行，二位表示列
 
3
 
arr2d[0,2]
 
2
 
arr2d[:2,-2:]
 
array([[2, 3],
       [6, 7]])
 
arr2d[:2,:-2]
 
array([[0, 1],
       [4, 5]])
 
arr2d[:2,2:]
 
array([[2, 3],       [6, 7]])
 
arr2d[:2,:2]
 
array([[0, 1],       [4, 5]])
 
5.3 花式索引和索引技巧 
整数数组进⾏索引即花式索引,其和切⽚不⼀样，它总是将数据复制到新数组中
 
# 一维索引arr1=np.arange(1,11)arr1
 
array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10])
 
arr2=arr1[[1,3,3,5,7,7,7]]arr2
 
array([2, 4, 4, 6, 8, 8, 8])
 
arr2[-1]=1024#不影响arr1arr2
 
array([   2,    4,    4,    6,    8,    8, 1024])
 
arr1
 
array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10])
 
# 二维索引arr2d=np.arange(20)arr2d
 
array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,       17, 18, 19])
 
arr2d.shape=(4,5)arr2d
 
array([[ 0,  1,  2,  3,  4],       [ 5,  6,  7,  8,  9],       [10, 11, 12, 13, 14],       [15, 16, 17, 18, 19]])
 
arr2d[[1,3]]#索引编号第1行和第第3行
 
array([[ 5,  6,  7,  8,  9],
       [15, 16, 17, 18, 19]])
 
arr2d[[0,2]]#索引编号第0行和第第2行
 
array([[ 0,  1,  2,  3,  4],
       [10, 11, 12, 13, 14]])
 
arr2d[([1,3],[2,4])]#索引编号第1行和第3行 与 第2列和第4列  的交叉点 元素，相当于坐标arr2d[3,4] 和arr2d[1,2]
 
array([ 7, 19])
 
arr2d[1,2] 
 
7
 
arr2d[3,4]
 
19
 
# 选择输出一个区域arr2d[np.ix_([1,3,3,3],[2,4,4])]   
 
array([[ 7,  9,  9],       [17, 19, 19],       [17, 19, 19],       [17, 19, 19]])
 
#相当于arr2d[[1,3,3,3]][:,[2,4,4]]
 
array([[ 7,  9,  9],       [17, 19, 19],       [17, 19, 19],       [17, 19, 19]])
 
#也相当于arr2d_tmp=arr2d[[1,3,3,3]]# arr2d_tmparr2d_tmp[:,[2,4,4]]
 
array([[ 7,  9,  9],       [17, 19, 19],       [17, 19, 19],       [17, 19, 19]])
 
# ix_()函数可⽤于组合不同的向量
# 第⼀个列表存的是待提取元素的⾏标，第⼆个列表存的是待提取元素的列
 
5.4 boolean值索引（布尔索引） 
# names =
# np.array(['softpo','Brandon','Will','Michael','Will','Ella','Daniel','softpo','
# Will','Brandon'])
# cond1 = names == 'Will'
# cond1
# # 输出array([False, False, True, False, True, False, False, False, True,
# False])
# names[cond1] # array(['Will', 'Will', 'Will'], dtype=' 90
# # 找到所有⼤于90的索引，返回boolean类型的数组 shape(10,8)，⼤于返回True，否则False
# arr[cond2] # 返回数据全部是⼤于90的
 
names =np.array(['softpo','Brandon','Will','Michael','Will','Ella','Daniel','softpo','Will','Brandon'])
 
names
 
array(['softpo', 'Brandon', 'Will', 'Michael', 'Will', 'Ella', 'Daniel',       'softpo', 'Will', 'Brandon'], dtype=' 
cond1 = names == 'Will'cond1 
 
array([False, False,  True, False,  True, False, False, False,  True,       False])
 
names[cond1]#索引为True 的对应元素
 
array(['Will', 'Will', 'Will'], dtype=' 
arr=np.random.randint(0,100,size=[10,8])arr
 
