{"id":1011417,"date":"2024-12-27T11:29:44","date_gmt":"2024-12-27T03:29:44","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1011417.html"},"modified":"2024-12-27T11:29:46","modified_gmt":"2024-12-27T03:29:46","slug":"%e5%a6%82%e4%bd%95%e5%ae%9a%e4%b9%89%e7%a7%af%e5%88%86%e5%87%bd%e6%95%b0python","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/1011417.html","title":{"rendered":"\u5982\u4f55\u5b9a\u4e49\u79ef\u5206\u51fd\u6570python"},"content":{"rendered":"

\"\u5982\u4f55\u5b9a\u4e49\u79ef\u5206\u51fd\u6570python\"<\/p>\n

\u5728Python\u4e2d\u5b9a\u4e49\u79ef\u5206\u51fd\u6570\u7684\u65b9\u6cd5\u5305\u62ec\uff1a\u4f7f\u7528SymPy\u5e93\u8fdb\u884c\u7b26\u53f7\u79ef\u5206\u3001\u4f7f\u7528SciPy\u5e93\u8fdb\u884c\u6570\u503c\u79ef\u5206\u3002<\/strong>\u5176\u4e2d\uff0cSciPy\u5e93\u7684quad<\/code>\u51fd\u6570\u662f\u6570\u503c\u79ef\u5206\u7684\u5e38\u7528\u5de5\u5177\u4e4b\u4e00\uff0c\u9002\u7528\u4e8e\u5904\u7406\u591a\u79cd\u7c7b\u578b\u7684\u51fd\u6570\uff0c\u800cSymPy\u5e93\u5219\u80fd\u63d0\u4f9b\u7b26\u53f7\u79ef\u5206\u7684\u7cbe\u786e\u89e3\u3002\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u8be6\u7ec6\u63a2\u8ba8\u5982\u4f55\u4f7f\u7528\u8fd9\u4e24\u79cd\u65b9\u6cd5\u6765\u5b9e\u73b0\u79ef\u5206\u51fd\u6570\u7684\u5b9a\u4e49\u3002<\/p>\n<\/p>\n

\u4e00\u3001\u4f7f\u7528SymPy\u5e93\u8fdb\u884c\u7b26\u53f7\u79ef\u5206<\/p>\n<\/p>\n

SymPy\u662fPython\u4e2d\u7684\u4e00\u4e2a\u5f3a\u5927\u7684\u7b26\u53f7\u8ba1\u7b97\u5e93\uff0c\u53ef\u4ee5\u7528\u4e8e\u5904\u7406\u6570\u5b66\u7b26\u53f7\u8868\u8fbe\u5f0f\uff0c\u5305\u62ec\u6c42\u89e3\u79ef\u5206\u3002\u4ee5\u4e0b\u662f\u5982\u4f55\u4f7f\u7528SymPy\u8fdb\u884c\u7b26\u53f7\u79ef\u5206\u7684\u8be6\u7ec6\u6b65\u9aa4\uff1a<\/p>\n<\/p>\n

    \n
  1. \n

    \u5b89\u88c5SymPy\u5e93<\/strong><\/p>\n<\/p>\n

    \u5728\u4f7f\u7528SymPy\u8fdb\u884c\u7b26\u53f7\u79ef\u5206\u4e4b\u524d\uff0c\u9700\u8981\u786e\u4fddSymPy\u5e93\u5df2\u5b89\u88c5\u3002\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u547d\u4ee4\u5b89\u88c5SymPy\uff1a<\/p>\n<\/p>\n

    pip install sympy<\/p>\n
    <\/code><\/pre>\n<\/p>\n<\/li>\n
  2. \n
    \u5b9a\u4e49\u7b26\u53f7\u53d8\u91cf<\/strong><\/p>\n<\/p>\n
    \u5728SymPy\u4e2d\uff0c\u9996\u5148\u9700\u8981\u5b9a\u4e49\u7b26\u53f7\u53d8\u91cf\u3002\u53ef\u4ee5\u4f7f\u7528symbols<\/code>\u51fd\u6570\u6765\u5b9a\u4e49\u3002\u4f8b\u5982\uff1a<\/p>\n<\/p>\n
    from sympy import symbols<\/p>\n
    x = symbols('x')<\/p>\n
    <\/code><\/pre>\n<\/p>\n
    \u8fd9\u91cc\uff0c\u6211\u4eec\u5b9a\u4e49\u4e86\u4e00\u4e2a\u7b26\u53f7\u53d8\u91cfx<\/code>\uff0c\u5b83\u5c06\u7528\u4e8e\u5b9a\u4e49\u6211\u4eec\u7684\u51fd\u6570\u3002<\/p>\n<\/p>\n<\/li>\n
