python sympy lambdify not working inside function

Question

I'm trying to write a function that has a literal function as a parameter:

def derive(x, y):
    x = symbols(x)
    y = symbols(y)
    return lambdify(x, y)    

derive(5, 'x**2')

This returns a syntax error:

  File "<lambdifygenerated-32>", line 1
    def _lambdifygenerated(25.0):
                           ^
SyntaxError: invalid syntax

If I write (outside the function scope):

f = lambdify(x, x**2) f(5)

it works. I appreciate any help on this.

Answer 1

In sympy you can get the derivative of a function via diff(). .subs(x, 5) fills in the value 5 for x. An example:

from sympy.abc import x

f = x**2
print(f.diff(x).subs(x,5))

Here is how a function that would calculate the derivative of a given function at a given value could look like. evalf() can be used to iron out symbolic parts (such as giving a numeric approximation for 2*pi or Sqrt(5) which sympy standard wants to keep in their exact symbolic form).

def derive_and_evaluate(x, f, xval):
    return f.diff(x).subs(x, xval).evalf()

derive_and_evaluate(x, x**2, 5)

If you need the same derivative for a lot of x-values, you can do:

from sympy import lambdify

g = lambdify(x, f.diff(x)) # now `g` is a numpy function with one parameter

Or, if you want a function that does the derivation and converts to numpy form:

def derive_and_lambdify(x, f):
    return lambdify(x, f.diff(x))

g = derive_and_lambdify(x, x**2)
print(g(5))

From then on, you can use g similar to other numpy functions. Here is a more elaborate example:

from sympy import lambdify, sin
from sympy.abc import x

f = sin(1 / (1 + x ** 2))
g = lambdify(x, f.diff(x))

import numpy as np
from matplotlib import pyplot as plt

xs = np.linspace(-5, 5, 100)
ys = g(xs)
plt.plot(xs, ys)
plt.show()