2017-09-15

利用Python进行数据分析

python基础: 数组和矢量计算

第四章: numpy基础

1 2	import numpy as np data=np.random.randn(4,4)

1	data.shape

(4, 4)

1	arr=np.array(data)

arr

array([[-2.92815868, -0.4693437 ,  0.92836325, -0.86445295],
       [-0.9575174 , -0.47274498, -1.98651175, -0.92836188],
       [-0.04815155,  0.11325496, -2.16331438,  0.12950206],
       [ 1.61292064, -1.14361762,  0.43682842, -1.26011755]])

data

array([[-2.92815868, -0.4693437 ,  0.92836325, -0.86445295],
       [-0.9575174 , -0.47274498, -1.98651175, -0.92836188],
       [-0.04815155,  0.11325496, -2.16331438,  0.12950206],
       [ 1.61292064, -1.14361762,  0.43682842, -1.26011755]])

1	print(arr)

[[-2.92815868 -0.4693437   0.92836325 -0.86445295]
 [-0.9575174  -0.47274498 -1.98651175 -0.92836188]
 [-0.04815155  0.11325496 -2.16331438  0.12950206]
 [ 1.61292064 -1.14361762  0.43682842 -1.26011755]]

1	np.zeros((10,2))

array([[ 0.,  0.],
       [ 0.,  0.],
       [ 0.,  0.],
       [ 0.,  0.],
       [ 0.,  0.],
       [ 0.,  0.],
       [ 0.,  0.],
       [ 0.,  0.],
       [ 0.,  0.],
       [ 0.,  0.]])

1	np.ones((2,4))

array([[ 1.,  1.,  1.,  1.],
       [ 1.,  1.,  1.,  1.]])

1	np.eye(10,10)

array([[ 1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
       [ 0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  1.,  0.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  1.,  0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  1.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.]])

1 2	ar1=np.array([[1,2,3],[4,5,6]]) ar1

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

ar2=ar1

注意矩阵操作和python的list的操作的不同

ar1*ar2

array([[ 1,  4,  9],
       [16, 25, 36]])

ar1-ar2

array([[0, 0, 0],
       [0, 0, 0]])

ar1+ar2

array([[ 2,  4,  6],
       [ 8, 10, 12]])

1	%timeit ar1+ar2

386 ns ± 1.56 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)

ar1/5

array([[ 0.2,  0.4,  0.6],
       [ 0.8,  1. ,  1.2]])

1/ar1

array([[ 1.        ,  0.5       ,  0.33333333],
       [ 0.25      ,  0.2       ,  0.16666667]])

1 2	b=np.arange(10) b

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

b-b

array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])

slice切片的使用，切片上的操作直接影响到源矩阵

1	bslice=b[4:6]

bslice

array([4, 5])

1	bslice[:]=100

array([  0,   1,   2,   3, 100, 100,   6,   7,   8,   9])

矩阵的布尔型索引

2.1 矩阵的比较运算也是矢量化的, 利用bool操作可以提供很多的方法去操作矩阵中的元素

1 2	names=np.array(["Jordan","Kobe","Magic","Lebron","Oneal","Ducan"]) names

array(['Jordan', 'Kobe', 'Magic', 'Lebron', 'Oneal', 'Ducan'],
      dtype='<U6')

1	names=="Kobe"

array([False,  True, False, False, False, False], dtype=bool)

1 2	arr3=np.random.randn(6,4) arr3

array([[-0.05387395,  0.63654347,  2.01167972, -0.85860418],
       [ 1.15355691, -0.52870696, -0.60051838, -2.14095282],
       [ 0.6170254 , -0.17970408,  0.5651644 , -0.32689396],
       [-0.9541369 , -0.83096901, -0.51250354,  0.76669871],
       [ 0.26518263, -0.02176463,  0.32238273,  2.26313526],
       [ 0.63746355, -0.96617442, -0.06673749, -1.4751273 ]])

