{"id":1079695,"date":"2025-01-08T12:23:17","date_gmt":"2025-01-08T04:23:17","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1079695.html"},"modified":"2025-01-08T12:23:20","modified_gmt":"2025-01-08T04:23:20","slug":"python%e9%87%8c%e9%9d%a2%e5%a6%82%e4%bd%95%e8%a1%a8%e7%a4%ba%e7%9f%a9%e9%98%b5%e7%9a%84%e5%8f%8d-2","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/1079695.html","title":{"rendered":"python\u91cc\u9762\u5982\u4f55\u8868\u793a\u77e9\u9635\u7684\u53cd"},"content":{"rendered":"

\"python\u91cc\u9762\u5982\u4f55\u8868\u793a\u77e9\u9635\u7684\u53cd\"<\/p>\n

\u5728Python\u4e2d\uff0c\u77e9\u9635\u53cd\u8f6c\uff08\u5373\u77e9\u9635\u7684\u9006\uff09\u53ef\u4ee5\u4f7f\u7528\u591a\u4e2a\u5e93\u6765\u5b9e\u73b0\uff0c\u6700\u5e38\u7528\u7684\u5e93\u662fNumPy\u3002\u4f7f\u7528NumPy\u5e93\u3001\u8ba1\u7b97\u77e9\u9635\u7684\u9006\u3001\u5904\u7406\u53ef\u80fd\u7684\u77e9\u9635\u4e0d\u53ef\u9006\u60c5\u51b5<\/strong>\u662f\u6838\u5fc3\u89c2\u70b9\u3002\u63a5\u4e0b\u6765\u5c06\u91cd\u70b9\u4ecb\u7ecd\u4f7f\u7528NumPy\u5e93\u6765\u8ba1\u7b97\u77e9\u9635\u7684\u9006\u3002<\/p>\n<\/p>\n

\u4e00\u3001\u4f7f\u7528NumPy\u5e93<\/h3>\n<\/p>\n

NumPy\u662fPython\u4e2d\u6700\u5e38\u7528\u7684\u79d1\u5b66\u8ba1\u7b97\u5e93\u4e4b\u4e00\uff0c\u5b83\u63d0\u4f9b\u4e86\u5f3a\u5927\u7684\u77e9\u9635\u8fd0\u7b97\u529f\u80fd\u3002\u8ba1\u7b97\u77e9\u9635\u7684\u9006\u5728NumPy\u4e2d\u975e\u5e38\u7b80\u5355\uff0c\u53ea\u9700\u8981\u4f7f\u7528numpy.linalg.inv<\/code>\u51fd\u6570\u5373\u53ef\u3002<\/p>\n<\/p>\n

import numpy as np<\/p>\n
\u521b\u5efa\u4e00\u4e2a\u77e9\u9635<\/strong><\/h2>\n
matrix = np.array([[1, 2], [3, 4]])<\/p>\n
\u8ba1\u7b97\u77e9\u9635\u7684\u9006<\/strong><\/h2>\n
inverse_matrix = np.linalg.inv(matrix)<\/p>\n
print("\u77e9\u9635\u7684\u9006\uff1a\\n", inverse_matrix)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5728\u4e0a\u8ff0\u4ee3\u7801\u4e2d\uff0c\u6211\u4eec\u9996\u5148\u5bfc\u5165NumPy\u5e93\uff0c\u7136\u540e\u521b\u5efa\u4e00\u4e2a2×2\u77e9\u9635\u3002\u63a5\u4e0b\u6765\uff0c\u4f7f\u7528numpy.linalg.inv<\/code>\u51fd\u6570\u8ba1\u7b97\u8be5\u77e9\u9635\u7684\u9006\uff0c\u5e76\u8f93\u51fa\u7ed3\u679c\u3002<\/p>\n<\/p>\n
\u4e8c\u3001\u5904\u7406\u4e0d\u53ef\u9006\u77e9\u9635<\/h3>\n<\/p>\n
