Newton Python

# -*- coding: utf-8 -*-

"""

Numericka Integracia - Lichobeznikova metoda.

"""

from sympy import Abs

from numa import logger, float_input, int_input, expr_input, eval_expr

def trapezoid(a, b, m, fn, e):

"""

Na intervale <a,b>, ktory sa rozdeli na m lichobeznikov, vypocita

aproximaciu urciteho integralu funkcie fn.

"""

assert a < b, 'Cislo b musi byt vacsie ako cislo a'

assert e > 0, 'Presnost e musi byt vacsia ako nula'

f = lambda x: eval_expr(fn, x=x)

I = []

J1 = 0

J2 = 0

k = 0

# rozdelenie intervalu na m rovnako dlhych dielov

h = (b - a) / m

for i in range(m):

J1 += f(a + (h * i))

J2 += f(a + h * (i + 1))

I.append((h / 2) * (J1 + J2))

while True:

J1 = 0

J2 = 0

m *= 2

# skratenie intervalu na polovicu

h /= 2

for i in range(m):

J1 += f(a + (h * i))

J2 += f(a + h * (i + 1))

I.append((h / 2) * (J1 + J2))

logger.info('m = {0}, h = {1}, Abs(I[k] - I[k + 1]) = {2}'.format(

m, h, I[k] - I[k + 1]))

# skonci pri dosiahnuti presnosti

if Abs(I[k] - I[k + 1]) <= e:

return I[k + 1]

k += 1

if __name__ == '__main__':

a = float_input('Zadajte cislo a')

b = float_input('Zadajte cislo b')

m = int_input('Zadajte pocet delenia intervalu m')

fn = expr_input('Zadajte funkciu fn')

e = float_input('Zadajte presnost e', default=0.01)