Jupyter中python3之numpy练习

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Numpy_pratice

In [2]:
n = 10
L = [i for i in range(n)]
In [3]:

L * 2
Out[3]:
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
In [4]:

import numpy as np
X = np.arange(1,16).reshape(3,5)
X
Out[4]:
array([[ 1,  2,  3,  4,  5],
       [ 6,  7,  8,  9, 10],
       [11, 12, 13, 14, 15]])
In [5]:

X+1
Out[5]:
array([[ 2,  3,  4,  5,  6],
       [ 7,  8,  9, 10, 11],
       [12, 13, 14, 15, 16]])
In [6]:

X//2
Out[6]:
array([[0, 1, 1, 2, 2],
       [3, 3, 4, 4, 5],
       [5, 6, 6, 7, 7]])
In [7]:

X%2
Out[7]:
array([[1, 0, 1, 0, 1],
       [0, 1, 0, 1, 0],
       [1, 0, 1, 0, 1]])
In [8]:

1/X
Out[8]:
array([[1.        , 0.5       , 0.33333333, 0.25      , 0.2       ],
       [0.16666667, 0.14285714, 0.125     , 0.11111111, 0.1       ],
       [0.09090909, 0.08333333, 0.07692308, 0.07142857, 0.06666667]])
In [9]:

np.abs(X)
Out[9]:
array([[ 1,  2,  3,  4,  5],
       [ 6,  7,  8,  9, 10],
       [11, 12, 13, 14, 15]])
In [10]:

np.sin(X)
Out[10]:
array([[ 0.84147098,  0.90929743,  0.14112001, -0.7568025 , -0.95892427],
       [-0.2794155 ,  0.6569866 ,  0.98935825,  0.41211849, -0.54402111],
       [-0.99999021, -0.53657292,  0.42016704,  0.99060736,  0.65028784]])
In [11]:

np.log2(X)
Out[11]:
array([[0.        , 1.        , 1.5849625 , 2.        , 2.32192809],
       [2.5849625 , 2.80735492, 3.        , 3.169925  , 3.32192809],
       [3.45943162, 3.5849625 , 3.70043972, 3.80735492, 3.9068906 ]])
In [12]:

np.exp(X)
Out[12]:
array([[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,
        2.20264658e+04],
       [5.98741417e+04, 1.62754791e+05, 4.42413392e+05, 1.20260428e+06,
        3.26901737e+06]])
In [13]:

np.exp2(X) # 指定幂，结果同下述power(2,x)
Out[13]:
array([[2.0000e+00, 4.0000e+00, 8.0000e+00, 1.6000e+01, 3.2000e+01],
       [6.4000e+01, 1.2800e+02, 2.5600e+02, 5.1200e+02, 1.0240e+03],
       [2.0480e+03, 4.0960e+03, 8.1920e+03, 1.6384e+04, 3.2768e+04]])
In [14]:

np.power(2,X)
Out[14]:
array([[    2,     4,     8,    16,    32],
       [   64,   128,   256,   512,  1024],
       [ 2048,  4096,  8192, 16384, 32768]])
In [15]:

2**X
Out[15]:
array([[    2,     4,     8,    16,    32],
       [   64,   128,   256,   512,  1024],
       [ 2048,  4096,  8192, 16384, 32768]])
In [16]:

np.log2(X)
Out[16]:
array([[0.        , 1.        , 1.5849625 , 2.        , 2.32192809],
       [2.5849625 , 2.80735492, 3.        , 3.169925  , 3.32192809],
       [3.45943162, 3.5849625 , 3.70043972, 3.80735492, 3.9068906 ]])
In [17]:

np.log10(X)
Out[17]:
array([[0.        , 0.30103   , 0.47712125, 0.60205999, 0.69897   ],
       [0.77815125, 0.84509804, 0.90308999, 0.95424251, 1.        ],
       [1.04139269, 1.07918125, 1.11394335, 1.14612804, 1.17609126]])
矩阵运算
In [18]:

Ａ = np.arange(4).reshape(2,2)
A
Out[18]:
array([[0, 1],
       [2, 3]])
In [19]:

B = np.full((2,2),10)
B
Out[19]:
array([[10, 10],
       [10, 10]])
In [20]:

A+B
Out[20]:
array([[10, 11],
       [12, 13]])
In [21]:

A*B
Out[21]:
array([[ 0, 10],
       [20, 30]])
In [22]:

A.dot(B)
Out[22]:
array([[10, 10],
       [50, 50]])
In [23]:

A.T
Out[23]:
array([[0, 2],
       [1, 3]])
向量和矩阵运算
In [24]:

V = np.array([1,2])
V
Out[24]:
array([1, 2])
In [25]:

