{"id":1157865,"date":"2025-01-13T18:33:47","date_gmt":"2025-01-13T10:33:47","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1157865.html"},"modified":"2025-01-13T18:33:49","modified_gmt":"2025-01-13T10:33:49","slug":"python%e9%ab%98%e6%96%af%e5%a6%82%e4%bd%95%e6%b6%88%e9%99%a4%e7%9f%a9%e9%98%b5","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/1157865.html","title":{"rendered":"python\u9ad8\u65af\u5982\u4f55\u6d88\u9664\u77e9\u9635"},"content":{"rendered":"

\"python\u9ad8\u65af\u5982\u4f55\u6d88\u9664\u77e9\u9635\"<\/p>\n

Python\u4e2d\u53ef\u4ee5\u4f7f\u7528\u9ad8\u65af\u6d88\u53bb\u6cd5\u6765\u6d88\u9664\u77e9\u9635\uff0c\u4ee5\u4fbf\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u3002<\/strong>\u3001\u9ad8\u65af\u6d88\u53bb\u6cd5\u5305\u62ec\u4e24\u4e2a\u4e3b\u8981\u6b65\u9aa4\uff1a\u524d\u5411\u6d88\u53bb\u548c\u56de\u4ee3<\/strong>\u3002\u4e0b\u9762\u5c06\u8be6\u7ec6\u4ecb\u7ecd\u5982\u4f55\u5728Python\u4e2d\u5b9e\u73b0\u9ad8\u65af\u6d88\u53bb\u6cd5\uff0c\u5e76\u6d88\u9664\u77e9\u9635\u3002<\/p>\n<\/p>\n

\u4e00\u3001\u524d\u5411\u6d88\u53bb<\/h3>\n<\/p>\n

\u524d\u5411\u6d88\u53bb\u7684\u76ee\u7684\u662f\u5c06\u77e9\u9635\u8f6c\u5316\u4e3a\u4e0a\u4e09\u89d2\u5f62\u77e9\u9635\u3002\u901a\u8fc7\u5bf9\u77e9\u9635\u8fdb\u884c\u884c\u53d8\u6362\uff0c\u4f7f\u5f97\u77e9\u9635\u7684\u4e0b\u4e09\u89d2\u90e8\u5206\u5143\u7d20\u5168\u90e8\u4e3a\u96f6\u3002<\/p>\n<\/p>\n

    \n
  1. \u9009\u62e9\u4e3b\u5143\uff1a<\/strong> \u5728\u6bcf\u4e00\u5217\u4e2d\u9009\u62e9\u7edd\u5bf9\u503c\u6700\u5927\u7684\u5143\u7d20\u4f5c\u4e3a\u4e3b\u5143\uff0c\u5e76\u5c06\u5176\u6240\u5728\u7684\u884c\u4e0e\u5f53\u524d\u884c\u4ea4\u6362\u3002<\/li>\n
  2. \u884c\u53d8\u6362\uff1a<\/strong> \u4f7f\u7528\u4e3b\u5143\u6240\u5728\u7684\u884c\u5bf9\u4e0b\u9762\u7684\u6240\u6709\u884c\u8fdb\u884c\u6d88\u53bb\u64cd\u4f5c\uff0c\u4f7f\u5f97\u5f53\u524d\u5217\u4ee5\u4e0b\u7684\u5143\u7d20\u5168\u90e8\u4e3a\u96f6\u3002<\/li>\n<\/ol>\n

    \u4e8c\u3001\u56de\u4ee3<\/h3>\n<\/p>\n

    \u5728\u77e9\u9635\u88ab\u8f6c\u5316\u4e3a\u4e0a\u4e09\u89d2\u5f62\u77e9\u9635\u4e4b\u540e\uff0c\u901a\u8fc7\u56de\u4ee3\u8fc7\u7a0b\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u3002<\/p>\n<\/p>\n