1 2	arr3[names=="Kobe"]=24 arr3

array([[ -5.38739483e-02,   6.36543473e-01,   2.01167972e+00,
         -8.58604177e-01],
       [  2.40000000e+01,   2.40000000e+01,   2.40000000e+01,
          2.40000000e+01],
       [  6.17025403e-01,  -1.79704076e-01,   5.65164401e-01,
         -3.26893956e-01],
       [ -9.54136897e-01,  -8.30969009e-01,  -5.12503540e-01,
          7.66698707e-01],
       [  2.65182629e-01,  -2.17646337e-02,   3.22382726e-01,
          2.26313526e+00],
       [  6.37463550e-01,  -9.66174425e-01,  -6.67374854e-02,
         -1.47512730e+00]])

1	names!="Kobe"

array([ True, False,  True,  True,  True,  True], dtype=bool)

1 2	arr3[~(names=="Kobe")]=0 arr3

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

1 2	mask=(names=="Kobe")\|(names=="Jordan") mask

array([ True,  True, False, False, False, False], dtype=bool)

1	arr3[mask]

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

1 2	arr3[arr3==0]=23 arr3

array([[ 23.,  23.,  23.,  23.],
       [ 24.,  24.,  24.,  24.],
       [ 23.,  23.,  23.,  23.],
       [ 23.,  23.,  23.,  23.],
       [ 23.,  23.,  23.,  23.],
       [ 23.,  23.,  23.,  23.]])

1 2	arr3[names!="Kobe"]=1 arr3

array([[  1.,   1.,   1.,   1.],
       [ 24.,  24.,  24.,  24.],
       [  1.,   1.,   1.,   1.],
       [  1.,   1.,   1.,   1.],
       [  1.,   1.,   1.,   1.],
       [  1.,   1.,   1.,   1.]])

2.2 矩阵的花式索引(Fancy Indexing)

注意花式索引和切片不一样，它总是把数据复制到新的矩阵中

1 2	arr4=np.empty((8,4),dtype=np.int32) arr4

array([[  -44820527,  1071986160,   439455978,  1072162656],
       [ 2007969062,  1071146177, -2127231235,  1073869197],
       [ 1030511985,  1072188309,   319262802,  1072268317],
       [  -70212269,  1069666599,   882987624,  1069846423],
       [-1786127844,  1073164946,  -346589487,  1072269064],
       [  620329821,  1071448489,  1609482608,  1073348103],
       [ -412357061,  1068019309,  1058021927,  1070818026],
       [-1785317863,  1069873909,  -981128963,  1072298188]], dtype=int32)

1
2
3

for i in range(8):
    arr4[i][0:2]=i
arr4

array([[0, 0, 0, 0],
       [1, 1, 1, 1],
       [2, 2, 2, 2],
       [3, 3, 3, 3],
       [4, 4, 4, 4],
       [5, 5, 5, 5],
       [6, 6, 6, 6],
       [7, 7, 7, 7]], dtype=int32)

1	arr4[[5,3,2,7]]

array([[5, 5, 5, 5],
       [3, 3, 3, 3],
       [2, 2, 2, 2],
       [7, 7, 7, 7]], dtype=int32)

矩阵的转置和轴对换

arr4.T

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],
       [0, 1, 2, 3, 4, 5, 6, 7]], dtype=int32)

1	arr4.reshape((1,32)).T

array([[0],
       [0],
       [0],
       [0],
       [1],
       [1],
       [1],
       [1],
       [2],
       [2],
       [2],
       [2],
       [3],
       [3],
       [3],
       [3],
       [4],
       [4],
       [4],
       [4],
       [5],
       [5],
       [5],
       [5],
       [6],
       [6],
       [6],
       [6],
       [7],
       [7],
       [7],
       [7]], dtype=int32)

1	arr4.transpose((1,2))

