How To Plot A Math Function From String?
I have a string which represents a function, like 'x * (x - 32 ( 2 /x) )'. I'm using matplotlib, but I don't know how convert this string into an array of points to plot.
Solution 1:
You can turn a string into code by using pythons eval
function, but this is dangerous and generally considered bad style, See this: https://stackoverflow.com/a/661128/3838691.
If user can input the string, they could input something like
import subprocess; subprocess.check_call(['rm', '-rf', '*'], shell=True)
.
So be sure that you build in reasonable security into this.
You can define a function that takes a string and returns a function. We need to do a little preprocessing to allow the user to input formulas more like he is used to (^ etc.):
Edit: Second version – white list instead of blacklist
It seems better to define allowed and supported words than blacklisting some:
import re
replacements = {
'sin' : 'np.sin',
'cos' : 'np.cos',
'exp': 'np.exp',
'sqrt': 'np.sqrt',
'^': '**',
}
allowed_words = [
'x',
'sin',
'cos',
'sqrt',
'exp',
]
defstring2func(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 notin allowed_words:
raise ValueError(
'"{}" is forbidden to use in math expression'.format(word)
)
for old, new in replacements.items():
string = string.replace(old, new)
deffunc(x):
returneval(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()
Result:
$ python test.py
enter function: f(x) = x^2
enter lower limit: 0
enter upper limit: 2
And for a malicious user:
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 inmath expression
Edit: First version – blacklist hazardous words:
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',
]
defstring2func(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)
deffunc(x):
returneval(string)
return func
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