{"id":1157816,"date":"2025-01-13T18:33:13","date_gmt":"2025-01-13T10:33:13","guid":{"rendered":""},"modified":"2025-01-13T18:33:16","modified_gmt":"2025-01-13T10:33:16","slug":"python%e5%a6%82%e4%bd%95%e5%88%a4%e6%96%ad%e7%9f%a9%e9%98%b5%e5%af%b9%e7%a7%b0","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/1157816.html","title":{"rendered":"python\u5982\u4f55\u5224\u65ad\u77e9\u9635\u5bf9\u79f0"},"content":{"rendered":"<p style=\"text-align:center;\" ><img decoding=\"async\" src=\"https:\/\/cdn-kb.worktile.com\/kb\/wp-content\/uploads\/2024\/04\/25195938\/acfb6dfc-b0e2-4295-a468-3b2753b16ef4.webp\" alt=\"python\u5982\u4f55\u5224\u65ad\u77e9\u9635\u5bf9\u79f0\" \/><\/p>\n<p><p> \u5728Python\u4e2d\uff0c\u5224\u65ad\u77e9\u9635\u662f\u5426\u5bf9\u79f0\u7684\u6838\u5fc3\u65b9\u6cd5\u662f<strong>\u68c0\u67e5\u77e9\u9635\u662f\u5426\u7b49\u4e8e\u5176\u8f6c\u7f6e\u77e9\u9635<\/strong>\u3002\u5177\u4f53\u65b9\u6cd5\u6709\u591a\u79cd\uff0c\u6bd4\u5982\u53ef\u4ee5\u4f7f\u7528Numpy\u5e93\u8fdb\u884c\u9ad8\u6548\u7684\u77e9\u9635\u8fd0\u7b97\uff0c\u624b\u52a8\u7f16\u5199\u4ee3\u7801\u8fdb\u884c\u5143\u7d20\u6bd4\u8f83\uff0c\u6216\u8005\u7ed3\u5408\u5176\u4ed6\u5e93\u5982SciPy\u8fdb\u884c\u66f4\u9ad8\u7ea7\u7684\u77e9\u9635\u64cd\u4f5c\u3002<strong>\u6700\u5e38\u7528\u7684\u65b9\u6cd5\u662f\u5229\u7528Numpy\u5e93\uff0c\u4f7f\u7528<code>numpy.allclose<\/code>\u51fd\u6570\u6bd4\u8f83\u77e9\u9635\u4e0e\u5176\u8f6c\u7f6e\u77e9\u9635\u7684\u5143\u7d20\u662f\u5426\u4e00\u81f4<\/strong>\u3002\u4e0b\u9762\u5c06\u8be6\u7ec6\u4ecb\u7ecd\u8fd9\u79cd\u65b9\u6cd5\uff0c\u5e76\u4ecb\u7ecd\u5176\u4ed6\u4e00\u4e9b\u65b9\u6cd5\u548c\u7ec6\u8282\u3002<\/p>\n<\/p>\n<p><h3>\u4e00\u3001\u4f7f\u7528Numpy\u5e93<\/h3>\n<\/p>\n<p><p>Numpy\u5e93\u662fPython\u4e2d\u5904\u7406\u77e9\u9635\u548c\u6570\u7ec4\u7684\u6807\u51c6\u5e93\uff0c\u5176\u63d0\u4f9b\u4e86\u65b9\u4fbf\u7684\u77e9\u9635\u8fd0\u7b97\u529f\u80fd\u3002<\/p>\n<\/p>\n<p><h4>1. \u5b89\u88c5Numpy<\/h4>\n<\/p>\n<p><p>\u9996\u5148\uff0c\u786e\u4fdd\u4f60\u5df2\u7ecf\u5b89\u88c5\u4e86Numpy\u5e93\u3002\u5982\u679c\u6ca1\u6709\u5b89\u88c5\uff0c\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u547d\u4ee4\u8fdb\u884c\u5b89\u88c5\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-bash\">pip install