V+A
Out[25]:
array([[1, 3],
       [3, 5]])
In [26]:

np.vstack([V]*A.shape[0])
Out[26]:
array([[1, 2],
       [1, 2]])
In [27]:

np.vstack([V]*A.shape[0]) + A
Out[27]:
array([[1, 3],
       [3, 5]])
In [28]:

np.tile(V,(2,1)) # 堆叠，行叠成２次，列叠成１次
Out[28]:
array([[1, 2],
       [1, 2]])
In [29]:

np.tile(V,A.shape)
Out[29]:
array([[1, 2, 1, 2],
       [1, 2, 1, 2]])
In [30]:

np.tile(V,(2,1)) + A
Out[30]:
array([[1, 3],
       [3, 5]])
In [31]:

V.dot(A)
Out[31]:
array([4, 7])
In [32]:

A.dot(V)
Out[32]:
array([2, 8])
矩阵的逆
In [33]:

A
Out[33]:
array([[0, 1],
       [2, 3]])
In [34]:

np.linalg.inv(A)
Out[34]:
array([[-1.5,  0.5],
       [ 1. ,  0. ]])
In [35]:

invA = np.linalg.inv(A)
In [36]:

A.dot(invA)
Out[36]:
array([[1., 0.],
       [0., 1.]])
In [37]:

invA.dot(A)
Out[37]:
array([[1., 0.],
       [0., 1.]])
In [38]:

X
Out[38]:
array([[ 1,  2,  3,  4,  5],
       [ 6,  7,  8,  9, 10],
       [11, 12, 13, 14, 15]])
In [39]:

invX = np.linalg.inv(X)
invX
---------------------------------------------------------------------------
LinAlgError                               Traceback (most recent call last)
<ipython-input-39-870393757875> in <module>
----> 1 invX = np.linalg.inv(X)
      2 invX

~/anaconda3/lib/python3.7/site-packages/numpy/linalg/linalg.py in inv(a)
    525     a, wrap = _makearray(a)
    526     _assertRankAtLeast2(a)
--> 527     _assertNdSquareness(a)
    528     t, result_t = _commonType(a)
    529 

~/anaconda3/lib/python3.7/site-packages/numpy/linalg/linalg.py in _assertNdSquareness(*arrays)
    213         m, n = a.shape[-2:]
    214         if m != n:
--> 215             raise LinAlgError('Last 2 dimensions of the array must be square')
    216
    217 def _assertFinite(*arrays):

LinAlgError: Last 2 dimensions of the array must be square

矩阵的伪逆
In [40]:

invpX = np.linalg.pinv(X)
invpX
Out[40]:
array([[-2.46666667e-01, -6.66666667e-02,  1.13333333e-01],
       [-1.33333333e-01, -3.33333333e-02,  6.66666667e-02],
       [-2.00000000e-02, -2.51534904e-17,  2.00000000e-02],
       [ 9.33333333e-02,  3.33333333e-02, -2.66666667e-02],
       [ 2.06666667e-01,  6.66666667e-02, -7.33333333e-02]])
In [41]:

X.dot(invpX)
Out[41]:
array([[ 0.83333333,  0.33333333, -0.16666667],
       [ 0.33333333,  0.33333333,  0.33333333],
       [-0.16666667,  0.33333333,  0.83333333]])
In [42]:

invpX.dot(X)
Out[42]:
array([[ 6.00000000e-01,  4.00000000e-01,  2.00000000e-01,
        -1.33226763e-15, -2.00000000e-01],
       [ 4.00000000e-01,  3.00000000e-01,  2.00000000e-01,
         1.00000000e-01, -7.63278329e-16],
       [ 2.00000000e-01,  2.00000000e-01,  2.00000000e-01,
         2.00000000e-01,  2.00000000e-01],
       [ 1.73472348e-16,  1.00000000e-01,  2.00000000e-01,
         3.00000000e-01,  4.00000000e-01],
       [-2.00000000e-01,  4.99600361e-16,  2.00000000e-01,
         4.00000000e-01,  6.00000000e-01]])
矩阵的伪逆又被称为“广义逆矩阵”，有兴趣的同学可以翻看线性教材课本查看更多额广义逆矩阵相关的性质。中文wiki链接: https://zh.wikipedia.org/wiki/%E5%B9%BF%E4%B9%89%E9%80%86%E9%98%B5
Numpy 中的比较和Fancy Indexing
In [43]:

X
Out[43]:
array([[ 1,  2,  3,  4,  5],
       [ 6,  7,  8,  9, 10],
       [11, 12, 13, 14, 15]])
In [44]:

x = np.arange(16)
x
Out[44]:
array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15])
In [45]:

ind = [3, 5, 7]
x[ind]
Out[45]:
array([3, 5, 7])
In [46]:

ind = np.array([[0, 2], [1, 3],[5,7]])
x[ind]
Out[46]:
array([[0, 2],
       [1, 3],
       [5, 7]])
In [47]:

row = np.array([0, 1, 2])
col = np.array([1, 2, 3])
X[row, col]
Out[47]:
array([ 2,  8, 14])
In [48]:

