{"id":1097315,"date":"2025-01-08T15:10:41","date_gmt":"2025-01-08T07:10:41","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1097315.html"},"modified":"2025-01-08T15:10:45","modified_gmt":"2025-01-08T07:10:45","slug":"%e5%a6%82%e4%bd%95%e7%94%a8python%e6%b1%82%e8%a7%a3%e6%96%b9%e7%a8%8b%e7%bb%84-3","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/1097315.html","title":{"rendered":"\u5982\u4f55\u7528python\u6c42\u89e3\u65b9\u7a0b\u7ec4"},"content":{"rendered":"<p style=\"text-align:center;\" ><img decoding=\"async\" src=\"https:\/\/cdn-kb.worktile.com\/kb\/wp-content\/uploads\/2024\/04\/24212135\/50fbc82f-1548-469d-968c-be9f55a86e6a.webp\" alt=\"\u5982\u4f55\u7528python\u6c42\u89e3\u65b9\u7a0b\u7ec4\" \/><\/p>\n<p><p> <strong>\u7528Python\u6c42\u89e3\u65b9\u7a0b\u7ec4\u7684\u65b9\u6cd5\u6709\u5f88\u591a\uff0c\u5305\u62ec\u4f7f\u7528numpy\u5e93\u3001scipy\u5e93\u548csympy\u5e93\uff0c\u6700\u5e38\u7528\u7684\u65b9\u6cd5\u6709\uff1a\u6570\u503c\u89e3\u6cd5\u3001\u7b26\u53f7\u89e3\u6cd5\u3001\u7ebf\u6027\u65b9\u7a0b\u7ec4\u6c42\u89e3\u3002<\/strong>\u5176\u4e2d\uff0c<strong>\u4f7f\u7528numpy\u5e93\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4<\/strong>\u662f\u6700\u7b80\u5355\u548c\u9ad8\u6548\u7684\u3002\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u51e0\u79cd\u65b9\u6cd5\u6765\u6c42\u89e3\u65b9\u7a0b\u7ec4\u3002<\/p>\n<\/p>\n<p><p>\u4e00\u3001\u4f7f\u7528numpy\u5e93\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4<\/p>\n<\/p>\n<p><p>Numpy\u662f\u4e00\u4e2a\u5f3a\u5927\u7684\u6570\u503c\u8ba1\u7b97\u5e93\uff0c\u5b83\u63d0\u4f9b\u4e86\u4e00\u4e2a\u51fd\u6570<code>numpy.linalg.solve<\/code>\u4e13\u95e8\u7528\u4e8e\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u3002\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u4e2a\u7ebf\u6027\u65b9\u7a0b\u7ec4Ax = B\uff0c\u5176\u4e2dA\u662f\u7cfb\u6570\u77e9\u9635\uff0cB\u662f\u5e38\u6570\u9879\u5411\u91cf\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import numpy as np<\/p>\n<h2><strong>\u5b9a\u4e49\u7cfb\u6570\u77e9\u9635A\u548c\u5e38\u6570\u9879\u5411\u91cfB<\/strong><\/h2>\n<p>A = np.array([[3, 1], [1, 2]])<\/p>\n<p>B = np.array([9, 8])<\/p>\n<h2><strong>\u4f7f\u7528numpy.linalg.solve\u6c42\u89e3\u65b9\u7a0b\u7ec4<\/strong><\/h2>\n<p>solution = np.linalg.solve(A, B)<\/p>\n<p>print(&quot;Solution:&quot;, solution)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u7cfb\u6570\u77e9\u9635A\u662f\u4e00\u4e2a2&#215;2\u77e9\u9635\uff0c\u5e38\u6570\u9879\u5411\u91cfB\u662f\u4e00\u4e2a\u957f\u5ea6\u4e3a2\u7684\u5411\u91cf\u3002\u901a\u8fc7\u8c03\u7528<code>np.linalg.solve<\/code>\u51fd\u6570\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u65b9\u7a0b\u7ec4\u7684\u89e3\u3002<\/p>\n<\/p>\n<p><p><strong>\u7ec6\u8282\u63cf\u8ff0\uff1a<\/strong> <code>numpy.linalg.solve<\/code>\u51fd\u6570\u5185\u90e8\u4f7f\u7528\u7684\u662fLU\u5206\u89e3\u7b97\u6cd5\uff0c\u8fd9\u662f\u4e00\u79cd\u7a33\u5b9a\u4e14\u9ad8\u6548\u7684\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u65b9\u6cd5\u3002LU\u5206\u89e3\u5c06\u77e9\u9635A\u5206\u89e3\u4e3a\u4e00\u4e2a\u4e0b\u4e09\u89d2\u77e9\u9635L\u548c\u4e00\u4e2a\u4e0a\u4e09\u89d2\u77e9\u9635U\uff0c\u7136\u540e\u901a\u8fc7\u524d\u5411\u548c\u540e\u5411\u4ee3\u6570\u6c42\u89e3\u65b9\u7a0b\u7ec4\u3002\u8fd9\u79cd\u65b9\u6cd5\u5728\u8ba1\u7b97\u590d\u6742\u5ea6\u548c\u6570\u503c\u7a33\u5b9a\u6027\u65b9\u9762\u90fd\u8868\u73b0\u826f\u597d\u3002<\/p>\n<\/p>\n<p><p>\u4e8c\u3001\u4f7f\u7528scipy\u5e93\u6c42\u89e3\u7ebf\u6027\u548c\u975e\u7ebf\u6027\u65b9\u7a0b\u7ec4<\/p>\n<\/p>\n<p><p>Scipy\u5e93\u662f\u53e6\u4e00\u4e2a\u5e38\u7528\u7684\u79d1\u5b66\u8ba1\u7b97\u5e93\uff0c\u5b83\u63d0\u4f9b\u4e86\u66f4\u591a\u9ad8\u7ea7\u7684\u6570\u503c\u89e3\u6cd5\u3002\u5bf9\u4e8e\u7ebf\u6027\u65b9\u7a0b\u7ec4\uff0c<code>scipy.linalg.solve<\/code>\u51fd\u6570\u4e0e<code>numpy.linalg.solve<\/code>\u7c7b\u4f3c\uff0c\u4f46\u5b83\u652f\u6301\u66f4\u591a\u7684\u9009\u9879\u548c\u529f\u80fd\u3002\u5bf9\u4e8e\u975e\u7ebf\u6027\u65b9\u7a0b\u7ec4\uff0c<code>scipy.optimize.fsolve<\/code>\u51fd\u6570\u975e\u5e38\u6709\u7528\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">from scipy.linalg import solve<\/p>\n<p>import numpy as np<\/p>\n<h2><strong>\u5b9a\u4e49\u7cfb\u6570\u77e9\u9635A\u548c\u5e38\u6570\u9879\u5411\u91cfB<\/strong><\/h2>\n<p>A = np.array([[3, 1], [1, 2]])<\/p>\n<p>B = np.array([9, 8])<\/p>\n<h2><strong>\u4f7f\u7528scipy.linalg.solve\u6c42\u89e3\u65b9\u7a0b\u7ec4<\/strong><\/h2>\n<p>solution = solve(A, B)<\/p>\n<p>print(&quot;Solution:&quot;, solution)<\/p>\n<p>from scipy.optimize import fsolve<\/p>\n<h2><strong>\u5b9a\u4e49\u975e\u7ebf\u6027\u65b9\u7a0b\u7ec4<\/strong><\/h2>\n<p>def equations(vars):<\/p>\n<p>    x, y = vars<\/p>\n<p>    eq1 = x&lt;strong&gt;2 + y&lt;\/strong&gt;2 - 1<\/p>\n<p>    eq2 = x2 - y<\/p>\n<p>    return [eq1, eq2]<\/p>\n<h2><strong>\u4f7f\u7528scipy.optimize.fsolve\u6c42\u89e3\u65b9\u7a0b\u7ec4<\/strong><\/h2>\n<p>solution = fsolve(equations, [1, 