  3. \n
    \u5b9a\u4e49\u51fd\u6570\u5e76\u8ba1\u7b97\u79ef\u5206<\/strong><\/p>\n<\/p>\n
    \u4e00\u65e6\u5b9a\u4e49\u4e86\u7b26\u53f7\u53d8\u91cf\uff0c\u5c31\u53ef\u4ee5\u5b9a\u4e49\u51fd\u6570\u5e76\u8ba1\u7b97\u5176\u79ef\u5206\u3002\u4f8b\u5982\uff0c\u8ba1\u7b97\u51fd\u6570( f(x) = x^2 )\u7684\u79ef\u5206\uff1a<\/p>\n<\/p>\n
    from sympy import integrate<\/p>\n
    f = x2<\/p>\n
    integral_f = integrate(f, x)<\/p>\n
    print(integral_f)<\/p>\n
    <\/code><\/pre>\n<\/p>\n
    \u8fd9\u5c06\u8f93\u51fa\u79ef\u5206\u7ed3\u679c\uff0c\u5373(\\frac{x^3}{3})\u3002<\/p>\n<\/p>\n<\/li>\n
  4. \n
    \u8ba1\u7b97\u5b9a\u79ef\u5206<\/strong><\/p>\n<\/p>\n
    SymPy\u4e5f\u53ef\u4ee5\u7528\u4e8e\u8ba1\u7b97\u5b9a\u79ef\u5206\u3002\u5047\u8bbe\u6211\u4eec\u60f3\u8ba1\u7b97\u51fd\u6570( f(x) = x^2 )\u5728\u533a\u95f4[0, 1]\u4e0a\u7684\u5b9a\u79ef\u5206\uff0c\u53ef\u4ee5\u8fd9\u6837\u5b9e\u73b0\uff1a<\/p>\n<\/p>\n
    definite_integral_f = integrate(f, (x, 0, 1))<\/p>\n
    print(definite_integral_f)<\/p>\n
    <\/code><\/pre>\n<\/p>\n
    \u8fd9\u5c06\u8f93\u51fa\u5b9a\u79ef\u5206\u7ed3\u679c\uff0c\u5373(\\frac{1}{3})\u3002<\/p>\n<\/p>\n<\/li>\n<\/ol>\n
    \u4e8c\u3001\u4f7f\u7528SciPy\u5e93\u8fdb\u884c\u6570\u503c\u79ef\u5206<\/p>\n<\/p>\n
    SciPy\u662f\u4e00\u4e2a\u7528\u4e8e\u79d1\u5b66\u8ba1\u7b97\u7684Python\u5e93\uff0c\u63d0\u4f9b\u4e86\u4e00\u7cfb\u5217\u9ad8\u6548\u7684\u6570\u503c\u79ef\u5206\u51fd\u6570\u3002\u4ee5\u4e0b\u4ecb\u7ecd\u5982\u4f55\u4f7f\u7528SciPy\u8fdb\u884c\u6570\u503c\u79ef\u5206\uff1a<\/p>\n<\/p>\n
      \n
    1. \n
      \u5b89\u88c5SciPy\u5e93<\/strong><\/p>\n<\/p>\n
      \u5982\u679c\u5c1a\u672a\u5b89\u88c5SciPy\u5e93\uff0c\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u547d\u4ee4\u8fdb\u884c\u5b89\u88c5\uff1a<\/p>\n<\/p>\n
      pip install scipy<\/p>\n
      <\/code><\/pre>\n<\/p>\n<\/li>\n
    2. \n
      \u4f7f\u7528quad\u51fd\u6570\u8fdb\u884c\u6570\u503c\u79ef\u5206<\/strong><\/p>\n<\/p>\n
      SciPy\u7684quad<\/code>\u51fd\u6570\u662f\u7528\u4e8e\u8ba1\u7b97\u4e00\u7ef4\u5b9a\u79ef\u5206\u7684\u5e38\u7528\u5de5\u5177\u3002\u4ee5\u4e0b\u662f\u4f7f\u7528quad<\/code>\u51fd\u6570\u8ba1\u7b97\u79ef\u5206\u7684\u6b65\u9aa4\uff1a<\/p>\n<\/p>\n
      from scipy.integrate import quad<\/p>\n
      \u5b9a\u4e49\u88ab\u79ef\u51fd\u6570<\/strong><\/h2>\n
      def integrand(x):<\/p>\n
          return x2<\/p>\n
      \u8ba1\u7b97\u5b9a\u79ef\u5206<\/strong><\/h2>\n
      result, error = quad(integrand, 0, 1)<\/p>\n
      print("\u79ef\u5206\u7ed3\u679c:", result)<\/p>\n
