I Can't determine what's wrong with my python trapezoidal rule function

Question

I can not understand why the function gives me an incorrect result 1,000,100,000.7423575, instead of the original result is supposed to be 1,000,000,000.75. Work has given them to us, we need to implement the feature of Python, higher-order functions and built my code so so. Just mention that in some parts of the code used other code here in the community. I would be happy if you could help me solve the problem.

thank you

def summ(a, b, f, nextt):
    total = f(a) / 2.0
    while a <= b:
        total += f(a)
        a = nextt(a)
    total += f(b) / 2.0   
    return total

def Tr(fx, a, b, n):
    h = float(b - a) / n
    return summ(a, b, fx, lambda a:a + h)

print(Tr(lambda x:x**9, 0.0, 10.0, 100000))

http://stackoverflow.com/questions/588004/is-floating-point-math-broken — Łukasz Rogalski, Dec 15 '16 at 17:12
@TadhgMcDonald-Jensen Or a fuzzy comparison that takes into account significant digits. — brianpck, Dec 15 '16 at 17:23
@Silvering are you sure of A: you actually got `1 000 100 000.7423575` because I am getting `10 001 000 007 423.574` with the exact code you posted. and B: that the correct result should be 1e9+0.75 ? How do you know this? — Tadhg McDonald-Jensen, Dec 15 '16 at 17:35
The result I posted, its from an example run that was published with the exercise instructions. — Silvering, Dec 15 '16 at 18:40

score 0 · Answer 1 · answered Dec 15 '16 at 17:59

0

Here this should work:

def trapezoidal(a, b, next, f = lambda x:x**9):
     h = float(b - a) / next
     s = 0.0
     s += f(a)/2.0

     for i in range(1, next):
         s += f(a + i * h)

     s += f(b)/2.0

     return s * h

answered Dec 15 '16 at 17:59

Aaron Goidel

39
4

thanks for that but I need that the summation part will be in another function, like I posted on the top. – Silvering Dec 15 '16 at 18:44

Nick Matteo · Accepted Answer · 2016-12-15T18:12:27.233

First, you are adding the values of f(a) and f(b) twice, giving 1.5 times their value, instead of half their value as you want. Try

def summ(a, b, f, nextt):
    total = f(a) / 2.0
    a = nextt(a)
    while a < b - 1e-9:
        total += f(a)
        a = nextt(a)
    total += f(b) / 2.0   
    return total

This gets rid of the extra 100,000 in your result.

Secondly, you should multiply the sum by the width of each rectangle, i.e. h:

def Tr(fx, a, b, n):
    h = float(b - a) / n
    return summ(a, b, fx, lambda a:a + h) * h

Otherwise, the results are 10000 times too large in your example (contrary to the results you posted.)

Now the result I get is 1,000,000,000.7423584. You say it should be 1,000,000,000.75. The difference is probably rounding error. Perhaps you can reduce this by just using the builtin sum function:

def Tr(fx, a, b, n):
    h = float(b - a) / n
    tot = sum(fx(a + h*i) for i in range(1, n))
    tot += (fx(a) + fx(b)) / 2.
    return tot * h

Now I get 1,000,000,000.7500008, which is pretty close to your stated result.

I Can't determine what's wrong with my python trapezoidal rule function

2 Answers2