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Navigation

  • modules |
    • -
  • IDTxl 1.4 documentation »
    • +
  • IDTxl 1.5 documentation »
  • Module code »
  • idtxl.active_information_storage
    • @@ -678,7 +677,7 @@

    Source code for idtxl.active_information_storage

    Quick search

    - +
    @@ -697,14 +696,14 @@

    Navigation

  • modules |
    • -
  • IDTxl 1.4 documentation »
    • +
  • IDTxl 1.5 documentation »
  • Module code »
  • idtxl.active_information_storage
    • \ 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 816816b8..2a06b5e8 100644 --- a/docs/html/_modules/idtxl/bivariate_pid.html +++ b/docs/html/_modules/idtxl/bivariate_pid.html @@ -5,14 +5,13 @@ - idtxl.bivariate_pid — IDTxl 1.4 documentation - - - + idtxl.bivariate_pid — IDTxl 1.5 documentation + + + - @@ -32,7 +31,7 @@

    Navigation

  • modules |
    • -
  • IDTxl 1.4 documentation »
    • +
  • IDTxl 1.5 documentation »
  • Module code »
  • idtxl.bivariate_pid
    • @@ -53,7 +52,7 @@

    Source code for idtxl.bivariate_pid

     """
 import numpy as np
 from .single_process_analysis import SingleProcessAnalysis
-from .estimator import find_estimator
+from .estimator import get_estimator
 from .results import ResultsPID
 
 
@@ -252,11 +251,8 @@ 
    Source code for idtxl.bivariate_pid
         def _initialise(self, settings, data, target, sources):
         """Check input, set initial or default values for analysis settings."""
         # Check requested PID estimator.
-        try:
-            EstimatorClass = find_estimator(settings['pid_estimator'])
-        except KeyError:
-            raise RuntimeError('Estimator was not specified!')
-        self._pid_estimator = EstimatorClass(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])
@@ -363,7 +359,7 @@ 
    Source code for idtxl.bivariate_pid
       
    Quick search
    
     
    
     
    
-      
+      
       
     
    
     
    
@@ -382,14 +378,14 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
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    • 
         
  • idtxl.bivariate_pid
    •  
       
     
    
     
   
 
\ 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 f6664688..421ce0df 100644
--- a/docs/html/_modules/idtxl/estimators_Rudelt.html
+++ b/docs/html/_modules/idtxl/estimators_Rudelt.html
@@ -5,14 +5,13 @@
   
     
     
-    idtxl.estimators_Rudelt — IDTxl 1.4 documentation
-    
-    
-    
+    idtxl.estimators_Rudelt — IDTxl 1.5 documentation
+    
+    
+    
     
     
     
-    
     
     
 
@@ -32,7 +31,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.estimators_Rudelt
    •  
       
@@ -1187,7 +1186,7 @@ 
    Source code for idtxl.estimators_Rudelt
       
    Quick search
    
     
    
     
    
-      
+      
       
     
    
     
    
@@ -1206,14 +1205,14 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.estimators_Rudelt
    •  
       
     
    
     
   
 
\ No newline at end of file
diff --git a/docs/html/_modules/idtxl/estimators_jidt.html b/docs/html/_modules/idtxl/estimators_jidt.html
index d5118e74..7cf844b0 100644
--- a/docs/html/_modules/idtxl/estimators_jidt.html
+++ b/docs/html/_modules/idtxl/estimators_jidt.html
@@ -5,14 +5,13 @@
   
     
     
-    idtxl.estimators_jidt — IDTxl 1.4 documentation
-    
-    
-    
+    idtxl.estimators_jidt — IDTxl 1.5 documentation
+    
+    
+    
     
     
     
-    
     
     
 
@@ -32,7 +31,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5 documentation »
    • 
           
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    • 
         
  • idtxl.estimators_jidt
    •  
       
@@ -396,7 +395,6 @@ 
    Source code for idtxl.estimators_jidt
     
 
    [docs]    def estimate_surrogates_analytic(self, n_perm=200, **data):
         """Estimate the surrogate distribution analytically.
-
         This method must be implemented because this class'
         is_analytic_null_estimator() method returns true
 
@@ -1363,7 +1361,6 @@ 
    Source code for idtxl.estimators_jidt
     
     See parent class for references. Results are returned in nats.
 
-
     Args:
         settings : dict [optional]
             sets estimation parameters:
@@ -1858,7 +1855,7 @@ 
    Source code for idtxl.estimators_jidt
       
    Quick search
    
     
    
     
    
-      
+      
       
     
    
     
    
@@ -1877,14 +1874,14 @@ 
    Navigation
    
         
  • 
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-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5 documentation »
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    • 
         
  • idtxl.estimators_jidt
    •  
       
     
    
     
   
 
\ No newline at end of file
diff --git a/docs/html/_modules/idtxl/estimators_mpi.html b/docs/html/_modules/idtxl/estimators_mpi.html
new file mode 100644
index 00000000..4570af76
--- /dev/null
+++ b/docs/html/_modules/idtxl/estimators_mpi.html
@@ -0,0 +1,254 @@
+
+
+
+
+  
+    
+    
+    idtxl.estimators_mpi — IDTxl 1.5 documentation
+    
+    
+    
+    
+    
+    
+    
+    
+
+
+
+
+  
+
+      
+
+    
    
+      
    
+        
    
+          
    
+            
+  
    Source code for idtxl.estimators_mpi
    +from .estimator import Estimator
+from .estimator import get_estimator
+from . import idtxl_exceptions as ex
+from .idtxl_utils import timeout
+
+import numpy as np
+import itertools
+from uuid import uuid4
+
+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
+
+_worker_estimators = {}
+"""Estimator instances on worker ranks
+
+Used so that Estimators do not have to be created new for each task given to them.
+Estimators are indexed by the ID of the corresponding MPIEstimator instance on the MPI main rank.
+"""
+
+
+def _get_worker_estimator(id_, est, settings):
+    """Return Estimator instance on worker rank.
+    If no Estimator for the given MPIEstimator id exists, create a new one
+    """
+
+    # 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.
+        _worker_estimators.clear()
+
+        _worker_estimators[id_] = get_estimator(est, settings)
+
+    return _worker_estimators[id_]
+
+
+def _dispatch_task(id_, est, settings, data):
+    """Estimates a single chunk of data on an MPI worker rank.
+    Calls the estimate function of the base Estimator
+    """
+
+    estimator = _get_worker_estimator(id_, est, settings)
+
+    if estimator.is_parallel():
+        return estimator.estimate(n_chunks=1, **data)
+    else:
+        return estimator.estimate(**data)
+
+
+
    [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!
+
+    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>
+
+    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>
+
+    Call using slurm:
+    srun -n $SLURM_NTASKS --mpi=pmi2 python -m mpi4py.futures <python script> 
+
+    """
+
+    def __init__(self, est, settings):
+        """Creates new MPIEstimator instance
+
+        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
+        """
+
+        self._est = est
+        self._settings = self._check_settings(settings).copy()
+
+        # Create unique id for this instance to access cached estimators
+        self._id = uuid4().int
+
+        # Create the MPIPoolExecutor and initialize Estimators on worker ranks
+        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.'):
+            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
+        """
+
+        self._executor.shutdown()
+
+    def _chunk_data(self, data, chunksize, n_chunks):
+        """
+        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}
+
+
    [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
+        Returns:
+            numpy array: Estimates of information-theoretic quantities as np.double values
+        """
+
+        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 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)
+
+        return np.fromiter(result_generator, dtype=np.double)
    
+
+
    [docs]    def is_parallel(self):
+        return True
    
+
+
    [docs]    def is_analytic_null_estimator(self):
+        """Test if the base Estimator is an 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.
+        """
+
+        return _get_worker_estimator(self._id, self._est, self._settings).estimate_surrogates_analytic(**data)
    
+
    
+
+            
    
+          
    
+        
    
+      
    
+      
+      
    
+    
    
+    
+    
+  
+
\ No newline at end of file
diff --git a/docs/html/_modules/idtxl/estimators_python.html b/docs/html/_modules/idtxl/estimators_python.html
new file mode 100644
index 00000000..c9eedf6e
--- /dev/null
+++ b/docs/html/_modules/idtxl/estimators_python.html
@@ -0,0 +1,217 @@
+
+
+
+
+  
+    
+    
+    idtxl.estimators_python — IDTxl 1.5 documentation
+    
+    
+    
+    
+    
+    
+    
+    
+
+
+
+
+  
+
+      
+
+    
    
+      
    
+        
    
+          
    
+            
+  
    Source code for idtxl.estimators_python
    +import numpy as np
+
+from scipy.special import digamma
+
+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.
+    """
+
+    def __init__(self, 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.')
+
+        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)
+
+        # Set number of threads
+        num_threads = settings.get('num_threads', -1)
+        if num_threads == 'USE_ALL':
+            num_threads = -1
+        self._knn_finder_settings['num_threads'] = num_threads
+
+        # Init rng for added gaussian noise
+        self._noise_level = settings.get('noise_level', 1e-8)
+        if self._noise_level > 0:
+            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_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
+        conditional.
+        """
+
+        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]})'
+        
+
+        # 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]}).')
+
+        # Normalise data
+        if self._normalise:
+            var1 = self._normalise_data(var1)
+            var2 = self._normalise_data(var2)
+            conditional = self._normalise_data(conditional)
+
+        # Add noise to avoid duplicate points
+        # Do not add noise inplace, because it would change the input data
+        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)
+
+        # Compute distances to kth nearest neighbors in the joint space
+        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:
+            n_c = self._compute_n(conditional, epsilon)
+            mean_digamma_nc = np.mean(digamma(n_c))
+            del n_c
+
+        n_c_var1 = self._compute_n(np.concatenate((var1, conditional), axis=1), epsilon)
+        mean_digamma_nc_var1 = np.mean(digamma(n_c_var1))
+        del n_c_var1
+
+        n_c_var2 = self._compute_n(np.concatenate((var2, conditional), axis=1), epsilon)
+        mean_digamma_nc_var2 = np.mean(digamma(n_c_var2))
+        del n_c_var2
+
+        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)
+        else:
+            # Compute MI
+            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
+    
+    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
    
+
    
+
+            
    
+          
    
+        
    
+      
    
+      
+      
    
+    
    
+    
+    
+  
+
\ 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 441bea65..18ee79a2 100644
--- a/docs/html/_modules/idtxl/idtxl_io.html
+++ b/docs/html/_modules/idtxl/idtxl_io.html
@@ -5,14 +5,13 @@
   
     
     
-    idtxl.idtxl_io — IDTxl 1.4 documentation
-    
-    
-    
+    idtxl.idtxl_io — IDTxl 1.5 documentation
+    
+    
+    
     
     
     
-    
     
     
 
@@ -32,7 +31,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.idtxl_io
    •  
       
@@ -179,6 +178,7 @@ 
    Source code for idtxl.idtxl_io
     #         return d
 
 
+
 
    [docs]def save_pickle(obj, name):
     """Save objects using Python's pickle module.
 
