#biseccion

def f(x):
    return x**3-5*x-9

# Implementing Bisection Method
def bisection(x0,x1,e):
    step = 1
    print('\n\n*** BISECTION METHOD IMPLEMENTATION ***')
    condition = True
    while condition:
        x2 = (x0 + x1)/2
        print('Iteration-%d, x2 = %0.6f and f(x2) = %0.6f' % (step, x2, f(x2)))

        if f(x0) * f(x2) < 0:
            x1 = x2
        else:
            x0 = x2
        
        step = step + 1
        condition = abs(f(x2)) > e

    print('\nRequired Root is : %0.8f' % x2)


# Input Section
x0 = input('First Guess: ')
x1 = input('Second Guess: ')
e = input('Tolerable Error: ')

# Converting input to float
x0 = float(x0)
x1 = float(x1)
e = float(e)



# Checking Correctness of initial guess values and bisecting
if f(x0) * f(x1) > 0.0:
    print('Given guess values do not bracket the root.')
    print('Try Again with different guess values.')
else:
    bisection(x0,x1,e)
#false---------------------------------------
def f(x):
    return x**3-5*x-9

# Implementing False Position Method
def falsePosition(x0,x1,e):
    step = 1
    print('\n\n*** FALSE POSITION METHOD IMPLEMENTATION ***')
    condition = True
    while condition:
        x2 = x0 - (x1-x0) * f(x0)/( f(x1) - f(x0) )
        print('Iteration-%d, x2 = %0.6f and f(x2) = %0.6f' % (step, x2, f(x2)))

        if f(x0) * f(x2) < 0:
            x1 = x2
        else:
            x0 = x2

        step = step + 1
        condition = abs(f(x2)) > e

    print('\nRequired root is: %0.8f' % x2)


# Input Section
x0 = input('First Guess: ')
x1 = input('Second Guess: ')
e = input('Tolerable Error: ')

# Converting input to float
x0 = float(x0)
x1 = float(x1)
e = float(e)

#Note: You can combine above two section like this
# x0 = float(input('First Guess: '))
# x1 = float(input('Second Guess: '))
# e = float(input('Tolerable Error: '))


# Checking Correctness of initial guess values and false positioning
if f(x0) * f(x1) > 0.0:
    print('Given guess values do not bracket the root.')
    print('Try Again with different guess values.')
else:
    falsePosition(x0,x1,e)
#-------------------------------------------------------
def f(x):
    return x**3 - 5*x - 9

# Defining derivative of function
def g(x):
    return 3*x**2 - 5

# Implementing Newton Raphson Method

def newtonRaphson(x0,e,N):
    print('\n\n*** NEWTON RAPHSON METHOD IMPLEMENTATION ***')
    step = 1
    flag = 1
    condition = True
    while condition:
        if g(x0) == 0.0:
            print('Divide by zero error!')
            break
        
        x1 = x0 - f(x0)/g(x0)
        print('Iteration-%d, x1 = %0.6f and f(x1) = %0.6f' % (step, x1, f(x1)))
        x0 = x1
        step = step + 1
        
        if step > N:
            flag = 0
            break
        
        condition = abs(f(x1)) > e
    
    if flag==1:
        print('\nRequired root is: %0.8f' % x1)
    else:
        print('\nNot Convergent.')


# Input Section
x0 = input('Enter Guess: ')
e = input('Tolerable Error: ')
N = input('Maximum Step: ')

# Converting x0 and e to float
x0 = float(x0)
e = float(e)

# Converting N to integer
N = int(N)


# Starting Newton Raphson Method
newtonRaphson(x0,e,N)
#-------------------------------------------------------
def f(x):
    return x**3 - 5*x - 9

# Implementing Secant Method

def secant(x0,x1,e,N):
    print('\n\n*** SECANT METHOD IMPLEMENTATION ***')
    step = 1
    condition = True
    while condition:
        if f(x0) == f(x1):
            print('Divide by zero error!')
            break
        
        x2 = x0 - (x1-x0)*f(x0)/( f(x1) - f(x0) ) 
        print('Iteration-%d, x2 = %0.6f and f(x2) = %0.6f' % (step, x2, f(x2)))
        x0 = x1
        x1 = x2
        step = step + 1
        
        if step > N:
            print('Not Convergent!')
            break
        
        condition = abs(f(x2)) > e
    print('\n Required root is: %0.8f' % x2)


# Input Section
x0 = input('Enter First Guess: ')
x1 = input('Enter Second Guess: ')
e = input('Tolerable Error: ')
N = input('Maximum Step: ')

# Converting x0 and e to float
x0 = float(x0)
x1 = float(x1)
e = float(e)

# Converting N to integer
N = int(N)


# Starting Secant Method
secant(x0,x1,e,N)