numpy基礎知識(二)

數組轉置和軸對換

In [4]: arr = np.random.randn(3,2)

In [5]: arr.T
Out[5]: 
array([[-1.61958612,  0.51404498,  1.27702971],
       [-1.49568441, -0.62306175,  0.27173435]])

In [6]: np.dot(arr.T,arr)
Out[6]: 
array([[4.5181063 , 2.44912079],
       [2.44912079, 2.69911737]])

In [7]: arr = np.arange(16).reshape((2,2,4))

In [8]: arr
Out[8]: 
array([[[ 0,  1,  2,  3],
        [ 4,  5,  6,  7]],

       [[ 8,  9, 10, 11],
        [12, 13, 14, 15]]])

In [9]: arr.transpose((1,0,2))
Out[9]: 
array([[[ 0,  1,  2,  3],
        [ 8,  9, 10, 11]],

       [[ 4,  5,  6,  7],
        [12, 13, 14, 15]]])

transpose須要獲得有一個有軸編號組成的元組才能對這些軸進行轉置

In [10]: arr.swapaxes(1,2)
Out[10]: 
array([[[ 0,  4],
        [ 1,  5],
        [ 2,  6],
        [ 3,  7]],

       [[ 8, 12],
        [ 9, 13],
        [10, 14],
        [11, 15]]])

通用函數

In [11]: arr = np.arange(10)

In [12]: arr
Out[12]: array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

In [13]: np.sqrt(arr)
Out[13]: 
array([0.        , 1.        , 1.41421356, 1.73205081, 2.        ,
       2.23606798, 2.44948974, 2.64575131, 2.82842712, 3.        ])

In [14]: np.exp(arr)
Out[14]: 
array([1.00000000e+00, 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])

還有許多函數，你們能夠去官網查看

利用數組進行數據處理

In [16]: point
Out[16]: array([1, 2, 3, 4])

In [17]: xs,ys = np.meshgrid(point,point)

In [18]: xs
Out[18]: 
array([[1, 2, 3, 4],
       [1, 2, 3, 4],
       [1, 2, 3, 4],
       [1, 2, 3, 4]])

In [19]: ys
Out[19]: 
array([[1, 1, 1, 1],
       [2, 2, 2, 2],
       [3, 3, 3, 3],
       [4, 4, 4, 4]])
In [20]: z = np.sqrt(xs**2+ys**2)

In [21]: z
Out[21]: 
array([[1.41421356, 2.23606798, 3.16227766, 4.12310563],
       [2.23606798, 2.82842712, 3.60555128, 4.47213595],
       [3.16227766, 3.60555128, 4.24264069, 5.        ],
       [4.12310563, 4.47213595, 5.        , 5.65685425]])

條件邏輯表述數組計算

In [23]: xarr = np.array([1.1,1.2,1.3,1.4,1.5])

In [24]: yarr = np.array([2.1,2.2,2.3,2.4,2.5])

In [25]: cond = np.array([True,False,True,True,False])

In [26]: result = [(x if c else y) for x,y,c in zip (xarr,yarr,cond)]

In [27]: result
Out[27]: [1.1, 2.2, 1.3, 1.4, 2.5]
In [28]: result = np.where(cond,xarr,yarr)

In [29]: result
Out[29]: array([1.1, 2.2, 1.3, 1.4, 2.5])

numpy.where 能夠用 x if condition esle y,這種方式處理的速度不是很快；沒法用於多維數組。np.where比較簡潔;np.where的條件是與，或，非邏輯計算

數學和統計方法

In [1]: arr = np.random.randn(5,4)

In [2]: arr
Out[2]: 
array([[-0.96566616, -0.69396553, -1.44922124,  1.25770641],
       [-0.60834685, -0.1550649 ,  0.12900002, -0.51405016],
       [ 0.69804581, -0.5674765 , -0.49269238, -1.09732552],
       [ 2.3316344 ,  0.31030837,  0.06029882,  0.44382971],
       [ 0.29524057, -1.13612158,  0.91402251,  2.34230133]])
In [4]: arr.mean()
Out[4]: 0.055122857216706934

In [5]: np.mean(arr)
Out[5]: 0.055122857216706934

In [6]: arr.mean(axis=1)
Out[6]: array([-0.46278663, -0.28711547, -0.36486215,  0.78651783,  0.60386071])

In [7]: arr.sum(0)
Out[7]: array([ 1.75090777, -2.24232013, -0.83859227,  2.43246177])

mean和sum這類函數能夠接受喲個axix參數，最終能夠獲得一個少一維的數組

In [9]: arr = np.array([[0,1,2],[3,4,5],[6,7,8]])

In [10]: arr
Out[10]: 
array([[0, 1, 2],
       [3, 4, 5],
       [6, 7, 8]])

In [11]: arr.cumsum()
Out[11]: array([ 0,  1,  3,  6, 10, 15, 21, 28, 36])

In [12]: arr.cumsum(0)
Out[12]: 
array([[ 0,  1,  2],
       [ 3,  5,  7],
       [ 9, 12, 15]])

cumsum計算全部元素的累計和，不加參數生成一維數組的累計值，0表明向下累計

In [13]: arr.cumprod(1)
Out[13]: 
array([[  0,   0,   0],
       [  3,  12,  60],
       [  6,  42, 336]])

In [14]: arr.cumprod(0)
Out[14]: 
array([[ 0,  1,  2],
       [ 0,  4, 10],
       [ 0, 28, 80]])

cumprod是計算全部元素的累計積 ##用於布爾類型數組的方法

In [21]: arr = np.random.randn(100)

In [22]: (arr>0).sum()
Out[22]: 52

In [23]: bools = np.array([False,False,True,False])
In [25]: bools.any()
Out[25]: True

