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def condition_tpm ( tpm , fixed_nodes , state ) : conditioning_indices = [ [ slice ( None ) ] ] * len ( state ) for i in fixed_nodes : # Preserve singleton dimensions with `np.newaxis` conditioning_indices [ i ] = [ state [ i ] , np . newaxis ] # Flatten the indices. conditioning_indices = list ( chain . from_iterable ( conditioning_indices ) ) # Obtain the actual conditioned TPM by indexing with the conditioning # indices. return tpm [ tuple ( conditioning_indices ) ]
Return a TPM conditioned on the given fixed node indices whose states are fixed according to the given state - tuple .
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def expand_tpm ( tpm ) : unconstrained = np . ones ( [ 2 ] * ( tpm . ndim - 1 ) + [ tpm . shape [ - 1 ] ] ) return tpm * unconstrained
Broadcast a state - by - node TPM so that singleton dimensions are expanded over the full network .
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def marginalize_out ( node_indices , tpm ) : return tpm . sum ( tuple ( node_indices ) , keepdims = True ) / ( np . array ( tpm . shape ) [ list ( node_indices ) ] . prod ( ) )
Marginalize out nodes from a TPM .
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def infer_edge ( tpm , a , b , contexts ) : def a_in_context ( context ) : """Given a context C(A), return the states of the full system with A OFF and ON, respectively. """ a_off = context [ : a ] + OFF + context [ a : ] a_on = context [ : a ] + ON + context [ a : ] return ( a_off , a_on ) def a_affects_b_in_context ( context ) : """Return ``True`` if A has an effect on B, given a context.""" a_off , a_on = a_in_context ( context ) return tpm [ a_off ] [ b ] != tpm [ a_on ] [ b ] return any ( a_affects_b_in_context ( context ) for context in contexts )
Infer the presence or absence of an edge from node A to node B .
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def infer_cm ( tpm ) : network_size = tpm . shape [ - 1 ] all_contexts = tuple ( all_states ( network_size - 1 ) ) cm = np . empty ( ( network_size , network_size ) , dtype = int ) for a , b in np . ndindex ( cm . shape ) : cm [ a ] [ b ] = infer_edge ( tpm , a , b , all_contexts ) return cm
Infer the connectivity matrix associated with a state - by - node TPM in multidimensional form .
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def get_num_processes ( ) : cpu_count = multiprocessing . cpu_count ( ) if config . NUMBER_OF_CORES == 0 : raise ValueError ( 'Invalid NUMBER_OF_CORES; value may not be 0.' ) if config . NUMBER_OF_CORES > cpu_count : log . info ( 'Requesting %s cores; only %s available' , config . NUMBER_OF_CORES , cpu_count ) return cpu_count if config . NUMBER_OF_CORES < 0 : num = cpu_count + config . NUMBER_OF_CORES + 1 if num <= 0 : raise ValueError ( 'Invalid NUMBER_OF_CORES; negative value is too negative: ' 'requesting {} cores, {} available.' . format ( num , cpu_count ) ) return num return config . NUMBER_OF_CORES
Return the number of processes to use in parallel .
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def init_progress_bar ( self ) : # Forked worker processes can't show progress bars. disable = MapReduce . _forked or not config . PROGRESS_BARS # Don't materialize iterable unless we have to: huge iterables # (e.g. of `KCuts`) eat memory. if disable : total = None else : self . iterable = list ( self . iterable ) total = len ( self . iterable ) return tqdm ( total = total , disable = disable , leave = False , desc = self . description )
Initialize and return a progress bar .
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def worker ( compute , task_queue , result_queue , log_queue , complete , * context ) : try : MapReduce . _forked = True log . debug ( 'Worker process starting...' ) configure_worker_logging ( log_queue ) for obj in iter ( task_queue . get , POISON_PILL ) : if complete . is_set ( ) : log . debug ( 'Worker received signal - exiting early' ) break log . debug ( 'Worker got %s' , obj ) result_queue . put ( compute ( obj , * context ) ) log . debug ( 'Worker finished %s' , obj ) result_queue . put ( POISON_PILL ) log . debug ( 'Worker process exiting' ) except Exception as e : # pylint: disable=broad-except result_queue . put ( ExceptionWrapper ( e ) )
A worker process run by multiprocessing . Process .
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def start_parallel ( self ) : self . num_processes = get_num_processes ( ) self . task_queue = multiprocessing . Queue ( maxsize = Q_MAX_SIZE ) self . result_queue = multiprocessing . Queue ( ) self . log_queue = multiprocessing . Queue ( ) # Used to signal worker processes when a result is found that allows # the computation to terminate early. self . complete = multiprocessing . Event ( ) args = ( self . compute , self . task_queue , self . result_queue , self . log_queue , self . complete ) + self . context self . processes = [ multiprocessing . Process ( target = self . worker , args = args , daemon = True ) for i in range ( self . num_processes ) ] for process in self . processes : process . start ( ) self . log_thread = LogThread ( self . log_queue ) self . log_thread . start ( ) self . initialize_tasks ( )
Initialize all queues and start the worker processes and the log thread .
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def initialize_tasks ( self ) : # Add a poison pill to shutdown each process. self . tasks = chain ( self . iterable , [ POISON_PILL ] * self . num_processes ) for task in islice ( self . tasks , Q_MAX_SIZE ) : log . debug ( 'Putting %s on queue' , task ) self . task_queue . put ( task )
Load the input queue to capacity .
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def maybe_put_task ( self ) : try : task = next ( self . tasks ) except StopIteration : pass else : log . debug ( 'Putting %s on queue' , task ) self . task_queue . put ( task )
Enqueue the next task if there are any waiting .
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def run_parallel ( self ) : try : self . start_parallel ( ) result = self . empty_result ( * self . context ) while self . num_processes > 0 : r = self . result_queue . get ( ) self . maybe_put_task ( ) if r is POISON_PILL : self . num_processes -= 1 elif isinstance ( r , ExceptionWrapper ) : r . reraise ( ) else : result = self . process_result ( r , result ) self . progress . update ( 1 ) # Did `process_result` decide to terminate early? if self . done : self . complete . set ( ) self . finish_parallel ( ) except Exception : raise finally : log . debug ( 'Removing progress bar' ) self . progress . close ( ) return result
Perform the computation in parallel reading results from the output queue and passing them to process_result .
