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

# example code, Lecture 6, Fall 2008s = 0for i in range(10):  s += 0.1print (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 guessdef 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)