In [26]: bools.all()
Out[26]: False

any只要有一個符合就返回ture，all必須都符合才返回true

數組排序

In [28]: arr = np.random.randn(8)

In [29]: arr
Out[29]: 
array([-1.08477468, -1.05278807, -2.27882676,  0.08437624,  0.50895675,
        0.50632641,  0.80177614, -0.56485938])

In [30]: arr.sort()

In [31]: arr
Out[31]: 
array([-2.27882676, -1.08477468, -1.05278807, -0.56485938,  0.08437624,
        0.50632641,  0.50895675,  0.80177614])
In [32]: arr = np.random.randn(5,3)

In [33]: arr
Out[33]: 
array([[-0.52836361, -0.82969488,  0.89826385],
       [-0.13202188, -0.38917723, -0.551128  ],
       [ 0.35644031,  0.82714182,  0.45963875],
       [-1.17120769, -0.42217203,  0.14108125],
       [ 0.95581486, -0.77846096,  1.74493614]])

In [34]: arr.sort()

In [35]: arr
Out[35]: 
array([[-0.82969488, -0.52836361,  0.89826385],
       [-0.551128  , -0.38917723, -0.13202188],
       [ 0.35644031,  0.45963875,  0.82714182],
       [-1.17120769, -0.42217203,  0.14108125],
       [-0.77846096,  0.95581486,  1.74493614]])

In [36]: arr.sort(1)

In [37]: arr
Out[37]: 
array([[-0.82969488, -0.52836361,  0.89826385],
       [-0.551128  , -0.38917723, -0.13202188],
       [ 0.35644031,  0.45963875,  0.82714182],
       [-1.17120769, -0.42217203,  0.14108125],
       [-0.77846096,  0.95581486,  1.74493614]])

多維數組能夠在任何一個軸上排序

In [41]: large_arr = np.random.randn(5)

In [42]: large_arr
Out[42]: array([-1.69314145, -0.73522386, -1.42118609,  0.30122406,  0.5861573 ])

In [43]: large_arr.sort()

In [44]: large_arr[int(0.05*len(large_arr))]
Out[44]: -1.693141452075213

利用排序求分位數

數組集合的去重

In [45]: names = np.array(['Bob','Joe','Will','Bob','Will','Joe','Joe']
    ...: )

In [46]: names
Out[46]: array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe'], dtype='|S4')

In [47]: np.unique(names)
Out[47]: array(['Bob', 'Joe', 'Will'], dtype='|S4')

In [48]: values = np.array([6,0,0,3,2,5,6])

In [49]: np.in1d(values,[2,3,6])
Out[49]: array([ True, False, False,  True,  True, False,  True])

測試一個數組是否在在另外一個數組裏，並返回一個布爾數組,數組集合還有差集並集等

將數組已二進制形式保存到內存

In [50]: arr = np.arange(10)

In [51]: np.save('test',arr)

In [52]: np.load('test')
In [53]: np.load('test.npy')
Out[53]: array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

保存文件的時候會自動加載文件擴展名

In [54]: np.savez('two',a=arr,b=arr)

In [56]: arch = np.load('two.npz')

In [57]: arch['a']
Out[57]: array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

In [58]: arch['b']
Out[58]: array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

能夠把多個數組保存成壓縮文件，壓縮文件的擴展名是npz,加載時會獲得相似字典的對象

In [1]: np.loadtxt('test.txt',delimiter=',')
Out[1]: 
array([[ 1.,  2.,  3.,  4.],
       [ 5.,  6.,  7.,  8.],
       [ 9., 19., 19., 19.]])

In [2]: arr = np.loadtxt('test.txt',delimiter=',')

In [3]: arr
Out[3]: 
array([[ 1.,  2.,  3.,  4.],
       [ 5.,  6.,  7.,  8.],
       [ 9., 19., 19., 19.]])

numpy也能夠加載文本文件，也能夠保存文本文件，np.savetxt()

線性代數

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

In [2]: x
Out[2]: 
array([[1, 2, 3],
       [4, 5, 6]])

In [3]: y = np.array([[6,23],[-1,7],[8,9]])

In [4]: y
Out[4]: 
array([[ 6, 23],
       [-1,  7],
       [ 8,  9]])

In [5]: x.dot(y)
Out[5]: 
array([[ 28,  64],
       [ 67, 181]])

矩陣的乘法 x.dot(y),前面已經講過

In [6]: np.ones(3)
Out[6]: array([1., 1., 1.])

In [7]: np.dot(x,np.ones(3))
Out[7]: array([ 6., 15.])

一個二維數組跟一個一維數組的矩陣點積運算以後獲得一個一維數組

In [1]: arr = np.array([[3,-1,4],[1,0,0],[2,1,-5]])

In [2]: arr
Out[2]: 
array([[ 3, -1,  4],
       [ 1,  0,  0],
       [ 2,  1, -5]])
In [3]: arr.T.dot(arr)
Out[3]: 
array([[14, -1,  2],
       [-1,  2, -9],
       [ 2, -9, 41]])

In [4]: mat = arr.T.dot(arr)

In [5]: mat
Out[5]: 
array([[14, -1,  2],
       [-1,  2, -9],
       [ 2, -9, 41]])
In [8]: inv(mat)
Out[8]: 
array([[  1.,  23.,   5.],
       [ 23., 570., 124.],
       [  5., 124.,  27.]])

In [9]: q,r = qr(mat)

In [10]: r
Out[10]: 
array([[-1.41774469e+01,  2.39817509e+00, -8.39361283e+00],
       [ 0.00000000e+00, -8.95816701e+00,  4.11770227e+01],
       [ 0.00000000e+00,  0.00000000e+00,  7.87377166e-03]])

inv計算方陣的逆；qr計算qr分解