numpy<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><h4>2. \u4f7f\u7528Numpy\u5224\u65ad\u77e9\u9635\u5bf9\u79f0\u6027<\/h4>\n<\/p>\n<p><p>\u4e0b\u9762\u662f\u4e00\u4e2a\u4f7f\u7528Numpy\u5224\u65ad\u77e9\u9635\u662f\u5426\u5bf9\u79f0\u7684\u793a\u4f8b\u4ee3\u7801\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import numpy as np<\/p>\n<p>def is_symmetric(matrix):<\/p>\n<p>    return np.allclose(matrix, matrix.T)<\/p>\n<h2><strong>\u793a\u4f8b\u77e9\u9635<\/strong><\/h2>\n<p>matrix = np.array([[1, 2, 3],<\/p>\n<p>                   [2, 4, 5],<\/p>\n<p>                   [3, 5, 6]])<\/p>\n<p>print(is_symmetric(matrix))  # \u8f93\u51fa: True<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u4e0a\u8ff0\u4ee3\u7801\u4e2d\uff0c<code>np.allclose<\/code>\u51fd\u6570\u7528\u4e8e\u5224\u65ad\u4e24\u4e2a\u6570\u7ec4\u662f\u5426\u5728\u5143\u7d20\u7ea7\u522b\u4e0a\u76f8\u7b49\uff0c<code>matrix.T<\/code>\u662f\u77e9\u9635\u7684\u8f6c\u7f6e\u3002<\/p>\n<\/p>\n<p><h3>\u4e8c\u3001\u624b\u52a8\u6bd4\u8f83\u77e9\u9635\u5143\u7d20<\/h3>\n<\/p>\n<p><p>\u5982\u679c\u4e0d\u4f7f\u7528Numpy\u5e93\uff0c\u4e5f\u53ef\u4ee5\u624b\u52a8\u7f16\u5199\u4ee3\u7801\u6765\u9010\u5143\u7d20\u6bd4\u8f83\u77e9\u9635\u4e0e\u5176\u8f6c\u7f6e\u77e9\u9635\u3002\u8fd9\u4e2a\u65b9\u6cd5\u9002\u5408\u5bf9\u5c0f\u578b\u77e9\u9635\u8fdb\u884c\u64cd\u4f5c\u3002<\/p>\n<\/p>\n<p><h4>1. \u7f16\u5199\u51fd\u6570<\/h4>\n<\/p>\n<p><p>\u4e0b\u9762\u662f\u4e00\u4e2a\u624b\u52a8\u6bd4\u8f83\u77e9\u9635\u5143\u7d20\u7684\u793a\u4f8b\u4ee3\u7801\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">def is_symmetric(matrix):<\/p>\n<p>    rows = len(matrix)<\/p>\n<p>    for i in range(rows):<\/p>\n<p>        for j in range(i, rows):<\/p>\n<p>            if matrix[i][j] != matrix[j][i]:<\/p>\n<p>                return False<\/p>\n<p>    return True<\/p>\n<h2><strong>\u793a\u4f8b\u77e9\u9635<\/strong><\/h2>\n<p>matrix = [[1, 2, 3],<\/p>\n<p>          [2, 4, 5],<\/p>\n<p>          [3, 5, 6]]<\/p>\n<p>print(is_symmetric(matrix))  # \u8f93\u51fa: True<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u4e0a\u8ff0\u4ee3\u7801\u4e2d\uff0c\u5916\u5c42\u5faa\u73af\u904d\u5386\u77e9\u9635\u7684\u884c\uff0c\u5185\u5c42\u5faa\u73af\u4ece\u5f53\u524d\u884c\u7684\u5bf9\u89d2\u5143\u7d20\u5f00\u59cb\u904d\u5386\uff0c\u6bd4\u8f83\u5bf9\u79f0\u4f4d\u7f6e\u7684\u5143\u7d20\u662f\u5426\u76f8\u7b49\u3002<\/p>\n<\/p>\n<p><h3>\u4e09\u3001\u4f7f\u7528SciPy\u5e93<\/h3>\n<\/p>\n<p><p>SciPy\u5e93\u63d0\u4f9b\u4e86\u66f4\u591a\u9ad8\u7ea7\u7684\u77e9\u9635\u64cd\u4f5c\u529f\u80fd\uff0c\u53ef\u4ee5\u7528\u6765\u5904\u7406\u66f4\u590d\u6742\u7684\u77e9\u9635\u5224\u65ad\u3002<\/p>\n<\/p>\n<p><h4>1. \u5b89\u88c5SciPy<\/h4>\n<\/p>\n<p><p>\u9996\u5148\uff0c\u786e\u4fdd\u4f60\u5df2\u7ecf\u5b89\u88c5\u4e86SciPy\u5e93\u3002\u5982\u679c\u6ca1\u6709\u5b89\u88c5\uff0c\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u547d\u4ee4\u8fdb\u884c\u5b89\u88c5\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-bash\">pip install scipy<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><h4>2. \u4f7f\u7528SciPy\u5224\u65ad\u77e9\u9635\u5bf9\u79f0\u6027<\/h4>\n<\/p>\n<p><p>\u4e0b\u9762\u662f\u4e00\u4e2a\u4f7f\u7528SciPy\u5224\u65ad\u77e9\u9635\u662f\u5426\u5bf9\u79f0\u7684\u793a\u4f8b\u4ee3\u7801\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">from scipy.linalg import issymmetric<\/p>\n<p>import numpy as np<\/p>\n<h2><strong>\u793a\u4f8b\u77e9\u9635<\/strong><\/h2>\n<p>matrix = np.array([[1, 2, 3],<\/p>\n<p>                   [2, 4, 5],<\/p>\n<p>                   [3, 5, 6]])<\/p>\n<p>print(issymmetric(matrix))  # \u8f93\u51fa: True<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u4e0a\u8ff0\u4ee3\u7801\u4e2d\uff0c<code>issymmetric<\/code>\u51fd\u6570\u53ef\u4ee5\u76f4\u63a5\u5224\u65ad\u77e9\u9635\u662f\u5426\u5bf9\u79f0\u3002<\/p>\n<\/p>\n<p><h3>\u56db\u3001\u5224\u65ad\u77e9\u9635\u5bf9\u79f0\u6027\u7684\u5e94\u7528\u573a\u666f<\/h3>\n<\/p>\n<p><p>\u5224\u65ad\u77e9\u9635\u662f\u5426\u5bf9\u79f0\u6709\u8bb8\u591a\u5b9e\u9645\u5e94\u7528\u573a\u666f\uff0c\u6bd4\u5982\uff1a<\/p>\n<\/p>\n<p><h4>1. \u56fe\u8bba\u4e2d\u7684\u5bf9\u79f0\u6027\u5224\u65ad<\/h4>\n<\/p>\n<p><p>\u5728\u56fe\u8bba\u4e2d\uff0c\u90bb\u63a5\u77e9\u9635\u662f\u5426\u5bf9\u79f0\u53ef\u4ee5\u5224\u65ad\u56fe\u662f\u5426\u662f\u65e0\u5411\u56fe\u3002\u65e0\u5411\u56fe\u7684\u90bb\u63a5\u77e9\u9635\u662f\u5bf9\u79f0\u7684\u3002<\/p>\n<\/p>\n<p><h4>2. \u7ebf\u6027\u4ee3\u6570\u4e2d\u7684\u7279\u5f81\u503c\u95ee\u9898<\/h4>\n<\/p>\n<p><p>\u5728\u7ebf\u6027\u4ee3\u6570\u4e2d\uff0c\u