From 4a65931870adf9e9c666dd9525653e7c64c1a4d2 Mon Sep 17 00:00:00 2001 From: Patricia Wollstadt Date: Mon, 15 Jan 2024 15:27:23 +0100 Subject: [PATCH] Update sphinx-generated docs --- docs/doctrees/environment.pickle | Bin 923773 -> 921680 bytes docs/doctrees/idtxl.doctree | Bin 1835072 -> 1843274 bytes docs/doctrees/idtxl_data_class.doctree | Bin 170574 -> 170576 bytes docs/doctrees/idtxl_estimators.doctree | Bin 415198 -> 423381 bytes docs/doctrees/idtxl_results_class.doctree | Bin 149073 -> 149071 bytes docs/html/.buildinfo | 2 +- .../idtxl/active_information_storage.html | 371 +++--- docs/html/_modules/idtxl/bivariate_mi.html | 116 +- docs/html/_modules/idtxl/bivariate_pid.html | 151 +-- docs/html/_modules/idtxl/bivariate_te.html | 119 +- docs/html/_modules/idtxl/data.html | 362 +++--- .../embedding_optimization_ais_Rudelt.html | 990 +++++++++------- .../_modules/idtxl/estimators_Rudelt.html | 559 +++++---- docs/html/_modules/idtxl/estimators_jidt.html | 6 +- docs/html/_modules/idtxl/estimators_mpi.html | 118 +- .../idtxl/estimators_multivariate_pid.html | 17 +- .../_modules/idtxl/estimators_opencl.html | 17 +- docs/html/_modules/idtxl/estimators_pid.html | 372 +++--- .../_modules/idtxl/estimators_python.html | 113 +- .../html/_modules/idtxl/idtxl_exceptions.html | 24 +- docs/html/_modules/idtxl/idtxl_io.html | 199 ++-- docs/html/_modules/idtxl/idtxl_utils.html | 55 +- docs/html/_modules/idtxl/multivariate_mi.html | 113 +- .../html/_modules/idtxl/multivariate_pid.html | 138 ++- docs/html/_modules/idtxl/multivariate_te.html | 111 +- .../html/_modules/idtxl/network_analysis.html | 301 +++-- .../_modules/idtxl/network_comparison.html | 496 ++++---- .../_modules/idtxl/network_inference.html | 817 +++++++------ docs/html/_modules/idtxl/postprocessing.html | 518 ++++---- docs/html/_modules/idtxl/results.html | 362 +++--- .../idtxl/single_process_analysis.html | 8 +- docs/html/_modules/idtxl/stats.html | 1047 +++++++++-------- docs/html/_modules/idtxl/visualise_graph.html | 225 ++-- docs/html/_modules/index.html | 6 +- docs/html/_static/documentation_options.js | 2 +- docs/html/genindex.html | 6 +- docs/html/idtxl.html | 93 +- docs/html/idtxl_data_class.html | 14 +- docs/html/idtxl_estimators.html | 81 +- docs/html/idtxl_helper.html | 6 +- docs/html/idtxl_network_comparison.html | 6 +- docs/html/idtxl_network_inference.html | 6 +- docs/html/idtxl_postprocessing.html | 6 +- docs/html/idtxl_process_analysis.html | 6 +- docs/html/idtxl_results_class.html | 6 +- docs/html/index.html | 6 +- docs/html/modules.html | 6 +- docs/html/objects.inv | Bin 2759 -> 2761 bytes docs/html/py-modindex.html | 6 +- docs/html/search.html | 6 +- docs/html/searchindex.js | 2 +- 51 files changed, 4503 insertions(+), 3488 deletions(-) diff --git a/docs/doctrees/environment.pickle b/docs/doctrees/environment.pickle index 2570b90f0251d4414cebf79367d79e2b793256b9..9863270cf0dd7068c9d32998da6e6b2f726e3f64 100644 GIT binary patch delta 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version 1 # This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done. -config: ac063bd26c9fc26cbf87edb5d4832784 +config: b08cb61c48070e6f8470e0fc861bc3eb tags: 645f666f9bcd5a90fca523b33c5a78b7 diff --git a/docs/html/_modules/idtxl/active_information_storage.html b/docs/html/_modules/idtxl/active_information_storage.html index f2ed60fe..27dc08d6 100644 --- a/docs/html/_modules/idtxl/active_information_storage.html +++ b/docs/html/_modules/idtxl/active_information_storage.html @@ -5,7 +5,7 @@ - idtxl.active_information_storage — IDTxl 1.5 documentation + idtxl.active_information_storage — IDTxl 1.5.1 documentation @@ -31,7 +31,7 @@

Navigation

  • modules |
    • -
  • IDTxl 1.5 documentation »
    • +
  • IDTxl 1.5.1 documentation »
  • Module code »
  • idtxl.active_information_storage
    • @@ -100,9 +100,13 @@

    Source code for idtxl.active_information_storage

    """ def __init__(self): + self.process = None + self.pvalue = None + self.sign = False + self.ais = None super().__init__() -
    [docs] def analyse_network(self, settings, data, processes='all'): +
    [docs] def analyse_network(self, settings, data, processes="all"): """Estimate active information storage for multiple network processes. Estimate active information storage for all or a subset of processes in @@ -155,44 +159,42 @@

    Source code for idtxl.active_information_storage

    ResultsSingleProcessAnalysis() """ # Set defaults for AIS estimation. - settings.setdefault('verbose', True) - settings.setdefault('fdr_correction', True) + settings.setdefault("verbose", True) + settings.setdefault("fdr_correction", True) # Check provided processes for analysis. - if processes == 'all': - processes = [t for t in range(data.n_processes)] - if (type(processes) is list) and (type(processes[0]) is int): + if processes == "all": + processes = list(range(data.n_processes)) + if isinstance(processes, list) and isinstance(processes[0], int): pass else: - raise ValueError('Processes were not specified correctly: ' - '{0}.'.format(processes)) + raise ValueError(f"Processes were not specified correctly: {processes}.") # Check and set defaults for checkpointing. - self.settings = self._set_checkpointing_defaults( - settings, data, [], processes) + self.settings = self._set_checkpointing_defaults(settings, data, [], processes) # Perform AIS estimation for each target individually. results = ResultsSingleProcessAnalysis( n_nodes=data.n_processes, n_realisations=data.n_realisations(), - normalised=data.normalise) - for t in range(len(processes)): - if settings['verbose']: - print('\n####### analysing process {0} of {1}'.format( - processes[t], processes)) - res_single = self.analyse_single_process( - settings, data, processes[t]) + normalised=data.normalise, + ) + for t, process in enumerate(processes): + if settings["verbose"]: + print(f"\n####### analysing process {process} of {processes}") + res_single = self.analyse_single_process(settings, data, process) results.combine_results(res_single) # Get no. realisations actually used for estimation from single target # analysis. results.data_properties.n_realisations = ( - res_single.data_properties.n_realisations) + res_single.data_properties.n_realisations + ) # Perform FDR-correction on the network level. Add FDR-corrected # results as an extra field. Network_fdr/combine_results internally # creates a deep copy of the results. - if settings['fdr_correction']: + if settings["fdr_correction"]: results = stats.ais_fdr(settings, results) return results
    @@ -266,31 +268,34 @@

    Source code for idtxl.active_information_storage

    self._initialise(settings, data, process) # Main algorithm. - print('\n---------------------------- (1) include candidates') + print("\n---------------------------- (1) include candidates") self._include_process_candidates(data) - print('\n---------------------------- (2) prune source candidates') + print("\n---------------------------- (2) prune source candidates") self._prune_candidates(data) - print('\n---------------------------- (3) final statistics') + print("\n---------------------------- (3) final statistics") self._test_final_conditional(data) # Clean up and return results. - if self.settings['verbose']: - print('final conditional samples: {0}'.format( - self._idx_to_lag(self.selected_vars_full))) + if self.settings["verbose"]: + print( + f"final conditional samples: {self._idx_to_lag(self.selected_vars_full)}" + ) results = ResultsSingleProcessAnalysis( n_nodes=data.n_processes, n_realisations=data.n_realisations(self.current_value), - normalised=data.normalise) + normalised=data.normalise, + ) results._add_single_result( process=self.process, settings=self.settings, results={ - 'current_value': self.current_value, - 'selected_vars': self._idx_to_lag(self.selected_vars_full), - 'ais': self.ais, - 'ais_pval': self.pvalue, - 'ais_sign': self.sign - }) + "current_value": self.current_value, + "selected_vars": self._idx_to_lag(self.selected_vars_full), + "ais": self.ais, + "ais_pval": self.pvalue, + "ais_sign": self.sign, + }, + ) self._reset() # remove realisations and min_stats surrogate table return results
    @@ -298,20 +303,22 @@

    Source code for idtxl.active_information_storage

    """Check input, set initial or default values for analysis settings.""" # Check analysis settings and set defaults. self.settings = settings.copy() - self.settings.setdefault('verbose', True) - self.settings.setdefault('add_conditionals', None) - self.settings.setdefault('tau', 1) - self.settings.setdefault('local_values', False) - - if type(self.settings['max_lag']) is not int or ( - self.settings['max_lag'] < 0): - raise RuntimeError('max_lag has to be an integer >= 0.') - if type(self.settings['tau']) is not int or self.settings['tau'] <= 0: - raise RuntimeError('tau has to be an integer > 0.') - if self.settings['tau'] > self.settings['max_lag']: - raise RuntimeError('tau ({0}) has to be equal to or smaller than max_lag ({1})' - '.'.format(self.settings['tau'], - self.settings['max_lag'])) + self.settings.setdefault("verbose", True) + self.settings.setdefault("add_conditionals", None) + self.settings.setdefault("tau", 1) + self.settings.setdefault("local_values", False) + + if not isinstance(self.settings["max_lag"], int) or ( + self.settings["max_lag"] < 0 + ): + raise RuntimeError("max_lag has to be an integer >= 0.") + if not isinstance(self.settings["tau"], int) or self.settings["tau"] <= 0: + raise RuntimeError("tau has to be an integer > 0.") + if self.settings["tau"] > self.settings["max_lag"]: + raise RuntimeError( + f"tau ({self.settings['tau']}) has to be equal to or smaller than max_lag " + f"({self.settings['max_lag']})." + ) # Set CMI estimator. self._set_cmi_estimator() @@ -320,24 +327,26 @@

    Source code for idtxl.active_information_storage

    self._min_stats_surr_table = None # Check process to be analysed. - if type(process) is not int or process < 0: - raise RuntimeError('The index of the process ({0}) has to be an ' - 'int >= 0.'.format(process)) + if not isinstance(process, int) or process < 0: + raise RuntimeError( + f"The index of the process ({process}) has to be an int >= 0." + ) if process > data.n_processes: - raise RuntimeError('Trying to analyse process with index {0}, ' - 'which greater than the number of processes in ' - 'the data ({1}).'.format(process, - data.n_processes)) + raise RuntimeError( + f"Trying to analyse process with index {process}, which greater than the number " + f"of processes in the data ({data.n_processes})." + ) self.process = process # Check provided search depths for source and target - assert(data.n_samples >= self.settings['max_lag'] + 1), ( - 'Not enough samples in data ({0}) to allow for the chosen maximum ' - 'lag ({1})'.format(data.n_samples, self.settings['max_lag'])) - self.current_value = (process, self.settings['max_lag']) + assert data.n_samples >= self.settings["max_lag"] + 1, ( + f"Not enough samples in data ({data.n_samples}) to allow for the chosen maximum lag " + f"({self.settings['max_lag']})" + ) + self.current_value = (process, self.settings["max_lag"]) [cv_realisation, repl_idx] = data.get_realisations( - current_value=self.current_value, - idx_list=[self.current_value]) + current_value=self.current_value, idx_list=[self.current_value] + ) self._current_value_realisations = cv_realisation # Remember which realisations come from which replication. This may be @@ -350,7 +359,8 @@

    Source code for idtxl.active_information_storage

    # Check and set defaults for checkpointing. self.settings = self._set_checkpointing_defaults( - self.settings, data, [], process) + self.settings, data, [], process + ) # Reset all attributes to inital values if the instance has been used # before. @@ -366,16 +376,17 @@

    Source code for idtxl.active_information_storage

    # Check if the user provided a list of candidates that must go into # the conditioning set. These will be added and used for TE estimation, # but never tested for significance. - if self.settings['add_conditionals'] is not None: - self._force_conditionals(self.settings['add_conditionals'], data) + if self.settings["add_conditionals"] is not None: + self._force_conditionals(self.settings["add_conditionals"], data) def _include_process_candidates(self, data): """Test candidates in the process's past.""" process = [self.process] samples = np.arange( - self.current_value[1] - 1, - self.current_value[1] - self.settings['max_lag'] - 1, - -self.settings['tau']) + self.current_value[1] - 1, + self.current_value[1] - self.settings["max_lag"] - 1, + -self.settings["tau"], + ) candidates = self._define_candidates(process, samples) print(candidates) self._include_candidates(candidates, data) @@ -402,30 +413,31 @@

    Source code for idtxl.active_information_storage

    True if a significant variable was found in the process's past. """ success = False - if self.settings['verbose']: - print('testing candidate set: {0}'.format( - self._idx_to_lag(candidate_set))) + if self.settings["verbose"]: + print(f"testing candidate set: {self._idx_to_lag(candidate_set)}") while candidate_set: # Get realisations for all candidates. - cand_real = data.get_realisations(self.current_value, - candidate_set)[0] + cand_real = data.get_realisations(self.current_value, candidate_set)[0] cand_real = cand_real.T.reshape(cand_real.size, 1) # Calculate the (C)MI for each candidate and the target. try: temp_te = self._cmi_estimator.estimate_parallel( - n_chunks=len(candidate_set), - re_use=['var2', 'conditional'], - var1=cand_real, - var2=self._current_value_realisations, - conditional=self._selected_vars_realisations) + n_chunks=len(candidate_set), + re_use=["var2", "conditional"], + var1=cand_real, + var2=self._current_value_realisations, + conditional=self._selected_vars_realisations, + ) except ex.AlgorithmExhaustedError as aee: # The algorithm cannot continue here, so # we'll terminate the search for more candidates, # though those identified already remain valid - print('AlgorithmExhaustedError encountered in ' - 'estimations: ' + aee.message) - print('Halting current estimation set.') + print( + "AlgorithmExhaustedError encountered in " + "estimations: " + aee.message + ) + print("Halting current estimation set.") # For now we don't need a stack trace: # traceback.print_tb(aee.__traceback__) break @@ -433,21 +445,31 @@

    Source code for idtxl.active_information_storage

    # Test max CMI for significance with maximum statistics. te_max_candidate = max(temp_te) max_candidate = candidate_set[np.argmax(temp_te)] - if self.settings['verbose']: - print('testing candidate {0} '.format( - self._idx_to_lag([max_candidate])[0]), end='') + if self.settings["verbose"]: + print( + "testing candidate {0} ".format( + self._idx_to_lag([max_candidate])[0] + ), + end="", + ) significant = False try: significant = stats.max_statistic( - self, data, candidate_set, te_max_candidate, - conditional=self._selected_vars_realisations)[0] + self, + data, + candidate_set, + te_max_candidate, + conditional=self._selected_vars_realisations, + )[0] except ex.AlgorithmExhaustedError as aee: # The algorithm cannot continue here, so # we'll terminate the check on the max stats and not let the # source pass - print('AlgorithmExhaustedError encountered in ' - 'estimations: ' + aee.message) - print('Halting max stats and further selection for target.') + print( + "AlgorithmExhaustedError encountered in " + "estimations: " + aee.message + ) + print("Halting max stats and further selection for target.") # For now we don't need a stack trace: # traceback.print_tb(aee.__traceback__) break @@ -463,14 +485,14 @@

    Source code for idtxl.active_information_storage

    # selected variables (used as the conditioning set). candidate_set.pop(np.argmax(temp_te)) self._append_selected_vars( - [max_candidate], - data.get_realisations(self.current_value, - [max_candidate])[0]) - if self.settings['write_ckp']: + [max_candidate], + data.get_realisations(self.current_value, [max_candidate])[0], + ) + if self.settings["write_ckp"]: self._write_checkpoint() else: - if self.settings['verbose']: - print(' -- not significant') + if self.settings["verbose"]: + print(" -- not significant") break return success @@ -487,55 +509,66 @@

    Source code for idtxl.active_information_storage

    raw data """ # FOR LATER we don't need to test the last included in the first round - if self.settings['verbose']: + if self.settings["verbose"]: if self.selected_vars_sources: - print('testing candidate set: {0}'.format( - self._idx_to_lag(self.selected_vars_sources)), end='') + print( + "testing candidate set: {0}".format( + self._idx_to_lag(self.selected_vars_sources) + ), + end="", + ) else: - print('no sources selected, nothing to prune ...') + print("no sources selected, nothing to prune ...") while self.selected_vars_sources: # Find the candidate with the minimum TE into the target. cond_dim = len(self.selected_vars_sources) - 1 candidate_realisations = np.empty( - (data.n_realisations(self.current_value) * - len(self.selected_vars_sources), - 1)).astype(data.data_type) + ( + data.n_realisations(self.current_value) + * len(self.selected_vars_sources), + 1, + ) + ).astype(data.data_type) conditional_realisations = np.empty( - (data.n_realisations(self.current_value) * - len(self.selected_vars_sources), - cond_dim)).astype(data.data_type) + ( + data.n_realisations(self.current_value) + * len(self.selected_vars_sources), + cond_dim, + ) + ).astype(data.data_type) i_1 = 0 i_2 = data.n_realisations(self.current_value) for candidate in self.selected_vars_sources: # Separate the candidate realisations and all other # realisations to test the candidate's individual contribution. [temp_cond, temp_cand] = self._separate_realisations( - self.selected_vars_sources, - candidate) + self.selected_vars_sources, candidate + ) if temp_cond is None: conditional_realisations = None - re_use = ['var2', 'conditional'] + re_use = ["var2", "conditional"] else: - conditional_realisations[i_1:i_2, ] = temp_cond - re_use = ['var2'] - candidate_realisations[i_1:i_2, ] = temp_cand + conditional_realisations[i_1:i_2,] = temp_cond + re_use = ["var2"] + candidate_realisations[i_1:i_2,] = temp_cand i_1 = i_2 i_2 += data.n_realisations(self.current_value) try: temp_te = self._cmi_estimator.estimate_parallel( - n_chunks=len(self.selected_vars_sources), - re_use=re_use, - var1=candidate_realisations, - var2=self._current_value_realisations, - conditional=conditional_realisations) + n_chunks=len(self.selected_vars_sources), + re_use=re_use, + var1=candidate_realisations, + var2=self._current_value_realisations, + conditional=conditional_realisations, + ) except ex.AlgorithmExhaustedError as aee: # The algorithm cannot continue here, so we'll terminate the # pruning check, assuming that we need not prune any more - print('AlgorithmExhaustedError encountered in ' - 'estimations: ' + aee.message) - print('Halting current pruning and allowing others to' - ' remain.') + print( + "AlgorithmExhaustedError encountered in estimations: " + aee.message + ) + print("Halting current pruning and allowing others to remain.") # For now we don't need a stack trace: # traceback.print_tb(aee.__traceback__) break @@ -543,28 +576,30 @@

    Source code for idtxl.active_information_storage

    # Test min TE for significance with minimum statistics. te_min_candidate = min(temp_te) min_candidate = self.selected_vars_sources[np.argmin(temp_te)] - if self.settings['verbose']: - print('testing candidate: {0}'.format( - self._idx_to_lag([min_candidate])[0])) + if self.settings["verbose"]: + print(f"testing candidate: {self._idx_to_lag([min_candidate])[0]}") remaining_candidates = set(self.selected_vars_sources).difference( - set([min_candidate])) + set([min_candidate]) + ) conditional_realisations = data.get_realisations( - self.current_value, remaining_candidates)[0] + self.current_value, remaining_candidates + )[0] try: [significant, p, surr_table] = stats.min_statistic( - analysis_setup=self, - data=data, - candidate_set=self.selected_vars_sources, - te_min_candidate=te_min_candidate, - conditional=conditional_realisations) + analysis_setup=self, + data=data, + candidate_set=self.selected_vars_sources, + te_min_candidate=te_min_candidate, + conditional=conditional_realisations, + ) except ex.AlgorithmExhaustedError as aee: # The algorithm cannot continue here, so # we'll terminate the min statistics # assuming that we need not prune any more - print('AlgorithmExhaustedError encountered in ' - 'estimations: ' + aee.message) - print('Halting current pruning and allowing others to' - ' remain.') + print( + "AlgorithmExhaustedError encountered in estimations: " + aee.message + ) + print("Halting current pruning and allowing others to remain.") # For now we don't need a stack trace: # traceback.print_tb(aee.__traceback__) break @@ -576,29 +611,32 @@

    Source code for idtxl.active_information_storage

    # if self.settings['verbose']: # print(' -- not significant') self._remove_selected_var(min_candidate) - if self.settings['write_ckp']: + if self.settings["write_ckp"]: self._write_checkpoint() else: - if self.settings['verbose']: - print(' -- significant') + if self.settings["verbose"]: + print(" -- significant") self._min_stats_surr_table = surr_table break def _test_final_conditional(self, data): """Perform statistical test on AIS using the final conditional set.""" if self._selected_vars_full: - if self.settings['verbose']: - print('selected sources: {0}'.format( - self._idx_to_lag(self.selected_vars_full))) + if self.settings["verbose"]: + print(f"selected sources: {self._idx_to_lag(self.selected_vars_full)}") try: - [ais, s, p] = stats.mi_against_surrogates(self, data) + ais, s, p = stats.mi_against_surrogates(self, data) except ex.AlgorithmExhaustedError as aee: # The algorithm cannot continue here, so # we'll set the results to zero - print('AlgorithmExhaustedError encountered in ' - 'estimations: ' + aee.message) - print('Halting AIS final conditional test and setting to not ' - 'significant.') + print( + "AlgorithmExhaustedError encountered in " + "estimations: " + aee.message + ) + print( + "Halting AIS final conditional test and setting to not " + "significant." + ) # For now we don't need a stack trace: # traceback.print_tb(aee.__traceback__) ais = 0 @@ -607,42 +645,49 @@

    Source code for idtxl.active_information_storage

    # If a parallel estimator was used, an array of AIS estimates is # returned. Make the output uniform for both estimator types. - if type(ais) is np.ndarray: - assert ais.shape[0] == 1, 'AIS result is not a scalar.' + if isinstance(ais, np.ndarray): + assert ais.shape[0] == 1, "AIS result is not a scalar." ais = ais[0] - if self.settings['local_values']: + if self.settings["local_values"]: replication_ind = data.get_realisations( - self.current_value, self._selected_vars_sources)[1] + self.current_value, self._selected_vars_sources + )[1] try: local_ais = self._cmi_estimator_local.estimate( - var1=self._current_value_realisations, - var2=self._selected_vars_realisations, - conditional=None) + var1=self._current_value_realisations, + var2=self._selected_vars_realisations, + conditional=None, + ) except ex.AlgorithmExhaustedError as aee: # The algorithm cannot continue here, so # we'll set the results to zero - print('AlgorithmExhaustedError encountered in ' - 'final local AIS estimations: ' + aee.message) - print('Setting all local results to zero (but leaving' - ' surrogate statistical test results)') + print( + "AlgorithmExhaustedError encountered in " + "final local AIS estimations: " + aee.message + ) + print( + "Setting all local results to zero (but leaving surrogate statistical test results)" + ) # For now we don't need a stack trace: # traceback.print_tb(aee.__traceback__) # Return local AIS values of all zeros: # (length gleaned from line below) local_ais = np.zeros( - (max(replication_ind) + 1)*sum(replication_ind == 0)) + (max(replication_ind) + 1) * sum(replication_ind == 0) + ) # Reshape local AIS to a [replications x samples] matrix. self.ais = local_ais.reshape( - max(replication_ind) + 1, sum(replication_ind == 0)) + max(replication_ind) + 1, sum(replication_ind == 0) + ) else: self.ais = ais self.sign = s self.pvalue = p else: - if self.settings['verbose']: - print('no sources selected') + if self.settings["verbose"]: + print("no sources selected") self.ais = np.nan self.sign = False self.pvalue = 1.0 @@ -651,11 +696,11 @@

    Source code for idtxl.active_information_storage

    """Enforce a given conditioning set.""" if type(cond) is tuple: # easily add single variable cond = [cond] - print('Adding the following variables to the conditioning set: {0}.'. - format(cond)) + print("Adding the following variables to the conditioning set: {cond}.") cond_idx = self._lag_to_idx(cond) self._append_selected_vars( - cond_idx, data.get_realisations(self.current_value, cond_idx)[0]) + cond_idx, data.get_realisations(self.current_value, cond_idx)[0] + ) def _reset(self): """Reset instance after analysis.""" @@ -696,7 +741,7 @@

    Navigation

  • modules |
    • -
  • IDTxl 1.5 documentation »
    • +
  • IDTxl 1.5.1 documentation »
  • Module code »
  • idtxl.active_information_storage
    • diff --git a/docs/html/_modules/idtxl/bivariate_mi.html b/docs/html/_modules/idtxl/bivariate_mi.html index 8441a77e..53a8d8e0 100644 --- a/docs/html/_modules/idtxl/bivariate_mi.html +++ b/docs/html/_modules/idtxl/bivariate_mi.html @@ -5,14 +5,13 @@ - idtxl.bivariate_mi — IDTxl 1.4 documentation - - - + idtxl.bivariate_mi — IDTxl 1.5.1 documentation + + + - @@ -32,7 +31,7 @@

    Navigation

  • modules |
    • -
  • IDTxl 1.4 documentation »
    • +
  • IDTxl 1.5.1 documentation »
  • Module code »
  • idtxl.bivariate_mi
    • @@ -109,7 +108,7 @@

    Source code for idtxl.bivariate_mi

         def __init__(self):
         super().__init__()
 
-
    [docs]    def analyse_network(self, settings, data, targets='all', sources='all'):
+
    [docs]    def analyse_network(self, settings, data, targets="all", sources="all"):
         """Find bivariate mutual information between all nodes in the network.
 
         Estimate bivariate mutual information (MI) between all nodes in the
@@ -168,53 +167,56 @@ 
    Source code for idtxl.bivariate_mi
                     analyse_single_target()
         """
         # Set defaults for network inference.
-        settings.setdefault('verbose', True)
-        settings.setdefault('fdr_correction', True)
+        settings.setdefault("verbose", True)
+        settings.setdefault("fdr_correction", True)
 
         # Check which targets and sources are requested for analysis.
-        if targets == 'all':
-            targets = [t for t in range(data.n_processes)]
-        if sources == 'all':
-            sources = ['all' for t in targets]
-        if (type(sources) is list) and (type(sources[0]) is int):
+        if targets == "all":
+            targets = list(range(data.n_processes))
+        if sources == "all":
+            sources = ["all" for t in targets]
+        elif isinstance(sources, list) and isinstance(sources[0], int):
             sources = [sources for t in targets]
-        if (type(sources) is list) and (type(sources[0]) is list):
+        elif isinstance(sources, list) and isinstance(sources[0], list):
             pass
         else:
-            ValueError('Sources was not specified correctly: {0}.'.format(
-                                                                    sources))
-        assert(len(sources) == len(targets)), (
-            'List of targets and list of sources have to have the same length')
+            raise ValueError(f"Sources was not specified correctly: {sources}.")
+        assert len(sources) == len(
+            targets
+        ), "List of targets and list of sources have to have the same length"
 
         # Check and set defaults for checkpointing. If requested, initialise
         # checkpointing.
         self.settings = self._set_checkpointing_defaults(
-            settings, data, sources, targets)
+            settings, data, sources, targets
+        )
 
         # Perform MI estimation for each target individually
-        results = ResultsNetworkInference(n_nodes=data.n_processes,
-                                          n_realisations=data.n_realisations(),
-                                          normalised=data.normalise)
-        for t in range(len(targets)):
-            if settings['verbose']:
-                print('####### analysing target {0} of {1}'.format(t, targets))
-            res_single = self.analyse_single_target(
-                settings, data, targets[t], sources[t])
+        results = ResultsNetworkInference(
+            n_nodes=data.n_processes,
+            n_realisations=data.n_realisations(),
+            normalised=data.normalise,
+        )
+        for t, target in enumerate(targets):
+            if settings["verbose"]:
+                print(f"####### analysing target {t} of {targets}")
+            res_single = self.analyse_single_target(settings, data, target, sources[t])
             results.combine_results(res_single)
 
         # Get no. realisations actually used for estimation from single target
         # analysis.
         results.data_properties.n_realisations = (
-            res_single.data_properties.n_realisations)
+            res_single.data_properties.n_realisations
+        )
 
         # Perform FDR-correction on the network level. Add FDR-corrected
         # results as an extra field. Network_fdr/combine_results internally
         # creates a deep copy of the results.
-        if settings['fdr_correction']:
+        if settings["fdr_correction"]:
             results = network_fdr(settings, results)
         return results
    
 
-
    [docs]    def analyse_single_target(self, settings, data, target, sources='all'):
+
    [docs]    def analyse_single_target(self, settings, data, target, sources="all"):
         """Find bivariate mutual information between sources and a target.
 
         Find bivariate mutual information (MI) between all potential source
@@ -325,40 +327,42 @@ 
    Source code for idtxl.bivariate_mi
             self._initialise(settings, data, sources, target)
 
         # Main algorithm.
-        print('\n---------------------------- (1) include source candidates')
+        print("\n---------------------------- (1) include source candidates")
         self._include_source_candidates(data)
-        print('\n---------------------------- (2) prune candidates')
+        print("\n---------------------------- (2) prune candidates")
         self._prune_candidates(data)
-        print('\n---------------------------- (3) final statistics')
+        print("\n---------------------------- (3) final statistics")
         self._test_final_conditional(data)
 
         # Clean up and return results.
-        if self.settings['verbose']:
-            print('final source samples: {0}'.format(
-                    self._idx_to_lag(self.selected_vars_sources)))
-            print('final target samples: {0}\n\n'.format(
-                    self._idx_to_lag(self.selected_vars_target)))
+        if self.settings["verbose"]:
+            print(
+                f"final source samples: {self._idx_to_lag(self.selected_vars_sources)}"
+            )
+            print(
+                f"final target samples: {self._idx_to_lag(self.selected_vars_target)}\n\n"
+            )
         results = ResultsNetworkInference(
             n_nodes=data.n_processes,
             n_realisations=data.n_realisations(self.current_value),
-            normalised=data.normalise)
+            normalised=data.normalise,
+        )
         results._add_single_result(
             target=self.target,
             settings=self.settings,
             results={
-                'sources_tested': self.source_set,
-                'current_value': self.current_value,
-                'selected_vars_sources': self._idx_to_lag(
-                    self.selected_vars_sources),
-                'selected_vars_target': self._idx_to_lag(
-                    self.selected_vars_target),
-                'selected_sources_pval': self.pvalues_sign_sources,
-                'selected_sources_mi': self.statistic_sign_sources,
-                'omnibus_mi': self.statistic_omnibus,
-                'omnibus_pval': self.pvalue_omnibus,
-                'omnibus_sign': self.sign_omnibus,
-                'mi': self.statistic_single_link
-            })
+                "sources_tested": self.source_set,
+                "current_value": self.current_value,
+                "selected_vars_sources": self._idx_to_lag(self.selected_vars_sources),
+                "selected_vars_target": self._idx_to_lag(self.selected_vars_target),
+                "selected_sources_pval": self.pvalues_sign_sources,
+                "selected_sources_mi": self.statistic_sign_sources,
+                "omnibus_mi": self.statistic_omnibus,
+                "omnibus_pval": self.pvalue_omnibus,
+                "omnibus_sign": self.sign_omnibus,
+                "mi": self.statistic_single_link,
+            },
+        )
 
         self._reset()  # remove attributes
         return results
    
@@ -374,7 +378,7 @@ 
    Source code for idtxl.bivariate_mi
       
    Quick search
    
     
    
     
    
-      
+      
       
     
    
     
    
@@ -393,14 +397,14 @@ 
    Navigation
    
         
  • 
           modules |
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-        
  • IDTxl 1.4 documentation »
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+        
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    • 
         
  • idtxl.bivariate_mi
    •  
       
     
    
     
   
 
\ No newline at end of file
diff --git a/docs/html/_modules/idtxl/bivariate_pid.html b/docs/html/_modules/idtxl/bivariate_pid.html
index 2a06b5e8..7ae3f85a 100644
--- a/docs/html/_modules/idtxl/bivariate_pid.html
+++ b/docs/html/_modules/idtxl/bivariate_pid.html
@@ -5,7 +5,7 @@
   
     
     
-    idtxl.bivariate_pid — IDTxl 1.5 documentation
+    idtxl.bivariate_pid — IDTxl 1.5.1 documentation
     
     
     
@@ -31,7 +31,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.5 documentation »
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+        
  • IDTxl 1.5.1 documentation »
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    • 
         
  • idtxl.bivariate_pid
    •  
       
@@ -87,6 +87,10 @@ 
    Source code for idtxl.bivariate_pid
         """
 
     def __init__(self):
+        self._pid_estimator = None
+        self.sources = None
+        self.target = None
+        self.results = None
         super().__init__()
 
 
    [docs]    def analyse_network(self, settings, data, targets, sources):
@@ -147,32 +151,33 @@ 
    Source code for idtxl.bivariate_pid
                     ResultsPID()
         """
         # Set defaults for PID estimation.
-        settings.setdefault('verbose', True)
-        settings.setdefault('lags_pid', np.array([[1, 1]] * len(targets)))
+        settings.setdefault("verbose", True)
+        settings.setdefault("lags_pid", np.array([[1, 1]] * len(targets)))
 
         # Check inputs.
-        if not len(targets) == len(sources) == len(settings['lags_pid']):
-            raise RuntimeError('Lists of targets, sources, and lags must have'
-                               'the same lengths.')
-        list_of_lags = settings['lags_pid']
+        if not len(targets) == len(sources) == len(settings["lags_pid"]):
+            raise RuntimeError(
+                "Lists of targets, sources, and lags must have" "the same lengths."
+            )
+        list_of_lags = settings["lags_pid"]
 
         # Perform PID estimation for each target individually
         results = ResultsPID(
             n_nodes=data.n_processes,
             n_realisations=data.n_realisations(),
-            normalised=data.normalise)
-        for t in range(len(targets)):
-            if settings['verbose']:
-                print('\n####### analysing target with index {0} from list {1}'
-                      .format(t, targets))
-            settings['lags_pid'] = list_of_lags[t]
-            res_single = self.analyse_single_target(
-                settings, data, targets[t], sources[t])
+            normalised=data.normalise,
+        )
+        for t, target in enumerate(targets):
+            if settings["verbose"]:
+                print(f"\n####### analysing target with index {t} from list {targets}")
+            settings["lags_pid"] = list_of_lags[t]
+            res_single = self.analyse_single_target(settings, data, target, sources[t])
             results.combine_results(res_single)
         # Get no. realisations actually used for estimation from single target
         # analysis.
         results.data_properties.n_realisations = (
-            res_single.data_properties.n_realisations)
+            res_single.data_properties.n_realisations
+        )
         return results
    
 
 
    [docs]    def analyse_single_target(self, settings, data, target, sources):
@@ -236,61 +241,64 @@ 
    Source code for idtxl.bivariate_pid
             # Estimate PID and significance.
         self._calculate_pid(data)
 
-        # Add analyis info.
+        # Add analysis info.
         results = ResultsPID(
             n_nodes=data.n_processes,
             n_realisations=data.n_realisations(self.current_value),
-            normalised=data.normalise)
+            normalised=data.normalise,
+        )
         results._add_single_result(
-            settings=self.settings,
-            target=self.target,
-            results=self.results)
+            settings=self.settings, target=self.target, results=self.results
+        )
         self._reset()
         return results
    
 
     def _initialise(self, settings, data, target, sources):
         """Check input, set initial or default values for analysis settings."""
         # Check requested PID estimator.
-        assert 'pid_estimator' in settings, 'Estimator was not specified!'
-        self._pid_estimator = get_estimator(settings['pid_estimator'], settings)
+        assert "pid_estimator" in settings, "Estimator was not specified!"
+        self._pid_estimator = get_estimator(settings["pid_estimator"], settings)
 
         self.settings = settings.copy()
-        self.settings.setdefault('lags_pid', [1, 1])
-        self.settings.setdefault('verbose', True)
+        self.settings.setdefault("lags_pid", [1, 1])
+        self.settings.setdefault("verbose", True)
 
         # Check if provided lags are correct and work with the number of
         # samples in the data.
-        if len(self.settings['lags_pid']) != 2:
-            raise RuntimeError('List of lags must have length 2.')
-        if self.settings['lags_pid'][0] >= data.n_samples:
+        if len(self.settings["lags_pid"]) != 2:
+            raise RuntimeError("List of lags must have length 2.")
+        if self.settings["lags_pid"][0] >= data.n_samples:
             raise RuntimeError(
-                'Lag 1 ({0}) is larger than the number of samples in the data '
-                'set ({1}).'.format(
-                    self.settings['lags_pid'][0], data.n_samples))
-        if self.settings['lags_pid'][1] >= data.n_samples:
+                f"Lag 1 ({self.settings['lags_pid'][0]}) is larger than the number of "
+                f"samples in the data set ({data.n_samples})."
+            )
+        if self.settings["lags_pid"][1] >= data.n_samples:
             raise RuntimeError(
-                'Lag 2 ({0}) is larger than the number of samples in the data '
-                'set ({1}).'.format(
-                    self.settings['lags_pid'][1], data.n_samples))
+                f"Lag 2 ({self.settings['lags_pid'][1]}) is larger than the number of "
+                "samples in the data set ({data.n_samples})."
+            )
 
         # Check if target and sources are provided correctly.
-        if type(target) is not int:
-            raise RuntimeError('Target must be an integer.')
+        if not isinstance(target, int):
+            raise RuntimeError("Target must be an integer.")
         if len(sources) != 2:
-            raise RuntimeError('List of sources must have length 2.')
+            raise RuntimeError("List of sources must have length 2.")
         if target in sources:
-            raise RuntimeError('The target ({0}) should not be in the list '
-                               'of sources ({1}).'.format(target, sources))
+            raise RuntimeError(
+                f"The target ({target}) should not be in the list of sources ({sources})."
+            )
 
-        self.current_value = (target, max(self.settings['lags_pid']))
+        self.current_value = (target, max(self.settings["lags_pid"]))
         self.target = target
         # TODO works for single vars only, change to multivariate?
-        self.sources = self._lag_to_idx([
-                                (sources[0], self.settings['lags_pid'][0]),
-                                (sources[1], self.settings['lags_pid'][1])])
+        self.sources = self._lag_to_idx(
+            [
+                (sources[0], self.settings["lags_pid"][0]),
+                (sources[1], self.settings["lags_pid"][1]),
+            ]
+        )
 
     def _calculate_pid(self, data):
-
         # TODO Discuss how and if the following statistical testing should be
         # included included. Remove dummy results.
         # [orig_pid, sign_1, p_val_1,
@@ -302,32 +310,33 @@ 
    Source code for idtxl.bivariate_pid
             # p_val_1 = p_val_2 = p_val_shd = p_val_syn = 1.0
 
         target_realisations = data.get_realisations(
-                                            self.current_value,
-                                            [self.current_value])[0]
+            self.current_value, [self.current_value]
+        )[0]
         source_1_realisations = data.get_realisations(
-                                            self.current_value,
-                                            [self.sources[0]])[0]
+            self.current_value, [self.sources[0]]
+        )[0]
         source_2_realisations = data.get_realisations(
-                                            self.current_value,
-                                             [self.sources[1]])[0]
+            self.current_value, [self.sources[1]]
+        )[0]
         orig_pid = self._pid_estimator.estimate(
-                                s1=source_1_realisations,
-                                s2=source_2_realisations,
-                                t=target_realisations)
-
-        if self.settings['verbose']:
-            print('\nunq information s1: {0:.8f}, s2: {1:.8f}'.format(
-                                                           orig_pid['unq_s1'],
-                                                           orig_pid['unq_s2']))
-            print('shd information: {0:.8f}, syn information: {1:.8f}'.format(
-                                                        orig_pid['shd_s1_s2'],
-                                                        orig_pid['syn_s1_s2']))
+            s1=source_1_realisations, s2=source_2_realisations, t=target_realisations
+        )
+
+        if self.settings["verbose"]:
+            print(
+                f"\nunq information s1: {orig_pid['unq_s1']:.8f}, s2: {orig_pid['unq_s2']:.8f}"
+            )
+            print(
+                f"shd information: {orig_pid['shd_s1_s2']:.8f}, syn information: {orig_pid['syn_s1_s2']:.8f}"
+            )
         self.results = orig_pid
-        self.results['source_1'] = self._idx_to_lag([self.sources[0]])
-        self.results['source_2'] = self._idx_to_lag([self.sources[1]])
-        self.results['selected_vars_sources'] = [
-            self.results['source_1'][0], self.results['source_2'][0]]
-        self.results['current_value'] = self.current_value
+        self.results["source_1"] = self._idx_to_lag([self.sources[0]])
+        self.results["source_2"] = self._idx_to_lag([self.sources[1]])
+        self.results["selected_vars_sources"] = [
+            self.results["source_1"][0],
+            self.results["source_2"][0],
+        ]
+        self.results["current_value"] = self.current_value
         # self.results['unq_s1_sign'] = sign_1
         # self.results['unq_s2_sign'] = sign_2
         # self.results['unq_s1_p_val'] = p_val_1
@@ -338,8 +347,8 @@ 
    Source code for idtxl.bivariate_pid
             # self.results['shd_p_val'] = p_val_shd
 
         # TODO make mi_against_surrogates in stats more generic, such that
-        # it becomes an arbitrary permutation test where one arguemnt gets
-        # shuffled and then all arguents are passed to the provided estimator
+        # it becomes an arbitrary permutation test where one argument gets
+        # shuffled and then all arguments are passed to the provided estimator
 
     def _reset(self):
         """Reset instance after analysis."""
@@ -378,7 +387,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.5 documentation »
    • 
+        
  • IDTxl 1.5.1 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.bivariate_pid
    •  
       
diff --git a/docs/html/_modules/idtxl/bivariate_te.html b/docs/html/_modules/idtxl/bivariate_te.html
index e27b65be..fb12e492 100644
--- a/docs/html/_modules/idtxl/bivariate_te.html
+++ b/docs/html/_modules/idtxl/bivariate_te.html
@@ -5,14 +5,13 @@
   
     
     
-    idtxl.bivariate_te — IDTxl 1.4 documentation
-    
-    
-    
+    idtxl.bivariate_te — IDTxl 1.5.1 documentation
+    
+    
+    
     
     
     
-    
     
     
 
@@ -32,7 +31,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5.1 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.bivariate_te
    •  
       
@@ -115,7 +114,7 @@ 
    Source code for idtxl.bivariate_te
         def __init__(self):
         super().__init__()
 
-
    [docs]    def analyse_network(self, settings, data, targets='all', sources='all'):
+
    [docs]    def analyse_network(self, settings, data, targets="all", sources="all"):
         """Find bivariate transfer entropy between all nodes in the network.
 
         Estimate bivariate transfer entropy (TE) between all nodes in the
@@ -171,54 +170,56 @@ 
    Source code for idtxl.bivariate_te
                     ResultsNetworkInference()
         """
         # Set defaults for network inference.
-        settings.setdefault('verbose', True)
-        settings.setdefault('fdr_correction', True)
+        settings.setdefault("verbose", True)
+        settings.setdefault("fdr_correction", True)
 
         # Check which targets and sources are requested for analysis.
-        if targets == 'all':
-            targets = [t for t in range(data.n_processes)]
-        if sources == 'all':
-            sources = ['all' for t in targets]
-        if (type(sources) is list) and (type(sources[0]) is int):
+        if targets == "all":
+            targets = list(range(data.n_processes))
+        if sources == "all":
+            sources = ["all" for t in targets]
+        elif isinstance(sources, list) and isinstance(sources[0], int):
             sources = [sources for t in targets]
-        if (type(sources) is list) and (type(sources[0]) is list):
+        elif isinstance(sources, list) and isinstance(sources[0], list):
             pass
         else:
-            ValueError('Sources was not specified correctly: {0}.'.format(
-                                                                    sources))
-        assert(len(sources) == len(targets)), (
-            'List of targets and list of sources have to have the length')
+            raise ValueError(f"Sources was not specified correctly: {sources}.")
+        assert len(sources) == len(
+            targets
+        ), "List of targets and list of sources have to have the length"
 
         # Check and set defaults for checkpointing. If requested, initialise
         # checkpointing.
         self.settings = self._set_checkpointing_defaults(
-            settings, data, sources, targets)
+            settings, data, sources, targets
+        )
 
         # Perform TE estimation for each target individually
-        results = ResultsNetworkInference(n_nodes=data.n_processes,
-                                          n_realisations=data.n_realisations(),
-                                          normalised=data.normalise)
-        for t in range(len(targets)):
-            if settings['verbose']:
-                print('\n####### analysing target with index {0} from list {1}'
-                      .format(t, targets))
-            res_single = self.analyse_single_target(
-                settings, data, targets[t], sources[t])
+        results = ResultsNetworkInference(
+            n_nodes=data.n_processes,
+            n_realisations=data.n_realisations(),
+            normalised=data.normalise,
+        )
+        for t, target in enumerate(targets):
+            if settings["verbose"]:
+                print("\n####### analysing target with index {t} from list {targets}")
+            res_single = self.analyse_single_target(settings, data, target, sources[t])
             results.combine_results(res_single)
 
         # Get no. realisations actually used for estimation from single target
         # analysis.
         results.data_properties.n_realisations = (
-            res_single.data_properties.n_realisations)
+            res_single.data_properties.n_realisations
+        )
 
         # Perform FDR-correction on the network level. Add FDR-corrected
         # results as an extra field. Network_fdr/combine_results internally
         # creates a deep copy of the results.
-        if settings['fdr_correction']:
+        if settings["fdr_correction"]:
             results = network_fdr(settings, results)
         return results
    
 
-
    [docs]    def analyse_single_target(self, settings, data, target, sources='all'):
+
    [docs]    def analyse_single_target(self, settings, data, target, sources="all"):
         """Find bivariate transfer entropy between sources and a target.
 
         Find bivariate transfer entropy (TE) between all potential source
@@ -328,42 +329,44 @@ 
    Source code for idtxl.bivariate_te
             self._initialise(settings, data, sources, target)
 
         # Main algorithm.
-        print('\n---------------------------- (1) include target candidates')
+        print("\n---------------------------- (1) include target candidates")
         self._include_target_candidates(data)
-        print('\n---------------------------- (2) include source candidates')
+        print("\n---------------------------- (2) include source candidates")
         self._include_source_candidates(data)
-        print('\n---------------------------- (3) prune candidates')
+        print("\n---------------------------- (3) prune candidates")
         self._prune_candidates(data)
-        print('\n---------------------------- (4) final statistics')
+        print("\n---------------------------- (4) final statistics")
         self._test_final_conditional(data)
 
         # Clean up and return results.
-        if self.settings['verbose']:
-            print('final source samples: {0}'.format(
-                    self._idx_to_lag(self.selected_vars_sources)))
-            print('final target samples: {0}\n\n'.format(
-                    self._idx_to_lag(self.selected_vars_target)))
+        if self.settings["verbose"]:
+            print(
+                f"final source samples: {self._idx_to_lag(self.selected_vars_sources)}"
+            )
+            print(
+                f"final target samples: {self._idx_to_lag(self.selected_vars_target)}\n\n"
+            )
         results = ResultsNetworkInference(
             n_nodes=data.n_processes,
             n_realisations=data.n_realisations(self.current_value),
-            normalised=data.normalise)
+            normalised=data.normalise,
+        )
         results._add_single_result(
             target=self.target,
             settings=self.settings,
             results={
-                'sources_tested': self.source_set,
-                'current_value': self.current_value,
-                'selected_vars_sources': self._idx_to_lag(
-                    self.selected_vars_sources),
-                'selected_vars_target': self._idx_to_lag(
-                    self.selected_vars_target),
-                'selected_sources_pval': self.pvalues_sign_sources,
-                'selected_sources_te': self.statistic_sign_sources,
-                'omnibus_te': self.statistic_omnibus,
-                'omnibus_pval': self.pvalue_omnibus,
-                'omnibus_sign': self.sign_omnibus,
-                'te': self.statistic_single_link
-            })
+                "sources_tested": self.source_set,
+                "current_value": self.current_value,
+                "selected_vars_sources": self._idx_to_lag(self.selected_vars_sources),
+                "selected_vars_target": self._idx_to_lag(self.selected_vars_target),
+                "selected_sources_pval": self.pvalues_sign_sources,
+                "selected_sources_te": self.statistic_sign_sources,
+                "omnibus_te": self.statistic_omnibus,
+                "omnibus_pval": self.pvalue_omnibus,
+                "omnibus_sign": self.sign_omnibus,
+                "te": self.statistic_single_link,
+            },
+        )
         self._reset()  # remove attributes
         return results
    
 
    
@@ -378,7 +381,7 @@ 
    Source code for idtxl.bivariate_te
       
    Quick search
    
     
    
     
    
-      
+      
       
     
    
     
    
@@ -397,14 +400,14 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5.1 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.bivariate_te
    •  
       
     
    
     
   
 
\ No newline at end of file
diff --git a/docs/html/_modules/idtxl/data.html b/docs/html/_modules/idtxl/data.html
index 30eb98f1..ecb19811 100644
--- a/docs/html/_modules/idtxl/data.html
+++ b/docs/html/_modules/idtxl/data.html
@@ -5,14 +5,13 @@
   
     
     
-    idtxl.data — IDTxl 1.4 documentation
-    
-    
-    
+    idtxl.data — IDTxl 1.5.1 documentation
+    
+    
+    
     
     
     
-    
     
     
 
@@ -32,7 +31,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5.1 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.data
    •  
       
@@ -51,7 +50,7 @@ 
    Source code for idtxl.data
     VERBOSE = False
 
 
-
    [docs]class Data():
+
    [docs]class Data:
     """Store data for information dynamics estimation.
 
     Data takes a 1- to 3-dimensional array representing realisations of random
@@ -114,10 +113,13 @@ 
    Source code for idtxl.data
                 initial state of the seed for shuffled permutations
     """
 
-    def __init__(self, data=None, dim_order='psr', normalise=True, seed=None):
+    def __init__(self, data=None, dim_order="psr", normalise=True, seed=None):
         np.random.seed(seed)
         self.initial_state = np.random.get_state()
         self.normalise = normalise
+        self.n_processes = 0
+        self.n_samples = 0
+        self.n_replications = 0
         if data is not None:
             self.set_data(data, dim_order)
 
@@ -132,8 +134,7 @@ 
    Source code for idtxl.data
                     samples to the embedding); if no current_value is provided, the
                 number of all samples is used
         """
-        return (self.n_realisations_samples(current_value) *
-                self.n_realisations_repl())
    
+        return self.n_realisations_samples(current_value) * self.n_realisations_repl()
    
 
 
    [docs]    def n_realisations_samples(self, current_value=None):
         """Number of realisations over samples.
@@ -147,13 +148,12 @@ 
    Source code for idtxl.data
             """
         if current_value is None:
             return self.n_samples
-        else:
-            if current_value[1] >= self.n_samples:
-                raise RuntimeError('The sample index of the current value '
-                                   '({0}) is larger than the number of samples'
-                                   ' in the data set ({1}).'.format(
-                                              current_value, self.n_samples))
-            return self.n_samples - current_value[1]
    
+        if current_value[1] >= self.n_samples:
+            raise RuntimeError(
+                f"The sample index of the current value ({current_value}) is larger than the"
+                f" number of samples in the data set ({self.n_samples})."
+            )
+        return self.n_samples - current_value[1]
    
 
 
    [docs]    def n_realisations_repl(self):
         """Number of realisations over replications."""
@@ -166,16 +166,17 @@ 
    Source code for idtxl.data
     
     @data.setter
     def data(self, d):
-        if hasattr(self, 'data'):
-            raise AttributeError('You can not assign a value to this attribute'
-                                 ' directly, use the set_data method instead.')
-        else:
-            self._data = d
+        if hasattr(self, "data"):
+            raise AttributeError(
+                "You can not assign a value to this attribute"
+                " directly, use the set_data method instead."
+            )
+        self._data = d
 
     @data.deleter
     def data(self):
-        print('overwriting existing data')
-        del(self._data)
+        print("overwriting existing data")
+        del self._data
 
 
    [docs]    def set_data(self, data, dim_order):
         """Overwrite data in an existing Data object.
@@ -189,22 +190,23 @@ 
    Source code for idtxl.data
                     must have the same length as number of dimensions in data
         """
         if len(dim_order) > 3:
-            raise RuntimeError('dim_order can not have more than three '
-                               'entries')
+            raise RuntimeError("dim_order can not have more than three " "entries")
         if len(dim_order) != data.ndim:
-            raise RuntimeError('Data array dimension ({0}) and length of '
-                               'dim_order ({1}) are not equal.'.format(
-                                           data.ndim, len(dim_order)))
+            raise RuntimeError(
+                f"Data array dimension ({data.ndim}) and length of "
+                f"dim_order ({len(dim_order)}) are not equal."
+            )
 
         # Bring data into the order processes x samples x replications and set
         # set data.
         data_ordered = self._reorder_data(data, dim_order)
         self._set_data_size(data_ordered)
-        print('Adding data with properties: {0} processes, {1} samples, {2} '
-              'replications'.format(self.n_processes, self.n_samples,
-                                    self.n_replications))
+        print(
+            "Adding data with properties: {0} processes, {1} samples, {2} "
+            "replications".format(self.n_processes, self.n_samples, self.n_replications)
+        )
         try:
-            delattr(self, 'data')
+            delattr(self, "data")
         except AttributeError:
             pass
         if self.normalise:
@@ -218,29 +220,30 @@ 
    Source code for idtxl.data
             d_standardised = np.empty(d.shape)
         for process in range(self.n_processes):
             s = utils.standardise(
-                            d[process, :, :].reshape(1, self.n_realisations()),
-                            dimension=1)
-            d_standardised[process, :, :] = s.reshape(self.n_samples,
-                                                      self.n_replications)
+                d[process, :, :].reshape(1, self.n_realisations()), dimension=1
+            )
+            d_standardised[process, :, :] = s.reshape(
+                self.n_samples, self.n_replications
+            )
         return d_standardised
 
     def _reorder_data(self, data, dim_order):
         """Reorder data dimensions to processes x samples x replications."""
         # add singletons for missing dimensions
-        missing_dims = 'psr'
+        missing_dims = "psr"
         for dim in dim_order:
-            missing_dims = missing_dims.replace(dim, '')
+            missing_dims = missing_dims.replace(dim, "")
         for dim in missing_dims:
             data = np.expand_dims(data, data.ndim)
             dim_order += dim
 
         # reorder array dims if necessary
-        if dim_order[0] != 'p':
-            ind_p = dim_order.index('p')
+        if dim_order[0] != "p":
+            ind_p = dim_order.index("p")
             data = data.swapaxes(0, ind_p)
             dim_order = utils.swap_chars(dim_order, 0, ind_p)
-        if dim_order[1] != 's':
-            data = data.swapaxes(1, dim_order.index('s'))
+        if dim_order[1] != "s":
+            data = data.swapaxes(1, dim_order.index("s"))
         return data
 
     def _set_data_size(self, data):
@@ -297,24 +300,24 @@ 
    Source code for idtxl.data
                     replication index for each realisation with dimensions (no.
                 samples * no.replications) x number of indices
         """
-        if not hasattr(self, 'data'):
-            raise AttributeError('No data has been added to this Data() '
-                                 'instance.')
+        if not hasattr(self, "data"):
+            raise AttributeError("No data has been added to this Data() " "instance.")
         # Return None if index list is empty.
         if not idx_list:
             return None, None
         # Check if requested indices are smaller than the current_value.
         if not all(np.array([x[1] for x in idx_list]) <= current_value[1]):
-            print('Index list: {0}\ncurrent value: {1}'.format(idx_list,
-                                                               current_value))
-            raise RuntimeError('All indices for which data is retrieved must '
-                               ' be smaller than the current value.')
+            print(f"Index list: {idx_list}\ncurrent value: {current_value}")
+            raise RuntimeError(
+                "All indices for which data is retrieved must be smaller than the current value."
+            )
 
         # Allocate memory.
         n_real_time = self.n_realisations_samples(current_value)
         n_real_repl = self.n_realisations_repl()
-        realisations = np.empty((n_real_time * n_real_repl,
-                                 len(idx_list))).astype(self.data_type)
+        realisations = np.empty((n_real_time * n_real_repl, len(idx_list))).astype(
+            self.data_type
+        )
 
         # Shuffle the replication order if requested. This creates surrogate
         # data by permuting replications while keeping the order of samples
@@ -331,30 +334,31 @@ 
    Source code for idtxl.data
                 # get the last sample as negative value, i.e., no. samples from the
             # end of the array
             last_sample = idx[1] - current_value[1]  # indexing is much faster
-            if last_sample == 0:                     # than looping over time!
+            if last_sample == 0:  # than looping over time!
                 last_sample = None
             for replication in replications_order:
                 try:
-                    realisations[r:r + n_real_time, i] = self.data[
-                                                        idx[0],
-                                                        idx[1]: last_sample,
-                                                        replication]
+                    realisations[r : r + n_real_time, i] = self.data[
+                        idx[0], idx[1] : last_sample, replication
+                    ]
                 except IndexError:
-                    raise IndexError('You tried to access variable {0} in a '
-                                     'data set with {1} processes and {2} '
-                                     'samples.'.format(idx, self.n_processes,
-                                                       self.n_samples))
+                    raise IndexError(
+                        "You tried to access variable {0} in a "
+                        "data set with {1} processes and {2} "
+                        "samples.".format(idx, self.n_processes, self.n_samples)
+                    )
                 r += n_real_time
 
-            assert(not np.isnan(realisations[:, i]).any()), ('There are nans '
-                                                             'in the retrieved'
-                                                             ' realisations.')
+            assert not np.isnan(
+                realisations[:, i]
+            ).any(), "There are nans in the retrieved realisations."
             i += 1
 
         # For each realisation keep the index of the replication it came from.
         replications_index = np.repeat(replications_order, n_real_time)
-        assert(replications_index.shape[0] == realisations.shape[0]), (
-               'There seems to be a problem with the replications index.')
+        assert (
+            replications_index.shape[0] == realisations.shape[0]
+        ), "There seems to be a problem with the replications index."
 
         return realisations, replications_index
    
 
@@ -362,7 +366,7 @@ 
    Source code for idtxl.data
             """Return data slice for a single process.
 
         Return data slice for process. Optionally, an offset can be provided
-        such that data are returnded from sample 'offset_samples' onwards.
+        such that data are returned from sample 'offset_samples' onwards.
         Also, data
         can be shuffled over replications to create surrogate data for
         statistical testing. For shuffling, data blocks are permuted over
@@ -402,10 +406,12 @@ 
    Source code for idtxl.data
                     list of replications indices
         """
         # Check if requested indices are smaller than the current_value.
-        if not offset_samples <= self.n_samples:
-            print('Offset {0} must be smaller than number of samples in the '
-                  ' data ({1})'.format(offset_samples, self.n_samples))
-            raise RuntimeError('Offset must be smaller than no. samples.')
+        if offset_samples > self.n_samples:
+            print(
+                "Offset {0} must be smaller than number of samples in the "
+                " data ({1})".format(offset_samples, self.n_samples)
+            )
+            raise RuntimeError("Offset must be smaller than no. samples.")
 
         # Shuffle the replication order if requested. This creates surrogate
         # data by permuting replications while keeping the order of samples
@@ -418,13 +424,16 @@ 
    Source code for idtxl.data
             try:
             data_slice = self.data[process, offset_samples:, replication_index]
         except IndexError:
-            raise IndexError('You tried to access process {0} with an offset '
-                             'of {1} in a data set of {2} processes and {3} '
-                             'samples.'.format(process, offset_samples,
-                                               self.n_processes,
-                                               self.n_samples))
-        assert(not np.isnan(data_slice).any()), ('There are nans in the '
-                                                 'retrieved data slice.')
+            raise IndexError(
+                "You tried to access process {0} with an offset "
+                "of {1} in a data set of {2} processes and {3} "
+                "samples.".format(
+                    process, offset_samples, self.n_processes, self.n_samples
+                )
+            )
+        assert not np.isnan(
+            data_slice
+        ).any(), "There are nans in the retrieved data slice."
         return data_slice.T, replication_index
 
 
    [docs]    def slice_permute_replications(self, process):
@@ -526,7 +535,7 @@ 
    Source code for idtxl.data
                     data slice with data permuted over samples with dimensions
                 samples x number of replications
             numpy array
-                index of permutet samples
+                index of permuted samples
 
         Note:
             This permutation scheme is the fall-back option if the number of
@@ -535,8 +544,7 @@ 
    Source code for idtxl.data
             """
         data_slice = self._get_data_slice(process, shuffle=True)[0]
         data_slice_perm = np.empty(data_slice.shape).astype(self.data_type)
-        perm = self._get_permutation_samples(data_slice.shape[0],
-                                             perm_settings)
+        perm = self._get_permutation_samples(data_slice.shape[0], perm_settings)
         for r in range(self.n_replications):
             data_slice_perm[:, r] = data_slice[perm, r]
         return data_slice_perm, perm
    
@@ -581,8 +589,8 @@ 
    Source code for idtxl.data
             Raises:
             TypeError if idx_realisations is not a list
         """
-        if type(idx_list) is not list:
-            raise TypeError('idx needs to be a list of tuples.')
+        if not isinstance(idx_list, list):
+            raise TypeError("idx needs to be a list of tuples.")
         return self.get_realisations(current_value, idx_list, shuffle=True)
    
 
 
    [docs]    def permute_samples(self, current_value, idx_list, perm_settings):
@@ -697,8 +705,7 @@ 
    Source code for idtxl.data
                 replications is too small to generate the requested number of
             permutations.
         """
-        [realisations, replication_idx] = self.get_realisations(current_value,
-                                                                idx_list)
+        [realisations, replication_idx] = self.get_realisations(current_value, idx_list)
         n_samples = sum(replication_idx == 0)
         perm = self._get_permutation_samples(n_samples, perm_settings)
         # Apply the permutation to data from each replication.
@@ -734,37 +741,36 @@ 
    Source code for idtxl.data
                 numpy Array
                 permuted indices of samples
         """
-        perm_type = perm_settings['perm_type']
+        perm_type = perm_settings["perm_type"]
 
-        # Get the permutaion 'mask' for one replication (the same mask is then
+        # Get the permutation 'mask' for one replication (the same mask is then
         # applied to each replication).
-        if perm_type == 'random':
+        if perm_type == "random":
             perm = np.random.permutation(n_samples)
 
-        elif perm_type == 'circular':
-            max_shift = perm_settings['max_shift']
-            if type(max_shift) is not int or max_shift < 1:
-                raise TypeError(' ''max_shift'' has to be an int > 0.')
+        elif perm_type == "circular":
+            max_shift = perm_settings["max_shift"]
+            if not isinstance(max_shift, int) or max_shift < 1:
+                raise TypeError(" " "max_shift" " has to be an int > 0.")
             perm = self._circular_shift(n_samples, max_shift)[0]
 
-        elif perm_type == 'block':
-            block_size = perm_settings['block_size']
-            perm_range = perm_settings['perm_range']
-            if type(block_size) is not int or block_size < 1:
-                raise TypeError(' ''block_size'' has to be an int > 0.')
-            if type(perm_range) is not int or perm_range < 1:
-                raise TypeError(' ''perm_range'' has to be an int > 0.')
+        elif perm_type == "block":
+            block_size = perm_settings["block_size"]
+            perm_range = perm_settings["perm_range"]
+            if not isinstance(block_size, int) or block_size < 1:
+                raise TypeError(" " "block_size" " has to be an int > 0.")
+            if not isinstance(perm_range, int) or perm_range < 1:
+                raise TypeError(" " "perm_range" " has to be an int > 0.")
             perm = self._swap_blocks(n_samples, block_size, perm_range)
 
-        elif perm_type == 'local':
-            perm_range = perm_settings['perm_range']
-            if type(perm_range) is not int or perm_range < 1:
-                raise TypeError(' ''perm_range'' has to be an int > 0.')
+        elif perm_type == "local":
+            perm_range = perm_settings["perm_range"]
+            if not isinstance(perm_range, int) or perm_range < 1:
+                raise TypeError(" " "perm_range" " has to be an int > 0.")
             perm = self._swap_local(n_samples, perm_range)
 
         else:
-            raise ValueError('Unknown permutation type ({0}).'.format(
-                                                                    perm_type))
+            raise ValueError(f"Unknown permutation type ({perm_type}).")
         return perm
 
     def _swap_local(self, n, perm_range):
@@ -780,12 +786,14 @@ 
    Source code for idtxl.data
                 numpy array
                 permuted indices with length n
         """
-        assert (perm_range > 1), ('Permutation range has to be larger than 1',
-                                  'otherwise there is nothing to permute.')
-        assert (n >= perm_range), ('Not enough realisations per replication '
-                                   '({0}) to allow for the requested '
-                                   '"perm_range" of {1}.' .format(n,
-                                                                  perm_range))
+        assert perm_range > 1, (
+            "Permutation range has to be larger than 1",
+            "otherwise there is nothing to permute.",
+        )
+        assert n >= perm_range, (
+            f"Not enough realisations per replication ({n}) to allow for the requested "
+            f"'perm_range' of {perm_range}."
+        )
 
         if perm_range == n:  # permute all n samples randomly
             perm = np.random.permutation(n)
@@ -794,7 +802,7 @@ 
    Source code for idtxl.data
                 remainder = n % perm_range
             i = 0
             for p in range(n // perm_range):
-                perm[i:i + perm_range] = np.random.permutation(perm_range) + i
+                perm[i : i + perm_range] = np.random.permutation(perm_range) + i
                 i += perm_range
             if remainder > 0:
                 perm[-remainder:] = np.random.permutation(remainder) + i
@@ -831,17 +839,19 @@ 
    Source code for idtxl.data
     
             i = 0
             for p in range(n_blocks // perm_range):
-                perm_blocks[i:i + perm_range] = np.random.permutation(
-                                                                perm_range) + i
+                perm_blocks[i : i + perm_range] = np.random.permutation(perm_range) + i
                 i += perm_range
             if rem_blocks > 0:
-                perm_blocks[-rem_blocks:] = np.random.permutation(
-                                                                rem_blocks) + i
+                perm_blocks[-rem_blocks:] = np.random.permutation(rem_blocks) + i
 
         # Get the block index for each sample index, take into account that the
         # last block may have fewer samples if n_samples % block_size isn't 0.
-        idx_blocks = np.hstack((np.repeat(np.arange(n_blocks - 1), block_size),
-                                np.repeat(n_blocks - 1, rem_samples)))
+        idx_blocks = np.hstack(
+            (
+                np.repeat(np.arange(n_blocks - 1), block_size),
+                np.repeat(n_blocks - 1, rem_samples),
+            )
+        )
 
         # Permute samples indices according to permuted block indices.
         perm = np.zeros(n).astype(int)  # allocate memory
@@ -875,22 +885,22 @@ 
    Source code for idtxl.data
                 int
                 no. samples by which the time series was shifted
         """
-        assert (max_shift <= n), ('Max_shift ({0}) has to be equal to or '
-                                  'smaller than the number of samples in the '
-                                  'time series ({1}).'.format(max_shift, n))
+        assert max_shift <= n, (
+            f"Max_shift ({max_shift}) has to be equal to or smaller than the number of samples in the "
+            f"time series ({n})."
+        )
         shift = np.random.randint(low=1, high=max_shift + 1)
         if VERBOSE:
-            print("replications are shifted by {0} samples".format(shift))
-        return np.hstack((np.arange(n - shift, n),
-                          np.arange(n - shift))), shift
+            print(f"replications are shifted by {shift} samples")
+        return np.hstack((np.arange(n - shift, n), np.arange(n - shift))), shift
 
 
    [docs]    def generate_mute_data(self, n_samples=1000, n_replications=10):
         """Generate example data for a 5-process network.
 
         Generate example data and overwrite the instance's current data. The
         network is used as an example the paper on the MuTE toolbox (Montalto,
-        PLOS ONE, 2014, eq. 14) and was orginially proposed by Baccala &
-        Sameshima (2001). The network consists of five autoregressive (AR)
+        PLOS ONE, 2014, eq. 14) and was orginally proposed by Baccala &
+        Sameshima (2001). The network consists of five auto-regressive (AR)
         processes with model orders 2 and the following (non-linear) couplings:
 
         0 -> 1, u = 2 (non-linear)
@@ -916,39 +926,42 @@ 
    Source code for idtxl.data
                     number of replications
         """
         n_processes = 5
-        n_samples = n_samples
-        n_replications = n_replications
 
-        x = np.zeros((n_processes, n_samples + 3,
-                      n_replications))
-        x[:, 0:3, :] = np.random.normal(size=(n_processes, 3,
-                                              n_replications))
+        x = np.zeros((n_processes, n_samples + 3, n_replications))
+        x[:, 0:3, :] = np.random.normal(size=(n_processes, 3, n_replications))
         term_1 = 0.95 * np.sqrt(2)
         term_2 = 0.25 * np.sqrt(2)
         term_3 = -0.25 * np.sqrt(2)
         for r in range(n_replications):
             for n in range(3, n_samples + 3):
-                x[0, n, r] = (term_1 * x[0, n - 1, r] -
-                              0.9025 * x[0, n - 2, r] + np.random.normal())
+                x[0, n, r] = (
+                    term_1 * x[0, n - 1, r]
+                    - 0.9025 * x[0, n - 2, r]
+                    + np.random.normal()
+                )
                 x[1, n, r] = 0.5 * x[0, n - 2, r] ** 2 + np.random.normal()
                 x[2, n, r] = -0.4 * x[0, n - 3, r] + np.random.normal()
-                x[3, n, r] = (-0.5 * x[0, n - 2, r] ** 2 +
-                              term_2 * x[3, n - 1, r] +
-                              term_2 * x[4, n - 1, r] +
-                              np.random.normal())
-                x[4, n, r] = (term_3 * x[3, n - 1, r] +
-                              term_2 * x[4, n - 1, r] +
-                              np.random.normal())
-        self.set_data(x[:, 3:, :], 'psr')
    
+                x[3, n, r] = (
+                    -0.5 * x[0, n - 2, r] ** 2
+                    + term_2 * x[3, n - 1, r]
+                    + term_2 * x[4, n - 1, r]
+                    + np.random.normal()
+                )
+                x[4, n, r] = (
+                    term_3 * x[3, n - 1, r]
+                    + term_2 * x[4, n - 1, r]
+                    + np.random.normal()
+                )
+        self.set_data(x[:, 3:, :], "psr")
    
 
 
    [docs]    def generate_var_data(
         self,
         n_samples=1000,
         n_replications=10,
         coefficient_matrices=np.array([[[0.5, 0], [0.4, 0.5]]]),
-        noise_std=0.1
+        noise_std=0.1,
     ):
-        """Generate discrete-time VAR (vector autoregressive) time series.
+        """Generate discrete-time VAR (vector auto-regressive) time series.
 
         Generate data and overwrite the instance's current data.
 
@@ -974,39 +987,33 @@ 
    Source code for idtxl.data
     
         # Check stability of the VAR process, which is a sufficient condition
         # for stationarity.
-        var_reduced_form = np.zeros((
-            n_processes * order,
-            n_processes * order
-        ))
+        var_reduced_form = np.zeros((n_processes * order, n_processes * order))
         var_reduced_form[0:n_processes, :] = np.reshape(
             np.transpose(coefficient_matrices, (1, 0, 2)),
-            [n_processes, n_processes * order]
-            )
-        var_reduced_form[n_processes:, 0:n_processes * (order - 1)] = np.eye(
+            [n_processes, n_processes * order],
+        )
+        var_reduced_form[n_processes:, 0 : n_processes * (order - 1)] = np.eye(
             n_processes * (order - 1)
         )
         # Condition for stability: the absolute values of all the eigenvalues
-        # of the reduced-form coefficeint matrix are smaller than 1. A stable
+        # of the reduced-form coefficient matrix are smaller than 1. A stable
         # VAR process is also stationary.
         is_stable = max(np.abs(np.linalg.eigvals(var_reduced_form))) < 1
         if not is_stable:
-            RuntimeError('VAR process is not stable and may be nonstationary.')
+            raise RuntimeError("VAR process is not stable and may be nonstationary.")
 
         # Initialise time series matrix. The 3 dimensions represent
         # (processes, samples, replications). Only the last n_samples will be
         # kept, in order to discard transient effects.
-        x = np.zeros((
-            n_processes,
-            order + samples_transient + n_samples,
-            n_replications
-        ))
+        x = np.zeros(
+            (n_processes, order + samples_transient + n_samples, n_replications)
+        )
 
         # Generate (different) initial conditions for each replication:
         # Uniformly sample from the [0,1] interval and tile as many times as
         # the VAR process order along the second dimension.
         x[:, 0:order, :] = np.tile(
-            np.random.rand(n_processes, 1, n_replications),
-            (1, order, 1)
+            np.random.rand(n_processes, 1, n_replications), (1, order, 1)
         )
 
         # Compute time series
@@ -1015,24 +1022,22 @@ 
    Source code for idtxl.data
                     for i_delay in range(1, order + 1):
                     x[:, i_sample, i_repl] += np.dot(
                         coefficient_matrices[i_delay - 1, :, :],
-                        x[:, i_sample - i_delay, i_repl]
+                        x[:, i_sample - i_delay, i_repl],
                     )
                 # Add uncorrelated Gaussian noise vector
                 x[:, i_sample, i_repl] += np.random.normal(
-                    0,  # mean
-                    noise_std,
-                    x[:, i_sample, i_repl].shape
+                    0, noise_std, x[:, i_sample, i_repl].shape  # mean
                 )
 
         # Discard transient effects (only take end of time series)
-        self.set_data(x[:, -(n_samples + 1):-1, :], 'psr')
    
+        self.set_data(x[:, -(n_samples + 1) : -1, :], "psr")
    
 
 
    [docs]    def generate_logistic_maps_data(
         self,
         n_samples=1000,
         n_replications=10,
         coefficient_matrices=np.array([[[0.5, 0], [0.4, 0.5]]]),
-        noise_std=0.1
+        noise_std=0.1,
     ):
         """Generate discrete-time coupled-logistic-maps time series.
 
@@ -1067,18 +1072,15 @@ 
    Source code for idtxl.data
             # Initialise time series matrix. The 3 dimensions represent
         # (processes, samples, replications). Only the last n_samples will be
         # kept, in order to discard transient effects.
-        x = np.zeros((
-            n_processes,
-            order + samples_transient + n_samples,
-            n_replications
-        ))
+        x = np.zeros(
+            (n_processes, order + samples_transient + n_samples, n_replications)
+        )
 
         # Generate (different) initial conditions for each replication:
         # Uniformly sample from the [0,1] interval and tile as many times as
         # the stochastic process order along the second dimension.
         x[:, 0:order, :] = np.tile(
-            np.random.rand(n_processes, 1, n_replications),
-            (1, order, 1)
+            np.random.rand(n_processes, 1, n_replications), (1, order, 1)
         )
 
         # Compute time series
@@ -1087,21 +1089,19 @@ 
    Source code for idtxl.data
                     for i_delay in range(1, order + 1):
                     x[:, i_sample, i_repl] += np.dot(
                         coefficient_matrices[i_delay - 1, :, :],
-                        x[:, i_sample - i_delay, i_repl]
+                        x[:, i_sample - i_delay, i_repl],
                     )
                 # Compute activation function
                 x[:, i_sample, i_repl] = f(x[:, i_sample, i_repl])
                 # Add uncorrelated Gaussian noise vector
                 x[:, i_sample, i_repl] += np.random.normal(
-                    0,  # mean
-                    noise_std,
-                    x[:, i_sample, i_repl].shape
+                    0, noise_std, x[:, i_sample, i_repl].shape  # mean
                 )
                 # ensure values are in the [0, 1] range
                 x[:, i_sample, i_repl] = x[:, i_sample, i_repl] % 1
 
         # Discard transient effects (only take end of time series)
-        self.set_data(x[:, -(n_samples + 1):-1, :], 'psr')
    
+        self.set_data(x[:, -(n_samples + 1) : -1, :], "psr")
    
 
    
 
             
    
@@ -1114,7 +1114,7 @@ 
    Source code for idtxl.data
       
    Quick search
    
     
    
     
    
-      
+      
       
     
    
     
    
@@ -1133,14 +1133,14 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5.1 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.data
    •  
       
     
    
     
   
 
\ No newline at end of file
diff --git a/docs/html/_modules/idtxl/embedding_optimization_ais_Rudelt.html b/docs/html/_modules/idtxl/embedding_optimization_ais_Rudelt.html
index 4f526f5f..78886841 100644
--- a/docs/html/_modules/idtxl/embedding_optimization_ais_Rudelt.html
+++ b/docs/html/_modules/idtxl/embedding_optimization_ais_Rudelt.html
@@ -5,14 +5,13 @@
   
     
     
-    idtxl.embedding_optimization_ais_Rudelt — IDTxl 1.4 documentation
-    
-    
-    
+    idtxl.embedding_optimization_ais_Rudelt — IDTxl 1.5.1 documentation
+    
+    
+    
     
     
     
-    
     
     
 
@@ -32,7 +31,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5.1 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.embedding_optimization_ais_Rudelt
    •  
       
@@ -57,7 +56,7 @@ 
    Source code for idtxl.embedding_optimization_ais_Rudelt
    # noinspection PyAttributeOutsideInit
-
    [docs]class OptimizationRudelt():
+
    [docs]class OptimizationRudelt:
     """
     Optimization of embedding parameters of spike times using the history dependence estimators
 
@@ -180,47 +179,110 @@ 
    Source code for idtxl.embedding_optimization_ais_Rudelt
    settings = self._check_settings(settings)
         self.settings = settings.copy()
 
-        self.settings.setdefault('embedding_step_size', 0.005)
-        self.settings.setdefault('embedding_past_range_set', [0.005, 0.00561, 0.00629, 0.00706, 0.00792, 0.00889,
-                                                              0.00998, 0.01119, 0.01256, 0.01409, 0.01581, 0.01774,
-                                                              0.01991, 0.02233, 0.02506, 0.02812, 0.03155, 0.0354,
-                                                              0.03972, 0.04456, 0.05, 0.0561, 0.06295, 0.07063,
-                                                              0.07924, 0.08891, 0.09976, 0.11194, 0.12559, 0.14092,
-                                                              0.15811, 0.17741, 0.19905, 0.22334, 0.25059, 0.28117,
-                                                              0.31548, 0.35397, 0.39716, 0.44563, 0.5, 0.56101, 0.62946,
-                                                              0.70627, 0.79245, 0.88914, 0.99763, 1.11936, 1.25594,
-                                                              1.40919, 1.58114, 1.77407, 1.99054, 2.23342, 2.50594,
-                                                              2.81171, 3.15479, 3.53973, 3.97164, 4.45625, 5.0])
-        self.settings.setdefault('embedding_number_of_bins_set', [1, 2, 3, 4, 5])
-        self.settings.setdefault('embedding_scaling_exponent_set',
-                                 {'number_of_scalings': 10,
-                                  'min_first_bin_size': 0.005,
-                                  'min_step_for_scaling': 0.01})
-
-        self.settings.setdefault('bbc_tolerance', 0.05)
-        self.settings.setdefault('return_averaged_R', True)
-        self.settings.setdefault('timescale_minimum_past_range', 0.01)
-
-        self.settings.setdefault('analyse_auto_MI', True)
-        self.settings.setdefault('auto_MI_bin_size_set', [0.005, 0.01, 0.025, 0.05, 0.25, 0.5])
-        self.settings.setdefault('auto_MI_max_delay', 5)
-
-        self.settings.setdefault('number_of_bootstraps_R_max', 250)
-        self.settings.setdefault('number_of_bootstraps_R_tot', 250)
-        self.settings.setdefault('number_of_bootstraps_nonessential', 0)
-        self.settings.setdefault('symbol_block_length', None)
-        self.settings.setdefault('bootstrap_CI_use_sd', True)
-        self.settings.setdefault('bootstrap_CI_percentile_lo', 2.5)
-        self.settings.setdefault('bootstrap_CI_percentile_hi', 97.5)
-        self.settings.setdefault('visualization', False)
-        self.settings.setdefault('debug', False)
-
-        self.check_inputs()                                 # ------------------------------------------------------------- TODO CHECK INPUTS
-
-        self.embeddings = self.get_embeddings(self.settings['embedding_past_range_set'],
-                                              self.settings['embedding_number_of_bins_set'],
-                                              self.settings['embedding_scaling_exponent_set'])
-
+        self.settings.setdefault("embedding_step_size", 0.005)
+        self.settings.setdefault(
+            "embedding_past_range_set",
+            [
+                0.005,
+                0.00561,
+                0.00629,
+                0.00706,
+                0.00792,
+                0.00889,
+                0.00998,
+                0.01119,
+                0.01256,
+                0.01409,
+                0.01581,
+                0.01774,
+                0.01991,
+                0.02233,
+                0.02506,
+                0.02812,
+                0.03155,
+                0.0354,
+                0.03972,
+                0.04456,
+                0.05,
+                0.0561,
+                0.06295,
+                0.07063,
+                0.07924,
+                0.08891,
+                0.09976,
+                0.11194,
+                0.12559,
+                0.14092,
+                0.15811,
+                0.17741,
+                0.19905,
+                0.22334,
+                0.25059,
+                0.28117,
+                0.31548,
+                0.35397,
+                0.39716,
+                0.44563,
+                0.5,
+                0.56101,
+                0.62946,
+                0.70627,
+                0.79245,
+                0.88914,
+                0.99763,
+                1.11936,
+                1.25594,
+                1.40919,
+                1.58114,
+                1.77407,
+                1.99054,
+                2.23342,
+                2.50594,
+                2.81171,
+                3.15479,
+                3.53973,
+                3.97164,
+                4.45625,
+                5.0,
+            ],
+        )
+        self.settings.setdefault("embedding_number_of_bins_set", [1, 2, 3, 4, 5])
+        self.settings.setdefault(
+            "embedding_scaling_exponent_set",
+            {
+                "number_of_scalings": 10,
+                "min_first_bin_size": 0.005,
+                "min_step_for_scaling": 0.01,
+            },
+        )
+
+        self.settings.setdefault("bbc_tolerance", 0.05)
+        self.settings.setdefault("return_averaged_R", True)
+        self.settings.setdefault("timescale_minimum_past_range", 0.01)
+
+        self.settings.setdefault("analyse_auto_MI", True)
+        self.settings.setdefault(
+            "auto_MI_bin_size_set", [0.005, 0.01, 0.025, 0.05, 0.25, 0.5]
+        )
+        self.settings.setdefault("auto_MI_max_delay", 5)
+
+        self.settings.setdefault("number_of_bootstraps_R_max", 250)
+        self.settings.setdefault("number_of_bootstraps_R_tot", 250)
+        self.settings.setdefault("number_of_bootstraps_nonessential", 0)
+        self.settings.setdefault("symbol_block_length", None)
+        self.settings.setdefault("bootstrap_CI_use_sd", True)
+        self.settings.setdefault("bootstrap_CI_percentile_lo", 2.5)
+        self.settings.setdefault("bootstrap_CI_percentile_hi", 97.5)
+        self.settings.setdefault("visualization", False)
+        self.settings.setdefault("debug", False)
+
+        self.check_inputs()  # ------------------------------------------------------------- TODO CHECK INPUTS
+
+        self.embeddings = self.get_embeddings(
+            self.settings["embedding_past_range_set"],
+            self.settings["embedding_number_of_bins_set"],
+            self.settings["embedding_scaling_exponent_set"],
+        )
 
     @staticmethod
     def _check_settings(settings=None):
@@ -233,7 +295,7 @@ 
    Source code for idtxl.embedding_optimization_ais_Rudelt
    if settings is None:
             return {}
         elif type(settings) is not dict:
-            raise TypeError('settings should be a dictionary.')
+            raise TypeError("settings should be a dictionary.")
         else:
             return settings
 
@@ -243,110 +305,149 @@ 
    Source code for idtxl.embedding_optimization_ais_Rudelt
            """
 
-        args_float = ['embedding_step_size',
-                      'timescale_minimum_past_range',
-                      'bootstrap_CI_percentile_lo',
-                      'bootstrap_CI_percentile_hi',
-                      'bbc_tolerance']
+        args_float = [
+            "embedding_step_size",
+            "timescale_minimum_past_range",
+            "bootstrap_CI_percentile_lo",
+            "bootstrap_CI_percentile_hi",
+            "bbc_tolerance",
+        ]
         for key in args_float:
-            assert (key in self.settings), \
-                (key + ' has to be specified (see help)!')
-            assert (isinstance(self.settings[key], float)), \
-                ("Error: setting '" + key + "' needs to an floating point value (see help!!). Aborting.")
-
-        args_int = ['number_of_bootstraps_R_max',
-                    'number_of_bootstraps_R_tot',
-                    'number_of_bootstraps_nonessential']
+            assert key in self.settings, key + " has to be specified (see help)!"
+            assert isinstance(self.settings[key], float), (
+                "Error: setting '"
+                + key
+                + "' needs to an floating point value (see help!!). Aborting."
+            )
+
+        args_int = [
+            "number_of_bootstraps_R_max",
+            "number_of_bootstraps_R_tot",
+            "number_of_bootstraps_nonessential",
+        ]
         for key in args_int:
-            assert (key in self.settings), \
-                (key + ' has to be specified (see help)!')
-            assert (isinstance(self.settings[key], int)), \
-                ("Error: setting '" + key + "' needs to an integer value (see help!!). Aborting.")
-
-        args_bool = ['return_averaged_R',
-                     'bootstrap_CI_use_sd',
-                     'debug']
+            assert key in self.settings, key + " has to be specified (see help)!"
+            assert isinstance(self.settings[key], int), (
+                "Error: setting '"
+                + key
+                + "' needs to an integer value (see help!!). Aborting."
+            )
+
+        args_bool = ["return_averaged_R", "bootstrap_CI_use_sd", "debug"]
         for key in args_bool:
-            assert (key in self.settings), \
-                (key + ' has to be specified (see help)!')
-            assert (isinstance(self.settings[key], bool)), \
-                ("Error: setting '" + key + "' needs to a boolean expression (see help!!). Aborting.")
-
-        assert('embedding_past_range_set' in self.settings), \
-            'embedding_past_range_set has to be specified (see help)!'
-        assert (isinstance(self.settings['embedding_past_range_set'], list)), \
-            "Error: setting 'embedding_past_range_set' needs to be a list but is defined as {0}. " \
-            "Aborting.".format(type(self.settings['embedding_past_range_set']))
-
-        assert ('embedding_number_of_bins_set' in self.settings), \
-            'embedding_number_of_bins_set has to be specified (see help)!'
-        assert (isinstance(self.settings['embedding_number_of_bins_set'], list)), \
-            "Error: setting 'embedding_number_of_bins_set' needs to a list but is defined as {0}. " \
-            "Aborting.".format(type(self.settings['embedding_number_of_bins_set']))
-
-        assert ('embedding_scaling_exponent_set' in self.settings), \
-            'embedding_scaling_exponent_set has to be specified (see help)!'
-
-        assert ('number_of_scalings' in self.settings['embedding_scaling_exponent_set']), \
-            "'number_of_scalings' have to be specified in self.settings['embedding_scaling_exponent_set'] (see help)!"
-        assert (isinstance(self.settings['embedding_scaling_exponent_set']['number_of_scalings'], int)), \
-            "Error: setting 'number_of_scalings' needs to be an integer value but is defined as {0}. " \
-            "Aborting.".format(type(self.settings['number_of_scalings']))
-        assert ('min_first_bin_size' in self.settings['embedding_scaling_exponent_set']), \
-            "'min_first_bin_size' have to be specified in self.settings['embedding_scaling_exponent_set'] (see help)!"
-        assert (isinstance(self.settings['embedding_scaling_exponent_set']['min_first_bin_size'], float)), \
-            "Error: setting 'min_first_bin_sizes' needs to be a floating point value but is defined as {0}. " \
-            "Aborting.".format(type(self.settings['min_first_bin_sizes']))
-        assert ('min_step_for_scaling' in self.settings['embedding_scaling_exponent_set']), \
-            "'min_step_for_scaling' have to be specified in self.settings['embedding_scaling_exponent_set'] (see help)!"
-        assert (isinstance(self.settings['embedding_scaling_exponent_set']['min_step_for_scaling'], float)), \
-            "Error: setting 'min_step_for_scaling' needs to be a floating point value but is defined as {0}. " \
-            "Aborting.".format(type(self.settings['min_step_for_scaling']))
-
-        assert ('symbol_block_length' in self.settings), \
-            'symbol_block_length has to be specified (see help)!'
-        if self.settings['symbol_block_length'] is not None:
-            assert (isinstance(self.settings['symbol_block_length'], int)), \
-                "Error: setting 'symbol_block_length' needs to an integer value but is defined as {0}. " \
-                "Aborting.".format(type(self.settings['symbol_block_length']))
-
-        if self.settings['analyse_auto_MI']:
-            assert (isinstance(self.settings['analyse_auto_MI'], bool)), \
-                "Error: setting 'analyse_auto_MI' needs to be a boolean expression but is defined as {0}. " \
-                "Aborting.".format(type(self.settings['analyse_auto_MI']))
-            assert ('auto_MI_bin_size_set' in self.settings), \
-                'If analyse_auto_MI is set to True, auto_MI_bin_size_set has to be specified (see help)!'
-            assert (isinstance(self.settings['auto_MI_bin_size_set'], list)), \
-                "Error: setting 'auto_MI_bin_size_set' needs to a list but is defined as {0}. " \
-                "Aborting.".format(type(self.settings['auto_MI_bin_size_set']))
-            assert ('auto_MI_max_delay' in self.settings), \
-                'If analyse_auto_MI is set to True, auto_MI_max_delay has to be specified (see help)!'
-            assert (isinstance(self.settings['auto_MI_max_delay'], int)), \
-                "Error: setting 'auto_MI_max_delay' needs to be an integer value but is defined as {0}. " \
-                "Aborting.".format(type(self.settings['auto_MI_max_delay']))
-
-        if self.settings['visualization']:
-            assert (isinstance(self.settings['visualization'], bool)), \
-                "Error: setting 'visualization' needs to be boolean but is defined as {0}. " \
-                "Aborting.".format(type(self.settings['visualization']))
-            assert ('output_path' in self.settings), \
-                'If visualization is set to True an output path has to be specified (see help)!'
-            assert ('output_prefix' in self.settings), \
-                'If visualization is set to True an output prefix has to be specified (see help)!'
+            assert key in self.settings, key + " has to be specified (see help)!"
+            assert isinstance(self.settings[key], bool), (
+                "Error: setting '"
+                + key
+                + "' needs to a boolean expression (see help!!). Aborting."
+            )
+
+        assert (
+            "embedding_past_range_set" in self.settings
+        ), "embedding_past_range_set has to be specified (see help)!"
+        assert isinstance(self.settings["embedding_past_range_set"], list), (
+            "Error: setting 'embedding_past_range_set' needs to be a list but is defined as {0}. "
+            "Aborting.".format(type(self.settings["embedding_past_range_set"]))
+        )
+
+        assert (
+            "embedding_number_of_bins_set" in self.settings
+        ), "embedding_number_of_bins_set has to be specified (see help)!"
+        assert isinstance(self.settings["embedding_number_of_bins_set"], list), (
+            "Error: setting 'embedding_number_of_bins_set' needs to a list but is defined as {0}. "
+            "Aborting.".format(type(self.settings["embedding_number_of_bins_set"]))
+        )
+
+        assert (
+            "embedding_scaling_exponent_set" in self.settings
+        ), "embedding_scaling_exponent_set has to be specified (see help)!"
+
+        assert (
+            "number_of_scalings" in self.settings["embedding_scaling_exponent_set"]
+        ), "'number_of_scalings' have to be specified in self.settings['embedding_scaling_exponent_set'] (see help)!"
+        assert isinstance(
+            self.settings["embedding_scaling_exponent_set"]["number_of_scalings"], int
+        ), (
+            "Error: setting 'number_of_scalings' needs to be an integer value but is defined as {0}. "
+            "Aborting.".format(type(self.settings["number_of_scalings"]))
+        )
+        assert (
+            "min_first_bin_size" in self.settings["embedding_scaling_exponent_set"]
+        ), "'min_first_bin_size' have to be specified in self.settings['embedding_scaling_exponent_set'] (see help)!"
+        assert isinstance(
+            self.settings["embedding_scaling_exponent_set"]["min_first_bin_size"], float
+        ), (
+            "Error: setting 'min_first_bin_sizes' needs to be a floating point value but is defined as {0}. "
+            "Aborting.".format(type(self.settings["min_first_bin_sizes"]))
+        )
+        assert (
+            "min_step_for_scaling" in self.settings["embedding_scaling_exponent_set"]
+        ), "'min_step_for_scaling' have to be specified in self.settings['embedding_scaling_exponent_set'] (see help)!"
+        assert isinstance(
+            self.settings["embedding_scaling_exponent_set"]["min_step_for_scaling"],
+            float,
+        ), (
+            "Error: setting 'min_step_for_scaling' needs to be a floating point value but is defined as {0}. "
+            "Aborting.".format(type(self.settings["min_step_for_scaling"]))
+        )
+
+        assert (
+            "symbol_block_length" in self.settings
+        ), "symbol_block_length has to be specified (see help)!"
+        if self.settings["symbol_block_length"] is not None:
+            assert isinstance(self.settings["symbol_block_length"], int), (
+                "Error: setting 'symbol_block_length' needs to an integer value but is defined as {0}. "
+                "Aborting.".format(type(self.settings["symbol_block_length"]))
+            )
+
+        if self.settings["analyse_auto_MI"]:
+            assert isinstance(self.settings["analyse_auto_MI"], bool), (
+                "Error: setting 'analyse_auto_MI' needs to be a boolean expression but is defined as {0}. "
+                "Aborting.".format(type(self.settings["analyse_auto_MI"]))
+            )
+            assert (
+                "auto_MI_bin_size_set" in self.settings
+            ), "If analyse_auto_MI is set to True, auto_MI_bin_size_set has to be specified (see help)!"
+            assert isinstance(self.settings["auto_MI_bin_size_set"], list), (
+                "Error: setting 'auto_MI_bin_size_set' needs to a list but is defined as {0}. "
+                "Aborting.".format(type(self.settings["auto_MI_bin_size_set"]))
+            )
+            assert (
+                "auto_MI_max_delay" in self.settings
+            ), "If analyse_auto_MI is set to True, auto_MI_max_delay has to be specified (see help)!"
+            assert isinstance(self.settings["auto_MI_max_delay"], int), (
+                "Error: setting 'auto_MI_max_delay' needs to be an integer value but is defined as {0}. "
+                "Aborting.".format(type(self.settings["auto_MI_max_delay"]))
+            )
+
+        if self.settings["visualization"]:
+            assert isinstance(self.settings["visualization"], bool), (
+                "Error: setting 'visualization' needs to be boolean but is defined as {0}. "
+                "Aborting.".format(type(self.settings["visualization"]))
+            )
+            assert (
+                "output_path" in self.settings
+            ), "If visualization is set to True an output path has to be specified (see help)!"
+            assert (
+                "output_prefix" in self.settings
+            ), "If visualization is set to True an output prefix has to be specified (see help)!"
 