@@ -599,7 +599,7 @@ 
    Source code for idtxl.idtxl_io
       
    Quick search
    
     
    
     
    
-      
+      
       
     
    
     
    
@@ -618,14 +618,14 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.idtxl_io
    •  
       
     
    
     
   
 
\ No newline at end of file
diff --git a/docs/html/_modules/idtxl/idtxl_utils.html b/docs/html/_modules/idtxl/idtxl_utils.html
index 580a6a39..0da3b5e1 100644
--- a/docs/html/_modules/idtxl/idtxl_utils.html
+++ b/docs/html/_modules/idtxl/idtxl_utils.html
@@ -5,14 +5,13 @@
   
     
     
-    idtxl.idtxl_utils — IDTxl 1.4 documentation
-    
-    
-    
+    idtxl.idtxl_utils — IDTxl 1.5 documentation
+    
+    
+    
     
     
     
-    
     
     
 
@@ -32,7 +31,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.idtxl_utils
    •  
       
@@ -46,7 +45,9 @@ 
    Navigation
    
   
    Source code for idtxl.idtxl_utils
     """Provide IDTxl utility functions."""
 import pprint
+import copy as cp
 import numpy as np
+import threading
 
 
 
    [docs]def swap_chars(s, i_1, i_2):
@@ -365,6 +366,27 @@ 
    Source code for idtxl.idtxl_utils
     
    [docs]def calculate_mi(corr):
     """Calculate mutual information from correlation coefficient."""
     return -0.5 * np.log(1 - corr**2)
    
+
+
    [docs]class timeout(object):
+    """Context manager for a timeout using threading module.
+    args:
+        timeout_duration: float, number of seconds to wait before timeout is triggered
+        exception_message: string, message to put in the exception
+    """
+    def __init__(self, timeout_duration, exception_message='Timeout'):
+        self.timeout_duration = timeout_duration
+        self.exception_message = exception_message
+
+    def __enter__(self):
+        self.timer = threading.Timer(self.timeout_duration, self.timeout_handler)
+        self.timer.start()
+        return self.timer
+
+    def __exit__(self, exc_type, exc_value, traceback):
+        self.timer.cancel()
+
+
    [docs]    def timeout_handler(self):
+        raise TimeoutError(self.exception_message)
    
 
    
 
             
    
@@ -377,7 +399,7 @@ 
    Source code for idtxl.idtxl_utils
       
    Quick search
    
     
    
     
    
-      
+      
       
     
    
     
    
@@ -396,14 +418,14 @@ 
    Navigation
    
         
  • 
           modules |
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-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.idtxl_utils
    •  
       
     
    
     
   
 
\ No newline at end of file
diff --git a/docs/html/_modules/idtxl/multivariate_pid.html b/docs/html/_modules/idtxl/multivariate_pid.html
index 77f13ea3..328c264f 100644
--- a/docs/html/_modules/idtxl/multivariate_pid.html
+++ b/docs/html/_modules/idtxl/multivariate_pid.html
@@ -5,14 +5,13 @@
   
     
     
-    idtxl.multivariate_pid — IDTxl 1.4 documentation
-    
-    
-    
+    idtxl.multivariate_pid — IDTxl 1.5 documentation
+    
+    
+    
     
     
     
-    
     
     
 
@@ -32,7 +31,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.multivariate_pid
    •  
       
@@ -54,7 +53,7 @@ 
    Source code for idtxl.multivariate_pid
     """
 import numpy as np
 from .single_process_analysis import SingleProcessAnalysis
-from .estimator import find_estimator
+from .estimator import get_estimator
 from .results import ResultsMultivariatePID
 
 
@@ -260,11 +259,8 @@ 
    Source code for idtxl.multivariate_pid
         def _initialise(self, settings, data, target, sources):
         """Check input, set initial or default values for analysis settings."""
         # Check requested PID estimator.
-        try:
-            EstimatorClass = find_estimator(settings['pid_estimator'])
-        except KeyError:
-            raise RuntimeError('Estimator was not specified!')
-        self._pid_estimator = EstimatorClass(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 for i in range(len(sources))])
@@ -367,7 +363,7 @@ 
    Source code for idtxl.multivariate_pid
       
    Quick search
    
     
    
     
    
-      
+      
       
     
    
     
    
@@ -386,14 +382,14 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.multivariate_pid
    •  
       
     
    
     
   
 
\ No newline at end of file
diff --git a/docs/html/_modules/idtxl/multivariate_te.html b/docs/html/_modules/idtxl/multivariate_te.html
index 299c1387..d637e5c7 100644
--- a/docs/html/_modules/idtxl/multivariate_te.html
+++ b/docs/html/_modules/idtxl/multivariate_te.html
@@ -5,14 +5,13 @@
   
     
     
-    idtxl.multivariate_te — IDTxl 1.4 documentation
-    
-    
-    
+    idtxl.multivariate_te — IDTxl 1.5 documentation
+    
+    
+    
     
     
     
-    
     
     
 
@@ -32,7 +31,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.multivariate_te
    •  
       
@@ -84,7 +83,6 @@ 
    Source code for idtxl.multivariate_te
           http://doi.org/10.1103/PhysRevE.83.051112
 
     Attributes:
-
         source_set : list
             indices of source processes tested for their influence on the
             target
@@ -385,7 +383,7 @@ 
    Source code for idtxl.multivariate_te
       
    Quick search
    
     
    
     
    
-      
+      
       
     
    
     
    
@@ -404,14 +402,14 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.multivariate_te
    •  
       
     
    
     
   
 
\ No newline at end of file
diff --git a/docs/html/_modules/idtxl/network_analysis.html b/docs/html/_modules/idtxl/network_analysis.html
index 58c8083a..f6ca12f0 100644
--- a/docs/html/_modules/idtxl/network_analysis.html
+++ b/docs/html/_modules/idtxl/network_analysis.html
@@ -5,14 +5,13 @@
   
     
     
-    idtxl.network_analysis — IDTxl 1.4 documentation
-    
-    
-    
+    idtxl.network_analysis — IDTxl 1.5 documentation
+    
+    
+    
     
     
     
-    
     
     
 
@@ -32,7 +31,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.network_analysis
    •  
       
@@ -54,7 +53,7 @@ 
    Source code for idtxl.network_analysis
     import copy as cp
 import itertools as it
 import numpy as np
-from .estimator import find_estimator
+from .estimator import get_estimator
 from . import idtxl_utils as utils
 from . import idtxl_io as io
 
@@ -248,17 +247,15 @@ 
    Source code for idtxl.network_analysis
             # average estimator. Internally, the average estimator is used for
         # building the non-uniform embedding, etc. The local estimator is used
         # to estimate single-link MI/TE or single-process AIS in the end.
-        try:
-            EstimatorClass = find_estimator(self.settings['cmi_estimator'])
-        except KeyError:
-            raise RuntimeError('Please provide an estimator class or name!')
+        assert 'cmi_estimator' in self.settings, 'Estimator was not specified!'
+
         if self.settings['local_values']:
             self.settings['local_values'] = False
-            self._cmi_estimator = EstimatorClass(self.settings)
+            self._cmi_estimator = get_estimator(self.settings['cmi_estimator'], self.settings)
             self.settings['local_values'] = True
-            self._cmi_estimator_local = EstimatorClass(self.settings)
+            self._cmi_estimator_local = get_estimator(self.settings['cmi_estimator'], self.settings)
         else:
-            self._cmi_estimator = EstimatorClass(self.settings)
+            self._cmi_estimator = get_estimator(self.settings['cmi_estimator'], self.settings)
 
     def _separate_realisations(self, idx_full, idx_single):
         """Separate single index realisations from a set of realisations.
@@ -545,16 +542,16 @@ 
    Source code for idtxl.network_analysis
     
             if self.settings['local_values']:
                 local_values = self._cmi_estimator_local.estimate(
-                    current_value_realisations,
-                    source_realisations,
-                    conditional_realisations)
+                    var1=current_value_realisations,
+                    var2=source_realisations,
+                    conditional=conditional_realisations)
                 links[i] = local_values.reshape(
                     max(replication_ind) + 1, sum(replication_ind == 0)).T
             else:
                 links[i] = self._cmi_estimator.estimate(
-                    current_value_realisations,
-                    source_realisations,
-                    conditional_realisations)
+                    var1=current_value_realisations,
+                    var2=source_realisations,
+                    conditional=conditional_realisations)
 
         return links
 
@@ -720,7 +717,7 @@ 
    Source code for idtxl.network_analysis
       
    Quick search
    
     
    
     
    
-      
+      
       
     
    
     
    
@@ -739,14 +736,14 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.network_analysis
    •  
       
     
    
     
   
 
\ No newline at end of file
diff --git a/docs/html/_modules/idtxl/network_comparison.html b/docs/html/_modules/idtxl/network_comparison.html
index 95f672f7..42a739ad 100644
--- a/docs/html/_modules/idtxl/network_comparison.html
+++ b/docs/html/_modules/idtxl/network_comparison.html
@@ -5,14 +5,13 @@
   
     
     
-    idtxl.network_comparison — IDTxl 1.4 documentation
-    
-    
-    
+    idtxl.network_comparison — IDTxl 1.5 documentation
+    
+    
+    
     
     
     
-    
     
     
 
@@ -32,7 +31,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.network_comparison
    •  
       
@@ -48,7 +47,7 @@ 
    Source code for idtxl.network_comparison
     import copy as cp
 import numpy as np
 from scipy.special import binom
-from .estimator import find_estimator
+from .estimator import get_estimator
 from . import stats
 from . import idtxl_utils as utils
 from .network_analysis import NetworkAnalysis
@@ -302,6 +301,7 @@ 
    Source code for idtxl.network_comparison
     
         # Main comparison.
         print('\n-------------------------- (1) create union of networks')
+        network_all = np.hstack((network_set_a, network_set_b))
         self._create_union(*network_all)
         print('\n-------------------------- (2) calculate differences in TE '
               'values')
@@ -505,7 +505,7 @@ 
    Source code for idtxl.network_comparison
             # Compare raw TE values between conditions.
         self.cmi_comp = self._compare_union_cmi_within(cmi_a, cmi_b)
 
-    def _calculate_cmi_diff_between(self, data_set_a, data_set_b):
+    def _calculate_cmi_diff_between(self):
         """Calculate the difference in CMI between two groups of subjects.
 
         Calculate the difference in the conditional mutual information (CMI)
@@ -987,11 +987,8 @@ 
    Source code for idtxl.network_comparison
                                'or "independent".')
 
         # Add CMI estimator to class.
-        try:
-            EstimatorClass = find_estimator(settings['cmi_estimator'])
-        except KeyError:
-            raise KeyError('Please provide an estimator class or name!')
-        self._cmi_estimator = EstimatorClass(settings)
+        assert 'cmi_estimator' in settings, 'Estimator was not specified!'
+        self._cmi_estimator = get_estimator(settings['cmi_estimator'], settings)
 
         if 'local_values' in settings and settings['local_values']:
             raise RuntimeError('Can''t run network comparison on local values.')
@@ -1037,7 +1034,7 @@ 
    Source code for idtxl.network_comparison
       
    Quick search
    
     
    
     
    
-      
+      
       
     
    
     
    
@@ -1056,14 +1053,14 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.network_comparison
    •  
       
     
    
     
   
 
\ No newline at end of file
diff --git a/docs/html/_modules/idtxl/postprocessing.html b/docs/html/_modules/idtxl/postprocessing.html
index 44d124af..af68bf80 100644
--- a/docs/html/_modules/idtxl/postprocessing.html
+++ b/docs/html/_modules/idtxl/postprocessing.html
@@ -5,14 +5,13 @@
   
     
     
-    idtxl.postprocessing — IDTxl 1.4 documentation
-    
-    
-    
+    idtxl.postprocessing — IDTxl 1.5 documentation
+    
+    
+    
     
     
     
-    
     
     
 
@@ -32,7 +31,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.postprocessing
    •  
       
@@ -1666,7 +1665,7 @@ 
    Source code for idtxl.postprocessing
       
    Quick search
    
     
    
     
    
-      
+      
       
     
    
     
    
@@ -1685,14 +1684,14 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.postprocessing
    •  
       
     
    
     
   
 
\ No newline at end of file
diff --git a/docs/html/_modules/idtxl/results.html b/docs/html/_modules/idtxl/results.html
index 8c720917..29ef3c24 100644
--- a/docs/html/_modules/idtxl/results.html
+++ b/docs/html/_modules/idtxl/results.html
@@ -5,14 +5,13 @@
   
