code: """
  The MIT License (MIT)
  
  Copyright (c) 2013-2017 pgmpy
  
  Permission is hereby granted, free of charge, to any person obtaining a copy of
  this software and associated documentation files (the "Software"), to deal in
  the Software without restriction, including without limitation the rights to
  use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
  the Software, and to permit persons to whom the Software is furnished to do so,
  subject to the following conditions:
  
  The above copyright notice and this permission notice shall be included in all
  copies or substantial portions of the Software.
  
  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
  FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
  COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
  IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
  CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
  """
  
  import copy
  import numpy as np
  
  
  class DiscreteFactor:
  
      def __init__(self, variables, cardinality, values=None, state_names=None):
          """
          Args
              variables: list,
                  variables in the scope of the factor
              cardinality: list,
                  cardinalities of each variable, where len(cardinality)=len(variables)
              values: list,
                  row vector of values of variables with ordering such that right-most variables
                  defined in `variables` cycle through their values the fastest
              state_names: dictionary,
                  mapping variables to their states, of format {label_name: ['state1', 'state2']}
          """
          self.variables = list(variables)
          self.cardinality = list(cardinality)
          if values is None:
              self._values = None
          else:
              self._values = np.array(values).reshape(self.cardinality)
          self.state_names = state_names
  
      def __mul__(self, other):
          return self.product(other)
  
      def copy(self):
          """Return a copy of the factor"""
          return self.__class__(self.variables,
                                self.cardinality,
                                self._values,
                                copy.deepcopy(self.state_names))
  
      @property
      def values(self):
          return self._values
  
      def update_values(self, new_values):
          """We make this available because _values is allowed to be None on init"""
          self._values = np.array(new_values).reshape(self.cardinality)
  
      def get_value_for_state_vector(self, dict_of_states):
          """
          Return the value for a dictionary of variable states.
  
          Args
              dict_of_states: dictionary,
                  of format {label_name1: 'state1', label_name2: 'True'}
          Returns
              probability, a float, the factor value for a specific combination of variable states
          """
          assert sorted(dict_of_states.keys()) == sorted(self.variables), \
              "The keys for the dictionary of states must match the variables in factor scope."
          state_coordinates = []
          for var in self.variables:
              var_state = dict_of_states[var]
              idx_in_var_axis = self.state_names[var].index(var_state)
              state_coordinates.append(idx_in_var_axis)
          return self.values[tuple(state_coordinates)]
  
      def add_new_variables_from_other_factor(self, other):
          """Add new variables from `other` factor to the factor."""
          extra_vars = set(other.variables) - set(self.variables)
          # if all of these variables already exist there is nothing to do
          if len(extra_vars) == 0:
              return
          # otherwise, extend the values array
          slice_ = [slice(None)] * len(self.variables)
          slice_.extend([np.newaxis] * len(extra_vars))
          self._values = self._values[slice_]
          self.variables.extend(extra_vars)
  
          new_card_var = other.get_cardinality(extra_vars)
          self.cardinality.extend([new_card_var[var] for var in extra_vars])
  
      def get_cardinality(self, variables):
          return {var: self.cardinality[self.variables.index(var)] for var in variables}
  
      def product(self, other):
          left = self.copy()
  
          if isinstance(other, (int, float)):
              return self.values * other
          else:
              assert isinstance(other, DiscreteFactor), \
                  "__mul__ is only defined between subclasses of DiscreteFactor"
              right = other.copy()
              left.add_new_variables_from_other_factor(right)
              right.add_new_variables_from_other_factor(left)
  
          # reorder variables in right factor to match order in left
          source_axes = list(range(right.values.ndim))
          destination_axes = [right.variables.index(var) for var in left.variables]
          right.variables = [right.variables[idx] for idx in destination_axes]
  
          # rearrange values in right factor to correspond to the reordered variables
          right._values = np.moveaxis(right.values, source_axes, destination_axes)
          left._values = left.values * right.values
          return left
  
      def marginalize(self, vars):
          """
          Args
              vars: list,
                  variables over which to marginalize the factor
          Returns
              DiscreteFactor, whose scope is set(self.variables) - set(vars)
          """
          phi = copy.deepcopy(self)
  
          var_indexes = []
          for var in vars:
              if var not in phi.variables:
                  raise ValueError('{} not in scope'.format(var))
              else:
                  var_indexes.append(self.variables.index(var))
  
          index_to_keep = sorted(set(range(len(self.variables))) - set(var_indexes))
          phi.variables = [self.variables[index] for index in index_to_keep]
          phi.cardinality = [self.cardinality[index] for index in index_to_keep]
          phi._values = np.sum(phi.values, axis=tuple(var_indexes))
          return phi
  
apis: numpy.array numpy.moveaxis