\u5e76\u4e0d\u662f\u6240\u6709\u77e9\u9635\u90fd\u6709\u9006\uff0c\u53ea\u6709\u884c\u5217\u5f0f\u4e0d\u4e3a\u96f6\u7684\u65b9\u9635\u624d\u6709\u9006\u77e9\u9635\u3002\u5bf9\u4e8e\u4e0d\u53ef\u9006\u7684\u77e9\u9635\uff0c\u8ba1\u7b97\u9006\u77e9\u9635\u4f1a\u5f15\u53d1LinAlgError<\/code>\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u9700\u8981\u5728\u8ba1\u7b97\u77e9\u9635\u7684\u9006\u4e4b\u524d\u68c0\u67e5\u77e9\u9635\u662f\u5426\u53ef\u9006\u3002<\/p>\n<\/p>\n
import numpy as np<\/p>\n
def inverse_matrix(matrix):<\/p>\n
    try:<\/p>\n
        inv_matrix = np.linalg.inv(matrix)<\/p>\n
        return inv_matrix<\/p>\n
    except np.linalg.LinAlgError:<\/p>\n
        print("\u8be5\u77e9\u9635\u4e0d\u53ef\u9006")<\/p>\n
        return None<\/p>\n
matrix = np.array([[1, 2], [2, 4]])<\/p>\n
inv_matrix = inverse_matrix(matrix)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5728\u4e0a\u8ff0\u4ee3\u7801\u4e2d\uff0c\u6211\u4eec\u5b9a\u4e49\u4e86\u4e00\u4e2ainverse_matrix<\/code>\u51fd\u6570\uff0c\u5c1d\u8bd5\u8ba1\u7b97\u77e9\u9635\u7684\u9006\u3002\u5982\u679c\u77e9\u9635\u4e0d\u53ef\u9006\uff0c\u5219\u6355\u83b7LinAlgError<\/code>\u5e76\u8f93\u51fa\u63d0\u793a\u4fe1\u606f\u3002<\/p>\n<\/p>\n
\u4e09\u3001\u4e0d\u540c\u7ef4\u5ea6\u7684\u77e9\u9635<\/h3>\n<\/p>\n
NumPy\u4e0d\u4ec5\u53ef\u4ee5\u5904\u74062×2\u77e9\u9635\uff0c\u8fd8\u53ef\u4ee5\u5904\u7406\u66f4\u9ad8\u7ef4\u5ea6\u7684\u77e9\u9635\u3002\u4ee5\u4e0b\u662f\u4e00\u4e2a3×3\u77e9\u9635\u7684\u4f8b\u5b50\uff1a<\/p>\n<\/p>\n
import numpy as np<\/p>\n
matrix = np.array([[1, 2, 3], [0, 1, 4], [5, 6, 0]])<\/p>\n
inverse_matrix = np.linalg.inv(matrix)<\/p>\n
print("3x3\u77e9\u9635\u7684\u9006\uff1a\\n", inverse_matrix)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5728\u4e0a\u8ff0\u4ee3\u7801\u4e2d\uff0c\u6211\u4eec\u521b\u5efa\u4e86\u4e00\u4e2a3×3\u77e9\u9635\uff0c\u5e76\u4f7f\u7528numpy.linalg.inv<\/code>\u51fd\u6570\u8ba1\u7b97\u5176\u9006\u77e9\u9635\u3002<\/p>\n<\/p>\n
\u56db\u3001\u77e9\u9635\u7684\u57fa\u7840\u77e5\u8bc6<\/h3>\n<\/p>\n
\u5728\u8ba1\u7b97\u77e9\u9635\u9006\u4e4b\u524d\uff0c\u7406\u89e3\u77e9\u9635\u7684\u4e00\u4e9b\u57fa\u7840\u77e5\u8bc6\u662f\u6709\u5e2e\u52a9\u7684\u3002\u77e9\u9635\u662f\u4e00\u79cd\u4e8c\u7ef4\u6570\u7ec4\uff0c\u5e38\u7528\u4e8e\u7ebf\u6027\u4ee3\u6570\u8fd0\u7b97\u3002\u77e9\u9635\u7684\u9006\u662f\u6307\u5f53\u77e9\u9635A\u4e58\u4ee5\u5176\u9006\u77e9\u9635A\u207b\u00b9\u65f6\uff0c\u7ed3\u679c\u662f\u5355\u4f4d\u77e9\u9635I\u3002<\/p>\n<\/p>\n