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

AxisError                                 Traceback (most recent call last)

<ipython-input-120-a96838d4801a> in <module>()
----> 1 arr4.transpose((1,2))


AxisError: axis 2 is out of bounds for array of dimension 2

通用操作: 快速的元素级的函数

1	np.sqrt(arr4)

array([[ 0.        ,  0.        ,  0.        ,  0.        ],
       [ 1.        ,  1.        ,  1.        ,  1.        ],
       [ 1.41421356,  1.41421356,  1.41421356,  1.41421356],
       [ 1.73205081,  1.73205081,  1.73205081,  1.73205081],
       [ 2.        ,  2.        ,  2.        ,  2.        ],
       [ 2.23606798,  2.23606798,  2.23606798,  2.23606798],
       [ 2.44948974,  2.44948974,  2.44948974,  2.44948974],
       [ 2.64575131,  2.64575131,  2.64575131,  2.64575131]])

1	np.square(arr4)

array([[ 0,  0,  0,  0],
       [ 1,  1,  1,  1],
       [ 4,  4,  4,  4],
       [ 9,  9,  9,  9],
       [16, 16, 16, 16],
       [25, 25, 25, 25],
       [36, 36, 36, 36],
       [49, 49, 49, 49]], dtype=int32)

1 2	arr5=np.empty(arr4.shape,dtype=np.float32) arr5

array([[  3.86403988e+36,   4.58364728e-41,   3.86403988e+36,
          4.58364728e-41],
       [  4.84138582e+36,   4.58364728e-41,   8.40779079e-45,
          4.58364728e-41],
       [  5.17916907e+36,   1.26116862e-44,   5.75883764e+34,
          4.58364728e-41],
       [  1.68155816e-44,   4.58364728e-41,   5.85750672e+31,
          2.10194770e-44],
       [  4.77523712e+08,   4.58364728e-41,   2.52233724e-44,
          0.00000000e+00],
       [  0.00000000e+00,   2.94272678e-44,   0.00000000e+00,
          0.00000000e+00],
       [  3.36311631e-44,   4.58364728e-41,   0.00000000e+00,
          3.78350585e-44],
       [  0.00000000e+00,   0.00000000e+00,   4.20389539e-44,
          0.00000000e+00]], dtype=float32)

1	np.subtract(arr4,arr5)

array([[ -3.86403988e+36,  -4.58364728e-41,  -3.86403988e+36,
         -4.58364728e-41],
       [ -4.84138582e+36,   1.00000000e+00,   1.00000000e+00,
          1.00000000e+00],
       [ -5.17916907e+36,   2.00000000e+00,  -5.75883764e+34,
          2.00000000e+00],
       [  3.00000000e+00,   3.00000000e+00,  -5.85750672e+31,
          3.00000000e+00],
       [ -4.77523708e+08,   4.00000000e+00,   4.00000000e+00,
          4.00000000e+00],
       [  5.00000000e+00,   5.00000000e+00,   5.00000000e+00,
          5.00000000e+00],
       [  6.00000000e+00,   6.00000000e+00,   6.00000000e+00,
          6.00000000e+00],
       [  7.00000000e+00,   7.00000000e+00,   7.00000000e+00,
          7.00000000e+00]])

