I am typing a code to produce values for integration via the Trapezoidal method and Simpson's rule as well as the absolute difference of these values given an input 'n'. The 'n' input is a function in itself of n = 2 ** i if i is in the range (1, 19).
The table that my code outputs is as follows
n Trapezoidal Simpson Absolute Difference
------ ------------- --------- ---------------------
2 -0.929894 -0.68338 0.246515
4 -0.687139 -0.606221 0.0809183
8 -0.614581 -0.590396 0.024186
16 -0.594187 -0.587389 0.00679814
32 -0.588796 -0.587 0.00179688
64 -0.587422 -0.586964 0.000458234
128 -0.587076 -0.586961 0.000115222
256 -0.58699 -0.586961 2.88492e-05
512 -0.586968 -0.586961 7.21507e-06
1024 -0.586962 -0.586961 1.80394e-06
2048 -0.586961 -0.586961 4.50996e-07
4096 -0.586961 -0.586961 1.1275e-07
8192 -0.586961 -0.586961 2.81874e-08
16384 -0.586961 -0.586961 7.04687e-09
32768 -0.586961 -0.586961 1.7617e-09
65536 -0.586961 -0.586961 4.40314e-10
131072 -0.586961 -0.586961 1.10276e-10
262144 -0.586961 -0.586961 2.76881e-11
524288 -0.586961 -0.586961 7.86082e-12
however, I would like for the values in my table to all be rounded to 7 decimal values and not be formatted with e/E so that my table looks like this :
n Trapezoidal Simpson Absolute Difference
------------------------------------------------------------------------
2 -0.9298943 -0.6833796 0.2465147
4 -0.6871394 -0.6062211 0.0809183
8 -0.6145815 -0.5903955 0.0241860
16 -0.5941871 -0.5873889 0.0067981
32 -0.5887964 -0.5869996 0.0017969
64 -0.5874217 -0.5869635 0.0004582
128 -0.5870761 -0.5869609 0.0001152
256 -0.5869895 -0.5869607 0.0000288
512 -0.5869679 -0.5869607 0.0000072
1024 -0.5869625 -0.5869607 0.0000018
2048 -0.5869611 -0.5869607 0.0000005
4096 -0.5869608 -0.5869607 0.0000001
8192 -0.5869607 -0.5869607 0.0000000
16384 -0.5869607 -0.5869607 0.0000000
32768 -0.5869607 -0.5869607 0.0000000
65536 -0.5869607 -0.5869607 0.0000000
131072 -0.5869607 -0.5869607 0.0000000
262144 -0.5869607 -0.5869607 0.0000000
524288 -0.5869607 -0.5869607 0.0000000
Below is the code that I have used to get my table
from numpy import arange
import numpy as np
from numpy import subtract
from tabulate import tabulate
from math import cos, sin
def trapezoidal(f, n, a, b):
h = (b-a)/ n
x = a + arange(n + 1) * h
integral_approx = 0.5 * h * (f(x[0]) + f(x[n]))
for i in arange(1, n):
integral_approx = integral_approx + h * f(x[i])
return integral_approx
def simpson(f, n, a, b):
if n % 2 is not 0:
return None
h = (b - a)/n
first = f(a)
last = f(b)
x = a
summ = 0
for i in range(n - 1):
x += h
value = f(x)
if i % 2 == 0:
summ += 4 * value
else:
summ += 2 * value
integral_approx = (h/3) * (first + summ + last)
return integral_approx
a = 0.1
b = pi/2
f = lambda x: (cos(x)*np.log(sin(x)))/((sin(x)**2) + 1)
d = []
for i in range(1, 20):
n = 2**i
absdiff = abs(subtract(trapezoidal(f, n, a, b), simpson(f, n, a, b)))
d.append([n, trapezoidal(f, n, a, b), simpson(f, n, a, b), absdiff])
print(tabulate(d, headers = ["n", "Trapezoidal", "Simpson", "Absolute Difference"]))
I am not sure if the difference exists because of the way that I have formatted my functions. Please help if you can.
def truncate(n, decimals=0):
multiplier = 10 ** decimals
return int(n * multiplier) / multiplier
print(truncate(0.123456789,7))
Output: 0.1234567
Hope this function helps