      \n
    1. \u4ece\u6700\u540e\u4e00\u884c\u5f00\u59cb\uff1a<\/strong> \u4ece\u6700\u4e0b\u9762\u7684\u884c\u5f00\u59cb\uff0c\u9010\u6b65\u5411\u4e0a\u6c42\u89e3\u6bcf\u4e00\u4e2a\u672a\u77e5\u6570\u3002<\/li>\n
    2. \u4ee3\u5165\u6c42\u89e3\uff1a<\/strong> \u6bcf\u6c42\u89e3\u4e00\u4e2a\u672a\u77e5\u6570\uff0c\u5c06\u5176\u4ee3\u5165\u5230\u4e0a\u9762\u7684\u65b9\u7a0b\u4e2d\uff0c\u7ee7\u7eed\u6c42\u89e3\u4e0a\u4e00\u4e2a\u672a\u77e5\u6570\u3002<\/li>\n<\/ol>\n

      \u5b9e\u73b0\u9ad8\u65af\u6d88\u53bb\u6cd5\u7684Python\u4ee3\u7801\u793a\u4f8b<\/h3>\n<\/p>\n

      import numpy as np<\/p>\n
      def gaussian_elimination(A, b):<\/p>\n
          n = len(b)<\/p>\n
          # Augment the matrix A with the vector b<\/p>\n
          Ab = np.hstack([A, b.reshape(-1, 1)])<\/p>\n
          for i in range(n):<\/p>\n
              # Pivoting: find the maximum element in the current column<\/p>\n
              max_row = np.argmax(np.abs(Ab[i:, i])) + i<\/p>\n
              if Ab[max_row, i] == 0:<\/p>\n
                  rAI<\/a>se ValueError("Matrix is singular or nearly singular")<\/p>\n
              # Swap the current row with the row of the maximum element<\/p>\n
              Ab[[i, max_row]] = Ab[[max_row, i]]<\/p>\n
              # Eliminate below the pivot<\/p>\n
              for j in range(i + 1, n):<\/p>\n
                  factor = Ab[j, i] \/ Ab[i, i]<\/p>\n
                  Ab[j, i:] -= factor * Ab[i, i:]<\/p>\n
          # Back substitution<\/p>\n
          x = np.zeros(n)<\/p>\n
          for i in range(n - 1, -1, -1):<\/p>\n
              x[i] = (Ab[i, -1] - np.dot(Ab[i, i + 1:n], x[i + 1:n])) \/ Ab[i, i]<\/p>\n
          return x<\/p>\n
      Example usage:<\/strong><\/h2>\n
      A = np.array([[3, 2, -4], [2, 3, 3], [5, -3, 1]], dtype=float)<\/p>\n
      b = np.array([3, 15, 14], dtype=float)<\/p>\n
      solution = gaussian_elimination(A, b)<\/p>\n
      print("Solution:", solution)<\/p>\n
      <\/code><\/pre>\n<\/p>\n
      \u4e09\u3001\u8be6\u7ec6\u89e3\u91ca<\/h3>\n<\/p>\n
      1\u3001\u9009\u62e9\u4e3b\u5143\u548c\u884c\u4ea4\u6362<\/h4>\n<\/p>\n
      \u9009\u62e9\u4e3b\u5143\u662f\u4e3a\u4e86\u51cf\u5c11\u6570\u503c\u8ba1\u7b97\u4e2d\u7684\u8bef\u5dee\u3002\u5728\u4ee3\u7801\u4e2d\uff0c\u901a\u8fc7np.argmax<\/code>\u51fd\u6570\u627e\u5230\u5f53\u524d\u5217\u4e2d\u7edd\u5bf9\u503c\u6700\u5927\u7684\u5143\u7d20\uff0c\u5e76\u5c06\u5176\u6240\u5728\u7684\u884c\u4e0e\u5f53\u524d\u884c\u4ea4\u6362\u3002\u8fd9\u6837\u53ef\u4ee5\u786e\u4fdd\u4e3b\u5143\u5c3d\u53ef\u80fd\u5927\uff0c\u51cf\u5c11\u8bef\u5dee\u3002<\/p>\n<\/p>\n
