# 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 collections as _co
import bisect as _bs
import itertools as _iter
import numpy as _np 
import scipy.sparse as _sparse
import scipy.sparse.linalg as _sla
import scipy.linalg as _la
import scipy as _sp
from pathpy.Log import Log
from pathpy.Log import Severity
    
        T = self.getTransitionMatrix(includeSubPaths)
        I  = _sparse.identity( self.vcount() )

        return I-T


    def getEigenValueGap(self, includeSubPaths=True, lanczosVecs = 15, maxiter = 20):
        """
        Returns the eigenvalue gap of the transition matrix.

        @param includeSubPaths: whether or not to include subpath statistics in the 
            calculation of transition probabilities.
        """
    
        #NOTE to myself: most of the time goes for construction of the 2nd order
        #NOTE            null graph, then for the 2nd order null transition matrix   
    
        Log.add('Calculating eigenvalue gap ... ', Severity.INFO)

        # Build transition matrices
        T = self.getTransitionMatrix(includeSubPaths)
    
        # Compute the two largest eigenvalues
        # NOTE: ncv sets additional auxiliary eigenvectors that are computed
        # NOTE: in order to be more confident to actually find the one with the largest
        # NOTE: magnitude, see https://github.com/scipy/scipy/issues/4987
        w2 = _sla.eigs(T, which="LM", k=2, ncv=lanczosVecs, return_eigenvectors=False, maxiter = maxiter)
        evals2_sorted = _np.sort(-_np.absolute(w2))
        

# 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/HigherOrderNetwork.py
import collections as _co
import bisect as _bs
import itertools as _iter
import numpy as _np 
import scipy.sparse as _sparse
import scipy.sparse.linalg as _sla
import scipy.linalg as _la
import scipy as _sp
from pathpy.Log import Log
from pathpy.Log import Severity

    
        T = self.getTransitionMatrix(includeSubPaths)
        I  = _sparse.identity( self.vcount() )

        return I-T


    def getEigenValueGap(self, includeSubPaths=True, lanczosVecs = 15, maxiter = 20):
        """
        Returns the eigenvalue gap of the transition matrix.

        @param includeSubPaths: whether or not to include subpath statistics in the 
            calculation of transition probabilities.
        """
    
        #NOTE to myself: most of the time goes for construction of the 2nd order
        #NOTE            null graph, then for the 2nd order null transition matrix   
    
        Log.add('Calculating eigenvalue gap ... ', Severity.INFO)

        # Build transition matrices
        T = self.getTransitionMatrix(includeSubPaths)
    
        # Compute the two largest eigenvalues
        # NOTE: ncv sets additional auxiliary eigenvectors that are computed
        # NOTE: in order to be more confident to actually find the one with the largest
        # NOTE: magnitude, see https://github.com/scipy/scipy/issues/4987
        w2 = _sla.eigs(T, which="LM", k=2, ncv=lanczosVecs, return_eigenvectors=False, maxiter = maxiter)
        evals2_sorted = _np.sort(-_np.absolute(w2))
        

        Log.add('finished.', Severity.INFO)