# Path: pathpy/Log.py
# class Log:
#     """ A simple logging class, that allows to select what messages should
#         be recorded in the output, and where these message should be directed.
#     """
# 
#     ## the output stream to which log entries will be written
#     output_stream = sys.stdout
# 
#     ## The minimum severity level of messages to be logged
#     min_severity  = Severity.INFO
# 
# 
#     @staticmethod
#     def setMinSeverity(severity):
#         """ Sets the minimum sveerity level a message
#         needs to have in order to be recorded in the output stream.
#         By default, any message which has a severity of at least
#         Severity.INFO will be written to the output stream. All messages
#         with lower priority will be surpressed.
#         """
#         Log.min_severity = severity
# 
# 
#     @staticmethod
#     def setOutputStream(stream):
#         """ Sets the output stream to which all messages will be
#             written. By default, this is sys.stdout, but it can be
#             changed in order to redirect the log to a logfile.
#         """
#         output_stream = stream
# 
# 
#     @staticmethod
#     def add(msg, severity=Severity.INFO):
#         """ Adds a message with the given severity to the log. This message will be written
#             to the log output stream, which by default is sys.stdout. A newline character
#             will be added to the message by default.
#         """
#         if severity >= Log.min_severity:
#             ts = time.strftime("%Y-%m-%d %H:%M:%S", time.gmtime())
#             Log.output_stream.write(ts + ' [' + str(severity) + ']\t' + msg + '\n')
#             Log.output_stream.flush()
# 
# Path: pathpy/Log.py
# class Severity(enum.IntEnum):
#     """ An enumeration that can be used to indicate
#         the severity of log messages, and which can be
#         used tpo filter messages based on severities.
#     """
# 
#     ## Error messages
#     ERROR = 4
# 
#     ## Warning messages
#     WARNING = 3
# 
#     ## Informational messages (default minimum level)
#     INFO = 2
# 
#     ## Messages regarding timing and performance
#     TIMING = 1
# 
#     ## Debug messages (really verbose)
#     DEBUG = 0


import numpy as _np
import collections as _co
import bisect as _bs
import itertools as _iter
import scipy.sparse as _sparse
import scipy.misc as _misc
import scipy.sparse.linalg as _sla
import scipy.linalg as _la
from scipy.stats import chi2
from pathpy.Log import Log
from pathpy.Log import Severity
        s = len(self.states[1])
        n = len(self.sequence)-k

        # the transition matrix of a first-order model with s states has s**2 entries, subject to the
        # constraint that entries in each row must sum up to one (thus effectively reducing
        # the degrees of freedom by a factor of s, i.e. we have s**2-s**1. Generalizing this to order k,
        # we arrive at s**k * (s-1) = s**(k+1) - s**k derees of freedom
        bic = _np.log(n) * (s**k - s**m) * (s-1) - 2.0 * (L_k-L_m)

        return bic


    def getAIC(self, k=1, m=1):
        """ Returns the Aikake Information Criterion
            assuming a k-th order Markov model """

        if k not in self.P:
            self.fitMarkovModel(k)

        if m not in self.P:
            self.fitMarkovModel(m)

        L_k = self.getLikelihood(k, log=True)
        L_m = self.getLikelihood(m, log=True)

        s = len(self.states[1])
        n = len(self.sequence)

        aic = 2 * (s**k - s**m) * (s-1) - 2.0 * (L_k - L_m)


# Path: pathpy/Log.py
# class Log:
#     """ A simple logging class, that allows to select what messages should
#         be recorded in the output, and where these message should be directed.
#     """
# 
#     ## the output stream to which log entries will be written
#     output_stream = sys.stdout
# 
#     ## The minimum severity level of messages to be logged
#     min_severity  = Severity.INFO
# 
# 
#     @staticmethod
#     def setMinSeverity(severity):
#         """ Sets the minimum sveerity level a message
#         needs to have in order to be recorded in the output stream.
#         By default, any message which has a severity of at least
#         Severity.INFO will be written to the output stream. All messages
#         with lower priority will be surpressed.
#         """
#         Log.min_severity = severity
# 
# 
#     @staticmethod
#     def setOutputStream(stream):
#         """ Sets the output stream to which all messages will be
#             written. By default, this is sys.stdout, but it can be
#             changed in order to redirect the log to a logfile.
#         """
#         output_stream = stream
# 
# 
#     @staticmethod
#     def add(msg, severity=Severity.INFO):
#         """ Adds a message with the given severity to the log. This message will be written
#             to the log output stream, which by default is sys.stdout. A newline character
#             will be added to the message by default.
#         """
#         if severity >= Log.min_severity:
#             ts = time.strftime("%Y-%m-%d %H:%M:%S", time.gmtime())
#             Log.output_stream.write(ts + ' [' + str(severity) + ']\t' + msg + '\n')
#             Log.output_stream.flush()
# 
# Path: pathpy/Log.py
# class Severity(enum.IntEnum):
#     """ An enumeration that can be used to indicate
#         the severity of log messages, and which can be
#         used tpo filter messages based on severities.
#     """
# 
#     ## Error messages
#     ERROR = 4
# 
#     ## Warning messages
#     WARNING = 3
# 
#     ## Informational messages (default minimum level)
#     INFO = 2
# 
#     ## Messages regarding timing and performance
#     TIMING = 1
# 
#     ## Debug messages (really verbose)
#     DEBUG = 0


# Path: pathpy/MarkovSequence.py
import numpy as _np
import collections as _co
import bisect as _bs
import itertools as _iter
import scipy.sparse as _sparse
import scipy.misc as _misc
import scipy.sparse.linalg as _sla
import scipy.linalg as _la
from scipy.stats import chi2
from pathpy.Log import Log
from pathpy.Log import Severity

        s = len(self.states[1])
        n = len(self.sequence)-k

        # the transition matrix of a first-order model with s states has s**2 entries, subject to the
        # constraint that entries in each row must sum up to one (thus effectively reducing
        # the degrees of freedom by a factor of s, i.e. we have s**2-s**1. Generalizing this to order k,
        # we arrive at s**k * (s-1) = s**(k+1) - s**k derees of freedom
        bic = _np.log(n) * (s**k - s**m) * (s-1) - 2.0 * (L_k-L_m)

        return bic


    def getAIC(self, k=1, m=1):
        """ Returns the Aikake Information Criterion
            assuming a k-th order Markov model """

        if k not in self.P:
            self.fitMarkovModel(k)

        if m not in self.P:
            self.fitMarkovModel(m)

        L_k = self.getLikelihood(k, log=True)
        L_m = self.getLikelihood(m, log=True)

        s = len(self.states[1])
        n = len(self.sequence)

        aic = 2 * (s**k - s**m) * (s-1) - 2.0 * (L_k - L_m)


        return aic