I am trying to use SciPy to integrate this function:
y(x) = (e^-ax)*cos(x) between 0 and 4pi.
Here is the code I have so far:
from numpy import *
from scipy.integrate import simps
a = 0
x = linspace(0 , 4*pi, 100)
y = (e^-(a*x))*cos(x)
integral_value = simps(y,x)
print integral_value
However it doesn't seem to be working. Any help would be appreciated, thanks!
Well if you run the program you obtain the following error:
TypeError: ufunc 'bitwise_xor' not supported for the input types, and the inputs could not be safely coerced to any supported types according to the casting rule ''safe''
So you know the problem is with the ^ (bitwise xor) in your function. In Python one uses ** to take the exponent.
If one writes:
y = (e**-(a*x))*cos(x)
instead, one gets:
>>> print integral_value
-0.000170200006112
The full program:
from numpy import *
from scipy.integrate import simps
a = 0
x = linspace(0 , 4*pi, 100)
y = (e**-(a*x))*cos(x)
integral_value = simps(y,x)
print integral_valueYou can also make explicit use of numpy functions with:
from numpy import *
from scipy.integrate import simps
a = 0
x = linspace(0 , 4*pi, 100)
y = exp(-a*x)*cos(x)
integral_value = simps(y,x)
print integral_valueIn order to increase the precision, you can increase the number of points (100 is not that much).
import numpy as np
import math
from scipy.integrate import simps
a = 0
x = np.linspace(0 , 4*math.pi, 100)
#create a vectorized function which can be applied directly to an array
fn = np.vectorize(lambda x: math.exp(-a*x)*math.cos(x))
y = fn(x)
integral_value = simps(y, x)
print integral_value
this indeed yields value of -0.000170200006112. Note that for a=0, the integral is equal to zero, so in order to get "closer" you would need to refine the grid...
Cracking a nut with a sledgehammer ...
>>> from sympy import *
>>> var('a x')
(a, x)
>>> y = exp(-a*x)*cos(x)
>>> y.subs(a,0)
cos(x)
Should it surprise any of us to find that this integrates to 0 (zero) over the given interval?