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def finish_parallel ( self ) : for process in self . processes : process . join ( ) # Shutdown the log thread log . debug ( 'Joining log thread' ) self . log_queue . put ( POISON_PILL ) self . log_thread . join ( ) self . log_queue . close ( ) # Close all queues log . debug ( 'Closing queues' ) self . task_queue . close ( ) self . result_queue . close ( )
Orderly shutdown of workers .
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def run_sequential ( self ) : try : result = self . empty_result ( * self . context ) for obj in self . iterable : r = self . compute ( obj , * self . context ) result = self . process_result ( r , result ) self . progress . update ( 1 ) # Short-circuited? if self . done : break except Exception as e : raise e finally : self . progress . close ( ) return result
Perform the computation sequentially only holding two computed objects in memory at a time .
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def configure_logging ( conf ) : logging . config . dictConfig ( { 'version' : 1 , 'disable_existing_loggers' : False , 'formatters' : { 'standard' : { 'format' : '%(asctime)s [%(name)s] %(levelname)s ' '%(processName)s: %(message)s' } } , 'handlers' : { 'file' : { 'level' : conf . LOG_FILE_LEVEL , 'filename' : conf . LOG_FILE , 'class' : 'logging.FileHandler' , 'formatter' : 'standard' , } , 'stdout' : { 'level' : conf . LOG_STDOUT_LEVEL , 'class' : 'pyphi.log.TqdmHandler' , 'formatter' : 'standard' , } } , 'root' : { 'level' : 'DEBUG' , 'handlers' : ( [ 'file' ] if conf . LOG_FILE_LEVEL else [ ] ) + ( [ 'stdout' ] if conf . LOG_STDOUT_LEVEL else [ ] ) } } )
Reconfigure PyPhi logging based on the current configuration .
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def _validate ( self , value ) : if self . values and value not in self . values : raise ValueError ( '{} is not a valid value for {}' . format ( value , self . name ) )
Validate the new value .
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def options ( cls ) : return { k : v for k , v in cls . __dict__ . items ( ) if isinstance ( v , Option ) }
Return a dictionary of the Option objects for this config .
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def defaults ( self ) : return { k : v . default for k , v in self . options ( ) . items ( ) }
Return the default values of this configuration .
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def load_dict ( self , dct ) : for k , v in dct . items ( ) : setattr ( self , k , v )
Load a dictionary of configuration values .
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def load_file ( self , filename ) : filename = os . path . abspath ( filename ) with open ( filename ) as f : self . load_dict ( yaml . load ( f ) ) self . _loaded_files . append ( filename )
Load config from a YAML file .
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def log ( self ) : log . info ( 'PyPhi v%s' , __about__ . __version__ ) if self . _loaded_files : log . info ( 'Loaded configuration from %s' , self . _loaded_files ) else : log . info ( 'Using default configuration (no configuration file ' 'provided)' ) log . info ( 'Current PyPhi configuration:\n %s' , str ( self ) )
Log current settings .
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def be2le_state_by_state ( tpm ) : le = np . empty ( tpm . shape ) N = tpm . shape [ 0 ] n = int ( log2 ( N ) ) for i in range ( N ) : le [ i , : ] = tpm [ be2le ( i , n ) , : ] return le
Convert a state - by - state TPM from big - endian to little - endian or vice versa .
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def to_multidimensional ( tpm ) : # Cast to np.array. tpm = np . array ( tpm ) # Get the number of nodes. N = tpm . shape [ - 1 ] # Reshape. We use Fortran ordering here so that the rows use the # little-endian convention (least-significant bits correspond to low-index # nodes). Note that this does not change the actual memory layout (C- or # Fortran-contiguous), so there is no performance loss. return tpm . reshape ( [ 2 ] * N + [ N ] , order = "F" ) . astype ( float )
Reshape a state - by - node TPM to the multidimensional form .
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def state_by_state2state_by_node ( tpm ) : # Cast to np.array. tpm = np . array ( tpm ) # Get the number of states from the length of one side of the TPM. S = tpm . shape [ - 1 ] # Get the number of nodes from the number of states. N = int ( log2 ( S ) ) # Initialize the new state-by node TPM. sbn_tpm = np . zeros ( ( [ 2 ] * N + [ N ] ) ) # Map indices to state-tuples with the little-endian convention. states = { i : le_index2state ( i , N ) for i in range ( S ) } # Get an array for each node with 1 in positions that correspond to that # node being on in the next state, and a 0 otherwise. node_on = np . array ( [ [ states [ i ] [ n ] for i in range ( S ) ] for n in range ( N ) ] ) on_probabilities = [ tpm * node_on [ n ] for n in range ( N ) ] for i , state in states . items ( ) : # Get the probability of each node being on given the previous state i, # i.e., a row of the state-by-node TPM. # Assign that row to the ith state in the state-by-node TPM. sbn_tpm [ state ] = [ np . sum ( on_probabilities [ n ] [ i ] ) for n in range ( N ) ] return sbn_tpm
Convert a state - by - state TPM to a state - by - node TPM .
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def state_by_node2state_by_state ( tpm ) : # Cast to np.array. tpm = np . array ( tpm ) # Convert to multidimensional form. tpm = to_multidimensional ( tpm ) # Get the number of nodes from the last dimension of the TPM. N = tpm . shape [ - 1 ] # Get the number of states. S = 2 ** N # Initialize the state-by-state TPM. sbs_tpm = np . zeros ( ( S , S ) ) if not np . any ( np . logical_and ( tpm < 1 , tpm > 0 ) ) : # TPM is deterministic. for previous_state_index in range ( S ) : # Use the little-endian convention to get the row and column # indices. previous_state = le_index2state ( previous_state_index , N ) current_state_index = state2le_index ( tpm [ previous_state ] ) sbs_tpm [ previous_state_index , current_state_index ] = 1 else : # TPM is nondeterministic. for previous_state_index in range ( S ) : # Use the little-endian convention to get the row and column # indices. previous_state = le_index2state ( previous_state_index , N ) marginal_tpm = tpm [ previous_state ] for current_state_index in range ( S ) : current_state = np . array ( [ i for i in le_index2state ( current_state_index , N ) ] ) sbs_tpm [ previous_state_index , current_state_index ] = ( np . prod ( marginal_tpm [ current_state == 1 ] ) * np . prod ( 1 - marginal_tpm [ current_state == 0 ] ) ) return sbs_tpm
Convert a state - by - node TPM to a state - by - state TPM .
