{"id":1069994,"date":"2025-01-08T10:54:06","date_gmt":"2025-01-08T02:54:06","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1069994.html"},"modified":"2025-01-08T10:54:09","modified_gmt":"2025-01-08T02:54:09","slug":"python%e5%a6%82%e4%bd%95%e6%b1%82%e6%9c%aa%e7%9f%a5%e6%9b%b2%e7%ba%bf%e7%9a%84%e5%88%87%e7%ba%bf%e6%96%b9%e7%a8%8b-2","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/1069994.html","title":{"rendered":"python\u5982\u4f55\u6c42\u672a\u77e5\u66f2\u7ebf\u7684\u5207\u7ebf\u65b9\u7a0b"},"content":{"rendered":"<p style=\"text-align:center;\" ><img decoding=\"async\" src=\"https:\/\/cdn-kb.worktile.com\/kb\/wp-content\/uploads\/2024\/04\/25100843\/18f29473-2946-464b-bc60-2edd9460f4d5.webp\" alt=\"python\u5982\u4f55\u6c42\u672a\u77e5\u66f2\u7ebf\u7684\u5207\u7ebf\u65b9\u7a0b\" \/><\/p>\n<p><p> \u5728Python\u4e2d\uff0c\u6c42\u89e3\u672a\u77e5\u66f2\u7ebf\u7684\u5207\u7ebf\u65b9\u7a0b\u662f\u4e00\u9879\u6bd4\u8f83\u590d\u6742\u7684\u4efb\u52a1\uff0c\u901a\u5e38\u9700\u8981\u5229\u7528\u6570\u503c\u8ba1\u7b97\u548c\u7b26\u53f7\u8ba1\u7b97\u7684\u65b9\u6cd5\u3002<strong>\u53ef\u4ee5\u901a\u8fc7\u5bfc\u6570\u8ba1\u7b97\u3001\u6570\u503c\u5fae\u5206\u3001\u7b26\u53f7\u8ba1\u7b97\u7b49\u65b9\u6cd5<\/strong>\uff0c\u6765\u6c42\u89e3\u672a\u77e5\u66f2\u7ebf\u7684\u5207\u7ebf\u65b9\u7a0b\u3002\u4e0b\u9762\u5c06\u8be6\u7ec6\u4ecb\u7ecd\u4e00\u79cd\u5e38\u89c1\u7684\u65b9\u6cd5\uff1a\u5229\u7528SymPy\u5e93\u8fdb\u884c\u7b26\u53f7\u8ba1\u7b97\u6765\u6c42\u89e3\u5207\u7ebf\u65b9\u7a0b\u3002<\/p>\n<\/p>\n<p><p>SymPy\u662fPython\u7684\u4e00\u4e2a\u7b26\u53f7\u8ba1\u7b97\u5e93\uff0c\u80fd\u591f\u8fdb\u884c\u7b26\u53f7\u5fae\u5206\u3001\u79ef\u5206\u3001\u89e3\u65b9\u7a0b\u7b49\u64cd\u4f5c\uff0c\u975e\u5e38\u9002\u5408\u5904\u7406\u6570\u5b66\u95ee\u9898\u3002\u4e0b\u9762\u5c06\u4ecb\u7ecd\u5982\u4f55\u4f7f\u7528SymPy\u5e93\u6765\u6c42\u89e3\u672a\u77e5\u66f2\u7ebf\u7684\u5207\u7ebf\u65b9\u7a0b\u3002<\/p>\n<\/p>\n<p><h3>\u4e00\u3001\u5bfc\u5165\u5fc5\u8981\u7684\u5e93<\/h3>\n<\/p>\n<p><p>\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u5bfc\u5165\u5fc5\u8981\u7684\u5e93\uff0c\u5305\u62ecSymPy\u548cNumPy\u3002SymPy\u7528\u4e8e\u7b26\u53f7\u8ba1\u7b97\uff0cNumPy\u7528\u4e8e\u6570\u503c\u8ba1\u7b97\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import sympy as sp<\/p>\n<p>import numpy as np<\/p>\n<p>import matplotlib.pyplot as plt<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><h3>\u4e8c\u3001\u5b9a\u4e49\u66f2\u7ebf\u65b9\u7a0b<\/h3>\n<\/p>\n<p><p>\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u4e2a\u66f2\u7ebf\u65b9\u7a0by=f(x)\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528SymPy\u5b9a\u4e49\u8fd9\u4e2a\u65b9\u7a0b\u3002\u6bd4\u5982\uff0c\u6211\u4eec\u5b9a\u4e49\u4e00\u4e2a\u4e8c\u6b21\u51fd\u6570y=x^2\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">x = sp.symbols(&#39;x&#39;)<\/p>\n<p>y = x2<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><h3>\u4e09\u3001\u8ba1\u7b97\u5bfc\u6570<\/h3>\n<\/p>\n<p><p>\u4e3a\u4e86\u6c42\u89e3\u5207\u7ebf\u65b9\u7a0b\uff0c\u6211\u4eec\u9700\u8981\u8ba1\u7b97\u66f2\u7ebf\u5728\u67d0\u4e00\u70b9\u5904\u7684\u5bfc\u6570\u3002\u4f7f\u7528SymPy\u7684diff\u51fd\u6570\u53ef\u4ee5\u5f88\u65b9\u4fbf\u5730\u8ba1\u7b97\u5bfc\u6570\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">dy_dx = sp.diff(y, x)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><h3>\u56db\u3001\u8ba1\u7b97\u5207\u7ebf\u65b9\u7a0b<\/h3>\n<\/p>\n<p><p>\u5207\u7ebf\u65b9\u7a0b\u7684\u5f62\u5f0f\u4e3ay = mx + c\uff0c\u5176\u4e2dm\u662f\u5bfc\u6570\u7684\u503c\uff0cc\u662f\u622a\u8ddd\u3002\u4e3a\u4e86\u6c42\u89e3\u67d0\u4e00\u70b9(x0, y0)\u5904\u7684\u5207\u7ebf\u65b9\u7a0b\uff0c\u6211\u4eec\u9700\u8981\u8ba1\u7b97\u8be5\u70b9\u7684\u5bfc\u6570\u503c\u548c\u622a\u8ddd\u3002<\/p>\n<\/p>\n<p><p>\u5047\u8bbe\u6211\u4eec\u8981\u6c42\u70b9(1, 1)\u5904\u7684\u5207\u7ebf\u65b9\u7a0b\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">x0 = 1<\/p>\n<p>y0 = y.subs(x, x0)<\/p>\n<p>m = dy_dx.subs(x, x0)<\/p>\n<p>c = y0 - m*x0<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><h3>\u4e94\u3001\u8f93\u51fa\u5207\u7ebf\u65b9\u7a0b<\/h3>\n<\/p>\n<p><p>\u5207\u7ebf\u65b9\u7a0b\u53ef\u4ee5\u8868\u793a\u4e3ay = mx + c\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528SymPy\u5c06\u5176\u8f93\u51fa\u4e3a\u4e00\u4e2a\u65b9\u7a0b\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">tangent_line = m*x + c<\/p>\n<p>print(f&quot;\u5207\u7ebf\u65b9\u7a0b\u4e3a: y = {sp.expand(tangent_line)}&quot;)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><h3>\u516d\u3001\u7ed8\u5236\u66f2\u7ebf\u548c\u5207\u7ebf<\/h3>\n<\/p>\n<p><p>\u4e3a\u4e86\u66f4\u76f4\u89c2\u5730\u5c55\u793a\u7ed3\u679c\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528Matplotlib\u7ed8\u5236\u66f2\u7ebf\u548c\u5207\u7ebf\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\"># \u5b9a\u4e49\u66f2\u7ebf\u548c\u5207\u7ebf\u65b9\u7a0b<\/p>\n<p>f = sp.lambdify(x, y, &#39;numpy&#39;)<\/p>\n<p>tangent = sp.lambdify(x, tangent_line, &#39;numpy&#39;)<\/p>\n<h2><strong>\u751f\u6210\u6570\u636e\u70b9<\/strong><\/h2>\n<p>x_vals = np.linspace(-2, 2, 400)<\/p>\n<p>y_vals = f(x_vals)<\/p>\n<p>tangent_vals = tangent(x_vals)<\/p>\n<h2><strong>\u7ed8\u5236\u66f2\u7ebf\u548c\u5207\u7ebf<\/strong><\/h2>\n<p>plt.plot(x_vals, y_vals, label=&#39;\u66f2\u7ebf y=x^2&#39;)<\/p>\n<p>plt.plot(x_vals, tangent_vals, label=f&#39;\u5207\u7ebf y={sp.expand(tangent_line)}&#39;, linestyle=&#39;--&#39;)<\/p>\n<p>plt.scatter([x0], [y0], color=&#39;red&#39;)  # \u6807\u8bb0\u5207\u70b9<\/p>\n<p>plt.legend()<\/p>\n<p>plt.xlabel(&#39;x&#39;)<\/p>\n<p>plt.ylabel(&#39;y&#39;)<\/p>\n<p>plt.title(&#39;\u66f2\u7ebf\u53ca\u5176\u5207\u7ebf&#39;)<\/p>\n<p>plt.grid(True)<\/p>\n<p>plt.show()<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><h3>\u4e03\u3001\u603b\u7ed3<\/h3>\n<\/p>\n<p><p>\u901a\u8fc7\u4e0a\u8ff0\u6b65\u9aa4\uff0c\u6211\u4eec\u53ef\u4ee5\u5229\u7528Python\u4e2d\u7684SymPy\u5e93\u6c42\u89e3\u672a\u77e5\u66f2\u7ebf\u7684\u5207\u7ebf\u65b9\u7a0b\u3002<strong>\u9996\u5148\u5b9a\u4e49\u66f2\u7ebf\u65b9\u7a0b\uff0c\u7136\u540e\u8ba1\u7b97\u5bfc\u6570\uff0c\u63a5\u7740\u5728\u6307\u5b9a\u70b9\u5904\u6c42\u89e3\u5bfc\u6570\u503c\u548c\u622a\u8ddd\uff0c\u6700\u540e\u8f93\u51fa\u5207\u7ebf\u65b9\u7a0b\u5e76\u7ed8\u5236\u66f2\u7ebf\u548c\u5207\u7ebf<\/strong>\u3002\u8fd9\u79cd\u65b9\u6cd5\u975e\u5e38\u9002\u5408\u5904\u7406\u590d\u6742\u7684\u7b26\u53f7\u8ba1\u7b97\u95ee\u9898\uff0c\u5e76\u4e14\u53ef\u4ee5\u901a\u8fc7\u53ef\u89c6\u5316\u5de5\u5177\u76f4\u89c2\u5730\u5c55\u793a\u7ed3\u679c\u3002<\/p>\n<\/p>\n<p><p>\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u66f2\u7ebf\u65b9\u7a0b\u53ef\u80fd\u4f1a\u66f4\u52a0\u590d\u6742\uff0c\u751a\u81f3\u662f\u9690\u51fd\u6570\u6216\u53c2\u6570\u65b9\u7a0b\u3002\u5bf9\u4e8e\u8fd9\u4e9b\u60c5\u51b5\uff0c\u6211\u4eec\u53ef\u4ee5\u5229\u7528\u6570\u503c\u5fae\u5206\u7684\u65b9\u6cd5\u6765\u8fd1\u4f3c\u6c42\u89e3\u5207\u7ebf\u65b9\u7a0b\u3002\u65e0\u8bba\u662f\u54ea\u79cd\u65b9\u6cd5\uff0cPython\u90fd\u63d0\u4f9b\u4e86\u4e30\u5bcc\u7684\u5de5\u5177\u548c\u5e93\u6765\u5e2e\u52a9\u6211\u4eec\u8fdb\u884c\u6570\u503c\u548c\u7b26\u53f7\u8ba1\u7b97\uff0c\u4ece\u800c\u89e3\u51b3\u5404\u79cd\u6570\u5b66\u95ee\u9898\u3002<\/p>\n<\/p>\n<h2><strong>\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n<p> <strong>\u5982\u4f55\u4f7f\u7528Python\u7ed8\u5236\u672a\u77e5\u66f2\u7ebf\u7684\u5207\u7ebf\uff1f<\/strong><br \/>\u8981\u7ed8\u5236\u672a\u77e5\u66f2\u7ebf\u7684\u5207\u7ebf\uff0c\u60a8\u9700\u8981\u9996\u5148\u786e\u5b9a\u66f2\u7ebf\u7684\u65b9\u7a0b\u6216\u901a\u8fc7\u6570\u636e\u70b9\u8fdb\u884c\u62df\u5408\u3002\u53ef\u4ee5\u4f7f\u7528<code>matplotlib<\/code>\u5e93\u6765\u7ed8\u5236\u66f2\u7ebf\uff0c\u5e76\u5229\u7528<code>numpy<\/code>\u6216<code>scipy<\/code>\u5e93\u8ba1\u7b97\u5207\u7ebf\u7684\u659c\u7387\u3002\u901a\u8fc7\u6c42\u5bfc\u6216\u6570\u503c\u65b9\u6cd5\u83b7\u53d6\u5207\u70b9\u7684\u659c\u7387\u540e\uff0c\u60a8\u53ef\u4ee5\u4f7f\u7528\u70b9\u659c\u5f0f\u65b9\u7a0b\u6765\u7ed8\u5236\u5207\u7ebf\u3002<\/p>\n<p><strong>\u5728Python\u4e2d\u5982\u4f55\u6c42\u89e3\u66f2\u7ebf\u7684\u5bfc\u6570\uff1f<\/strong><br \/>\u5728Python\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528<code>SymPy<\/code>\u5e93\u6765\u8fdb\u884c\u7b26\u53f7\u8ba1\u7b97\uff0c\u4ece\u800c\u6c42\u89e3\u66f2\u7ebf\u7684\u5bfc\u6570\u3002\u901a\u8fc7\u5b9a\u4e49\u66f2\u7ebf\u7684\u65b9\u7a0b\uff0c\u60a8\u53ef\u4ee5\u76f4\u63a5\u8ba1\u7b97\u5bfc\u6570\uff0c\u5f97\u5230\u5207\u7ebf\u7684\u659c\u7387\u3002\u6b64\u5916\uff0c<code>numpy<\/code>\u5e93\u4e5f\u53ef\u4ee5\u7528\u4e8e\u6570\u503c\u5bfc\u6570\uff0c\u9002\u5408\u5904\u7406\u79bb\u6563\u6570\u636e\u70b9\u3002<\/p>\n<p><strong>\u6709\u54ea\u4e9b\u5e38\u7528\u7684Python\u5e93\u9002\u5408\u5904\u7406\u66f2\u7ebf\u62df\u5408\u548c\u6c42\u5207\u7ebf\u65b9\u7a0b\uff1f<\/strong><br \/>\u5e38\u7528\u7684Python\u5e93\u5305\u62ec<code>numpy<\/code>\u548c<code>scipy<\/code>\u7528\u4e8e\u6570\u503c\u8ba1\u7b97\u548c\u66f2\u7ebf\u62df\u5408\uff0c<code>SymPy<\/code>\u7528\u4e8e\u7b26\u53f7\u8ba1\u7b97\uff0c<code>matplotlib<\/code>\u7528\u4e8e\u53ef\u89c6\u5316\u3002\u901a\u8fc7\u7ed3\u5408\u8fd9\u4e9b\u5e93\uff0c\u60a8\u53ef\u4ee5\u6709\u6548\u5730\u5904\u7406\u672a\u77e5\u66f2\u7ebf\u7684\u5207\u7ebf\u65b9\u7a0b\u95ee\u9898\uff0c\u5b9e\u73b0\u6570\u636e\u5206\u6790\u548c\u56fe\u5f62\u5c55\u793a\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"\u5728Python\u4e2d\uff0c\u6c42\u89e3\u672a\u77e5\u66f2\u7ebf\u7684\u5207\u7ebf\u65b9\u7a0b\u662f\u4e00\u9879\u6bd4\u8f83\u590d\u6742\u7684\u4efb\u52a1\uff0c\u901a\u5e38\u9700\u8981\u5229\u7528\u6570\u503c\u8ba1\u7b97\u548c\u7b26\u53f7\u8ba1\u7b97\u7684\u65b9\u6cd5\u3002\u53ef\u4ee5\u901a\u8fc7\u5bfc [&hellip;]","protected":false},"author":3,"featured_media":1069999,"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\/1069994"}],"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=1069994"}],"version-history":[{"count":"1","href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1069994\/revisions"}],"predecessor-version":[{"id":1070000,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1069994\/revisions\/1070000"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/1069999"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=1069994"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=1069994"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=1069994"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}