大数据的Python基础课件第10章numpy与pandas基础.pptx

1、第10章 numpy与pandas基础1本章学习目标 熟练掌握numpy数组运算与矩阵运算 理解pandas的Series和DataFrame结构 熟练掌握pandas读取不同类型数据的方法 熟练掌握pandas访问和修改数据的方法 熟练掌握缺失值处理方法 熟练掌握重复值处理方法 熟练掌握异常值处理方法210.1 numpy数组运算与矩阵运算基础 Python扩展库numpy支持N维数组运算、处理大型矩阵、成熟的广播函数库、矢量运算、线性代数、傅里叶变换、随机数生成，并可与C+/Fortran语言无缝结合。310.1.1 数组生成与常用操作（1）生成数组 np.array(1,2,3,4,5)

2、#把列表转换为数组array(1,2,3,4,5)np.array(1,2,3,4,5)#把元组转换成数组array(1,2,3,4,5)np.array(range(5)#把range对象转换成数组array(0,1,2,3,4)np.array(1,2,3,4,5,6)#二维数组array(1,2,3,4,5,6)np.arange(8)#类似于内置函数range()array(0,1,2,3,4,5,6,7)np.arange(1,10,2)array(1,3,5,7,9)410.1.1 数组生成与常用操作 np.linspace(0,10,11)#等差数组，包含11个数array(0.

3、,1.,2.,3.,4.,5.,6.,7.,8.,9.,10.)np.linspace(0,10,11,endpoint=False)#不包含终点array(0.,0.90909091,1.81818182,2.72727273,3.63636364,4.54545455,5.45454545,6.36363636,7.27272727,8.18181818,9.09090909)np.logspace(0,100,10)#相当于10*np.linspace(0,100,10)array(1.00000000e+000,1.29154967e+011,1.66810054e+022,2.154

4、43469e+033,2.78255940e+044,3.59381366e+055,4.64158883e+066,5.99484250e+077,7.74263683e+088,1.00000000e+100)np.logspace(1,6,5,base=2)#相当于2*np.linspace(1,6,5)array(2.,4.75682846,11.3137085,26.90868529,64.)np.zeros(3)#全0一维数组array(0.,0.,0.)510.1.1 数组生成与常用操作 np.ones(3)#全1一维数组array(1.,1.,1.)np.zeros(3,3)#

5、全0二维数组，3行3列array(0.,0.,0.,0.,0.,0.,0.,0.,0.)np.zeros(3,1)#全0二维数组，3行1列array(0.,0.,0.)np.zeros(1,3)#全0二维数组，1行3列array(0.,0.,0.)np.ones(3,3)#全1二维数组array(1.,1.,1.,1.,1.,1.,1.,1.,1.)610.1.1 数组生成与常用操作 np.ones(1,3)#全1二维数组array(1.,1.,1.)np.identity(3)#单位矩阵array(1.,0.,0.,0.,1.,0.,0.,0.,1.)np.identity(2)array(

6、1.,0.,0.,1.)np.empty(3,3)#空数组array(0.,0.,0.,0.,0.,0.,0.,0.,0.)710.1.1 数组生成与常用操作 np.hamming(20)#Hamming窗口array(0.08 ,0.10492407,0.17699537,0.28840385,0.42707668,0.5779865,0.7247799,0.85154952,0.94455793,0.9937262,0.9937262,0.94455793,0.85154952,0.7247799,0.5779865,0.42707668,0.28840385,0.17699537,0.1

7、0492407,0.08 )np.blackman(10)#Blackman窗口array(-1.38777878e-17,5.08696327e-02,2.58000502e-01,6.30000000e-01,9.51129866e-01,9.51129866e-01,6.30000000e-01,2.58000502e-01,5.08696327e-02,-1.38777878e-17)np.kaiser(12,5)#Kaiser窗口array(0.03671089,0.16199525,0.36683806,0.61609304,0.84458838,0.98167828,0.9816