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def load_json_network ( json_dict ) : network = pyphi . Network . from_json ( json_dict [ 'network' ] ) state = json_dict [ 'state' ] return ( network , state )
Load a network from a json file
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def all_network_files ( ) : # TODO: list explicitly since some are missing? network_types = [ 'AND-circle' , 'MAJ-specialized' , 'MAJ-complete' , 'iit-3.0-modular' ] network_sizes = range ( 5 , 8 ) network_files = [ ] for n in network_sizes : for t in network_types : network_files . append ( '{}-{}' . format ( n , t ) ) return network_files
All network files
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def profile_network ( filename ) : log = logging . getLogger ( filename ) logfile = os . path . join ( LOGS , filename + '.log' ) os . makedirs ( os . path . dirname ( logfile ) , exist_ok = True ) handler = logging . FileHandler ( logfile ) handler . setFormatter ( formatter ) log . addHandler ( handler ) log . setLevel ( logging . INFO ) try : with open ( os . path . join ( NETWORKS , filename + '.json' ) ) as f : network , state = load_json_network ( json . load ( f ) ) log . info ( 'Profiling %s...' , filename ) log . info ( 'PyPhi configuration:\n%s' , pyphi . config . get_config_string ( ) ) start = time ( ) pr = cProfile . Profile ( ) pr . enable ( ) results = tuple ( pyphi . compute . complexes ( network , state ) ) pr . disable ( ) end = time ( ) pstatsfile = os . path . join ( PSTATS , filename + '.pstats' ) os . makedirs ( os . path . dirname ( pstatsfile ) , exist_ok = True ) pr . dump_stats ( pstatsfile ) log . info ( 'Finished in %i seconds.' , end - start ) resultfile = os . path . join ( RESULTS , filename + '-results.pkl' ) os . makedirs ( os . path . dirname ( resultfile ) , exist_ok = True ) with open ( resultfile , 'wb' ) as f : pickle . dump ( results , f ) except Exception as e : log . error ( e ) raise e
Profile a network .
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def run_tpm ( tpm , time_scale ) : sbs_tpm = convert . state_by_node2state_by_state ( tpm ) if sparse ( tpm ) : tpm = sparse_time ( sbs_tpm , time_scale ) else : tpm = dense_time ( sbs_tpm , time_scale ) return convert . state_by_state2state_by_node ( tpm )
Iterate a TPM by the specified number of time steps .
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def run_cm ( cm , time_scale ) : cm = np . linalg . matrix_power ( cm , time_scale ) # Round non-unitary values back to 1 cm [ cm > 1 ] = 1 return cm
Iterate a connectivity matrix the specified number of steps .
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def _reachable_subsystems ( network , indices , state ) : validate . is_network ( network ) # Return subsystems largest to smallest to optimize parallel # resource usage. for subset in utils . powerset ( indices , nonempty = True , reverse = True ) : try : yield Subsystem ( network , state , subset ) except exceptions . StateUnreachableError : pass
A generator over all subsystems in a valid state .
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def all_complexes ( network , state ) : engine = FindAllComplexes ( subsystems ( network , state ) ) return engine . run ( config . PARALLEL_COMPLEX_EVALUATION )
Return a generator for all complexes of the network .
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def complexes ( network , state ) : engine = FindIrreducibleComplexes ( possible_complexes ( network , state ) ) return engine . run ( config . PARALLEL_COMPLEX_EVALUATION )
Return all irreducible complexes of the network .
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def major_complex ( network , state ) : log . info ( 'Calculating major complex...' ) result = complexes ( network , state ) if result : result = max ( result ) else : empty_subsystem = Subsystem ( network , state , ( ) ) result = _null_sia ( empty_subsystem ) log . info ( "Finished calculating major complex." ) return result
Return the major complex of the network .
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def condensed ( network , state ) : result = [ ] covered_nodes = set ( ) for c in reversed ( sorted ( complexes ( network , state ) ) ) : if not any ( n in covered_nodes for n in c . subsystem . node_indices ) : result . append ( c ) covered_nodes = covered_nodes | set ( c . subsystem . node_indices ) return result
Return a list of maximal non - overlapping complexes .
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def basic_network ( cm = False ) : tpm = np . array ( [ [ 0 , 0 , 0 ] , [ 0 , 0 , 1 ] , [ 1 , 0 , 1 ] , [ 1 , 0 , 0 ] , [ 1 , 1 , 0 ] , [ 1 , 1 , 1 ] , [ 1 , 1 , 1 ] , [ 1 , 1 , 0 ] ] ) if cm is False : cm = np . array ( [ [ 0 , 0 , 1 ] , [ 1 , 0 , 1 ] , [ 1 , 1 , 0 ] ] ) else : cm = None return Network ( tpm , cm = cm , node_labels = LABELS [ : tpm . shape [ 1 ] ] )
A 3 - node network of logic gates .
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def basic_noisy_selfloop_network ( ) : tpm = np . array ( [ [ 0.271 , 0.19 , 0.244 ] , [ 0.919 , 0.19 , 0.756 ] , [ 0.919 , 0.91 , 0.756 ] , [ 0.991 , 0.91 , 0.244 ] , [ 0.919 , 0.91 , 0.756 ] , [ 0.991 , 0.91 , 0.244 ] , [ 0.991 , 0.99 , 0.244 ] , [ 0.999 , 0.99 , 0.756 ] ] ) cm = np . array ( [ [ 1 , 0 , 1 ] , [ 1 , 1 , 1 ] , [ 1 , 1 , 1 ] ] ) return Network ( tpm , cm = cm )
Based on the basic_network but with added selfloops and noisy edges .
