# 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
        """ Generates a k-th order Markov model
            for the underlying sequence
        """

        # TODO: Add support for k=0

        assert len(self.sequence)>0, "Error: Empty sequence"

        # MLE fit of transition probabilities
        self.P[k] = _co.defaultdict( lambda:  _co.defaultdict( lambda: 0.0 )  )

        Log.add('Fitting Markov model with order k = ' + str(k))

        # Generate initial memory prefix
        mem = (())
        for s in self.sequence[:k]:
            mem += (s,)

        # count state transitions
        for s in self.sequence[k:]:
            self.P[k][mem][s] += 1.0

            # shift memory by one element
            mem = mem[1:] + (s,)

        # normalize transitions
        for m in self.P[k]:
            S = float(sum(self.P[k][m].values()))
            for s in self.P[k][m]:
                self.P[k][m][s] /= S

# 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

        """ Generates a k-th order Markov model
            for the underlying sequence
        """

        # TODO: Add support for k=0

        assert len(self.sequence)>0, "Error: Empty sequence"

        # MLE fit of transition probabilities
        self.P[k] = _co.defaultdict( lambda:  _co.defaultdict( lambda: 0.0 )  )

        Log.add('Fitting Markov model with order k = ' + str(k))

        # Generate initial memory prefix
        mem = (())
        for s in self.sequence[:k]:
            mem += (s,)

        # count state transitions
        for s in self.sequence[k:]:
            self.P[k][mem][s] += 1.0

            # shift memory by one element
            mem = mem[1:] + (s,)

        # normalize transitions
        for m in self.P[k]:
            S = float(sum(self.P[k][m].values()))
            for s in self.P[k][m]:
                self.P[k][m][s] /= S

        Log.add('finished.')