import numpy as np<\/p>\n
matrix = np.array([[1, 2], [3, 4]])<\/p>\n
identity_matrix = np.dot(matrix, np.linalg.inv(matrix))<\/p>\n
print("\u5355\u4f4d\u77e9\u9635\uff1a\\n", identity_matrix)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5728\u4e0a\u8ff0\u4ee3\u7801\u4e2d\uff0c\u6211\u4eec\u9a8c\u8bc1\u4e86\u77e9\u9635\u4e0e\u5176\u9006\u77e9\u9635\u76f8\u4e58\u7684\u7ed3\u679c\u662f\u5355\u4f4d\u77e9\u9635\u3002<\/p>\n<\/p>\n
\u4e94\u3001\u5b9e\u9645\u5e94\u7528<\/h3>\n<\/p>\n
\u77e9\u9635\u7684\u9006\u5728\u8bb8\u591a\u5b9e\u9645\u5e94\u7528\u4e2d\u90fd\u975e\u5e38\u91cd\u8981\u3002\u4f8b\u5982\uff0c\u5728\u89e3\u51b3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u3001\u8ba1\u7b97\u53d8\u6362\u77e9\u9635\u3001\u56fe\u50cf\u5904\u7406\u548c\u673a\u5668\u5b66\u4e60<\/a>\u4e2d\uff0c\u77e9\u9635\u7684\u9006\u90fd\u662f\u57fa\u672c\u64cd\u4f5c\u3002<\/p>\n<\/p>\n
import numpy as np<\/p>\n
\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u4f8b\u5b50\uff1aAx = B<\/strong><\/h2>\n
A = np.array([[3, 1], [1, 2]])<\/p>\n
B = np.array([9, 8])<\/p>\n
\u8ba1\u7b97x<\/strong><\/h2>\n
x = np.linalg.solve(A, B)<\/p>\n
print("\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u89e3\uff1a", x)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5728\u4e0a\u8ff0\u4ee3\u7801\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528\u77e9\u9635\u7684\u9006\u6765\u89e3\u51b3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u3002<\/p>\n<\/p>\n
\u516d\u3001\u77e9\u9635\u9006\u7684\u8ba1\u7b97\u539f\u7406<\/h3>\n<\/p>\n
\u4e86\u89e3\u77e9\u9635\u9006\u7684\u8ba1\u7b97\u539f\u7406\u6709\u52a9\u4e8e\u66f4\u6df1\u5165\u7684\u7406\u89e3\u3002\u5bf9\u4e8e2×2\u77e9\u9635\uff0c\u77e9\u9635A\u7684\u9006\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97\uff1a<\/p>\n<\/p>\n
[ A = \\begin{pmatrix} a & b \\ c & d \\end{pmatrix} ]<\/p>\n<\/p>\n
[ A^{-1} = \\frac{1}{ad – bc} \\begin{pmatrix} d & -b \\ -c & a \\end{pmatrix} ]<\/p>\n<\/p>\n
\u8fd9\u4e2a\u516c\u5f0f\u5c55\u793a\u4e86\u5982\u4f55\u901a\u8fc7\u884c\u5217\u5f0f\u548c\u4f34\u968f\u77e9\u9635\u8ba1\u7b97\u77e9\u9635\u7684\u9006\u3002<\/p>\n<\/p>\n
import numpy as np<\/p>\n
def manual_inverse(matrix):<\/p>\n
    a, b, c, d = matrix.flatten()<\/p>\n
    determinant = a*d - b*c<\/p>\n
    if determinant == 0:<\/p>\n
        return None<\/p>\n