5bf9\u79f0\u77e9\u9635\u5177\u6709\u8bb8\u591a\u4f18\u826f\u6027\u8d28\uff0c\u6bd4\u5982\u5176\u7279\u5f81\u503c\u90fd\u662f\u5b9e\u6570\uff0c\u8fd9\u5728\u6570\u503c\u8ba1\u7b97\u4e2d\u975e\u5e38\u91cd\u8981\u3002<\/p>\n<\/p>\n<p><h4>3. \u7269\u7406\u5b66\u4e2d\u7684\u5bf9\u79f0\u6027<\/h4>\n<\/p>\n<p><p>\u5728\u7269\u7406\u5b66\u4e2d\uff0c\u5bf9\u79f0\u77e9\u9635\u53ef\u4ee5\u63cf\u8ff0\u8bb8\u591a\u5bf9\u79f0\u6027\u95ee\u9898\uff0c\u6bd4\u5982\u5206\u5b50\u7ed3\u6784\u7684\u5bf9\u79f0\u6027\u3002<\/p>\n<\/p>\n<p><h3>\u4e94\u3001\u66f4\u591aNumpy\u51fd\u6570\u7684\u4f7f\u7528<\/h3>\n<\/p>\n<p><p>Numpy\u5e93\u63d0\u4f9b\u4e86\u8bb8\u591a\u4fbf\u6377\u7684\u51fd\u6570\u6765\u5904\u7406\u77e9\u9635\u548c\u6570\u7ec4\uff0c\u8fd9\u91cc\u4ecb\u7ecd\u4e00\u4e9b\u5e38\u7528\u7684\u51fd\u6570\uff1a<\/p>\n<\/p>\n<p><h4>1. <code>numpy.all<\/code><\/h4>\n<\/p>\n<p><p>\u5224\u65ad\u6570\u7ec4\u4e2d\u7684\u6240\u6709\u5143\u7d20\u662f\u5426\u90fd\u4e3aTrue\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import numpy as np<\/p>\n<p>a = np.array([1, 2, 3, 4])<\/p>\n<p>print(np.all(a))  # \u8f93\u51fa: True<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><h4>2. <code>numpy.any<\/code><\/h4>\n<\/p>\n<p><p>\u5224\u65ad\u6570\u7ec4\u4e2d\u7684\u4efb\u610f\u4e00\u4e2a\u5143\u7d20\u662f\u5426\u4e3aTrue\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import numpy as np<\/p>\n<p>a = np.array([0, 0, 0, 4])<\/p>\n<p>print(np.any(a))  # \u8f93\u51fa: True<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><h4>3. <code>numpy.zeros<\/code><\/h4>\n<\/p>\n<p><p>\u521b\u5efa\u4e00\u4e2a\u5168\u96f6\u6570\u7ec4\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import numpy as np<\/p>\n<p>a = np.zeros((3, 3))<\/p>\n<p>print(a)<\/p>\n<h2><strong>\u8f93\u51fa:<\/strong><\/h2>\n<h2><strong>[[0. 0. 0.]<\/strong><\/h2>\n<h2><strong> [0. 0. 0.]<\/strong><\/h2>\n<h2><strong> [0. 0. 0.]]<\/strong><\/h2>\n<p><\/code><\/pre>\n<\/p>\n<p><h4>4. <code>numpy.ones<\/code><\/h4>\n<\/p>\n<p><p>\u521b\u5efa\u4e00\u4e2a\u5168\u4e00\u6570\u7ec4\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import numpy as np<\/p>\n<p>a = np.ones((3, 3))<\/p>\n<p>print(a)<\/p>\n<h2><strong>\u8f93\u51fa:<\/strong><\/h2>\n<h2><strong>[[1. 1. 1.]<\/strong><\/h2>\n<h2><strong> [1. 