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def residue_network ( ) : tpm = np . array ( [ [ int ( s ) for s in bin ( x ) [ 2 : ] . zfill ( 5 ) [ : : - 1 ] ] for x in range ( 32 ) ] ) tpm [ np . where ( np . sum ( tpm [ 0 : , 2 : 4 ] , 1 ) == 2 ) , 0 ] = 1 tpm [ np . where ( np . sum ( tpm [ 0 : , 3 : 5 ] , 1 ) == 2 ) , 1 ] = 1 tpm [ np . where ( np . sum ( tpm [ 0 : , 2 : 4 ] , 1 ) < 2 ) , 0 ] = 0 tpm [ np . where ( np . sum ( tpm [ 0 : , 3 : 5 ] , 1 ) < 2 ) , 1 ] = 0 cm = np . zeros ( ( 5 , 5 ) ) cm [ 2 : 4 , 0 ] = 1 cm [ 3 : , 1 ] = 1 return Network ( tpm , cm = cm , node_labels = LABELS [ : tpm . shape [ 1 ] ] )
The network for the residue example .
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def propagation_delay_network ( ) : num_nodes = 9 num_states = 2 ** num_nodes tpm = np . zeros ( ( num_states , num_nodes ) ) for previous_state_index , previous in enumerate ( all_states ( num_nodes ) ) : current_state = [ 0 for i in range ( num_nodes ) ] if previous [ 2 ] == 1 or previous [ 7 ] == 1 : current_state [ 0 ] = 1 if previous [ 0 ] == 1 : current_state [ 1 ] = 1 current_state [ 8 ] = 1 if previous [ 3 ] == 1 : current_state [ 2 ] = 1 current_state [ 4 ] = 1 if previous [ 1 ] == 1 ^ previous [ 5 ] == 1 : current_state [ 3 ] = 1 if previous [ 4 ] == 1 and previous [ 8 ] == 1 : current_state [ 6 ] = 1 if previous [ 6 ] == 1 : current_state [ 5 ] = 1 current_state [ 7 ] = 1 tpm [ previous_state_index , : ] = current_state cm = np . array ( [ [ 0 , 1 , 0 , 0 , 0 , 0 , 0 , 0 , 1 ] , [ 0 , 0 , 0 , 1 , 0 , 0 , 0 , 0 , 0 ] , [ 1 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 ] , [ 0 , 0 , 1 , 0 , 1 , 0 , 0 , 0 , 0 ] , [ 0 , 0 , 0 , 0 , 0 , 0 , 1 , 0 , 0 ] , [ 0 , 0 , 0 , 1 , 0 , 0 , 0 , 0 , 0 ] , [ 0 , 0 , 0 , 0 , 0 , 1 , 0 , 1 , 0 ] , [ 1 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 ] , [ 0 , 0 , 0 , 0 , 0 , 0 , 1 , 0 , 0 ] ] ) return Network ( tpm , cm = cm , node_labels = LABELS [ : tpm . shape [ 1 ] ] )
A version of the primary example from the IIT 3 . 0 paper with deterministic COPY gates on each connection . These copy gates essentially function as propagation delays on the signal between OR AND and XOR gates from the original system .
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def macro_network ( ) : tpm = np . array ( [ [ 0.3 , 0.3 , 0.3 , 0.3 ] , [ 0.3 , 0.3 , 0.3 , 0.3 ] , [ 0.3 , 0.3 , 0.3 , 0.3 ] , [ 0.3 , 0.3 , 1.0 , 1.0 ] , [ 0.3 , 0.3 , 0.3 , 0.3 ] , [ 0.3 , 0.3 , 0.3 , 0.3 ] , [ 0.3 , 0.3 , 0.3 , 0.3 ] , [ 0.3 , 0.3 , 1.0 , 1.0 ] , [ 0.3 , 0.3 , 0.3 , 0.3 ] , [ 0.3 , 0.3 , 0.3 , 0.3 ] , [ 0.3 , 0.3 , 0.3 , 0.3 ] , [ 0.3 , 0.3 , 1.0 , 1.0 ] , [ 1.0 , 1.0 , 0.3 , 0.3 ] , [ 1.0 , 1.0 , 0.3 , 0.3 ] , [ 1.0 , 1.0 , 0.3 , 0.3 ] , [ 1.0 , 1.0 , 1.0 , 1.0 ] ] ) return Network ( tpm , node_labels = LABELS [ : tpm . shape [ 1 ] ] )
A network of micro elements which has greater integrated information after coarse graining to a macro scale .
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def blackbox_network ( ) : num_nodes = 6 num_states = 2 ** num_nodes tpm = np . zeros ( ( num_states , num_nodes ) ) for index , previous_state in enumerate ( all_states ( num_nodes ) ) : current_state = [ 0 for i in range ( num_nodes ) ] if previous_state [ 5 ] == 1 : current_state [ 0 ] = 1 current_state [ 1 ] = 1 if previous_state [ 0 ] == 1 and previous_state [ 1 ] : current_state [ 2 ] = 1 if previous_state [ 2 ] == 1 : current_state [ 3 ] = 1 current_state [ 4 ] = 1 if previous_state [ 3 ] == 1 and previous_state [ 4 ] == 1 : current_state [ 5 ] = 1 tpm [ index , : ] = current_state cm = np . array ( [ [ 0 , 0 , 1 , 0 , 0 , 0 ] , [ 0 , 0 , 1 , 0 , 0 , 0 ] , [ 0 , 0 , 0 , 1 , 1 , 0 ] , [ 0 , 0 , 0 , 0 , 0 , 1 ] , [ 0 , 0 , 0 , 0 , 0 , 1 ] , [ 1 , 1 , 0 , 0 , 0 , 0 ] ] ) return Network ( tpm , cm , node_labels = LABELS [ : tpm . shape [ 1 ] ] )
A micro - network to demonstrate blackboxing .