    return np.array([[d, -b], [-c, a]]) \/ determinant<\/p>\n
matrix = np.array([[1, 2], [3, 4]])<\/p>\n
inv_matrix = manual_inverse(matrix)<\/p>\n
print("\u624b\u52a8\u8ba1\u7b97\u7684\u77e9\u9635\u9006\uff1a\\n", inv_matrix)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5728\u4e0a\u8ff0\u4ee3\u7801\u4e2d\uff0c\u6211\u4eec\u624b\u52a8\u5b9e\u73b0\u4e862×2\u77e9\u9635\u7684\u9006\u8ba1\u7b97\u3002<\/p>\n<\/p>\n
\u4e03\u3001\u4f7f\u7528\u5176\u4ed6\u5e93<\/h3>\n<\/p>\n
\u9664\u4e86NumPy\uff0c\u8fd8\u6709\u5176\u4ed6\u5e93\u53ef\u4ee5\u7528\u6765\u8ba1\u7b97\u77e9\u9635\u7684\u9006\u3002\u4f8b\u5982\uff0cSciPy\u5e93\u4e2d\u7684scipy.linalg.inv<\/code>\u51fd\u6570\u4e5f\u53ef\u4ee5\u7528\u6765\u8ba1\u7b97\u77e9\u9635\u7684\u9006\u3002<\/p>\n<\/p>\n
import scipy.linalg<\/p>\n
matrix = np.array([[1, 2], [3, 4]])<\/p>\n
inverse_matrix = scipy.linalg.inv(matrix)<\/p>\n
print("\u4f7f\u7528SciPy\u8ba1\u7b97\u7684\u77e9\u9635\u9006\uff1a\\n", inverse_matrix)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5728\u4e0a\u8ff0\u4ee3\u7801\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528SciPy\u5e93\u8ba1\u7b97\u4e86\u77e9\u9635\u7684\u9006\u3002<\/p>\n<\/p>\n
\u516b\u3001\u6027\u80fd\u8003\u8651<\/h3>\n<\/p>\n
\u5728\u5904\u7406\u5927\u89c4\u6a21\u77e9\u9635\u65f6\uff0c\u8ba1\u7b97\u77e9\u9635\u7684\u9006\u53ef\u80fd\u4f1a\u975e\u5e38\u8017\u65f6\u3002\u56e0\u6b64\uff0c\u6027\u80fd\u4f18\u5316\u662f\u4e00\u4e2a\u91cd\u8981\u7684\u8003\u8651\u56e0\u7d20\u3002NumPy\u548cSciPy\u90fd\u8fdb\u884c\u4e86\u9ad8\u5ea6\u4f18\u5316\uff0c\u53ef\u4ee5\u6709\u6548\u5730\u5904\u7406\u5927\u89c4\u6a21\u77e9\u9635\u3002<\/p>\n<\/p>\n
import numpy as np<\/p>\n
import time<\/p>\n
\u521b\u5efa\u4e00\u4e2a1000x1000\u7684\u968f\u673a\u77e9\u9635<\/strong><\/h2>\n
matrix = np.random.rand(1000, 1000)<\/p>\n
start_time = time.time()<\/p>\n
inverse_matrix = np.linalg.inv(matrix)<\/p>\n
end_time = time.time()<\/p>\n
print("\u8ba1\u7b971000x1000\u77e9\u9635\u7684\u9006\u8017\u65f6\uff1a", end_time - start_time, "\u79d2")<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5728\u4e0a\u8ff0\u4ee3\u7801\u4e2d\uff0c\u6211\u4eec\u521b\u5efa\u4e86\u4e00\u4e2a1000×1000\u7684\u968f\u673a\u77e9\u9635\uff0c\u5e76\u6d4b\u91cf\u4e86\u8ba1\u7b97\u5176\u9006\u77e9\u9635\u6240\u9700\u7684\u65f6\u95f4\u3002<\/p>\n<\/p>\n
\u4e5d\u3001\u603b\u7ed3<\/h3>\n<\/p>\n
