{"id":953337,"date":"2024-12-27T01:42:35","date_gmt":"2024-12-26T17:42:35","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/953337.html"},"modified":"2024-12-27T01:42:38","modified_gmt":"2024-12-26T17:42:38","slug":"%e5%a6%82%e4%bd%95%e7%94%a8python%e5%ae%9e%e7%8e%b0%e7%a7%af%e5%88%86","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/953337.html","title":{"rendered":"\u5982\u4f55\u7528python\u5b9e\u73b0\u79ef\u5206"},"content":{"rendered":"<p style=\"text-align:center;\" ><img decoding=\"async\" src=\"https:\/\/cdn-kb.worktile.com\/kb\/wp-content\/uploads\/2024\/04\/25090846\/0fcd1d89-c05d-4ce0-a9ac-769554e4e843.webp\" alt=\"\u5982\u4f55\u7528python\u5b9e\u73b0\u79ef\u5206\" \/><\/p>\n<p><p> <strong>\u5728Python\u4e2d\u5b9e\u73b0\u79ef\u5206\u7684\u65b9\u6cd5\u6709\u591a\u79cd\uff0c\u4e3b\u8981\u5305\u62ec\u4f7f\u7528SciPy\u5e93\u4e2d\u7684<code>quad<\/code>\u51fd\u6570\u3001SymPy\u5e93\u4e2d\u7684\u7b26\u53f7\u79ef\u5206\u3001\u4ee5\u53caNumPy\u5e93\u7684\u6570\u503c\u79ef\u5206\u3002\u8fd9\u4e9b\u65b9\u6cd5\u5404\u6709\u4f18\u7f3a\u70b9\uff0c\u9002\u7528\u4e8e\u4e0d\u540c\u7684\u573a\u666f\u3002\u5bf9\u4e8e\u9700\u8981\u9ad8\u7cbe\u5ea6\u548c\u7b26\u53f7\u8ba1\u7b97\u7684\u573a\u666f\uff0cSymPy\u662f\u4e00\u4e2a\u4e0d\u9519\u7684\u9009\u62e9\uff1b\u800c\u5bf9\u4e8e\u9700\u8981\u5feb\u901f\u6570\u503c\u8ba1\u7b97\u7684\u573a\u666f\uff0cSciPy\u548cNumPy\u5219\u662f\u66f4\u4e3a\u9ad8\u6548\u7684\u5de5\u5177\u3002<\/strong><\/p>\n<\/p>\n<p><p>Python\u4f5c\u4e3a\u4e00\u79cd\u5f3a\u5927\u7684\u7f16\u7a0b\u8bed\u8a00\uff0c\u5728\u79d1\u5b66\u8ba1\u7b97\u9886\u57df\u6709\u7740\u5e7f\u6cdb\u7684\u5e94\u7528\u3002\u79ef\u5206\u4f5c\u4e3a\u6570\u5b66\u548c\u7269\u7406\u5b66\u4e2d\u91cd\u8981\u7684\u6982\u5ff5\uff0cPython\u63d0\u4f9b\u4e86\u591a\u79cd\u5b9e\u73b0\u65b9\u5f0f\u3002\u4e0b\u9762\u5c06\u8be6\u7ec6\u4ecb\u7ecd\u5982\u4f55\u7528Python\u5b9e\u73b0\u79ef\u5206\u3002<\/p>\n<\/p>\n<p><p>\u4e00\u3001\u4f7f\u7528SCIPY\u5e93\u8fdb\u884c\u79ef\u5206<\/p>\n<\/p>\n<p><p>SciPy\u662f\u4e00\u4e2a\u57fa\u4e8eNumPy\u7684\u79d1\u5b66\u8ba1\u7b97\u5e93\uff0c\u63d0\u4f9b\u4e86\u8bb8\u591a\u7528\u4e8e\u79ef\u5206\u7684\u51fd\u6570\u3002\u5176\u4e2d\uff0c<code>scipy.integrate<\/code>\u6a21\u5757\u63d0\u4f9b\u4e86\u591a\u79cd\u6570