Integrals in Python: adding an object to non-callable

Question

I am trying to solve the integral of the taylor approximation of the function sin (x) using the trapezoid rule. The code seems fine, but it continues to give me the following error: "TypeError: Add object cannot be called"

This is my code:

 import math
 import numpy
 import sympy as sy
 import numpy as np
 from sympy.functions import sin,cos
 import matplotlib.pyplot as plt
 x = sy.Symbol('x')
 f = sin(x)
 # Factorial function
     if n <= 0:
         return 1
     else:
         return n*factorial(n-1)

 taylor_series = sin(x).series(n=None)
 # Do a trapezoid integration
     xedge = numpy.linspace(a,b,N+1)
     integral = 0.0
     n = 0
     while n < N:
         integral += 0.5*(xedge[n+1] - xedge[n])*(f(xedge[n]) + f(xedge[n+1]))
         n += 1
     return integral

 N = 3
 a = 0.0
 b = 1.0

 z = sum([next(taylor_series) for i in range(N)])
 print("Taylor series:",z)
 # Trapezoid rule result 
 N = 2
 while (N <= 2):
     dd = trap(a,b,z,N)
     print ('Trapezoid rule result:', dd)
     N *= 2

Track:

Error: Traceback (most recent call last):
  File "Question1.py", line 86, in <module>
    dd = trap(a,b,z,N)
  File "Question1.py", line 67, in trap
    integral += 0.5*(xedge[n+1] - xedge[n])*(f(xedge[n]) + f(xedge[n+1]))
TypeError: 'Add' object is not callable

Answer 1

In your case f, an expression sympy. You cannot just appreciate it by calling it; you should use the method evalf():

...
integral += 0.5*(xedge[n+1] - xedge[n])*(f.evalf(xedge[n]) + f.evalf(xedge[n+1]))
...

Outputs:

Taylor series: x**5/120 - x**3/6 + x
Trapezoid rule result: 0.0079345703125*x**5 - 0.158203125*x**3 + 1.0*x

End

Answer 2

Your command f = sin (x) is invalid; the argument is a character symbol, not a legal argument to the sin function .

, , , . f sin ... , , , .

import math
import numpy
import sympy as sy
import numpy as np
from sympy.functions import sin,cos
import matplotlib.pyplot as plt
x = sy.Symbol('x')
print "sy.Symbol('x') is", x, type(x)
f = sin(x)

# Factorial function that will be used in the Taylor approximation
def factorial(n):
    if n <= 0:
        return 1
    else:
        return n*factorial(n-1)

taylor_series = sin(x).series(n=None)

#def fun(x):
#   return numpy.sin(x)


# Do a trapezoid integration by breaking up the domain [a,b] into N slabs
def trap(a,b,f,N):

    xedge = numpy.linspace(a,b,N+1)

    integral = 0.0

    n = 0
    while n < N:
        x0 = xedge[n]
        x1 = xedge[n+1]
        print x0, x1
        sub1 = x1 - x0
        f0 = math.sin(x0)
        f1 = math.sin(x1)
        sub2 = f0 + f1
        integral = integral + 0.5 * sub1 * sub2
        n += 1

    return integral


N = 3
a = 0.0
b = 1.0
# takes the number of terms desired for your generator
z = sum([next(taylor_series) for i in range(N)])
print("Taylor series:",z)

# Trapezoid rule result and calculaiton of error term
N = 2

while (N <= 2):
    dd = trap(a,b,z,N)
    print ('Trapezoid rule result:', dd)
    N *= 2