     
     
-    idtxl.results — IDTxl 1.4 documentation
-    
-    
-    
+    idtxl.results — IDTxl 1.5 documentation
+    
+    
+    
     
     
     
-    
     
     
 
@@ -32,7 +31,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.results
    •  
       
@@ -1235,7 +1234,7 @@ 
    Source code for idtxl.results
       
    Quick search
    
     
    
     
    
-      
+      
       
     
    
     
    
@@ -1254,14 +1253,14 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.results
    •  
       
     
    
     
   
 
\ No newline at end of file
diff --git a/docs/html/_modules/idtxl/single_process_analysis.html b/docs/html/_modules/idtxl/single_process_analysis.html
index f7517adc..288c28a7 100644
--- a/docs/html/_modules/idtxl/single_process_analysis.html
+++ b/docs/html/_modules/idtxl/single_process_analysis.html
@@ -5,14 +5,13 @@
   
     
     
-    idtxl.single_process_analysis — IDTxl 1.4 documentation
-    
-    
-    
+    idtxl.single_process_analysis — IDTxl 1.5 documentation
+    
+    
+    
     
     
     
-    
     
     
 
@@ -32,7 +31,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.single_process_analysis
    •  
       
@@ -47,7 +46,6 @@ 
    Source code for idtxl.single_process_analysis
    """Parent class for analysis of single processes in the network."""
 from .network_analysis import NetworkAnalysis
 
-
 
    [docs]class SingleProcessAnalysis(NetworkAnalysis):
     def __init__(self):
         super().__init__()
    
@@ -63,7 +61,7 @@ 
    Source code for idtxl.single_process_analysis
    Quick search
     
    
     
    
-      
+      
       
     
    
     
    
@@ -82,14 +80,14 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.single_process_analysis
    •  
       
     
    
     
   
 
\ No newline at end of file
diff --git a/docs/html/_modules/idtxl/visualise_graph.html b/docs/html/_modules/idtxl/visualise_graph.html
index 3971fac9..fac50df8 100644
--- a/docs/html/_modules/idtxl/visualise_graph.html
+++ b/docs/html/_modules/idtxl/visualise_graph.html
@@ -5,14 +5,13 @@
   
     
     
-    idtxl.visualise_graph — IDTxl 1.4 documentation
-    
-    
-    
+    idtxl.visualise_graph — IDTxl 1.5 documentation
+    
+    
+    
     
     
     
-    
     
     
 
@@ -32,7 +31,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.visualise_graph
    •  
       
@@ -251,6 +250,41 @@ 
    Source code for idtxl.visualise_graph
         return cbar
 
 
+def _plot_adj_matrix(adj_matrix, mat_color='gray_r', diverging=False,
+                     cbar_label='delay', cbar_stepsize=1):
+    """Plot adjacency matrix."""
+    # Plot matrix, set minimum and maximum values to the same value for
+    # diverging plots to center colormap at 0, i.e., 0 is plotted in white
+    # https://stackoverflow.com/questions/25500541/
+    # matplotlib-bwr-colormap-always-centered-on-zero
+    if diverging:
+        max_val = np.max(abs(adj_matrix))
+        min_val = -max_val
+    else:
+        max_val = np.max(adj_matrix)
+        min_val = -np.min(adj_matrix)
+    plt.imshow(adj_matrix, cmap=mat_color, interpolation='nearest',
+               vmin=min_val, vmax=max_val)
+
+    # Set the colorbar and make colorbar match the image in size using the
+    # fraction and pad parameters (see https://stackoverflow.com/a/26720422).
+    if cbar_label == 'delay':
+        cbar_label = 'delay [samples]'
+        cbar_ticks = np.arange(0, max_val + 1, cbar_stepsize)
+    else:
+        cbar_ticks = np.arange(min_val, max_val + 0.01 * max_val,
+                               cbar_stepsize)
+    cbar = plt.colorbar(fraction=0.046, pad=0.04, ticks=cbar_ticks)
+    cbar.set_label(cbar_label, rotation=90)
+
+    # Set x- and y-ticks.
+    plt.xticks(np.arange(adj_matrix.shape[1]))
+    plt.yticks(np.arange(adj_matrix.shape[0]))
+    ax = plt.gca()
+    ax.xaxis.tick_top()
+    return cbar
+
+
 
    [docs]def plot_mute_graph():
     """Plot MuTE example network.
 
@@ -359,7 +393,7 @@ 
    Source code for idtxl.visualise_graph
       
    Quick search
    
     
    
     
    
-      
+      
       
     
    
     
    
@@ -378,14 +412,14 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5 documentation »
    • 
           
  • Module code »
    • 
         
  • idtxl.visualise_graph
    •  
       
     
    
     
   
 
\ No newline at end of file
diff --git a/docs/html/_modules/index.html b/docs/html/_modules/index.html
index e8a979d4..5ef8872d 100644
--- a/docs/html/_modules/index.html
+++ b/docs/html/_modules/index.html
@@ -5,14 +5,13 @@
   
     
     
-    Overview: module code — IDTxl 1.4 documentation
-    
-    
-    
+    Overview: module code — IDTxl 1.5 documentation
+    
+    
+    
     
     
     
-    
     
     
 
@@ -32,7 +31,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5 documentation »
    • 
         
  • Overview: module code
    •  
       
     
      
@@ -51,9 +50,11 @@ 
    All modules for which code is available
    
 
  • idtxl.embedding_optimization_ais_Rudelt
    • 
 
  • idtxl.estimators_Rudelt
    • 
 
  • idtxl.estimators_jidt
    • 
+
  • idtxl.estimators_mpi
    • 
 
  • idtxl.estimators_multivariate_pid
    • 
 
  • idtxl.estimators_opencl
    • 
 
  • idtxl.estimators_pid
    • 
+
  • idtxl.estimators_python
    • 
 
  • idtxl.idtxl_exceptions
    • 
 
  • idtxl.idtxl_io
    • 
 
  • idtxl.idtxl_utils
    • 
@@ -80,7 +81,7 @@ 
    All modules for which code is available
    
   
    Quick search
    
     
    
     
    
-      
+      
       
     
    
     
    
@@ -99,13 +100,13 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5 documentation »
    • 
         
  • Overview: module code
    •  
       
     
    
     
   
 
\ No newline at end of file
diff --git a/docs/html/_sources/idtxl.rst.txt b/docs/html/_sources/idtxl.rst.txt
index 6dc6d645..c7d1de0f 100644
--- a/docs/html/_sources/idtxl.rst.txt
+++ b/docs/html/_sources/idtxl.rst.txt
@@ -101,6 +101,25 @@ idtxl.estimators_opencl module
     :undoc-members:
     :show-inheritance:
 
+
+idtxl.estimators_mpi module
+------------------------------
+
+.. automodule:: idtxl.estimators_mpi
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+
+idtxl.estimators_python module
+------------------------------
+
+.. automodule:: idtxl.estimators_python
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+
 idtxl.estimators_multivariate_pid module
 ----------------------------------------
 
diff --git a/docs/html/_sources/idtxl_estimators.rst.txt b/docs/html/_sources/idtxl_estimators.rst.txt
index 95e8f492..a30caeb0 100644
--- a/docs/html/_sources/idtxl_estimators.rst.txt
+++ b/docs/html/_sources/idtxl_estimators.rst.txt
@@ -7,12 +7,24 @@ JIDT Estimators (CPU)
     :members:
     :noindex:
 
+Python Estimators (CPU)
+-----------------------
+.. automodule:: idtxl.estimators_python
+    :members:
+    :noindex:
+
 OpenCL Estimators (GPU)
 -----------------------
 .. automodule:: idtxl.estimators_opencl
     :members:
     :noindex:
 
+MPI Estimators (CPU)
+-------------------------
+.. automodule:: idtxl.estimators_mpi
+    :members:
+    :noindex:
+
 PID Estimators
 --------------
 .. automodule:: idtxl.estimators_pid
diff --git a/docs/html/_static/basic.css b/docs/html/_static/basic.css
index 24bc73e7..bf18350b 100644
--- a/docs/html/_static/basic.css
+++ b/docs/html/_static/basic.css
@@ -4,7 +4,7 @@
  *
  * Sphinx stylesheet -- basic theme.
  *
- * :copyright: Copyright 2007-2020 by the Sphinx team, see AUTHORS.
+ * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
  * :license: BSD, see LICENSE for details.
  *
  */
@@ -130,7 +130,7 @@ ul.search li a {
     font-weight: bold;
 }
 
-ul.search li div.context {
+ul.search li p.context {
     color: #888;
     margin: 2px 0 0 30px;
     text-align: left;
@@ -277,25 +277,25 @@ p.rubric {
     font-weight: bold;
 }
 
-img.align-left, .figure.align-left, object.align-left {
+img.align-left, figure.align-left, .figure.align-left, object.align-left {
     clear: left;
     float: left;
     margin-right: 1em;
 }
 
-img.align-right, .figure.align-right, object.align-right {
+img.align-right, figure.align-right, .figure.align-right, object.align-right {
     clear: right;
     float: right;
     margin-left: 1em;
 }
 
-img.align-center, .figure.align-center, object.align-center {
+img.align-center, figure.align-center, .figure.align-center, object.align-center {
   display: block;
   margin-left: auto;
   margin-right: auto;
 }
 
-img.align-default, .figure.align-default {
+img.align-default, figure.align-default, .figure.align-default {
   display: block;
   margin-left: auto;
   margin-right: auto;
@@ -319,7 +319,8 @@ img.align-default, .figure.align-default {
 
 /* -- sidebars -------------------------------------------------------------- */
 
-div.sidebar {
+div.sidebar,
+aside.sidebar {
     margin: 0 0 0.5em 1em;
     border: 1px solid #ddb;
     padding: 7px;
@@ -377,12 +378,14 @@ div.body p.centered {
 /* -- content of sidebars/topics/admonitions -------------------------------- */
 
 div.sidebar > :last-child,
+aside.sidebar > :last-child,
 div.topic > :last-child,
 div.admonition > :last-child {
     margin-bottom: 0;
 }
 
 div.sidebar::after,
+aside.sidebar::after,
 div.topic::after,
 div.admonition::after,
 blockquote::after {
@@ -455,20 +458,22 @@ td > :last-child {
 
 /* -- figures --------------------------------------------------------------- */
 
-div.figure {
+div.figure, figure {
     margin: 0.5em;
     padding: 0.5em;
 }
 
-div.figure p.caption {
+div.figure p.caption, figcaption {
     padding: 0.3em;
 }
 
-div.figure p.caption span.caption-number {
+div.figure p.caption span.caption-number,
+figcaption span.caption-number {
     font-style: italic;
 }
 
-div.figure p.caption span.caption-text {
+div.figure p.caption span.caption-text,
+figcaption span.caption-text {
 }
 
 /* -- field list styles ----------------------------------------------------- */
@@ -503,6 +508,63 @@ table.hlist td {
     vertical-align: top;
 }
 
+/* -- object description styles --------------------------------------------- */
+
+.sig {
+	font-family: 'Consolas', 'Menlo', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', monospace;
+}
+
+.sig-name, code.descname {
+    background-color: transparent;
+    font-weight: bold;
+}
+
+.sig-name {
+	font-size: 1.1em;
+}
+
+code.descname {
+    font-size: 1.2em;
+}
+
+.sig-prename, code.descclassname {
+    background-color: transparent;
+}
+
+.optional {
+    font-size: 1.3em;
+}
+
+.sig-paren {
+    font-size: larger;
+}
+
+.sig-param.n {
+	font-style: italic;
+}
+
+/* C++ specific styling */
+
+.sig-inline.c-texpr,
+.sig-inline.cpp-texpr {
+	font-family: unset;
+}
+
+.sig.c   .k, .sig.c   .kt,
+.sig.cpp .k, .sig.cpp .kt {
+	color: #0033B3;
+}
+
+.sig.c   .m,
+.sig.cpp .m {
+	color: #1750EB;
+}
+
+.sig.c   .s, .sig.c   .sc,
+.sig.cpp .s, .sig.cpp .sc {
+	color: #067D17;
+}
+
 