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def actual_causation ( ) : tpm = np . array ( [ [ 1 , 0 , 0 , 0 ] , [ 0 , 1 , 0 , 0 ] , [ 0 , 1 , 0 , 0 ] , [ 0 , 0 , 0 , 1 ] ] ) cm = np . array ( [ [ 1 , 1 ] , [ 1 , 1 ] ] ) return Network ( tpm , cm , node_labels = ( 'OR' , 'AND' ) )
The actual causation example network consisting of an OR and AND gate with self - loops .
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def prevention ( ) : tpm = np . array ( [ [ 0.5 , 0.5 , 1 ] , [ 0.5 , 0.5 , 0 ] , [ 0.5 , 0.5 , 1 ] , [ 0.5 , 0.5 , 1 ] , [ 0.5 , 0.5 , 1 ] , [ 0.5 , 0.5 , 0 ] , [ 0.5 , 0.5 , 1 ] , [ 0.5 , 0.5 , 1 ] ] ) cm = np . array ( [ [ 0 , 0 , 1 ] , [ 0 , 0 , 1 ] , [ 0 , 0 , 0 ] ] ) network = Network ( tpm , cm , node_labels = [ 'A' , 'B' , 'F' ] ) x_state = ( 1 , 1 , 1 ) y_state = ( 1 , 1 , 1 ) return Transition ( network , x_state , y_state , ( 0 , 1 ) , ( 2 , ) )
The |Transition| for the prevention example from Actual Causation Figure 5D .
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def clear_subsystem_caches ( subsys ) : try : # New-style caches subsys . _repertoire_cache . clear ( ) subsys . _mice_cache . clear ( ) except TypeError : try : # Pre cache.clear() implementation subsys . _repertoire_cache . cache = { } subsys . _mice_cache . cache = { } except AttributeError : # Old school, pre cache refactor subsys . _repertoire_cache = { } subsys . _repertoire_cache_info = [ 0 , 0 ] subsys . _mice_cache = { }
Clear subsystem caches
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def all_states ( n , big_endian = False ) : if n == 0 : return for state in product ( ( 0 , 1 ) , repeat = n ) : if big_endian : yield state else : yield state [ : : - 1 ]
Return all binary states for a system .
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def np_hash ( a ) : if a is None : return hash ( None ) # Ensure that hashes are equal whatever the ordering in memory (C or # Fortran) a = np . ascontiguousarray ( a ) # Compute the digest and return a decimal int return int ( hashlib . sha1 ( a . view ( a . dtype ) ) . hexdigest ( ) , 16 )
Return a hash of a NumPy array .
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def powerset ( iterable , nonempty = False , reverse = False ) : iterable = list ( iterable ) if nonempty : # Don't include 0-length subsets start = 1 else : start = 0 seq_sizes = range ( start , len ( iterable ) + 1 ) if reverse : seq_sizes = reversed ( seq_sizes ) iterable . reverse ( ) return chain . from_iterable ( combinations ( iterable , r ) for r in seq_sizes )
Generate the power set of an iterable .
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def load_data ( directory , num ) : root = os . path . abspath ( os . path . dirname ( __file__ ) ) def get_path ( i ) : # pylint: disable=missing-docstring return os . path . join ( root , 'data' , directory , str ( i ) + '.npy' ) return [ np . load ( get_path ( i ) ) for i in range ( num ) ]
Load numpy data from the data directory .
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def time_annotated ( func , * args , * * kwargs ) : start = time ( ) result = func ( * args , * * kwargs ) end = time ( ) result . time = round ( end - start , config . PRECISION ) return result
Annotate the decorated function or method with the total execution time .
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def _null_ria ( direction , mechanism , purview , repertoire = None , phi = 0.0 ) : # TODO Use properties here to infer mechanism and purview from # partition yet access them with .mechanism and .partition return RepertoireIrreducibilityAnalysis ( direction = direction , mechanism = mechanism , purview = purview , partition = None , repertoire = repertoire , partitioned_repertoire = None , phi = phi )
The irreducibility analysis for a reducible mechanism .
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def damaged_by_cut ( self , subsystem ) : return ( subsystem . cut . splits_mechanism ( self . mechanism ) or np . any ( self . _relevant_connections ( subsystem ) * subsystem . cut . cut_matrix ( subsystem . network . size ) == 1 ) )
Return True if this MICE is affected by the subsystem s cut .
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def eq_repertoires ( self , other ) : return ( np . array_equal ( self . cause_repertoire , other . cause_repertoire ) and np . array_equal ( self . effect_repertoire , other . effect_repertoire ) )
Return whether this concept has the same repertoires as another .
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def emd_eq ( self , other ) : return ( self . phi == other . phi and self . mechanism == other . mechanism and self . eq_repertoires ( other ) )
Return whether this concept is equal to another in the context of an EMD calculation .
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def directed_account ( transition , direction , mechanisms = False , purviews = False , allow_neg = False ) : if mechanisms is False : mechanisms = utils . powerset ( transition . mechanism_indices ( direction ) , nonempty = True ) links = [ transition . find_causal_link ( direction , mechanism , purviews = purviews , allow_neg = allow_neg ) for mechanism in mechanisms ] # Filter out causal links with zero alpha return DirectedAccount ( filter ( None , links ) )
Return the set of all |CausalLinks| of the specified direction .
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def account ( transition , direction = Direction . BIDIRECTIONAL ) : if direction != Direction . BIDIRECTIONAL : return directed_account ( transition , direction ) return Account ( directed_account ( transition , Direction . CAUSE ) + directed_account ( transition , Direction . EFFECT ) )
Return the set of all causal links for a |Transition| .
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def _evaluate_cut ( transition , cut , unpartitioned_account , direction = Direction . BIDIRECTIONAL ) : cut_transition = transition . apply_cut ( cut ) partitioned_account = account ( cut_transition , direction ) log . debug ( "Finished evaluating %s." , cut ) alpha = account_distance ( unpartitioned_account , partitioned_account ) return AcSystemIrreducibilityAnalysis ( alpha = round ( alpha , config . PRECISION ) , direction = direction , account = unpartitioned_account , partitioned_account = partitioned_account , transition = transition , cut = cut )
Find the |AcSystemIrreducibilityAnalysis| for a given cut .
