class_docstr: Class to represent a Markov Chain with multiple kernels for factored state space,
  along with methods to simulate a run.
  
  Examples
  --------
  
  Create an empty Markov Chain:
  
  >>> from pgmpy.models import MarkovChain as MC
  >>> model = MC()
  
  And then add variables to it
  
  >>> model.add_variables_from(['intel', 'diff'], [2, 3])
  
  Or directly create a Markov Chain from a list of variables and their cardinalities
  
  >>> model = MC(['intel', 'diff'], [2, 3])
  
  Add transition models
  
  >>> intel_tm = {0: {0: 0.25, 1: 0.75}, 1: {0: 0.5, 1: 0.5}}
  >>> model.add_transition_model('intel', intel_tm)
  >>> diff_tm = {0: {0: 0.1, 1: 0.5, 2: 0.4}, 1: {0: 0.2, 1: 0.2, 2: 0.6 }, 2: {0: 0.7, 1: 0.15, 2: 0.15}}
  >>> model.add_transition_model('diff', diff_tm)
  
  Set a start state
  
  >>> from pgmpy.factors.discrete import State
  >>> model.set_start_state([State('intel', 0), State('diff', 2)])
  
  Sample from it
  
  >>> model.sample(size=5)
     intel  diff
  0      0     2
  1      1     0
  2      0     1
  3      1     0
  4      0     2
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docstr: Returns a copy of Markov Chain Model.
  
  Returns
  -------
  MarkovChain : Copy of MarkovChain.
  
  Examples
  --------
  >>> from pgmpy.models import MarkovChain
  >>> from pgmpy.factors.discrete import State
  >>> model = MarkovChain()
  >>> model.add_variables_from(['intel', 'diff'], [3, 2])
  >>> intel_tm = {0: {0: 0.2, 1: 0.4, 2:0.4}, 1: {0: 0, 1: 0.5, 2: 0.5}, 2: {0: 0.3, 1: 0.3, 2: 0.4}}
  >>> model.add_transition_model('intel', intel_tm)
  >>> diff_tm = {0: {0: 0.5, 1: 0.5}, 1: {0: 0.25, 1:0.75}}
  >>> model.add_transition_model('diff', diff_tm)
  >>> model.set_start_state([State('intel', 0), State('diff', 1)])
  >>> model_copy = model.copy()
  >>> model_copy.transition_models
  >>> {'diff': {0: {0: 0.1, 1: 0.5, 2: 0.4}, 1: {0: 0.2, 1: 0.2, 2: 0.6}, 2: {0: 0.7, 1: 0.15, 2: 0.15}},
  ...  'intel': {0: {0: 0.25, 1: 0.75}, 1: {0: 0.5, 1: 0.5}}}
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code: def copy(self):
      """
      Returns a copy of Markov Chain Model.
  
      Returns
      -------
      MarkovChain : Copy of MarkovChain.
  
      Examples
      --------
      >>> from pgmpy.models import MarkovChain
      >>> from pgmpy.factors.discrete import State
      >>> model = MarkovChain()
      >>> model.add_variables_from(['intel', 'diff'], [3, 2])
      >>> intel_tm = {0: {0: 0.2, 1: 0.4, 2:0.4}, 1: {0: 0, 1: 0.5, 2: 0.5}, 2: {0: 0.3, 1: 0.3, 2: 0.4}}
      >>> model.add_transition_model('intel', intel_tm)
      >>> diff_tm = {0: {0: 0.5, 1: 0.5}, 1: {0: 0.25, 1:0.75}}
      >>> model.add_transition_model('diff', diff_tm)
      >>> model.set_start_state([State('intel', 0), State('diff', 1)])
      >>> model_copy = model.copy()
      >>> model_copy.transition_models
      >>> {'diff': {0: {0: 0.1, 1: 0.5, 2: 0.4}, 1: {0: 0.2, 1: 0.2, 2: 0.6}, 2: {0: 0.7, 1: 0.15, 2: 0.15}},
      ...  'intel': {0: {0: 0.25, 1: 0.75}, 1: {0: 0.5, 1: 0.5}}}
      """
      markovchain_copy = MarkovChain(
          variables=list(self.cardinalities.keys()),
          card=list(self.cardinalities.values()),
          start_state=self.state,
      )
      if self.transition_models:
          markovchain_copy.transition_models = (
              self.transition_models.copy()
          )
  
      return markovchain_copy
  
imports: from collections import defaultdict
  import numpy
  from pandas import DataFrame
  from scipy.linalg import eig
  from pgmpy.factors.discrete import State
  from pgmpy.global_vars import logger
  from pgmpy.utils import sample_discrete
label_desc: Use image node_id 12 for calling the MarkovChain obj's underlying member method code with example usage: obj.copy() and returns: markovchain_copy