      print("\u8bef\u5dee\u4f30\u8ba1:", error)<\/p>\n
      <\/code><\/pre>\n<\/p>\n
      \u8fd9\u91cc\uff0cintegrand<\/code>\u662f\u6211\u4eec\u5b9a\u4e49\u7684\u88ab\u79ef\u51fd\u6570\uff0cquad<\/code>\u51fd\u6570\u8fd4\u56de\u79ef\u5206\u7684\u8fd1\u4f3c\u503c\u548c\u8bef\u5dee\u4f30\u8ba1\u3002<\/p>\n<\/p>\n<\/li>\n
    3. \n
      \u5904\u7406\u591a\u53d8\u91cf\u51fd\u6570<\/strong><\/p>\n<\/p>\n
      \u5bf9\u4e8e\u591a\u53d8\u91cf\u51fd\u6570\uff0cSciPy\u63d0\u4f9b\u4e86dblquad<\/code>\u548ctplquad<\/code>\u51fd\u6570\uff0c\u5206\u522b\u7528\u4e8e\u8ba1\u7b97\u4e8c\u91cd\u79ef\u5206\u548c\u4e09\u91cd\u79ef\u5206\u3002\u4f8b\u5982\uff0c\u8ba1\u7b97\u51fd\u6570( f(x, y) = x^2 + y^2 )\u5728\u533a\u57df[0, 1] x [0, 1]\u4e0a\u7684\u4e8c\u91cd\u79ef\u5206\uff1a<\/p>\n<\/p>\n
      from scipy.integrate import dblquad<\/p>\n
      \u5b9a\u4e49\u88ab\u79ef\u51fd\u6570<\/strong><\/h2>\n
      def integrand(x, y):<\/p>\n
          return x<strong>2 + y<\/strong>2<\/p>\n
      \u8ba1\u7b97\u4e8c\u91cd\u79ef\u5206<\/strong><\/h2>\n
      result, error = dblquad(integrand, 0, 1, lambda x: 0, lambda x: 1)<\/p>\n
      print("\u4e8c\u91cd\u79ef\u5206\u7ed3\u679c:", result)<\/p>\n
      print("\u8bef\u5dee\u4f30\u8ba1:", error)<\/p>\n
      <\/code><\/pre>\n<\/p>\n
      \u8fd9\u91cc\uff0c\u6211\u4eec\u4f7f\u7528dblquad<\/code>\u51fd\u6570\u8fdb\u884c\u4e8c\u91cd\u79ef\u5206\u8ba1\u7b97\u3002<\/p>\n<\/p>\n<\/li>\n<\/ol>\n
      \u4e09\u3001\u5e94\u7528\u573a\u666f\u4e0e\u6ce8\u610f\u4e8b\u9879<\/p>\n<\/p>\n
        \n
      1. \n
        \u9009\u62e9\u5408\u9002\u7684\u65b9\u6cd5<\/strong><\/p>\n<\/p>\n
        \u5728\u9009\u62e9\u79ef\u5206\u65b9\u6cd5\u65f6\uff0c\u9700\u8981\u6839\u636e\u5177\u4f53\u5e94\u7528\u573a\u666f\u8fdb\u884c\u9009\u62e9\u3002\u5bf9\u4e8e\u7b80\u5355\u7684\u7b26\u53f7\u8868\u8fbe\u5f0f\uff0cSymPy\u53ef\u4ee5\u63d0\u4f9b\u7cbe\u786e\u7684\u7b26\u53f7\u89e3\u3002\u7136\u800c\uff0c\u5bf9\u4e8e\u590d\u6742\u51fd\u6570\u6216\u65e0\u6cd5\u7b26\u53f7\u5316\u7684\u51fd\u6570\uff0c\u4f7f\u7528SciPy\u7684\u6570\u503c\u79ef\u5206\u65b9\u6cd5\u53ef\u80fd\u66f4\u4e3a\u5408\u9002\u3002<\/p>\n<\/p>\n<\/li>\n
      2. \n
        \u5904\u7406\u79ef\u5206\u7cbe\u5ea6<\/strong><\/p>\n<\/p>\n
        SciPy\u7684\u6570\u503c\u79ef\u5206\u65b9\u6cd5\u63d0\u4f9b\u4e86\u79ef\u5206\u7ed3\u679c\u7684\u8bef\u5dee\u4f30\u8ba1\uff0c\u8fd9\u5bf9\u4e8e\u8bc4\u4f30\u79ef\u5206\u7684\u7cbe\u5ea6\u975e\u5e38\u6709\u7528\u3002\u7528\u6237\u53ef\u4ee5\u6839\u636e\u8bef\u5dee\u4f30\u8ba1\u6765\u8c03\u6574\u79ef\u5206\u8fc7\u7a0b\u4e2d\u7684\u53c2\u6570\uff0c\u4ee5\u63d0\u9ad8\u79ef\u5206\u7cbe\u5ea6\u3002<\/p>\n<\/p>\n<\/li>\n