      2\u3001\u884c\u53d8\u6362<\/h4>\n<\/p>\n
      \u884c\u53d8\u6362\u7684\u76ee\u6807\u662f\u5c06\u5f53\u524d\u5217\u4ee5\u4e0b\u7684\u5143\u7d20\u53d8\u4e3a\u96f6\u3002\u901a\u8fc7\u8ba1\u7b97\u6d88\u53bb\u56e0\u5b50factor<\/code>\uff0c\u5e76\u7528\u4e3b\u5143\u6240\u5728\u884c\u7684\u500d\u6570\u51cf\u53bb\u5f53\u524d\u884c\uff0c\u5b9e\u73b0\u884c\u53d8\u6362\u3002\u8fd9\u6837\u5904\u7406\u4e4b\u540e\uff0c\u77e9\u9635\u7684\u4e0b\u4e09\u89d2\u90e8\u5206\u5c06\u9010\u6b65\u53d8\u4e3a\u96f6\u3002<\/p>\n<\/p>\n
      3\u3001\u56de\u4ee3\u6c42\u89e3<\/h4>\n<\/p>\n
      \u5728\u77e9\u9635\u88ab\u8f6c\u5316\u4e3a\u4e0a\u4e09\u89d2\u5f62\u77e9\u9635\u4e4b\u540e\uff0c\u53ef\u4ee5\u4ece\u6700\u540e\u4e00\u884c\u5f00\u59cb\uff0c\u9010\u6b65\u5411\u4e0a\u6c42\u89e3\u6bcf\u4e00\u4e2a\u672a\u77e5\u6570\u3002\u901a\u8fc7\u4ee3\u5165\u5df2\u77e5\u7684\u89e3\uff0c\u7ee7\u7eed\u6c42\u89e3\u4e0a\u4e00\u4e2a\u672a\u77e5\u6570\uff0c\u6700\u7ec8\u5f97\u5230\u6574\u4e2a\u65b9\u7a0b\u7ec4\u7684\u89e3\u3002<\/p>\n<\/p>\n
      \u56db\u3001\u6539\u8fdb\u548c\u4f18\u5316<\/h3>\n<\/p>\n
      1\u3001\u5904\u7406\u5947\u5f02\u77e9\u9635<\/h4>\n<\/p>\n
      \u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u77e9\u9635\u53ef\u80fd\u662f\u5947\u5f02\u7684\uff08\u5373\u884c\u5217\u5f0f\u4e3a\u96f6\uff09\uff0c\u8fd9\u4f1a\u5bfc\u81f4\u9ad8\u65af\u6d88\u53bb\u6cd5\u65e0\u6cd5\u8fdb\u884c\u3002\u53ef\u4ee5\u5728\u9009\u62e9\u4e3b\u5143\u65f6\u68c0\u67e5\u77e9\u9635\u7684\u5947\u5f02\u6027\uff0c\u5e76\u8fdb\u884c\u9002\u5f53\u5904\u7406\u3002<\/p>\n<\/p>\n
      2\u3001\u6570\u503c\u7a33\u5b9a\u6027<\/h4>\n<\/p>\n
      \u4e3a\u4e86\u63d0\u9ad8\u6570\u503c\u7a33\u5b9a\u6027\uff0c\u53ef\u4ee5\u5728\u9009\u62e9\u4e3b\u5143\u65f6\u8003\u8651\u5217\u4e3b\u5143\u9009\u62e9\u6cd5\uff0c\u907f\u514d\u6570\u503c\u8ba1\u7b97\u4e2d\u7684\u8bef\u5dee\u79ef\u7d2f\u3002<\/p>\n<\/p>\n
      3\u3001\u7a00\u758f\u77e9\u9635<\/h4>\n<\/p>\n
      \u5bf9\u4e8e\u5927\u578b\u7a00\u758f\u77e9\u9635\uff0c\u53ef\u4ee5\u4f7f\u7528\u7a00\u758f\u77e9\u9635\u7684\u7279\u6b8a\u7b97\u6cd5\uff0c\u5982\u8d85\u8282\u70b9\u9ad8\u65af\u6d88\u53bb\u6cd5\uff0c\u4ee5\u63d0\u9ad8\u8ba1\u7b97\u6548\u7387\u3002<\/p>\n<\/p>\n