array([[81, 59, 92, 17, 87, 49, 89, 45],       [ 3,  1, 12, 17, 54, 68, 11, 11],       [35, 86, 20, 44, 38, 80, 39, 52],       [80,  5, 50, 16, 20, 78, 94, 91],       [90, 68, 25, 35, 27, 67, 43, 44],       [23, 54, 45, 75, 14, 10, 21, 72],       [84, 26, 63, 50, 56,  3, 67, 90],       [98, 15, 25, 96, 58, 44,  9, 19],       [35, 75, 46, 79,  8, 94, 83, 88],       [ 8, 52, 68, 69, 72, 71, 31, 88]])
 
arr_bool=arr>90arr_bool
 
array([[False, False,  True, False, False, False, False, False],       [False, False, False, False, False, False, False, False],       [False, False, False, False, False, False, False, False],       [False, False, False, False, False, False,  True,  True],       [False, False, False, False, False, False, False, False],       [False, False, False, False, False, False, False, False],       [False, False, False, False, False, False, False, False],       [ True, False, False,  True, False, False, False, False],       [False, False, False, False, False,  True, False, False],       [False, False, False, False, False, False, False, False]])
 
arr[arr_bool]
 
array([92, 94, 91, 98, 96, 94])
 
第六部分 形状操作 
6.1 数组变形 
arr1=np.random.randint(1,100,size=(3,4,5))arr1
 
array([[[68, 40, 48, 91, 49],
        [96, 37, 30, 75, 78],
        [79, 74, 75, 26, 51],
        [15, 45, 20, 59, 54]],

       [[73,  5, 71, 88, 62],
        [16,  6, 36, 49, 89],
        [40,  7, 42, 34, 97],
        [62, 87, 82, 70, 96]],

       [[94, 85, 62, 11, 26],
        [ 2, 76, 43,  9, 40],
        [21, 23, 99, 36, 78],
        [69, 71, 30, 11, 98]]])
 
arr1.reshape(12,5) # 修改形状
 
array([[68, 40, 48, 91, 49],
       [96, 37, 30, 75, 78],
       [79, 74, 75, 26, 51],
       [15, 45, 20, 59, 54],
       [73,  5, 71, 88, 62],
       [16,  6, 36, 49, 89],
       [40,  7, 42, 34, 97],
       [62, 87, 82, 70, 96],
       [94, 85, 62, 11, 26],
       [ 2, 76, 43,  9, 40],
       [21, 23, 99, 36, 78],
       [69, 71, 30, 11, 98]])
 
arr1.reshape(-1,5)# 为负数的值会被自动赋值相应的行或列数
 
array([[68, 40, 48, 91, 49],       [96, 37, 30, 75, 78],       [79, 74, 75, 26, 51],       [15, 45, 20, 59, 54],       [73,  5, 71, 88, 62],       [16,  6, 36, 49, 89],       [40,  7, 42, 34, 97],       [62, 87, 82, 70, 96],       [94, 85, 62, 11, 26],       [ 2, 76, 43,  9, 40],       [21, 23, 99, 36, 78],       [69, 71, 30, 11, 98]])
 
arr1.reshape(6,-1)# 为负数的值会被自动赋值相应的行或列数
 
array([[68, 40, 48, 91, 49, 96, 37, 30, 75, 78],       [79, 74, 75, 26, 51, 15, 45, 20, 59, 54],       [73,  5, 71, 88, 62, 16,  6, 36, 49, 89],       [40,  7, 42, 34, 97, 62, 87, 82, 70, 96],       [94, 85, 62, 11, 26,  2, 76, 43,  9, 40],       [21, 23, 99, 36, 78, 69, 71, 30, 11, 98]])
 
6.2 数组转换 
arr1=np.random.randint(1,100,size=(3,5))arr1
 
array([[15, 31, 44, 13, 74],       [54, 82, 18, 33, 56],       [76, 84, 71, 23, 29]])
 
arr1.T
 
array([[15, 54, 76],       [31, 82, 84],       [44, 18, 71],       [13, 33, 23],       [74, 56, 29]])
 
arr2=np.random.randint(1,100,size=(3,4,5,6))arr2
 
array([[[[89,  5,  9, 23, 15, 45],
         [83, 72, 90, 98, 14, 54],
         [41, 16, 31, 28, 25, 28],
         [ 6, 48,  8, 62, 69,  4],
         [36,  1, 63, 52, 40, 17]],