利用矩阵进行数据处理

1 2	points=np.arange(-5,5,0.01) points

array([ -5.00000000e+00,  -4.99000000e+00,  -4.98000000e+00,
        -4.97000000e+00,  -4.96000000e+00,  -4.95000000e+00,
        -4.94000000e+00,  -4.93000000e+00,  -4.92000000e+00,
        -4.91000000e+00,  -4.90000000e+00,  -4.89000000e+00,
        -4.88000000e+00,  -4.87000000e+00,  -4.86000000e+00,
        -4.85000000e+00,  -4.84000000e+00,  -4.83000000e+00,
        -4.82000000e+00,  -4.81000000e+00,  -4.80000000e+00,
        -4.79000000e+00,  -4.78000000e+00,  -4.77000000e+00,
        -4.76000000e+00,  -4.75000000e+00,  -4.74000000e+00,
        -4.73000000e+00,  -4.72000000e+00,  -4.71000000e+00,
        -4.70000000e+00,  -4.69000000e+00,  -4.68000000e+00,
        -4.67000000e+00,  -4.66000000e+00,  -4.65000000e+00,
        -4.64000000e+00,  -4.63000000e+00,  -4.62000000e+00,
        -4.61000000e+00,  -4.60000000e+00,  -4.59000000e+00,
        -4.58000000e+00,  -4.57000000e+00,  -4.56000000e+00,
        -4.55000000e+00,  -4.54000000e+00,  -4.53000000e+00,
        -4.52000000e+00,  -4.51000000e+00,  -4.50000000e+00,
        -4.49000000e+00,  -4.48000000e+00,  -4.47000000e+00,
        -4.46000000e+00,  -4.45000000e+00,  -4.44000000e+00,
        -4.43000000e+00,  -4.42000000e+00,  -4.41000000e+00,
        -4.40000000e+00,  -4.39000000e+00,  -4.38000000e+00,
        -4.37000000e+00,  -4.36000000e+00,  -4.35000000e+00,
        -4.34000000e+00,  -4.33000000e+00,  -4.32000000e+00,
        -4.31000000e+00,  -4.30000000e+00,  -4.29000000e+00,
        -4.28000000e+00,  -4.27000000e+00,  -4.26000000e+00,
        -4.25000000e+00,  -4.24000000e+00,  -4.23000000e+00,
        -4.22000000e+00,  -4.21000000e+00,  -4.20000000e+00,
        -4.19000000e+00,  -4.18000000e+00,  -4.17000000e+00,
        -4.16000000e+00,  -4.15000000e+00,  -4.14000000e+00,
        -4.13000000e+00,  -4.12000000e+00,  -4.11000000e+00,
        -4.10000000e+00,  -4.09000000e+00,  -4.08000000e+00,
        -4.07000000e+00,  -4.06000000e+00,  -4.05000000e+00,
        -4.04000000e+00,  -4.03000000e+00,  -4.02000000e+00,
        -4.01000000e+00,  -4.00000000e+00,  -3.99000000e+00,
        -3.98000000e+00,  -3.97000000e+00,  -3.96000000e+00,
        -3.95000000e+00,  -3.94000000e+00,  -3.93000000e+00,
        -3.92000000e+00,  -3.91000000e+00,  -3.90000000e+00,
        -3.89000000e+00,  -3.88000000e+00,  -3.87000000e+00,
        -3.86000000e+00,  -3.85000000e+00,  -3.84000000e+00,
        -3.83000000e+00,  -3.82000000e+00,  -3.81000000e+00,
        -3.80000000e+00,  -3.79000000e+00,  -3.78000000e+00,
        -3.77000000e+00,  -3.76000000e+00,  -3.75000000e+00,
        -3.74000000e+00,  -3.73000000e+00,  -3.72000000e+00,
        -3.71000000e+00,  -3.70000000e+00,  -3.69000000e+00,
        -3.68000000e+00,  -3.67000000e+00,  -3.66000000e+00,
        -3.65000000e+00,  -3.64000000e+00,  -3.63000000e+00,
        -3.62000000e+00,  -3.61000000e+00,  -3.60000000e+00,
        -3.59000000e+00,  -3.58000000e+00,  -3.57000000e+00,
        -3.56000000e+00,  -3.55000000e+00,  -3.54000000e+00,
        -3.53000000e+00,  -3.52000000e+00,  -3.51000000e+00,
        -3.50000000e+00,  -3.49000000e+00,  -3.48000000e+00,
        -3.47000000e+00,  -3.46000000e+00,  -3.45000000e+00,
        -3.44000000e+00,  -3.43000000e+00,  -3.42000000e+00,
        -3.41000000e+00,  -3.40000000e+00,  -3.39000000e+00,
        -3.38000000e+00,  -3.37000000e+00,  -3.36000000e+00,
        -3.35000000e+00,  -3.34000000e+00,  -3.33000000e+00,
        -3.32000000e+00,  -3.31000000e+00,  -3.30000000e+00,
        -3.29000000e+00,  -3.28000000e+00,  -3.27000000e+00,
        -3.26000000e+00,  -3.25000000e+00,  -3.24000000e+00,
        -3.23000000e+00,  -3.22000000e+00,  -3.21000000e+00,
        -3.20000000e+00,  -3.19000000e+00,  -3.18000000e+00,
        -3.17000000e+00,  -3.16000000e+00,  -3.15000000e+00,
        -3.14000000e+00,  -3.13000000e+00,  -3.12000000e+00,