8、7828,0.84458838,0.61609304,0.36683806,0.16199525,0.03671089)810.1.1 数组生成与常用操作 np.random.randint(0,50,5)#随机数组，5个0到50之间的数字array(13,47,31,26,9)np.random.randint(0,50,(3,5)#3行5列array(34,2,33,14,40,9,5,10,27,11,26,17,10,46,30)np.random.rand(10)#10个介于0,1)的随机数array(0.98139326,0.35675498,0.30580776,0.303796

9、27,0.19527425,0.59159936,0.31132305,0.20219211,0.20073821,0.02435331)np.random.standard_normal(5)#从标准正态分布中随机采样5个数字array(2.82669067,0.9773194,-0.72595951,-0.11343254,0.74813065)910.1.1 数组生成与常用操作 x=np.random.standard_normal(size=(3,4,2)xarray(0.5218421,-1.10892934,2.27295689,0.9598461,-0.92229318,2.25

10、708573,0.0070173,-0.30608704,1.05133704,-0.4094823,-0.03457527,-2.3034343,-0.45156185,-1.26174441,0.59367951,-0.78355627,0.0424474,-1.75202307,-0.43457619,-0.96445206,0.28342028,1.27303125,-0.15312326,2.0399687)1010.1.1 数组生成与常用操作 np.diag(1,2,3)#对角矩阵array(1,0,0,0,2,0,0,0,3)np.diag(1,2,3,4)#对角矩阵array(

11、1,0,0,0,0,2,0,0,0,0,3,0,0,0,0,4)1110.1.1 数组生成与常用操作（2）测试两个数组的对应元素是否都足够接近 x=np.array(1,2,3,4.001,5)y=np.array(1,1.999,3,4.01,5.1)np.allclose(x,y)False np.allclose(x,y,rtol=0.2)#设置相对误差参数True np.allclose(x,y,atol=0.2)#设置绝对误差参数True1210.1.1 数组生成与常用操作（3）修改数组中的元素值 x=np.arange(8)xarray(0,1,2,3,4,5,6,7)np.app

12、end(x,8)#返回新数组，增加元素array(0,1,2,3,4,5,6,7,8)np.append(x,9,10)#返回新数组，在尾部追加多个元素array(0,1,2,3,4,5,6,7,9,10)x#不影响原来的数组array(0,1,2,3,4,5,6,7)x3=8#原地修改元素值 xarray(0,1,2,8,4,5,6,7)1310.1.1 数组生成与常用操作 np.insert(x,1,8)#返回新数组，插入元素array(0,8,1,2,8,4,5,6,7)x=np.array(1,2,3,4,5,6,7,8,9)x0,2=4#修改第0行第2列的元素值 x1:,1:=1#切

13、片，同时修改多个值 xarray(1,2,4,4,1,1,7,1,1)1410.1.1 数组生成与常用操作 x1:,1:=1,2#同时修改多个元素值 xarray(1,2,4,4,1,2,7,1,2)x1:,1:=1,2,3,4#同时修改多个元素值 xarray(1,2,4,4,1,2,7,3,4)1510.1.1 数组生成与常用操作（4）数组与标量的计算 x=np.array(1,2,3,4,5)#创建数组对象 xarray(1,2,3,4,5)x*2#数组与数值相乘，返回新数组array(2,4,6,8,10)x/2#数组与数值相除array(0.5,1.,1.5,2.,2.5)x/2#数

14、组与数值整除array(0,1,1,2,2,dtype=int32)x*3#幂运算array(1,8,27,64,125,dtype=int32)x+2#数组与数值相加array(3,4,5,6,7)1610.1.1 数组生成与常用操作 x%3#余数array(1,2,0,1,2,dtype=int32)2*x#分别计算2*1、2*2、2*3、2*4、2*5array(2,4,8,16,32,dtype=int32)2/xarray(2.,1.,0.66666667,0.5,0.4)63/xarray(63,31,21,15,12,dtype=int32)1710.1.1 数组生成与常用操作（

15、5）数组与数组的四则运算 np.array(1,2,3,4)+np.array(4,3,2,1)#等长数组相加，对应元素相加array(5,5,5,5)np.array(1,2,3,4)+np.array(4)#数组中每个元素加4array(5,6,7,8)a=np.array(1,2,3)a+a#等长数组之间的加法运算，对应元素相加array(2,4,6)a*a#等长数组之间的乘法运算，对应元素相乘array(1,4,9)1810.1.1 数组生成与常用操作 a-a#等长数组之间的减法运算，对应元素相减array(0,0,0)a/a#等长数组之间的除法运算，对应元素相除array(1.,1.