        [[22, 19, 56, 69, 75, 30],
         [43,  7,  3, 76, 15, 79],
         [13, 45, 78, 19, 81, 77],
         [60, 51, 81, 40, 48, 65],
         [99, 79, 74, 52,  4, 27]],

        [[73, 12, 54, 42, 67, 43],
         [81, 78, 35, 71, 80, 66],
         [90, 43,  2, 24, 55,  3],
         [98, 56, 76, 15, 65,  5],
         [64, 85, 92, 22, 39, 79]],

        [[55, 24, 54,  6, 35, 42],
         [88, 84, 46, 15, 30, 83],
         [ 9, 62, 55, 81, 65, 75],
         [14, 99, 34, 75, 63, 53],
         [19, 39, 61, 88, 95,  6]]],
 
​
 
       [[[57, 37, 14, 32, 79, 88],
         [ 1, 32, 80,  8, 52, 86],
         [42, 38, 11, 75, 56, 22],
         [70, 43, 24, 14, 77, 26],
         [75, 68,  1, 94, 98, 88]],

        [[99, 73, 68, 14, 48,  5],
         [29, 52, 72, 99, 10, 16],
         [21, 86, 85, 15, 29, 43],
         [87, 52, 83,  6, 59, 83],
         [51, 61, 67,  7, 14, 50]],

        [[ 4, 77, 14, 45, 13,  9],
         [58,  6, 24, 59, 88, 92],
         [11, 72, 35, 60, 94, 37],
         [59, 94, 67, 92, 75, 84],
         [77, 23, 39, 77, 67, 14]],

        [[63,  8, 16, 69, 16, 74],
         [34, 61, 64, 72, 15, 15],
         [33, 62, 49, 37, 64, 84],
         [94, 22,  9,  4, 56, 48],
         [53, 16, 14, 61, 56, 63]]],
 
​
 
       [[[28, 90, 96, 64, 61, 15],         [41, 99, 61, 83, 37, 14],         [97, 92, 99, 16, 72, 46],         [42, 30, 83, 83, 15, 31],         [52, 98, 16, 98, 90, 31]],        [[37, 35, 37, 66, 97,  6],         [18, 29, 14, 26, 96, 11],         [78, 40, 75, 41, 17, 15],         [77, 82, 29, 87, 65, 30],         [56, 69, 40, 90, 67,  2]],        [[14, 43, 51, 60, 52, 91],         [66, 45, 11, 74, 11,  2],         [25, 44, 72,  6, 13, 22],         [63, 24, 90, 86, 43,  3],         [78, 29, 36, 18, 94, 10]],        [[56, 64, 86, 32, 76, 90],         [61, 42, 25, 98,  3, 32],         [ 6, 51, 25, 60, 36, 68],         [19, 24, 51, 20, 35, 27],         [22, 21, 85, 17, 82, 30]]]])
 
arr3=arr2.T
 
arr3.shape
 
(6, 5, 4, 3)
 
arr2.shape
 
(3, 4, 5, 6)
 
# transpose改变数组维度  对原数组形状进行排序，然后利用索引调换顺序arr4=np.transpose(arr2,axes=(3,0,2,1))
 
arr4.shape
 
(6, 3, 5, 4)
 
6.3 数组堆叠 
arr1=np.array([range(1,4)])arr2=np.array([range(4,7)])
 
arr1
 
array([[1, 2, 3]])
 
np.concatenate([arr1,arr2],axis=0)  # 记忆 0代表在下方合并相当于union，1代表在右侧合并相当于right join
 
array([[1, 2, 3],
       [4, 5, 6]])
 
np.concatenate([arr1,arr2],axis=1)  # 记忆 0代表在下方合并相当于union，1代表在右侧合并相当于right join
 
array([[1, 2, 3, 4, 5, 6]])
 
np.hstack((arr1,arr2)) #水平方向叠加
 
array([[1, 2, 3, 4, 5, 6]])
 
np.vstack((arr1,arr2)) # 竖直方向叠加
 
array([[1, 2, 3],
       [4, 5, 6]])
 