        -3.11000000e+00,  -3.10000000e+00,  -3.09000000e+00,
        -3.08000000e+00,  -3.07000000e+00,  -3.06000000e+00,
        -3.05000000e+00,  -3.04000000e+00,  -3.03000000e+00,
        -3.02000000e+00,  -3.01000000e+00,  -3.00000000e+00,
        -2.99000000e+00,  -2.98000000e+00,  -2.97000000e+00,
        -2.96000000e+00,  -2.95000000e+00,  -2.94000000e+00,
        -2.93000000e+00,  -2.92000000e+00,  -2.91000000e+00,
        -2.90000000e+00,  -2.89000000e+00,  -2.88000000e+00,
        -2.87000000e+00,  -2.86000000e+00,  -2.85000000e+00,
        -2.84000000e+00,  -2.83000000e+00,  -2.82000000e+00,
        -2.81000000e+00,  -2.80000000e+00,  -2.79000000e+00,
        -2.78000000e+00,  -2.77000000e+00,  -2.76000000e+00,
        -2.75000000e+00,  -2.74000000e+00,  -2.73000000e+00,
        -2.72000000e+00,  -2.71000000e+00,  -2.70000000e+00,
        -2.69000000e+00,  -2.68000000e+00,  -2.67000000e+00,
        -2.66000000e+00,  -2.65000000e+00,  -2.64000000e+00,
        -2.63000000e+00,  -2.62000000e+00,  -2.61000000e+00,
        -2.60000000e+00,  -2.59000000e+00,  -2.58000000e+00,
        -2.57000000e+00,  -2.56000000e+00,  -2.55000000e+00,
        -2.54000000e+00,  -2.53000000e+00,  -2.52000000e+00,
        -2.51000000e+00,  -2.50000000e+00,  -2.49000000e+00,
        -2.48000000e+00,  -2.47000000e+00,  -2.46000000e+00,
        -2.45000000e+00,  -2.44000000e+00,  -2.43000000e+00,
        -2.42000000e+00,  -2.41000000e+00,  -2.40000000e+00,
        -2.39000000e+00,  -2.38000000e+00,  -2.37000000e+00,
        -2.36000000e+00,  -2.35000000e+00,  -2.34000000e+00,
        -2.33000000e+00,  -2.32000000e+00,  -2.31000000e+00,
        -2.30000000e+00,  -2.29000000e+00,  -2.28000000e+00,
        -2.27000000e+00,  -2.26000000e+00,  -2.25000000e+00,
        -2.24000000e+00,  -2.23000000e+00,  -2.22000000e+00,
        -2.21000000e+00,  -2.20000000e+00,  -2.19000000e+00,
        -2.18000000e+00,  -2.17000000e+00,  -2.16000000e+00,
        -2.15000000e+00,  -2.14000000e+00,  -2.13000000e+00,
        -2.12000000e+00,  -2.11000000e+00,  -2.10000000e+00,
        -2.09000000e+00,  -2.08000000e+00,  -2.07000000e+00,
        -2.06000000e+00,  -2.05000000e+00,  -2.04000000e+00,
        -2.03000000e+00,  -2.02000000e+00,  -2.01000000e+00,
        -2.00000000e+00,  -1.99000000e+00,  -1.98000000e+00,
        -1.97000000e+00,  -1.96000000e+00,  -1.95000000e+00,
        -1.94000000e+00,  -1.93000000e+00,  -1.92000000e+00,
        -1.91000000e+00,  -1.90000000e+00,  -1.89000000e+00,
        -1.88000000e+00,  -1.87000000e+00,  -1.86000000e+00,
        -1.85000000e+00,  -1.84000000e+00,  -1.83000000e+00,
        -1.82000000e+00,  -1.81000000e+00,  -1.80000000e+00,
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         4.45000000e+00,   4.46000000e+00,   4.47000000e+00,
         4.48000000e+00,   4.49000000e+00,   4.50000000e+00,
         4.51000000e+00,   4.52000000e+00,   4.53000000e+00,
         4.54000000e+00,   4.55000000e+00,   4.56000000e+00,
         4.57000000e+00,   4.58000000e+00,   4.59000000e+00,
         4.60000000e+00,   4.61000000e+00,   4.62000000e+00,
         4.63000000e+00,   4.64000000e+00,   4.65000000e+00,
         4.66000000e+00,   4.67000000e+00,   4.68000000e+00,
         4.69000000e+00,   4.70000000e+00,   4.71000000e+00,
         4.72000000e+00,   4.73000000e+00,   4.74000000e+00,
         4.75000000e+00,   4.76000000e+00,   4.77000000e+00,
         4.78000000e+00,   4.79000000e+00,   4.80000000e+00,
         4.81000000e+00,   4.82000000e+00,   4.83000000e+00,
         4.84000000e+00,   4.85000000e+00,   4.86000000e+00,
         4.87000000e+00,   4.88000000e+00,   4.89000000e+00,
         4.90000000e+00,   4.91000000e+00,   4.92000000e+00,
         4.93000000e+00,   4.94000000e+00,   4.95000000e+00,
         4.96000000e+00,   4.97000000e+00,   4.98000000e+00,
         4.99000000e+00])