         # Cython implementation uses 64bit unsigned integers for the symbols,
         # we allow up to 62 bins (window has 1 bin more..)
-        assert (max(self.settings['embedding_number_of_bins_set']) <= 62), \
-            'Error: Max number of bins too large; use less than 63. Aborting.'
+        assert (
+            max(self.settings["embedding_number_of_bins_set"]) <= 62
+        ), "Error: Max number of bins too large; use less than 63. Aborting."
 
         # If R_tot is computed as an average over Rs, no confidence interval can be estimated
-        if self.settings['return_averaged_R']:
-            self.settings['number_of_bootstraps_R_tot'] = 0
    
-
-
    [docs]    def get_embeddings(self,
-                       embedding_past_range_set,
-                       embedding_number_of_bins_set,
-                       embedding_scaling_exponent_set):
+        if self.settings["return_averaged_R"]:
+            self.settings["number_of_bootstraps_R_tot"] = 0
    
+
+
    [docs]    def get_embeddings(
+        self,
+        embedding_past_range_set,
+        embedding_number_of_bins_set,
+        embedding_scaling_exponent_set,
+    ):
         """
         Get all combinations of parameters T, d, k, based on the
         sets of selected parameters.
@@ -356,14 +457,19 @@ 
    Source code for idtxl.embedding_optimization_ais_Rudelt
    for past_range_T in embedding_past_range_set:
             for number_of_bins_d in embedding_number_of_bins_set:
                 if not isinstance(number_of_bins_d, int) or number_of_bins_d < 1:
-                    print("Error: number of bins {} is not a positive integer. Skipping.".format(number_of_bins_d),
-                          file=stderr, flush=True)
+                    print(
+                        "Error: number of bins {} is not a positive integer. Skipping.".format(
+                            number_of_bins_d
+                        ),
+                        file=stderr,
+                        flush=True,
+                    )
                     continue
 
                 if type(embedding_scaling_exponent_set) == dict:
-                    scaling_set_given_T_and_d = self.get_set_of_scalings(past_range_T,
-                                                                         number_of_bins_d,
-                                                                         **embedding_scaling_exponent_set)
+                    scaling_set_given_T_and_d = self.get_set_of_scalings(
+                        past_range_T, number_of_bins_d, **embedding_scaling_exponent_set
+                    )
                 else:
                     scaling_set_given_T_and_d = embedding_scaling_exponent_set
 
@@ -372,11 +478,14 @@ 
    Source code for idtxl.embedding_optimization_ais_Rudelt
    return embeddings
    
 
-
    [docs]    def get_set_of_scalings(self, past_range_T,
-                            number_of_bins_d,
-                            number_of_scalings,
-                            min_first_bin_size,
-                            min_step_for_scaling):
+
    [docs]    def get_set_of_scalings(
+        self,
+        past_range_T,
+        number_of_bins_d,
+        number_of_scalings,
+        min_first_bin_size,
+        min_step_for_scaling,
+    ):
         """
         Get scaling exponents such that the uniform embedding as well as
         the embedding for which the first bin has a length of
@@ -386,19 +495,28 @@ 
    Source code for idtxl.embedding_optimization_ais_Rudelt
            """
 
         min_scaling = 0
-        if past_range_T / number_of_bins_d <= min_first_bin_size or number_of_bins_d == 1:
+        if (
+            past_range_T / number_of_bins_d <= min_first_bin_size
+            or number_of_bins_d == 1
+        ):
             max_scaling = 0
         else:
             # for the initial guess assume the largest bin dominates, so k is approx. log(T) / d
 
-            max_scaling = newton(lambda scaling: self.get_past_range(number_of_bins_d,
-                                                                     min_first_bin_size,
-                                                                     scaling) - past_range_T,
-                                 np.log10(past_range_T / min_first_bin_size) / (number_of_bins_d - 1),
-                                 tol=1e-04, maxiter=500)
-
-        while np.linspace(min_scaling, max_scaling,
-                          number_of_scalings, retstep=True)[1] < min_step_for_scaling:
+            max_scaling = newton(
+                lambda scaling: self.get_past_range(
+                    number_of_bins_d, min_first_bin_size, scaling
+                )
+                - past_range_T,
+                np.log10(past_range_T / min_first_bin_size) / (number_of_bins_d - 1),
+                tol=1e-04,
+                maxiter=500,
+            )
+
+        while (
+            np.linspace(min_scaling, max_scaling, number_of_scalings, retstep=True)[1]
+            < min_step_for_scaling
+        ):
             number_of_scalings -= 1
 
         return np.linspace(min_scaling, max_scaling, number_of_scalings)
    
@@ -408,67 +526,82 @@ 
    Source code for idtxl.embedding_optimization_ais_Rudelt
            Get the past range T of the embedding, based on the parameters d, tau_1 and k.
         """
 
-        return np.sum([first_bin_size * 10 ** ((number_of_bins_d - i) * scaling_k)
-                       for i in range(1, number_of_bins_d + 1)])
    
+        return np.sum(
+            [
+                first_bin_size * 10 ** ((number_of_bins_d - i) * scaling_k)
+                for i in range(1, number_of_bins_d + 1)
+            ]
+        )
    
 
 
    [docs]    def get_history_dependence(self, data, process):
         """
-            Estimate the history dependence for each embedding to all given processes.
+        Estimate the history dependence for each embedding to all given processes.
         """
 
         # load estimators
-        if self.settings['estimation_method'] == 'bbc':
+        if self.settings["estimation_method"] == "bbc":
             estbbc = RudeltBBCEstimator()
-        elif self.settings['estimation_method'] == 'shuffling':
+        elif self.settings["estimation_method"] == "shuffling":
             estshu = RudeltShufflingEstimator()
 
         # get history dependence
         history_dependence = np.empty(shape=(len(self.embeddings)))
-        if self.settings['estimation_method'] == 'bbc':
+        if self.settings["estimation_method"] == "bbc":
             bbc_term = np.empty(shape=(len(self.embeddings)))
 
         embedding_count = 0
         for embedding in self.embeddings:
-
-            if self.settings['debug']:
-                print("Embedding: " + str(embedding[0]) + ", " + str(embedding[1]) + ", " + str(embedding[2]))
-
-            symbol_array, past_symbol_array, current_symbol_array, symbol_array_length = \
-                    data.get_realisations_symbols(process,
-                                                  embedding[0],
-                                                  embedding[1],
-                                                  embedding[2],
-                                                  self.settings['embedding_step_size'],
-                                                  output_spike_times=False)
-
-            if self.settings['estimation_method'] == 'bbc':
-                I_bbc, R_bbc, bbc_t = \
-                            estbbc.estimate(symbol_array[0], past_symbol_array[0], current_symbol_array[0])
+            if self.settings["debug"]:
+                print(
+                    "Embedding: "
+                    + str(embedding[0])
+                    + ", "
+                    + str(embedding[1])
+                    + ", "
+                    + str(embedding[2])
+                )
+
+            (
+                symbol_array,
+                past_symbol_array,
+                current_symbol_array,
+                symbol_array_length,
+            ) = data.get_realisations_symbols(
+                process,
+                embedding[0],
+                embedding[1],
+                embedding[2],
+                self.settings["embedding_step_size"],
+                output_spike_times=False,
+            )
+
+            if self.settings["estimation_method"] == "bbc":
+                I_bbc, R_bbc, bbc_t = estbbc.estimate(
+                    symbol_array[0], past_symbol_array[0], current_symbol_array[0]
+                )
                 history_dependence[embedding_count] = R_bbc
                 bbc_term[embedding_count] = bbc_t
 
-                if self.settings['debug']:
+                if self.settings["debug"]:
                     print("\tHD: " + str(R_bbc) + " BBC: " + str(bbc_t))
 
-            elif self.settings['estimation_method'] == 'shuffling':
+            elif self.settings["estimation_method"] == "shuffling":
                 I_sh, R_sh = estshu.estimate(symbol_array[0])
                 history_dependence[embedding_count] = R_sh
 
-                if self.settings['debug']:
+                if self.settings["debug"]:
                     print("\tHD: " + str(R_sh))
 
             embedding_count += 1
 
-        if self.settings['estimation_method'] == 'bbc':
+        if self.settings["estimation_method"] == "bbc":
             return history_dependence, bbc_term
-        elif self.settings['estimation_method'] == 'shuffling':
+        elif self.settings["estimation_method"] == "shuffling":
             return history_dependence
    
 
-
    [docs]    def get_bootstrap_history_dependence(self,
-                                         data,
-                                         embedding,
-                                         number_of_bootstraps,
-                                         symbol_block_length=None):
+
    [docs]    def get_bootstrap_history_dependence(
+        self, data, embedding, number_of_bootstraps, symbol_block_length=None
+    ):
         """
         For a given embedding, return bootstrap replications for R.
         """
@@ -482,27 +615,35 @@ 
    Source code for idtxl.embedding_optimization_ais_Rudelt
    bs_Rs = np.zeros(number_of_bootstraps)
 
         for rep in range(number_of_bootstraps):
-            bs_symbol_array, bs_past_symbol_array, bs_current_symbol_array = \
-                data.get_bootstrap_realisations_symbols(self.process,
-                                                        embedding[0],
-                                                        embedding[1],
-                                                        embedding[2],
-                                                        self.settings['embedding_step_size'],
-                                                        symbol_block_length=symbol_block_length)
-
-            if self.settings['estimation_method'] == 'bbc':
-                I_bbc, R_bbc, bbc_t = \
-                    estbbc.estimate(bs_symbol_array[0], bs_past_symbol_array[0], bs_current_symbol_array[0])
+            (
+                bs_symbol_array,
+                bs_past_symbol_array,
+                bs_current_symbol_array,
+            ) = data.get_bootstrap_realisations_symbols(
+                self.process,
+                embedding[0],
+                embedding[1],
+                embedding[2],
+                self.settings["embedding_step_size"],
+                symbol_block_length=symbol_block_length,
+            )
+
+            if self.settings["estimation_method"] == "bbc":
+                I_bbc, R_bbc, bbc_t = estbbc.estimate(
+                    bs_symbol_array[0],
+                    bs_past_symbol_array[0],
+                    bs_current_symbol_array[0],
+                )
                 bs_Rs[rep] = R_bbc
 
-                if self.settings['debug']:
+                if self.settings["debug"]:
                     print("\tHD: " + str(R_bbc) + " BBC: " + str(bbc_t))
 
-            elif self.settings['estimation_method'] == 'shuffling':
+            elif self.settings["estimation_method"] == "shuffling":
                 I_sh, R_sh = estshu.estimate(bs_symbol_array[0])
                 bs_Rs[rep] = R_sh
 
-                if self.settings['debug']:
+                if self.settings["debug"]:
                     print("\tHD: " + str(R_sh))
 
         return bs_Rs
    
@@ -520,8 +661,7 @@ 
    Source code for idtxl.embedding_optimization_ais_Rudelt
            """
 
         # load data
-        embedding_maximising_R_at_T, max_Rs \
-            = self.get_embeddings_that_maximise_R()
+        embedding_maximising_R_at_T, max_Rs = self.get_embeddings_that_maximise_R()
 
         Ts = sorted([key for key in max_Rs.keys()])
         Rs = [max_Rs[T] for T in Ts]
@@ -553,10 +693,9 @@ 
    Source code for idtxl.embedding_optimization_ais_Rudelt
    else:
             return T_D, R_tot_thresh
    
 
-
    [docs]    def get_embeddings_that_maximise_R(self,
-                                       bbc_tolerance=None,
-                                       dependent_var="T",
-                                       get_as_list=False):
+
    [docs]    def get_embeddings_that_maximise_R(
+        self, bbc_tolerance=None, dependent_var="T", get_as_list=False
+    ):
         """
         For each T (or d), get the embedding for which R is maximised.
 
@@ -579,30 +718,46 @@ 
    Source code for idtxl.embedding_optimization_ais_Rudelt
    scaling_k = float(embedding[2])
             history_dependence = self.history_dependence[i]
 
-            if self.settings['estimation_method'] == "bbc":
-                if self.bbc_term[i] >= self.settings['bbc_tolerance']:                          # ----------------------- TODO check
+            if self.settings["estimation_method"] == "bbc":
+                if (
+                    self.bbc_term[i] >= self.settings["bbc_tolerance"]
+                ):  # ----------------------- TODO check
                     continue
 
             if dependent_var == "T":
-                if not past_range_T in embeddings_that_maximise_R \
-                                or history_dependence > max_Rs[past_range_T]:
+                if (
+                    not past_range_T in embeddings_that_maximise_R
+                    or history_dependence > max_Rs[past_range_T]
+                ):
                     max_Rs[past_range_T] = history_dependence
-                    embeddings_that_maximise_R[past_range_T] = (number_of_bins_d, scaling_k)
+                    embeddings_that_maximise_R[past_range_T] = (
+                        number_of_bins_d,
+                        scaling_k,
+                    )
             elif dependent_var == "d":
-                if not number_of_bins_d in embeddings_that_maximise_R \
-                                or history_dependence > max_Rs[number_of_bins_d]:
+                if (
+                    not number_of_bins_d in embeddings_that_maximise_R
+                    or history_dependence > max_Rs[number_of_bins_d]
+                ):
                     max_Rs[number_of_bins_d] = history_dependence
-                    embeddings_that_maximise_R[number_of_bins_d] = (past_range_T, scaling_k)
+                    embeddings_that_maximise_R[number_of_bins_d] = (
+                        past_range_T,
+                        scaling_k,
+                    )
 
         if get_as_list:
             embeddings = []
             if dependent_var == "T":
                 for past_range_T in embeddings_that_maximise_R:
-                    number_of_bins_d, scaling_k = embeddings_that_maximise_R[past_range_T]
+                    number_of_bins_d, scaling_k = embeddings_that_maximise_R[
+                        past_range_T
+                    ]
                     embeddings += [(past_range_T, number_of_bins_d, scaling_k)]
             elif dependent_var == "d":
                 for number_of_bins_d in embeddings_that_maximise_R:
-                    past_range_T, scaling_k = embeddings_that_maximise_R[number_of_bins_d]
+                    past_range_T, scaling_k = embeddings_that_maximise_R[
+                        number_of_bins_d
+                    ]
                     embeddings += [(past_range_T, number_of_bins_d, scaling_k)]
             return embeddings
         else:
@@ -626,14 +781,13 @@ 
    Source code for idtxl.embedding_optimization_ais_Rudelt
    # get dRs
         dRs = []
-        R_prev = 0.
+        R_prev = 0.0
 
         # No values higher than R_tot are allowed,
         # otherwise the information timescale might be
         # misestimated because of spurious contributions
         # at large T
         for R, T in zip(Rs[Rs <= R_tot], Ts[Rs <= R_tot]):
-
             # No negative increments are allowed
             dRs += [np.amax([0.0, R - R_prev])]
 
@@ -641,8 +795,7 @@ 
    Source code for idtxl.embedding_optimization_ais_Rudelt
    if R > R_prev:
                 R_prev = R
 
-        dRs = np.pad(dRs, (0, len(Rs) - len(dRs)),
-                     mode='constant', constant_values=0)
+        dRs = np.pad(dRs, (0, len(Rs) - len(dRs)), mode="constant", constant_values=0)
 
         # compute tau_R
         Ts_0 = np.append([0], Ts)
@@ -652,17 +805,14 @@ 
    Source code for idtxl.embedding_optimization_ais_Rudelt
    Ts_0 = Ts_0[Ts_0 >= T_0]
         norm = np.sum(dRs_0)
 
-        if norm == 0.:
+        if norm == 0.0:
             tau = 0.0
         else:
             Ts_0 -= Ts_0[0]
             tau = np.dot(((Ts_0[:-1] + Ts_0[1:]) / 2), dRs_0) / norm
         return tau
    
 
-
    [docs]    def get_R_tot(self,
-                  return_averaged_R=False,
-                  **kwargs):
-
+
    [docs]    def get_R_tot(self, return_averaged_R=False, **kwargs):
         max_Rs = self.max_Rs
 
         if return_averaged_R:
@@ -682,15 +832,11 @@ 
    Source code for idtxl.embedding_optimization_ais_Rudelt
    return np.average([R for R, T in zip(Rs, Ts) if T_D <= T < T_max])
 
         else:
-
             temporal_depth_T_D = self.get_temporal_depth_T_D()
 
             return max_Rs[temporal_depth_T_D]
    
 
-
    [docs]    def compute_CIs(self,
-                    data,
-                    target_R='R_max',
-                    symbol_block_length=None):
+
    [docs]    def compute_CIs(self, data, target_R="R_max", symbol_block_length=None):
         """
         Compute bootstrap replications of the history dependence estimate
         which can be used to obtain confidence intervals.
@@ -715,26 +861,25 @@ 
    Source code for idtxl.embedding_optimization_ais_Rudelt
                    on heuristics
         """
 
-        assert target_R in ['nonessential', 'R_max', 'R_tot']
+        assert target_R in ["nonessential", "R_max", "R_tot"]
 
-        number_of_bootstraps = self.settings['number_of_bootstraps_{}'.format(target_R)]
+        number_of_bootstraps = self.settings["number_of_bootstraps_{}".format(target_R)]
 
         if number_of_bootstraps == 0:
             return
 
-        embedding_maximising_R_at_T, max_Rs \
-            = self.get_embeddings_that_maximise_R()
+        embedding_maximising_R_at_T, max_Rs = self.get_embeddings_that_maximise_R()
         self.embedding_maximising_R_at_T = embedding_maximising_R_at_T
         self.max_Rs = max_Rs
 
-        if target_R == 'nonessential':
+        if target_R == "nonessential":
             # bootstrap R for unessential Ts (not required for the main analysis)
             embeddings = []
             for past_range_T in embedding_maximising_R_at_T:
                 number_of_bins_d, scaling_k = embedding_maximising_R_at_T[past_range_T]
                 embeddings += [(past_range_T, number_of_bins_d, scaling_k)]
 
-        elif target_R == 'R_max':
+        elif target_R == "R_max":
             # bootstrap R for the max R, to get a good estimate for the standard deviation
             # which is used to determine R_tot
             max_R, max_R_T = utl.get_max_R_T(max_Rs)
@@ -743,14 +888,13 @@ 
    Source code for idtxl.embedding_optimization_ais_Rudelt
    number_of_bins_d, scaling_k = embedding_maximising_R_at_T[max_R_T]
             embeddings = [(max_R_T, number_of_bins_d, scaling_k)]
 
-        elif target_R == 'R_tot':
+        elif target_R == "R_tot":
             T_D = self.get_temporal_depth_T_D()
             number_of_bins_d, scaling_k = embedding_maximising_R_at_T[T_D]
 
             embeddings = [(T_D, number_of_bins_d, scaling_k)]
 
         for embedding in embeddings:
-
             embindex = self.embeddings.index(embedding)
 
             if hasattr(self, "bs_history_dependence"):
@@ -767,11 +911,12 @@ 
    Source code for idtxl.embedding_optimization_ais_Rudelt
    if not number_of_bootstraps > number_of_stored_bootstraps:
                 continue
 
-            bs_R = \
-                self.get_bootstrap_history_dependence(data,
-                                                      embedding,
-                                                      number_of_bootstraps - number_of_stored_bootstraps,
-                                                      symbol_block_length=symbol_block_length)
+            bs_R = self.get_bootstrap_history_dependence(
+                data,
+                embedding,
+                number_of_bootstraps - number_of_stored_bootstraps,
+                symbol_block_length=symbol_block_length,
+            )
 
             if stored_bs_Rs is not None:
                 bs_R = np.concatenate([stored_bs_Rs, bs_R])
@@ -784,13 +929,12 @@ 
    Source code for idtxl.embedding_optimization_ais_Rudelt
            it, else compute it.
         """
 
-        auto_MI_data = {
-            "delay": [],
-            "auto_MI": []
-        }
+        auto_MI_data = {"delay": [], "auto_MI": []}
         auto_MI_dict = {}
-        for auto_MI_bin_size in self.settings['auto_MI_bin_size_set']:
-            number_of_delays = int(self.settings['auto_MI_max_delay'] / auto_MI_bin_size) + 1
+        for auto_MI_bin_size in self.settings["auto_MI_bin_size_set"]:
+            number_of_delays = (
+                int(self.settings["auto_MI_max_delay"] / auto_MI_bin_size) + 1
+            )
 
             # perform the MI analysis
             auto_MI = self.get_auto_MI(spike_times, auto_MI_bin_size, number_of_delays)
@@ -799,7 +943,7 @@ 
    Source code for idtxl.embedding_optimization_ais_Rudelt
    auto_MI_dict[auto_MI_bin_size] = auto_MI
 
-        auto_MI_data['auto_MI'] = auto_MI_dict
+        auto_MI_data["auto_MI"] = auto_MI_dict
         self.auto_MI = auto_MI_data
    
 
 
    [docs]    def get_auto_MI(self, spike_times, bin_size, number_of_delays):
@@ -808,38 +952,55 @@ 
    Source code for idtxl.embedding_optimization_ais_Rudelt
            measure closely related to history dependence.
         """
 
-        binned_neuron_activity = utl.get_binned_neuron_activity(spike_times, bin_size, relative_to_median_activity=True)
+        binned_neuron_activity = utl.get_binned_neuron_activity(
+            spike_times, bin_size, relative_to_median_activity=True
+        )
 
         p_spike = sum(binned_neuron_activity) / len(binned_neuron_activity)
 
-        self.H_spiking = utl.get_shannon_entropy([p_spike,
-                                         1 - p_spike])
+        self.H_spiking = utl.get_shannon_entropy([p_spike, 1 - p_spike])
 
         auto_MIs = np.empty(number_of_delays)
 
         # compute auto MI
         for delay in range(number_of_delays):
-
             symbol_counts = []
             number_of_symbols = len(binned_neuron_activity) - delay - 1
-            symbols = np.array([2 * binned_neuron_activity[i] + binned_neuron_activity[i + delay + 1]
-                                for i in range(number_of_symbols)])
-            symbol_counts += [dict([(unq_symbol, len(np.where(symbols == unq_symbol)[0]))
-                                    for unq_symbol in np.unique(symbols)])]
+            symbols = np.array(
+                [
+                    2 * binned_neuron_activity[i]
+                    + binned_neuron_activity[i + delay + 1]
+                    for i in range(number_of_symbols)
+                ]
+            )
+            symbol_counts += [
+                dict(
+                    [
+                        (unq_symbol, len(np.where(symbols == unq_symbol)[0]))
+                        for unq_symbol in np.unique(symbols)
+                    ]
+                )
+            ]
 
             symbol_counts = utl.add_up_dicts(symbol_counts)
             number_of_symbols = sum(symbol_counts.values())
 
-            H_joint = utl.get_shannon_entropy([number_of_occurrences / number_of_symbols
-                                           for number_of_occurrences in symbol_counts.values()])
+            H_joint = utl.get_shannon_entropy(
+                [
+                    number_of_occurrences / number_of_symbols
+                    for number_of_occurrences in symbol_counts.values()
+                ]
+            )
 
             # I(X : Y) = H(X) - H(X|Y) = H(X) - (H(X,Y) - H(Y)) = H(X) + H(Y) - H(X,Y)
             # auto_MI = 2 * H_spiking - H_joint
-            auto_MIs[delay] = 2 - H_joint / self.H_spiking  # normalized auto MI = auto MI / H_spiking
+            auto_MIs[delay] = (
+                2 - H_joint / self.H_spiking
+            )  # normalized auto MI = auto MI / H_spiking
 
         return auto_MIs
    
 
-
    [docs]    def optimize(self, data, processes='all'):
+
    [docs]    def optimize(self, data, processes="all"):
         """
         Optimize the embedding parameters of spike time data using the Rudelt history dependence estimator.
 