      \u4e94\u3001\u5e94\u7528\u5b9e\u4f8b<\/h3>\n<\/p>\n
      1\u3001\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4<\/h4>\n<\/p>\n
      \u9ad8\u65af\u6d88\u53bb\u6cd5\u662f\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u5e38\u7528\u65b9\u6cd5\uff0c\u5e7f\u6cdb\u5e94\u7528\u4e8e\u5de5\u7a0b\u8ba1\u7b97\u548c\u79d1\u5b66\u7814\u7a76\u4e2d\u3002\u4f8b\u5982\uff0c\u5728\u7535\u8def\u5206\u6790\u4e2d\uff0c\u4f7f\u7528\u9ad8\u65af\u6d88\u53bb\u6cd5\u53ef\u4ee5\u6c42\u89e3\u7535\u8def\u4e2d\u7684\u7535\u538b\u548c\u7535\u6d41\u5206\u5e03\u3002<\/p>\n<\/p>\n
      2\u3001\u77e9\u9635\u6c42\u9006<\/h4>\n<\/p>\n
      \u9ad8\u65af\u6d88\u53bb\u6cd5\u4e5f\u53ef\u4ee5\u7528\u4e8e\u77e9\u9635\u6c42\u9006\u3002\u901a\u8fc7\u5c06\u5355\u4f4d\u77e9\u9635\u9644\u52a0\u5230\u539f\u77e9\u9635\u4e0a\uff0c\u5bf9\u5176\u8fdb\u884c\u9ad8\u65af\u6d88\u53bb\uff0c\u6700\u7ec8\u5f97\u5230\u9006\u77e9\u9635\u3002<\/p>\n<\/p>\n
      3\u3001\u6700\u5c0f\u4e8c\u4e58\u6cd5<\/h4>\n<\/p>\n
      \u5728\u6570\u636e\u62df\u5408\u548c\u56de\u5f52\u5206\u6790\u4e2d\uff0c\u9ad8\u65af\u6d88\u53bb\u6cd5\u53ef\u4ee5\u7528\u4e8e\u6c42\u89e3\u6700\u5c0f\u4e8c\u4e58\u6cd5\u95ee\u9898\u3002\u4f8b\u5982\uff0c\u5728\u591a\u9879\u5f0f\u62df\u5408\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528\u9ad8\u65af\u6d88\u53bb\u6cd5\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\uff0c\u5f97\u5230\u62df\u5408\u591a\u9879\u5f0f\u7684\u7cfb\u6570\u3002<\/p>\n<\/p>\n
      \u516d\u3001\u4ee3\u7801\u4f18\u5316<\/h3>\n<\/p>\n
      \u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u53ef\u4ee5\u5bf9\u9ad8\u65af\u6d88\u53bb\u6cd5\u7684\u4ee3\u7801\u8fdb\u884c\u4f18\u5316\uff0c\u4ee5\u63d0\u9ad8\u8ba1\u7b97\u6548\u7387\u548c\u7a33\u5b9a\u6027\u3002\u4f8b\u5982\uff0c\u53ef\u4ee5\u4f7f\u7528\u77e9\u9635\u5206\u5757\u65b9\u6cd5\uff0c\u5c06\u5927\u77e9\u9635\u5206\u89e3\u4e3a\u591a\u4e2a\u5c0f\u77e9\u9635\uff0c\u63d0\u9ad8\u8ba1\u7b97\u6548\u7387\u3002<\/p>\n<\/p>\n
      \u4e03\u3001\u5e76\u884c\u8ba1\u7b97<\/h3>\n<\/p>\n
      \u5bf9\u4e8e\u5927\u578b\u77e9\u9635\uff0c\u53ef\u4ee5\u8003\u8651\u4f7f\u7528\u5e76\u884c\u8ba1\u7b97\u6280\u672f\uff0c\u63d0\u9ad8\u8ba1\u7b97\u6548\u7387\u3002\u4f8b\u5982\uff0c\u53ef\u4ee5\u4f7f\u7528MPI\u6216OpenMP\u8fdb\u884c\u5e76\u884c\u5316\u5904\u7406\uff0c\u5c06\u5927\u77e9\u9635\u5206\u89e3\u4e3a\u591a\u4e2a\u5b50\u77e9\u9635\uff0c\u5206\u522b\u8fdb\u884c\u9ad8\u65af\u6d88\u53bb\u64cd\u4f5c\uff0c\u6700\u540e\u5408\u5e76\u7ed3\u679c\u3002<\/p>\n<\/p>\n
