numpy模块介绍

import numpy as np

np.array([1,2,3])

array([1, 2, 3])

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

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

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

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

把它给看成一个矩阵,或者看成一个ndarray数组的话,我们去获取他的形状.

arr = np.array([[1,2,3],[4,5,6],[7,8,9],[10,11,12]])
arr.shape

(4, 3)

arr.shape[0]
print(arr.shape[0])

20

arr.shape[1]

3

切割矩阵

arr = np.array([1,2,3])
arr
arr[:]

array([1, 2, 3])

arr = np.array([[1,2,3],[4,5,6],[7,8,9],[10,11,12]])
arr

array([[ 1,  2,  3],
       [ 4,  5,  6],
       [ 7,  8,  9],
       [10, 11, 12]])

arr[:,:]

array([[ 1,  2,  3],
       [ 4,  5,  6],
       [ 7,  8,  9],
       [10, 11, 12]])

arr[1:2,:]

array([[4, 5, 6]])

arr[1:2,1:2]

array([[5]])

arr[1:2,1:10000]

array([[5, 6]])

arr[1:2,[1,2]]

array([[5, 6]])

arr[1:2,(1,2)]

array([[5, 6]])

矩阵元素的替换

arr = np.array([[1,2,3],[4,5,6],[7,8,9],[10,11,12]])
arr

array([[ 1,  2,  3],
       [ 4,  5,  6],
       [ 7,  8,  9],
       [10, 11, 12]])

l = [4,5,6]
l[1] = 0
l

[4, 0, 6]

# arr[1:2,:] = 0
# arr

arr1 = arr.copy()
arr1[1:2,:] = 0
arr1

array([[ 1,  2,  3],
       [ 0,  0,  0],
       [ 7,  8,  9],
       [10, 11, 12]])

arr

array([[ 1,  2,  3],
       [ 4,  5,  6],
       [ 7,  8,  9],
       [10, 11, 12]])

arr[(1,),(1,)] = 0
arr

array([[ 1,  2,  3],
       [ 4,  0,  6],
       [ 7,  8,  9],
       [10, 11, 12]])

矩阵的合并

l1 = [1,2,3]
l2 = [4,5,6]
# l1.extend(l2)
# l1

l1+l2

[1, 2, 3, 4, 5, 6]

arr1 = np.array([[1, 2], [3, 4], [5, 6]])
arr1

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

arr2 = np.array([[7, 8,8], [9, 10,9], [11, 12,10]])
arr2

array([[ 7,  8,  8],
       [ 9, 10,  9],
       [11, 12, 10]])

np.hstack((arr1,arr2)) # h=horizontal水平的

array([[ 1,  2,  7,  8,  8],
       [ 3,  4,  9, 10,  9],
       [ 5,  6, 11, 12, 10]])

np.hstack([arr1,arr2])

array([[ 1,  2,  7,  8,  8],
       [ 3,  4,  9, 10,  9],
       [ 5,  6, 11, 12, 10]])

np.vstack((arr1,arr2)) # v=vertical垂直的

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

ValueError                                Traceback (most recent call last)

<ipython-input-53-4122b6300983> in <module>
----> 1 np.vstack((arr1,arr2)) # v=vertical垂直的

d:\python36\lib\site-packages\numpy\core\shape_base.py in vstack(tup)
    281     """
    282     _warn_for_nonsequence(tup)
--> 283     return _nx.concatenate([atleast_2d(_m) for _m in tup], 0)
    284
    285 

ValueError: all the input array dimensions except for the concatenation axis must match exactly

arr1 = np.array([[1, 2,3], [3, 4,4], [5, 6,4]])
arr1

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

arr2 = np.array([[7, 8,8], [9, 10,9], [11, 12,10]])
arr2

array([[ 7,  8,  8],
       [ 9, 10,  9],
       [11, 12, 10]])

np.vstack((arr1,arr2)) # v=vertical垂直的

array([[ 1,  2,  3],
       [ 3,  4,  4],
       [ 5,  6,  4],
       [ 7,  8,  8],
       [ 9, 10,  9],
       [11, 12, 10]])

通过函数创建矩阵

range(10)

range(0, 10)

list(range(5,10,2))

[5, 7, 9]

np.arange(10,20,2)

array([10, 12, 14, 16, 18])

# 取头也取尾
arr = np.linspace(1,10,20)
arr

array([ 1.        ,  1.47368421,  1.94736842,  2.42105263,  2.89473684,
        3.36842105,  3.84210526,  4.31578947,  4.78947368,  5.26315789,
        5.73684211,  6.21052632,  6.68421053,  7.15789474,  7.63157895,
        8.10526316,  8.57894737,  9.05263158,  9.52631579, 10.        ])

len(arr)