1])<\/p>\n<p>print(&quot;Solution:&quot;, solution)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u9996\u5148\u4f7f\u7528<code>scipy.linalg.solve<\/code>\u51fd\u6570\u6765\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\uff0c\u7136\u540e\u4f7f\u7528<code>scipy.optimize.fsolve<\/code>\u51fd\u6570\u6765\u6c42\u89e3\u4e00\u4e2a\u7b80\u5355\u7684\u975e\u7ebf\u6027\u65b9\u7a0b\u7ec4\u3002<code>fsolve<\/code>\u51fd\u6570\u4f7f\u7528\u7684\u662f\u4e00\u79cd\u57fa\u4e8e\u725b\u987f\u6cd5\u7684\u8fed\u4ee3\u7b97\u6cd5\uff0c\u5b83\u9700\u8981\u4e00\u4e2a\u521d\u59cb\u731c\u6d4b\u503c\uff0c\u5e76\u5c1d\u8bd5\u627e\u5230\u4f7f\u5f97\u6240\u6709\u65b9\u7a0b\u4e3a\u96f6\u7684\u89e3\u3002<\/p>\n<\/p>\n<p><p>\u4e09\u3001\u4f7f\u7528sympy\u5e93\u8fdb\u884c\u7b26\u53f7\u8ba1\u7b97<\/p>\n<\/p>\n<p><p>Sympy\u5e93\u662f\u4e00\u4e2a\u7b26\u53f7\u8ba1\u7b97\u5e93\uff0c\u5b83\u53ef\u4ee5\u7528\u6765\u8fdb\u884c\u7cbe\u786e\u7684\u4ee3\u6570\u8fd0\u7b97\u3002\u4f7f\u7528sympy\u5e93\uff0c\u6211\u4eec\u53ef\u4ee5\u6c42\u89e3\u7ebf\u6027\u548c\u975e\u7ebf\u6027\u65b9\u7a0b\u7ec4\uff0c\u5e76\u5f97\u5230\u7b26\u53f7\u89e3\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">from sympy import symbols, Eq, solve<\/p>\n<h2><strong>\u5b9a\u4e49\u7b26\u53f7\u53d8\u91cf<\/strong><\/h2>\n<p>x, y = symbols(&#39;x y&#39;)<\/p>\n<h2><strong>\u5b9a\u4e49\u65b9\u7a0b<\/strong><\/h2>\n<p>eq1 = Eq(3*x + y, 9)<\/p>\n<p>eq2 = Eq(x + 2*y, 8)<\/p>\n<h2><strong>\u4f7f\u7528sympy.solve\u6c42\u89e3\u65b9\u7a0b\u7ec4<\/strong><\/h2>\n<p>solution = solve((eq1, eq2), (x, y))<\/p>\n<p>print(&quot;Solution:&quot;, solution)<\/p>\n<h2><strong>\u5b9a\u4e49\u975e\u7ebf\u6027\u65b9\u7a0b\u7ec4<\/strong><\/h2>\n<p>eq1 = Eq(x&lt;strong&gt;2 + y&lt;\/strong&gt;2, 1)<\/p>\n<p>eq2 = Eq(x2 - y, 0)<\/p>\n<h2><strong>\u4f7f\u7528sympy.solve\u6c42\u89e3\u65b9\u7a0b\u7ec4<\/strong><\/h2>\n<p>solution = solve((eq1, eq2), (x, y))<\/p>\n<p>print(&quot;Solution:&quot;, solution)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u9996\u5148\u4f7f\u7528<code>sympy.symbols<\/code>\u51fd\u6570\u5b9a\u4e49\u7b26\u53f7\u53d8\u91cf\uff0c\u7136\u540e\u4f7f\u7528<code>sympy.Eq<\/code>\u51fd\u6570\u5b9a\u4e49\u65b9\u7a0b\u3002\u901a\u8fc7\u8c03\u7528<code>sympy.solve<\/code>\u51fd\u6570\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u65b9\u7a0b\u7ec4\u7684\u7b26\u53f7\u89e3\u3002\u5bf9\u4e8e\u7ebf\u6027\u65b9\u7a0b\u7ec4\uff0csympy\u5e93\u4f1a\u4f7f\u7528\u9ad8\u65af\u6d88\u5143\u6cd5\u6765\u6c42\u89e3\u3002\u5bf9\u4e8e\u975e\u7ebf\u6027\u65b9\u7a0b\u7ec4\uff0csympy\u5e93\u4f1a\u5c1d\u8bd5\u4f7f\u7528\u5404\u79cd\u4ee3\u6570\u65b9\u6cd5\u6765\u627e\u5230\u89e3\u3002<\/p>\n<\/p>\n<p><p>\u56db\u3001\u4f7f\u7528\u77e9\u9635\u5206\u89e3\u6cd5\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4<\/p>\n<\/p>\n<p><p>\u9664\u4e86\u76f4\u63a5\u4f7f\u7528\u6c42\u89e3\u51fd\u6570\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u901a\u8fc7\u77e9\u9635\u5206\u89e3\u7684\u65b9\u6cd5\u6765\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u3002\u5e38\u7528\u7684\u77e9\u9635\u5206\u89e3\u65b9\u6cd5\u5305\u62ecLU\u5206\u89e3\u3001QR\u5206\u89e3\u548cCholesky\u5206\u89e3\u3002<\/p>\n<\/p>\n<ol>\n<li>LU\u5206\u89e3\uff1a<\/li>\n<\/ol>\n<p><pre><code