## module newtonRaphson
''' root = newtonRaphson(f,df,a,b,tol=1.0e-9).
    Finds a root of f(x) = 0 by combining the Newton-Raphson
    method with bisection. The root must be bracketed in (a,b).
    Calls user-supplied functions f(x) and its derivative df(x).   
'''    
def newtonRaphson(f,df,a,b,tol=1.0e-9):
    import error
    from numpy import sign
    
    fa = f(a)
    if fa == 0.0: return a
    fb = f(b)
    if fb == 0.0: return b
    if sign(fa) == sign(fb): error.err('Root is not bracketed')
    x = 0.5*(a + b)                    
    for i in range(30):
        fx = f(x)
        if fx == 0.0: return x
        # Tighten the brackets on the root 
        if sign(fa) != sign(fx): b = x  
        else: a = x
        # Try a Newton-Raphson step    
        dfx = df(x)
        # If division by zero, push x out of bounds
        try: dx = -fx/dfx
        except ZeroDivisionError: dx = b - a
        x = x + dx
        # If the result is outside the brackets, use bisection  
        if (b - x)*(x - a) < 0.0:  
            dx = 0.5*(b - a)                      
            x = a + dx
        # Check for convergence     
        if abs(dx) < tol*max(abs(b),1.0): return x
    print('Too many iterations in Newton-Raphson')