      3. \n
        \u6027\u80fd\u8003\u8651<\/strong><\/p>\n<\/p>\n
        SymPy\u7684\u7b26\u53f7\u79ef\u5206\u5728\u5904\u7406\u590d\u6742\u51fd\u6570\u65f6\u53ef\u80fd\u4f1a\u6bd4\u8f83\u8017\u65f6\uff0c\u800cSciPy\u7684\u6570\u503c\u79ef\u5206\u901a\u5e38\u901f\u5ea6\u8f83\u5feb\uff0c\u4f46\u9700\u8981\u6ce8\u610f\u8bef\u5dee\u63a7\u5236\u3002\u5728\u4f7f\u7528\u6570\u503c\u79ef\u5206\u65f6\uff0c\u53ef\u4ee5\u901a\u8fc7\u8c03\u6574\u79ef\u5206\u7684\u6b65\u957f\u548c\u8fed\u4ee3\u6b21\u6570\u6765\u4f18\u5316\u6027\u80fd\u3002<\/p>\n<\/p>\n<\/li>\n<\/ol>\n
        \u56db\u3001\u603b\u7ed3\u4e0e\u6269\u5c55<\/p>\n<\/p>\n
        \u79ef\u5206\u5728\u6570\u5b66\u548c\u79d1\u5b66\u8ba1\u7b97\u4e2d\u626e\u6f14\u7740\u91cd\u8981\u89d2\u8272\u3002Python\u63d0\u4f9b\u4e86\u591a\u79cd\u5de5\u5177\u6765\u5904\u7406\u79ef\u5206\u95ee\u9898\uff0c\u5305\u62ecSymPy\u548cSciPy\u5e93\u3002\u901a\u8fc7\u672c\u6587\u7684\u4ecb\u7ecd\uff0c\u6211\u4eec\u4e86\u89e3\u4e86\u5982\u4f55\u4f7f\u7528\u8fd9\u4e9b\u5e93\u5b9e\u73b0\u7b26\u53f7\u79ef\u5206\u548c\u6570\u503c\u79ef\u5206\uff0c\u5e76\u5728\u4e0d\u540c\u5e94\u7528\u573a\u666f\u4e2d\u7075\u6d3b\u9009\u62e9\u5408\u9002\u7684\u65b9\u6cd5\u3002<\/p>\n<\/p>\n
        \u6b64\u5916\uff0c\u8fd8\u53ef\u4ee5\u7ed3\u5408Matplotlib\u7b49\u53ef\u89c6\u5316\u5de5\u5177\uff0c\u5bf9\u79ef\u5206\u7ed3\u679c\u8fdb\u884c\u76f4\u89c2\u5c55\u793a\uff0c\u5e2e\u52a9\u6211\u4eec\u66f4\u597d\u5730\u7406\u89e3\u79ef\u5206\u8fc7\u7a0b\u548c\u7ed3\u679c\u3002\u901a\u8fc7\u4e0d\u65ad\u5b9e\u8df5\u548c\u5b66\u4e60\uff0c\u6211\u4eec\u53ef\u4ee5\u66f4\u6df1\u5165\u5730\u638c\u63e1Python\u4e2d\u79ef\u5206\u51fd\u6570\u7684\u5b9a\u4e49\u548c\u5e94\u7528\u3002<\/p>\n<\/p>\n
        \u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n
         \u5982\u4f55\u5728Python\u4e2d\u5b9a\u4e49\u548c\u4f7f\u7528\u79ef\u5206\u51fd\u6570\uff1f<\/strong>
        \u5728Python\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528\u591a\u79cd\u5e93\u6765\u5b9a\u4e49\u548c\u8ba1\u7b97\u79ef\u5206\u51fd\u6570\uff0c\u4f8b\u5982NumPy\u548cSciPy\u3002NumPy\u63d0\u4f9b\u4e86\u57fa\u672c\u7684\u6570\u503c\u8ba1\u7b97\u529f\u80fd\uff0c\u800cSciPy\u5219\u5305\u542b\u4e86\u66f4\u590d\u6742\u7684\u79ef\u5206\u65b9\u6cd5\u3002\u901a\u8fc7\u8fd9\u4e9b\u5e93\uff0c\u7528\u6237\u53ef\u4ee5\u8f7b\u677e\u5b9e\u73b0\u4e00\u7ef4\u548c\u591a\u7ef4\u79ef\u5206\u8ba1\u7b97\u3002<\/p>\n
        Python\u4e2d\u6709\u54ea\u4e9b\u5e93\u53ef\u4ee5\u7528\u4e8e\u79ef\u5206\u8ba1\u7b97\uff1f<\/strong>
