I want to plot the function x^-x along with it's derivatives. However the derivatives become tedious to write. Therefore I want to have Python find the derivatives for me and then plot them however I keep getting a syntax error. This is what I have so far.
我想绘制函数x ^ -x及其衍生物。然而，衍生品变得单调乏味。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。这就是我到目前为止所拥有的。
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()
The full trackback of the error message is as follows:
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)
How would I get Python to plot this in a quick and efficient way?
我如何让Python以快速有效的方式绘制它？
1 个解决方案
#1
1
It seems the differentiation functions in sympy are in the mpath library. Maybe there are other ways, how experienced sympy users can address the problem, but here is one solution:
似乎在sympy中的区分功能在mpath库中。也许有其他方式，经验丰富的用户如何解决问题，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()
The line style of each function can be defined for instance by using cycler objects. There are of course other ways to control the colour of the lines in matplotlib.
例如，可以通过使用循环器对象来定义每个函数的线条样式。当然还有其他方法可以控制matplotlib中线条的颜色。
Output:
输出：
#1
1
It seems the differentiation functions in sympy are in the mpath library. Maybe there are other ways, how experienced sympy users can address the problem, but here is one solution:
似乎在sympy中的区分功能在mpath库中。也许有其他方式，经验丰富的用户如何解决问题，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()
The line style of each function can be defined for instance by using cycler objects. There are of course other ways to control the colour of the lines in matplotlib.
例如，可以通过使用循环器对象来定义每个函数的线条样式。当然还有其他方法可以控制matplotlib中线条的颜色。
Output:
输出：