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                                                                              当前位置 > 首页 > 技术文档 > Numpy学习(2)

                                                                              Numpy学习(2)

                                                                              来源:CPDA数据分析师学习网 | 时间:2018-02-09 | 作者:数据分析学习网

                                                                              我们接着《Python数据分析之numpy学习(一)》继续讲解有关numpy方面的知识!

                                                                              统计函数与线性代数运算

                                                                              统计运算中常见的聚合函数有:最小值、最大值、中位数、均值、?#35762;睢?#26631;准差等。首先来看看数组元素级别的计算

                                                                              In [94]: arr11 = 5-np.arange(1,13).reshape(4,3)

                                                                              In [95]: arr12 = np.random.randint(1,10,size = 12).reshape(4,3)

                                                                              In [96]: arr11

                                                                              Out[96]:

                                                                              array([[ 4, ?3, ?2],

                                                                              [ 1, ?0, -1],

                                                                              [-2, -3, -4],

                                                                              [-5, -6, -7]])

                                                                              In [97]: arr12

                                                                              Out[97]:

                                                                              array([[1, 3, 7],

                                                                              [7, 3, 7],

                                                                              [3, 7, 4],

                                                                              [6, 1, 2]])

                                                                              In [98]: arr11 ** 2 ? ?#计算每个元素的平方

                                                                              Out[98]:

                                                                              array([[16, ?9, ?4],

                                                                              [ 1, ?0, ?1],

                                                                              [ 4, ?9, 16],

                                                                              [25, 36, 49]])

                                                                              In [99]: np.sqrt(arr11) ?#计算每个元素的平方根

                                                                              Out[99]:

                                                                              array([[ 2. ? ? ? ?, ?1.73205081, ?1.41421356],

                                                                              [ 1. ? ? ? ?, ?0. ? ? ? ?, ? ? ? ? nan],

                                                                              [ ? ? ? ?nan, ? ? ? ? nan, ? ? ? ? nan],

                                                                              [ ? ? ? ?nan, ? ? ? ? nan, ? ? ? ? nan]])

                                                                              由于负值的平方根没有意义,故返回nan

                                                                              In [100]: np.exp(arr11) ? #计算每个元素的指数值

                                                                              Out[100]:

                                                                              array([[ ?5.45981500e+01, ? 2.00855369e+01, ? 7.38905610e+00],

                                                                              [ ?2.71828183e+00, ? 1.00000000e+00, ? 3.67879441e-01],

                                                                              [ ?1.35335283e-01, ? 4.97870684e-02, ? 1.83156389e-02],

                                                                              [ ?6.73794700e-03, ? 2.47875218e-03, ? 9.11881966e-04]])

                                                                              In [101]: np.log(arr12) ? #计算每个元素的自然对数值

                                                                              Out[101]:

                                                                              array([[ 0. ? ? ? ?, ?1.09861229, ?1.94591015],

                                                                              [ 1.94591015, ?1.09861229, ?1.94591015],

                                                                              [ 1.09861229, ?1.94591015, ?1.38629436],

                                                                              [ 1.79175947, ?0. ? ? ? ?, ?0.69314718]])

                                                                              In [102]: np.abs(arr11) ? #计算每个元素的绝对值

                                                                              Out[102]:

                                                                              array([[4, 3, 2],

                                                                              [1, 0, 1],

                                                                              [2, 3, 4],

                                                                              [5, 6, 7]])

                                                                              相同形状数组间元素的操作:

                                                                              In [103]: arr11 + arr12 ? #加

                                                                              Out[103]:

                                                                              array([[ 5, ?6, ?9],

                                                                              [ 8, ?3, ?6],

                                                                              [ 1, ?4, ?0],

                                                                              [ 1, -5, -5]])

                                                                              In [104]: arr11 - arr12 ? #减

                                                                              Out[104]:

                                                                              array([[ ?3, ? 0, ?-5],

                                                                              [ -6, ?-3, ?-8],

                                                                              [ -5, -10, ?-8],

                                                                              [-11, ?-7, ?-9]])

                                                                              In [105]: arr11 * arr12 ? #乘

                                                                              Out[105]:

                                                                              array([[ ?4, ? 9, ?14],

                                                                              [ ?7, ? 0, ?-7],

                                                                              [ -6, -21, -16],

                                                                              [-30, ?-6, -14]])

                                                                              In [106]: arr11 / arr12 ? #除

                                                                              Out[106]:

                                                                              array([[ 4. ? ? ? ?, ?1. ? ? ? ?, ?0.28571429],

                                                                              [ 0.14285714, ?0. ? ? ? ?, -0.14285714],

                                                                              [-0.66666667, -0.42857143, -1. ? ? ? ?],

                                                                              [-0.83333333, -6. ? ? ? ?, -3.5 ? ? ? ]])

                                                                              In [107]: arr11 // arr12 ?#整除

                                                                              Out[107]:

                                                                              array([[ 4, ?1, ?0],

                                                                              [ 0, ?0, -1],

                                                                              [-1, -1, -1],

                                                                              [-1, -6, -4]], dtype=int32)

                                                                              In [108]: arr11 % arr12 ? #取余

                                                                              Out[108]:

                                                                              array([[0, 0, 2],

                                                                              [1, 0, 6],

                                                                              [1, 4, 0],

                                                                              [1, 0, 1]], dtype=int32)

                                                                              接下来我们看看统计运算函数:

                                                                              In [109]: np.sum(arr11) ? #计算所有元素的和

                                                                              Out[109]: -18

                                                                              In [110]: np.sum(arr11,axis = 0) ? ?#对每一列求和

                                                                              Out[110]: array([ -2, ?-6, -10])

                                                                              In [111]: np.sum(arr11, axis = 1) #对每一行求和

                                                                              Out[111]: array([ ?9, ? 0, ?-9, -18])

                                                                              In [112]: np.cumsum(arr11) #对每一个元素求累积和(从上到下,从左?#25509;业?#20803;素顺序)

                                                                              Out[112]: array([ ?4, ? 7, ? 9, ?10, ?10, ? 9, ? 7, ? 4, ? 0, ?-5, -11, -18], dtype=int32)

                                                                              In [113]: np.cumsum(arr11, axis = 0) #计算每一列的累积和,并返回二维数组

                                                                              Out[113]:

                                                                              array([[ ?4, ? 3, ? 2],

                                                                              [ ?5, ? 3, ? 1],

                                                                              [ ?3, ? 0, ?-3],

                                                                              [ -2, ?-6, -10]], dtype=int32)

                                                                              In [114]: np.cumprod(arr11, axis = 1) #计算每一行的累计积,并返回二维数组

                                                                              Out[114]:

                                                                              array([[ ? 4, ? 12, ? 24],

                                                                              [ ? 1, ? ?0, ? ?0],

                                                                              [ ?-2, ? ?6, ?-24],

                                                                              [ ?-5, ? 30, -210]], dtype=int32)

                                                                              In [115]: np.min(arr11) ? #计算所有元素的最小值

                                                                              Out[115]: -7

                                                                              In [116]: np.max(arr11, axis = 0) #计算每一列的最大值

                                                                              Out[116]: array([4, 3, 2])

                                                                              In [117]: np.mean(arr11) ?#计算所有元素的均值

                                                                              Out[117]: -1.5

                                                                              In [118]: np.mean(arr11, axis = 1) #计算每一行的均值

                                                                              Out[118]: array([ 3., ?0., -3., -6.])

                                                                              In [119]: np.median(arr11) ? #计算所有元素的中位数

                                                                              Out[119]: -1.5

                                                                              In [120]: np.median(arr11, axis = 0) ? #计算每一列的中位数

                                                                              Out[120]: array([-0.5, -1.5, -2.5])

                                                                              In [121]: np.var(arr12) ? #计算所有元素的?#35762;?/p>

                                                                              Out[121]: 5.354166666666667

                                                                              In [122]: np.std(arr12, axis = 1) ? #计算每一行的标准差

                                                                              Out[122]: array([ 2.49443826, ?1.88561808, ?1.69967317, ?2.1602469 ])

                                                                              numpy中的统计函数运算是非常灵活的,既可以计算所有元素的统计值,?#37096;?#20197;计算指定行或列的统计指标。还有其他常用的函数,如符号函数sign,ceil(>=x的最小整数),floor(<=x的最大整数),modf(将浮点数的整数部分与小数部分分别存入两个独立的数组),cos,arccos,sin,arcsin,tan,arctan等。

                                                                              让我很兴奋的一个函数是where(),它类似于Excel中的if函数,可以进行灵活的变换:

                                                                              In [123]: arr11

                                                                              Out[123]:

                                                                              array([[ 4, ?3, ?2],

                                                                              [ 1, ?0, -1],

                                                                              [-2, -3, -4],

                                                                              [-5, -6, -7]])

                                                                              In [124]: np.where(arr11 < 0, 'negtive','positive')

                                                                              Out[124]:

                                                                              array([['positive', 'positive', 'positive'],

                                                                              ['positive', 'positive', 'negtive'],

                                                                              ['negtive', 'negtive', 'negtive'],

                                                                              ['negtive', 'negtive', 'negtive']],

                                                                              dtype='<U8')