 /* -- other body styles ----------------------------------------------------- */
 
@@ -629,14 +691,6 @@ dl.glossary dt {
     font-size: 1.1em;
 }
 
-.optional {
-    font-size: 1.3em;
-}
-
-.sig-paren {
-    font-size: larger;
-}
-
 .versionmodified {
     font-style: italic;
 }
@@ -677,8 +731,9 @@ dl.glossary dt {
 
 .classifier:before {
     font-style: normal;
-    margin: 0.5em;
+    margin: 0 0.5em;
     content: ":";
+    display: inline-block;
 }
 
 abbr, acronym {
@@ -702,6 +757,7 @@ span.pre {
     -ms-hyphens: none;
     -webkit-hyphens: none;
     hyphens: none;
+    white-space: nowrap;
 }
 
 div[class*="highlight-"] {
@@ -764,8 +820,13 @@ div.code-block-caption code {
 }
 
 table.highlighttable td.linenos,
-div.doctest > div.highlight span.gp {  /* gp: Generic.Prompt */
-    user-select: none;
+span.linenos,
+div.highlight span.gp {  /* gp: Generic.Prompt */
+  user-select: none;
+  -webkit-user-select: text; /* Safari fallback only */
+  -webkit-user-select: none; /* Chrome/Safari */
+  -moz-user-select: none; /* Firefox */
+  -ms-user-select: none; /* IE10+ */
 }
 
 div.code-block-caption span.caption-number {
@@ -780,16 +841,6 @@ div.literal-block-wrapper {
     margin: 1em 0;
 }
 
-code.descname {
-    background-color: transparent;
-    font-weight: bold;
-    font-size: 1.2em;
-}
-
-code.descclassname {
-    background-color: transparent;
-}
-
 code.xref, a code {
     background-color: transparent;
     font-weight: bold;
diff --git a/docs/html/_static/doctools.js b/docs/html/_static/doctools.js
index daccd209..e509e483 100644
--- a/docs/html/_static/doctools.js
+++ b/docs/html/_static/doctools.js
@@ -4,7 +4,7 @@
  *
  * Sphinx JavaScript utilities for all documentation.
  *
- * :copyright: Copyright 2007-2020 by the Sphinx team, see AUTHORS.
+ * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
  * :license: BSD, see LICENSE for details.
  *
  */
@@ -29,9 +29,14 @@ if (!window.console || !console.firebug) {
 
 /**
  * small helper function to urldecode strings
+ *
+ * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL
  */
 jQuery.urldecode = function(x) {
-  return decodeURIComponent(x).replace(/\+/g, ' ');
+  if (!x) {
+    return x
+  }
+  return decodeURIComponent(x.replace(/\+/g, ' '));
 };
 
 /**
@@ -259,6 +264,9 @@ var Documentation = {
   hideSearchWords : function() {
     $('#searchbox .highlight-link').fadeOut(300);
     $('span.highlighted').removeClass('highlighted');
+    var url = new URL(window.location);
+    url.searchParams.delete('highlight');
+    window.history.replaceState({}, '', url);
   },
 
   /**
@@ -285,9 +293,10 @@ var Documentation = {
   initOnKeyListeners: function() {
     $(document).keydown(function(event) {
       var activeElementType = document.activeElement.tagName;
-      // don't navigate when in search box or textarea
+      // don't navigate when in search box, textarea, dropdown or button
       if (activeElementType !== 'TEXTAREA' && activeElementType !== 'INPUT' && activeElementType !== 'SELECT'
-          && !event.altKey && !event.ctrlKey && !event.metaKey && !event.shiftKey) {
+          && activeElementType !== 'BUTTON' && !event.altKey && !event.ctrlKey && !event.metaKey
+          && !event.shiftKey) {
         switch (event.keyCode) {
           case 37: // left
             var prevHref = $('link[rel="prev"]').prop('href');
@@ -295,12 +304,14 @@ var Documentation = {
               window.location.href = prevHref;
               return false;
             }
+            break;
           case 39: // right
             var nextHref = $('link[rel="next"]').prop('href');
             if (nextHref) {
               window.location.href = nextHref;
               return false;
             }
+            break;
         }
       }
     });
diff --git a/docs/html/_static/documentation_options.js b/docs/html/_static/documentation_options.js
index 42f10a87..eecd2571 100644
--- a/docs/html/_static/documentation_options.js
+++ b/docs/html/_static/documentation_options.js
@@ -1,6 +1,6 @@
 var DOCUMENTATION_OPTIONS = {
     URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'),
-    VERSION: '1.4',
+    VERSION: '1.5',
     LANGUAGE: 'None',
     COLLAPSE_INDEX: false,
     BUILDER: 'html',
diff --git a/docs/html/_static/epub.css b/docs/html/_static/epub.css
index 270e9570..165f41d5 100644
--- a/docs/html/_static/epub.css
+++ b/docs/html/_static/epub.css
@@ -4,7 +4,7 @@
  *
  * Sphinx stylesheet -- default theme.
  *
- * :copyright: Copyright 2007-2020 by the Sphinx team, see AUTHORS.
+ * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
  * :license: BSD, see LICENSE for details.
  *
  */
diff --git a/docs/html/_static/language_data.js b/docs/html/_static/language_data.js
index d2b4ee91..ebe2f03b 100644
--- a/docs/html/_static/language_data.js
+++ b/docs/html/_static/language_data.js
@@ -5,7 +5,7 @@
  * This script contains the language-specific data used by searchtools.js,
  * namely the list of stopwords, stemmer, scorer and splitter.
  *
- * :copyright: Copyright 2007-2020 by the Sphinx team, see AUTHORS.
+ * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
  * :license: BSD, see LICENSE for details.
  *
  */
@@ -13,7 +13,8 @@
 var stopwords = ["a","and","are","as","at","be","but","by","for","if","in","into","is","it","near","no","not","of","on","or","such","that","the","their","then","there","these","they","this","to","was","will","with"];
 
 
-/* Non-minified version JS is _stemmer.js if file is provided */ 
+/* Non-minified version is copied as a separate JS file, is available */
+
 /**
  * Porter Stemmer
  */
@@ -199,7 +200,6 @@ var Stemmer = function() {
 
 
 
-
 var splitChars = (function() {
     var result = {};
     var singles = [96, 180, 187, 191, 215, 247, 749, 885, 903, 907, 909, 930, 1014, 1648,
diff --git a/docs/html/_static/pygments.css b/docs/html/_static/pygments.css
index d14395ef..691aeb82 100644
--- a/docs/html/_static/pygments.css
+++ b/docs/html/_static/pygments.css
@@ -1,8 +1,8 @@
-pre { line-height: 125%; margin: 0; }
-td.linenos pre { color: #000000; background-color: #f0f0f0; padding: 0 5px 0 5px; }
-span.linenos { color: #000000; background-color: #f0f0f0; padding: 0 5px 0 5px; }
-td.linenos pre.special { color: #000000; background-color: #ffffc0; padding: 0 5px 0 5px; }
-span.linenos.special { color: #000000; background-color: #ffffc0; padding: 0 5px 0 5px; }
+pre { line-height: 125%; }
+td.linenos .normal { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; }
+span.linenos { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; }
+td.linenos .special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }
+span.linenos.special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }
 .highlight .hll { background-color: #ffffcc }
 .highlight { background: #eeffcc; }
 .highlight .c { color: #408090; font-style: italic } /* Comment */
diff --git a/docs/html/_static/pyramid.css b/docs/html/_static/pyramid.css
index dbc19d26..e0b1cfac 100644
--- a/docs/html/_static/pyramid.css
+++ b/docs/html/_static/pyramid.css
@@ -4,15 +4,15 @@
  *
  * Sphinx stylesheet -- pylons theme.
  *
- * :copyright: Copyright 2007-2020 by the Sphinx team, see AUTHORS.
+ * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
  * :license: BSD, see LICENSE for details.
  *
  */
- 
+
 @import url("basic.css");
- 
+
 /* -- page layout ----------------------------------------------------------- */
- 
+
 body {
     font-family: "Nobile", sans-serif;
     font-size: 100%;
@@ -34,7 +34,7 @@ div.bodywrapper {
 hr {
     border: 1px solid #B1B4B6;
 }
- 
+
 div.document {
     background-color: #eee;
 }
@@ -59,7 +59,7 @@ div.body {
     border-right-style: none;
     overflow: auto;
 }
- 
+
 div.footer {
     color: #ffffff;
     width: 100%;
@@ -69,7 +69,7 @@ div.footer {
     background: transparent;
     clear:both;
 }
- 
+
 div.footer a {
     color: #ffffff;
     text-decoration: none;
@@ -79,14 +79,14 @@ div.footer a:hover {
     color: #e88f00;
     text-decoration: underline;
 }
- 
+
 div.related {
     line-height: 30px;
     color: #373839;
     font-size: 0.8em;
     background-color: #eee;
 }
- 
+
 div.related a {
     color: #1b61d6;
 }
@@ -94,7 +94,7 @@ div.related a {
 div.related ul {
     padding-left: calc(230px + 10px);
 }
- 
+
 div.sphinxsidebar {
     font-size: 0.75em;
     line-height: 1.5em;
@@ -103,7 +103,7 @@ div.sphinxsidebar {
 div.sphinxsidebarwrapper{
     padding: 10px 0;
 }
- 
+
 div.sphinxsidebar h3,
 div.sphinxsidebar h4 {
     font-family: "Neuton", sans-serif;
@@ -118,30 +118,30 @@ div.sphinxsidebar h4 {
 div.sphinxsidebar h4{
     font-size: 1.3em;
 }
- 
+
 div.sphinxsidebar h3 a {
     color: #000000;
 }
- 
- 
+
+
 div.sphinxsidebar p {
     color: #888;
     padding: 5px 20px;
 }
- 
+
 div.sphinxsidebar p.topless {
 }
- 
+
 div.sphinxsidebar ul {
     margin: 10px 20px;
     padding: 0;
     color: #373839;
 }
- 
+
 div.sphinxsidebar a {
     color: #444;
 }
- 
+
 div.sphinxsidebar input {
     border: 1px solid #ccc;
     font-family: sans-serif;
@@ -171,16 +171,16 @@ p.sidebar-title {
 }
 