16、,1.)b=np.array(1,2,3,4,5,6,7,8,9)c=a*b#不同维度的数组与数组相乘 c#a中的每个元素乘以b中的对应列元素array(1,4,9,4,10,18,7,16,27)c/b#数组之间的除法运算array(1.,2.,3.,1.,2.,3.,1.,2.,3.)1910.1.1 数组生成与常用操作 c/aarray(1.,2.,3.,4.,5.,6.,7.,8.,9.)a+b#a中每个元素加b中的每一列元素array(2,4,6,5,7,9,8,10,12)2010.1.1 数组生成与常用操作（6）数组排序 x=np.array(3,1,2)np.argsort(x

17、)#返回排序后元素的原下标array(1,2,0,dtype=int64)x_#使用数组做下标，获取排序后的元素array(1,2,3)x=np.array(3,1,2,4)x.argmax(),x.argmin()#最大值和最小值的下标(3,1)np.argsort(x)array(1,2,0,3,dtype=int64)x_array(1,2,3,4)x.sort()#原地排序 xarray(1,2,3,4)2110.1.1 数组生成与常用操作（7）数组的内积运算 a=np.array(5,6,7)b=np.array(6,6,6)a.dot(b)#向量内积108 np.dot(a,b)1

18、08 sum(a*b)1082210.1.1 数组生成与常用操作（8）数组元素访问 b=np.array(1,2,3,4,5,6,7,8,9)barray(1,2,3,4,5,6,7,8,9)b0#第0行array(1,2,3)b00#第0行第0列的元素值1 b0,2#第0行第2列的元素值3 b0,1#第0行和第1行array(1,2,3,4,5,6)b0,1,1,2#第0行第1列的元素和第1行第2列的元素#内部第一个列表表示行下标，第二个列表表示列下标array(2,6)2310.1.1 数组生成与常用操作（9）数组对函数运算的支持 x=np.arange(0,100,10,dtype=np

19、.floating)np.sin(x)#一维数组中所有元素求正弦值array(0.,-0.54402111,0.91294525,-0.98803162,0.74511316,-0.26237485,-0.30481062,0.77389068,-0.99388865,0.89399666)b=np.array(1,2,3,4,5,6,7,8,9)np.cos(b)#二维数组中所有元素求余弦值array(0.54030231,-0.41614684,-0.9899925,-0.65364362,0.28366219,0.96017029,0.75390225,-0.14550003,-0.91

20、113026)np.round(_)#四舍五入array(1.,-0.,-1.,-1.,0.,1.,1.,-0.,-1.)2410.1.1 数组生成与常用操作（10）改变数组大小 a=np.arange(1,11,1)aarray(1,2,3,4,5,6,7,8,9,10)a.shape=2,5#改为2行5列，原地修改 aarray(1,2,3,4,5,6,7,8,9,10)a.shape=5,-1#-1表示自动计算，原地修改 aarray(1,2,3,4,5,6,7,8,9,10)2510.1.1 数组生成与常用操作 b=a.reshape(2,5)#reshape()方法返回新数组 bar

21、ray(1,2,3,4,5,6,7,8,9,10)x=np.array(range(5)x.reshape(1,10)#reshape()不能修改数组元素个数Traceback(most recent call last):File,line 1,in x.reshape(1,10)ValueError:total size of new array must be unchanged x.resize(1,10)#resize()可以改变数组元素个数 xarray(0,1,2,3,4,0,0,0,0,0)2610.1.1 数组生成与常用操作（11）数组切片操作 a=np.arange(10)