\u503c\u79ef\u5206\u7684\u65b9\u6cd5\u3002<\/p>\n<\/p>\n<p><h3>1. \u4f7f\u7528quad\u51fd\u6570<\/h3>\n<\/p>\n<p><p><code>quad<\/code>\u51fd\u6570\u662fSciPy\u4e2d\u6700\u5e38\u7528\u7684\u79ef\u5206\u51fd\u6570\u4e4b\u4e00\uff0c\u9002\u7528\u4e8e\u8ba1\u7b97\u5b9a\u79ef\u5206\u3002\u5b83\u4f7f\u7528\u81ea\u9002\u5e94\u9ad8\u65af\u6c42\u79ef\u6cd5\u6765\u8fdb\u884c\u6570\u503c\u79ef\u5206\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">from scipy.integrate import quad<\/p>\n<h2><strong>\u5b9a\u4e49\u88ab\u79ef\u51fd\u6570<\/strong><\/h2>\n<p>def integrand(x):<\/p>\n<p>    return x2<\/p>\n<h2><strong>\u8ba1\u7b97\u79ef\u5206<\/strong><\/h2>\n<p>result, error = quad(integrand, 0, 1)<\/p>\n<p>print(f&quot;\u79ef\u5206\u7ed3\u679c: {result}, \u8bef\u5dee: {error}&quot;)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u4e0a\u9762\u7684\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u8ba1\u7b97\u4e86\u51fd\u6570 (x^2) \u5728\u533a\u95f4 ([0, 1]) \u4e0a\u7684\u5b9a\u79ef\u5206\u3002<code>quad<\/code>\u51fd\u6570\u8fd4\u56de\u4e24\u4e2a\u503c\uff1a\u79ef\u5206\u7ed3\u679c\u548c\u4f30\u8ba1\u8bef\u5dee\u3002<\/p>\n<\/p>\n<p><h3>2. \u4f7f\u7528dblquad\u548ctplquad\u51fd\u6570<\/h3>\n<\/p>\n<p><p>\u5bf9\u4e8e\u591a\u91cd\u79ef\u5206\uff0cSciPy\u63d0\u4f9b\u4e86<code>dblquad<\/code>\u548c<code>tplquad<\/code>\u51fd\u6570\uff0c\u5206\u522b\u7528\u4e8e\u8ba1\u7b97\u4e8c\u91cd\u79ef\u5206\u548c\u4e09\u91cd\u79ef\u5206\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">from scipy.integrate import dblquad<\/p>\n<h2><strong>\u5b9a\u4e49\u88ab\u79ef\u51fd\u6570<\/strong><\/h2>\n<p>def integrand(x, y):<\/p>\n<p>    return x * y<\/p>\n<h2><strong>\u8ba1\u7b97\u4e8c\u91cd\u79ef\u5206<\/strong><\/h2>\n<p>result, error = dblquad(integrand, 0, 1, lambda x: 0, lambda x: 1)<\/p>\n<p>print(f&quot;\u4e8c\u91cd\u79ef\u5206\u7ed3\u679c: {result}, \u8bef\u5dee: {error}&quot;)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u8ba1\u7b97\u4e86\u51fd\u6570 (xy) \u5728\u533a\u57df ([0, 1] \\times [0, 