 /* -- body styles ----------------------------------------------------------- */
- 
+
 a, a .pre {
     color: #1b61d6;
     text-decoration: none;
 }
- 
+
 a:hover, a:hover .pre {
     text-decoration: underline;
 }
- 
+
 div.body h1,
 div.body h2,
 div.body h3,
@@ -194,29 +194,29 @@ div.body h6 {
     margin: 30px 0px 10px 0px;
     padding: 5px 0;
 }
- 
+
 div.body h1 { border-top: 20px solid white; margin-top: 0; font-size: 200%; }
 div.body h2 { font-size: 150%; background-color: #ffffff; }
 div.body h3 { font-size: 120%; background-color: #ffffff; }
 div.body h4 { font-size: 110%; background-color: #ffffff; }
 div.body h5 { font-size: 100%; background-color: #ffffff; }
 div.body h6 { font-size: 100%; background-color: #ffffff; }
- 
+
 a.headerlink {
     color: #1b61d6;
     font-size: 0.8em;
     padding: 0 4px 0 4px;
     text-decoration: none;
 }
- 
+
 a.headerlink:hover {
     text-decoration: underline;
 }
- 
+
 div.body p, div.body dd, div.body li {
     line-height: 1.5em;
 }
- 
+
 div.admonition p.admonition-title + p {
     display: inline;
 }
@@ -236,7 +236,7 @@ div.note {
     padding: 10px 20px 10px 60px;
     background: #e1ecfe url(dialog-note.png) no-repeat 10px 8px;
 }
- 
+
 div.seealso {
     background: #fff6bf url(dialog-seealso.png) no-repeat 10px 8px;
     border: 2px solid #ffd324;
@@ -244,7 +244,7 @@ div.seealso {
     border-right-style: none;
     padding: 10px 20px 10px 60px;
 }
- 
+
 div.topic {
     background: #eeeeee;
     border: 2px solid #C6C9CB;
@@ -252,7 +252,7 @@ div.topic {
     border-right-style: none;
     border-left-style: none;
 }
- 
+
 div.warning {
     background: #fbe3e4 url(dialog-warning.png) no-repeat 10px 8px;
     border: 2px solid #fbc2c4;
@@ -268,18 +268,18 @@ div.admonition-todo {
     border-left-style: none;
     padding: 10px 20px 10px 60px;
 }
- 
+
 div.note p.admonition-title,
 div.warning p.admonition-title,
 div.seealso p.admonition-title,
 div.admonition-todo p.admonition-title {
     display: none;
 }
- 
+
 p.admonition-title:after {
     content: ":";
 }
- 
+
 pre {
     padding: 10px;
     line-height: 1.2em;
@@ -289,7 +289,7 @@ pre {
     border-right-style: none;
     border-left-style: none;
 }
- 
+
 code {
     background-color: transparent;
     color: #222;
diff --git a/docs/html/_static/searchtools.js b/docs/html/_static/searchtools.js
index 970d0d97..2d778593 100644
--- a/docs/html/_static/searchtools.js
+++ b/docs/html/_static/searchtools.js
@@ -4,7 +4,7 @@
  *
  * Sphinx JavaScript utilities for the full-text search.
  *
- * :copyright: Copyright 2007-2020 by the Sphinx team, see AUTHORS.
+ * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
  * :license: BSD, see LICENSE for details.
  *
  */
@@ -59,10 +59,10 @@ var Search = {
   _pulse_status : -1,
 
   htmlToText : function(htmlString) {
-      var htmlElement = document.createElement('span');
-      htmlElement.innerHTML = htmlString;
-      $(htmlElement).find('.headerlink').remove();
-      docContent = $(htmlElement).find('[role=main]')[0];
+      var virtualDocument = document.implementation.createHTMLDocument('virtual');
+      var htmlElement = $(htmlString, virtualDocument);
+      htmlElement.find('.headerlink').remove();
+      docContent = htmlElement.find('[role=main]')[0];
       if(docContent === undefined) {
           console.warn("Content block not found. Sphinx search tries to obtain it " +
                        "via '[role=main]'. Could you check your theme or template.");
@@ -248,7 +248,7 @@ var Search = {
       // results left, load the summary and display it
       if (results.length) {
         var item = results.pop();
-        var listItem = $('
  • ');
+        var listItem = $('
  • ');
         var requestUrl = "";
         var linkUrl = "";
         if (DOCUMENTATION_OPTIONS.BUILDER === 'dirhtml') {
@@ -273,28 +273,31 @@ var Search = {
         if (item[3]) {
           listItem.append($(' (' + item[3] + ')'));
           Search.output.append(listItem);
-          listItem.slideDown(5, function() {
+          setTimeout(function() {
             displayNextItem();
-          });
+          }, 5);
         } else if (DOCUMENTATION_OPTIONS.HAS_SOURCE) {
           $.ajax({url: requestUrl,
                   dataType: "text",
                   complete: function(jqxhr, textstatus) {
                     var data = jqxhr.responseText;
                     if (data !== '' && data !== undefined) {
-                      listItem.append(Search.makeSearchSummary(data, searchterms, hlterms));
+                      var summary = Search.makeSearchSummary(data, searchterms, hlterms);
+                      if (summary) {
+                        listItem.append(summary);
+                      }
                     }
                     Search.output.append(listItem);
-                    listItem.slideDown(5, function() {
+                    setTimeout(function() {
                       displayNextItem();
-                    });
+                    }, 5);
                   }});
         } else {
           // no source available, just display title
           Search.output.append(listItem);
-          listItem.slideDown(5, function() {
+          setTimeout(function() {
             displayNextItem();
-          });
+          }, 5);
         }
       }
       // search finished, update title and status message
@@ -325,7 +328,9 @@ var Search = {
     var results = [];
 
     for (var prefix in objects) {
-      for (var name in objects[prefix]) {
+      for (var iMatch = 0; iMatch != objects[prefix].length; ++iMatch) {
+        var match = objects[prefix][iMatch];
+        var name = match[4];
         var fullname = (prefix ? prefix + '.' : '') + name;
         var fullnameLower = fullname.toLowerCase()
         if (fullnameLower.indexOf(object) > -1) {
@@ -339,7 +344,6 @@ var Search = {
           } else if (parts[parts.length - 1].indexOf(object) > -1) {
             score += Scorer.objPartialMatch;
           }
-          var match = objects[prefix][name];
           var objname = objnames[match[1]][2];
           var title = titles[match[0]];
           // If more than one term searched for, we require other words to be
@@ -379,6 +383,13 @@ var Search = {
     return results;
   },
 