class=\"language-python\">import numpy as np<\/p>\n<p>from scipy.linalg import lu<\/p>\n<h2><strong>\u5b9a\u4e49\u7cfb\u6570\u77e9\u9635A\u548c\u5e38\u6570\u9879\u5411\u91cfB<\/strong><\/h2>\n<p>A = np.array([[3, 1], [1, 2]])<\/p>\n<p>B = np.array([9, 8])<\/p>\n<h2><strong>\u8fdb\u884cLU\u5206\u89e3<\/strong><\/h2>\n<p>P, L, U = lu(A)<\/p>\n<h2><strong>\u6c42\u89e3Ly = PB<\/strong><\/h2>\n<p>y = np.linalg.solve(L, np.dot(P, B))<\/p>\n<h2><strong>\u6c42\u89e3Ux = y<\/strong><\/h2>\n<p>x = np.linalg.solve(U, y)<\/p>\n<p>print(&quot;Solution:&quot;, x)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<ol start=\"2\">\n<li>QR\u5206\u89e3\uff1a<\/li>\n<\/ol>\n<p><pre><code class=\"language-python\">import numpy as np<\/p>\n<p>from scipy.linalg import qr<\/p>\n<h2><strong>\u5b9a\u4e49\u7cfb\u6570\u77e9\u9635A\u548c\u5e38\u6570\u9879\u5411\u91cfB<\/strong><\/h2>\n<p>A = np.array([[3, 1], [1, 2]])<\/p>\n<p>B = np.array([9, 8])<\/p>\n<h2><strong>\u8fdb\u884cQR\u5206\u89e3<\/strong><\/h2>\n<p>Q, R = qr(A)<\/p>\n<h2><strong>\u6c42\u89e3Q.T * B<\/strong><\/h2>\n<p>y = np.dot(Q.T, B)<\/p>\n<h2><strong>\u6c42\u89e3Rx = y<\/strong><\/h2>\n<p>x = np.linalg.solve(R, y)<\/p>\n<p>print(&quot;Solution:&quot;, x)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<ol start=\"3\">\n<li>Cholesky\u5206\u89e3\uff08\u9002\u7528\u4e8e\u6b63\u5b9a\u77e9\u9635\uff09\uff1a<\/li>\n<\/ol>\n<p><pre><code class=\"language-python\">import numpy as np<\/p>\n<p>from scipy.linalg import cholesky<\/p>\n<h2><strong>\u5b9a\u4e49\u7cfb\u6570\u77e9\u9635A\u548c\u5e38\u6570\u9879\u5411\u91cfB<\/strong><\/h2>\n<p>A = np.array([[3, 1], [1, 2]])<\/p>\n<p>B = np.array([9, 8])<\/p>\n<h2><strong>\u8fdb\u884cCholesky\u5206\u89e3<\/strong><\/h2>\n<p>L = cholesky(A, lower=True)<\/p>\n<h2><strong>\u6c42\u89e3Ly = B<\/strong><\/h2>\n<p>y = np.linalg.solve(L, B)<\/p>\n<h2><strong>\u6c42\u89e3L.T * x = y<\/strong><\/h2>\n<p>x = np.linalg.solve(L.T, y)<\/p>\n<p>print(&quot;Solution:&quot;, x)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u4e94\u3001\u4f7f\u7528\u8fed\u4ee3\u6cd5\u6c42\u89e3\u975e\u7ebf\u6027\u65b9\u7a0b\u7ec4<\/p>\n<\/p>\n<p><p>\u5bf9\u4e8e\u67d0\u4e9b\u590d\u6742\u7684\u975e\u7ebf\u6027\u65b9\u7a0b\u7ec4\uff0c\u76f4\u63a5\u6c42\u89e3\u53ef\u80fd\u975e\u5e38\u56f0\u96be\u3002\u6b64\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u8fed\u4ee3\u6cd5\u6765\u9010\u6b65\u903c\u8fd1\u65b9\u7a0b\u7ec4\u7684\u89e3\u3002\u5e38\u7528\u7684\u8fed\u4ee3\u6cd5\u5305\u62ec\u725b\u987f\u6cd5\u548c\u7b80\u5316\u725b\u987f\u6cd5\u3002<\/p>\n<\/p>\n<ol>\n<li>\u725b\u987f\u6cd5\uff1a<\/li>\n<\/ol>\n<p><pre><code