                                                                              当然,np.where还可以嵌?#36164;?#29992;,完成复杂的运算。

                                                                              其它函数

                                                                              unique(x):计算x的唯一元素,并返回?#34892;?#32467;果

                                                                              intersect(x,y):计算x和y的公共元素,即交集

                                                                              union1d(x,y):计算x和y的并集

                                                                              setdiff1d(x,y):计算x和y的差集,即元素在x中,不在y中

                                                                              setxor1d(x,y):计算集合的对称差,?#21019;?#22312;于一个数组中,但不同时存在于两个数组中

                                                                              in1d(x,y):判断x的元素是否包含于y中

                                                                              线性代数运算

                                                                              同样numpu也跟R语言一样,可以非常方便的进行线性代数方面的计算,如行列式、逆、迹、特征根、特征向量等。但需要注意的是,有关线性代数的函数并不在numpy中,而是numpy的子例linalg中。

                                                                              In [125]: arr13 = np.array([[1,2,3,5],[2,4,1,6],[1,1,4,3],[2,5,4,1]])

                                                                              In [126]: arr13

                                                                              Out[126]:

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

                                                                              [2, 4, 1, 6],

                                                                              [1, 1, 4, 3],

                                                                              [2, 5, 4, 1]])

                                                                              In [127]: np.linalg.det(arr13) ? ?#返回方阵的行列式

                                                                              Out[127]: 51.000000000000021

                                                                              In [128]: np.linalg.inv(arr13) ? ?#返回方阵的逆

                                                                              Out[128]:

                                                                              array([[-2.23529412, ?1.05882353, ?1.70588235, -0.29411765],

                                                                              [ 0.68627451, -0.25490196, -0.7254902 , ?0.2745098 ],

                                                                              [ 0.19607843, -0.21568627, ?0.07843137, ?0.07843137],

                                                                              [ 0.25490196, ?0.01960784, -0.09803922, -0.09803922]])

                                                                              In [129]: np.trace(arr13) #返回方阵的迹(对角线元素之和),注意迹的求解不在linalg子例程中

                                                                              Out[129]: 10

                                                                              In [130]: np.linalg.eig(arr13) ? ?#返回?#21830;?#24449;根和特征向量组成的元组

                                                                              Out[130]:

                                                                              (array([ 11.35035004, ?-3.99231852, ?-0.3732631 , ? 3.01523159]),

                                                                              array([[-0.4754174 , -0.48095078, -0.95004728, ?0.19967185],

                                                                              [-0.60676806, -0.42159999, ?0.28426325, -0.67482638],

                                                                              [-0.36135292, -0.16859677, ?0.08708826, ?0.70663129],

                                                                              [-0.52462832, ?0.75000995, ?0.09497472, -0.07357122]]))

                                                                              In [131]: np.linalg.qr(arr13) #返回方阵的QR分解

                                                                              Out[131]:

                                                                              (array([[-0.31622777, -0.07254763, -0.35574573, -0.87645982],

                                                                              [-0.63245553, -0.14509525, ?0.75789308, -0.06741999],

                                                                              [-0.31622777, -0.79802388, -0.38668014, ?0.33709993],

                                                                              [-0.63245553, ?0.580381 ?, -0.38668014, ?0.33709993]]),

                                                                              array([[-3.16227766, -6.64078309, -5.37587202, -6.95701085],

                                                                              [ 0. ? ? ? ?, ?1.37840488, -1.23330963, -3.04700025],

                                                                              [ 0. ? ? ? ?, ?0. ? ? ? ?, -3.40278524, ?1.22190924],

                                                                              [ 0. ? ? ? ?, ?0. ? ? ? ?, ?0. ? ? ? ?, -3.4384193 ]]))

                                                                              In [132]:np.linalg.svd(arr13) ? ?#返回方阵的奇异值分解

                                                                              Out[132]:

                                                                              (array([[-0.50908395, ?0.27580803, ?0.35260559, -0.73514132],

                                                                              [-0.59475561, ?0.4936665 , -0.53555663, ?0.34020325],

                                                                              [-0.39377551, -0.10084917, ?0.70979004, ?0.57529852],

                                                                              [-0.48170545, -0.81856751, -0.29162732, -0.11340459]]),

                                                                              array([ 11.82715609, ? 4.35052602, ? 3.17710166, ? 0.31197297]),

                                                                              array([[-0.25836994, -0.52417446, -0.47551003, -0.65755329],

                                                                              [-0.10914615, -0.38326507, -0.54167613, ?0.74012294],

                                                                              [-0.18632462, -0.68784764, ?0.69085326, ?0.12194478],

                                                                              [ 0.94160248, -0.32436807, -0.05655931, -0.07050652]]))

                                                                              In [133]: np.dot(arr13,arr13) ? ? #方阵的正真乘积运算

                                                                              Out[133]:

                                                                              array([[18, 38, 37, 31],

                                                                              [23, 51, 38, 43],

                                                                              [13, 25, 32, 26],

                                                                              [18, 33, 31, 53]])

                                                                              In [134]:arr14 = np.array([[1,-2,1],[0,2,-8],[-4,5,9]])

                                                                              In [135]: vector = np.array([0,8,-9])

                                                                              In [136]: np.linalg.solve(arr14,vector)

                                                                              Out[136]: array([ 29., ?16., ? 3.])