@@ -874,30 +1035,32 @@ 
    Source code for idtxl.embedding_optimization_ais_Rudelt
    # check input data
         if type(data) != Data_spiketime:
-            raise ValueError('Input Data nneds to be Data_spiketime object but is defined as: '
-                             '{0}.'.format(type(data)))
+            raise ValueError(
+                "Input Data nneds to be Data_spiketime object but is defined as: "
+                "{0}.".format(type(data))
+            )
 
         # check input process list
-        if processes == 'all':
+        if processes == "all":
             processes = [t for t in range(data.n_processes)]
         elif (type(processes) is list) and (type(processes[0]) is int):
             pass
         else:
-            raise ValueError('Processes were not specified correctly: '
-                             '{0}.'.format(processes))
+            raise ValueError(
+                "Processes were not specified correctly: " "{0}.".format(processes)
+            )
 
-        if self.settings['debug']:
+        if self.settings["debug"]:
             import pprint
+
             pprint.pprint(self.settings, width=1)
 
         # open result dict
-        results = ResultsSingleProcessRudelt(
-            processes=processes)
+        results = ResultsSingleProcessRudelt(processes=processes)
 
         # start optimizing given processes
         process_count = 0
         for process in processes:
-
             # optimize single process
             single_result = self.optimize_single_run(data, process)
 
@@ -906,13 +1069,15 @@ 
    Source code for idtxl.embedding_optimization_ais_Rudelt
    process_count=process_count,
                 process=process,
                 settings=self.settings,
-                results=single_result)
+                results=single_result,
+            )
 
             process_count += 1
 
-            if self.settings['visualization'] == True:
-                filename = Path(self.settings['output_path']).joinpath(
-                     '{}_process{}.svg'.format(self.settings['output_prefix'], process))
+            if self.settings["visualization"] == True:
+                filename = Path(self.settings["output_path"]).joinpath(
+                    "{}_process{}.svg".format(self.settings["output_prefix"], process)
+                )
                 utl.hde_visualize_results(results, process, filename)
 
             # remove results from single process from self
@@ -922,100 +1087,106 @@ 
    Source code for idtxl.embedding_optimization_ais_Rudelt
    [docs]    def optimize_single_run(self, data, process):
         """
-            optimizes a single realisation of spike time data given the process number
-
-            Args:
-                data : Data_spiketime instance
-                    raw data for analysis
-                process : int
-                    index of process;
-
-            Returns:
-                DotDict
-                    with the following keys
-
-                    Process : int
-                        Process that was optimized
-                    estimation_method : String
-                        Estimation method that was used for optimization
-                    T_D : float
-                        Estimated optimal value for the temporal depth TD
-                    tau_R :
-                        Information timescale tau_R, a characteristic timescale of history
-                        dependence similar to an autocorrelation time.
-                    R_tot : float
-                        Estimated value for the total history dependence Rtot,
-                    AIS_tot : float
-                        Estimated value for the total active information storage
-                    opt_number_of_bins_d : int
-                        Number of bins d for the embedding that yields (R̂tot ,T̂D)
-                    opt_scaling_k : int
-                        Scaling exponent κ for the embedding that yields (R̂tot , T̂D)
-                    opt_first_bin_size : int
-                        Size of the first bin τ1 for the embedding that yields (R̂tot , T̂D ),
-                    history_dependence : array with floating-point values
-                        Estimated history dependence for each embedding
-                    firing_rate : float
-                        Firing rate of the neuron/ spike train
-                    recording_length : float
-                        Length of the recording (in seconds)
-                    H_spiking : float
-                        Entropy of the spike times
-
-            if analyse_auto_MI was set to True additionally:
-                auto_MI : dict
-                    numpy array of MI values for each delay
-                auto_MI_delays : list of int
-                    list of delays depending on the given auto_MI_bin_sizes and auto_MI_max_delay
+        optimizes a single realisation of spike time data given the process number
+
+        Args:
+            data : Data_spiketime instance
+                raw data for analysis
+            process : int
+                index of process;
+
+        Returns:
+            DotDict
+                with the following keys
+
+                Process : int
+                    Process that was optimized
+                estimation_method : String
+                    Estimation method that was used for optimization
+                T_D : float
+                    Estimated optimal value for the temporal depth TD
+                tau_R :
+                    Information timescale tau_R, a characteristic timescale of history
+                    dependence similar to an autocorrelation time.
+                R_tot : float
+                    Estimated value for the total history dependence Rtot,
+                AIS_tot : float
+                    Estimated value for the total active information storage
+                opt_number_of_bins_d : int
+                    Number of bins d for the embedding that yields (R̂tot ,T̂D)
+                opt_scaling_k : int
+                    Scaling exponent κ for the embedding that yields (R̂tot , T̂D)
+                opt_first_bin_size : int
+                    Size of the first bin τ1 for the embedding that yields (R̂tot , T̂D ),
+                history_dependence : array with floating-point values
+                    Estimated history dependence for each embedding
+                firing_rate : float
+                    Firing rate of the neuron/ spike train
+                recording_length : float
+                    Length of the recording (in seconds)
+                H_spiking : float
+                    Entropy of the spike times
+
+        if analyse_auto_MI was set to True additionally:
+            auto_MI : dict
+                numpy array of MI values for each delay
+            auto_MI_delays : list of int
+                list of delays depending on the given auto_MI_bin_sizes and auto_MI_max_delay
         """
 
-        if (type(process) is int):
+        if type(process) is int:
             pass
         else:
-            raise ValueError('Process is not specified correctly: '
-                             '{0}.'.format(process))
+            raise ValueError(
+                "Process is not specified correctly: " "{0}.".format(process)
+            )
 
         self.process = process
 
         # get history dependence
-        if self.settings['debug']:
+        if self.settings["debug"]:
             print("\n\nGet History dependence\n")
 
-        if self.settings['estimation_method'] == 'bbc':
-            self.history_dependence, self.bbc_term = \
-                self.get_history_dependence(data, process)
-        elif self.settings['estimation_method'] == 'shuffling':
-            self.history_dependence = \
-                self.get_history_dependence(data, process)
+        if self.settings["estimation_method"] == "bbc":
+            self.history_dependence, self.bbc_term = self.get_history_dependence(
+                data, process
+            )
+        elif self.settings["estimation_method"] == "shuffling":
+            self.history_dependence = self.get_history_dependence(data, process)
 
-        if self.settings['debug']:
+        if self.settings["debug"]:
             print("\n\nCompute CI\n")
 
         # get bootstrap history dependence (CI)
-        if self.settings['debug']:
+        if self.settings["debug"]:
             print("R_max")
-        self.compute_CIs(data,
-                         target_R='R_max',
-                         symbol_block_length=self.settings['symbol_block_length'])
-        if self.settings['debug']:
+        self.compute_CIs(
+            data,
+            target_R="R_max",
+            symbol_block_length=self.settings["symbol_block_length"],
+        )
+        if self.settings["debug"]:
             print("R_tot")
-        self.compute_CIs(data,
-                         target_R='R_tot',
-                         symbol_block_length=self.settings['symbol_block_length'])
-        if self.settings['debug']:
+        self.compute_CIs(
+            data,
+            target_R="R_tot",
+            symbol_block_length=self.settings["symbol_block_length"],
+        )
+        if self.settings["debug"]:
             print("R_nonessential")
-        self.compute_CIs(data,
-                         target_R='nonessential',
-                         symbol_block_length=self.settings['symbol_block_length'])
+        self.compute_CIs(
+            data,
+            target_R="nonessential",
+            symbol_block_length=self.settings["symbol_block_length"],
+        )
 
         # analyse auto MI
-        if self.settings['analyse_auto_MI']:
-            if self.settings['debug']:
+        if self.settings["analyse_auto_MI"]:
+            if self.settings["debug"]:
                 print("\nAnalyse auto MI\n")
             spike_times = data.get_spike_times_single(process)
             self.analyse_auto_MI(spike_times)
 
-
         # get output values
         T_D = self.get_temporal_depth_T_D()
         tau_R = self.get_information_timescale_tau_R()
@@ -1024,63 +1195,70 @@ 
    Source code for idtxl.embedding_optimization_ais_Rudelt
    max_Rs = self.max_Rs
         mr = np.array(list(max_Rs.items()), dtype=float)
         HD_max_R = mr[:, 1]
-        opt_first_bin_size = newton(lambda first_bin_size: self.get_past_range(opt_number_of_bins_d,
-                                                              first_bin_size,
-                                                              opt_scaling_k) - T_D,
-                                    0.005, tol=1e-03, maxiter=100)
-        firing_rate = data.get_firingrate(process, self.settings['embedding_step_size'])
+        opt_first_bin_size = newton(
+            lambda first_bin_size: self.get_past_range(
+                opt_number_of_bins_d, first_bin_size, opt_scaling_k
+            )
+            - T_D,
+            0.005,
+            tol=1e-03,
+            maxiter=100,
+        )
+        firing_rate = data.get_firingrate(process, self.settings["embedding_step_size"])
         recording_length = data.get_recording_length(process)
-        H_spiking = data.get_H_spiking(process, self.settings['embedding_step_size'])
+        H_spiking = data.get_H_spiking(process, self.settings["embedding_step_size"])
 
         # get CI bounds
-        if not self.settings['return_averaged_R']:
-            embedding = (T_D,
-                         opt_number_of_bins_d,
-                         opt_scaling_k)
+        if not self.settings["return_averaged_R"]:
+            embedding = (T_D, opt_number_of_bins_d, opt_scaling_k)
             emb_ind = self.embeddings.index(embedding)
-            R_tot_CI_lo, R_tot_CI_hi = utl.get_CI_bounds(R_tot,
-                                                         self.bs_history_dependence[emb_ind],
-                                                         self.settings['bootstrap_CI_use_sd'],
-                                                         self.settings['bootstrap_CI_percentile_lo'],
-                                                         self.settings['bootstrap_CI_percentile_hi'])
+            R_tot_CI_lo, R_tot_CI_hi = utl.get_CI_bounds(
+                R_tot,
+                self.bs_history_dependence[emb_ind],
+                self.settings["bootstrap_CI_use_sd"],
+                self.settings["bootstrap_CI_percentile_lo"],
+                self.settings["bootstrap_CI_percentile_hi"],
+            )
         else:
             R_tot_CI_lo = None
             R_tot_CI_hi = None
         R_tot_CI = [R_tot_CI_lo, R_tot_CI_hi]
 
-        if self.settings['debug']:
-            print('Process: ' + str(process))
-            print('T_D: ' + str(T_D))
-            print('tau_R: ' + str(tau_R))
-            print('R_tot: ' + str(R_tot))
-            print('R_tot_CI: ' + str(R_tot_CI))
-            print('opt_number_of_bins_d: ' + str(opt_number_of_bins_d))
-            print('opt_scaling_k: ' + str(opt_scaling_k))
-            print('opt_first_bin_size: ' + str(opt_first_bin_size))
-            print('firing_rate: ' + str(firing_rate))
-            print('recording_length: ' + str(recording_length))
-            print('H_spiking: ' + str(H_spiking))
+        if self.settings["debug"]:
+            print("Process: " + str(process))
+            print("T_D: " + str(T_D))
+            print("tau_R: " + str(tau_R))
+            print("R_tot: " + str(R_tot))
+            print("R_tot_CI: " + str(R_tot_CI))
+            print("opt_number_of_bins_d: " + str(opt_number_of_bins_d))
+            print("opt_scaling_k: " + str(opt_scaling_k))
+            print("opt_first_bin_size: " + str(opt_first_bin_size))
+            print("firing_rate: " + str(firing_rate))
+            print("recording_length: " + str(recording_length))
+            print("H_spiking: " + str(H_spiking))
 
         # create output dict
-        results = {'Process': process,
-                   'estimation_method': self.settings['estimation_method'],
-                   'T_D': T_D,
-                   'tau_R': tau_R,
-                   'R_tot': R_tot,
-                   'R_tot_CI': R_tot_CI,
-                   'AIS_tot': R_tot * H_spiking,
-                   'opt_number_of_bins_d': opt_number_of_bins_d,
-                   'opt_scaling_k': opt_scaling_k,
-                   'opt_first_bin_size': opt_first_bin_size,
-                   'history_dependence': self.history_dependence,
-                   'firing_rate': firing_rate,
-                   'recording_length': recording_length,
-                   'H_spiking': H_spiking,
-                   'max_R': max_Rs}
-
-        if self.settings['analyse_auto_MI']:
-            results['auto_MI'] = self.auto_MI.get('auto_MI')
-            results['auto_MI_delays'] = self.auto_MI.get('delay')
+        results = {
+            "Process": process,
+            "estimation_method": self.settings["estimation_method"],
+            "T_D": T_D,
+            "tau_R": tau_R,
+            "R_tot": R_tot,
+            "R_tot_CI": R_tot_CI,
+            "AIS_tot": R_tot * H_spiking,
+            "opt_number_of_bins_d": opt_number_of_bins_d,
+            "opt_scaling_k": opt_scaling_k,
+            "opt_first_bin_size": opt_first_bin_size,
+            "history_dependence": self.history_dependence,
+            "firing_rate": firing_rate,
+            "recording_length": recording_length,
+            "H_spiking": H_spiking,
+            "max_R": max_Rs,
+        }
+
+        if self.settings["analyse_auto_MI"]:
+            results["auto_MI"] = self.auto_MI.get("auto_MI")
+            results["auto_MI_delays"] = self.auto_MI.get("delay")
 
         results_d = DotDict(results)
 
@@ -1097,10 +1275,10 @@ 
    Source code for idtxl.embedding_optimization_ais_Rudelt
    del self.max_R_T
         del self.process
         # del self.T_D
-        if self.settings['analyse_auto_MI']:
+        if self.settings["analyse_auto_MI"]:
             del self.auto_MI
             del self.H_spiking
-        if self.settings['estimation_method'] == 'bbc':
+        if self.settings["estimation_method"] == "bbc":
             del self.bbc_term
    
 
    
 
@@ -1114,7 +1292,7 @@ 
    Source code for idtxl.embedding_optimization_ais_Rudelt
    Quick search
     
    
     
    
-      
+      
       
     
    
     
    
@@ -1133,14 +1311,14 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5.1 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.embedding_optimization_ais_Rudelt
    •  
       
     
    
     
   
 
\ No newline at end of file
diff --git a/docs/html/_modules/idtxl/estimators_Rudelt.html b/docs/html/_modules/idtxl/estimators_Rudelt.html
index 421ce0df..b352b7b9 100644
--- a/docs/html/_modules/idtxl/estimators_Rudelt.html
+++ b/docs/html/_modules/idtxl/estimators_Rudelt.html
@@ -5,7 +5,7 @@
   
     
     
-    idtxl.estimators_Rudelt — IDTxl 1.5 documentation
+    idtxl.estimators_Rudelt — IDTxl 1.5.1 documentation
     
     
     
@@ -31,7 +31,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.5 documentation »
    • 
+        
  • IDTxl 1.5.1 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.estimators_Rudelt
    •  
       
@@ -60,11 +60,15 @@ 
    Source code for idtxl.estimators_Rudelt
         import idtxl.hde_fast_embedding as fast_emb
 except:
     FAST_EMBEDDING_AVAILABLE = False
-    print("""
-    Error importing Cython fast embedding module for HDE estimator.\n
-    When running the HDE estimator, the slow Python implementation for optimizing the HDE embedding will be used,\n
-    this may take a long time. Other estimators are not affected.\n
-    """, file=stderr, flush=True)
+    print(
+        """
+    Error importing Cython fast embedding module for HDE estimator.\n
+    When running the HDE estimator, the slow Python implementation for optimizing the HDE embedding will be used,\n
+    this may take a long time. Other estimators are not affected.\n
+    """,
+        file=stderr,
+        flush=True,
+    )
 
 
 logger = logging.getLogger(__name__)
@@ -109,9 +113,9 @@ 
    Source code for idtxl.estimators_Rudelt
             self.settings = settings.copy()
 
         # Get defaults for estimator settings
-        self.settings.setdefault('normalize', True)
-        self.settings.setdefault('embedding_step_size', 0.005)
-        self.settings.setdefault('return_averaged_R', True)
+        self.settings.setdefault("normalize", True)
+        self.settings.setdefault("embedding_step_size", 0.005)
+        self.settings.setdefault("return_averaged_R", True)
 
         # check settings
         self._check_input_settings()
@@ -132,81 +136,93 @@ 
    Source code for idtxl.estimators_Rudelt
             if settings is None:
             return {}
         elif type(settings) is not dict:
-            raise TypeError('settings should be a dictionary.')
+            raise TypeError("settings should be a dictionary.")
         else:
             return settings
 
     def _check_input_settings(self):
-
         # check that required settings are defined
-        required_settings = ['normalize',
-                             'embedding_step_size',
-                             'return_averaged_R']
+        required_settings = ["normalize", "embedding_step_size", "return_averaged_R"]
 
         # check if all settings are defined
         for required_setting in required_settings:
             if not required_setting in self.settings:
-                sys.exit("Error in settings file: {} is not defined. Aborting.".format(required_setting))
-
-        assert (isinstance(self.settings['normalize'], bool)), \
-                                    "Error: setting 'normalize' needs to be boolean but is defined as {0}. " \
-                                     "Aborting.".format(type(self.settings['normalize']))
-
-        assert (isinstance(self.settings['return_averaged_R'], bool)),\
-                                    "Error: setting 'return_averaged_R' needs to be boolean but is " \
-                                    "defined as {0}. Aborting.".format(type(self.settings['normalize']))
-
-        assert (isinstance(self.settings['embedding_step_size'], float)),\
-                                    "Error: setting 'embedding_step_size' " \
-                                    "needs to be float but is defined " \
-                                    "as {0}. Aborting.".format(type(self.settings['embedding_step_size']))
-
-    def _check_estimator_inputs(self,
-                                symbol_array,
-                                past_symbol_array,
-                                current_symbol_array,
-                                bbc_tolerance):
-        assert (isinstance(symbol_array, np.ndarray)), \
-            "Error: symbol_array needs to be a numpy array but is defines as {0}." \
+                sys.exit(
+                    "Error in settings file: {} is not defined. Aborting.".format(
+                        required_setting
+                    )
+                )
+
+        assert isinstance(self.settings["normalize"], bool), (
+            "Error: setting 'normalize' needs to be boolean but is defined as {0}. "
+            "Aborting.".format(type(self.settings["normalize"]))
+        )
+
+        assert isinstance(self.settings["return_averaged_R"], bool), (
+            "Error: setting 'return_averaged_R' needs to be boolean but is "
+            "defined as {0}. Aborting.".format(type(self.settings["normalize"]))
+        )
+
+        assert isinstance(self.settings["embedding_step_size"], float), (
+            "Error: setting 'embedding_step_size' "
+            "needs to be float but is defined "
+            "as {0}. Aborting.".format(type(self.settings["embedding_step_size"]))
+        )
+
+    def _check_estimator_inputs(
+        self, symbol_array, past_symbol_array, current_symbol_array, bbc_tolerance
+    ):
+        assert isinstance(symbol_array, np.ndarray), (
+            "Error: symbol_array needs to be a numpy array but is defines as {0}."
             "Aborting.".format(type(symbol_array))
+        )
 
         if past_symbol_array is not None:
-            assert (isinstance(past_symbol_array, np.ndarray)), \
-                "Error: past_symbol_array needs to be a numpy array but is defines as {0}." \
+            assert isinstance(past_symbol_array, np.ndarray), (
+                "Error: past_symbol_array needs to be a numpy array but is defines as {0}."
                 "Aborting.".format(type(past_symbol_array))
-            assert (len(past_symbol_array) == len(symbol_array)), \
-                "Error: symbol_array and past_symbol_array need to have the same length but have:" \
-                "len(symbol_array): {0} len(past_symbol_array): {1}. " \
-                "Aborting". format(len(symbol_array), len(past_symbol_array))
+            )
+            assert len(past_symbol_array) == len(symbol_array), (
+                "Error: symbol_array and past_symbol_array need to have the same length but have:"
+                "len(symbol_array): {0} len(past_symbol_array): {1}. "
+                "Aborting".format(len(symbol_array), len(past_symbol_array))
+            )
 
         if current_symbol_array is not None:
-            assert (isinstance(current_symbol_array, np.ndarray)), \
-                "Error: current_symbol_array needs to be a numpy array but is defines as {0}." \
+            assert isinstance(current_symbol_array, np.ndarray), (
+                "Error: current_symbol_array needs to be a numpy array but is defines as {0}."
                 "Aborting.".format(type(current_symbol_array))
-            assert (len(current_symbol_array) == len(symbol_array)), \
-                "Error: symbol_array and current_symbol_array need to have the same length but have:" \
-                "len(symbol_array): {0} len(current_symbol_array): {1}. " \
+            )
+            assert len(current_symbol_array) == len(symbol_array), (
+                "Error: symbol_array and current_symbol_array need to have the same length but have:"
+                "len(symbol_array): {0} len(current_symbol_array): {1}. "
                 "Aborting".format(len(symbol_array), len(current_symbol_array))
+            )
 
         if bbc_tolerance is not None:
-            assert (isinstance(bbc_tolerance, np.ndarray)), \
-                "Error: symbol array needs to be a numpy array but is defines as {0}." \
+            assert isinstance(bbc_tolerance, np.ndarray), (
+                "Error: symbol array needs to be a numpy array but is defines as {0}."
                 "Aborting.".format(type(current_symbol_array))
+            )
 
     def _ensure_one_dim(self, var):
         """
         check if array is 1D
         """
         var = np.squeeze(var)
-        assert (var.ndim == 1), "Input variable needs to be one dimensional. Aborting"
+        assert var.ndim == 1, "Input variable needs to be one dimensional. Aborting"
 
 
    [docs]    def get_past_range(self, number_of_bins_d, first_bin_size, scaling_k):
         """
         Get the past range T of the embedding, based on the parameters d, tau_1 and k.
         """
 
-        return np.sum([first_bin_size * 10 ** ((number_of_bins_d - i) * scaling_k)
-                       for i in range(1, number_of_bins_d + 1)])
    
+        return sum(
+            [
+                first_bin_size * 10 ** ((number_of_bins_d - i) * scaling_k)
+                for i in range(1, number_of_bins_d + 1)
+            ]
+        )
    
 
 
    [docs]    def get_window_delimiters(self, number_of_bins_d, scaling_k, first_bin_size):
         """
@@ -217,11 +233,18 @@ 
    Source code for idtxl.estimators_Rudelt
             two consequent bins.
         """
 
-        bin_sizes = [first_bin_size * 10 ** ((number_of_bins_d - i) * scaling_k)
-                     for i in range(1, number_of_bins_d + 1)]
-        window_delimiters = [sum([bin_sizes[j] for j in range(i)])
-                             for i in range(1, number_of_bins_d + 1)]
-        window_delimiters.append(window_delimiters[number_of_bins_d - 1] + self.settings['embedding_step_size'])
+        bin_sizes = [
+            first_bin_size * 10 ** ((number_of_bins_d - i) * scaling_k)
+            for i in range(1, number_of_bins_d + 1)
+        ]
+        window_delimiters = [
+            sum([bin_sizes[j] for j in range(i)])
+            for i in range(1, number_of_bins_d + 1)
+        ]
+        window_delimiters.append(
+            window_delimiters[number_of_bins_d - 1]
+            + self.settings["embedding_step_size"]
+        )
         return window_delimiters
    
 
 
    [docs]    def get_median_number_of_spikes_per_bin(self, raw_symbols):
@@ -274,13 +297,14 @@ 
    Source code for idtxl.estimators_Rudelt
             # as in get_median_number_of_spikes_per_bin, ie
         # including the response
 
-        return sum([2 ** (number_of_bins_d - i - 1) * spikes_in_window[i]
-                    for i in range(0, number_of_bins_d)])
    
+        return sum(
+            [
+                2 ** (number_of_bins_d - i - 1) * spikes_in_window[i]
+                for i in range(0, number_of_bins_d)
+            ]
+        )
    
 
-
    [docs]    def get_raw_symbols(self,
-                        spike_times,
-                        embedding,
-                        first_bin_size):
+
    [docs]    def get_raw_symbols(self, spike_times, embedding, first_bin_size):
         """
         Get the raw symbols (in which the number of spikes per bin are counted,
         ie not necessarily binary quantity), as obtained by applying the
@@ -291,14 +315,16 @@ 
    Source code for idtxl.estimators_Rudelt
     
         # the window is the embedding plus the response,
         # ie the embedding and one additional bin of size embedding_step_size
-        window_delimiters = self.get_window_delimiters(number_of_bins_d,
-                                                       scaling_k,
-                                                       first_bin_size)
+        window_delimiters = self.get_window_delimiters(
+            number_of_bins_d, scaling_k, first_bin_size
+        )
         window_length = window_delimiters[-1]
         num_spike_times = len(spike_times)
         last_spike_time = spike_times[-1]
 
-        num_symbols = int((last_spike_time - window_length) / self.settings['embedding_step_size'])
+        num_symbols = int(
+            (last_spike_time - window_length) / self.settings["embedding_step_size"]
+        )
 
         raw_symbols = []
 
@@ -306,24 +332,31 @@ 
    Source code for idtxl.estimators_Rudelt
             spike_index_lo = 0
 
         for symbol_num in range(num_symbols):
-            while spike_index_lo < num_spike_times and spike_times[spike_index_lo] < time:
+            while (
+                spike_index_lo < num_spike_times and spike_times[spike_index_lo] < time
+            ):
                 spike_index_lo += 1
             spike_index_hi = spike_index_lo
-            while (spike_index_hi < num_spike_times and
-                   spike_times[spike_index_hi] < time + window_length):
+            while (
+                spike_index_hi < num_spike_times
+                and spike_times[spike_index_hi] < time + window_length
+            ):
                 spike_index_hi += 1
 
             spikes_in_window = np.zeros(number_of_bins_d + 1)
 
             embedding_bin_index = 0
             for spike_index in range(spike_index_lo, spike_index_hi):
-                while (spike_times[spike_index] > time + window_delimiters[embedding_bin_index]):
+                while (
+                    spike_times[spike_index]
+                    > time + window_delimiters[embedding_bin_index]
+                ):
                     embedding_bin_index += 1
                 spikes_in_window[embedding_bin_index] += 1
 
             raw_symbols += [spikes_in_window]
 
-            time += self.settings['embedding_step_size']
+            time += self.settings["embedding_step_size"]
 
         return raw_symbols
    
 
@@ -350,7 +383,9 @@ 
    Source code for idtxl.estimators_Rudelt
             """
 
         mk = dict(((value, 0) for value in symbol_counts.values()))
-        number_of_observed_symbols = np.count_nonzero([value for value in symbol_counts.values()])
+        number_of_observed_symbols = np.count_nonzero(
+            [value for value in symbol_counts.values()]
+        )
 
         for symbol in symbol_counts.keys():
             mk[symbol_counts[symbol]] += 1
@@ -407,21 +442,21 @@ 
    Source code for idtxl.estimators_Rudelt
             d_xi is the prior for the nsb estimator
         """
 
-        return K * mp.psi(1, K * beta + 1.) - mp.psi(1, beta + 1.)
    
+        return K * mp.psi(1, K * beta + 1.0) - mp.psi(1, beta + 1.0)
    
 
 
    [docs]    def d2_xi(self, beta, K):
         """
         Second derivative of xi(beta) (cf d_xi).
         """
 
-        return K ** 2 * mp.psi(2, K * beta + 1) - mp.psi(2, beta + 1)
    
+        return K**2 * mp.psi(2, K * beta + 1) - mp.psi(2, beta + 1)
    
 
 
    [docs]    def d3_xi(self, beta, K):
         """
         Third derivative of xi(beta) (cf d_xi).
         """
 
-        return K ** 3 * mp.psi(3, K * beta + 1) - mp.psi(3, beta + 1)
    
+        return K**3 * mp.psi(3, K * beta + 1) - mp.psi(3, beta + 1)
    
 
 
    [docs]    def rho(self, beta, mk, K, N):
         """
@@ -431,8 +466,9 @@ 
    Source code for idtxl.estimators_Rudelt
             the posterior for the nsb estimator
         """
 
-        return np.prod([mp.power(mp.rf(beta, np.double(n)), mk[n]) for n in mk]) / mp.rf(K * beta,
-                                                                                         np.double(N))
    
+        return np.prod(
+            [mp.power(mp.rf(beta, np.double(n)), mk[n]) for n in mk]
+        ) / mp.rf(K * beta, np.double(N))
    
 
 
    [docs]    def unnormalized_posterior(self, beta, mk, K, N):
         """
@@ -449,16 +485,22 @@ 
    Source code for idtxl.estimators_Rudelt
             First derivate of the logarithm of the Dirichlet multinomial likelihood.
         """
 
-        return K * (mp.psi(0, K * beta) - mp.psi(0, K * beta + N)) - K * mp.psi(0, beta) \
-               + np.sum((mk[n] * mp.psi(0, n + beta) for n in mk))
    
+        return (
+            K * (mp.psi(0, K * beta) - mp.psi(0, K * beta + N))
+            - K * mp.psi(0, beta)
+            + sum((mk[n] * mp.psi(0, n + beta) for n in mk))
+        )
    
 
 
    [docs]    def d2_log_rho(self, beta, mk, K, N):
         """
         Second derivate of the logarithm of the Dirichlet multinomial likelihood.
         """
 
-        return K ** 2 * (mp.psi(1, K * beta) - mp.psi(1, K * beta + N)) - K * mp.psi(1, beta) \
-               + np.sum((mk[n] * mp.psi(1, n + beta) for n in mk))
    
+        return (
+            K**2 * (mp.psi(1, K * beta) - mp.psi(1, K * beta + N))
+            - K * mp.psi(1, beta)
+            + sum((mk[n] * mp.psi(1, n + beta) for n in mk))
+        )
    
 
 
    [docs]    def d_log_rho_xi(self, beta, mk, K, N):
         """
@@ -472,15 +514,18 @@ 
    Source code for idtxl.estimators_Rudelt
             Second derivative of the logarithm of the nsb (unnormalized) posterior.
         """
 
-        return self.d2_log_rho(beta, mk, K, N) \
-               + (self.d3_xi(beta, K) * self.d_xi(beta, K) - self.d2_xi(beta, K) ** 2) / self.d_xi(beta, K) ** 2
    
+        return (
+            self.d2_log_rho(beta, mk, K, N)
+            + (self.d3_xi(beta, K) * self.d_xi(beta, K) - self.d2_xi(beta, K) ** 2)
+            / self.d_xi(beta, K) ** 2
+        )
    
 
 
    [docs]    def log_likelihood_DP_alpha(self, a, K1, N):
         """
         Alpha-dependent terms of the log-likelihood of a Dirichlet Process.
         """
 
-        return (K1 - 1.) * mp.log(a) - mp.log(mp.rf(a + 1., N - 1.))
    
