{"id":970208,"date":"2024-12-27T05:24:03","date_gmt":"2024-12-26T21:24:03","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/970208.html"},"modified":"2024-12-27T05:24:05","modified_gmt":"2024-12-26T21:24:05","slug":"python%e5%a6%82%e4%bd%95%e6%b1%82%e5%81%8f%e5%af%bc","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/970208.html","title":{"rendered":"python\u5982\u4f55\u6c42\u504f\u5bfc"},"content":{"rendered":"

\"python\u5982\u4f55\u6c42\u504f\u5bfc\"<\/p>\n

\u5728Python\u4e2d\u6c42\u504f\u5bfc\u53ef\u4ee5\u901a\u8fc7\u4f7f\u7528\u7b26\u53f7\u6570\u5b66\u5e93\u5982SymPy\u3001\u81ea\u52a8\u5fae\u5206\u5e93\u5982Autograd\u3001\u4ee5\u53ca\u6570\u503c\u8ba1\u7b97\u5e93\u5982NumPy\u548cSciPy\u6765\u5b9e\u73b0\u3002SymPy\u53ef\u4ee5\u7528\u4e8e\u7b26\u53f7\u5fae\u5206\u3001Autograd\u9002\u5408\u81ea\u52a8\u5fae\u5206\uff0c\u800cNumPy\u548cSciPy\u5219\u901a\u8fc7\u6570\u503c\u65b9\u6cd5\u8fdb\u884c\u8fd1\u4f3c\u8ba1\u7b97\u3002<\/strong>\u5176\u4e2d\uff0cSymPy<\/strong>\u662f\u4e00\u4e2a\u5f3a\u5927\u7684\u5de5\u5177\uff0c\u5b83\u5141\u8bb8\u7528\u6237\u5b9a\u4e49\u7b26\u53f7\u53d8\u91cf\u5e76\u5bf9\u5176\u8fdb\u884c\u5fae\u5206\u3002Autograd<\/strong>\u5219\u64c5\u957f\u5728\u9700\u8981\u8ba1\u7b97\u68af\u5ea6\u7684\u673a\u5668\u5b66\u4e60<\/a>\u4e2d\u5e94\u7528\uff0c\u80fd\u591f\u81ea\u52a8\u8ba1\u7b97\u590d\u6742\u51fd\u6570\u7684\u504f\u5bfc\u6570\u3002\u5bf9\u4e8e\u6570\u503c\u65b9\u6cd5\uff0cNumPy<\/strong>\u548cSciPy<\/strong>\u63d0\u4f9b\u4e86\u6570\u503c\u8fd1\u4f3c\u7684\u529f\u80fd\uff0c\u53ef\u4ee5\u5bf9\u79bb\u6563\u6570\u636e\u8fdb\u884c\u5fae\u5206\u3002\u63a5\u4e0b\u6765\uff0c\u5c06\u8be6\u7ec6\u4ecb\u7ecd\u8fd9\u4e9b\u65b9\u6cd5\u7684\u4f7f\u7528\u3002<\/p>\n<\/p>\n

\u4e00\u3001\u4f7f\u7528SYMPY\u8fdb\u884c\u7b26\u53f7\u5fae\u5206<\/p>\n<\/p>\n

SymPy\u662fPython\u7684\u4e00\u4e2a\u7b26\u53f7\u8ba1\u7b97\u5e93\uff0c\u5b83\u53ef\u4ee5\u7528\u4e8e\u8868\u8fbe\u5f0f\u7684\u7b26\u53f7\u5fae\u5206\u3002SymPy\u63d0\u4f9b\u4e86\u4e00\u4e2a\u975e\u5e38\u76f4\u89c2\u7684\u65b9\u6cd5\u6765\u6c42\u89e3\u504f\u5bfc\u6570\u3002<\/p>\n<\/p>\n

    \n
  1. \u5b89\u88c5\u548c\u5bfc\u5165SymPy<\/strong><\/li>\n<\/ol>\n

    \u9996\u5148\uff0c\u786e\u4fdd\u5b89\u88c5\u4e86SymPy\u5e93\uff0c\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u547d\u4ee4\u8fdb\u884c\u5b89\u88c5\uff1a<\/p>\n<\/p>\n

