如何从字符串中绘制数学函数？

1 回答

• 7

  您可以使用pythons eval function， but this is dangerous and generally considered bad style 将字符串转换为代码，请参阅：https://stackoverflow.com/a/661128/3838691 . 如果用户可以输入字符串，他们可以输入类似 import subprocess; subprocess.check_call(['rm', '-rf', '*'], shell=True) 的内容 .

  因此，请确保为此构建合理的安全性 .

  您可以定义一个接受字符串并返回函数的函数 . 我们需要做一些预处理，以允许用户输入更像他习惯的公式（^等）：

  编辑：第二个版本 - 白名单而不是黑名单

  定义允许和支持的单词似乎比将某些单词列入黑名单更好：

  import re
  
  replacements = {
      'sin' : 'np.sin',
      'cos' : 'np.cos',
      'exp': 'np.exp',
      'sqrt': 'np.sqrt',
      '^': '**',
  }
  
  allowed_words = [
      'x',
      'sin',
      'cos',
      'sqrt',
      'exp',
  ]
  
  def string2func(string):
      ''' evaluates the string and returns a function of x '''
      # find all words and check if all are allowed:
      for word in re.findall('[a-zA-Z_]+', string):
          if word not in allowed_words:
              raise ValueError(
                  '"{}" is forbidden to use in math expression'.format(word)
              )
  
      for old, new in replacements.items():
          string = string.replace(old, new)
  
      def func(x):
          return eval(string)
  
      return func
  
  
  if __name__ == '__main__':
  
      func = string2func(input('enter function: f(x) = '))
      a = float(input('enter lower limit: '))
      b = float(input('enter upper limit: '))
      x = np.linspace(a, b, 250)
  
      plt.plot(x, func(x))
      plt.xlim(a, b)
      plt.show()
  

  结果：

  $ python test.py
  enter function: f(x) = x^2
  enter lower limit: 0
  enter upper limit: 2
  

  

  对于恶意用户：

  enter function: f(x) = import subprocess; subprocess.check_call(['rm', '-rf', '*'], shell=True)
  Traceback (most recent call last):
    File "test.py", line 35, in <module>
      func = string2func(input('enter function: f(x) = '))
    File "test.py", line 22, in string2func
      '"{}" is forbidden to use in math expression'.format(word)
  ValueError: "import" is forbidden to use in math expression
  

  编辑：第一版 - 黑名单危险词：

  import numpy as np
  import matplotlib.pyplot as plt
  
  # there should be a better way using regex
  replacements = {
      'sin' : 'np.sin',
      'cos' : 'np.cos',
      'exp': 'np.exp',
      '^': '**',
  }
  
  # think of more security hazards here
  forbidden_words = [
      'import',
      'shutil',
      'sys',
      'subprocess',
  ]
  
  def string2func(string):
      ''' evaluates the string and returns a function of x '''
      for word in forbidden_words:
          if word in string:
              raise ValueError(
                  '"{}" is forbidden to use in math expression'.format(word)
              )
  
      for old, new in replacements.items():
          string = string.replace(old, new)
  
      def func(x):
          return eval(string)
  
      return func
  

  回复于 2024-05-03T10:19:27+08:00