Numerical-Analysis/TrapezAndSimpsonMethod.py at master · shaiMatz/Numerical-Analysis · GitHub

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import math
from math import *

# Input your upper,lower and interval variables


def simpsonsrule(n, upper, lower, h, function,stage):
    rule = 0
    x = lower + h  # Calculates for all odd valures
    for i in range(1, int(n + 1)):
        rule += 4 * function(x)  # adds all calculations to variable rule
        x += 2 * h

    x = lower + 2 * h  # Calculates for all even values
    for i in range(1, int(n)):
        rule += 2 * function(x)  # adds all calculations to variable rule
        x += 2 * h
    ans = (h / 3) * (function(lower) + function(upper) + rule)  # This is carrying out the formula
    print("Formula in stage {4} = ({0} / 3) * ({1} + {2} + {3})".format(h,function(lower),function(upper),rule,stage))
    return (ans)


def trapeRule(n, upper, lower, intervals, h, function):
    rule = 0
    x = lower
    rule += function(x)  # adds lower value to rule
    x = upper
    rule += function(x)  # adds upper value to rule
    for i in range(1, int(intervals)):  # all values inbetween
        x = lower + h * i
        rule += 2 * (function(x))  # adds these to the rule
    ans = (h / 2) * rule  # completes the function
    return (ans)


def useSimpson(n, upper, lower, h, func, err=0.000001):
    n = int(n)
    results=[]
    if n % 2 == 1:
        n += 1
    stage=1
    res1 = simpsonsrule(n, upper, lower, h, func,stage)
    print("Mid result point is " + str(res1)+"\n")
    stage=2
    n2 = n*2
    res2 = simpsonsrule(n2, upper, lower, h, func,stage)
    print("Mid result point is " + str(res2)+"\n")
    while abs(res2 - res1) >= err:
        n2 *= 2
        res1 = res2
        stage+=1
        res2 = simpsonsrule(n, upper, lower, h, func,stage)
        print("Mid result point is " + str(res2)+"\n")
    print("\nNumber of parts that were divided " + str(n2))
    return res2


def useTrapez(n, upper, lower, h, func, intervals, err=0.000001):
    n = int(n)
    res1 = trapeRule(n, upper, lower, intervals, h, func)
    n *= 2
    res2 = trapeRule(n, upper, lower, intervals, h, func)
    while abs(res2 - res1) >= err:
        n *= 2
        res1 = res2
        res2 = trapeRule(n, upper, lower, intervals, h, func)
    return res2


def f(x):
    f = (math.cos(x**2))**2+7*x+7
    return (f)


def trapezium(n, a, b, func,  ) -> float:
    dx = (b - a)/n
    sum = (func(a) + func(b))/2
    for i in range(1, n, 1):
        sum += func(a + i*dx)
    return sum*dx


def main():
    upper = 1
    lower = 0.5
    n = 4
    z = n / 2  # The number of even functions(z+1 is the number of odd functions)
    ans = 0
    h = (upper - lower) / n
    print("Trapez: ", useTrapez(n, upper, lower, h,f ,n))
    #print("Simpson: ", useSimpson(z, upper, lower, h, f))
    print(trapezium(n,lower,upper,f))


main()