1]) \u4e0a\u7684\u4e8c\u91cd\u79ef\u5206\u3002<\/p>\n<\/p>\n<p><p>\u4e8c\u3001\u4f7f\u7528SYMPY\u5e93\u8fdb\u884c\u7b26\u53f7\u79ef\u5206<\/p>\n<\/p>\n<p><p>SymPy\u662f\u4e00\u4e2aPython\u7684\u7b26\u53f7\u6570\u5b66\u5e93\uff0c\u53ef\u4ee5\u7528\u4e8e\u7b26\u53f7\u8ba1\u7b97\uff0c\u5305\u62ec\u7b26\u53f7\u79ef\u5206\u3002\u5b83\u7279\u522b\u9002\u7528\u4e8e\u9700\u8981\u89e3\u6790\u89e3\u7684\u60c5\u51b5\u3002<\/p>\n<\/p>\n<p><h3>1. \u8ba1\u7b97\u4e0d\u5b9a\u79ef\u5206<\/h3>\n<\/p>\n<p><p>\u4e0d\u5b9a\u79ef\u5206\u662f\u6307\u6ca1\u6709\u79ef\u5206\u9650\u7684\u79ef\u5206\uff0cSymPy\u53ef\u4ee5\u7528\u4e8e\u8ba1\u7b97\u4e0d\u5b9a\u79ef\u5206\u7684\u89e3\u6790\u89e3\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">from sympy import symbols, integrate<\/p>\n<h2><strong>\u5b9a\u4e49\u7b26\u53f7\u53d8\u91cf<\/strong><\/h2>\n<p>x = symbols(&#39;x&#39;)<\/p>\n<h2><strong>\u8ba1\u7b97\u4e0d\u5b9a\u79ef\u5206<\/strong><\/h2>\n<p>integral = integrate(x2, x)<\/p>\n<p>print(f&quot;\u4e0d\u5b9a\u79ef\u5206\u7ed3\u679c: {integral}&quot;)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u8ba1\u7b97\u4e86\u51fd\u6570 (x^2) \u7684\u4e0d\u5b9a\u79ef\u5206\uff0c\u7ed3\u679c\u4e3a (\\frac{x^3}{3})\u3002<\/p>\n<\/p>\n<p><h3>2. \u8ba1\u7b97\u5b9a\u79ef\u5206<\/h3>\n<\/p>\n<p><p>SymPy\u4e5f\u53ef\u4ee5\u7528\u4e8e\u8ba1\u7b97\u5b9a\u79ef\u5206\uff0c\u7ed3\u679c\u4e3a\u89e3\u6790\u89e3\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\"># \u8ba1\u7b97\u5b9a\u79ef\u5206<\/p>\n<p>definite_integral = integrate(x2, (x, 0, 1))<\/p>\n<p>print(f&quot;\u5b9a\u79ef\u5206\u7ed3\u679c: {definite_integral}&quot;)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u8ba1\u7b97\u4e86\u51fd\u6570 (x^2) \u5728\u533a\u95f4 ([0, 1]) \u4e0a\u7684\u5b9a\u79ef\u5206\uff0c\u7ed3\u679c\u4e3a (\\frac{1}{3})\u3002<\/p>\n<\/p>\n<p><p>\u4e09\u3001\u4f7f\u7528NUMPY\u5e93\u8fdb\u884c\u6570\u503c\u79ef\u5206<\/p>\n<\/p>\n<p><p>\u867d\u7136NumPy\u6ca1\u6709\u4e13\u95e8\u7684\u79ef\u5206\u51fd\u6570\uff0c\u4f46\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528NumPy\u7684\u6570\u7ec4\u8fd0\u7b97\u6765\u5b9e\u73b0\u7b80\u5355\u7684\u6570\u503c\u79ef\u5206\u3002<\/p>\n<\/p>\n<p><h3>1. \u4f7f\u7528\u68af\u5f62\u6cd5\u5219<\/h3>\n<\/p>\n<p><p>\u68af\u5f62\u6cd5\u5219\u662f\u4e00\u79cd\u7b80\u5355\u7684\u6570\u503c\u79ef\u5206\u65b9\u6cd5\uff0c\u901a\u8fc7\u5c06\u51fd\u6570\u66f2\u7ebf\u5206\u5272\u6210\u68af\u5f62\u6765\u8ba1\u7b97\u79ef\u5206\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import