二等分法を使用して平方根を求めます。

二等分法を使用して平方根を求めます。

def sqrtBI(x, epsilon):
    assert x>0, 'X must be non-nagtive, not ' + str(x)
    assert epsilon > 0, 'epsilon must be postive, not ' + str(epsilon)
  
    low = 0
    high = x
    guess = (low + high)/2.0
    counter = 1
    while (abs(guess ** 2 - x) > epsilon) and (counter <= 100):
        if guess ** 2 < x:
            low = guess
        else :
            high = guess
        guess = (low + high)/2.0
        counter += 1
    return guess

確認してください。

>>> sqrtBI(2,0.000001)

>>> 1.41421365738

X

>>> sqrtBI(0.25,0.000001)

>>> 0.25

では、0.25 の平方根を求めるにはどうすればよいでしょうか?

上記のコードを少し変更するだけです。コードの 6 行目と 7 行目に注目してください。

def sqrtBI(x, epsilon):
    assert x>0, 'X must be non-nagtive, not ' + str(x)
    assert epsilon > 0, 'epsilon must be postive, not ' + str(epsilon)
  
    low = 0
    high = max(x, 1.0)
    ## high = x
    guess = (low + high)/2.0
    counter = 1
    while (abs(guess ** 2 - x) > epsilon) and (counter <= 100):
        if guess ** 2 < x:
            low = guess
        else :
            high = guess
        guess = (low + high)/2.0
        counter += 1
    return guess

確認してください:

>>> sqrtBI(0.25,0.000001)

>>> 0.5