22、aarray(0,1,2,3,4,5,6,7,8,9)a:-1#反向切片array(9,8,7,6,5,4,3,2,1,0)a:2#隔一个取一个元素array(0,2,4,6,8)a:5#前5个元素array(0,1,2,3,4)2710.1.1 数组生成与常用操作 c=np.arange(25)#创建数组 c.shape=5,5#修改数组大小 carray(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)c0,2:5#第0行中下标2,5)之间的元素值array(2,3,4)c1#第0行所有元素array(5,6

23、,7,8,9)2810.1.1 数组生成与常用操作 c2:5,2:5#行下标和列下标都介于2,5)之间的元素值array(12,13,14,17,18,19,22,23,24)c1,3,2,4#第1行第2列的元素和第3行第4列的元素array(7,19)c1,3,2:4#第1行和第3行的第2、3列array(7,8,17,18)c1,3#第1行和第3行所有元素array(5,6,7,8,9,15,16,17,18,19)c1,3:,2,4#第1、3行的2、4列元素array(7,9,17,19)2910.1.1 数组生成与常用操作（12）数组布尔运算 x=np.random.rand(10)#

24、包含10个随机数的数组 xarray(0.56707504,0.07527513,0.0149213,0.49157657,0.75404095,0.40330683,0.90158037,0.36465894,0.37620859,0.62250594)x 0.5#比较数组中每个元素值是否大于0.5array(True,False,False,False,True,False,True,False,False,True,dtype=bool)xx0.5#获取数组中大于0.5的元素array(0.56707504,0.75404095,0.90158037,0.62250594)x np.al

25、l(x np.any(1,2,3,4)#是否存在等价于True的元素True np.any(0)False a=np.array(1,2,3)b=np.array(3,2,1)a b#两个数组中对应位置上的元素比较array(False,False,True,dtype=bool)aab#数组a中大于b数组对应位置上元素的值array(3)a=barray(False,True,False,dtype=bool)aa=barray(2)3110.1.1 数组生成与常用操作 x=np.arange(1,10)xarray(1,2,3,4,5,6,7,8,9)x(x%2=0)&(x5)#布尔与运算

26、array(6,8)x(x%2=0)|(x5)#布尔或运算array(2,4,6,7,8,9)3210.1.1 数组生成与常用操作 import numpy as np data=np.array(1,2,3,2,3,3,3,4,5,1,2,3,4,5,6,1,2,3)data=1,2,3array(True,True,True,False,False,True,False,False,False,True,True,True,False,False,False,True,True,True)index=list(map(lambda row:all(row=1,2,3),data)datai

27、ndex#获取所有1,2,3的行array(1,2,3,1,2,3,1,2,3)3310.1.1 数组生成与常用操作（13）分段函数 x=np.random.randint(0,10,size=(1,10)xarray(0,4,3,3,8,4,7,3,1,7)np.where(x np.piecewise(x,x7,lambda x:x*2,lambda x:x*3)#小于4的元素乘以2#大于7的元素乘以3#其他元素变为0array(0,0,6,6,24,0,0,6,2,0)3410.1.1 数组生成与常用操作（14）计算唯一值与出现次数 x=np.random.randint(0,10,7)

28、xarray(8,7,7,5,3,8,0)np.bincount(x)#元素出现次数，0出现1次，#1、2没出现，3出现1次，以此类推array(1,0,0,1,0,1,0,2,2,dtype=int64)np.sum(_)#所有元素出现次数之和等于数组长度7 len(x)7 np.unique(x)#返回唯一元素值array(0,3,5,7,8)3510.1.2 矩阵生成与常用操作（1）生成矩阵 a_list=3,5,7 a_mat=np.matrix(a_list)#创建矩阵 a_matmatrix(3,5,7)c_mat=np.matrix(1,5,3,2,9,6)#创建矩阵 c_mat