        \u5e38\u7528\u7684\u5e93\u5305\u62ecNumPy\u3001SciPy\u548cSymPy\u3002NumPy\u9002\u5408\u5904\u7406\u7b80\u5355\u7684\u6570\u503c\u8ba1\u7b97\uff0cSciPy\u63d0\u4f9b\u4e86\u66f4\u5f3a\u5927\u7684\u79ef\u5206\u51fd\u6570\uff0c\u6bd4\u5982scipy.integrate.quad<\/code>\uff0c\u7528\u4e8e\u4e00\u7ef4\u79ef\u5206\uff0c\u800cSymPy\u5219\u9002\u5408\u7b26\u53f7\u79ef\u5206\uff0c\u80fd\u591f\u5904\u7406\u89e3\u6790\u8868\u8fbe\u5f0f\u3002<\/p>\n
        \u5982\u4f55\u4f7f\u7528SciPy\u5e93\u8fdb\u884c\u4e00\u7ef4\u79ef\u5206\uff1f<\/strong>
        \u4f7f\u7528SciPy\u8fdb\u884c\u4e00\u7ef4\u79ef\u5206\u901a\u5e38\u6d89\u53ca\u5bfc\u5165scipy.integrate<\/code>\u6a21\u5757\u4e2d\u7684quad<\/code>\u51fd\u6570\u3002\u7528\u6237\u9700\u8981\u5b9a\u4e49\u4e00\u4e2a\u88ab\u79ef\u51fd\u6570\uff0c\u5e76\u4f7f\u7528quad<\/code>\u51fd\u6570\u8fdb\u884c\u79ef\u5206\u8ba1\u7b97\uff0c\u8fd4\u56de\u7ed3\u679c\u5305\u62ec\u79ef\u5206\u503c\u548c\u4f30\u8ba1\u7684\u8bef\u5dee\u3002<\/p>\n
        \u5728Python\u4e2d\uff0c\u5982\u4f55\u5b9e\u73b0\u5b9a\u79ef\u5206\u548c\u4e0d\u5b9a\u79ef\u5206\u7684\u8ba1\u7b97\uff1f<\/strong>
        \u5b9a\u79ef\u5206\u53ef\u4ee5\u901a\u8fc7SciPy\u7684quad<\/code>\u51fd\u6570\u5b9e\u73b0\uff0c\u800c\u4e0d\u5b9a\u79ef\u5206\u5219\u53ef\u4ee5\u4f7f\u7528SymPy\u5e93\u4e2d\u7684integrate<\/code>\u51fd\u6570\u3002\u7528\u6237\u9700\u8981\u6839\u636e\u5177\u4f53\u9700\u6c42\u9009\u62e9\u5408\u9002\u7684\u51fd\u6570\uff0c\u5b9a\u79ef\u5206\u9002\u5408\u6c42\u89e3\u5728\u7279\u5b9a\u533a\u95f4\u5185\u7684\u9762\u79ef\uff0c\u4e0d\u5b9a\u79ef\u5206\u5219\u7528\u4e8e\u627e\u5230\u539f\u51fd\u6570\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"\u5728Python\u4e2d\u5b9a\u4e49\u79ef\u5206\u51fd\u6570\u7684\u65b9\u6cd5\u5305\u62ec\uff1a\u4f7f\u7528SymPy\u5e93\u8fdb\u884c\u7b26\u53f7\u79ef\u5206\u3001\u4f7f\u7528SciPy\u5e93\u8fdb\u884c\u6570\u503c\u79ef\u5206\u3002\u5176\u4e2d\uff0cSc […]","protected":false},"author":3,"featured_media":1011425,"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\/1011417"}],"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=1011417"}],"version-history":[{"count":"1","href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1011417\/revisions"}],"predecessor-version":[{"id":1011427,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1011417\/revisions\/1011427"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/1011425"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=1011417"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=1011417"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=1011417"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}