1. 1.]<\/strong><\/h2>\n<h2><strong> [1. 1. 1.]]<\/strong><\/h2>\n<p><\/code><\/pre>\n<\/p>\n<p><h4>5. <code>numpy.eye<\/code><\/h4>\n<\/p>\n<p><p>\u521b\u5efa\u4e00\u4e2a\u5355\u4f4d\u77e9\u9635\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import numpy as np<\/p>\n<p>a = np.eye(3)<\/p>\n<p>print(a)<\/p>\n<h2><strong>\u8f93\u51fa:<\/strong><\/h2>\n<h2><strong>[[1. 0. 0.]<\/strong><\/h2>\n<h2><strong> [0. 1. 0.]<\/strong><\/h2>\n<h2><strong> [0. 0. 1.]]<\/strong><\/h2>\n<p><\/code><\/pre>\n<\/p>\n<p><h3>\u516d\u3001\u77e9\u9635\u5bf9\u79f0\u6027\u7684\u8fdb\u4e00\u6b65\u63a2\u8ba8<\/h3>\n<\/p>\n<p><p>\u5bf9\u79f0\u77e9\u9635\u5728\u6570\u5b66\u548c\u5de5\u7a0b\u9886\u57df\u5177\u6709\u91cd\u8981\u7684\u5e94\u7528\u4ef7\u503c\u3002\u5bf9\u79f0\u77e9\u9635\u7684\u7279\u6027\u53ef\u4ee5\u7528\u6765\u7b80\u5316\u8ba1\u7b97\uff0c\u63d0\u9ad8\u7b97\u6cd5\u6548\u7387\u3002\u4ee5\u4e0b\u662f\u4e00\u4e9b\u6df1\u5165\u63a2\u8ba8\uff1a<\/p>\n<\/p>\n<p><h4>1. \u5bf9\u79f0\u77e9\u9635\u7684\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf<\/h4>\n<\/p>\n<p><p>\u5bf9\u79f0\u77e9\u9635\u7684\u7279\u5f81\u503c\u603b\u662f\u5b9e\u6570\uff0c\u5176\u7279\u5f81\u5411\u91cf\u53ef\u4ee5\u6b63\u4ea4\u5316\u3002\u5bf9\u4e8e\u4e00\u4e2a\u5bf9\u79f0\u77e9\u9635A\uff0c\u5b58\u5728\u4e00\u4e2a\u6b63\u4ea4\u77e9\u9635Q\uff0c\u4f7f\u5f97\uff1a<\/p>\n<\/p>\n<p><p>[ A = Q \\Lambda Q^T ]<\/p>\n<\/p>\n<p><p>\u5176\u4e2d\uff0c(\\Lambda)\u662f\u4e00\u4e2a\u5bf9\u89d2\u77e9\u9635\uff0c\u5305\u542b\u4e86A\u7684\u7279\u5f81\u503c\uff0cQ\u7684\u5217\u662fA\u7684\u7279\u5f81\u5411\u91cf\u3002<\/p>\n<\/p>\n<p><h4>2. \u5bf9\u79f0\u77e9\u9635\u7684\u5206\u89e3<\/h4>\n<\/p>\n<p><p>\u5bf9\u79f0\u77e9\u9635\u53ef\u4ee5\u8fdb\u884c\u8bb8\u591a\u6709\u7528\u7684\u5206\u89e3\uff0c\u6bd4\u5982Cholesky\u5206\u89e3\u3001LU\u5206\u89e3\u7b49\u3002\u8fd9\u4e9b\u5206\u89e3\u5728\u6570\u503c\u7ebf\u6027\u4ee3\u6570\u4e2d\u8d77\u5230\u91cd\u8981\u4f5c\u7528\u3002<\/p>\n<\/p>\n<p><h4>3. \u6b63\u5b9a\u77e9\u9635<\/h4>\n<\/p>\n<p><p>\u5bf9\u79f0\u77e9\u9635\u7684\u4e00\u79cd\u91cd\u8981\u7c7b\u578b\u662f\u6b63\u5b9a\u77e9\u9635\u3002\u5bf9\u4e8e\u4e00\u4e2a\u6b63\u5b9a\u77e9\u9635A\uff0c\u6240\u6709\u7279\u5f81\u503c\u90fd\u662f\u6b63\u6570\uff0c\u4e14\u5bf9\u4e8e\u4efb\u610f\u975e\u96f6\u5411\u91cfx\uff0c\u6709\uff1a<\/p>\n<\/p>\n<p><p>[ x^T A x &gt; 0 ]<\/p>\n<\/p>\n<p><p>\u6b63\u5b9a\u77e9\u9635\u5728\u4f18\u5316\u95ee\u9898\u4e2d\u5177\u6709\u91cd\u8981\u5e94\u7528\uff0c\u6bd4\u5982\u5728\u4e8c\u6b21\u89c4\u5212\u4e2d\u3002<\/p>\n<\/p>\n<p><h3>\u4e03\u3001Python\u4e2d\u77e9\u9635\u64cd\u4f5c\u7684\u6700\u4f73\u5b9e\u8df5<\/h3>\n<\/p>\n<p><p>\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u5408\u7406\u4f7f\u7528Python\u5e93\u8fdb\u884c\u77e9\u9635\u64cd\u4f5c\u53ef\u4ee5\u663e\u8457\u63d0\u9ad8\u5de5\u4f5c\u6548\u7387\u3002\u4ee5\u4e0b\u662f\u4e00\u4e9b\u6700\u4f73\u5b9e\u8df5\uff1a<\/p>\n<\/p>\n<p><h4>1. \u4f7f\u7528Numpy\u8fdb\u884c\u9ad8\u6548\u77e9\u9635\u8fd0\u7b97<\/h4>\n<\/p>\n<p><p>Numpy\u5e93\u63d0\u4f9b\u4e86\u9ad8\u6548\u7684\u77e9\u9635\u8fd0\u7b97\u529f\u80fd\uff0c\u907f\u514d\u624b\u52a8\u7f16\u5199\u590d\u6742\u7684\u77e9\u9635\u64cd\u4f5c\u4ee3\u7801\u3002<\/p>\n<\/p>\n<p><h4>2. \u5229\u7528SciPy\u8fdb\u884c\u9ad8\u7ea7\u77e9\u9635\u64cd\u4f5c<\/h4>\n<\/p>\n<p><p>\u5bf9\u4e8e\u590d\u6742\u7684\u77e9\u9635\u64cd\u4f5c\uff0cSciPy\u5e93\u63d0\u4f9b\u4e86\u66f4\u591a\u9ad8\u7ea7\u529f\u80fd\uff0c\u6bd4\u5982\u7a00\u758f\u77e9\u9635\u8fd0\u7b97\u3001\u77e9\u9635\u5206\u89e3\u7b49\u3002<\/p>\n<\/p>\n<p><h4>3. \u7ed3\u5408Matplotlib\u8fdb\u884c\u53ef\u89c6\u5316<\/h4>\n<\/p>\n<p><p>\u7ed3\u5408Matplotlib\u5e93\uff0c\u53ef\u4ee5\u5bf9\u77e9\u9635\u8fdb\u884c\u53ef\u89c6\u5316\u5c55\u793a\uff0c\u6709\u52a9\u4e8e\u7406\u89e3\u77e9\u9635\u7684\u7ed3\u6784\u548c\u6027\u8d28\u3002<\/p>\n<\/p>\n<p><h4>4. \u8003\u8651\u6570\u503c\u7a33\u5b9a\u6027<\/h4>\n<\/p>\n<p><p>\u5728\u8fdb\u884c\u77e9\u9635\u8fd0\u7b97\u65f6\uff0c\u9700\u8981\u8003\u8651\u6570\u503c\u7a33\u5b9a\u6027\u95ee\u9898\uff0c\u907f\u514d\u7531\u4e8e\u6570\u503c\u8bef\u5dee\u5f15\u8d77\u7684\u8ba1\u7b97\u9519\u8bef\u3002<\/p>\n<\/p>\n<p><h3>\u516b\u3001\u603b\u7ed3<\/h3>\n<\/p>\n<p><p>\u672c\u6587\u8be6\u7ec6\u4ecb\u7ecd\u4e86\u5982\u4f55\u5728Python\u4e2d\u5224\u65ad\u77e9\u9635\u662f\u5426\u5bf9\u79f0\uff0c\u5305\u62ec\u4f7f\u7528Numpy\u5e93\u3001\u624b\u52a8\u6bd4\u8f83\u77e9\u9635\u5143\u7d20\u3001\u4f7f\u7528SciPy\u5e93\u7b49\u65b9\u6cd5\u3002\u5bf9\u79f0\u77e9\u9635\u5728\u6570\u5b66\u548c\u5de5\u7a0b\u9886\u57df\u5177\u6709\u91cd\u