6.4 数组拆分split 
import numpy as pd arr = np.random.randint(0,10,size=(6,5))np.split(arr,indices_or_sections=2,axis=0)
 
[array([[6, 7, 3, 3, 2],        [1, 5, 8, 5, 4],        [6, 0, 7, 6, 9]]), array([[2, 1, 2, 3, 3],        [0, 4, 5, 4, 7],        [9, 9, 2, 1, 4]])]
 
np.split(arr,indices_or_sections=2,axis=0)# 竖向分割 确保竖向（行数）为偶数
 
[array([[6, 7, 3, 3, 2],        [1, 5, 8, 5, 4],        [6, 0, 7, 6, 9]]), array([[2, 1, 2, 3, 3],        [0, 4, 5, 4, 7],        [9, 9, 2, 1, 4]])]
 
np.split(arr,indices_or_sections=[2,],axis=1)# 横向切割向分割 确保横向（列数）为偶数,否则传入 indices_or_sections=[2,]，2为第二列，留空时分成两份
 
[array([[6, 7],        [1, 5],        [6, 0],        [2, 1],        [0, 4],        [9, 9]]), array([[3, 3, 2],        [8, 5, 4],        [7, 6, 9],        [2, 3, 3],        [5, 4, 7],        [2, 1, 4]])]
 
np.split(arr,indices_or_sections=[2,3],axis=1)# 横向切割向分割 确保横向（列数）为偶数,否则可传入 indices_or_sections=[2,3]，2为第二列，3为第三列，# 于是数组被分为分成1，2列，3列，至最后一列
 
[array([[6, 7],        [1, 5],        [6, 0],        [2, 1],        [0, 4],        [9, 9]]), array([[3],        [8],        [7],        [2],        [5],        [2]]), array([[3, 2],        [5, 4],        [6, 9],        [3, 3],        [4, 7],        [1, 4]])]
 
arr
 
array([[6, 7, 3, 3, 2],
       [1, 5, 8, 5, 4],
       [6, 0, 7, 6, 9],
       [2, 1, 2, 3, 3],
       [0, 4, 5, 4, 7],
       [9, 9, 2, 1, 4]])
 
np.vsplit(arr,indices_or_sections=3)# 在竖直方向被平均分成三份
 
[array([[6, 7, 3, 3, 2],
        [1, 5, 8, 5, 4]]), array([[6, 0, 7, 6, 9],
        [2, 1, 2, 3, 3]]), array([[0, 4, 5, 4, 7],
        [9, 9, 2, 1, 4]])]
 
np.hsplit(arr,indices_or_sections=[1,4])# 在水平方向以索引1,4为断点分割成三份（此处索引标注从1开始，不是从0开始）
 
[array([[6],
        [1],
        [6],
        [2],
        [0],
        [9]]), array([[7, 3, 3],
        [5, 8, 5],
        [0, 7, 6],
        [1, 2, 3],
        [4, 5, 4],
        [9, 2, 1]]), array([[2],
        [4],
        [9],
        [3],
        [7],
        [4]])]
 
第七部分 广播机制 
当两个数组的形状并不相同的时候，我们可以通过扩展数组的方法来实现加减乘（除）等操作，这种机制叫广播机制
 
7.1排序规则np.sort(array,[axis=1,0]) 
import numpy as np
arr1=np.sort(np.array([1,2,3,4]*3)).reshape(4,3)
 
arr2=np.sort(np.array([1,2,3,4]*3)).reshape(4,3)
arr2
 
array([[1, 1, 1],
       [2, 2, 2],
       [3, 3, 3],
       [4, 4, 4]])
 