29、matrix(1,5,3,2,9,6)3610.1.2 矩阵生成与常用操作（2）矩阵转置 a_mat.T#矩阵转置matrix(3,5,7)a_mat.shape#矩阵形状(1,3)a_mat.size#元素个数33710.1.2 矩阵生成与常用操作（3）计算矩阵特征 a_mat.mean()#元素平均值5.0 a_mat.sum()#所有元素之和15 a_mat.max()#最大值7 a_mat.max(axis=1)#横向最大值matrix(7)a_mat.max(axis=0)#纵向最大值matrix(3,5,7)3810.1.2 矩阵生成与常用操作（4）矩阵相乘 b_mat=np.ma

30、trix(1,2,3)#创建矩阵 b_matmatrix(1,2,3)a_mat*b_mat.T#矩阵相乘matrix(34)3910.1.2 矩阵生成与常用操作（5）矩阵元素排序 c_mat.argsort(axis=0)#纵向排序后的元素序号matrix(0,0,0,1,1,1,dtype=int64)c_mat.argsort(axis=1)#横向排序后的元素序号matrix(0,2,1,0,2,1,dtype=int64)4010.1.2 矩阵生成与常用操作（6）计算相关系数矩阵（对称矩阵，对角线上元素表示自相关系数）np.corrcoef(1,2,3,4,4,3,2,1)#负相关，变

31、化方向相反array(1.,-1.,-1.,1.)np.corrcoef(1,2,3,4,1,2,3,4)#正相关，变化方向一致array(1.,1.,1.,1.)np.corrcoef(1,2,3,4,1,2,3,40)#正相关，变化趋势接近array(1.,0.8010362,0.8010362,1.)4110.1.2 矩阵生成与常用操作（7）矩阵行列扩展 import numpy as np data=np.matrix(np.random.randint(1,10,5)for _ in range(6)newCols=np.matrix(np.random.randint(1,10,2

32、)for _ in range(6)newRows=np.matrix(np.random.randint(1,10,5)for _ in range(3)datamatrix(8,7,7,6,1,1,9,8,5,9,1,8,7,9,6,1,4,5,5,2,4,3,1,9,2,6,3,2,7,7)4210.1.2 矩阵生成与常用操作 newColsmatrix(7,1,6,3,9,1,2,7,8,8,9,1)newRowsmatrix(8,3,7,5,8,7,4,7,3,8,2,8,5,2,3)4310.1.2 矩阵生成与常用操作 np.c_data,newCols#在右侧增加列matrix(

33、8,7,7,6,1,7,1,1,9,8,5,9,6,3,1,8,7,9,6,9,1,1,4,5,5,2,2,7,4,3,1,9,2,8,8,6,3,2,7,7,9,1)np.c_newCols,data#在左侧增加列matrix(7,1,8,7,7,6,1,6,3,1,9,8,5,9,9,1,1,8,7,9,6,2,7,1,4,5,5,2,8,8,4,3,1,9,2,9,1,6,3,2,7,7)4410.1.2 矩阵生成与常用操作 np.r_data,newRows#在下面增加行matrix(8,7,7,6,1,1,9,8,5,9,1,8,7,9,6,1,4,5,5,2,4,3,1,9,2,6

34、,3,2,7,7,8,3,7,5,8,7,4,7,3,8,2,8,5,2,3)4510.1.2 矩阵生成与常用操作 np.r_newRows,data#在上面增加行matrix(8,3,7,5,8,7,4,7,3,8,2,8,5,2,3,8,7,7,6,1,1,9,8,5,9,1,8,7,9,6,1,4,5,5,2,4,3,1,9,2,6,3,2,7,7)4610.1.2 矩阵生成与常用操作 np.r_data,newRows,newRows#在下面增加行matrix(8,7,7,6,1,1,9,8,5,9,1,8,7,9,6,1,4,5,5,2,4,3,1,9,2,6,3,2,7,7,8,3