+  /**
+   * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions
+   */
+  escapeRegExp : function(string) {
+    return string.replace(/[.*+\-?^${}()|[\]\\]/g, '\\$&'); // $& means the whole matched string
+  },
+
   /**
    * search for full-text terms in the index
    */
@@ -402,13 +413,14 @@ var Search = {
       ];
       // add support for partial matches
       if (word.length > 2) {
+        var word_regex = this.escapeRegExp(word);
         for (var w in terms) {
-          if (w.match(word) && !terms[word]) {
+          if (w.match(word_regex) && !terms[word]) {
             _o.push({files: terms[w], score: Scorer.partialTerm})
           }
         }
         for (var w in titleterms) {
-          if (w.match(word) && !titleterms[word]) {
+          if (w.match(word_regex) && !titleterms[word]) {
               _o.push({files: titleterms[w], score: Scorer.partialTitle})
           }
         }
@@ -490,6 +502,9 @@ var Search = {
    */
   makeSearchSummary : function(htmlText, keywords, hlwords) {
     var text = Search.htmlToText(htmlText);
+    if (text == "") {
+      return null;
+    }
     var textLower = text.toLowerCase();
     var start = 0;
     $.each(keywords, function() {
@@ -501,7 +516,7 @@ var Search = {
     var excerpt = ((start > 0) ? '...' : '') +
       $.trim(text.substr(start, 240)) +
       ((start + 240 - text.length) ? '...' : '');
-    var rv = $('
    ').text(excerpt);
+    var rv = $('
    ').text(excerpt);
     $.each(hlwords, function() {
       rv = rv.highlightText(this, 'highlighted');
     });
diff --git a/docs/html/_static/underscore.js b/docs/html/_static/underscore.js
index 5b55f32b..cf177d42 100644
--- a/docs/html/_static/underscore.js
+++ b/docs/html/_static/underscore.js
@@ -1,31 +1,6 @@
-// Underscore.js 1.3.1
-// (c) 2009-2012 Jeremy Ashkenas, DocumentCloud Inc.
-// Underscore is freely distributable under the MIT license.
-// Portions of Underscore are inspired or borrowed from Prototype,
-// Oliver Steele's Functional, and John Resig's Micro-Templating.
-// For all details and documentation:
-// http://documentcloud.github.com/underscore
-(function(){function q(a,c,d){if(a===c)return a!==0||1/a==1/c;if(a==null||c==null)return a===c;if(a._chain)a=a._wrapped;if(c._chain)c=c._wrapped;if(a.isEqual&&b.isFunction(a.isEqual))return a.isEqual(c);if(c.isEqual&&b.isFunction(c.isEqual))return c.isEqual(a);var e=l.call(a);if(e!=l.call(c))return false;switch(e){case "[object String]":return a==String(c);case "[object Number]":return a!=+a?c!=+c:a==0?1/a==1/c:a==+c;case "[object Date]":case "[object Boolean]":return+a==+c;case "[object RegExp]":return a.source==
-c.source&&a.global==c.global&&a.multiline==c.multiline&&a.ignoreCase==c.ignoreCase}if(typeof a!="object"||typeof c!="object")return false;for(var f=d.length;f--;)if(d[f]==a)return true;d.push(a);var f=0,g=true;if(e=="[object Array]"){if(f=a.length,g=f==c.length)for(;f--;)if(!(g=f in a==f in c&&q(a[f],c[f],d)))break}else{if("constructor"in a!="constructor"in c||a.constructor!=c.constructor)return false;for(var h in a)if(b.has(a,h)&&(f++,!(g=b.has(c,h)&&q(a[h],c[h],d))))break;if(g){for(h in c)if(b.has(c,
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-b.isArguments=function(a){return l.call(a)=="[object Arguments]"};if(!b.isArguments(arguments))b.isArguments=function(a){return!(!a||!b.has(a,"callee"))};b.isFunction=function(a){return l.call(a)=="[object Function]"};b.isString=function(a){return l.call(a)=="[object String]"};b.isNumber=function(a){return l.call(a)=="[object Number]"};b.isNaN=function(a){return a!==a};b.isBoolean=function(a){return a===true||a===false||l.call(a)=="[object Boolean]"};b.isDate=function(a){return l.call(a)=="[object Date]"};
-b.isRegExp=function(a){return l.call(a)=="[object RegExp]"};b.isNull=function(a){return a===null};b.isUndefined=function(a){return a===void 0};b.has=function(a,b){return I.call(a,b)};b.noConflict=function(){r._=G;return this};b.identity=function(a){return a};b.times=function(a,b,d){for(var e=0;e/g,">").replace(/"/g,""").replace(/'/g,"'").replace(/\//g,"/")};b.mixin=function(a){j(b.functions(a),
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-true;return this};m.prototype.value=function(){return this._wrapped}}).call(this);
+!function(n,r){"object"==typeof exports&&"undefined"!=typeof module?module.exports=r():"function"==typeof define&&define.amd?define("underscore",r):(n="undefined"!=typeof globalThis?globalThis:n||self,function(){var t=n._,e=n._=r();e.noConflict=function(){return n._=t,e}}())}(this,(function(){
+//     Underscore.js 1.13.1
+//     https://underscorejs.org
+//     (c) 2009-2021 Jeremy Ashkenas, Julian Gonggrijp, and DocumentCloud and Investigative Reporters & Editors
+//     Underscore may be freely distributed under the MIT license.
+var n="1.13.1",r="object"==typeof self&&self.self===self&&self||"object"==typeof global&&global.global===global&&global||Function("return this")()||{},t=Array.prototype,e=Object.prototype,u="undefined"!=typeof Symbol?Symbol.prototype:null,o=t.push,i=t.slice,a=e.toString,f=e.hasOwnProperty,c="undefined"!=typeof ArrayBuffer,l="undefined"!=typeof DataView,s=Array.isArray,p=Object.keys,v=Object.create,h=c&&ArrayBuffer.isView,y=isNaN,d=isFinite,g=!{toString:null}.propertyIsEnumerable("toString"),b=["valueOf","isPrototypeOf","toString","propertyIsEnumerable","hasOwnProperty","toLocaleString"],m=Math.pow(2,53)-1;function j(n,r){return r=null==r?n.length-1:+r,function(){for(var t=Math.max(arguments.length-r,0),e=Array(t),u=0;u=0&&t<=m}}function J(n){return function(r){return null==r?void 0:r[n]}}var G=J("byteLength"),H=K(G),Q=/\[object ((I|Ui)nt(8|16|32)|Float(32|64)|Uint8Clamped|Big(I|Ui)nt64)Array\]/;var X=c?function(n){return h?h(n)&&!q(n):H(n)&&Q.test(a.call(n))}:C(!1),Y=J("length");function Z(n,r){r=function(n){for(var r={},t=n.length,e=0;e":">",'"':""","'":"'","`":"`"},Cn=Ln($n),Kn=Ln(_n($n)),Jn=tn.templateSettings={evaluate:/<%([\s\S]+?)%>/g,interpolate:/<%=([\s\S]+?)%>/g,escape:/<%-([\s\S]+?)%>/g},Gn=/(.)^/,Hn={"'":"'","\\":"\\","\r":"r","\n":"n","\u2028":"u2028","\u2029":"u2029"},Qn=/\\|'|\r|\n|\u2028|\u2029/g;function Xn(n){return"\\"+Hn[n]}var Yn=/^\s*(\w|\$)+\s*$/;var Zn=0;function nr(n,r,t,e,u){if(!(e instanceof r))return n.apply(t,u);var o=Mn(n.prototype),i=n.apply(o,u);return _(i)?i:o}var rr=j((function(n,r){var t=rr.placeholder,e=function(){for(var u=0,o=r.length,i=Array(o),a=0;a1)ur(a,r-1,t,e),u=e.length;else for(var f=0,c=a.length;f0&&(t=r.apply(this,arguments)),n<=1&&(r=null),t}}var lr=rr(cr,2);function sr(n,r,t){r=qn(r,t);for(var e,u=nn(n),o=0,i=u.length;o0?0:u-1;o>=0&&o0?a=o>=0?o:Math.max(o+f,a):f=o>=0?Math.min(o+1,f):o+f+1;else if(t&&o&&f)return e[o=t(e,u)]===u?o:-1;if(u!=u)return(o=r(i.call(e,a,f),$))>=0?o+a:-1;for(o=n>0?a:f-1;o>=0&&o0?0:i-1;for(u||(e=r[o?o[a]:a],a+=n);a>=0&&a=3;return r(n,Fn(t,u,4),e,o)}}var Ar=wr(1),xr=wr(-1);function Sr(n,r,t){var e=[];return r=qn(r,t),jr(n,(function(n,t,u){r(n,t,u)&&e.push(n)})),e}function Or(n,r,t){r=qn(r,t);for(var e=!er(n)&&nn(n),u=(e||n).length,o=0;o=0}var Br=j((function(n,r,t){var e,u;return D(r)?u=r:(r=Nn(r),e=r.slice(0,-1),r=r[r.length-1]),_r(n,(function(n){var o=u;if(!o){if(e&&e.length&&(n=In(n,e)),null==n)return;o=n[r]}return null==o?o:o.apply(n,t)}))}));function Nr(n,r){return _r(n,Rn(r))}function Ir(n,r,t){var e,u,o=-1/0,i=-1/0;if(null==r||"number"==typeof r&&"object"!=typeof n[0]&&null!=n)for(var a=0,f=(n=er(n)?n:jn(n)).length;ao&&(o=e);else r=qn(r,t),jr(n,(function(n,t,e){((u=r(n,t,e))>i||u===-1/0&&o===-1/0)&&(o=n,i=u)}));return o}function Tr(n,r,t){if(null==r||t)return er(n)||(n=jn(n)),n[Wn(n.length-1)];var e=er(n)?En(n):jn(n),u=Y(e);r=Math.max(Math.min(r,u),0);for(var o=u-1,i=0;i1&&(e=Fn(e,r[1])),r=an(n)):(e=qr,r=ur(r,!1,!1),n=Object(n));for(var u=0,o=r.length;u1&&(t=r[1])):(r=_r(ur(r,!1,!1),String),e=function(n,t){return!Er(r,t)}),Ur(n,e,t)}));function zr(n,r,t){return i.call(n,0,Math.max(0,n.length-(null==r||t?1:r)))}function Lr(n,r,t){return null==n||n.length<1?null==r||t?void 0:[]:null==r||t?n[0]:zr(n,n.length-r)}function $r(n,r,t){return i.call(n,null==r||t?1:r)}var Cr=j((function(n,r){return r=ur(r,!0,!0),Sr(n,(function(n){return!Er(r,n)}))})),Kr=j((function(n,r){return Cr(n,r)}));function Jr(n,r,t,e){A(r)||(e=t,t=r,r=!1),null!=t&&(t=qn(t,e));for(var u=[],o=[],i=0,a=Y(n);ir?(e&&(clearTimeout(e),e=null),a=c,i=n.apply(u,o),e||(u=o=null)):e||!1===t.trailing||(e=setTimeout(f,l)),i};return c.cancel=function(){clearTimeout(e),a=0,e=u=o=null},c},debounce:function(n,r,t){var e,u,o,i,a,f=function(){var c=zn()-u;r>c?e=setTimeout(f,r-c):(e=null,t||(i=n.apply(a,o)),e||(o=a=null))},c=j((function(c){return a=this,o=c,u=zn(),e||(e=setTimeout(f,r),t&&(i=n.apply(a,o))),i}));return c.cancel=function(){clearTimeout(e),e=o=a=null},c},wrap:function(n,r){return rr(r,n)},negate:fr,compose:function(){var n=arguments,r=n.length-1;return function(){for(var t=r,e=n[r].apply(this,arguments);t--;)e=n[t].call(this,e);return e}},after:function(n,r){return function(){if(--n<1)return r.apply(this,arguments)}},before:cr,once:lr,findKey:sr,findIndex:vr,findLastIndex:hr,sortedIndex:yr,indexOf:gr,lastIndexOf:br,find:mr,detect:mr,findWhere:function(n,r){return mr(n,Dn(r))},each:jr,forEach:jr,map:_r,collect:_r,reduce:Ar,foldl:Ar,inject:Ar,reduceRight:xr,foldr:xr,filter:Sr,select:Sr,reject:function(n,r,t){return Sr(n,fr(qn(r)),t)},every:Or,all:Or,some:Mr,any:Mr,contains:Er,includes:Er,include:Er,invoke:Br,pluck:Nr,where:function(n,r){return Sr(n,Dn(r))},max:Ir,min:function(n,r,t){var e,u,o=1/0,i=1/0;if(null==r||"number"==typeof r&&"object"!=typeof n[0]&&null!=n)for(var a=0,f=(n=er(n)?n:jn(n)).length;ae||void 0===t)return 1;if(t
     
     
-    Index — IDTxl 1.4 documentation
-    
-    
-    
+    Index — IDTxl 1.5 documentation
+    
+    
+    
     
     
     
-    
     
     
 
@@ -32,7 +31,7 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5 documentation »
    • 
         
  • Index
    •  
       
     
      
@@ -173,7 +172,7 @@ 
    C
    
 
       
  • conflicting_entries() (in module idtxl.idtxl_utils)
 
    • 
-      
  • current_value() (idtxl.network_analysis.NetworkAnalysis property)
+      
  • current_value (idtxl.network_analysis.NetworkAnalysis property)
 
    • 
   
 
@@ -199,7 +198,7 @@ 
    D
    
 
       
  • Data (class in idtxl.data)
 
    • 
-      
  • data() (idtxl.data.Data property)
+      
  • data (idtxl.data.Data property)
 
    • 
       
  • discretise() (in module idtxl.idtxl_utils)
 
    • 
@@ -239,6 +238,8 @@ 
    E
    
         
  • (idtxl.estimators_jidt.JidtKraskovMI method)
 
    • 
         
  • (idtxl.estimators_jidt.JidtKraskovTE method)
+
    • 
+        
  • (idtxl.estimators_mpi.MPIEstimator method)
 
    • 
         
  • (idtxl.estimators_multivariate_pid.SxPID method)
 
    • 
@@ -249,6 +250,8 @@ 
    E
    
         
  • (idtxl.estimators_pid.SydneyPID method)
 
    • 
         
  • (idtxl.estimators_pid.TartuPID method)
+
    • 
+        
  • (idtxl.estimators_python.PythonKraskovCMI method)
 
    • 
         
  • (idtxl.estimators_Rudelt.RudeltBBCEstimator method)
 
    • 
@@ -265,6 +268,8 @@ 
    E
    
 
       
       
  • export_brain_net_viewer() (in module idtxl.idtxl_io)
@@ -473,6 +478,13 @@ 
    I
    
 
       
    • 
+      
  • 
+    idtxl.estimators_mpi
+
+      
    • 
       
  • 
@@ -494,6 +506,13 @@ 
    I
    
 
       
    • 
+      
  • 
+    idtxl.estimators_python
+
+      
    • 
       
  • 
@@ -606,6 +625,8 @@ 
    I
    
         
  • (idtxl.estimators_jidt.JidtGaussian method)
 
    • 
         
  • (idtxl.estimators_jidt.JidtKraskov method)
+
    • 
+        
  • (idtxl.estimators_mpi.MPIEstimator method)
 
    • 
         
  • (idtxl.estimators_multivariate_pid.SxPID method)
 
    • 
@@ -614,6 +635,8 @@ 
    I
    
         
  • (idtxl.estimators_pid.SydneyPID method)
 
    • 
         
  • (idtxl.estimators_pid.TartuPID method)
+
    • 
+        
  • (idtxl.estimators_python.PythonKraskovCMI method)
 
    • 
         
  • (idtxl.estimators_Rudelt.RudeltAbstractEstimator method)
 
    • 
@@ -621,6 +644,8 @@ 
    I
    
       
  • is_parallel() (idtxl.estimators_jidt.JidtEstimator method)
 
       
    • 
   
   
-  
+  
       
  • print_matrix() (idtxl.results.AdjacencyMatrix method)
 
    • 
-      
  • processes_analysed() (idtxl.results.ResultsSingleProcessAnalysis property)
+      
  • processes_analysed (idtxl.results.ResultsSingleProcessAnalysis property)
 
       
    • 
+      
  • PythonKraskovCMI (class in idtxl.estimators_python)
+
    • 
   
 
 
@@ -925,11 +960,11 @@ 
    S
    
 
       
  • save_pickle() (in module idtxl.idtxl_io)
 
    • 
-      
  • selected_vars_full() (idtxl.network_analysis.NetworkAnalysis property)
+      
  • selected_vars_full (idtxl.network_analysis.NetworkAnalysis property)
 
    • 
-      
  • selected_vars_sources() (idtxl.network_analysis.NetworkAnalysis property)
+      
  • selected_vars_sources (idtxl.network_analysis.NetworkAnalysis property)
 
    • 
-      
  • selected_vars_target() (idtxl.network_analysis.NetworkAnalysis property)
+      
  • selected_vars_target (idtxl.network_analysis.NetworkAnalysis property)
 
    • 
       
  • separate_arrays() (in module idtxl.idtxl_utils)
 
    • 
@@ -967,11 +1002,15 @@ 
    S
    
 
    T
    
 
    
   
   
 
    
@@ -1000,7 +1039,7 @@ 
    U
    
   
    Quick search
    
     
    
     
    
-      
+      
       
     
    
     
    
@@ -1019,13 +1058,13 @@ 
    Navigation
    
         
  • 
           modules |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5 documentation »
    • 
         
  • Index
    •  
       
     
    
     
   
 
\ No newline at end of file
diff --git a/docs/html/idtxl.html b/docs/html/idtxl.html
index 46386ce4..7dc80d8e 100644
--- a/docs/html/idtxl.html
+++ b/docs/html/idtxl.html
@@ -4,16 +4,15 @@
 
   
     
-    
+    
 
-    idtxl package — IDTxl 1.4 documentation
-    
-    
-    
+    idtxl package — IDTxl 1.5 documentation
+    
+    
+    
     
     
     
-    
     
     
     
@@ -37,7 +36,7 @@ 
    Navigation
    
         
  • 
           previous |
    • 
-        
  • IDTxl 1.4 documentation »
    • 
+        
  • IDTxl 1.5 documentation »
    • 
         
  • idtxl package
    •  
       
     
      
@@ -56,8 +55,8 @@ 
    Submodules
    idtxl.data module
    
 
    Provide data structures for IDTxl analysis.
    
