numpy数组转置与轴变换

Posted 2022-12-13 mengxiaoleng

numpy数组转置与轴变换

矩阵的转置

>>> import numpy as np
>>> arr=np.arange(15).reshape((3,5))
>>> arr
array([[ 0,  1,  2,  3,  4],
       [ 5,  6,  7,  8,  9],
       [10, 11, 12, 13, 14]])
>>> arr.T
array([[ 0,  5, 10],
       [ 1,  6, 11],
       [ 2,  7, 12],
       [ 3,  8, 13],
       [ 4,  9, 14]])

矩阵的内积

>>> import numpy as np
>>> arr=np.arange(15).reshape((3,5))
>>> arr
array([[ 0,  1,  2,  3,  4],
       [ 5,  6,  7,  8,  9],
       [10, 11, 12, 13, 14]])
>>> arr.T
array([[ 0,  5, 10],
       [ 1,  6, 11],
       [ 2,  7, 12],
       [ 3,  8, 13],
       [ 4,  9, 14]])
>>> np.dot(arr.T,arr)
array([[125, 140, 155, 170, 185],
       [140, 158, 176, 194, 212],
       [155, 176, 197, 218, 239],
       [170, 194, 218, 242, 266],
       [185, 212, 239, 266, 293]])

轴变换

二维轴变换

1.两轴交换

>>> import numpy as np
>>> arr=np.arange(15).reshape((3,5))
>>> arr
array([[ 0,  1,  2,  3,  4],
       [ 5,  6,  7,  8,  9],
       [10, 11, 12, 13, 14]])
>>> arr.transpose(1,0)#1轴和0轴进行交换
array([[ 0,  5, 10],
       [ 1,  6, 11],
       [ 2,  7, 12],
       [ 3,  8, 13],
       [ 4,  9, 14]])

三维轴变换

>>> arr = np.arange(16).reshape((2, 2, 4))
>>> arr
array([[[ 0,  1,  2,  3],
        [ 4,  5,  6,  7]],

       [[ 8,  9, 10, 11],
        [12, 13, 14, 15]]])
>>> arr.transpose((1,0,2))
array([[[ 0,  1,  2,  3],
        [ 8,  9, 10, 11]],

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

1.这种变化有点麻烦，不好理解。但是如果简单化就好了，加入用P(x,y,z)来表示矩阵中的每一个点，那么在numpy中，这个x,y,z就分别对应0,1,2

2.举个例子比如原来数组中0这个元素，它原来的坐标是(0,0,0),那么transpose(1,0,2)对于这个点来说就是把x,y坐标互换，而z坐标不变，则其在新的矩阵中坐标依旧是(0,0,0)不变

3.举个另外点的例子比如4这个点，其坐标是(0,1,1),那么它的x和y坐标交换之后是(1,0,1),所以它在新的矩阵中位置是(1,0,1)

4.事实上transpose函数正是对原来矩阵中每个点做这个变换，最后得到新的矩阵

两轴交换

交换1轴和2轴

>>> arr
array([[[ 0,  1,  2,  3],
        [ 4,  5,  6,  7]],

       [[ 8,  9, 10, 11],
        [12, 13, 14, 15]]])
>>> arr.swapaxes(1,2)
array([[[ 0,  4],
        [ 1,  5],
        [ 2,  6],
        [ 3,  7]],

       [[ 8, 12],
        [ 9, 13],
        [10, 14],
        [11, 15]]])
>>> arr
array([[[ 0,  1,  2,  3],
        [ 4,  5,  6,  7]],

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