class=\"language-python\">import numpy as np<\/p>\n<p>from scipy.optimize import fsolve<\/p>\n<h2><strong>\u5b9a\u4e49\u975e\u7ebf\u6027\u65b9\u7a0b\u7ec4<\/strong><\/h2>\n<p>def equations(vars):<\/p>\n<p>    x, y = vars<\/p>\n<p>    eq1 = x&lt;strong&gt;2 + y&lt;\/strong&gt;2 - 1<\/p>\n<p>    eq2 = x2 - y<\/p>\n<p>    return [eq1, eq2]<\/p>\n<h2><strong>\u521d\u59cb\u731c\u6d4b\u503c<\/strong><\/h2>\n<p>initial_guess = [1, 1]<\/p>\n<h2><strong>\u4f7f\u7528scipy.optimize.fsolve\u6c42\u89e3\u65b9\u7a0b\u7ec4<\/strong><\/h2>\n<p>solution = fsolve(equations, initial_guess)<\/p>\n<p>print(&quot;Solution:&quot;, solution)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<ol start=\"2\">\n<li>\u7b80\u5316\u725b\u987f\u6cd5\uff1a<\/li>\n<\/ol>\n<p><pre><code class=\"language-python\">import numpy as np<\/p>\n<h2><strong>\u5b9a\u4e49\u975e\u7ebf\u6027\u65b9\u7a0b\u7ec4<\/strong><\/h2>\n<p>def equations(vars):<\/p>\n<p>    x, y = vars<\/p>\n<p>    eq1 = x&lt;strong&gt;2 + y&lt;\/strong&gt;2 - 1<\/p>\n<p>    eq2 = x2 - y<\/p>\n<p>    return np.array([eq1, eq2])<\/p>\n<h2><strong>\u5b9a\u4e49\u96c5\u53ef\u6bd4\u77e9\u9635<\/strong><\/h2>\n<p>def jacobian(vars):<\/p>\n<p>    x, y = vars<\/p>\n<p>    return np.array([[2*x, 2*y], [2*x, -1]])<\/p>\n<h2><strong>\u521d\u59cb\u731c\u6d4b\u503c<\/strong><\/h2>\n<p>initial_guess = np.array([1, 1])<\/p>\n<p>tolerance = 1e-6<\/p>\n<p>max_iterations = 100<\/p>\n<h2><strong>\u7b80\u5316\u725b\u987f\u6cd5<\/strong><\/h2>\n<p>def simplified_newton(equations, jacobian, initial_guess, tolerance, max_iterations):<\/p>\n<p>    x = initial_guess<\/p>\n<p>    for i in range(max_iterations):<\/p>\n<p>        delta = np.linalg.solve(jacobian(x), -equations(x))<\/p>\n<p>        x = x + delta<\/p>\n<p>        if np.linalg.norm(delta) &lt; tolerance:<\/p>\n<p>            break<\/p>\n<p>    return x<\/p>\n<h2><strong>\u6c42\u89e3\u65b9\u7a0b\u7ec4<\/strong><\/h2>\n<p>solution = simplified_newton(equations, jacobian, initial_guess, tolerance, max_iterations)<\/p>\n<p>print(&quot;Solution:&quot;, solution)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p><strong>\u603b\u7ed3\uff1a<\/strong> \u4f7f\u7528Python\u6c42\u89e3\u65b9\u7a0b\u7ec4\u7684\u65b9\u6cd5\u6709\u5f88\u591a\uff0c\u9009\u62e9\u5408\u9002\u7684\u65b9\u6cd5\u53d6\u51b3\u4e8e\u65b9\u7a0b\u7ec4\u7684\u6027\u8d28\u548c\u8981\u6c42\u3002\u5bf9\u4e8e\u7ebf\u6027\u65b9\u7a0b\u7ec4\uff0c\u4f7f\u7528numpy\u5e93\u7684<code>np.linalg.solve<\/code>\u51fd\u6570\u662f\u6700\u7b80\u5355\u548c\u9ad8\u6548\u7684\u9009\u62e9\u3002\u5bf9\u4e8e\u975e\u7ebf\u6027\u65b9\u7a0b\u7ec4\uff0cscipy\u5e93\u63d0\u4f9b\u4e86\u5f3a\u5927\u7684<code>fsolve<\/code>\u51fd\u6570\uff0c\u53ef\u4ee5\u5904\u7406\u5927\u591a\u6570\u60c5\u51b5\u3002\u5bf9\u4e8e\u7b26\u53f7\u8ba1\u7b97\uff0csympy\u5e93\u662f\u4e00\u4e2a\u975e\u5e38\u6709\u7528\u7684\u5de5\u5177\u3002\u6b64\u5916\uff0c\u638c\u63e1\u77e9\u9635\u5206\u89e3\u6cd5\u548c\u8fed\u4ee3\u6cd5\u4e5f\u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u66f4\u7075\u6d3b\u5730\u89e3\u51b3\u590d\u6742\u7684\u65b9\u7a0b\u7ec4\u95ee\u9898\u3002<\/p>\n<\/p>\n<h2><strong>\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n<p> <strong>\u5982\u4f55\u4f7f\u7528Python\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\uff1f<\/strong><br \/>Python\u63d0\u4f9b\u4e86\u591a\u79cd\u65b9\u6cd5\u6765\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\uff0c\u5176\u4e2d\u6700\u5e38\u7528\u7684\u662f\u4f7f\u7528NumPy\u5e93\u3002\u60a8\u53ef\u4ee5\u4f7f\u7528<code>numpy.linalg.solve<\/code>\u51fd\u6570\uff0c\u8be5\u51fd\u6570\u63a5\u53d7\u7cfb\u6570\u77e9\u9635\u548c\u5e38\u6570\u5411\u91cf\u4f5c\u4e3a\u8f93\u5165\uff0c\u8fd4\u56de\u53d8\u91cf\u7684\u89e3\u3002\u4f8b\u5982\uff0c\u5bf9\u4e8e\u65b9\u7a0b\u7ec4Ax = b\uff0c\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u65b9\u5f0f\u5b9e\u73b0\uff1a<\/p>\n<pre><code class=\"language-python\">import numpy as np\n\nA = np.array([[3, 2], [1, 2]])\nb = np.array([5, 5])\nsolution = np.linalg.solve(A, b)\nprint(solution)\n<\/code><\/pre>\n<p>\u8fd9\u79cd\u65b9\u5f0f\u7b80\u5355\u4e14\u9ad8\u6548\uff0c\u9002\u5408\u89e3\u51b3\u89c4\u6a21\u8f83\u5c0f\u7684\u65b9\u7a0b\u7ec4\u3002<\/p>\n<p><strong>Python\u4e2d\u662f\u5426\u6709\u5176\u4ed6\u5e93\u53ef\u4ee5\u7528\u4e8e\u6c42\u89e3\u975e\u7ebf\u6027\u65b9\u7a0b\u7ec4\uff1f<\/strong><br \/>\u9664\u4e86NumPy\uff0cSciPy\u5e93\u4e5f\u63d0\u4f9b\u4e86\u6c42\u89e3\u975e\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u529f\u80fd\u3002\u4f7f\u7528<code>scipy.optimize.fsolve<\/code>\u53ef\u4ee5\u6c42\u89e3\u590d\u6742\u7684\u975e\u7ebf\u6027\u65b9\u7a0b\u7ec4\u3002\u60a8\u9700\u8981\u5b9a\u4e49\u4e00\u4e2a\u8fd4\u56de\u65b9\u7a0b\u7ec4\u6b8b\u5dee\u7684\u51fd\u6570\uff0c\u5e76\u5c06\u5176\u4f20\u9012\u7ed9<code>fsolve<\/code>\u3002\u793a\u4f8b\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n<pre><code class=\"language-python\">from scipy.optimize