 
    
-
    
-class idtxl.data.Data(data=None, dim_order='psr', normalise=True, seed=None)[source]
    
+
    
+class idtxl.data.Data(data=None, dim_order='psr', normalise=True, seed=None)[source]
    
 
    Bases: object
    
 
    Store data for information dynamics estimation.
    
 
    Data takes a 1- to 3-dimensional array representing realisations of random
@@ -121,15 +120,15 @@ 
    Submodules
-
    
-property data
    
+
    
+
    
+property data
    
 
    Return data array.
    
 
    
 
 
    
-
    
-generate_logistic_maps_data(n_samples=1000, n_replications=10, coefficient_matrices=array([[[0.5, 0.0], [0.4, 0.5]]]), noise_std=0.1)[source]
    
+
    
+generate_logistic_maps_data(n_samples=1000, n_replications=10, coefficient_matrices=array([[[0.5, 0.], [0.4, 0.5]]]), noise_std=0.1)[source]
    
 
    Generate discrete-time coupled-logistic-maps time series.
    
 
    Generate data and overwrite the instance’s current data.
    
 
    The implemented logistic map function is f(x) = 4 * x * (1 - x).
    
@@ -155,8 +154,8 @@ 
    Submodules
-
    
-generate_mute_data(n_samples=1000, n_replications=10)[source]
    
+
    
+generate_mute_data(n_samples=1000, n_replications=10)[source]
    
 
    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,
@@ -190,8 +189,8 @@ 
    Submodules
-
    
-generate_var_data(n_samples=1000, n_replications=10, coefficient_matrices=array([[[0.5, 0.0], [0.4, 0.5]]]), noise_std=0.1)[source]
    
+
    
+generate_var_data(n_samples=1000, n_replications=10, coefficient_matrices=array([[[0.5, 0.], [0.4, 0.5]]]), noise_std=0.1)[source]
    
 
    Generate discrete-time VAR (vector autoregressive) time series.
    
 
    Generate data and overwrite the instance’s current data.
    
 
    
@@ -216,8 +215,8 @@ 
    Submodules
-
    
-get_realisations(current_value, idx_list, shuffle=False)[source]
    
+
    
+get_realisations(current_value, idx_list, shuffle=False)[source]
    
 
    Return realisations for a list of indices.
    
 
    Return realisations for indices in list. Optionally, realisations can
 be shuffled to create surrogate data for statistical testing. For
@@ -225,6 +224,15 @@ 
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@@ -290,20 +307,20 @@ 
    Submodules
-
    
-get_seed()[source]
    
+
    
+get_seed()[source]
    
 
    return the initial seed of the data
    
 
    
 
 
    
-
    
-get_state()[source]
    
+
    
+get_state()[source]
    
 
    return the current state of the random seed
    
 
    
 
 
    
-
    
-n_realisations(current_value=None)[source]
    
+
    
+n_realisations(current_value=None)[source]
    
 
    Number of realisations over samples and replications.
    
 
    
 
    Args:
    
@@ -319,14 +336,14 @@ 
    Submodules
-
    
-n_realisations_repl()[source]
    
+
    
+n_realisations_repl()[source]
    
 
    Number of realisations over replications.
    
 
    
 
 
    
-
    
-n_realisations_samples(current_value=None)[source]
    
+
    
+n_realisations_samples(current_value=None)[source]
    
 
    Number of realisations over samples.
    
 
    
 
    Args:
    
@@ -341,8 +358,8 @@ 
    Submodules
-
    
-permute_replications(current_value, idx_list)[source]
    
+
    
+permute_replications(current_value, idx_list)[source]
    
 
    Return realisations with permuted replications (time stays intact).
    
 
    Create surrogate data by permuting realisations over replications while
 keeping the temporal structure (order of samples) intact. Return
@@ -351,6 +368,15 @@ 
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    repl. ind.
    
 
    3 3 3 3
    
@@ -413,8 +448,8 @@ 
    Submodules
-
    
-permute_samples(current_value, idx_list, perm_settings)[source]
    
+
    
+permute_samples(current_value, idx_list, perm_settings)[source]
    
 
    Return realisations with permuted samples (repl. stays intact).
    
 
    Create surrogate data by permuting realisations over samples (time)
 while keeping the order of replications intact. Surrogates can be
@@ -433,6 +468,13 @@ 
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    repl. ind.
    
 
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    repl. ind.
    
 
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@@ -589,8 +659,8 @@ 
    Submodules
-
    
-set_data(data, dim_order)[source]
    
+
    
+set_data(data, dim_order)[source]
    
 
    Overwrite data in an existing Data object.
    
 
    
 
    Args:
    
@@ -606,8 +676,8 @@ 
    Submodules
-
    
-slice_permute_replications(process)[source]
    
+
    
+slice_permute_replications(process)[source]
    
 
    Return data slice with permuted replications (time stays intact).
    
 
    Create surrogate data by permuting realisations over replications while
 keeping the temporal structure (order of samples) intact. Return
@@ -617,8 +687,8 @@ 
    Submodules
-
    
-slice_permute_samples(process, perm_settings)[source]
    
+
    
+slice_permute_samples(process, perm_settings)[source]
    
 
    Return slice of data with permuted samples (repl. stays intact).
    
 
    Create surrogate data by permuting data in a slice over samples (time)
 while keeping the order of replications intact. Return slice for the
@@ -626,6 +696,13 @@ 
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    repl. ind.
    
 
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    repl. ind.
    
 
    1 1 1 1 1 1 1 1
    
@@ -794,8 +899,8 @@ 
    Submodules
-
    
-class idtxl.bivariate_te.BivariateTE[source]
    
+
    
+class idtxl.bivariate_te.BivariateTE[source]
    
 
    Bases: idtxl.network_inference.NetworkInferenceTE, idtxl.network_inference.NetworkInferenceBivariate
    
 
    Perform network inference using bivariate transfer entropy.
    
 
    Perform network inference using bivariate transfer entropy (TE). To
@@ -851,8 +956,8 @@ 
    Submodules
-
    
-analyse_network(settings, data, targets='all', sources='all')[source]
    
+
    
+analyse_network(settings, data, targets='all', sources='all')[source]
    
 
    Find bivariate transfer entropy between all nodes in the network.
    
 
    Estimate bivariate transfer entropy (TE) between all nodes in the
 network or between selected sources and targets.
    
@@ -913,8 +1018,8 @@ 
    Submodules
-
    
-analyse_single_target(settings, data, target, sources='all')[source]
    
+
    
+analyse_single_target(settings, data, target, sources='all')[source]
    
 
    Find bivariate transfer entropy between sources and a target.
    
 
    Find bivariate transfer entropy (TE) between all potential source
 processes and the target process. Uses bivariate, non-uniform embedding
@@ -1039,8 +1144,8 @@ 
    Submodules
-
    
-class idtxl.bivariate_mi.BivariateMI[source]
    
+
    
+class idtxl.bivariate_mi.BivariateMI[source]
    
 
    Bases: idtxl.network_inference.NetworkInferenceMI, idtxl.network_inference.NetworkInferenceBivariate
    
 
    Perform network inference using bivariate mutual information.
    
 
    Perform network inference using bivariate mutual information (MI). To
@@ -1090,8 +1195,8 @@ 
    Submodules
-
    
-analyse_network(settings, data, targets='all', sources='all')[source]
    
+
    
+analyse_network(settings, data, targets='all', sources='all')[source]
    
 
    Find bivariate mutual information between all nodes in the network.
    
 
    Estimate bivariate mutual information (MI) between all nodes in the
 network or between selected sources and targets.
    
@@ -1155,8 +1260,8 @@ 
    Submodules
-
    
-analyse_single_target(settings, data, target, sources='all')[source]
    
+
    
+analyse_single_target(settings, data, target, sources='all')[source]
    
 
    Find bivariate mutual information between sources and a target.
    
 
    Find bivariate mutual information (MI) between all potential source
 processes and the target process. Uses bivariate, non-uniform embedding
@@ -1280,8 +1385,8 @@ 
    Submodules
-
    
-class idtxl.bivariate_pid.BivariatePID[source]
    
+
    
+class idtxl.bivariate_pid.BivariatePID[source]
    
 
    Bases: idtxl.single_process_analysis.SingleProcessAnalysis
    
 
    Perform partial information decomposition for individual processes.
    
 
    Perform partial information decomposition (PID) for two source processes
@@ -1313,8 +1418,8 @@ 
    Submodules
-
    
-analyse_network(settings, data, targets, sources)[source]
    
+
    
+analyse_network(settings, data, targets, sources)[source]
    
 
    Estimate partial information decomposition for network nodes.
    
 
    Estimate partial information decomposition (PID) for multiple nodes in
 the network.
    
@@ -1377,8 +1482,8 @@ 
    Submodules
-
    
-analyse_single_target(settings, data, target, sources)[source]
    
+
    
+analyse_single_target(settings, data, target, sources)[source]
    
 
    Estimate partial information decomposition for a network node.
    
 
    Estimate partial information decomposition (PID) for a target node in
 the network.
    
@@ -1454,8 +1559,8 @@ 
    Submodules
-
    
-class idtxl.multivariate_te.MultivariateTE[source]
    
+
    
+class idtxl.multivariate_te.MultivariateTE[source]
    
 
    Bases: idtxl.network_inference.NetworkInferenceTE, idtxl.network_inference.NetworkInferenceMultivariate
    
 
    Perform network inference using multivariate transfer entropy.
    
 
    Perform network inference using multivariate transfer entropy (TE). To
@@ -1479,9 +1584,8 @@ 
    Submoduleshttp://doi.org/10.1103/PhysRevE.83.051112
    
 
-
    Attributes:
    
-
    
-
    
+
    
+
    Attributes:
    
 
    source_setlist
    indices of source processes tested for their influence on the
 target
    
 
    
@@ -1509,10 +1613,11 @@ 
    Submodulesbool
    statistical significance of the over-all TE
    
 
    
 
    
-
    
+
    
+
    
 
    
-
    
-analyse_network(settings, data, targets='all', sources='all')[source]
    
+
    
+analyse_network(settings, data, targets='all', sources='all')[source]
    
 
    Find multivariate transfer entropy between all nodes in the network.
    
 
    Estimate multivariate transfer entropy (TE) between all nodes in the
 network or between selected sources and targets.
    
@@ -1574,8 +1679,8 @@ 
    Submodules
-
    
-analyse_single_target(settings, data, target, sources='all')[source]
    
+
    
+analyse_single_target(settings, data, target, sources='all')[source]
    
 
    Find multivariate transfer entropy between sources and a target.
    
 
    Find multivariate transfer entropy (TE) between all source processes
 and the target process. Uses multivariate, non-uniform embedding found
@@ -1683,8 +1788,8 @@ 
    Submodules
-
    
-getit()[source]
    
+
    
+getit()[source]
    
 
    
 
 
    
@@ -1701,8 +1806,8 @@ 
    Submodules
-
    
-class idtxl.multivariate_mi.MultivariateMI[source]
    
+
    
+class idtxl.multivariate_mi.MultivariateMI[source]
    
 
    Bases: idtxl.network_inference.NetworkInferenceMI, idtxl.network_inference.NetworkInferenceMultivariate
    
 
    Perform network inference using multivariate mutual information.
    