                                                                              随机数生成

                                                                              统计学中经常会讲到数据的分?#32487;?#24449;,如正态分布、指数分布、卡方分布、二项分布、泊松分布等,下面就讲讲有关分布的随机数生成。

                                                                              正态分布直方图

                                                                              In [137]: import matplotlib #用于绘图的模块

                                                                              In [138]: np.random.seed(1234) ? ?#设置随机种子

                                                                              In [139]: N = 10000 ? #随机产生的样本量

                                                                              In [140]: randnorm = np.random.normal(size = N) ? #生成正态随机数

                                                                              In [141]: counts, bins, path = matplotlib.pylab.hist(randnorm, bins = np.sqrt(N), normed = True, color = 'blue') ?#绘制直方图

                                                                              以上将直方图的频数和组距存放在counts和bins内。

                                                                              In [142]: sigma = 1; mu = 0

                                                                              In [143]: norm_dist = (1/np.sqrt(2*sigma*np.pi))*np.exp(-((bins-mu)**2)/2) ? ?#正态分?#27982;?#24230;函数

                                                                              In [144]: matplotlib.pylab.plot(bins,norm_dist,color = 'red') #绘制正态分?#27982;?#24230;函数图

                                                                              1

                                                                              使用二项分布进行赌博

                                                                              同时抛弃9枚硬币,如果正面朝上少于5枚,则输掉8元,否则就赢8元。如果手中有1000元作为赌资,请?#35782;?#21338;10000次后可能会是什么情况呢?

                                                                              In [146]: np.random.seed(1234)

                                                                              In [147]: binomial = np.random.binomial(9,0.5,10000) ?#生成二项分布随机数

                                                                              In [148]: money = np.zeros(10000) #生成10000次赌资的列表

                                                                              In [149]: money[0] = 1000 #?#29366;?#36172;资为1000元

                                                                              In [150]: for i in range(1,10000):

                                                                              ...: ? ? if binomial[i] < 5:

                                                                              ...: ? ? ? ? money[i] = money[i-1] - 8

                                                                              #如果少于5枚正面,则在上一次赌资的基础上输掉8元

                                                                              ...: ? ? else:

                                                                              ...: ? ? ? ? money[i] = money[i-1] + 8

                                                                              #如果至少5枚正面,则在上一次赌资的基础上赢取8元

                                                                              In [151]: matplotlib.pylab.plot(np.arange(10000), money)

                                                                              2

                                                                              使用随机整数实现随机游走

                                                                              一个醉汉在原始位置上行走10000步后将会在什么地方呢?如果他每走一步是随机的,即下一步可能是1?#37096;?#33021;是-1。

                                                                              In [152]: np.random.seed(1234) ? ?#设定随机种子

                                                                              In [153]: position = 0 ? ?#设置初始位置

                                                                              In [154]: walk = [] ? #创建空列表

                                                                              In [155]: steps = 10000 ? #假设接下来行走10000步

                                                                              In [156]: for i in np.arange(steps):

                                                                              ...: ? ? step = 1 if np.random.randint(0,2) else -1 ?#每一步都是随机的

                                                                              ...: ? ? position = position + step ?#对每一步进行累计求和

                                                                              ...: ? ? walk.append(position) ? #确定每一步所在的位置

                                                                              In [157]: matplotlib.pylab.plot(np.arange(10000), walk) ? #绘制随机游走图

                                                                              1

                                                                              上面的代码还可以写成(结合前面所讲的where函数,cumsum函数):

                                                                              In [158]: np.random.seed(1234)

                                                                              In [159]: step = np.where(np.random.randint(0,2,10000)>0,1,-1)

                                                                              In [160]: position = np.cumsum(step)

                                                                              In [161]: matplotlib.pylab.plot(np.arange(10000), position)

                                                                              1
                                                                              避免for循环,可?#28304;?#21040;同样的效果。

                                                                              使用Python进行数据分析,一般都会使用到numpy,pandas,scipy和matplotlib等模块,而numpy是最为基础的模块,其他模块的使用都是以numpy为核?#27169;?#25152;以这里讲解了有关numpy的方方面面,这部分的学习非常重要,希望?#34892;?#36259;的朋友多看看这方面的文档和动手操作。在接下来Python一期中将会讲到pandas模块的学习。

                                                                               

                                                                              作者:刘顺祥

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                                                                                                                                                          快3赚钱方法如下

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