Question

我想绘制函数x ^ -x及其衍生物。然而，衍生品变得乏味可编。因此，我想让Python为我找到衍生物，然后绘制它们然而我不断收到语法错误。这是我到目前为止所做的。

import math 
import sympy as sp
import numpy as np 
import matplotlib.pyplot as plt
x,y,z = sp.symbols('x y z')

n=1 # order of derivative
def f(x):
   g=z**(-z)
   h=sp.diff(g,z,n)
   q=h.subs(z,x)
   return q

x1=np.arange(0,5,0.5)
plt.plot(x1,f(x1))
plt.show()

错误消息的完整引用如下：

SyntaxError                               Traceback (most recent call last)
C:\Users\Nathaniel\Anaconda3\lib\site-packages\sympy\core\sympify.py in 
sympify(a, locals, convert_xor, strict, rational, evaluate)
    321         a = a.replace('\n', '')
--> 322         expr = parse_expr(a, local_dict=locals, 
transformations=transformations, evaluate=evaluate)
    323     except (TokenError, SyntaxError) as exc:

C:\Users\Nathaniel\Anaconda3\lib\site-packages\sympy\parsing\sympy_parser.py 
in parse_expr(s, local_dict, transformations, global_dict, evaluate)
    893 
--> 894     return eval_expr(code, local_dict, global_dict)
    895 

C:\Users\Nathaniel\Anaconda3\lib\site-packages\sympy\parsing\sympy_parser.py 
in eval_expr(code, local_dict, global_dict)
    806     expr = eval(
--> 807         code, global_dict, local_dict)  # take local objects in 
    preference
    808 

SyntaxError: invalid syntax (<string>, line 1)

During handling of the above exception, another exception occurred:

SympifyError                              Traceback (most recent call last)
<ipython-input-2-13b1385304a2> in <module>()
     13 
     14 x1=np.arange(0,5,0.5)
---> 15 plt.plot(x1,f(x1))
     16 plt.show()

<ipython-input-2-13b1385304a2> in f(x)
      9     g=z**(-z)
     10     h=sp.diff(g,z,n)
---> 11     q=h.subs(z,x)
     12     return q
     13 

C:\Users\Nathaniel\Anaconda3\lib\site-packages\sympy\core\basic.py in 
subs(self, *args, **kwargs)
    851         for i in range(len(sequence)):
    852             o, n = sequence[i]
--> 853             so, sn = sympify(o), sympify(n)
    854             if not isinstance(so, Basic):
    855                 if type(o) is str:

C:\Users\Nathaniel\Anaconda3\lib\site-packages\sympy\core\sympify.py in 
sympify(a, locals, convert_xor, strict, rational, evaluate)
    322         expr = parse_expr(a, local_dict=locals, 
    transformations=transformations, evaluate=evaluate)
    323     except (TokenError, SyntaxError) as exc:
--> 324         raise SympifyError('could not parse %r' % a, exc)
    325 
    326     return expr

SympifyError: Sympify of expression 'could not parse '[ 0.   0.5  1.   1.5  
2.   2.5  3.   3.5  4.   4.5]'' failed, because of exception being raised:
SyntaxError: invalid syntax (<string>, line 1)

我如何让Python以快速有效的方式绘制它？

Answer 1

sympy中的差异函数似乎在mpath library中。也许有其他方式，经验丰富的sympy用户如何解决问题，但这是一个解决方案：

import matplotlib.pyplot as plt
from mpmath import diff
from cycler import cycler
#create cycler objects that matplotlib uses as linestyles 
col = cycler("color", ["r", "b", "g"])
styl = cycler("linestyle", ["-", "-."])
plt.rc('axes', prop_cycle =  styl * col)

#define function to differentiate
def g(z):
    return z ** (-z)
#define the differentiation function
def f(xrange):
    return [diff(lambda x: g(x), xr, n) for xr in xrange]
#I prefer linspace over arange because you don't run into float point problems
x1 = np.linspace(1, 5, 100)
#cycle through derivative order
for n in range(5):
    plt.plot(x1, f(x1), label = "Order = {}".format(n))

plt.legend()
plt.show()

每个函数的线条样式可以通过使用cycler objects.来定义。当然还有其他方法来控制colour of the lines in matplotlib。

输出：

用用户定义的函数绘制衍生物

1 个答案: