Lecture 6: Bisection methods, Newton/Raphson, introduction to lists

# example code, Lecture 6, Fall 2008

s = 0
for i in range(10):
  s += 0.1
print (s)

def squareRootBi(x,epsilon):
    '''Assumes x >= 0 and epsilon > 0
        return y s.t. y*y is within epsilon of x'''
    assert x >= 0, 'x must be non-negative, not' + str(x)
    assert epsilon > 0, 'epsilon must be postive, not' + str(epsilon)
    low = 0
    high = max(x, 1.0)
    guess = (low + high)/2.0
    ctr = 1
    while abs(guess**2 - x) > epsilon and ctr <= 100:
        #epsilon is the smallest value to approximate the square
        if guess**2 < x:
            low = guess
        else:
            high = guess
        guess = (low + high)/2.0
        ctr += 1
    assert ctr <= 100, 'Iteration count exceeded'
    print ('Bi method. Num. iterations:', ctr, 'Estimate:', guess)
    return guess

def testBi():
    print ('squareRootBi(4, 0.001)')
    squareRootBi(4,0.001)
    print ('squareRootBi(9, 0.001)')
    squareRootBi(9, 0.001)
    print ('squareRootBi(2, 0.001)')
    squareRootBi(2, 0.001)
    print ('squareRootBi(0.25, 0.0001)')
    squareRootBi(0.25, 0.0001)

def squareRootNR(x, epsilon):
    assert x >= 0, 'a must be non-negative, not' + str(x)
    assert epsilon > 0, 'epsilon must be postive, not' + str(epsilon)
    x = float(x)
    guess = x/2.0
    guess = 0.001
    diff = guess**2 - x
    ctr = 1
    while abs(diff) > epsilon and ctr <= 100:
        guess = guess - diff/(2.0*guess)
        diff = guess**2 - x
        ctr += 1
    assert ctr <= 100, 'Iteration count exceeded'
    print ('NR method. Num. iterations:', ctr, 'Estimate:', guess)
    return guess    
    
def compareMethods():
    print ('squareRoot(2, 0.01)')
    squareRootBi(2, 0.01)
    squareRootNR(2, 0.01)
    input()
    print ('squareRoot(2, 0.0001)')
    squareRootBi(2, 0.001)
    squareRootNR(2, 0.001)
    input ()
    print ('squareRoot(2, 0.000001)')
    squareRootBi(2, 0.000001)
    squareRootNR(2, 0.000001)
    input ()
    print ('squareRoot(1234567890, 0.0001)')
    squareRootBi(1234567890, 0.0001)
    squareRootNR(1234567890, 0.0001)
    input ()
    print ('squareRoot(1234567890, 0.000001)')
    squareRootBi(1234567890, 0.000001)
    squareRootNR(1234567890, 0.000001)
    input ()
    print ('squareRoot(2736336100, 0.0001)')
    squareRootBi(2736336100, 0.0001)
    squareRootNR(2736336100, 0.0001)

def showLists():
    Techs = ['MIT', 'Cal Tech']
    print (Techs)
    input()
    Ivys = ['Harvard', 'Yale', 'Brown']
    print (Ivys)
    input()
    Univs = []
    Univs.append(Techs)
    print (Univs)
    input()
    Univs.append(Ivys)
    print (Univs)
    input()
    for e in Univs:
        print (e)
        for c in e: print (c)
    input()
    Univs = Techs + Ivys
    print (Univs)
    input()
    Univs.remove('Harvard')
    print (Univs)

def list():
    list = ["A", "B", "C", "B", "D"]
    list.remove("B")
    print (list)