鬼の领地

#!/usr/bin/env python
# -*- coding: utf-8 -*-
 
import math
sqrt = math.sqrt
 
def gen_imet(func):
  def retfunc(self, other):
    ret = func(self, other)
    self.ave = ret.ave
    self.u = ret.u
    self.digs = ret.digs
    return self
  return retfunc
 
def get_digs(a, b):
  if a == 0: return b
  elif b == 0: return a
  else: return min(a, b)
 
class PhyStat:
  """
  物理实验数据
 
  PhyStat(ave, u = 0.0, digs = 0)
  ave   表示平均值，如果传入一列数则自动计算平均值及其标准误差
  u     表示标准误差，如果 ave 传入数据列表则此处表示仪器精度
  digs  表示有效数字个数，0 表示不限制
  """
 
  def __init__(self, ave, u = 0.0, digs = 0):
    """
    对于 ave 为数据列表的情况，使用下面公式计算平均值：
    ave = Σx[i] / n
    根据下面公式计算标准误差：
    S = Sqrt(Σ(x[i]-ave)^2 / (n - 1))
    u = Δinst / Sqrt(3)
    U = Sqrt(S^2 + u^2)
    """
    self.digs = digs
 
    if isinstance(ave, tuple) or isinstance(ave, list):
      data = ave
      n = len(data)
      ave = math.fsum(ave) / n
      self.ave = ave
 
      s = 0.0
      for i in data:
        s += (i - ave) ** 2
      s = sqrt(s / (n - 1))
      u /= sqrt(3)
      self.u = sqrt(s ** 2 + u ** 2)
    else:
      self.ave = float(ave)
      self.u = abs(float(u))
 
  def __repr__(self):
    ave = self.ave
    exp = int(math.floor(math.log10(ave)))
    exp10 = 10 ** exp
    ave = ave / exp10
    u = self.u / exp10
    digs = self.digs
    if digs == 0:
      ret = '%f ±%f'
    else:
      ret = '%%.%df ±%%.%df' % (digs, digs)
    if exp:
      ret = '(%s) E %d' % (ret, exp)
    return ret % (ave, u)
 
  __neg__ = lambda self: PhyStat(-self.ave, self.u, self.digs)
  __pos__ = lambda self: self
  __abs__ = lambda self: PhyStat(abs(self.ave), self.u, self.digs)
 
  def __add__(self, other):
    if isinstance(other, PhyStat):
      ave = self.ave + other.ave
      u = sqrt(self.u ** 2 + other.u ** 2)
      digs = get_digs(self.digs, other.digs)
      return PhyStat(ave, u, digs)
    else:
      ave = self.ave + other
      return PhyStat(ave, self.u, self.digs)
 
  __radd__ = __add__
  __sub__ = lambda self, other: self + (-other)
  __rsub__ = lambda self, other: other + (-self)
 
  def __mul__(self, other):
    if isinstance(other, PhyStat):
      a = self.ave
      b = other.ave
      ave = a * b
      u = ave * sqrt((self.u / a) ** 2 + (other.u / b) ** 2)
      digs = get_digs(self.digs, other.digs)
      return PhyStat(ave, u, digs)
    else:
      ave = self.ave * other
      u = self.u * other
      return PhyStat(ave, u, self.digs)
 
  __rmul__ = __mul__
 
  def __div__(self, other):
    if isinstance(other, PhyStat):
      return self * other ** -1
    else:
      return (1.0 / other) * self
 
  __rdiv__ = lambda self, other: other * self ** -1
 
  def __pow__(self, other):
    a = self.ave
    ave = a ** other
    u = abs(other * self.u / a * ave)
    return PhyStat(ave, u, self.digs)
 
  __iadd__ = gen_imet(lambda self, other: self + other)
  __isub__ = gen_imet(lambda self, other: self - other)
  __imul__ = gen_imet(lambda self, other: self * other)
  __idiv__ = gen_imet(lambda self, other: self / other)
  __ipow__ = gen_imet(lambda self, other: self ** other)
 
  __int__ = lambda self: int(self.ave)
  __long__ = lambda self: long(self.ave)
  __float__ = lambda self: self.ave