20

zeros/ones/empty

np.zeros((3,2)) # zeros零

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

np.ones((3,2)) # ones一

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

np.empty((3,3)) # 随机元素的矩阵

array([[0.00000000e+000, 0.00000000e+000, 0.00000000e+000],
       [0.00000000e+000, 0.00000000e+000, 7.37145944e-321],
       [8.70018274e-313, 2.22507386e-306, 3.91786943e-317]])

np.eye(4) # I=1

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

np.eye(7)

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

矩阵的运算

列表无法进行+-*/运算,但是矩阵是可以的.

l1 =[1,3,4]
l1*2

[1, 3, 4, 1, 3, 4]

l1+l1

[1, 3, 4, 1, 3, 4]

arr2 = np.array([[7, 8,8], [9, 10,9], [11, 12,10]])
arr2

array([[ 7,  8,  8],
       [ 9, 10,  9],
       [11, 12, 10]])

arr2*2

array([[14, 16, 16],
       [18, 20, 18],
       [22, 24, 20]])

arr2/2

array([[3.5, 4. , 4. ],
       [4.5, 5. , 4.5],
       [5.5, 6. , 5. ]])

arr2%2

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

np.sin(arr2)

array([[ 0.6569866 ,  0.98935825,  0.98935825],
       [ 0.41211849, -0.54402111,  0.41211849],
       [-0.99999021, -0.53657292, -0.54402111]])

矩阵函数	详解
np.sin(arr)	对矩阵arr中每个元素取正弦，$sin(x)$
np.cos(arr)	对矩阵arr中每个元素取余弦，$cos(x)$
np.tan(arr)	对矩阵arr中每个元素取正切，$tan(x)$
np.arcsin(arr)	对矩阵arr中每个元素取反正弦，$arcsin(x)$
np.arccos(arr)	对矩阵arr中每个元素取反余弦，$arccos(x)$
np.arctan(arr)	对矩阵arr中每个元素取反正切，$arctan(x)$
np.exp(arr)	对矩阵arr中每个元素取指数函数，$e^x$
np.sqrt(arr)	对矩阵arr中每个元素开根号$\sqrt{x}$

np.sqrt(arr2)

array([[2.64575131, 2.82842712, 2.82842712],
       [3.        , 3.16227766, 3.        ],
       [3.31662479, 3.46410162, 3.16227766]])

矩阵的点乘

arr1 = np.array([[1, 2,3], [3, 4,4], [5, 6,4]])
arr1

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

arr2 = np.array([[1, 2,3], [3, 4,4], [5, 6,4]])
arr2

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

arr1.dot(arr2)

array([[22, 28, 23],
       [35, 46, 41],
       [43, 58, 55]])

矩阵的转置

arr2 = np.array([[1, 2,3]])
arr2

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

arr2.T

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

矩阵的逆

$AA^{-1}=I=A{-1}A$

arr2 = np.array([[1, 2,3],[4,5,6],[7,8,9]])
arr2

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

np.linalg.inv(arr2)

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

LinAlgError                               Traceback (most recent call last)

<ipython-input-104-12b0a2fff5c3> in <module>
----> 1 np.linalg.inv(arr2)

d:\python36\lib\site-packages\numpy\linalg\linalg.py in inv(a)
    549     signature = 'D->D' if isComplexType(t) else 'd->d'
    550     extobj = get_linalg_error_extobj(_raise_linalgerror_singular)
--> 551     ainv = _umath_linalg.inv(a, signature=signature, extobj=extobj)
    552     return wrap(ainv.astype(result_t, copy=False))
    553 

d:\python36\lib\site-packages\numpy\linalg\linalg.py in _raise_linalgerror_singular(err, flag)
     95
     96 def _raise_linalgerror_singular(err, flag):
---> 97     raise LinAlgError("Singular matrix")
     98
     99 def _raise_linalgerror_nonposdef(err, flag):

LinAlgError: Singular matrix

其他的用法

arr2 = np.array([[1, 2,3],[4,5,6],[7,8,9]])
arr2

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

arr2.min()

1

arr2.max()

9

arr2.mean()

5.0

arr2.var()

6.666666666666667

函数名称	函数功能	参数说明
rand($d_0, d_1, \cdots , d_n$)	产生均匀分布的随机数	$d_n$为第n维数据的维度
randn($d_0, d_1, \cdots , d_n$)	产生标准正态分布随机数	$d_n$为第n维数据的维度
randint(low[, high, size, dtype])	产生随机整数	low:最小值；high:最大值；size:数据个数
random_sample([size])	在$[0,1)$内产生随机数	size为随机数的shape，可以为元祖或者列表
choice(a[, size])	从arr中随机选择指定数据	arr为1维数组；size为数据形状

np.random.randint(1,10,(3,3))

array([[8, 5, 6],
       [7, 5, 3],
       [6, 4, 6]])

np.random.randn(3,2)

array([[ 1.49020068e+00, -5.66224782e-01],
       [-1.26022246e+00,  1.41537705e+00],
       [-1.99081209e-03,  2.05245204e+00]])