1	xs,ys=np.meshgrid(points,points)

xs

array([[-5.  , -4.99, -4.98, ...,  4.97,  4.98,  4.99],
       [-5.  , -4.99, -4.98, ...,  4.97,  4.98,  4.99],
       [-5.  , -4.99, -4.98, ...,  4.97,  4.98,  4.99],
       ..., 
       [-5.  , -4.99, -4.98, ...,  4.97,  4.98,  4.99],
       [-5.  , -4.99, -4.98, ...,  4.97,  4.98,  4.99],
       [-5.  , -4.99, -4.98, ...,  4.97,  4.98,  4.99]])

ys

array([[-5.  , -5.  , -5.  , ..., -5.  , -5.  , -5.  ],
       [-4.99, -4.99, -4.99, ..., -4.99, -4.99, -4.99],
       [-4.98, -4.98, -4.98, ..., -4.98, -4.98, -4.98],
       ..., 
       [ 4.97,  4.97,  4.97, ...,  4.97,  4.97,  4.97],
       [ 4.98,  4.98,  4.98, ...,  4.98,  4.98,  4.98],
       [ 4.99,  4.99,  4.99, ...,  4.99,  4.99,  4.99]])

1
2
3

import matplotlib. pyplot as plt
%matplotlib inline
z = np.sqrt(xs**2+ys**2)

1
2
3

plt.imshow(z,cmap=plt.cm.gray)
plt.colorbar()
plt.title("Image plot of $\sqrt{x^2+y^2}$ for a grid of values")

<matplotlib.text.Text at 0x7fc6481e3390>

png