#2
np.sort(arr1,axis=0)
 
array([[1, 1, 1],
       [2, 2, 2],
       [3, 3, 3],
       [4, 4, 4]])
 
arr1
 
array([[1, 1, 1],
       [2, 2, 2],
       [3, 3, 3],
       [4, 4, 4]])
 
arr3=np.sort(arr1,axis=1)
arr3
 
array([[1, 1, 1],
       [2, 2, 2],
       [3, 3, 3],
       [4, 4, 4]])
 
np.sort(arr3,axis=0)
 
array([[1, 1, 1],
       [2, 2, 2],
       [3, 3, 3],
       [4, 4, 4]])
 
arr1
 
array([[1, 1, 1],
       [2, 2, 2],
       [3, 3, 3],
       [4, 4, 4]])
 
## 默认axis = 1 按行排序 水平方向从小到大排列，

arr2=np.sort(np.random.randint(1,10,(4,3)))
arr2 

##竖直方向从小到大排列，
np.sort(arr2,axis=0) 

##水平方向从小到大排列，
np.sort(arr2,axis=1)
 
array([[1, 5, 8],
       [3, 8, 9],
       [6, 8, 9],
       [1, 1, 2]])
 
7.2一维数组广播 
arr1=np.sort(np.array([1,2,3,4]*3)).reshape(4,3)
arr2=np.array([1,2,3])
arr3=arr1+arr3
arr3
 
array([[2, 2, 2],
       [4, 4, 4],
       [6, 6, 6],
       [8, 8, 8]])
 
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7.3二维数组广播 
arr1=np.sort(np.array([0,1,2,3,]*3)).reshape(4,3)
arr2=np.array([[1],[2],[3],[4]])
arr3=arr1+arr2
arr3
 
array([[1, 1, 1],
       [3, 3, 3],
       [5, 5, 5],
       [7, 7, 7]])
 
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7.4三维数组⼴播 
import numpy as np
arr1 = np.array([0,1,2,3,4,5,6,7]*3).reshape(3,4,2) #shape(3,4,2)
arr2 = np.array([0,1,2,3,4,5,6,7]).reshape(4,2) #shape(4,2)
arr3 = arr1 + arr2 # arr2数组在0维上复制3份 shape(3,4,2)
arr3
 
array([[[ 0,  2],
        [ 4,  6],
        [ 8, 10],
        [12, 14]],

       [[ 0,  2],
        [ 4,  6],
        [ 8, 10],
        [12, 14]],

       [[ 0,  2],
        [ 4,  6],
        [ 8, 10],
        [12, 14]]])
 
arr1
 
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]]])
 
arr2 
 
array([[0, 1],
       [2, 3],
       [4, 5],
       [6, 7]])
 
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#  维度只能从z轴方向运算广播

import numpy as np
arr1 = np.array([0,1,2,3,4,5,6,7]*3).reshape(3,4,2) #shape(3,4,2)
arr2 = np.arange(0,12).reshape(3,4) #shape(,2)
# arr3 = arr1 + arr2 # arr2数组在0维上复制3份 shape(3,4,2)
# arr3
 
第八部分 通用函数 
8.1 通用函数：元素级数字函数 
abs、sqrt、square、exp、log、sin、cos、tan，maxinmum、minimum、all、any、inner、clip、round、trace、ceil、floor
 
import numpy  as np 
arr=np.arange(1,10)
np.sqrt(arr)# 开平方
np.square(arr)#平方
np.clip(arr,2,9)## 盖帽法

x=np.array([1,5,2,9,3,6,8])
y=np.array([2,4,3,7,1,9,0])
np.maximum(x,y)# 返回两组数据的同位置最大值
arr2=np.arange(0,25).reshape(5,5)
np.inner(arr2[0],arr2)# 返回一维数组向量内积


print("数组最大值：%s"%(np.max(arr)))
print("数组最小值：%s"%(np.min(arr)))
print("以e为基数求e的数组次方%s"%np.exp(arr))
print("以10为低求数组对数%s"%np.log(arr))
print("开方%s"%np.sqrt(arr))
print("平均值%s"%np.mean(arr))
print("标准差%s"%np.std(arr))
print("极小值%s"%np.argmin(arr))
print("极大值%s"%np.argmax(arr))
print("判断极限值：%s"%np.isinf(arr))
 