+        return (K1 - 1.0) * mp.log(a) - mp.log(mp.rf(a + 1.0, N - 1.0))
    
 
 
    [docs]    def get_beta_MAP(self, mk, K, N):
         """
@@ -495,19 +540,27 @@ 
    Source code for idtxl.estimators_Rudelt
     
         K1 = K - mk[0]
 
-        if self.d_log_rho(10 ** 1, mk, K, N) > 0:
+        if self.d_log_rho(10**1, mk, K, N) > 0:
             print("Warning: No ML parameter was found.", file=stderr, flush=True)
-            beta_MAP = np.float('nan')
+            beta_MAP = np.nan
         else:
             try:
                 # first guess computed via posterior of Dirichlet process
                 DP_est = self.alpha_ML(mk, K1, N) / K
-                beta_MAP = newton(lambda beta: float(self.d_log_rho_xi(beta, mk, K, N)), DP_est,
-                                  lambda beta: float(self.d2_log_rho_xi(beta, mk, K, N)),
-                                  tol=5e-08, maxiter=500)
+                beta_MAP = newton(
+                    lambda beta: float(self.d_log_rho_xi(beta, mk, K, N)),
+                    DP_est,
+                    lambda beta: float(self.d2_log_rho_xi(beta, mk, K, N)),
+                    tol=5e-08,
+                    maxiter=500,
+                )
             except:
-                print("Warning: No ML parameter was found. (Exception caught.)", file=stderr, flush=True)
-                beta_MAP = np.float('nan')
+                print(
+                    "Warning: No ML parameter was found. (Exception caught.)",
+                    file=stderr,
+                    flush=True,
+                )
+                beta_MAP = np.nan
         return beta_MAP
    
 
 
    [docs]    def alpha_ML(self, mk, K1, N):
@@ -518,14 +571,17 @@ 
    Source code for idtxl.estimators_Rudelt
     
         mk = utl.remove_key(mk, 0)
         # rnsum      = np.array([_logvarrhoi_DP(n, mk[n]) for n in mk]).sum()
-        estlist = [N * (K1 - 1.) / r / (N - K1) for r in np.arange(6., 1.5, -0.5)]
+        estlist = [N * (K1 - 1.0) / r / (N - K1) for r in np.arange(6.0, 1.5, -0.5)]
         varrholist = {}
         for a in estlist:
             # varrholist[_logvarrho_DP(a, rnsum, K1, N)] = a
             varrholist[self.log_likelihood_DP_alpha(a, K1, N)] = a
         a_est = varrholist[max(varrholist.keys())]
-        res = minimize(lambda a: -self.log_likelihood_DP_alpha(a[0], K1, N),
-                       a_est, method='Nelder-Mead')
+        res = minimize(
+            lambda a: -self.log_likelihood_DP_alpha(a[0], K1, N),
+            a_est,
+            method="Nelder-Mead",
+        )
         return res.x[0]
    
 
 
    [docs]    def get_integration_bounds(self, mk, K, N):
@@ -539,11 +595,13 @@ 
    Source code for idtxl.estimators_Rudelt
     
         beta_MAP = self.get_beta_MAP(mk, K, N)
         if np.isnan(beta_MAP):
-            intbounds = np.float('nan')
+            intbounds = np.nan
         else:
-            std = np.sqrt(- self.d2_log_rho_xi(beta_MAP, mk, K, N) ** (-1))
-            intbounds = [np.float(np.amax([10 ** (-50), beta_MAP - 8 * std])),
-                         np.float(beta_MAP + 8 * std)]
+            std = np.sqrt(-self.d2_log_rho_xi(beta_MAP, mk, K, N) ** (-1))
+            intbounds = [
+                float(np.amax([10 ** (-50), beta_MAP - 8 * std])),
+                float(beta_MAP + 8 * std),
+            ]
 
         return intbounds
    
 
@@ -556,8 +614,10 @@ 
    Source code for idtxl.estimators_Rudelt
             """
 
         norm = N + beta * K
-        return mp.psi(0, norm + 1) - np.sum((mk[n] * (n + beta) *
-                                             mp.psi(0, n + beta + 1) for n in mk)) / norm
    
+        return (
+            mp.psi(0, norm + 1)
+            - sum((mk[n] * (n + beta) * mp.psi(0, n + beta + 1) for n in mk)) / norm
+        )
    
 
 
    [docs]    def nsb_entropy(self, mk, K, N):
         """
@@ -585,25 +645,45 @@ 
    Source code for idtxl.estimators_Rudelt
                 def unnormalized_posterior_w(w, mk, K, N):
                 sbeta = w / (1 - w)
                 beta = sbeta * sbeta
-                return self.unnormalized_posterior(beta, mk, K, N) * 2 * sbeta / (1 - w) / (1 - w)
+                return (
+                    self.unnormalized_posterior(beta, mk, K, N)
+                    * 2
+                    * sbeta
+                    / (1 - w)
+                    / (1 - w)
+                )
 
             def H1_w(w, mk, K, N):
                 sbeta = w / (1 - w)
                 beta = sbeta * sbeta
                 return self.H1(w, mk, K, N)
 
-            marginal_likelihood = mp.quadgl(lambda w: unnormalized_posterior_w(w, mk, K, N),
-                                            integration_bounds)
-            H_nsb = mp.quadgl(lambda w: H1_w(w, mk, K, N) * unnormalized_posterior_w(w, mk, K, N),
-                              integration_bounds) / marginal_likelihood
+            marginal_likelihood = mp.quadgl(
+                lambda w: unnormalized_posterior_w(w, mk, K, N), integration_bounds
+            )
+            H_nsb = (
+                mp.quadgl(
+                    lambda w: H1_w(w, mk, K, N) * unnormalized_posterior_w(w, mk, K, N),
+                    integration_bounds,
+                )
+                / marginal_likelihood
+            )
 
         else:
             # integrate over the possible entropies, weighted such that every entropy is equally likely
             # and normalize with the marginal likelihood
-            marginal_likelihood = mp.quadgl(lambda beta: self.unnormalized_posterior(beta, mk, K, N),
-                                            integration_bounds)
-            H_nsb = mp.quadgl(lambda beta: self.H1(beta, mk, K, N) * self.unnormalized_posterior(beta, mk, K, N),
-                              integration_bounds) / marginal_likelihood
+            marginal_likelihood = mp.quadgl(
+                lambda beta: self.unnormalized_posterior(beta, mk, K, N),
+                integration_bounds,
+            )
+            H_nsb = (
+                mp.quadgl(
+                    lambda beta: self.H1(beta, mk, K, N)
+                    * self.unnormalized_posterior(beta, mk, K, N),
+                    integration_bounds,
+                )
+                / marginal_likelihood
+            )
 
         return H_nsb
    
 
@@ -635,12 +715,14 @@ 
    Source code for idtxl.estimators_Rudelt
             # Set default estimator settings.
         super().__init__(settings)
 
-
    [docs]    def nsb_estimator(self,
-                      symbol_counts,
-                      past_symbol_counts,
-                      alphabet_size,
-                      alphabet_size_past,
-                      H_uncond):
+
    [docs]    def nsb_estimator(
+        self,
+        symbol_counts,
+        past_symbol_counts,
+        alphabet_size,
+        alphabet_size_past,
+        H_uncond,
+    ):
         """
         Estimate the entropy of a system using the NSB estimator.
         """
@@ -680,10 +762,9 @@ 
    Source code for idtxl.estimators_Rudelt
                     MI / H_uncond (History dependence)
         """
 
-        self._check_estimator_inputs(symbol_array,
-                                     past_symbol_array,
-                                     current_symbol_array,
-                                     None)
+        self._check_estimator_inputs(
+            symbol_array, past_symbol_array, current_symbol_array, None
+        )
 
         self._ensure_one_dim(symbol_array)
         self._ensure_one_dim(past_symbol_array)
@@ -701,13 +782,15 @@ 
    Source code for idtxl.estimators_Rudelt
             alphabet_size_past = 2 ** int(number_of_bins_d_join - 1)  # K for past activity
         alphabet_size = alphabet_size_past * 2  # K
 
-        I, R = self.nsb_estimator(symbol_counts,
-                                  past_symbol_counts,
-                                  alphabet_size,
-                                  alphabet_size_past,
-                                  H_uncond)
+        I, R = self.nsb_estimator(
+            symbol_counts,
+            past_symbol_counts,
+            alphabet_size,
+            alphabet_size_past,
+            H_uncond,
+        )
 
-        return np.float(I), np.float(R)
    
+        return float(I), float(R)
    
 
 
 
    [docs]class RudeltPluginEstimatorSymbolsMI(RudeltAbstractEstimator):
@@ -739,14 +822,16 @@ 
    Source code for idtxl.estimators_Rudelt
             """
 
         mk = utl.remove_key(mk, 0)
-        return - sum((mk[n] * (n / N) * np.log(n / N) for n in mk))
    
-
-
    [docs]    def plugin_estimator(self,
-                         symbol_counts,
-                         past_symbol_counts,
-                         alphabet_size,
-                         alphabet_size_past,
-                         H_uncond):
+        return -sum((mk[n] * (n / N) * np.log(n / N) for n in mk))
    
+
+
    [docs]    def plugin_estimator(
+        self,
+        symbol_counts,
+        past_symbol_counts,
+        alphabet_size,
+        alphabet_size_past,
+        H_uncond,
+    ):
         """
         Estimate the entropy of a system using the BBC estimator.
         """
@@ -786,10 +871,9 @@ 
    Source code for idtxl.estimators_Rudelt
                     MI / H_uncond (History dependence)
         """
 
-        self._check_estimator_inputs(symbol_array,
-                                     past_symbol_array,
-                                     current_symbol_array,
-                                     None)
+        self._check_estimator_inputs(
+            symbol_array, past_symbol_array, current_symbol_array, None
+        )
 
         self._ensure_one_dim(symbol_array)
         self._ensure_one_dim(past_symbol_array)
@@ -810,13 +894,15 @@ 
    Source code for idtxl.estimators_Rudelt
             alphabet_size_past = 2 ** int(number_of_bins_d_join - 1)  # K for past activity
         alphabet_size = alphabet_size_past * 2  # K
 
-        I, R = self.plugin_estimator(symbol_counts,
-                                     past_symbol_counts,
-                                     alphabet_size,
-                                     alphabet_size_past,
-                                     H_uncond)
+        I, R = self.plugin_estimator(
+            symbol_counts,
+            past_symbol_counts,
+            alphabet_size,
+            alphabet_size_past,
+            H_uncond,
+        )
 
-        return np.float(I), np.float(R)
    
+        return float(I), float(R)
    
 
 
 
    [docs]class RudeltBBCEstimator(RudeltAbstractEstimator):
@@ -872,7 +958,9 @@ 
    Source code for idtxl.estimators_Rudelt
             else:
             return np.inf
    
 
-
    [docs]    def estimate(self, symbol_array, past_symbol_array, current_symbol_array, bbc_tolerance=None):
+
    [docs]    def estimate(
+        self, symbol_array, past_symbol_array, current_symbol_array, bbc_tolerance=None
+    ):
         """
         Calculate the mutual information (MI) of one variable depending on its past
         using nsb and plugin estimator and check if bias criterion is passed/
@@ -898,29 +986,34 @@ 
    Source code for idtxl.estimators_Rudelt
                     criterion (bbc)
         """
 
-        self._check_estimator_inputs(symbol_array,
-                                     past_symbol_array,
-                                     current_symbol_array,
-                                     bbc_tolerance)
+        self._check_estimator_inputs(
+            symbol_array, past_symbol_array, current_symbol_array, bbc_tolerance
+        )
 
         self._ensure_one_dim(symbol_array)
         self._ensure_one_dim(past_symbol_array)
         self._ensure_one_dim(current_symbol_array)
 
         estnsb = RudeltNSBEstimatorSymbolsMI()
-        I_nsb, R_nsb = estnsb.estimate(symbol_array, past_symbol_array, current_symbol_array)
+        I_nsb, R_nsb = estnsb.estimate(
+            symbol_array, past_symbol_array, current_symbol_array
+        )
 
         estplugin = RudeltPluginEstimatorSymbolsMI()
-        I_plugin, R_plugin = estplugin.estimate(symbol_array, past_symbol_array, current_symbol_array)
+        I_plugin, R_plugin = estplugin.estimate(
+            symbol_array, past_symbol_array, current_symbol_array
+        )
 
         if not bbc_tolerance == None:
             if self.bayesian_bias_criterion(R_nsb, R_plugin, bbc_tolerance):
-                return np.float(I_nsb), np.float(R_nsb)
-            else:
-                return None
+                return float(I_nsb), float(R_nsb)
+            return None
         else:
-            return np.float(I_nsb), np.float(R_nsb), np.float(self.get_bbc_term(R_nsb,
-                                                  R_plugin))
    
+            return (
+                float(I_nsb),
+                float(R_nsb),
+                float(self.get_bbc_term(R_nsb, R_plugin)),
+            )
    
 
 
 
    [docs]class RudeltShufflingEstimator(RudeltAbstractEstimator):
@@ -938,8 +1031,10 @@ 
    Source code for idtxl.estimators_Rudelt
             the plug-in estimator.
         """
 
-        return [number_of_symbols[0] / sum(number_of_symbols),
-                number_of_symbols[1] / sum(number_of_symbols)]
    
+        return [
+            number_of_symbols[0] / sum(number_of_symbols),
+            number_of_symbols[1] / sum(number_of_symbols),
+        ]
    
 
 
    [docs]    def get_P_X_past_uncond(self, past_symbol_counts, number_of_symbols):
         """
@@ -969,18 +1064,22 @@ 
    Source code for idtxl.estimators_Rudelt
             P_X_past_cond_X = [{}, {}]
         for response in [0, 1]:
             for symbol in past_symbol_counts[response]:
-                P_X_past_cond_X[response][symbol] \
-                    = past_symbol_counts[response][symbol] / number_of_symbols[response]
+                P_X_past_cond_X[response][symbol] = (
+                    past_symbol_counts[response][symbol] / number_of_symbols[response]
+                )
         return P_X_past_cond_X
    
 
 
    [docs]    def get_H0_X_past_cond_X_eq_x(self, marginal_probabilities, number_of_bins_d):
         """
         Compute H_0(X_past | X = x), cf get_H0_X_past_cond_X.
         """
-        return utl.get_shannon_entropy(marginal_probabilities) \
-               + utl.get_shannon_entropy(1 - marginal_probabilities)
    
+        return utl.get_shannon_entropy(
+            marginal_probabilities
+        ) + utl.get_shannon_entropy(1 - marginal_probabilities)
    
 
-
    [docs]    def get_H0_X_past_cond_X(self, marginal_probabilities, number_of_bins_d, P_X_uncond):
+
    [docs]    def get_H0_X_past_cond_X(
+        self, marginal_probabilities, number_of_bins_d, P_X_uncond
+    ):
         """
         Compute H_0(X_past | X), the estimate of the entropy for the past
         symbols given a response, under the assumption that activity in
@@ -988,10 +1087,15 @@ 
    Source code for idtxl.estimators_Rudelt
             """
         H0_X_past_cond_X_eq_x = [0, 0]
         for response in [0, 1]:
-            H0_X_past_cond_X_eq_x[response] \
-                = self.get_H0_X_past_cond_X_eq_x(marginal_probabilities[response],
-                                            number_of_bins_d)
-        return sum([P_X_uncond[response] * H0_X_past_cond_X_eq_x[response] for response in [0, 1]])
    
+            H0_X_past_cond_X_eq_x[response] = self.get_H0_X_past_cond_X_eq_x(
+                marginal_probabilities[response], number_of_bins_d
+            )
+        return sum(
+            [
+                P_X_uncond[response] * H0_X_past_cond_X_eq_x[response]
+                for response in [0, 1]
+            ]
+        )
    
 
 
    [docs]    def get_H_X_past_uncond(self, P_X_past_uncond):
         """
@@ -1007,20 +1111,35 @@ 
    Source code for idtxl.estimators_Rudelt
             symbols, conditioned on the response X,  given their probabilities.
         """
 
-        return sum((P_X_uncond[response] * self.get_H_X_past_uncond(P_X_past_cond_X[response])
-                    for response in [0, 1]))
    
-
-
    [docs]    def get_marginal_frequencies_of_spikes_in_bins(self, symbol_counts, number_of_bins_d):
+        return sum(
+            (
+                P_X_uncond[response]
+                * self.get_H_X_past_uncond(P_X_past_cond_X[response])
+                for response in [0, 1]
+            )
+        )
    
+
+
    [docs]    def get_marginal_frequencies_of_spikes_in_bins(
+        self, symbol_counts, number_of_bins_d
+    ):
         """
         Compute for each past bin 1...d the sum of spikes found in that bin across all
         observed symbols.
         """
-        return np.array(sum((self.symbol_binary_to_array(symbol, number_of_bins_d)
-                             * symbol_counts[symbol]
-                             for symbol in symbol_counts)), dtype=int)
    
-
-
    [docs]    def get_shuffled_symbol_counts(self, symbol_counts, past_symbol_counts, number_of_bins_d,
-                                   number_of_symbols):
+        return np.array(
+            sum(
+                (
+                    self.symbol_binary_to_array(symbol, number_of_bins_d)
+                    * symbol_counts[symbol]
+                    for symbol in symbol_counts
+                )
+            ),
+            dtype=int,
+        )
    
+
+
    [docs]    def get_shuffled_symbol_counts(
+        self, symbol_counts, past_symbol_counts, number_of_bins_d, number_of_symbols
+    ):
         """
         Simulate new data by, for each past bin 1...d, permutating the activity
         across all observed past_symbols (for a given response X). The marginal
@@ -1029,22 +1148,37 @@ 
    Source code for idtxl.estimators_Rudelt
             """
         number_of_spikes = sum(past_symbol_counts[1].values())
 
-        marginal_frequencies = [self.get_marginal_frequencies_of_spikes_in_bins(past_symbol_counts[response],
-                                                                           number_of_bins_d)
-                                for response in [0, 1]]
+        marginal_frequencies = [
+            self.get_marginal_frequencies_of_spikes_in_bins(
+                past_symbol_counts[response], number_of_bins_d
+            )
+            for response in [0, 1]
+        ]
 
-        shuffled_past_symbols = [np.zeros(number_of_symbols[response]) for response in [0, 1]]
+        shuffled_past_symbols = [
+            np.zeros(number_of_symbols[response]) for response in [0, 1]
+        ]
 
         for i in range(0, number_of_bins_d):
             for response in [0, 1]:
-                shuffled_past_symbols[response] \
-                    += 2 ** (number_of_bins_d - i - 1) \
-                       * np.random.permutation(np.hstack((np.ones(marginal_frequencies[response][i]),
-                                                          np.zeros(number_of_symbols[response] \
-                                                                   - marginal_frequencies[response][i]))))
+                shuffled_past_symbols[response] += 2 ** (
+                    number_of_bins_d - i - 1
+                ) * np.random.permutation(
+                    np.hstack(
+                        (
+                            np.ones(marginal_frequencies[response][i]),
+                            np.zeros(
+                                number_of_symbols[response]
+                                - marginal_frequencies[response][i]
+                            ),
+                        )
+                    )
+                )
 
         for response in [0, 1]:
-            shuffled_past_symbols[response] = np.array(shuffled_past_symbols[response], dtype=int)
+            shuffled_past_symbols[response] = np.array(
+                shuffled_past_symbols[response], dtype=int
+            )
 
         shuffled_past_symbol_counts = [Counter(), Counter()]
 
@@ -1052,8 +1186,10 @@ 
    Source code for idtxl.estimators_Rudelt
                 for past_symbol in shuffled_past_symbols[response]:
                 shuffled_past_symbol_counts[response][past_symbol] += 1
 
-        marginal_probabilities = [marginal_frequencies[response] / number_of_symbols[response]
-                                  for response in [0, 1]]
+        marginal_probabilities = [
+            marginal_frequencies[response] / number_of_symbols[response]
+            for response in [0, 1]
+        ]
 
         return shuffled_past_symbol_counts, marginal_probabilities
    
 
@@ -1112,11 +1248,17 @@ 
    Source code for idtxl.estimators_Rudelt
     
         # plug-in estimate
         past_symbol_counts = utl.get_past_symbol_counts(symbol_counts, merge=False)
-        number_of_symbols = [sum(past_symbol_counts[response].values()) for response in [0, 1]]
+        number_of_symbols = [
+            sum(past_symbol_counts[response].values()) for response in [0, 1]
+        ]
 
         P_X_uncond = self.get_P_X_uncond(number_of_symbols)
-        P_X_past_uncond = self.get_P_X_past_uncond(past_symbol_counts, number_of_symbols)
-        P_X_past_cond_X = self.get_P_X_past_cond_X(past_symbol_counts, number_of_symbols)
+        P_X_past_uncond = self.get_P_X_past_uncond(
+            past_symbol_counts, number_of_symbols
+        )
+        P_X_past_cond_X = self.get_P_X_past_cond_X(
+            past_symbol_counts, number_of_symbols
+        )
 
         H_X_past_uncond = self.get_H_X_past_uncond(P_X_past_uncond)
         H_X_past_cond_X = self.get_H_X_past_cond_X(P_X_uncond, P_X_past_cond_X)
@@ -1124,13 +1266,20 @@ 
    Source code for idtxl.estimators_Rudelt
             I_plugin = H_X_past_uncond - H_X_past_cond_X
 
         # correction term
-        shuffled_past_symbol_counts, marginal_probabilities \
-            = self.get_shuffled_symbol_counts(symbol_counts, past_symbol_counts, number_of_bins_d,
-                                         number_of_symbols)
-
-        P0_sh_X_past_cond_X = self.get_P_X_past_cond_X(shuffled_past_symbol_counts, number_of_symbols)
-
-        H0_X_past_cond_X = self.get_H0_X_past_cond_X(marginal_probabilities, number_of_bins_d, P_X_uncond)
+        (
+            shuffled_past_symbol_counts,
+            marginal_probabilities,
+        ) = self.get_shuffled_symbol_counts(
+            symbol_counts, past_symbol_counts, number_of_bins_d, number_of_symbols
+        )
+
+        P0_sh_X_past_cond_X = self.get_P_X_past_cond_X(
+            shuffled_past_symbol_counts, number_of_symbols
+        )
+
+        H0_X_past_cond_X = self.get_H0_X_past_cond_X(
+            marginal_probabilities, number_of_bins_d, P_X_uncond
+        )
         H0_sh_X_past_cond_X = self.get_H_X_past_cond_X(P_X_uncond, P0_sh_X_past_cond_X)
 
         I_corr = H0_X_past_cond_X - H0_sh_X_past_cond_X
@@ -1154,10 +1303,7 @@ 
    Source code for idtxl.estimators_Rudelt
                     MI / H_uncond (History dependence)
         """
 
-        self._check_estimator_inputs(symbol_array,
-                                     None,
-                                     None,
-                                     None)
+        self._check_estimator_inputs(symbol_array, None, None, None)
 
         self._ensure_one_dim(symbol_array)
 
@@ -1168,8 +1314,7 @@ 
    Source code for idtxl.estimators_Rudelt
     
         H_uncond = utl.get_H_spiking(symbol_counts)
 
-        I_sh = self.shuffling_MI(symbol_counts,
-                            number_of_bins_d_join -1)
+        I_sh = self.shuffling_MI(symbol_counts, number_of_bins_d_join - 1)
 
         R_sh = I_sh / H_uncond
 
@@ -1205,7 +1350,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.5 documentation »
    • 
+        
  • IDTxl 1.5.1 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.estimators_Rudelt
    •  
       
diff --git a/docs/html/_modules/idtxl/estimators_jidt.html b/docs/html/_modules/idtxl/estimators_jidt.html
index 7cf844b0..907b2e58 100644
--- a/docs/html/_modules/idtxl/estimators_jidt.html
+++ b/docs/html/_modules/idtxl/estimators_jidt.html
@@ -5,7 +5,7 @@
   
     
     
-    idtxl.estimators_jidt — IDTxl 1.5 documentation
+    idtxl.estimators_jidt — IDTxl 1.5.1 documentation
     
     
     
@@ -31,7 +31,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.5 documentation »
    • 
+        
  • IDTxl 1.5.1 documentation »
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    • 
         
  • idtxl.estimators_jidt
    •  
       
@@ -1874,7 +1874,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.5 documentation »
    • 
+        
  • IDTxl 1.5.1 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.estimators_jidt
    •  
       
diff --git a/docs/html/_modules/idtxl/estimators_mpi.html b/docs/html/_modules/idtxl/estimators_mpi.html
index 4570af76..e6752b21 100644
--- a/docs/html/_modules/idtxl/estimators_mpi.html
+++ b/docs/html/_modules/idtxl/estimators_mpi.html
@@ -5,7 +5,7 @@
   
     
     
-    idtxl.estimators_mpi — IDTxl 1.5 documentation
+    idtxl.estimators_mpi — IDTxl 1.5.1 documentation
     
     
     
@@ -31,7 +31,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.5 documentation »
    • 
+        
  • IDTxl 1.5.1 documentation »
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  • Module code »
    • 
         
  • idtxl.estimators_mpi
    •  
       
@@ -55,10 +55,12 @@ 
    Source code for idtxl.estimators_mpi
     try:
     from mpi4py.futures import MPIPoolExecutor
 except ImportError as err:
-    ex.package_missing(err, 'MPI is not available on this system. Install it'
-                       'from https://pypi.org/project/mpi4py/ to use'
-                       'MPI parallelization.')
-    raise err
+    ex.package_missing(
+        err,
+        "MPI is not available on this system. Install it"
+        "from https://pypi.org/project/mpi4py/ to use"
+        "MPI parallelization.",
+    )
 
 _worker_estimators = {}
 """Estimator instances on worker ranks
@@ -75,7 +77,6 @@ 
    Source code for idtxl.estimators_mpi
     
     # Create new estimator if necessary
     if id_ not in _worker_estimators:
-
         # There is currently no good way to delete Estimators from _worker_estimators
         # caches when the corresponding MPIEstimator ceases to exist.
         # To avoid memory leaks, we currently allow only a single cached estimator that is replaced for new MPIEstimators.
@@ -102,20 +103,20 @@ 
    Source code for idtxl.estimators_mpi
     
    [docs]class MPIEstimator(Estimator):
     """MPI Wrapper for arbitrary Estimator implementations
 
-    Make sure to have an "if __name__=='__main__':" guard in your main script to avoid
-    infinite recursion!
+    Make sure to have an "if __name__=='__main__':" guard in your main script
+    to avoid infinite recursion!
 
-    To use MPI, add MPI=True to the Estimator settings dictionary and optionally provide max_workers
+    To use MPI, add MPI=True to the Estimator settings dictionary and
+    optionally provide max_workers
 
     Call using mpiexec:
-    mpiexec -n 1 -usize <max workers + 1> python <python script>
+        >>> mpiexec -n 1 -usize <max workers + 1> python <python script>
 
     or, if MPI does not support spawning new workers (i.e. MPI version < 2)
-    mpiexec -n <max workers + 1> python -m mpi4py.futures <python script>
+        >>> mpiexec -n <max workers + 1> python -m mpi4py.futures <python script>
 
     Call using slurm:
-    srun -n $SLURM_NTASKS --mpi=pmi2 python -m mpi4py.futures <python script> 
-
+        >>> srun -n $SLURM_NTASKS --mpi=pmi2 python -m mpi4py.futures <python script>
     """
 
     def __init__(self, est, settings):
@@ -124,9 +125,13 @@ 
    Source code for idtxl.estimators_mpi
             Immediately creates instances of est on each MPI worker.
 
         Args:
-            est (str | Callable[[dict], Estimator]): Name of of or callable returning an instance of the base Estimator
-            settings (dict): settings for the base Estimator.
-                max_workers (optional): Number of MPI workers. Default: MPI_UNIVERSE_SIZE
+            est : str | Callable[[dict], Estimator]
+                Name of of or callable returning an instance of the base
+                Estimator
+            settings : dict
+                settings for the base Estimator.
+            max_workers : int (optional)
+                Number of MPI workers, default=MPI_UNIVERSE_SIZE
         """
 
         self._est = est
@@ -136,23 +141,22 @@ 
    Source code for idtxl.estimators_mpi
             self._id = uuid4().int
 
         # Create the MPIPoolExecutor and initialize Estimators on worker ranks
-        self._executor = MPIPoolExecutor(
-            max_workers=settings.get('max_workers', None))
+        self._executor = MPIPoolExecutor(max_workers=settings.get("max_workers", None))
 
         # Boot up the executor with timeout
-        with timeout(timeout_duration=settings.get('mpi_bootup_timeout', 10), exception_message='Bootup of MPI workers timed out.\n\
-                Make sure the script was started in an MPI enrivonment using mpiexec, mpirun, srun (SLURM) or equivalent.\n\
-                If necessary, increase the timeout in the settings dictionary using the key mpi_bootup_timeout.'):
+        with timeout(
+            timeout_duration=settings.get("mpi_bootup_timeout", 10),
+            exception_message="Bootup of MPI workers timed out.\n\
+                Make sure the script was started in an MPI enrivonment using mpiexec, mpirun, srun (SLURM) or equivalent.\n\
+                If necessary, increase the timeout in the settings dictionary using the key mpi_bootup_timeout.",
+        ):
             self._executor.bootup(wait=True)
 
         # Create Estimator for rank 0.
         _get_worker_estimator(self._id, est, settings)
 
     def __del__(self):
-        """
-        Shut down MPIPoolExecutor upon deletion of MPIEstimator
-        """
-
+        """Shut down MPIPoolExecutor upon deletion of MPIEstimator"""
         self._executor.shutdown()
 
     def _chunk_data(self, data, chunksize, n_chunks):
@@ -160,37 +164,55 @@ 
    Source code for idtxl.estimators_mpi
             Iterator chopping data dictionary into n_chunks chunks of size chunksize
         """
         for i in range(n_chunks):
-            yield {var: (None if data[var] is None else data[var][i*chunksize:(i+1)*chunksize]) for var in data}
+            yield {
+                var: (
+                    None
+                    if data[var] is None
+                    else data[var][i * chunksize : (i + 1) * chunksize]
+                )
+                for var in data
+            }
 
 
    [docs]    def estimate(self, *, n_chunks=1, **data):
         """Distributes the given chunks of a task to Estimators on worker ranks using MPI.
+
         Needs to be called with kwargs only.
+
         Args:
-            n_chunks (int, optional): Number of chunks to split the data into. Defaults to 1.
-            data (dict[str, Sequence]): Dictionary of random variable realizations
+            n_chunks : int  [optional]
+                Number of chunks to split the data into, default=1.
+            data : dict[str, Sequence]
+                Dictionary of random variable realizations
         Returns:
-            numpy array: Estimates of information-theoretic quantities as np.double values
+            numpy array
+                Estimates of information-theoretic quantities as np.double
+                values
         """
 
-        assert n_chunks > 0, 'Number of chunks must be at least one.'
+        assert n_chunks > 0, "Number of chunks must be at least one."
 
         samplesize = len(next(iter(data.values())))
 
-        assert all(var is None or len(var) == samplesize for var in data.values(
-        )), 'All variables must have the same number of realizations.'
+        assert all(
+            var is None or len(var) == samplesize for var in data.values()
+        ), "All variables must have the same number of realizations."
 
-        assert samplesize % n_chunks == 0, 'Number of realizations must be divisible by number of chunks!'
+        assert (
+            samplesize % n_chunks == 0
+        ), "Number of realizations must be divisible by number of chunks!"
 
         # Split the data into chunks
         chunksize = samplesize // n_chunks
 
         chunked_data = self._chunk_data(data, chunksize, n_chunks)
 
-        result_generator = self._executor.map(_dispatch_task,
-                                              itertools.repeat(self._id),
-                                              itertools.repeat(self._est),
-                                              itertools.repeat(self._settings),
-                                              chunked_data)
+        result_generator = self._executor.map(
+            _dispatch_task,
+            itertools.repeat(self._id),
+            itertools.repeat(self._est),
+            itertools.repeat(self._settings),
+            chunked_data,
+        )
 
         return np.fromiter(result_generator, dtype=np.double)
    
 
@@ -198,18 +220,22 @@ 
    Source code for idtxl.estimators_mpi
             return True
    
 
 
    [docs]    def is_analytic_null_estimator(self):
-        """Test if the base Estimator is an analytic null estimator.
+        """Test if the base Estimator is an analytic null estimator."""
 