8981\u5e94\u7528\uff0c\u5176\u7279\u6027\u53ef\u4ee5\u7528\u6765\u7b80\u5316\u8ba1\u7b97\u3001\u63d0\u9ad8\u7b97\u6cd5\u6548\u7387\u3002\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u5408\u7406\u4f7f\u7528Python\u5e93\u8fdb\u884c\u77e9\u9635\u64cd\u4f5c\u53ef\u4ee5\u663e\u8457\u63d0\u9ad8\u5de5\u4f5c\u6548\u7387\uff0c\u540c\u65f6\u9700\u8981\u8003\u8651\u6570\u503c\u7a33\u5b9a\u6027\u95ee\u9898\u3002\u7ed3\u5408\u672c\u6587\u4ecb\u7ecd\u7684\u65b9\u6cd5\u548c\u6700\u4f73\u5b9e\u8df5\uff0c\u76f8\u4fe1\u4f60\u53ef\u4ee5\u5728\u5b9e\u9645\u5de5\u4f5c\u4e2d\u9ad8\u6548\u5730\u5904\u7406\u77e9\u9635\u5bf9\u79f0\u6027\u95ee\u9898\u3002<\/p>\n<\/p>\n<h2><strong>\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n<p> <strong>\u5982\u4f55\u5728Python\u4e2d\u68c0\u67e5\u4e00\u4e2a\u77e9\u9635\u662f\u5426\u4e3a\u5bf9\u79f0\u77e9\u9635\uff1f<\/strong><br \/>\u5728Python\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528NumPy\u5e93\u6765\u5224\u65ad\u4e00\u4e2a\u77e9\u9635\u662f\u5426\u4e3a\u5bf9\u79f0\u77e9\u9635\u3002\u5bf9\u79f0\u77e9\u9635\u7684\u5b9a\u4e49\u662f\u5b83\u7684\u8f6c\u7f6e\u77e9\u9635\u7b49\u4e8e\u5b83\u672c\u8eab\u3002\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u4ee3\u7801\u5b9e\u73b0\uff1a  <\/p>\n<pre><code class=\"language-python\">import numpy as np\n\ndef is_symmetric(matrix):\n    return np.array_equal(matrix, matrix.T)\n\n# \u793a\u4f8b\nmatrix = np.array([[1, 2, 3],\n                   [2, 4, 5],\n                   [3, 5, 6]])\nprint(is_symmetric(matrix))  # \u8f93\u51fa: True\n<\/code><\/pre>\n<p>\u8fd9\u4e2a\u51fd\u6570\u5c06\u8fd4\u56deTrue\u6216False\uff0c\u8868\u793a\u77e9\u9635\u662f\u5426\u5bf9\u79f0\u3002<\/p>\n<p><strong>\u4f7f\u7528Pandas\u5e93\u662f\u5426\u53ef\u4ee5\u5224\u65ad\u77e9\u9635\u7684\u5bf9\u79f0\u6027\uff1f<\/strong><br \/>\u5f53\u7136\u53ef\u4ee5\uff0cPandas\u5e93\u4e5f\u63d0\u4f9b\u4e86\u4fbf\u6377\u7684\u65b9\u6cd5\u6765\u5904\u7406\u6570\u636e\u3002\u60a8\u53ef\u4ee5\u5c06\u77e9\u9635\u8f6c\u6362\u4e3aDataFrame\u5bf9\u8c61\uff0c\u7136\u540e\u4f7f\u7528\u76f8\u540c\u7684\u903b\u8f91\u6765\u68c0\u67e5\u5bf9\u79f0\u6027\u3002\u793a\u4f8b\u5982\u4e0b\uff1a  <\/p>\n<pre><code class=\"language-python\">import pandas as pd\n\ndef is_symmetric_df(matrix):\n    df = pd.DataFrame(matrix)\n    return df.equals(df.T)\n\n# \u793a\u4f8b\nmatrix = [[1, 2, 3],\n          [2, 4, 5],\n          [3, 5, 6]]\nprint(is_symmetric_df(matrix))  # \u8f93\u51fa: True\n<\/code><\/pre>\n<p>\u8fd9\u79cd\u65b9\u6cd5\u540c\u6837\u53ef\u4ee5\u5224\u65ad\u77e9\u9635\u662f\u5426\u5bf9\u79f0\u3002<\/p>\n<p><strong>\u5982\u4f55\u5904\u7406\u975e\u65b9\u9635\u7684\u60c5\u51b5\uff1f<\/strong><br \/>\u975e\u65b9\u9635\uff08\u884c\u6570\u4e0e\u5217\u6570\u4e0d\u76f8\u7b49\u7684\u77e9\u9635\uff09\u65e0\u6cd5\u662f\u5bf9\u79f0\u77e9\u9635\uff0c\u56e0\u6b64\u5728\u68c0\u67e5\u5bf9\u79f0\u6027\u4e4b\u524d\uff0c\u60a8\u5e94\u5148\u786e\u8ba4\u77e9\u9635\u662f\u5426\u4e3a\u65b9\u9635\u3002\u53ef\u4ee5\u5728\u68c0\u67e5\u524d\u6dfb\u52a0\u4e00\u4e2a\u6761\u4ef6\u5224\u65ad\uff1a  <\/p>\n<pre><code class=\"language-python\">def is_symmetric(matrix):\n    if matrix.shape[0] != matrix.shape[1]:\n        return False\n    return np.array_equal(matrix, matrix.T)\n<\/code><\/pre>\n<p>\u8fd9\u79cd\u65b9\u5f0f\u786e\u4fdd\u53ea\u6709\u5728\u77e9\u9635\u4e3a\u65b9\u9635\u65f6\u624d\u4f1a\u8fdb\u884c\u5bf9\u79f0\u6027\u68c0\u67e5\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"\u5728Python\u4e2d\uff0c\u5224\u65ad\u77e9\u9635\u662f\u5426\u5bf9\u79f0\u7684\u6838\u5fc3\u65b9\u6cd5\u662f\u68c0\u67e5\u77e9\u9635\u662f\u5426\u7b49\u4e8e\u5176\u8f6c\u7f6e\u77e9\u9635\u3002\u5177\u4f53\u65b9\u6cd5\u6709\u591a\u79cd\uff0c\u6bd4\u5982\u53ef\u4ee5\u4f7f\u7528Nump [&hellip;]","protected":false},"author":3,"featured_media":1157820,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[37],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1157816"}],"collection":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/comments?post=1157816"}],"version-history":[{"count":"1","href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1157816\/revisions"}],"predecessor-version":[{"id":1157823,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1157816\/revisions\/1157823"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/1157820"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=1157816"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=1157816"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=1157816"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}