class Monitor(list):
    """ Monitored variables

    A Class for monitored variables, that is, variables that allow one
    to gather simple statistics.  A Monitor is a subclass of list and
    list operations can be performed on it. An object is established
    using m = Monitor(name = '..'). It can be given a
    unique name for use in debugging and in tracing and ylab and tlab
    strings for labelling graphs.
    """
    def __init__(self, env , name = 'a_Monitor', ylab = 'y', tlab = 't'):
        list.__init__(self)
        self.env = env
        self.startTime = 0.0
        self.name = name
        self.ylab = ylab
        self.tlab = tlab

    def observe(self, y,t = None):
        """record y and t"""
        if t is  None: t = self.env.now
        self.append([t, y])

    def tally(self, y):
        """ deprecated: tally for backward compatibility"""
        self.observe(y, 0)

    def accum(self, y,t = None):
        """ deprecated:  accum for backward compatibility"""
        self.observe(y, t)

    def reset(self, t = None):
        """reset the sums and counts for the monitored variable """
        self[:] = []
        if t is None: t = self.env.now
        self.startTime = t

    def tseries(self):
        """ the series of measured times"""
        return list(zip(*self))[0]

    def yseries(self):
        """ the series of measured values"""
        return list(zip(*self))[1]

    def count(self):
        """ deprecated: the number of observations made """
        return self.__len__()

    def total(self):
        """ the sum of the y"""
        if self.__len__() == 0:  return 0
        else:
            sum = 0.0
            for i in range(self.__len__()):
                sum += self[i][1]
            return sum # replace by sum() later

    def mean(self):
        """ the simple average of the monitored variable"""
        try:
            return 1.0 * self.total() / self.__len__()
        except ZeroDivisionError:
            raise ZeroDivisionError('SimPy: No observations for mean')

    def var(self):
        """ the sample variance of the monitored variable """
        n = len(self)
        tot = self.total()
        ssq = 0.0
        for i in range(self.__len__()):
            ssq += self[i][1] ** 2 # replace by sum() eventually
        try:
            return (ssq - float(tot * tot) / n) / n
        except:
            raise ZeroDivisionError(
                    'SimPy: No observations for sample variance')

    def timeAverage(self, t = None):
        """
        The time-weighted average of the monitored variable.

        If t is used it is assumed to be the current time,
        otherwise t =  self.sim.now

        """
        N = self.__len__()
        if N  == 0:
            return None

        if t is None: t = self.env.now
        sum = 0.0
        tlast = self[0][0]
        ylast = self[0][1]
        for i in range(N):
            ti, yi = self[i]
            sum += ylast * (ti - tlast)
            tlast = ti
            ylast = yi
        sum += ylast * (t - tlast)
        T = t - self[0][0]
        if T == 0:
             return None
        return sum / float(T)

    def timeVariance(self, t = None):
        """ the time - weighted Variance of the monitored variable.

            If t is used it is assumed to be the current time,
            otherwise t =  self.sim.now
        """
        N = self.__len__()
        if N  == 0:
            return None
        if t is None: t = self.env.now
        sm = 0.0
        ssq = 0.0
        tlast = self[0][0]
        # print 'DEBUG: 1 twVar ', t, tlast
        ylast = self[0][1]
        for i in range(N):
            ti, yi = self[i]
            sm  += ylast * (ti - tlast)
            ssq += ylast * ylast * (ti - tlast)
            tlast = ti
            ylast = yi
        sm  += ylast * (t - tlast)
        ssq += ylast * ylast * (t - tlast)
        T = t - self[0][0]
        if T == 0:
             return None
        mn = sm / float(T)
        return ssq / float(T) - mn * mn