X[[0,1,2],[1,2,3]]
Out[48]:
array([ 2,  8, 14])
In [49]:

X[[1,2],[2,3]] # X里面只能放两个坐标点，放３个报错，需要用到上面的方法，把行列都分开存放
Out[49]:
array([ 8, 14])
In [50]:

X[row]
Out[50]:
array([[ 1,  2,  3,  4,  5],
       [ 6,  7,  8,  9, 10],
       [11, 12, 13, 14, 15]])
In [51]:

X[-1,row]  # -1表示取最后一行
Out[51]:
array([11, 12, 13])
In [53]:

X[:,row] # :表示取所有行
Out[53]:
array([[ 1,  2,  3],
       [ 6,  7,  8],
       [11, 12, 13]])
In [54]:

chs = [True, False, True, True, False]
In [55]:

X[:,chs] # 取１，３，４列
Out[55]:
array([[ 1,  3,  4],
       [ 6,  8,  9],
       [11, 13, 14]])
numpy.array 的比较
In [56]:

x
Out[56]:
array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15])
In [57]:

x <= 6
Out[57]:
array([ True,  True,  True,  True,  True,  True,  True, False, False,
       False, False, False, False, False, False, False])
In [58]:

x != 3
Out[58]:
array([ True,  True,  True, False,  True,  True,  True,  True,  True,
        True,  True,  True,  True,  True,  True,  True])
In [59]:

X < 6
Out[59]:
array([[ True,  True,  True,  True,  True],
       [False, False, False, False, False],
       [False, False, False, False, False]])
使用 numpy.array 的比较结果
In [60]:

np.count_nonzero( x <= 3) # 统计小于等于３的数量－－有4个满足，所以是４个true，true用表示１，所以结果为４
Out[60]:
4
In [65]:

np.sum(x <= 3) # 统计小于等于３的数量
Out[65]:
4
In [66]:

X
Out[66]:
array([[ 1,  2,  3,  4,  5],
       [ 6,  7,  8,  9, 10],
       [11, 12, 13, 14, 15]])
In [67]:

np.sum(X % 2 == 0, axis=0) # 沿着行的方向　　即每列偶数的数量
Out[67]:
array([1, 2, 1, 2, 1])
In [71]:

np.sum(X % 2 == 0, axis=1) # 沿着列的方向　　即每行偶数的数量
Out[71]:
array([2, 3, 2])
In [91]:

np.any(x == 0) #  any 查找所有值，只要有一个满足条件　为true,则返回True
Out[91]:
True
In [92]:

np.any(x < 0)
Out[92]:
False
In [93]:

np.all(x<0)  #  all 查找所有值，只要有一个不满足条件　为false,则返回False
Out[93]:
False
In [94]:

np.all(x>=0)
Out[94]:
True
In [95]:

np.all(X>0)  # 整体判断，只返回一个布尔值
Out[95]:
True
In [96]:

np.all(X>3,axis=1) # 沿着列的方向，　即每行的值是否满足条件，有一个不满足，则返回false
Out[96]:
array([False,  True,  True])
In [97]:

np.all(X>3,axis=0) # 沿着行的方向，　即每列的值是否满足条件，有一个不满足，则返回false
Out[97]:
array([False, False, False,  True,  True])
In [98]:

np.any(X>14)  # 整体判断，只返回一个布尔值
Out[98]:
True
In [99]:

np.any(X>14,axis=0)
Out[99]:
array([False, False, False, False,  True])
In [100]:

np.any(X>14,axis=1)
Out[100]:
array([False, False,  True])
In [101]:

np.sum((x>3)&(x<10)) #  查询3<x<10的数量
Out[101]:
6
In [102]:

np.sum((x%2==0)|(x>10)) #  查询x为偶数或大于10的数量
Out[102]:
11
In [103]:

np.sum(~(x==0)) # 查询x中不等于０的值的数量
Out[103]:
15
In [104]:

x[x<5] # 返回满足条件的数组
Out[104]:
array([0, 1, 2, 3, 4])
In [105]:

x[x%2==0]
Out[105]:
array([ 0,  2,  4,  6,  8, 10, 12, 14])
In [106]:

X
Out[106]:
array([[ 1,  2,  3,  4,  5],
       [ 6,  7,  8,  9, 10],
       [11, 12, 13, 14, 15]])
In [107]:

X[X[:,-1]%3==0,:] # 返回最后一列中能被３整除的行
Out[107]:
array([[11, 12, 13, 14, 15]])
In [108]:

X[X[:,-1]%3==0]
Out[108]:
array([[11, 12, 13, 14, 15]])
In [109]:

X[:,X[-1,:]%3==0] # 返回最后一行中能被３整除的列
Out[109]:
array([[ 2,  5],
       [ 7, 10],
       [12, 15]])
In [110]:

X[-1,:]%3==0
Out[110]:
array([False,  True, False, False,  True])

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