README.md

Some numerical codes forked from swvist/num.py

Deliberately left existing tolerance calculation errors from original and deliberately introduced additional mistake in Secant method formula for purposes of testing diagnostic tools.

Do not deploy these codes!

num.py

"""
Bisection, Secant & Newton Raphson Method.
"""

import math
"""
* Variable Description:
*
* f			:	Given function
* f_		:	Derivative of f
* [a, b]	:	End point values
* TOL		:	Tolerance
* NMAX		:	Max number of iterations
"""


def bisection(f, a, b, TOL=0.001, NMAX=100):
    """
    Takes a function f, start values [a,b], tolerance value(optional) TOL and
    max number of iterations(optional) NMAX and returns the root of the equation
    using the bisection method.
    """
    n=1
    while n<=NMAX:
        c = (a+b)/2.0
        print("a=%s\tb=%s\tc=%s\tf(c)=%s"%(a,b,c,f(c)))
        if f(c)==0 or (b-a)/2.0 < TOL:
            return c
        else:
            n = n+1
            if f(c)*f(a) > 0:
                a=c
            else:
                b=c
    return False

def secant(f,x0,x1, TOL=0.001, NMAX=100):
    """
    Takes a function f, start values [x0,x1], tolerance value(optional) TOL and
    max number of iterations(optional) NMAX and returns the root of the equation
    using the secant method.
    """
    n=1
    while n<=NMAX:
        x2 = x1 - f(x1)*((x1-x0)/(f(x0)-f(x1)))
        if x2-x1 < TOL:
            return x2
        else:
            x0 = x1
            x1 = x2
    return False

def newtonraphson(f, f_, x0, TOL=0.001, NMAX=100):
    """
    Takes a function f, its derivative f_, initial value x0, tolerance value(optional) TOL and
    max number of iterations(optional) NMAX and returns the root of the equation
    using the newton-raphson method.
    """
    n=1
    while n<=NMAX:
        x1 = x0 - (f(x0)/f_(x0))
        if x1 - x0 < TOL:
            return x1
        else:
            x0 = x1
    return False

if __name__ == "__main__":

    def func(x):
        """
        Function x^3 - x -2
        We will calculate the root of this function using different methods.
        """
        return math.pow(x,3) - x -2

    def func_(x):
        """
        Derivative of the function f(x) = x^3 - x -2
        This will be used in Newton-Rahson method.
        """
        return 3*math.pow(x,2)-1

    #Invoking Bisection Method
    res = bisection(func,1,2)
    print res

    #Invoking Secant Method
    res = bisection(func,1,2)
    print res

    #Invoking Newton Raphson Method
    res = newtonraphson(func,func_,1)
    print res

Deliberately left existing tolerance calculation errors from original and deliberately introduced additional mistake in Secant method formula for purposes of testing diagnostic tools. Do not deploy these codes!