今天我們要來研究一下NumPy多維陣列，先從一點簡單的開始，二維陣列，俗稱矩陣(matrix)，

矩陣

基本運算

import numpy as np

if __name__ == "__main__":
    # 以二維列表來建立numpy二維陣列
    l1 = [[12, 14, 0], [5, 23, 3]]
    a1 = np.array(l1)
    l2 = [[34, 17, 97], [83, 18, 34]]
    a2 = np.array(l2)
    print(a1)
    # [[12 14  0] [ 5 23  3]]
    print(a2)
    # [[34 17 97] [83 18 34]]

    #矩陣加法
    print(a1 + a2)
    #[[46 31 97] [88 41 37]]
    #矩陣減法
    print(a1 - a2)
    #[[-22  -3 -97] [-78   5 -31]]
    #元素乘積(不是矩陣乘法)
    print(a1 * a2)
    #[[408 238   0] [415 414 102]]
    #矩陣除法
    print(a1 / a2)
    #[[0.35294118 0.82352941 0.        ] [0.06024096 1.27777778 0.08823529]]

矩陣轉置

矩陣轉置會將欄和列互換

import numpy as np

if __name__ == "__main__":
    # 以二維列表來建立numpy二維陣列
    l1 = [[12, 14, 0], [5, 23, 3]]
    a1 = np.array(l1)
    print(a1)
    # [[12 14  0]
    #  [ 5 23  3]]

    # 矩陣轉置
    print(a1.T)
    # [[12  5] 
    #  [14 23] 
    #  [ 0  3]]

矩陣點積

注意矩陣點積需要第一個矩陣的欄數等於第二個矩陣的列數喔

import numpy as np

if __name__ == "__main__":
    # 以二維列表來建立numpy二維陣列
    l1 = [[12, 14, 0], [5, 23, 3]]
    a1 = np.array(l1)
    l2 = [[34, 17, 97], [83, 18, 34], [44, 19, 22]]
    a2 = np.array(l2)
    print(a1)
    # [[12 14  0]
    #  [ 5 23  3]]
    print(a2)
    # [[34 17 97]
    #  [83 18 34]
    #  [44 19 22]]
    
    # 矩陣點積
    print(a1.dot(a2))
    # [[1570  456 1640]
    #  [2211  556 1333]]

    print(a2.dot(a1))
    # 報錯 a2的欄數是3 a1的列數是2

矩陣內積

import numpy as np

if __name__ == "__main__":
    # 以二維列表來建立numpy二維陣列
    l1 = [[12, 14, 0], [5, 23, 3]]
    a1 = np.array(l1)
    l2 = [[34, 17, 97], [83, 18, 34], [44, 19, 22]]
    a2 = np.array(l2)
    print(a1)
    # [[12 14  0]
    #  [ 5 23  3]]
    print(a2)
    # [[34 17 97]
    #  [83 18 34]
    #  [44 19 22]]
    
    # 矩陣內積
    print(np.inner(a1,a2))
    # [[ 646 1248  794]
    #  [ 852  931  723]]

矩陣外積

import numpy as np

if __name__ == "__main__":
    # 以二維列表來建立numpy二維陣列
    l1 = [[12, 14, 0], [5, 23, 3]]
    a1 = np.array(l1)
    l2 = [[34, 17, 97], [83, 18, 34], [44, 19, 22]]
    a2 = np.array(l2)
    print(a1)
    # [[12 14  0]
    #  [ 5 23  3]]
    print(a2)
    # [[34 17 97]
    #  [83 18 34]
    #  [44 19 22]]
    
    # 矩陣外積
    print(np.outer(a1,a2))
    # [[ 408  204 1164  996  216  408  528  228  264]
    #  [ 476  238 1358 1162  252  476  616  266  308]
    #  [   0    0    0    0    0    0    0    0    0]
    #  [ 170   85  485  415   90  170  220   95  110]
    #  [ 782  391 2231 1909  414  782 1012  437  506]
    #  [ 102   51  291  249   54  102  132   57   66]]