import fsolve\n\ndef equations(vars):\n    x, y = vars\n    return [x + y - 5, x * y - 6]\n\ninitial_guess = (1, 1)\nsolution = fsolve(equations, initial_guess)\nprint(solution)\n<\/code><\/pre>\n<p>\u8fd9\u79cd\u65b9\u6cd5\u9002\u7528\u4e8e\u9700\u8981\u5904\u7406\u975e\u7ebf\u6027\u65b9\u7a0b\u7684\u60c5\u51b5\u3002<\/p>\n<p><strong>\u5728\u4f7f\u7528Python\u6c42\u89e3\u65b9\u7a0b\u7ec4\u65f6\uff0c\u5982\u4f55\u5904\u7406\u65e0\u89e3\u6216\u591a\u89e3\u7684\u60c5\u51b5\uff1f<\/strong><br \/>\u5728\u6c42\u89e3\u65b9\u7a0b\u7ec4\u65f6\uff0c\u53ef\u80fd\u4f1a\u9047\u5230\u65e0\u89e3\u6216\u591a\u89e3\u7684\u60c5\u51b5\u3002\u4f7f\u7528NumPy\u7684<code>numpy.linalg.LinAlgError<\/code>\u5f02\u5e38\u53ef\u4ee5\u68c0\u6d4b\u8fd9\u4e9b\u60c5\u51b5\u3002\u5982\u679c\u60a8\u4f7f\u7528<code>numpy.linalg.solve<\/code>\uff0c\u5728\u77e9\u9635\u4e0d\u53ef\u9006\uff08\u5373\u884c\u5217\u5f0f\u4e3a\u96f6\uff09\u65f6\u4f1a\u5f15\u53d1\u6b64\u5f02\u5e38\u3002\u5bf9\u4e8e\u591a\u89e3\u7684\u60c5\u51b5\uff0c\u60a8\u53ef\u4ee5\u4f7f\u7528<code>numpy.linalg.pinv<\/code>\u6765\u83b7\u53d6\u4f2a\u9006\uff0c\u8fdb\u800c\u627e\u5230\u6700\u5c0f\u4e8c\u4e58\u89e3\u3002\u4f8b\u5982\uff1a<\/p>\n<pre><code class=\"language-python\">try:\n    solution = np.linalg.solve(A, b)\nexcept np.linalg.LinAlgError:\n    print(&quot;\u65b9\u7a0b\u7ec4\u65e0\u89e3\u6216\u6709\u65e0\u7a77\u591a\u89e3&quot;)\n    solution = np.linalg.pinv(A) @ b  # \u6700\u5c0f\u4e8c\u4e58\u89e3\n<\/code><\/pre>\n<p>\u8fd9\u6837\u7684\u5904\u7406\u65b9\u5f0f\u80fd\u591f\u66f4\u597d\u5730\u5e94\u5bf9\u590d\u6742\u7684\u65b9\u7a0b\u7ec4\u60c5\u51b5\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"\u7528Python\u6c42\u89e3\u65b9\u7a0b\u7ec4\u7684\u65b9\u6cd5\u6709\u5f88\u591a\uff0c\u5305\u62ec\u4f7f\u7528numpy\u5e93\u3001scipy\u5e93\u548csympy\u5e93\uff0c\u6700\u5e38\u7528\u7684\u65b9\u6cd5\u6709\uff1a\u6570\u503c\u89e3 [&hellip;]","protected":false},"author":3,"featured_media":1097332,"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\/1097315"}],"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=1097315"}],"version-history":[{"count":"1","href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1097315\/revisions"}],"predecessor-version":[{"id":1097333,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1097315\/revisions\/1097333"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/1097332"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=1097315"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=1097315"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=1097315"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}