NumPy函数库基础

from numpy import*导入numpy模块

random.rand()用来生成一个随机数组

例如：random.rand(4,4)，生成一个$4\times 4$的随机二维数组

>>> random.rand(4,4)
array([[0.5889423 , 0.38768404, 0.46706706, 0.88201106],
       [0.03742084, 0.30163653, 0.40948962, 0.22092582],
       [0.84407563, 0.42206233, 0.26600708, 0.8114246 ],
       [0.39277872, 0.88407207, 0.59209405, 0.19366928]])

用mat()函数可以将数组转换成矩阵

>>> mat(random.rand(4,4))
matrix([[0.27334161, 0.3052977 , 0.68240247, 0.65456973],
        [0.09794511, 0.74127397, 0.11178214, 0.18242132],
        [0.15790548, 0.99141967, 0.57665171, 0.90780008],
        [0.7987583 , 0.06336807, 0.94360913, 0.18242104]])

.I操作符实现了矩阵的求逆运算

矩阵求逆，即求矩阵的逆矩阵。设$A$是数域上的一个$n$阶方阵，若在相同数域上存在另一个$n$阶矩$B$，使得： $A\times B=B\times A=E$。 则我们称$B$是$A$的逆矩阵，而A则被称为可逆矩阵。其中，$E$为单位矩阵。

>>> randmat=mat(random.rand(4,4))
>>> invmat=randmat.I
>>> randmat
matrix([[0.48117984, 0.29220134, 0.34585956, 0.30547942],
        [0.42158584, 0.12684831, 0.56184421, 0.93906936],
        [0.25070707, 0.0770531 , 0.46094489, 0.18799276],
        [0.1206866 , 0.5818652 , 0.75019166, 0.69006769]])
>>> invmat
matrix([[ 2.23619026,  0.10754838,  0.07245331, -1.15601151],
        [ 1.7848114 , -1.14762783, -2.14901481,  1.35708167],
        [-1.33183128, -0.45568243,  3.15370035,  0.35053317],
        [-0.44817218,  1.44425573, -1.62909657,  0.12594335]])

如果执行矩阵乘法，将两个矩阵直接相乘即可：

>>> randmat*invmat
matrix([[ 1.00000000e+00,  0.00000000e+00,  5.55111512e-17,
          2.77555756e-17],
        [ 1.11022302e-16,  1.00000000e+00,  0.00000000e+00,
          8.32667268e-17],
        [-2.77555756e-16, -5.55111512e-17,  1.00000000e+00,
          9.02056208e-17],
        [-1.66533454e-16,  2.22044605e-16,  4.44089210e-16,
          1.00000000e+00]])

eye(4)用来创建$4\times 4$的单位矩阵，可以用来检测误差值

>>> eye(4)
array([[1., 0., 0., 0.],
       [0., 1., 0., 0.],
       [0., 0., 1., 0.],
       [0., 0., 0., 1.]])

>>> deviation=randmat*invmat
>>> deviation-eye(4)
matrix([[ 0.00000000e+00,  0.00000000e+00,  5.55111512e-17,
          2.77555756e-17],
        [ 1.11022302e-16, -2.22044605e-16,  0.00000000e+00,
          8.32667268e-17],
        [-2.77555756e-16, -5.55111512e-17,  0.00000000e+00,
          9.02056208e-17],
        [-1.66533454e-16,  2.22044605e-16,  4.44089210e-16,
          0.00000000e+00]])