数组最大值：9
数组最小值：1
以e为基数求e的数组次方[2.71828183e+00 7.38905610e+00 2.00855369e+01 5.45981500e+01
 1.48413159e+02 4.03428793e+02 1.09663316e+03 2.98095799e+03
 8.10308393e+03]
以10为低求数组对数[0.         0.69314718 1.09861229 1.38629436 1.60943791 1.79175947
 1.94591015 2.07944154 2.19722458]
开方[1.         1.41421356 1.73205081 2.         2.23606798 2.44948974
 2.64575131 2.82842712 3.        ]
平均值5.0
标准差2.581988897471611
极小值0
极大值8
判断极限值：[False False False False False False False False False]
 
8.2 where函数 
import numpy as np 
arr1=np.array([1,2,5,7,9])
arr2 = np.array([2,4,6,8,10])
bool_v=np.array([True,False,True,True,True])
np.where(bool_v,arr1,arr2)
np.where(arr1<5,arr1,-16)
 
array([  1,   2, -16, -16, -16])
 
8.3排序方法 
arr.sort()、np.sort()、arr.argsort()
 
import numpy as np
arr =np.array([9,3,11,6,17,5,4,15,1])
arr.sort()# 直接改变原数组
np.sort(arr)# 返回深拷贝结果


 
array([ 1,  3,  4,  5,  6,  9, 11, 15, 17])
 
arr =np.array([9,3,11,6,17,5,4,15,1])
arr.argsort()# 返回从小到大的排序索引
 
array([8, 1, 6, 5, 3, 0, 2, 7, 4], dtype=int64)
 
8.4集合运算函数 
a=np.arange(2,10,2)
b=np.arange(3,7)
np.intersect1d(a,b)#交集
np.union1d(a,b)#并集
np.setdiff1d(a,b)# 差集 a有b无的元素
 
array([2, 8])
 
8.5集合运算函数 
import numpy as np 
arr1=np.arange(0,50)
arr1.min()
arr1.max()
np.argmax(arr1)#返回最大值索引
np.argwhere(arr1>20)# 返回值符合条件（大于20）的索引
np.cumsum(arr1)# 累加计算

arr2=np.arange(0,50).reshape(5,10)
arr2.mean(axis=0)# 计算列的平均值
arr2.mean(axis=1)#计算行的平均值
np.cov(arr2,rowvar=True)# 协方差矩阵
np.corrcoef(arr2,rowvar=True)# 相关系数
 
array([[1., 1., 1., 1., 1.],
       [1., 1., 1., 1., 1.],
       [1., 1., 1., 1., 1.],
       [1., 1., 1., 1., 1.],
       [1., 1., 1., 1., 1.]])
 
arr2.mean(axis=0)
 
array([20., 21., 22., 23., 24., 25., 26., 27., 28., 29.])
 
np.cov(arr2,rowvar=True)#
 
array([[9.16666667, 9.16666667, 9.16666667, 9.16666667, 9.16666667],
       [9.16666667, 9.16666667, 9.16666667, 9.16666667, 9.16666667],
       [9.16666667, 9.16666667, 9.16666667, 9.16666667, 9.16666667],
       [9.16666667, 9.16666667, 9.16666667, 9.16666667, 9.16666667],
       [9.16666667, 9.16666667, 9.16666667, 9.16666667, 9.16666667]])
 
9 线性代数 
a=np.array([[4,2,3],[1,3,1]])
b=np.array([[2,7],[-5,-7],[9,3]])
 
a.dot(b)#矩阵运算 a的最后一维要求和b的第一维相等
np.dot(a,b)#
a@b #缩写
 
array([[ 25,  23],
       [ -4, -11]])
 
#矩阵的其他运算
from numpy.linalg import  inv,det,eig,qr,svd
 
a=np.array([[1,2,3],
           [2,3,4],
            [4,5,8]
           ])
b=inv(a)
 
a.dot(b)
 
array([[ 1.00000000e+00,  2.22044605e-16, -5.55111512e-17],
       [ 4.44089210e-16,  1.00000000e+00,  2.22044605e-16],
       [ 0.00000000e+00, -1.77635684e-15,  1.00000000e+00]])