-        """
-
-        return _get_worker_estimator(self._id, self._est, self._settings).is_analytic_null_estimator()
    
+        return _get_worker_estimator(
+            self._id, self._est, self._settings
+        ).is_analytic_null_estimator()
    
 
 
    [docs]    def estimate_surrogates_analytic(self, **data):
         """Forward analytic estimation to the base Estimator.
-        Analytic estimation is assumed to have shorter runtime and is thus performed on rank 0 alone for now.
+
+        Analytic estimation is assumed to have shorter runtime and is thus
+        performed on rank 0 alone for now.
         """
 
-        return _get_worker_estimator(self._id, self._est, self._settings).estimate_surrogates_analytic(**data)
    
+        return _get_worker_estimator(
+            self._id, self._est, self._settings
+        ).estimate_surrogates_analytic(**data)
    
 
    
 
             
    
@@ -241,7 +267,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.5 documentation »
    • 
+        
  • IDTxl 1.5.1 documentation »
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    • 
         
  • idtxl.estimators_mpi
    •  
       
diff --git a/docs/html/_modules/idtxl/estimators_multivariate_pid.html b/docs/html/_modules/idtxl/estimators_multivariate_pid.html
index 2935844e..66407fcb 100644
--- a/docs/html/_modules/idtxl/estimators_multivariate_pid.html
+++ b/docs/html/_modules/idtxl/estimators_multivariate_pid.html
@@ -5,14 +5,13 @@
   
     
     
-    idtxl.estimators_multivariate_pid — IDTxl 1.4 documentation
-    
-    
-    
+    idtxl.estimators_multivariate_pid — IDTxl 1.5.1 documentation
+    
+    
+    
     
     
     
-    
     
     
 
@@ -32,7 +31,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5.1 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.estimators_multivariate_pid
    •  
       
@@ -234,7 +233,7 @@ 
    Source code for idtxl.estimators_multivariate_pid
    Quick search
     
    
     
    
-      
+      
       
     
    
     
    
@@ -253,14 +252,14 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5.1 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.estimators_multivariate_pid
    •  
       
     
    
     
   
 
\ No newline at end of file
diff --git a/docs/html/_modules/idtxl/estimators_opencl.html b/docs/html/_modules/idtxl/estimators_opencl.html
index b7a015d3..e1d13da7 100644
--- a/docs/html/_modules/idtxl/estimators_opencl.html
+++ b/docs/html/_modules/idtxl/estimators_opencl.html
@@ -5,14 +5,13 @@
   
     
     
-    idtxl.estimators_opencl — IDTxl 1.4 documentation
-    
-    
-    
+    idtxl.estimators_opencl — IDTxl 1.5.1 documentation
+    
+    
+    
     
     
     
-    
     
     
 
@@ -32,7 +31,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5.1 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.estimators_opencl
    •  
       
@@ -871,7 +870,7 @@ 
    Source code for idtxl.estimators_opencl
       
    Quick search
    
     
    
     
    
-      
+      
       
     
    
     
    
@@ -890,14 +889,14 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5.1 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.estimators_opencl
    •  
       
     
    
     
   
 
\ No newline at end of file
diff --git a/docs/html/_modules/idtxl/estimators_pid.html b/docs/html/_modules/idtxl/estimators_pid.html
index edc3ac36..45b51bb9 100644
--- a/docs/html/_modules/idtxl/estimators_pid.html
+++ b/docs/html/_modules/idtxl/estimators_pid.html
@@ -5,14 +5,13 @@
   
     
     
-    idtxl.estimators_pid — IDTxl 1.4 documentation
-    
-    
-    
+    idtxl.estimators_pid — IDTxl 1.5.1 documentation
+    
+    
+    
     
     
     
-    
     
     
 
@@ -32,7 +31,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
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+        
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    • 
         
  • idtxl.estimators_pid
    •  
       
@@ -117,43 +116,46 @@ 
    Source code for idtxl.estimators_pid
                 - verbose : bool [optional] - print output to console
               (default=False)
     """
+
     def __init__(self, settings):
         try:
-            settings['alph_s1']
+            settings["alph_s1"]
         except KeyError:
             print('"alph_s1" is missing from the settings dictionary.')
             raise
         try:
-            settings['alph_s2']
+            settings["alph_s2"]
         except KeyError:
             print('"alph_s2" is missing from the settings dictionary.')
             raise
         try:
-            settings['alph_t']
+            settings["alph_t"]
         except KeyError:
             print('"alph_t" is missing from the settings dictionary.')
             raise
         try:
-            settings['max_unsuc_swaps_row_parm']
+            settings["max_unsuc_swaps_row_parm"]
         except KeyError:
-            print('"max_unsuc_swaps_row_parm" is missing from the settings '
-                  'dictionary.')
+            print(
+                '"max_unsuc_swaps_row_parm" is missing from the settings ' "dictionary."
+            )
             raise
         try:
-            settings['num_reps']
+            settings["num_reps"]
         except KeyError:
             print('"num_reps" is missing from the settings dictionary.')
             raise
-        if settings['num_reps'] > 63:
-            raise ValueError('Number of reps must be 63 or less to prevent '
-                             'integer overflow.')
+        if settings["num_reps"] > 63:
+            raise ValueError(
+                "Number of reps must be 63 or less to prevent " "integer overflow."
+            )
         try:
-            settings['max_iters']
+            settings["max_iters"]
         except KeyError:
             print('"max_iters" is missing from the settings dictionary.')
             raise
         self.settings = settings.copy()
-        self.settings.setdefault('verbose', False)
+        self.settings.setdefault("verbose", False)
 
 
    [docs]    def is_parallel():
         return False
    
@@ -184,34 +186,34 @@ 
    Source code for idtxl.estimators_pid
             except AttributeError as err:
             if "'module' object has no attribute 'longdouble'" == err.args[0]:
                 raise RuntimeError(
-                        'This system doesn''t seem to support longdouble '
-                        '(requirement for using the Sydney PID-estimator.')
+                    "This system doesn"
+                    "t seem to support longdouble "
+                    "(requirement for using the Sydney PID-estimator."
+                )
             else:
                 raise
 
         # -- DEFINE PARAMETERS -- #
 
         num_samples = len(t)
-        alph_t = self.settings['alph_t']
-        alph_s1 = self.settings['alph_s1']
-        alph_s2 = self.settings['alph_s2']
-        max_unsuc_swaps_row_parm = self.settings['max_unsuc_swaps_row_parm']
+        alph_t = self.settings["alph_t"]
+        alph_s1 = self.settings["alph_s1"]
+        alph_s2 = self.settings["alph_s2"]
+        max_unsuc_swaps_row_parm = self.settings["max_unsuc_swaps_row_parm"]
         # Max swaps = number of possible swaps * control parameter
-        num_pos_swaps = alph_t * alph_s1 * (alph_s1-1) * alph_s2 * (alph_s2-1)
-        max_unsuc_swaps_row = np.floor(num_pos_swaps *
-                                       max_unsuc_swaps_row_parm)
+        num_pos_swaps = alph_t * alph_s1 * (alph_s1 - 1) * alph_s2 * (alph_s2 - 1)
+        max_unsuc_swaps_row = np.floor(num_pos_swaps * max_unsuc_swaps_row_parm)
 
         # -- CALCULATE PROBABLITIES -- #
 
         # Declare arrays for counts
-        t_count = np.zeros(alph_t, dtype=np.int)
-        s1_count = np.zeros(alph_s1, dtype=np.int)
-        s2_count = np.zeros(alph_s2, dtype=np.int)
-        joint_t_s1_count = np.zeros((alph_t, alph_s1), dtype=np.int)
-        joint_t_s2_count = np.zeros((alph_t, alph_s2), dtype=np.int)
-        joint_s1_s2_count = np.zeros((alph_s1, alph_s2), dtype=np.int)
-        joint_t_s1_s2_count = np.zeros((alph_t, alph_s1, alph_s2),
-                                       dtype=np.int)
+        t_count = np.zeros(alph_t, dtype=int)
+        s1_count = np.zeros(alph_s1, dtype=int)
+        s2_count = np.zeros(alph_s2, dtype=int)
+        joint_t_s1_count = np.zeros((alph_t, alph_s1), dtype=int)
+        joint_t_s2_count = np.zeros((alph_t, alph_s2), dtype=int)
+        joint_s1_s2_count = np.zeros((alph_s1, alph_s2), dtype=int)
+        joint_t_s1_s2_count = np.zeros((alph_t, alph_s1, alph_s2), dtype=int)
 
         # Count observations
         for obs in range(0, num_samples):
@@ -228,43 +230,45 @@ 
    Source code for idtxl.estimators_pid
             #   			joint_t_s1_s2_count[np.nonzero(joint_t_s1_s2_count)])))
 
         max_joint_nonzero_count = np.max(
-                        joint_t_s1_s2_count[np.nonzero(joint_t_s1_s2_count)])
+            joint_t_s1_s2_count[np.nonzero(joint_t_s1_s2_count)]
+        )
 
         # Fixed probabilities
-        t_prob = np.divide(t_count, num_samples).astype('longdouble')
-        s1_prob = np.divide(s1_count, num_samples).astype('longdouble')
-        s2_prob = np.divide(s2_count, num_samples).astype('longdouble')
-        joint_t_s1_prob = np.divide(joint_t_s1_count,
-                                    num_samples).astype('longdouble')
-        joint_t_s2_prob = np.divide(joint_t_s2_count,
-                                    num_samples).astype('longdouble')
+        t_prob = np.divide(t_count, num_samples).astype("longdouble")
+        s1_prob = np.divide(s1_count, num_samples).astype("longdouble")
+        s2_prob = np.divide(s2_count, num_samples).astype("longdouble")
+        joint_t_s1_prob = np.divide(joint_t_s1_count, num_samples).astype("longdouble")
+        joint_t_s2_prob = np.divide(joint_t_s2_count, num_samples).astype("longdouble")
 
         # Variable probabilities
-        joint_s1_s2_prob = np.divide(joint_s1_s2_count,
-                                     num_samples).astype('longdouble')
-        joint_t_s1_s2_prob = np.divide(joint_t_s1_s2_count,
-                                       num_samples).astype('longdouble')
+        joint_s1_s2_prob = np.divide(joint_s1_s2_count, num_samples).astype(
+            "longdouble"
+        )
+        joint_t_s1_s2_prob = np.divide(joint_t_s1_s2_count, num_samples).astype(
+            "longdouble"
+        )
         max_prob = np.max(joint_t_s1_s2_prob[np.nonzero(joint_t_s1_s2_prob)])
 
-    #    # make copies of the variable probabilities for independent second
-    #    # optimization and comparison of KLDs for convergence check:
-    #    # KLDs should initially rise and then fall when close to the minimum
-    #    joint_s1_s2_prob_alt = joint_s1_s2_prob.copy()
-    #    joint_t_s1_s2_prob_alt = joint_t_s1_s2_prob.copy()
+        #    # make copies of the variable probabilities for independent second
+        #    # optimization and comparison of KLDs for convergence check:
+        #    # KLDs should initially rise and then fall when close to the minimum
+        #    joint_s1_s2_prob_alt = joint_s1_s2_prob.copy()
+        #    joint_t_s1_s2_prob_alt = joint_t_s1_s2_prob.copy()
 
         # -- VIRTUALISED SWAPS -- #
 
         # Calculate the initial cmi's and store them
         cond_mut_info1 = self._cmi_prob(
-            s2_prob, joint_t_s2_prob, joint_s1_s2_prob, joint_t_s1_s2_prob)
+            s2_prob, joint_t_s2_prob, joint_s1_s2_prob, joint_t_s1_s2_prob
+        )
         cur_cond_mut_info1 = cond_mut_info1
 
         joint_s2_s1_prob = np.transpose(joint_s1_s2_prob)
-        joint_t_s2_s1_prob = np.ndarray.transpose(joint_t_s1_s2_prob,
-                                                  [0, 2, 1])
+        joint_t_s2_s1_prob = np.ndarray.transpose(joint_t_s1_s2_prob, [0, 2, 1])
 
         cond_mut_info2 = self._cmi_prob(
-            s1_prob, joint_t_s1_prob, joint_s2_s1_prob, joint_t_s2_s1_prob)
+            s1_prob, joint_t_s1_prob, joint_s2_s1_prob, joint_t_s2_s1_prob
+        )
         cur_cond_mut_info2 = cond_mut_info2
 
         # sanity check: the curr cmi must be smaller than the joint, else
@@ -272,11 +276,13 @@ 
    Source code for idtxl.estimators_pid
             jointmi_s1s2_t = self._joint_mi(s1, s2, t, alph_s1, alph_s2, alph_t)
 
         if cond_mut_info1 > jointmi_s1s2_t:
-            raise ValueError('joint MI {0} smaller than cMI {1}'
-                             ''.format(jointmi_s1s2_t, cond_mut_info1))
+            raise ValueError(
+                "joint MI {0} smaller than cMI {1}"
+                "".format(jointmi_s1s2_t, cond_mut_info1)
+            )
         else:
-            if self.settings['verbose']:
-                print('Passed sanity check on jMI and cMI')
+            if self.settings["verbose"]:
+                print("Passed sanity check on jMI and cMI")
 
         # Declare reps array of repeated doubling to half the prob_inc
         # WARNING: num_reps greater than 63 results in integer overflow
@@ -290,42 +296,42 @@ 
    Source code for idtxl.estimators_pid
             # this does not run with the current code as it uses large powers of
         # integers another idea would be to decrement by something slightly
         # smaller than 2
-    #    num_reps = num_reps + np.int32(np.floor(np.log(max_joint_nonzero_count)/np.log(2)))
-        if self.settings['verbose']:
-            print('num_reps: {0}'.format(self.settings['num_reps']))
-        reps = np.array(np.power(2, range(0, self.settings['num_reps'])))
+        #    num_reps = num_reps + np.int32(np.floor(np.log(max_joint_nonzero_count)/np.log(2)))
+        if self.settings["verbose"]:
+            print("num_reps: {0}".format(self.settings["num_reps"]))
+        reps = np.array(np.power(2, range(0, self.settings["num_reps"])))
 
         # Replication loop
         for rep in reps:
             prob_inc = np.multiply(
-                np.longdouble(max_prob),
-                np.divide(np.longdouble(1), np.longdouble(rep)))
+                np.longdouble(max_prob), np.divide(np.longdouble(1), np.longdouble(rep))
+            )
             # Want to store number of succesive unsuccessful swaps
             unsuccessful_swaps_row = 0
             # SWAP LOOP
-            for attempt_swap in range(0, self.settings['max_iters']):
+            for attempt_swap in range(0, self.settings["max_iters"]):
                 # Pick a random candidate from the targets
                 t_cand = np.random.randint(0, alph_t)
                 s1_cand = np.random.randint(0, alph_s1)
                 s2_cand = np.random.randint(0, alph_s2)
 
                 # Pick a swap candidate
-                s1_prim = np.random.randint(0, alph_s1-1)
-                if (s1_prim >= s1_cand):
+                s1_prim = np.random.randint(0, alph_s1 - 1)
+                if s1_prim >= s1_cand:
                     s1_prim += 1
-                s2_prim = np.random.randint(0, alph_s2-1)
-                if (s2_prim >= s2_cand):
+                s2_prim = np.random.randint(0, alph_s2 - 1)
+                if s2_prim >= s2_cand:
                     s2_prim += 1
 
-    #            unsuccessful_swaps_row = _try_swap(cur_cond_mut_info,
-    #                                               joint_t_s1_s2_prob,
-    #                                               joint_s1_s2_prob,
-    #                                               joint_t_s2_prob, s2_prob,
-    #                                               t_cand, s1_prim, s2_prim,
-    #                                               s1_cand, s2_cand,
-    #                                               prob_inc,
-    #                                               unsuccessful_swaps_row)
-    #            print("unsuccessful_swaps_row: {0}".format(unsuccessful_swaps_row))
+                #            unsuccessful_swaps_row = _try_swap(cur_cond_mut_info,
+                #                                               joint_t_s1_s2_prob,
+                #                                               joint_s1_s2_prob,
+                #                                               joint_t_s2_prob, s2_prob,
+                #                                               t_cand, s1_prim, s2_prim,
+                #                                               s1_cand, s2_cand,
+                #                                               prob_inc,
+                #                                               unsuccessful_swaps_row)
+                #            print("unsuccessful_swaps_row: {0}".format(unsuccessful_swaps_row))
 
                 # START of a possible try_swap function
                 # based on a fixed set of candidates
@@ -335,11 +341,12 @@ 
    Source code for idtxl.estimators_pid
                     # Ensure we can decrement without introducing neg probs
                 # this is very important as we start swaps in the size of the
                 # maximum probability
-                if (joint_t_s1_s2_prob[t_cand, s1_cand, s2_cand] >= prob_inc and
-                        joint_t_s1_s2_prob[t_cand, s1_prim, s2_prim] >= prob_inc and
-                        joint_s1_s2_prob[s1_cand, s2_cand] >= prob_inc and
-                        joint_s1_s2_prob[s1_prim, s2_prim] >= prob_inc):
-
+                if (
+                    joint_t_s1_s2_prob[t_cand, s1_cand, s2_cand] >= prob_inc
+                    and joint_t_s1_s2_prob[t_cand, s1_prim, s2_prim] >= prob_inc
+                    and joint_s1_s2_prob[s1_cand, s2_cand] >= prob_inc
+                    and joint_s1_s2_prob[s1_prim, s2_prim] >= prob_inc
+                ):
                     joint_t_s1_s2_prob[t_cand, s1_cand, s2_cand] -= prob_inc
                     joint_t_s1_s2_prob[t_cand, s1_prim, s2_prim] -= prob_inc
                     joint_t_s1_s2_prob[t_cand, s1_cand, s2_prim] += prob_inc
@@ -351,19 +358,19 @@ 
    Source code for idtxl.estimators_pid
                         joint_s1_s2_prob[s1_prim, s2_cand] += prob_inc
 
                     # Calculate the cmi after this virtual swap
-                    cond_mut_info1 = self._cmi_prob(s2_prob,
-                                                    joint_t_s2_prob,
-                                                    joint_s1_s2_prob,
-                                                    joint_t_s1_s2_prob)
-                    cond_mut_info2 = self._cmi_prob(s2_prob,
-                                                    joint_t_s2_prob,
-                                                    joint_s1_s2_prob,
-                                                    joint_t_s1_s2_prob)
+                    cond_mut_info1 = self._cmi_prob(
+                        s2_prob, joint_t_s2_prob, joint_s1_s2_prob, joint_t_s1_s2_prob
+                    )
+                    cond_mut_info2 = self._cmi_prob(
+                        s2_prob, joint_t_s2_prob, joint_s1_s2_prob, joint_t_s1_s2_prob
+                    )
 
                     # If at least one of the cmis is improved keep it,
                     # reset the unsuccessful swap counter
-                    if (cond_mut_info1 < cur_cond_mut_info1 or
-                            cond_mut_info2 < cur_cond_mut_info2):
+                    if (
+                        cond_mut_info1 < cur_cond_mut_info1
+                        or cond_mut_info2 < cur_cond_mut_info2
+                    ):
                         cur_cond_mut_info1 = cond_mut_info1
                         cur_cond_mut_info2 = cond_mut_info2
                         unsuccessful_swaps_row = 0
@@ -385,7 +392,7 @@ 
    Source code for idtxl.estimators_pid
                         unsuccessful_swaps_row += 1
                 # END of a possible try_swap function
 
-                if (unsuccessful_swaps_row >= max_unsuc_swaps_row):
+                if unsuccessful_swaps_row >= max_unsuc_swaps_row:
                     break
 
         # print(cond_mut_info, '\t', prob_inc, '\t', unsuccessful_swaps_row)
@@ -395,10 +402,9 @@ 
    Source code for idtxl.estimators_pid
             # Classical mutual information terms
         mi_target_s1 = self._mi_prob(t_prob, s1_prob, joint_t_s1_prob)
         mi_target_s2 = self._mi_prob(t_prob, s2_prob, joint_t_s2_prob)
-        jointmi_s1s2_target = self._joint_mi(s1, s2, t, alph_s1, alph_s2,
-                                             alph_t)
-        if self.settings['verbose']:
-            print('jointmi_s1s2_target: {0}'.format(jointmi_s1s2_target))
+        jointmi_s1s2_target = self._joint_mi(s1, s2, t, alph_s1, alph_s2, alph_t)
+        if self.settings["verbose"]:
+            print("jointmi_s1s2_target: {0}".format(jointmi_s1s2_target))
 
         # PID terms
         unq_s1 = cond_mut_info1
@@ -407,39 +413,46 @@ 
    Source code for idtxl.estimators_pid
             syn_s1_s2 = jointmi_s1s2_target - unq_s1 - unq_s2 - shd_s1_s2
 
         # Return scalars instead of 1-element numpy arrays
-        return {'joint_mi_s1s2_t': jointmi_s1s2_target[0],
-                'unq_s1': unq_s1[0],
-                'unq_s2': unq_s2[0],
-                'shd_s1_s2': shd_s1_s2[0],
-                'syn_s1_s2': syn_s1_s2[0]}
    
-
-    def _cmi_prob(self, s2cond_prob, joint_t_s2cond_prob,
-                  joint_s1_s2cond_prob, joint_t_s1_s2cond_prob):
-        total = np.zeros(1).astype('longdouble')
+        return {
+            "joint_mi_s1s2_t": jointmi_s1s2_target[0],
+            "unq_s1": unq_s1[0],
+            "unq_s2": unq_s2[0],
+            "shd_s1_s2": shd_s1_s2[0],
+            "syn_s1_s2": syn_s1_s2[0],
+        }
    
+
+    def _cmi_prob(
+        self,
+        s2cond_prob,
+        joint_t_s2cond_prob,
+        joint_s1_s2cond_prob,
+        joint_t_s1_s2cond_prob,
+    ):
+        total = np.zeros(1).astype("longdouble")
 
         [alph_t, alph_s1, alph_s2cond] = np.shape(joint_t_s1_s2cond_prob)
 
         for sym_s1 in range(0, alph_s1):
             for sym_s2cond in range(0, alph_s2cond):
                 for sym_t in range(0, alph_t):
-
-                    if (s2cond_prob[sym_s2cond] *
-                            joint_t_s2cond_prob[sym_t, sym_s2cond] *
-                            joint_s1_s2cond_prob[sym_s1, sym_s2cond] *
-                            joint_t_s1_s2cond_prob[sym_t, sym_s1, sym_s2cond] >
-                            0):
-
+                    if (
+                        s2cond_prob[sym_s2cond]
+                        * joint_t_s2cond_prob[sym_t, sym_s2cond]
+                        * joint_s1_s2cond_prob[sym_s1, sym_s2cond]
+                        * joint_t_s1_s2cond_prob[sym_t, sym_s1, sym_s2cond]
+                        > 0
+                    ):
                         local_contrib = (
-                               np.log(joint_t_s1_s2cond_prob[sym_t, sym_s1,
-                                                             sym_s2cond]) +
-                               np.log(s2cond_prob[sym_s2cond]) -
-                               np.log(joint_t_s2cond_prob[sym_t, sym_s2cond]) -
-                               np.log(joint_s1_s2cond_prob[sym_s1, sym_s2cond])
-                                       ) / np.log(2)
+                            np.log(joint_t_s1_s2cond_prob[sym_t, sym_s1, sym_s2cond])
+                            + np.log(s2cond_prob[sym_s2cond])
+                            - np.log(joint_t_s2cond_prob[sym_t, sym_s2cond])
+                            - np.log(joint_s1_s2cond_prob[sym_s1, sym_s2cond])
+                        ) / np.log(2)
 
                         weighted_contrib = (
-                            joint_t_s1_s2cond_prob[sym_t, sym_s1, sym_s2cond] *
-                            local_contrib)
+                            joint_t_s1_s2cond_prob[sym_t, sym_s1, sym_s2cond]
+                            * local_contrib
+                        )
                     else:
                         weighted_contrib = 0
                     total += weighted_contrib
@@ -448,23 +461,22 @@ 
    Source code for idtxl.estimators_pid
     
     def _mi_prob(self, s1_prob, s2_prob, joint_s1_s2_prob):
         """MI estimator in the prob domain."""
-        total = np.zeros(1).astype('longdouble')
+        total = np.zeros(1).astype("longdouble")
         [alph_s1, alph_s2] = np.shape(joint_s1_s2_prob)
 
         for sym_s1 in range(0, alph_s1):
             for sym_s2 in range(0, alph_s2):
-
-                if (s1_prob[sym_s1] * s2_prob[sym_s2] *
-                        joint_s1_s2_prob[sym_s1, sym_s2] > 0):
-
+                if (
+                    s1_prob[sym_s1] * s2_prob[sym_s2] * joint_s1_s2_prob[sym_s1, sym_s2]
+                    > 0
+                ):
                     local_contrib = (
-                        np.log(joint_s1_s2_prob[sym_s1, sym_s2]) -
-                        np.log(s1_prob[sym_s1]) -
-                        np.log(s2_prob[sym_s2])
-                                    ) / np.log(2)
+                        np.log(joint_s1_s2_prob[sym_s1, sym_s2])
+                        - np.log(s1_prob[sym_s1])
+                        - np.log(s2_prob[sym_s2])
+                    ) / np.log(2)
 
-                    weighted_contrib = (joint_s1_s2_prob[sym_s1, sym_s2] *
-                                        local_contrib)
+                    weighted_contrib = joint_s1_s2_prob[sym_s1, sym_s2] * local_contrib
                 else:
                     weighted_contrib = 0
                 total += weighted_contrib
@@ -476,9 +488,9 @@ 
    Source code for idtxl.estimators_pid
     
         [s12, alph_s12] = _join_variables(s1, s2, alph_s1, alph_s2)
 
-        t_count = np.zeros(alph_t, dtype=np.int)
-        s12_count = np.zeros(alph_s12, dtype=np.int)
-        joint_t_s12_count = np.zeros((alph_t, alph_s12), dtype=np.int)
+        t_count = np.zeros(alph_t, dtype=int)
+        s12_count = np.zeros(alph_s12, dtype=int)
+        joint_t_s12_count = np.zeros((alph_t, alph_s12), dtype=int)
 
         num_samples = len(t)
 
@@ -487,10 +499,11 @@ 
    Source code for idtxl.estimators_pid
                 s12_count[s12[obs]] += 1
             joint_t_s12_count[t[obs], s12[obs]] += 1
 
-        t_prob = np.divide(t_count, num_samples).astype('longdouble')
-        s12_prob = np.divide(s12_count, num_samples).astype('longdouble')
-        joint_t_s12_prob = np.divide(joint_t_s12_count,
-                                     num_samples).astype('longdouble')
+        t_prob = np.divide(t_count, num_samples).astype("longdouble")
+        s12_prob = np.divide(s12_count, num_samples).astype("longdouble")
+        joint_t_s12_prob = np.divide(joint_t_s12_count, num_samples).astype(
+            "longdouble"
+        )
 
         return self._mi_prob(t_prob, s12_prob, joint_t_s12_prob)
    
 
@@ -542,9 +555,9 @@ 
    Source code for idtxl.estimators_pid
         def __init__(self, settings):
         # get estimation parameters
         self.settings = settings.copy()
-        self.settings.setdefault('verbose', False)
-        self.settings.setdefault('cone_solver', 'ECOS')
-        self.settings.setdefault('solver_args', {'keep_solver_object': False})
+        self.settings.setdefault("verbose", False)
+        self.settings.setdefault("cone_solver", "ECOS")
+        self.settings.setdefault("solver_args", {"keep_solver_object": False})
 
 
    [docs]    def is_parallel():
         return False
    
@@ -569,18 +582,20 @@ 
    Source code for idtxl.estimators_pid
             s1, s2, t, self.settings = _check_input(s1, s2, t, self.settings)
         pdf = _get_pdf_dict(s1, s2, t)
 
-        retval = synergy_tartu.pid(pdf_dirty=pdf,
-                                   cone_solver=self.settings['cone_solver'],
-                                   output=int(self.settings['verbose']),
-                                   **self.settings['solver_args'])
+        retval = synergy_tartu.pid(
+            pdf_dirty=pdf,
+            cone_solver=self.settings["cone_solver"],
+            output=int(self.settings["verbose"]),
+            **self.settings["solver_args"]
+        )
 
         results = {
-            'num_err': retval['Num_err'],
-            'solver': retval['Solver'],
-            'shd_s1_s2': retval['SI'],
-            'syn_s1_s2': retval['CI'],
-            'unq_s1': retval['UIY'],
-            'unq_s2': retval['UIZ'],
+            "num_err": retval["Num_err"],
+            "solver": retval["Solver"],
+            "shd_s1_s2": retval["SI"],
+            "syn_s1_s2": retval["CI"],
+            "unq_s1": retval["UIY"],
+            "unq_s2": retval["UIZ"],
         }
         return results
    
 
@@ -607,9 +622,8 @@ 
    Source code for idtxl.estimators_pid
     def _check_input(s1, s2, t, settings):
     """Check input to PID estimators."""
     # Check if inputs are numpy arrays.
-    if (type(s1) != np.ndarray or type(s2) != np.ndarray or
-            type(t) != np.ndarray):
-        raise TypeError('All inputs, s1, s2, t, must be numpy arrays.')
+    if type(s1) != np.ndarray or type(s2) != np.ndarray or type(t) != np.ndarray:
+        raise TypeError("All inputs, s1, s2, t, must be numpy arrays.")
 