35、,7,5,8,7,4,7,3,8,2,8,5,2,3,8,3,7,5,8,7,4,7,3,8,2,8,5,2,3)4710.1.2 矩阵生成与常用操作 np.insert(data,0,newRows,axis=0)#在第0行增加行matrix(8,3,7,5,8,7,4,7,3,8,2,8,5,2,3,8,7,7,6,1,1,9,8,5,9,1,8,7,9,6,1,4,5,5,2,4,3,1,9,2,6,3,2,7,7)4810.1.2 矩阵生成与常用操作 np.insert(data,3,newRows,axis=0)#在第3行增加行matrix(8,7,7,6,1,1,9,8,5,9,1

36、,8,7,9,6,8,3,7,5,8,7,4,7,3,8,2,8,5,2,3,1,4,5,5,2,4,3,1,9,2,6,3,2,7,7)4910.1.2 矩阵生成与常用操作 np.insert(data,4,newCols.T,axis=1)#在第4列处增加列matrix(8,7,7,6,7,1,1,1,9,8,5,6,3,9,1,8,7,9,9,1,6,1,4,5,5,2,7,2,4,3,1,9,8,8,2,6,3,2,7,9,1,7)5010.1.2 矩阵生成与常用操作 np.row_stack(data,newRows)#扩展行matrix(8,7,7,6,1,1,9,8,5,9,1,

37、8,7,9,6,1,4,5,5,2,4,3,1,9,2,6,3,2,7,7,8,3,7,5,8,7,4,7,3,8,2,8,5,2,3)5110.1.2 矩阵生成与常用操作 np.column_stack(data,newCols)#扩展列matrix(8,7,7,6,1,7,1,1,9,8,5,9,6,3,1,8,7,9,6,9,1,1,4,5,5,2,2,7,4,3,1,9,2,8,8,6,3,2,7,7,9,1)5210.1.2 矩阵生成与常用操作（8）计算方差、协方差。np.cov(1,1,1,1,1)#协方差array(0.0)x=-2.1,-1,4.3 y=3,1.1,0.12 X

38、=np.vstack(x,y)print(np.cov(X)#协方差 11.71 -4.286 -4.286 2.14413333 print(np.cov(x,y)11.71 -4.286 -4.286 2.14413333 print(np.cov(x)11.7099999999999995310.1.3 计算特征值与特征向量 import numpy as np e,v=np.linalg.eig(1,1,2,2)#特征值与特征向量 earray(0.,3.)varray(-0.70710678,-0.4472136,0.70710678,-0.89442719)array=np.ara

39、nge(1,10).reshape(3,3)e,v=np.linalg.eig(array)earray(1.61168440e+01,-1.11684397e+00,-9.75918483e-16)varray(-0.23197069,-0.78583024,0.40824829,-0.52532209,-0.08675134,-0.81649658,-0.8186735,0.61232756,0.40824829)5410.1.4 计算逆矩阵 import numpy as np x=np.matrix(1,2,3,4)y=np.linalg.inv(x)#计算逆矩阵 x*y#验证matr

40、ix(1.00000000e+00,1.11022302e-16,0.00000000e+00,1.00000000e+00)y*xmatrix(1.00000000e+00,4.44089210e-16,0.00000000e+00,1.00000000e+00)5510.1.5 矩阵QR分解 import numpy as np a=np.matrix(1,2,3,4,5,6)q,r=np.linalg.qr(a)np.dot(q,r)#验证matrix(1.,2.,3.,4.,5.,6.)5610.1.6 计算行列式 import numpy as np a=1,2,3,4 np.lin

41、alg.det(a)-2.0000000000000004 a=np.array(1,2,3,4,1,2,2,1,1,3,3,1)np.linalg.det(a)array(-2.,-3.,-8.)5710.1.7 矩阵奇异值分解 import numpy as np a=np.arange(60).reshape(5,-1)aarray(0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,4

42、6,47,48,49,50,51,52,53,54,55,56,57,58,59)U,s,V=np.linalg.svd(a,full_matrices=False)5810.1.7 矩阵奇异值分解 np.dot(U,np.dot(np.diag(s),V)array(7.01764278e-15,1.00000000e+00,2.00000000e+00,3.00000000e+00,4.00000000e+00,5.00000000e+00,6.00000000e+00,7.00000000e+00,8.00000000e+00,9.00000000e+00,1.00000000e+01,

