python的fractions.limit_denominator是如何实现的？

发布时间：2020-12-16 21:44:05 所属栏目：Python 来源：网络整理

导读：limit_denominator(max_denominator=1000000)Finds and returns the closest Fraction to self that has denominator at most max_denominator. This method is useful for finding rational approximations to a given floating-point number: from fractio

limit_denominator(max_denominator=1000000)
Finds and returns the closest Fraction to self that has denominator at most max_denominator. This method is useful for finding rational approximations to a given floating-point number:

>>>
>>> from fractions import Fraction
>>> Fraction('3.1415926535897932').limit_denominator(1000)
Fraction(355,113)

它不应该像尝试/ 999,b / 998,c / 997 ..并找到最佳近似值.

解决方法

分数模块是用Python编写的,您只需查看源代码即可.它包含以下注释.

# Algorithm notes: For any real number x,define a *best upper
    # approximation* to x to be a rational number p/q such that:
    #
    #   (1) p/q >= x,and
    #   (2) if p/q > r/s >= x then s > q,for any rational r/s.
    #
    # Define *best lower approximation* similarly.  Then it can be
    # proved that a rational number is a best upper or lower
    # approximation to x if,and only if,it is a convergent or
    # semiconvergent of the (unique shortest) continued fraction
    # associated to x.
    #
    # To find a best rational approximation with denominator <= M,# we find the best upper and lower approximations with
    # denominator <= M and take whichever of these is closer to x.
    # In the event of a tie,the bound with smaller denominator is
    # chosen.  If both denominators are equal (which can happen
    # only when max_denominator == 1 and self is midway between
    # two integers) the lower bound---i.e.,the floor of self,is
    # taken.

（编辑：李大同）

【声明】本站内容均来自网络，其相关言论仅代表作者个人观点，不代表本站立场。若无意侵犯到您的权利，请及时与联系站长删除相关内容!