     # In general, IDTxl expects 2D inputs because JIDT/JPYPE only accepts those
     # and we have a multivariate approach, i.e., a vector is a special case of
@@ -624,12 +638,12 @@ 
    Source code for idtxl.estimators_pid
                 alph_new = len(np.unique(s1[:, 0]))
             for col in range(1, s1.shape[1]):
                 alph_col = len(np.unique(s1[:, col]))
-                s1_joint, alph_new = _join_variables(s1_joint, s1[:, col],
-                                                     alph_new, alph_col)
-            settings['alph_s1'] = alph_new
+                s1_joint, alph_new = _join_variables(
+                    s1_joint, s1[:, col], alph_new, alph_col
+                )
+            settings["alph_s1"] = alph_new
         else:
-            raise ValueError('Input source 1 s1 has to be a 1D or 2D numpy '
-                             'array.')
+            raise ValueError("Input source 1 s1 has to be a 1D or 2D numpy " "array.")
 
     if s2.ndim != 1:
         if s2.shape[1] == 1:
@@ -639,36 +653,34 @@ 
    Source code for idtxl.estimators_pid
                 alph_new = len(np.unique(s2[:, 0]))
             for col in range(1, s2.shape[1]):
                 alph_col = len(np.unique(s2[:, col]))
-                s2_joint, alph_new = _join_variables(s2_joint, s2[:, col],
-                                                     alph_new, alph_col)
-            settings['alph_s2'] = alph_new
+                s2_joint, alph_new = _join_variables(
+                    s2_joint, s2[:, col], alph_new, alph_col
+                )
+            settings["alph_s2"] = alph_new
         else:
-            raise ValueError('Input source 2 s2 has to be a 1D or 2D numpy '
-                             'array.')
+            raise ValueError("Input source 2 s2 has to be a 1D or 2D numpy " "array.")
     if t.ndim != 1:
         if t.shape[1] == 1:
             t = np.squeeze(t)
         else:  # For now we only allow 1D-targets
-            raise ValueError('Input target t has to be a vector '
-                             '(t.shape[1]=1).')
+            raise ValueError("Input target t has to be a vector " "(t.shape[1]=1).")
 
     # Check types of remaining inputs.
     if type(settings) != dict:
-        raise TypeError('The settings argument should be a dictionary.')
+        raise TypeError("The settings argument should be a dictionary.")
 
     if not issubclass(s1.dtype.type, np.integer):
-        raise TypeError('Input s1 (source 1) must be an integer numpy array.')
+        raise TypeError("Input s1 (source 1) must be an integer numpy array.")
     if not issubclass(s2.dtype.type, np.integer):
-        raise TypeError('Input s2 (source 2) must be an integer numpy array.')
+        raise TypeError("Input s2 (source 2) must be an integer numpy array.")
     if not issubclass(t.dtype.type, np.integer):
-        raise TypeError('Input t (target) must be an integer numpy array.')
+        raise TypeError("Input t (target) must be an integer numpy array.")
 
     # Check if variables have equal length.
-    if (len(t) != len(s1) or len(t) != len(s2)):
-        raise ValueError('Number of samples s1, s2 and t must be equal')
+    if len(t) != len(s1) or len(t) != len(s2):
+        raise ValueError("Number of samples s1, s2 and t must be equal")
 
     return s1, s2, t, settings
-
 
    
 
             
    
@@ -681,7 +693,7 @@ 
    Source code for idtxl.estimators_pid
       
    Quick search
    
     
    
     
    
-      
+      
       
     
    
     
    
@@ -700,14 +712,14 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5.1 documentation »
    • 
           
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    • 
         
  • idtxl.estimators_pid
    •  
       
     
    
     
   
 
\ No newline at end of file
diff --git a/docs/html/_modules/idtxl/estimators_python.html b/docs/html/_modules/idtxl/estimators_python.html
index c9eedf6e..ef7d8042 100644
--- a/docs/html/_modules/idtxl/estimators_python.html
+++ b/docs/html/_modules/idtxl/estimators_python.html
@@ -5,7 +5,7 @@
   
     
     
-    idtxl.estimators_python — IDTxl 1.5 documentation
+    idtxl.estimators_python — IDTxl 1.5.1 documentation
     
     
     
@@ -31,7 +31,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.5 documentation »
    • 
+        
  • IDTxl 1.5.1 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.estimators_python
    •  
       
@@ -50,40 +50,62 @@ 
    Source code for idtxl.estimators_python
     from idtxl.estimator import Estimator
 from idtxl.knn.knn_finder_factory import get_knn_finder
 
+
 
    [docs]class PythonKraskovCMI(Estimator):
     """Estimate conditional mutual information using Kraskov's first estimator.
+
+    Args:
+        settings : dict [optional]
+            set estimator parameters:
+
+            - kraskov_k : int [optional] - no. nearest neighbours for KNN
+              search (default=4)
+            - base : float - base of returned values (default=np=e)
+            - normalise : bool [optional] - z-standardise data (default=False)
+            - noise_level : float [optional] - random noise added to the data
+              (default=1e-8)
+            - rng_seed : int | None [optional] - random seed if noise level > 0
+            - num_threads : int | str [optional] - number of threads used for
+              estimation (default='USE_ALL', note that this uses *all*
+              available threads on the current machine)
+            - knn_finder : str [optional] - knn algorithm to use, can be
+              'scipy_kdtree' (default), 'sklearn_kdtree', or 'sklearn_balltree'
     """
 
     def __init__(self, settings):
-        """Initialise estimator with settings.
-        """
+        """Initialise estimator with settings."""
 
         # Check for currently unsupported settings
-        if 'local_values' in settings or 'theiler_t' in settings or 'algorithm_num' in settings:
-            raise ValueError('This estimator currently does not support local_values, theiler_t or algorithm_num arguments.')
+        if (
+            "local_values" in settings
+            or "theiler_t" in settings
+            or "algorithm_num" in settings
+        ):
+            raise ValueError(
+                "This estimator currently does not support local_values, theiler_t or algorithm_num arguments."
+            )
 
-        self._knn_finder_settings = settings.get('knn_finder_settings', {})
+        self._knn_finder_settings = settings.get("knn_finder_settings", {})
 
-        self._kraskov_k = settings.get('kraskov_k', 4)
-        self._base = settings.get('base', np.e)
-        self._normalise = settings.get('normalise', False)
+        self._kraskov_k = settings.get("kraskov_k", 4)
+        self._base = settings.get("base", np.e)
+        self._normalise = settings.get("normalise", False)
 
         # Set number of threads
-        num_threads = settings.get('num_threads', -1)
-        if num_threads == 'USE_ALL':
+        num_threads = settings.get("num_threads", -1)
+        if num_threads == "USE_ALL":
             num_threads = -1
-        self._knn_finder_settings['num_threads'] = num_threads
+        self._knn_finder_settings["num_threads"] = num_threads
 
         # Init rng for added gaussian noise
-        self._noise_level = settings.get('noise_level', 1e-8)
+        self._noise_level = settings.get("noise_level", 1e-8)
         if self._noise_level > 0:
-            rng_seed = settings.get('rng_seed', None)
+            rng_seed = settings.get("rng_seed", None)
             self._rng = np.random.default_rng(rng_seed)
 
         # Get KNN finder class
-        self._knn_finder_name = settings.get('knn_finder', 'scipy_kdtree')
+        self._knn_finder_name = settings.get("knn_finder", "scipy_kdtree")
         self._knn_finder_class = get_knn_finder(self._knn_finder_name)
-        
 
 
    [docs]    def estimate(self, var1: np.ndarray, var2: np.ndarray, conditional=None):
         """Estimate conditional mutual information between var1 and var2, given
@@ -93,19 +115,20 @@ 
    Source code for idtxl.estimators_python
             if conditional is None:
             conditional = np.empty((len(var1), 0))
 
-
         # Check the input data
         var1 = self._ensure_two_dim_input(var1)
         var2 = self._ensure_two_dim_input(var2)
         conditional = self._ensure_two_dim_input(conditional)
 
-        assert var1.shape[0] == var2.shape[0] == conditional.shape[0], \
-            f'Unequal number of observations (var1: {var1.shape[0]}, var2: {var2.shape[0]}, conditional: {conditional.shape[0]})'
-        
+        assert (
+            var1.shape[0] == var2.shape[0] == conditional.shape[0]
+        ), f"Unequal number of observations (var1: {var1.shape[0]}, var2: {var2.shape[0]}, conditional: {conditional.shape[0]})"
 
         # Check if number of points is sufficient for estimation.
         if var1.shape[0] - 1 < self._kraskov_k:
-            raise ValueError(f'Not enough observations for Kraskov estimator (need at least {self._kraskov_k + 1}, got {var1.shape[0]}).')
+            raise ValueError(
+                f"Not enough observations for Kraskov estimator (need at least {self._kraskov_k + 1}, got {var1.shape[0]})."
+            )
 
         # Normalise data
         if self._normalise:
@@ -118,10 +141,14 @@ 
    Source code for idtxl.estimators_python
             if self._noise_level > 0:
             var1 = var1 + self._rng.normal(0, self._noise_level, var1.shape)
             var2 = var2 + self._rng.normal(0, self._noise_level, var2.shape)
-            conditional = conditional + self._rng.normal(0, self._noise_level, conditional.shape)
+            conditional = conditional + self._rng.normal(
+                0, self._noise_level, conditional.shape
+            )
 
         # Compute distances to kth nearest neighbors in the joint space
-        epsilon = self._compute_epsilon(np.concatenate((var1, var2, conditional), axis=1), self._kraskov_k)
+        epsilon = self._compute_epsilon(
+            np.concatenate((var1, var2, conditional), axis=1), self._kraskov_k
+        )
 
         # Count neighbors in the conditional space
         if conditional.shape[1] > 0:
@@ -139,38 +166,42 @@ 
    Source code for idtxl.estimators_python
     
         if conditional.shape[1] > 0:
             # Compute CMI
-            return (digamma(self._kraskov_k)
-                 + mean_digamma_nc
-                 - mean_digamma_nc_var1
-                 - mean_digamma_nc_var2
-                ) / np.log(self._base)
+            return (
+                digamma(self._kraskov_k)
+                + mean_digamma_nc
+                - mean_digamma_nc_var1
+                - mean_digamma_nc_var2
+            ) / np.log(self._base)
         else:
             # Compute MI
-            return (digamma(self._kraskov_k)
-                 + digamma(len(var1))
-                 - mean_digamma_nc_var1
-                 - mean_digamma_nc_var2
-                ) / np.log(self._base)
    
-        
+            return (
+                digamma(self._kraskov_k)
+                + digamma(len(var1))
+                - mean_digamma_nc_var1
+                - mean_digamma_nc_var2
+            ) / np.log(self._base)
    
+
     def _normalise_data(self, data: np.ndarray):
         """Standardise data to zero mean and unit variance."""
         return (data - np.mean(data, axis=0)) / np.std(data, axis=0)
-    
+
     def _compute_epsilon(self, data: np.ndarray, k: int):
         """Compute the distance to the kth nearest neighbor for each point in x."""
         knn_finder = self._knn_finder_class(data, **self._knn_finder_settings)
-        return knn_finder.find_dist_to_kth_neighbor(data, k + 1) # +1 because the point itself is included in the data
-    
+        return knn_finder.find_dist_to_kth_neighbor(
+            data, k + 1
+        )  # +1 because the point itself is included in the data
+
     def _compute_n(self, data: np.ndarray, r: np.ndarray):
         """Count the number of neighbors strictly within a given radius r for each point in x.
         Returns the number of neighbors plus one, because the point itself is included in the data.
         """
         knn_finder = self._knn_finder_class(data, **self._knn_finder_settings)
         return knn_finder.count_neighbors(data, r)
-    
+
 
    [docs]    def is_analytic_null_estimator(self):
         return False
    
-    
+
 
    [docs]    def is_parallel(self):
         return False
    
 
    
@@ -204,7 +235,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.5 documentation »
    • 
+        
  • IDTxl 1.5.1 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.estimators_python
    •  
       
diff --git a/docs/html/_modules/idtxl/idtxl_exceptions.html b/docs/html/_modules/idtxl/idtxl_exceptions.html
index 17100703..fab56512 100644
--- a/docs/html/_modules/idtxl/idtxl_exceptions.html
+++ b/docs/html/_modules/idtxl/idtxl_exceptions.html
@@ -5,14 +5,13 @@
   
     
     
-    idtxl.idtxl_exceptions — IDTxl 1.4 documentation
-    
-    
-    
+    idtxl.idtxl_exceptions — IDTxl 1.5.1 documentation
+    
+    
+    
     
     
     
-    
     
     
 
@@ -32,7 +31,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5.1 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.idtxl_exceptions
    •  
       
@@ -61,10 +60,11 @@ 
    Source code for idtxl.idtxl_exceptions
         """Exception raised to signal that the estimators can no longer be used
     for this particular target (e.g. because of memory errors in high
     dimensions) but that the estimation could continue for others.
-    
+
     Attributes:
         message -- explanation of the error
     """
+
     def __init__(self, message):
         self.message = message
    
 
@@ -72,11 +72,11 @@ 
    Source code for idtxl.idtxl_exceptions
     
    [docs]class JidtOutOfMemoryError(AlgorithmExhaustedError):
     """Exception raised to signal a Java OutOfMemoryException.
        It is a child class of AlgorithmExhaustedError.
-    
+
     Attributes:
         message -- explanation of the error
     """
-    
+
     def __init__(self, message):
         super().__init__(message)
    
 
@@ -95,7 +95,7 @@ 
    Source code for idtxl.idtxl_exceptions
       
    Quick search
    
     
    
     
    
-      
+      
       
     
    
     
    
@@ -114,14 +114,14 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5.1 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.idtxl_exceptions
    •  
       
     
    
     
   
 
\ No newline at end of file
diff --git a/docs/html/_modules/idtxl/idtxl_io.html b/docs/html/_modules/idtxl/idtxl_io.html
index 18ee79a2..6883e51b 100644
--- a/docs/html/_modules/idtxl/idtxl_io.html
+++ b/docs/html/_modules/idtxl/idtxl_io.html
@@ -5,7 +5,7 @@
   
     
     
-    idtxl.idtxl_io — IDTxl 1.5 documentation
+    idtxl.idtxl_io — IDTxl 1.5.1 documentation
     
     
     
@@ -31,7 +31,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.5 documentation »
    • 
+        
  • IDTxl 1.5.1 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.idtxl_io
    •  
       
@@ -59,14 +59,18 @@ 
    Source code for idtxl.idtxl_io
     from scipy.io import loadmat
 from .data import Data
 from . import idtxl_exceptions as ex
+
 try:
     import networkx as nx
 except ImportError as err:
     ex.package_missing(
         err,
-        ('networkx is not available on this system. Install it from '
-         'https://pypi.python.org/pypi/networkx/2.0 to export and plot IDTxl '
-         'results in this format.'))
+        (
+            "networkx is not available on this system. Install it from "
+            "https://pypi.python.org/pypi/networkx/2.0 to export and plot IDTxl "
+            "results in this format."
+        ),
+    )
 
 DEBUG = False
 
@@ -86,7 +90,7 @@ 
    Source code for idtxl.idtxl_io
         basic Python data types first.
     """
     data_json = _remove_numpy(d)
-    with open(file_path, 'w') as outfile:
+    with open(file_path, "w") as outfile:
         json.dump(obj=data_json, fp=outfile, sort_keys=True)
    
 
 
@@ -120,7 +124,7 @@ 
    Source code for idtxl.idtxl_io
         data_json = cp.copy(data)
     for k in data_json.keys():
         if DEBUG:
-            print('{0}, type: {1}'.format(data_json[k], type(data_json[k])))
+            print("{0}, type: {1}".format(data_json[k], type(data_json[k])))
         if type(data_json[k]) is np.ndarray:
             data_json[k] = data_json[k].tolist()
     return data_json
@@ -178,7 +182,6 @@ 
    Source code for idtxl.idtxl_io
     #         return d
 
 
-
 
    [docs]def save_pickle(obj, name):
     """Save objects using Python's pickle module.
 
@@ -186,13 +189,13 @@ 
    Source code for idtxl.idtxl_io
             pickle.HIGHEST_PROTOCOL is a binary format, which may be inconvenient,
         but is good for performance. Protocol 0 is a text format.
     """
-    with open(name, 'wb') as f:
+    with open(name, "wb") as f:
         pickle.dump(obj, f, pickle.HIGHEST_PROTOCOL)
    
 
 
 
    [docs]def load_pickle(name):
     """Load objects that have been saved using Python's pickle module."""
-    with open(name, 'rb') as f:
+    with open(name, "rb") as f:
         return pickle.load(f)
    
 
 
@@ -233,19 +236,22 @@ 
    Source code for idtxl.idtxl_io
                 sampling rate, corresponding to the 'fsample' field
     """
     if file_version != "v7.3":
-        raise RuntimeError('At present only m-files in format 7.3 are '
-                           'supported, please consider reopening and resaving '
-                           'your m-file in that version.')
+        raise RuntimeError(
+            "At present only m-files in format 7.3 are "
+            "supported, please consider reopening and resaving "
+            "your m-file in that version."
+        )
         # TODO we could write a fallback option using numpy's loadmat?
 
-    print('Creating Python dictionary from FT data structure: {0}'
-          .format(ft_struct_name))
+    print(
+        "Creating Python dictionary from FT data structure: {0}".format(ft_struct_name)
+    )
     trial_data = _ft_import_trial(file_name, ft_struct_name)
     label = _ft_import_label(file_name, ft_struct_name)
     fsample = _ft_fsample_2_float(file_name, ft_struct_name)
     timestamps = _ft_import_time(file_name, ft_struct_name)
 
-    data = Data(data=trial_data, dim_order='spr', normalise=normalise)
+    data = Data(data=trial_data, dim_order="spr", normalise=normalise)
     return data, label, timestamps, fsample
    
 
 
@@ -257,18 +263,21 @@ 
    Source code for idtxl.idtxl_io
         # Get the trial cells that contain the references (pointers) to the data
     # we need. Then get the data from matrices in cells of a 1 x numtrials cell
     # array in the original FieldTrip structure.
-    trial = ft_struct['trial']
+    trial = ft_struct["trial"]
 
     # Get the trial cells that contain the references (pointers) to the data
     # we need. Then get the data from matrices in cells of a 1 x numtrials cell
     # array in the original FieldTrip structure.
-    trial = ft_struct['trial']
+    trial = ft_struct["trial"]
 
     # Allocate memory to hold actual data, read shape of first trial to know
     # the data size.
     trial_data_tmp = np.array(ft_file[trial[0][0]])  # get data from 1st trial
-    print('Found data with first dimension: {0}, and second: {1}'
-          .format(trial_data_tmp.shape[0], trial_data_tmp.shape[1]))
+    print(
+        "Found data with first dimension: {0}, and second: {1}".format(
+            trial_data_tmp.shape[0], trial_data_tmp.shape[1]
+        )
+    )
     geometry = trial_data_tmp.shape + (trial.shape[0],)
     trial_data = np.empty(geometry)
 
@@ -286,10 +295,10 @@ 
    Source code for idtxl.idtxl_io
         # for details of the data handling see comments in _ft_import_trial
     ft_file = h5py.File(file_name)
     ft_struct = ft_file[ft_struct_name]
-    ft_label = ft_struct['label']
+    ft_label = ft_struct["label"]
 
     if DEBUG:
-        print('Converting FT labels to python list of strings')
+        print("Converting FT labels to python list of strings")
 
     label = []
     for ll in range(0, ft_label.shape[0]):
@@ -311,9 +320,9 @@ 
    Source code for idtxl.idtxl_io
         # for details of the data handling see comments in ft_trial_2_numpyarray
     ft_file = h5py.File(file_name)
     ft_struct = ft_file[ft_struct_name]
-    ft_time = ft_struct['time']
+    ft_time = ft_struct["time"]
     if DEBUG:
-        print('Converting FT time cell array to numpy array')
+        print("Converting FT time cell array to numpy array")
 
     np_timeaxis_tmp = np.array(ft_file[ft_time[0][0]])
     geometry = np_timeaxis_tmp.shape + (ft_time.shape[0],)
@@ -328,15 +337,14 @@ 
    Source code for idtxl.idtxl_io
     def _ft_fsample_2_float(file_name, ft_struct_name):
     ft_file = h5py.File(file_name)
     ft_struct = ft_file[ft_struct_name]
-    FTfsample = ft_struct['fsample']
+    FTfsample = ft_struct["fsample"]
     fsample = int(FTfsample[0])
     if DEBUG:
-        print('Converting FT fsample array (1x1) to numpy array (1x1)')
+        print("Converting FT fsample array (1x1) to numpy array (1x1)")
     return fsample
 
 
-
    [docs]def import_matarray(file_name, array_name, file_version, dim_order,
-                    normalise=True):
+
    [docs]def import_matarray(file_name, array_name, file_version, dim_order, normalise=True):
     """Read Matlab hdf5 file into IDTxl.
 
     reads a matlab hdf5 file ("-v7.3' or higher, .mat) or non-hdf5 files with a
@@ -370,32 +378,37 @@ 
    Source code for idtxl.idtxl_io
                 instance of IDTxl Data object, containing data from the 'trial'
             field
     """
-    if file_version == 'v7.3':
+    if file_version == "v7.3":
         mat_file = h5py.File(file_name)
         # Assert that at least one of the keys found at the top level of the
         # HDF file  matches the name of the array we wanted
         if array_name not in mat_file.keys():
-            raise RuntimeError('Array {0} not in mat file or not a variable '
-                               'at the file''s top level.'.format(array_name))
+            raise RuntimeError(
+                "Array {0} not in mat file or not a variable "
+                "at the file"
+                "s top level.".format(array_name)
+            )
 
         # 2. Create an object for the matlab array (from the hdf5 hierachy),
         # the trailing [()] ensures everything is read
         mat_data = np.squeeze(np.asarray(mat_file[array_name][()]))
 
-    elif file_version in ['v4', 'v6', 'v7']:
+    elif file_version in ["v4", "v6", "v7"]:
         try:
             m = loadmat(file_name, squeeze_me=True, variable_names=array_name)
         except NotImplementedError:
-            raise RuntimeError('You may have provided an incorrect file '
-                               'version. The mat file was probably saved as '
-                               'version 7.3 (hdf5).')
+            raise RuntimeError(
+                "You may have provided an incorrect file "
+                "version. The mat file was probably saved as "
+                "version 7.3 (hdf5)."
+            )
         mat_data = m[array_name]  # loadmat returns a dict containing variables
     else:
-        raise ValueError('Unkown file version: {0}.'.format(file_version))
+        raise ValueError("Unkown file version: {0}.".format(file_version))
 
     # Create output: IDTxl data object, list of labels, sampling info in unit
     # time steps (sampling rate of 1).
-    print('Creating Data object from matlab array: {0}.'.format(array_name))
+    print("Creating Data object from matlab array: {0}.".format(array_name))
     data = Data(mat_data, dim_order=dim_order, normalise=normalise)
     return data
    
 
@@ -459,39 +472,45 @@ 
    Source code for idtxl.idtxl_io
         # Replace time index of current value to be consistent with lag-notation
     # in exported graph. Remember the current value's index to later define the
     # proper candidate set.
-    current_value = (results.get_single_target(
-        target=target, fdr=fdr)['current_value'][0], 0)
-    idx_current_value = results.get_single_target(
-        target=target, fdr=fdr)['current_value'][1]
+    current_value = (
+        results.get_single_target(target=target, fdr=fdr)["current_value"][0],
+        0,
+    )
+    idx_current_value = results.get_single_target(target=target, fdr=fdr)[
+        "current_value"
+    ][1]
     # Add the target as a node and add omnibus p-value as an attribute
     # of the target node
-    graph.add_node(current_value,
-                   omnibus_te=results.get_single_target(
-                                target=target, fdr=fdr)['omnibus_te'],
-                   omnibus_sign=results.get_single_target(
-                                target=target, fdr=fdr)['omnibus_te'])
+    graph.add_node(
+        current_value,
+        omnibus_te=results.get_single_target(target=target, fdr=fdr)["omnibus_te"],
+        omnibus_sign=results.get_single_target(target=target, fdr=fdr)["omnibus_te"],
+    )
     # Get selected source variables
-    selected_vars_sources = results.get_single_target(
-        target=target, fdr=fdr)['selected_vars_sources']
+    selected_vars_sources = results.get_single_target(target=target, fdr=fdr)[
+        "selected_vars_sources"
+    ]
     # Get selected target variables
-    selected_vars_target = results.get_single_target(
-        target=target, fdr=fdr)['selected_vars_target']
+    selected_vars_target = results.get_single_target(target=target, fdr=fdr)[
+        "selected_vars_target"
+    ]
 
     if sign_sources:  # Add only significant past variables as nodes.
         graph.add_nodes_from(selected_vars_sources)
         graph.add_nodes_from(selected_vars_target)
-    else:   # Add all tested past variables as nodes.
+    else:  # Add all tested past variables as nodes.
         # Get all sample indices using the current value's actual index.
         samples_tested = np.arange(
             idx_current_value - results.settings.min_lag_sources,
             idx_current_value - results.settings.max_lag_sources,
-            -results.settings.tau_sources)
+            -results.settings.tau_sources,
+        )
         # Get source indices
-        sources_tested = results.get_single_target(
-            target=target, fdr=fdr)['sources_tested']
+        sources_tested = results.get_single_target(target=target, fdr=fdr)[
+            "sources_tested"
+        ]
         # Create tuples from source and sample indices
-        tested_vars_sources = [i for i in it.product(
-            sources_tested, samples_tested)]
+        tested_vars_sources = [i for i in it.product(sources_tested, samples_tested)]
         graph.add_nodes_from(tested_vars_sources)
 
     # Add edges from selected target variables to the target.
@@ -499,16 +518,21 @@ 
    Source code for idtxl.idtxl_io
             graph.add_edge(v, current_value)
 
     # Get TE and p-values fro selected source variables
-    selected_sources_te = results.get_single_target(
-        target=target, fdr=fdr)['selected_sources_te']
-    selected_sources_pval = results.get_single_target(
-        target=target, fdr=fdr)['selected_sources_pval']
+    selected_sources_te = results.get_single_target(target=target, fdr=fdr)[
+        "selected_sources_te"
+    ]
+    selected_sources_pval = results.get_single_target(target=target, fdr=fdr)[
+        "selected_sources_pval"
+    ]
     # Add edges from selected source variables to the target.
     # Also add TE and p-value as edge attributes
-    for (ind, v) in enumerate(selected_vars_sources):
-        graph.add_edge(v, current_value,
-                       te=selected_sources_te[ind],
-                       pval=selected_sources_pval[ind])
+    for ind, v in enumerate(selected_vars_sources):
+        graph.add_edge(
+            v,
+            current_value,
+            te=selected_sources_te[ind],
+            pval=selected_sources_pval[ind],
+        )
     return graph
    
 
 
@@ -553,40 +577,41 @@ 
    Source code for idtxl.idtxl_io
         # node labels is a list of '-' (no labels).
     n_nodes = adjacency_matrix.n_nodes()
     n_edges = adjacency_matrix.n_edges()
-    labels = kwargs.get('labels', ['-' for i in range(n_nodes)])
-    node_color = kwargs.get('node_color', np.ones(n_nodes))
-    node_size = kwargs.get('node_size', np.ones(n_nodes))
+    labels = kwargs.get("labels", ["-" for i in range(n_nodes)])
+    node_color = kwargs.get("node_color", np.ones(n_nodes))
+    node_size = kwargs.get("node_size", np.ones(n_nodes))
     if n_edges == 0:
-        Warning('No edges in results file. Nothing to plot.')
-    assert mni_coord.shape[0] == n_nodes and mni_coord.shape[1] == 3, (
-        'MNI coordinates must have shape [n_nodes, 3].')
-    assert len(labels) == n_nodes, (
-        'Labels must have same length as no. nodes.')
-    assert len(node_color) == n_nodes, (
-        'Node colors must have same length as no. nodes.')
-    assert len(node_size) == n_nodes, (
-        'Node size must have same length as no. nodes.')
+        Warning("No edges in results file. Nothing to plot.")
+    assert (
+        mni_coord.shape[0] == n_nodes and mni_coord.shape[1] == 3
+    ), "MNI coordinates must have shape [n_nodes, 3]."
+    assert len(labels) == n_nodes, "Labels must have same length as no. nodes."
+    assert len(node_color) == n_nodes, "Node colors must have same length as no. nodes."
+    assert len(node_size) == n_nodes, "Node size must have same length as no. nodes."
 
     # Check, if there are blanks in the labels and delete them, otherwise
     # BrainNet viewer chrashes
     labels_stripped = [l.replace(" ", "") for l in labels]
 
     # Write node file.
-    with open('{0}.node'.format(file_name), 'w') as text_file:
+    with open("{0}.node".format(file_name), "w") as text_file:
         for n in range(n_nodes):
-            print('{0}\t{1}\t{2}\t'.format(*mni_coord[n, :]),
-                  file=text_file, end='')
-            print('{0}\t{1}\t'.format(node_color[n], node_size[n]),
-                  file=text_file, end='')
-            print('{0}'.format(labels_stripped[n]), file=text_file)
+            print("{0}\t{1}\t{2}\t".format(*mni_coord[n, :]), file=text_file, end="")
+            print(
+                "{0}\t{1}\t".format(node_color[n], node_size[n]), file=text_file, end=""
+            )
+            print("{0}".format(labels_stripped[n]), file=text_file)
 
     # Write edge file.
-    with open('{0}.edge'.format(file_name), 'w') as text_file:
+    with open("{0}.edge".format(file_name), "w") as text_file:
         for i in range(n_nodes):
             for j in range(n_nodes):
-                print('{0}\t'.format(adjacency_matrix.edge_matrix[i, j]),
-                      file=text_file, end='')
-            print('', file=text_file)
    
+                print(
+                    "{0}\t".format(adjacency_matrix.edge_matrix[i, j]),
+                    file=text_file,
+                    end="",
+                )
+            print("", file=text_file)
    
 
    
 
             
    
@@ -618,7 +643,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.5 documentation »
    • 
+        
  • IDTxl 1.5.1 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.idtxl_io
    •  
       
diff --git a/docs/html/_modules/idtxl/idtxl_utils.html b/docs/html/_modules/idtxl/idtxl_utils.html
index 0da3b5e1..8e8fc0c2 100644
--- a/docs/html/_modules/idtxl/idtxl_utils.html
+++ b/docs/html/_modules/idtxl/idtxl_utils.html
@@ -5,7 +5,7 @@
   
     
     
-    idtxl.idtxl_utils — IDTxl 1.5 documentation
+    idtxl.idtxl_utils — IDTxl 1.5.1 documentation
     
     
     
@@ -31,7 +31,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.5 documentation »
    • 
+        
  • IDTxl 1.5.1 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.idtxl_utils
    •  
       
@@ -59,7 +59,7 @@ 
    Source code for idtxl.idtxl_utils
         """
     if i_1 > i_2:
         i_1, i_2 = i_2, i_1
-    return ''.join([s[0:i_1], s[i_2], s[i_1+1:i_2], s[i_1], s[i_2+1:]])
    
+    return "".join([s[0:i_1], s[i_2], s[i_1 + 1 : i_2], s[i_1], s[i_2 + 1 :]])