numpy as np<\/p>\n<h2><strong>\u5b9a\u4e49\u81ea\u53d8\u91cf\u548c\u88ab\u79ef\u51fd\u6570<\/strong><\/h2>\n<p>x = np.linspace(0, 1, 100)<\/p>\n<p>y = x2<\/p>\n<h2><strong>\u4f7f\u7528\u68af\u5f62\u6cd5\u5219\u8ba1\u7b97\u79ef\u5206<\/strong><\/h2>\n<p>integral = np.trapz(y, x)<\/p>\n<p>print(f&quot;\u68af\u5f62\u6cd5\u5219\u79ef\u5206\u7ed3\u679c: {integral}&quot;)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528\u68af\u5f62\u6cd5\u5219\u8ba1\u7b97\u4e86\u51fd\u6570 (x^2) \u5728\u533a\u95f4 ([0, 1]) \u4e0a\u7684\u5b9a\u79ef\u5206\u3002<\/p>\n<\/p>\n<p><h3>2. \u4f7f\u7528\u8f9b\u666e\u68ee\u6cd5\u5219<\/h3>\n<\/p>\n<p><p>\u8f9b\u666e\u68ee\u6cd5\u5219\u662f\u4e00\u79cd\u66f4\u7cbe\u786e\u7684\u6570\u503c\u79ef\u5206\u65b9\u6cd5\uff0c\u9002\u7528\u4e8e\u66f4\u590d\u6742\u7684\u51fd\u6570\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">from scipy.integrate import simps<\/p>\n<h2><strong>\u4f7f\u7528\u8f9b\u666e\u68ee\u6cd5\u5219\u8ba1\u7b97\u79ef\u5206<\/strong><\/h2>\n<p>integral_simps = simps(y, x)<\/p>\n<p>print(f&quot;\u8f9b\u666e\u68ee\u6cd5\u5219\u79ef\u5206\u7ed3\u679c: {integral_simps}&quot;)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528\u8f9b\u666e\u68ee\u6cd5\u5219\u8ba1\u7b97\u4e86\u540c\u6837\u7684\u79ef\u5206\u3002<\/p>\n<\/p>\n<p><p>\u56db\u3001\u79ef\u5206\u5728\u5b9e\u9645\u4e2d\u7684\u5e94\u7528<\/p>\n<\/p>\n<p><p>\u79ef\u5206\u5728\u5b9e\u9645\u4e2d\u7684\u5e94\u7528\u975e\u5e38\u5e7f\u6cdb\uff0c\u4ee5\u4e0b\u662f\u51e0\u4e2a\u5e38\u89c1\u7684\u5e94\u7528\u573a\u666f\u3002<\/p>\n<\/p>\n<p><h3>1. \u7269\u7406\u5b66\u4e2d\u7684\u5e94\u7528<\/h3>\n<\/p>\n<p><p>\u79ef\u5206\u5728\u7269\u7406\u5b66\u4e2d\u7528\u4e8e\u8ba1\u7b97\u9762\u79ef\u3001\u4f53\u79ef\u3001\u8d28\u91cf\u4e2d\u5fc3\u3001\u52a8\u91cf\u7b49\u3002\u4f8b\u5982\uff0c\u5728\u8ba1\u7b97\u7269\u4f53\u7684\u91cd\u5fc3\u65f6\uff0c\u9700\u8981\u5bf9\u7269\u4f53\u8fdb\u884c\u79ef\u5206\u3002<\/p>\n<\/p>\n<p><h3>2. \u5de5\u7a0b\u4e2d\u7684\u5e94\u7528<\/h3>\n<\/p>\n<p><p>\u5728\u5de5\u7a0b\u4e2d\uff0c\u79ef\u5206\u7528\u4e8e\u4fe1\u53f7\u5904\u7406\u3001\u6ee4\u6ce2\u5668\u8bbe\u8ba1\u3001\u63a7\u5236\u7cfb\u7edf\u5206\u6790\u7b49\u3002\u4f8b\u5982\uff0c\u5728\u7535\u8def\u5206\u6790\u4e2d\uff0c\u79ef\u5206\u7528\u4e8e\u8ba1\