進入Python Numpy 開發環境

1. 進入開發環境，匯入函式庫。

python
>>> from numpy import *
>>>

2. 構造隨機4*4的陣列。

>>> random.rand(4,4)
array([[0.768388  , 0.25985153, 0.22463279, 0.15207017],
       [0.54974659, 0.66975723, 0.43260259, 0.16968662],
       [0.99561439, 0.19247713, 0.06272048, 0.02427845],
       [0.37828522, 0.07717839, 0.82606638, 0.62284816]])
 

3. 呼叫mat()函式可以將陣列轉化為矩陣：

randMat = mat(random.rand(4,4))

4. .I操作符實現了矩陣求逆的運算：

>>> randMat.I
matrix([[ 1.82854954,  6.18721531, -1.23217589, -6.21081253],
        [-2.77985587, -6.95624578,  3.20273141,  6.39917325],
        [ 3.59647331,  4.48562014, -2.46083948, -4.08390475],
        [-5.94615554, -9.97699439,  3.74538554, 11.04422169]])
 

5. 執行矩陣的乘法運算，得到矩陣與其逆矩陣相乘的結果：

>>> invRandMat = randMat.I
>>> randMat*invRandMat
matrix([[ 1.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00],
        [ 8.8817842e-16,  1.0000000e+00,  0.0000000e+00,  0.0000000e+00],
        [-4.4408921e-16,  0.0000000e+00,  1.0000000e+00,  0.0000000e+00],
        [ 0.0000000e+00,  8.8817842e-16,  0.0000000e+00,  1.0000000e+00]])

結果應該是單位矩陣，除了對角線是1，其他都應該是0，但是實際運算中存在誤差。

6. eye(4)函式可以建立一個4*4的單位矩陣。用計算後的矩陣減去單位矩陣，計算誤差：

myEye = randMat*invRandMat
>>> myEye - eye(4)
matrix([[ 2.22044605e-16,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00],
        [ 8.88178420e-16,  1.77635684e-15,  0.00000000e+00,
          0.00000000e+00],
        [-4.44089210e-16,  0.00000000e+00,  4.44089210e-16,
          0.00000000e+00],
        [ 0.00000000e+00,  8.88178420e-16,  0.00000000e+00,
         -8.88178420e-16]])