43、1.10000000e+01,1.20000000e+01,1.30000000e+01,1.40000000e+01,1.50000000e+01,1.60000000e+01,1.70000000e+01,1.80000000e+01,1.90000000e+01,2.00000000e+01,2.10000000e+01,2.20000000e+01,2.30000000e+01,2.40000000e+01,2.50000000e+01,2.60000000e+01,2.70000000e+01,2.80000000e+01,2.90000000e+01,3.00000000e+01,

44、3.10000000e+01,3.20000000e+01,3.30000000e+01,3.40000000e+01,3.50000000e+01,3.60000000e+01,3.70000000e+01,3.80000000e+01,3.90000000e+01,4.00000000e+01,4.10000000e+01,4.20000000e+01,4.30000000e+01,4.40000000e+01,4.50000000e+01,4.60000000e+01,4.70000000e+01,4.80000000e+01,4.90000000e+01,5.00000000e+01,

45、5.10000000e+01,5.20000000e+01,5.30000000e+01,5.40000000e+01,5.50000000e+01,5.60000000e+01,5.70000000e+01,5.80000000e+01,5.90000000e+01)np.allclose(a,np.dot(U,np.dot(np.diag(s),V)True5910.1.8 求解线性方程组ax=b的解 import numpy as np a=np.array(3,1,1,2)#系数矩阵 b=np.array(9,8)#系数矩阵 x=np.linalg.solve(a,b)#求解 xarr

46、ay(2.,3.)np.dot(a,x)array(9.,8.)np.linalg.lstsq(a,b)#最小二乘解#返回解、余项、a的秩、a的奇异值(array(2.,3.),array(,dtype=float64),2,array(3.61803399,1.38196601)6010.1.9 计算矩阵和向量的范数 import numpy as np x=np.matrix(1,2,3,-4)np.linalg.norm(x)#(1*2+2*2+3*2+(-4)*2)*0.55.4772255750516612 np.linalg.norm(x,-2)#smallest singular

47、 value1.9543950758485487 np.linalg.norm(x,-1)#min(sum(abs(x),axis=0)4.0 np.linalg.norm(x,1)#max(sum(abs(x),axis=0)6.0 np.linalg.norm(np.array(1,2,3,4),3)4.64158883361277846110.2 pandas数据处理基础 pandas是Python用于处理数据的扩展库，主要提供了3种数据结构：1）Series，带标签的一维数组；2）DataFrame，带标签且大小可变的二维表格结构；3）Panel，带标签且大小可变的三维数组。6210.

48、2.1 一维数组Series与常用索引数组生成与操作（1）生成一维数组 import numpy as np import pandas as pd x=pd.Series(1,3,5,np.nan)x0 1.01 3.02 5.03 NaNdtype:float646310.2.1 一维数组Series与常用索引数组生成与操作（2）生成日期时间索引数组 pd.date_range(start=20190101,end=20191231,freq=H)DatetimeIndex(2019-01-01 00:00:00,2019-01-01 01:00:00,2019-01-01 02:00:0

49、0,2019-01-01 03:00:00,2019-01-01 04:00:00,2019-01-01 05:00:00,2019-01-01 06:00:00,2019-01-01 07:00:00,2019-01-01 08:00:00,2019-01-01 09:00:00,.2019-12-30 15:00:00,2019-12-30 16:00:00,2019-12-30 17:00:00,2019-12-30 18:00:00,2019-12-30 19:00:00,2019-12-30 20:00:00,2019-12-30 21:00:00,2019-12-30 22:00:

50、00,2019-12-30 23:00:00,2019-12-31 00:00:00,dtype=datetime64ns,length=8737,freq=H)6410.2.1 一维数组Series与常用索引数组生成与操作 dates=pd.date_range(start=20190101,end=20191231,freq=D)#间隔为天 datesDatetimeIndex(2019-01-01,2019-01-02,2019-01-03,2019-01-04,2019-01-05,2019-01-06,2019-01-07,2019-01-08,2019-01-09,2019-01-