    pip install sympy<\/p>\n
    <\/code><\/pre>\n<\/p>\n
    \u5728\u4ee3\u7801\u4e2d\u5bfc\u5165SymPy\uff1a<\/p>\n<\/p>\n
    from sympy import symbols, diff<\/p>\n
    <\/code><\/pre>\n<\/p>\n
      \n
    1. \u5b9a\u4e49\u7b26\u53f7\u53d8\u91cf\u548c\u51fd\u6570<\/strong><\/li>\n<\/ol>\n
      \u5728SymPy\u4e2d\uff0c\u9700\u8981\u9996\u5148\u5b9a\u4e49\u7b26\u53f7\u53d8\u91cf\u548c\u51fd\u6570\u3002\u4f8b\u5982\uff0c\u5b9a\u4e49\u4e00\u4e2a\u7b80\u5355\u7684\u4e8c\u5143\u51fd\u6570\uff1a<\/p>\n<\/p>\n
      x, y = symbols('x y')<\/p>\n
      f = x<strong>2 + y<\/strong>2<\/p>\n
      <\/code><\/pre>\n<\/p>\n
        \n
      1. \u6c42\u504f\u5bfc\u6570<\/strong><\/li>\n<\/ol>\n
        \u4f7f\u7528diff<\/code>\u51fd\u6570\u6765\u6c42\u504f\u5bfc\u6570\u3002\u4f8b\u5982\uff0c\u6c42\u51fd\u6570f<\/code>\u5173\u4e8ex<\/code>\u7684\u504f\u5bfc\u6570\uff1a<\/p>\n<\/p>\n
        df_dx = diff(f, x)<\/p>\n
        print(df_dx)  # \u8f93\u51fa: 2*x<\/p>\n
        <\/code><\/pre>\n<\/p>\n
        \u6c42\u5173\u4e8ey<\/code>\u7684\u504f\u5bfc\u6570\uff1a<\/p>\n<\/p>\n
        df_dy = diff(f, y)<\/p>\n
        print(df_dy)  # \u8f93\u51fa: 2*y<\/p>\n
        <\/code><\/pre>\n<\/p>\n
        SymPy\u53ef\u4ee5\u5904\u7406\u66f4\u52a0\u590d\u6742\u7684\u51fd\u6570\u548c\u591a\u53d8\u91cf\u7684\u5fae\u5206\uff0c\u8fd9\u4f7f\u5f97\u5b83\u5728\u7b26\u53f7\u8ba1\u7b97\u4e0a\u975e\u5e38\u6709\u7528\u3002<\/p>\n<\/p>\n
        \u4e8c\u3001\u4f7f\u7528AUTOGRAD\u8fdb\u884c\u81ea\u52a8\u5fae\u5206<\/p>\n<\/p>\n
        Autograd\u662f\u4e00\u4e2aPython\u5e93\uff0c\u4e13\u6ce8\u4e8e\u81ea\u52a8\u5fae\u5206\uff0c\u5e7f\u6cdb\u5e94\u7528\u4e8e\u673a\u5668\u5b66\u4e60\u9886\u57df\u3002\u5b83\u53ef\u4ee5\u81ea\u52a8\u8ba1\u7b97Python\u548cNumPy\u4ee3\u7801\u7684\u5bfc\u6570\u3002<\/p>\n<\/p>\n
          \n
        1. \u5b89\u88c5\u548c\u5bfc\u5165Autograd<\/strong><\/li>\n<\/ol>\n
          \u9996\u5148\uff0c\u786e\u4fdd\u5b89\u88c5\u4e86Autograd\u5e93\uff1a<\/p>\n<\/p>\n
          pip install autograd<\/p>\n
          <\/code><\/pre>\n<\/p>\n
          \u5728\u4ee3\u7801\u4e2d\u5bfc\u5165\u5fc5\u8981\u7684\u6a21\u5757\uff1a<\/p>\n<\/p>\n
          import autograd.numpy as np<\/p>\n
          from autograd import grad<\/p>\n
          <\/code><\/pre>\n<\/p>\n
            \n
          1. \u5b9a\u4e49\u51fd\u6570\u548c\u8ba1\u7b97\u5bfc\u6570<\/strong><\/li>\n<\/ol>\n
            \u5b9a\u4e49\u4e00\u4e2a\u666e\u901a\u7684Python\u51fd\u6570\uff0c\u7136\u540e\u4f7f\u7528grad<\/code>\u51fd\u6570\u6765\u8ba1\u7b97\u5176\u504f\u5bfc\u6570\u3002\u4f8b\u5982\uff0c\u5b9a\u4e49\u4e00\u4e2a\u7b80\u5355\u7684\u51fd\u6570\uff1a<\/p>\n<\/p>\n
            def f(x, y):<\/p>\n
                return x<strong>2 + y<\/strong>2<\/p>\n
            <\/code><\/pre>\n<\/p>\n
            \u4f7f\u7528grad<\/code>\u6765\u8ba1\u7b97\u504f\u5bfc\u6570\uff1a<\/p>\n<\/p>\n
            df_dx = grad(f, 0)  # \u7b2c\u4e00\u4e2a\u53c2\u6570\u662f\u51fd\u6570\uff0c\u7b2c\u4e8c\u4e2a\u53c2\u6570\u662f\u53d8\u91cf\u7684\u7d22\u5f15<\/p>\n
            df_dy = grad(f, 1)<\/p>\n
            <\/code><\/pre>\n<\/p>\n
              \n
            1. \u8ba1\u7b97\u7ed3\u679c<\/strong><\/li>\n<\/ol>\n
              \u8ba1\u7b97\u5e76\u6253\u5370\u7ed3\u679c\uff1a<\/p>\n<\/p>\n