      \u516b\u3001\u5e93\u51fd\u6570<\/h3>\n<\/p>\n
      \u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528Python\u7684\u79d1\u5b66\u8ba1\u7b97\u5e93\uff0c\u5982NumPy\u548cSciPy\uff0c\u7b80\u5316\u9ad8\u65af\u6d88\u53bb\u6cd5\u7684\u5b9e\u73b0\u3002\u4f8b\u5982\uff0cNumPy\u5e93\u63d0\u4f9b\u4e86numpy.linalg.solve<\/code>\u51fd\u6570\uff0c\u53ef\u4ee5\u76f4\u63a5\u7528\u4e8e\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u3002<\/p>\n<\/p>\n
      import numpy as np<\/p>\n
      A = np.array([[3, 2, -4], [2, 3, 3], [5, -3, 1]], dtype=float)<\/p>\n
      b = np.array([3, 15, 14], dtype=float)<\/p>\n
      solution = np.linalg.solve(A, b)<\/p>\n
      print("Solution:", solution)<\/p>\n
      <\/code><\/pre>\n<\/p>\n
      \u4f7f\u7528\u5e93\u51fd\u6570\u53ef\u4ee5\u5927\u5927\u7b80\u5316\u4ee3\u7801\uff0c\u63d0\u9ad8\u5f00\u53d1\u6548\u7387\uff0c\u540c\u65f6\u4fdd\u8bc1\u8ba1\u7b97\u7684\u51c6\u786e\u6027\u548c\u7a33\u5b9a\u6027\u3002<\/p>\n<\/p>\n
      \u4e5d\u3001\u6848\u4f8b\u5206\u6790<\/h3>\n<\/p>\n
      1\u3001\u7535\u8def\u5206\u6790<\/h4>\n<\/p>\n
      \u5728\u7535\u8def\u5206\u6790\u4e2d\uff0c\u4f7f\u7528\u9ad8\u65af\u6d88\u53bb\u6cd5\u53ef\u4ee5\u6c42\u89e3\u7535\u8def\u4e2d\u7684\u7535\u538b\u548c\u7535\u6d41\u5206\u5e03\u3002\u4f8b\u5982\uff0c\u5728\u4e00\u4e2a\u590d\u6742\u7535\u8def\u4e2d\uff0c\u4f7f\u7528\u9ad8\u65af\u6d88\u53bb\u6cd5\u53ef\u4ee5\u5feb\u901f\u6c42\u89e3\u5404\u4e2a\u8282\u70b9\u7684\u7535\u538b\uff0c\u8fdb\u800c\u8ba1\u7b97\u7535\u6d41\u548c\u529f\u7387\u5206\u5e03\u3002<\/p>\n<\/p>\n
      2\u3001\u7ed3\u6784\u5206\u6790<\/h4>\n<\/p>\n
      \u5728\u7ed3\u6784\u5206\u6790\u4e2d\uff0c\u4f7f\u7528\u9ad8\u65af\u6d88\u53bb\u6cd5\u53ef\u4ee5\u6c42\u89e3\u7ed3\u6784\u7684\u4f4d\u79fb\u548c\u5e94\u529b\u5206\u5e03\u3002\u4f8b\u5982\uff0c\u5728\u6709\u9650\u5143\u5206\u6790\u4e2d\uff0c\u4f7f\u7528\u9ad8\u65af\u6d88\u53bb\u6cd5\u53ef\u4ee5\u6c42\u89e3\u7ed3\u6784\u7684\u4f4d\u79fb\u573a\uff0c\u8fdb\u800c\u8ba1\u7b97\u5e94\u529b\u548c\u53d8\u5f62\u3002<\/p>\n<\/p>\n
      3\u3001\u6570\u636e\u62df\u5408<\/h4>\n<\/p>\n
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