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def _get_cuts ( transition , direction ) : n = transition . network . size if direction is Direction . BIDIRECTIONAL : yielded = set ( ) for cut in chain ( _get_cuts ( transition , Direction . CAUSE ) , _get_cuts ( transition , Direction . EFFECT ) ) : cm = utils . np_hashable ( cut . cut_matrix ( n ) ) if cm not in yielded : yielded . add ( cm ) yield cut else : mechanism = transition . mechanism_indices ( direction ) purview = transition . purview_indices ( direction ) for partition in mip_partitions ( mechanism , purview , transition . node_labels ) : yield ActualCut ( direction , partition , transition . node_labels )
A list of possible cuts to a transition .
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def sia ( transition , direction = Direction . BIDIRECTIONAL ) : validate . direction ( direction , allow_bi = True ) log . info ( "Calculating big-alpha for %s..." , transition ) if not transition : log . info ( 'Transition %s is empty; returning null SIA ' 'immediately.' , transition ) return _null_ac_sia ( transition , direction ) if not connectivity . is_weak ( transition . network . cm , transition . node_indices ) : log . info ( '%s is not strongly/weakly connected; returning null SIA ' 'immediately.' , transition ) return _null_ac_sia ( transition , direction ) log . debug ( "Finding unpartitioned account..." ) unpartitioned_account = account ( transition , direction ) log . debug ( "Found unpartitioned account." ) if not unpartitioned_account : log . info ( 'Empty unpartitioned account; returning null AC SIA ' 'immediately.' ) return _null_ac_sia ( transition , direction ) cuts = _get_cuts ( transition , direction ) engine = ComputeACSystemIrreducibility ( cuts , transition , direction , unpartitioned_account ) result = engine . run_sequential ( ) log . info ( "Finished calculating big-ac-phi data for %s." , transition ) log . debug ( "RESULT: \n%s" , result ) return result
Return the minimal information partition of a transition in a specific direction .
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def nexus ( network , before_state , after_state , direction = Direction . BIDIRECTIONAL ) : validate . is_network ( network ) sias = ( sia ( transition , direction ) for transition in transitions ( network , before_state , after_state ) ) return tuple ( sorted ( filter ( None , sias ) , reverse = True ) )
Return a tuple of all irreducible nexus of the network .
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def causal_nexus ( network , before_state , after_state , direction = Direction . BIDIRECTIONAL ) : validate . is_network ( network ) log . info ( "Calculating causal nexus..." ) result = nexus ( network , before_state , after_state , direction ) if result : result = max ( result ) else : null_transition = Transition ( network , before_state , after_state , ( ) , ( ) ) result = _null_ac_sia ( null_transition , direction ) log . info ( "Finished calculating causal nexus." ) log . debug ( "RESULT: \n%s" , result ) return result
Return the causal nexus of the network .
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def nice_true_ces ( tc ) : cause_list = [ ] next_list = [ ] cause = '<--' effect = '-->' for event in tc : if event . direction == Direction . CAUSE : cause_list . append ( [ "{0:.4f}" . format ( round ( event . alpha , 4 ) ) , event . mechanism , cause , event . purview ] ) elif event . direction == Direction . EFFECT : next_list . append ( [ "{0:.4f}" . format ( round ( event . alpha , 4 ) ) , event . mechanism , effect , event . purview ] ) else : validate . direction ( event . direction ) true_list = [ ( cause_list [ event ] , next_list [ event ] ) for event in range ( len ( cause_list ) ) ] return true_list
Format a true |CauseEffectStructure| .
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def true_ces ( subsystem , previous_state , next_state ) : network = subsystem . network nodes = subsystem . node_indices state = subsystem . state _events = events ( network , previous_state , state , next_state , nodes ) if not _events : log . info ( "Finished calculating, no echo events." ) return None result = tuple ( [ event . actual_cause for event in _events ] + [ event . actual_effect for event in _events ] ) log . info ( "Finished calculating true events." ) log . debug ( "RESULT: \n%s" , result ) return result
Set of all sets of elements that have true causes and true effects .
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def true_events ( network , previous_state , current_state , next_state , indices = None , major_complex = None ) : # TODO: validate triplet of states if major_complex : nodes = major_complex . subsystem . node_indices elif indices : nodes = indices else : major_complex = compute . major_complex ( network , current_state ) nodes = major_complex . subsystem . node_indices return events ( network , previous_state , current_state , next_state , nodes )
Return all mechanisms that have true causes and true effects within the complex .
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def extrinsic_events ( network , previous_state , current_state , next_state , indices = None , major_complex = None ) : if major_complex : mc_nodes = major_complex . subsystem . node_indices elif indices : mc_nodes = indices else : major_complex = compute . major_complex ( network , current_state ) mc_nodes = major_complex . subsystem . node_indices mechanisms = list ( utils . powerset ( mc_nodes , nonempty = True ) ) all_nodes = network . node_indices return events ( network , previous_state , current_state , next_state , all_nodes , mechanisms = mechanisms )
Set of all mechanisms that are in the major complex but which have true causes and effects within the entire network .
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def apply_cut ( self , cut ) : return Transition ( self . network , self . before_state , self . after_state , self . cause_indices , self . effect_indices , cut )
Return a cut version of this transition .
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def cause_repertoire ( self , mechanism , purview ) : return self . repertoire ( Direction . CAUSE , mechanism , purview )
Return the cause repertoire .
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def effect_repertoire ( self , mechanism , purview ) : return self . repertoire ( Direction . EFFECT , mechanism , purview )
Return the effect repertoire .