              x_val, y_val = 1.0, 2.0<\/p>\n
              print(df_dx(x_val, y_val))  # \u8f93\u51fa: 2.0<\/p>\n
              print(df_dy(x_val, y_val))  # \u8f93\u51fa: 4.0<\/p>\n
              <\/code><\/pre>\n<\/p>\n
              Autograd\u7684\u5f3a\u5927\u4e4b\u5904\u5728\u4e8e\u5b83\u80fd\u591f\u81ea\u52a8\u5904\u7406\u590d\u6742\u7f51\u7edc\u7684\u68af\u5ea6\u8ba1\u7b97\uff0c\u800c\u65e0\u9700\u624b\u52a8\u6c42\u5bfc\u3002<\/p>\n<\/p>\n
              \u4e09\u3001\u4f7f\u7528NUMPY\u548cSCIPY\u8fdb\u884c\u6570\u503c\u5fae\u5206<\/p>\n<\/p>\n
              \u5bf9\u4e8e\u4e00\u4e9b\u65e0\u6cd5\u7b26\u53f7\u5316\u6216\u590d\u6742\u7684\u51fd\u6570\uff0c\u6570\u503c\u5fae\u5206\u662f\u4e00\u79cd\u6709\u6548\u7684\u66ff\u4ee3\u65b9\u6848\u3002NumPy\u548cSciPy\u63d0\u4f9b\u4e86\u6570\u503c\u8ba1\u7b97\u7684\u5de5\u5177\u3002<\/p>\n<\/p>\n
                \n
              1. \u5bfc\u5165\u5fc5\u8981\u7684\u6a21\u5757<\/strong><\/li>\n<\/ol>\n
                import numpy as np<\/p>\n
                from scipy.misc import derivative<\/p>\n
                <\/code><\/pre>\n<\/p>\n
                  \n
                1. \u5b9a\u4e49\u51fd\u6570<\/strong><\/li>\n<\/ol>\n
                  \u5b9a\u4e49\u4e00\u4e2a\u9700\u8981\u6c42\u5bfc\u7684\u51fd\u6570\uff1a<\/p>\n<\/p>\n
                  def f(x, y):<\/p>\n
                      return x<strong>2 + y<\/strong>2<\/p>\n
                  <\/code><\/pre>\n<\/p>\n
                    \n
                  1. \u8ba1\u7b97\u6570\u503c\u5bfc\u6570<\/strong><\/li>\n<\/ol>\n
                    \u4f7f\u7528SciPy\u7684derivative<\/code>\u51fd\u6570\u8fdb\u884c\u6570\u503c\u5fae\u5206\uff1a<\/p>\n<\/p>\n
                    def partial_x(x, y):<\/p>\n
                        return derivative(lambda x: f(x, y), x, dx=1e-6)<\/p>\n
                    def partial_y(x, y):<\/p>\n
                        return derivative(lambda y: f(x, y), y, dx=1e-6)<\/p>\n
                    <\/code><\/pre>\n<\/p>\n
                      \n
                    1. \u8ba1\u7b97\u5e76\u6253\u5370\u7ed3\u679c<\/strong><\/li>\n<\/ol>\n
                      x_val, y_val = 1.0, 2.0<\/p>\n
                      print(partial_x(x_val, y_val))  # \u8f93\u51fa: 2.0<\/p>\n
                      print(partial_y(x_val, y_val))  # \u8f93\u51fa: 4.0<\/p>\n
                      <\/code><\/pre>\n<\/p>\n
                      \u6570\u503c\u5fae\u5206\u867d\u7136\u7cbe\u5ea6\u4e0d\u5982\u7b26\u53f7\u5fae\u5206\u548c\u81ea\u52a8\u5fae\u5206\uff0c\u4f46\u5728\u5904\u7406\u65e0\u6cd5\u7b26\u53f7\u5316\u7684\u590d\u6742\u51fd\u6570\u65f6\u975e\u5e38\u6709\u7528\u3002<\/p>\n<\/p>\n
                      \u56db\u3001\u7efc\u5408\u5e94\u7528\u4e0e\u4f18\u5316<\/p>\n<\/p>\n
                      \u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u53ef\u80fd\u9700\u8981\u6839\u636e\u5177\u4f53\u60c5\u51b5\u9009\u62e9\u4e0d\u540c\u7684\u65b9\u6cd5\u6765\u8ba1\u7b97\u504f\u5bfc\u6570\u3002\u4ee5\u4e0b\u662f\u4e00\u4e9b\u4f18\u5316\u548c\u7efc\u5408\u5e94\u7528\u7684\u5efa\u8bae\uff1a<\/p>\n<\/p>\n
                        \n
                      1. \n
                        \u9009\u62e9\u9002\u5408\u7684\u65b9\u6cd5<\/strong><\/p>\n<\/p>\n