u7b97\u7535\u6d41\u548c\u7535\u538b\u7684\u77ac\u6001\u54cd\u5e94\u3002<\/p>\n<\/p>\n<p><h3>3. \u7ecf\u6d4e\u5b66\u4e2d\u7684\u5e94\u7528<\/h3>\n<\/p>\n<p><p>\u5728\u7ecf\u6d4e\u5b66\u4e2d\uff0c\u79ef\u5206\u7528\u4e8e\u8ba1\u7b97\u7d2f\u79ef\u5229\u6da6\u3001\u6210\u672c\u51fd\u6570\u3001\u9700\u6c42\u66f2\u7ebf\u7b49\u3002\u4f8b\u5982\uff0c\u5728\u5206\u6790\u5e02\u573a\u9700\u6c42\u65f6\uff0c\u79ef\u5206\u7528\u4e8e\u8ba1\u7b97\u6d88\u8d39\u8005\u5269\u4f59\u3002<\/p>\n<\/p>\n<p><p>\u4e94\u3001\u9009\u62e9\u5408\u9002\u7684\u79ef\u5206\u65b9\u6cd5<\/p>\n<\/p>\n<p><p>\u5728\u9009\u62e9\u79ef\u5206\u65b9\u6cd5\u65f6\uff0c\u9700\u8981\u8003\u8651\u7cbe\u5ea6\u3001\u901f\u5ea6\u548c\u9002\u7528\u8303\u56f4\u3002<\/p>\n<\/p>\n<p><h3>1. \u7cbe\u5ea6\u8981\u6c42<\/h3>\n<\/p>\n<p><p>\u5bf9\u4e8e\u9700\u8981\u9ad8\u7cbe\u5ea6\u7684\u573a\u5408\uff0c\u4f7f\u7528\u7b26\u53f7\u79ef\u5206\u6216\u8005\u9ad8\u7cbe\u5ea6\u7684\u6570\u503c\u79ef\u5206\u65b9\u6cd5\uff0c\u5982\u8f9b\u666e\u68ee\u6cd5\u5219\u3002<\/p>\n<\/p>\n<p><h3>2. \u8ba1\u7b97\u901f\u5ea6<\/h3>\n<\/p>\n<p><p>\u5bf9\u4e8e\u9700\u8981\u5feb\u901f\u8ba1\u7b97\u7684\u573a\u5408\uff0c\u53ef\u4ee5\u9009\u62e9SciPy\u7684<code>quad<\/code>\u51fd\u6570\u6216\u8005NumPy\u7684\u68af\u5f62\u6cd5\u5219\u3002<\/p>\n<\/p>\n<p><h3>3. \u9002\u7528\u8303\u56f4<\/h3>\n<\/p>\n<p><p>\u6839\u636e\u5177\u4f53\u7684\u95ee\u9898\u9009\u62e9\u5408\u9002\u7684\u65b9\u6cd5\uff0c\u4f8b\u5982\uff0c\u5bf9\u4e8e\u591a\u91cd\u79ef\u5206\uff0c\u9009\u62e9<code>dblquad<\/code>\u6216\u8005<code>tplquad<\/code>\u51fd\u6570\u3002<\/p>\n<\/p>\n<p><p>\u901a\u8fc7\u4ee5\u4e0a\u4ecb\u7ecd\uff0c\u76f8\u4fe1\u4f60\u5df2\u7ecf\u4e86\u89e3\u4e86\u5982\u4f55\u7528Python\u5b9e\u73b0\u79ef\u5206\u3002\u6839\u636e\u5b9e\u9645\u9700\u6c42\u9009\u62e9\u5408\u9002\u7684\u65b9\u6cd5\uff0c\u53ef\u4ee5\u6709\u6548\u5730\u89e3\u51b3\u95ee\u9898\u3002Python\u5f3a\u5927\u7684\u79d1\u5b66\u8ba1\u7b97\u80fd\u529b\uff0c\u4f7f\u5f97\u79ef\u5206\u8ba1\u7b97\u53d8\u5f97\u7b80\u5355\u800c\u9ad8\u6548\u3002<\/p>\n<\/p>\n<h2><strong>\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n<p> <strong>\u5982\u4f55\u5728Python\u4e2d\u8fdb\u884c\u6570\u503c\u79ef\u5206\uff1f<\/strong><br 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