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def repertoire ( self , direction , mechanism , purview ) : system = self . system [ direction ] node_labels = system . node_labels if not set ( purview ) . issubset ( self . purview_indices ( direction ) ) : raise ValueError ( '{} is not a {} purview in {}' . format ( fmt . fmt_mechanism ( purview , node_labels ) , direction , self ) ) if not set ( mechanism ) . issubset ( self . mechanism_indices ( direction ) ) : raise ValueError ( '{} is no a {} mechanism in {}' . format ( fmt . fmt_mechanism ( mechanism , node_labels ) , direction , self ) ) return system . repertoire ( direction , mechanism , purview )
Return the cause or effect repertoire function based on a direction .
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def state_probability ( self , direction , repertoire , purview , ) : purview_state = self . purview_state ( direction ) index = tuple ( node_state if node in purview else 0 for node , node_state in enumerate ( purview_state ) ) return repertoire [ index ]
Compute the probability of the purview in its current state given the repertoire .
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def probability ( self , direction , mechanism , purview ) : repertoire = self . repertoire ( direction , mechanism , purview ) return self . state_probability ( direction , repertoire , purview )
Probability that the purview is in it s current state given the state of the mechanism .
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def purview_state ( self , direction ) : return { Direction . CAUSE : self . before_state , Direction . EFFECT : self . after_state } [ direction ]
The state of the purview when we are computing coefficients in direction .
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def mechanism_indices ( self , direction ) : return { Direction . CAUSE : self . effect_indices , Direction . EFFECT : self . cause_indices } [ direction ]
The indices of nodes in the mechanism system .
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def purview_indices ( self , direction ) : return { Direction . CAUSE : self . cause_indices , Direction . EFFECT : self . effect_indices } [ direction ]
The indices of nodes in the purview system .
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def cause_ratio ( self , mechanism , purview ) : return self . _ratio ( Direction . CAUSE , mechanism , purview )
The cause ratio of the purview given mechanism .
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def effect_ratio ( self , mechanism , purview ) : return self . _ratio ( Direction . EFFECT , mechanism , purview )
The effect ratio of the purview given mechanism .
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def partitioned_repertoire ( self , direction , partition ) : system = self . system [ direction ] return system . partitioned_repertoire ( direction , partition )
Compute the repertoire over the partition in the given direction .
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def partitioned_probability ( self , direction , partition ) : repertoire = self . partitioned_repertoire ( direction , partition ) return self . state_probability ( direction , repertoire , partition . purview )
Compute the probability of the mechanism over the purview in the partition .
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def find_mip ( self , direction , mechanism , purview , allow_neg = False ) : alpha_min = float ( 'inf' ) probability = self . probability ( direction , mechanism , purview ) for partition in mip_partitions ( mechanism , purview , self . node_labels ) : partitioned_probability = self . partitioned_probability ( direction , partition ) alpha = log2 ( probability / partitioned_probability ) # First check for 0 # Default: don't count contrary causes and effects if utils . eq ( alpha , 0 ) or ( alpha < 0 and not allow_neg ) : return AcRepertoireIrreducibilityAnalysis ( state = self . mechanism_state ( direction ) , direction = direction , mechanism = mechanism , purview = purview , partition = partition , probability = probability , partitioned_probability = partitioned_probability , node_labels = self . node_labels , alpha = 0.0 ) # Then take closest to 0 if ( abs ( alpha_min ) - abs ( alpha ) ) > constants . EPSILON : alpha_min = alpha acria = AcRepertoireIrreducibilityAnalysis ( state = self . mechanism_state ( direction ) , direction = direction , mechanism = mechanism , purview = purview , partition = partition , probability = probability , partitioned_probability = partitioned_probability , node_labels = self . node_labels , alpha = alpha_min ) return acria
Find the ratio minimum information partition for a mechanism over a purview .
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def find_causal_link ( self , direction , mechanism , purviews = False , allow_neg = False ) : purviews = self . potential_purviews ( direction , mechanism , purviews ) # Find the maximal RIA over the remaining purviews. if not purviews : max_ria = _null_ac_ria ( self . mechanism_state ( direction ) , direction , mechanism , None ) else : # This max should be most positive max_ria = max ( self . find_mip ( direction , mechanism , purview , allow_neg ) for purview in purviews ) # Construct the corresponding CausalLink return CausalLink ( max_ria )
Return the maximally irreducible cause or effect ratio for a mechanism .
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def find_actual_cause ( self , mechanism , purviews = False ) : return self . find_causal_link ( Direction . CAUSE , mechanism , purviews )
Return the actual cause of a mechanism .
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def find_actual_effect ( self , mechanism , purviews = False ) : return self . find_causal_link ( Direction . EFFECT , mechanism , purviews )
Return the actual effect of a mechanism .
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def find ( key ) : docs = list ( collection . find ( { KEY_FIELD : key } ) ) # Return None if we didn't find anything. if not docs : return None pickled_value = docs [ 0 ] [ VALUE_FIELD ] # Unpickle and return the value. return pickle . loads ( pickled_value )
Return the value associated with a key .
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def insert ( key , value ) : # Pickle the value. value = pickle . dumps ( value , protocol = constants . PICKLE_PROTOCOL ) # Store the value as binary data in a document. doc = { KEY_FIELD : key , VALUE_FIELD : Binary ( value ) } # Pickle and store the value with its key. If the key already exists, we # don't insert (since the key is a unique index), and we don't care. try : return collection . insert ( doc ) except pymongo . errors . DuplicateKeyError : return None
Store a value with a key .
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def generate_key ( filtered_args ) : # Convert the value to a (potentially singleton) tuple to be consistent # with joblib.filtered_args. if isinstance ( filtered_args , Iterable ) : return hash ( tuple ( filtered_args ) ) return hash ( ( filtered_args , ) )
Get a key from some input .
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def cache ( ignore = None ) : def decorator ( func ) : # Initialize both cached versions joblib_cached = constants . joblib_memory . cache ( func , ignore = ignore ) db_cached = DbMemoizedFunc ( func , ignore ) @ functools . wraps ( func ) def wrapper ( * args , * * kwargs ) : """Dynamically choose the cache at call-time, not at import.""" if func . __name__ == '_sia' and not config . CACHE_SIAS : f = func elif config . CACHING_BACKEND == 'fs' : f = joblib_cached elif config . CACHING_BACKEND == 'db' : f = db_cached return f ( * args , * * kwargs ) return wrapper return decorator
Decorator for memoizing a function using either the filesystem or a database .