\u4f7f\u7528NumPy\u5e93\u3001\u8ba1\u7b97\u77e9\u9635\u7684\u9006\u3001\u5904\u7406\u53ef\u80fd\u7684\u77e9\u9635\u4e0d\u53ef\u9006\u60c5\u51b5<\/strong>\u662fPython\u4e2d\u8868\u793a\u77e9\u9635\u53cd\u7684\u5173\u952e\u3002\u901a\u8fc7\u4e0a\u8ff0\u5185\u5bb9\uff0c\u6211\u4eec\u8be6\u7ec6\u4ecb\u7ecd\u4e86\u5982\u4f55\u4f7f\u7528NumPy\u5e93\u8ba1\u7b97\u77e9\u9635\u7684\u9006\uff0c\u5e76\u5904\u7406\u53ef\u80fd\u7684\u77e9\u9635\u4e0d\u53ef\u9006\u60c5\u51b5\u3002\u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u63a2\u8ba8\u4e86\u4e0d\u540c\u7ef4\u5ea6\u7684\u77e9\u9635\u3001\u77e9\u9635\u7684\u57fa\u7840\u77e5\u8bc6\u3001\u5b9e\u9645\u5e94\u7528\u3001\u77e9\u9635\u9006\u7684\u8ba1\u7b97\u539f\u7406\u3001\u4f7f\u7528\u5176\u4ed6\u5e93\u4ee5\u53ca\u6027\u80fd\u8003\u8651\u3002\u5e0c\u671b\u8fd9\u7bc7\u6587\u7ae0\u80fd\u5e2e\u52a9\u4f60\u66f4\u597d\u5730\u7406\u89e3\u548c\u5e94\u7528Python\u4e2d\u7684\u77e9\u9635\u9006\u64cd\u4f5c\u3002<\/p>\n<\/p>\n
\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n
 \u5982\u4f55\u5728Python\u4e2d\u521b\u5efa\u4e00\u4e2a\u77e9\u9635\uff1f<\/strong>
\u5728Python\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528NumPy\u5e93\u6765\u521b\u5efa\u77e9\u9635\u3002NumPy\u63d0\u4f9b\u4e86\u591a\u79cd\u65b9\u6cd5\uff0c\u6bd4\u5982\u4f7f\u7528numpy.array()<\/code>\u51fd\u6570\u6765\u521b\u5efa\u4e8c\u7ef4\u6570\u7ec4\uff0c\u4ece\u800c\u5b9e\u73b0\u77e9\u9635\u7684\u8868\u793a\u3002\u4f8b\u5982\uff1a<\/p>\n
import numpy as np\nmatrix = np.array([[1, 2], [3, 4]])\n<\/code><\/pre>\n
\u8fd9\u6bb5\u4ee3\u7801\u5c06\u521b\u5efa\u4e00\u4e2a2×2\u7684\u77e9\u9635\u3002<\/p>\n
\u5982\u4f55\u8ba1\u7b97\u77e9\u9635\u7684\u9006\uff1f<\/strong>
\u4f7f\u7528NumPy\u5e93\u8ba1\u7b97\u77e9\u9635\u7684\u9006\u662f\u975e\u5e38\u7b80\u5355\u7684\u3002\u53ef\u4ee5\u4f7f\u7528numpy.linalg.inv()<\/code>\u51fd\u6570\u6765\u5b9e\u73b0\u3002\u786e\u4fdd\u77e9\u9635\u662f\u53ef\u9006\u7684\uff08\u5373\u884c\u5217\u5f0f\u4e0d\u4e3a\u96f6\uff09\uff0c\u5426\u5219\u4f1a\u5f15\u53d1\u9519\u8bef\u3002\u4ee5\u4e0b\u662f\u4e00\u4e2a\u793a\u4f8b\uff1a<\/p>\n
inverse_matrix = np.linalg.inv(matrix)\n<\/code><\/pre>\n
\u8fd9\u4f1a\u8fd4\u56de\u539f\u59cb\u77e9\u9635\u7684\u9006\u3002<\/p>\n
\u77e9\u9635\u7684\u9006\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u6709\u54ea\u4e9b\u7528\u9014\uff1f<\/strong>
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