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def get_output_key ( self , args , kwargs ) : # Get a dictionary mapping argument names to argument values where # ignored arguments are omitted. filtered_args = joblib . func_inspect . filter_args ( self . func , self . ignore , args , kwargs ) # Get a sorted tuple of the filtered argument. filtered_args = tuple ( sorted ( filtered_args . values ( ) ) ) # Use native hash when hashing arguments. return db . generate_key ( filtered_args )
Return the key that the output should be cached with given arguments keyword arguments and a list of arguments to ignore .
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def load_output ( self , args , kwargs ) : return db . find ( self . get_output_key ( args , kwargs ) )
Return cached output .
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def cache_info ( self ) : return { 'single_node_repertoire' : self . _single_node_repertoire_cache . info ( ) , 'repertoire' : self . _repertoire_cache . info ( ) , 'mice' : self . _mice_cache . info ( ) }
Report repertoire cache statistics .
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def clear_caches ( self ) : self . _single_node_repertoire_cache . clear ( ) self . _repertoire_cache . clear ( ) self . _mice_cache . clear ( )
Clear the mice and repertoire caches .
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def apply_cut ( self , cut ) : return Subsystem ( self . network , self . state , self . node_indices , cut = cut , mice_cache = self . _mice_cache )
Return a cut version of this |Subsystem| .
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def indices2nodes ( self , indices ) : if set ( indices ) - set ( self . node_indices ) : raise ValueError ( "`indices` must be a subset of the Subsystem's indices." ) return tuple ( self . _index2node [ n ] for n in indices )
Return |Nodes| for these indices .
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def cause_repertoire ( self , mechanism , purview ) : # If the purview is empty, the distribution is empty; return the # multiplicative identity. if not purview : return np . array ( [ 1.0 ] ) # If the mechanism is empty, nothing is specified about the previous # state of the purview; return the purview's maximum entropy # distribution. if not mechanism : return max_entropy_distribution ( purview , self . tpm_size ) # Use a frozenset so the arguments to `_single_node_cause_repertoire` # can be hashed and cached. purview = frozenset ( purview ) # Preallocate the repertoire with the proper shape, so that # probabilities are broadcasted appropriately. joint = np . ones ( repertoire_shape ( purview , self . tpm_size ) ) # The cause repertoire is the product of the cause repertoires of the # individual nodes. joint *= functools . reduce ( np . multiply , [ self . _single_node_cause_repertoire ( m , purview ) for m in mechanism ] ) # The resulting joint distribution is over previous states, which are # rows in the TPM, so the distribution is a column. The columns of a # TPM don't necessarily sum to 1, so we normalize. return distribution . normalize ( joint )
Return the cause repertoire of a mechanism over a purview .
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def effect_repertoire ( self , mechanism , purview ) : # If the purview is empty, the distribution is empty, so return the # multiplicative identity. if not purview : return np . array ( [ 1.0 ] ) # Use a frozenset so the arguments to `_single_node_effect_repertoire` # can be hashed and cached. mechanism = frozenset ( mechanism ) # Preallocate the repertoire with the proper shape, so that # probabilities are broadcasted appropriately. joint = np . ones ( repertoire_shape ( purview , self . tpm_size ) ) # The effect repertoire is the product of the effect repertoires of the # individual nodes. return joint * functools . reduce ( np . multiply , [ self . _single_node_effect_repertoire ( mechanism , p ) for p in purview ] )
Return the effect repertoire of a mechanism over a purview .
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def repertoire ( self , direction , mechanism , purview ) : if direction == Direction . CAUSE : return self . cause_repertoire ( mechanism , purview ) elif direction == Direction . EFFECT : return self . effect_repertoire ( mechanism , purview ) return validate . direction ( direction )
Return the cause or effect repertoire based on a direction .
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def partitioned_repertoire ( self , direction , partition ) : repertoires = [ self . repertoire ( direction , part . mechanism , part . purview ) for part in partition ] return functools . reduce ( np . multiply , repertoires )
Compute the repertoire of a partitioned mechanism and purview .
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def expand_repertoire ( self , direction , repertoire , new_purview = None ) : if repertoire is None : return None purview = distribution . purview ( repertoire ) if new_purview is None : new_purview = self . node_indices # full subsystem if not set ( purview ) . issubset ( new_purview ) : raise ValueError ( "Expanded purview must contain original purview." ) # Get the unconstrained repertoire over the other nodes in the network. non_purview_indices = tuple ( set ( new_purview ) - set ( purview ) ) uc = self . unconstrained_repertoire ( direction , non_purview_indices ) # Multiply the given repertoire by the unconstrained one to get a # distribution over all the nodes in the network. expanded_repertoire = repertoire * uc return distribution . normalize ( expanded_repertoire )
Distribute an effect repertoire over a larger purview .
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def cause_info ( self , mechanism , purview ) : return repertoire_distance ( Direction . CAUSE , self . cause_repertoire ( mechanism , purview ) , self . unconstrained_cause_repertoire ( purview ) )
Return the cause information for a mechanism over a purview .
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def effect_info ( self , mechanism , purview ) : return repertoire_distance ( Direction . EFFECT , self . effect_repertoire ( mechanism , purview ) , self . unconstrained_effect_repertoire ( purview ) )
Return the effect information for a mechanism over a purview .
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def cause_effect_info ( self , mechanism , purview ) : return min ( self . cause_info ( mechanism , purview ) , self . effect_info ( mechanism , purview ) )
Return the cause - effect information for a mechanism over a purview .
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def evaluate_partition ( self , direction , mechanism , purview , partition , repertoire = None ) : if repertoire is None : repertoire = self . repertoire ( direction , mechanism , purview ) partitioned_repertoire = self . partitioned_repertoire ( direction , partition ) phi = repertoire_distance ( direction , repertoire , partitioned_repertoire ) return ( phi , partitioned_repertoire )
Return the |small_phi| of a mechanism over a purview for the given partition .
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