 
    Perform network inference using multivariate mutual information (MI). To
@@ -1750,8 +1855,8 @@ 
    Submodules
-
    
-analyse_network(settings, data, targets='all', sources='all')[source]
    
+
    
+analyse_network(settings, data, targets='all', sources='all')[source]
    
 
    Find multivariate mutual information between nodes in the network.
    
 
    Estimate multivariate mutual information (MI) between all nodes in the
 network or between selected sources and targets.
    
@@ -1819,8 +1924,8 @@ 
    Submodules
-
    
-analyse_single_target(settings, data, target, sources='all')[source]
    
+
    
+analyse_single_target(settings, data, target, sources='all')[source]
    
 
    Find multivariate mutual information between sources and a target.
    
 
    Find multivariate mutual information (MI) between all source processes
 and the target process. Uses multivariate, non-uniform embedding found
@@ -1942,8 +2047,8 @@ 
    Submodules
-
    
-class idtxl.multivariate_pid.MultivariatePID[source]
    
+
    
+class idtxl.multivariate_pid.MultivariatePID[source]
    
 
    Bases: idtxl.single_process_analysis.SingleProcessAnalysis
    
 
    Perform partial information decomposition for individual processes.
    
 
    Perform partial information decomposition (PID) for multiple source
@@ -1975,8 +2080,8 @@ 
    Submodules
-
    
-analyse_network(settings, data, targets, sources)[source]
    
+
    
+analyse_network(settings, data, targets, sources)[source]
    
 
    Estimate partial information decomposition for network nodes.
    
 
    Estimate, for multiple nodes (target processes), the partial
 information decomposition (PID) for multiple source processes
@@ -2040,8 +2145,8 @@ 
    Submodules
-
    
-analyse_single_target(settings, data, target, sources)[source]
    
+
    
+analyse_single_target(settings, data, target, sources)[source]
    
 
    Estimate partial information decomposition for a network node.
    
 
    Estimate partial information decomposition (PID) for multiple source
 processes (up to 4 sources) and a target process in the network.
    
@@ -2113,8 +2218,8 @@ 
    Submodules
-
    
-class idtxl.active_information_storage.ActiveInformationStorage[source]
    
+
    
+class idtxl.active_information_storage.ActiveInformationStorage[source]
    
 
    Bases: idtxl.single_process_analysis.SingleProcessAnalysis
    
 
    Estimate active information storage in individual processes.
    
 
    Estimate active information storage (AIS) in individual processes of the
@@ -2157,8 +2262,8 @@ 
    Submodules
-
    
-analyse_network(settings, data, processes='all')[source]
    
+
    
+analyse_network(settings, data, processes='all')[source]
    
 
    Estimate active information storage for multiple network processes.
    
 
    Estimate active information storage for all or a subset of processes in
 the network.
    
@@ -2216,8 +2321,8 @@ 
    Submodules
-
    
-analyse_single_process(settings, data, process)[source]
    
+
    
+analyse_single_process(settings, data, process)[source]
    
 
    Estimate active information storage for a single process.
    
 
    Estimate active information storage for one process in the network.
 Uses non-uniform embedding found through information maximisation. This
@@ -2294,8 +2399,8 @@ 
    Submodules
    idtxl.embedding_optimization_ais_Rudelt module
    
 
    Optimization of embedding parameters of spike times using the history dependence estimators
    
 
    
-
    
-class idtxl.embedding_optimization_ais_Rudelt.OptimizationRudelt(settings=None)[source]
    
+
    
+class idtxl.embedding_optimization_ais_Rudelt.OptimizationRudelt(settings=None)[source]
    
 
    Bases: object
    
 
    Optimization of embedding parameters of spike times using the history dependence estimators
    
 
    References:
    
@@ -2484,21 +2589,21 @@ 
    Submodules
-
    
-analyse_auto_MI(spike_times)[source]
    
+
    
+analyse_auto_MI(spike_times)[source]
    
 
    Get the auto MI for the spike times.  If it is available from file, load
 it, else compute it.
    
 
    
 
 
    
-
    
-check_inputs()[source]
    
+
    
+check_inputs()[source]
    
 
    Check input settings for completeness
    
 
    
 
 
    
-
    
-compute_CIs(data, target_R='R_max', symbol_block_length=None)[source]
    
+
    
+compute_CIs(data, target_R='R_max', symbol_block_length=None)[source]
    
 
    Compute bootstrap replications of the history dependence estimate
 which can be used to obtain confidence intervals.
    
 
    
@@ -2526,61 +2631,61 @@ 
    Submodules
-
    
-get_R_tot(return_averaged_R=False, **kwargs)[source]
    
+
    
+get_R_tot(return_averaged_R=False, **kwargs)[source]
    
 
    
 
 
    
-
    
-get_auto_MI(spike_times, bin_size, number_of_delays)[source]
    
+
    
+get_auto_MI(spike_times, bin_size, number_of_delays)[source]
    
 
    Compute the auto mutual information in the neuron’s activity, a
 measure closely related to history dependence.
    
 
    
 
 
    
-
    
-get_bootstrap_history_dependence(data, embedding, number_of_bootstraps, symbol_block_length=None)[source]
    
+
    
+get_bootstrap_history_dependence(data, embedding, number_of_bootstraps, symbol_block_length=None)[source]
    
 
    For a given embedding, return bootstrap replications for R.
    
 
    
 
 
    
-
    
-get_embeddings(embedding_past_range_set, embedding_number_of_bins_set, embedding_scaling_exponent_set)[source]
    
+
    
+get_embeddings(embedding_past_range_set, embedding_number_of_bins_set, embedding_scaling_exponent_set)[source]
    
 
    Get all combinations of parameters T, d, k, based on the
 sets of selected parameters.
    
 
    
 
 
    
-
    
-get_embeddings_that_maximise_R(bbc_tolerance=None, dependent_var='T', get_as_list=False)[source]
    
+
    
+get_embeddings_that_maximise_R(bbc_tolerance=None, dependent_var='T', get_as_list=False)[source]
    
 
    For each T (or d), get the embedding for which R is maximised.
    
 
    For the bbc estimator, here the bbc_tolerance is applied, ie
 get the unbiased embeddings that maximise R.
    
 
    
 
 
    
-
    
-get_history_dependence(data, process)[source]
    
+
    
+get_history_dependence(data, process)[source]
    
 
    Estimate the history dependence for each embedding to all given processes.
    
 
    
 
 
    
-
    
-get_information_timescale_tau_R()[source]
    
+
    
+get_information_timescale_tau_R()[source]
    
 
    Get the information timescale tau_R, a characteristic
 timescale of history dependence similar to an autocorrelation
 time.
    
 
    
 
 
    
-
    
-get_past_range(number_of_bins_d, first_bin_size, scaling_k)[source]
    
+
    
+get_past_range(number_of_bins_d, first_bin_size, scaling_k)[source]
    
 
    Get the past range T of the embedding, based on the parameters d, tau_1 and k.
    
 
    
 
 
    
-
    
-get_set_of_scalings(past_range_T, number_of_bins_d, number_of_scalings, min_first_bin_size, min_step_for_scaling)[source]
    
+
    
+get_set_of_scalings(past_range_T, number_of_bins_d, number_of_scalings, min_first_bin_size, min_step_for_scaling)[source]
    
 
    Get scaling exponents such that the uniform embedding as well as
 the embedding for which the first bin has a length of
 min_first_bin_size (in seconds), as well as linearly spaced
@@ -2589,8 +2694,8 @@ 
    Submodules
-
    
-get_temporal_depth_T_D(get_R_thresh=False)[source]
    
+
    
+get_temporal_depth_T_D(get_R_thresh=False)[source]
    
 
    Get the temporal depth T_D, the past range for the
 ‘optimal’ embedding parameters.
    
 
    Given the maximal history dependence R at each past range T,
@@ -2601,8 +2706,8 @@ 
    Submodules
-
    
-optimize(data, processes='all')[source]
    
+
    
+optimize(data, processes='all')[source]
    
 
    Optimize the embedding parameters of spike time data using the Rudelt history dependence estimator.
    
 
    References:
    
 
    
@@ -2642,8 +2747,8 @@ 
    Submodules
-
    
-optimize_single_run(data, process)[source]
    
+
    
+optimize_single_run(data, process)[source]
    
 
    optimizes a single realisation of spike time data given the process number
    
 
    
 
    Args:
    
@@ -2698,8 +2803,8 @@ 
    Submodules
-
    
-remove_subresults_single_process()[source]
    
+
    
+remove_subresults_single_process()[source]
    
 
    delete results from self from single process
    
 
    
 
@@ -2710,8 +2815,8 @@ 
    Submodules
    idtxl.estimators_Rudelt module
    
 
    Provide HDE estimators.
    
 
    
-
    
-class idtxl.estimators_Rudelt.RudeltAbstractEstimator(settings=None)[source]
    
+
    
+class idtxl.estimators_Rudelt.RudeltAbstractEstimator(settings=None)[source]
    
 
    Bases: idtxl.estimator.Estimator
    
 
    Abstract class for implementation of nsb and plugin estimators from Rudelt.
    
 
    Abstract class for implementation of nsb and plugin estimators, child classes
@@ -2755,16 +2860,16 @@ 
    Submodules
-
    
-get_median_number_of_spikes_per_bin(raw_symbols)[source]
    
+
    
+get_median_number_of_spikes_per_bin(raw_symbols)[source]
    
 
    Given raw symbols (in which the number of spikes per bin are counted,
 ie not necessarily binary quantity), get the median number of spikes
 for each bin, among all symbols obtained by the embedding.
    
 
    
 
 
    
-
    
-get_multiplicities(symbol_counts, alphabet_size)[source]
    
+
    
+get_multiplicities(symbol_counts, alphabet_size)[source]
    
 
    Get the multiplicities of some given symbol counts.
    
 
    To estimate the entropy of a system, it is only important how
 often a symbol/ event occurs (the probability that it occurs), not
@@ -2774,28 +2879,28 @@ 
    Submodules
-
    
-get_past_range(number_of_bins_d, first_bin_size, scaling_k)[source]
    
+
    
+get_past_range(number_of_bins_d, first_bin_size, scaling_k)[source]
    
 
    Get the past range T of the embedding, based on the parameters d, tau_1 and k.
    
 
    
 
 
    
-
    
-get_raw_symbols(spike_times, embedding, first_bin_size)[source]
    
+
    
+get_raw_symbols(spike_times, embedding, first_bin_size)[source]
    
 
    Get the raw symbols (in which the number of spikes per bin are counted,
 ie not necessarily binary quantity), as obtained by applying the
 embedding.
    
 
    
 
 
    
-
    
-get_symbol_counts(symbol_array)[source]
    
+
    
+get_symbol_counts(symbol_array)[source]
    
 
    Count how often symbols occur
    
 
    
 
 
    
-
    
-get_window_delimiters(number_of_bins_d, scaling_k, first_bin_size)[source]
    
+
    
+get_window_delimiters(number_of_bins_d, scaling_k, first_bin_size)[source]
    
 
    Get delimiters of the window, used to describe the embedding. The
 window includes both the past embedding and the response.
    
 
    The delimiters are times, relative to the first bin, that separate
@@ -2803,8 +2908,8 @@ 
    Submodules
-
    
-is_analytic_null_estimator()[source]
    
+
    
+is_analytic_null_estimator()[source]
    
 
    Indicate if estimator supports analytic surrogates.
    
 
    Return true if the estimator implements estimate_surrogates_analytic()
 where data is formatted as per the estimate method for this estimator.
    
@@ -2815,8 +2920,8 @@ 
    Submodules
-
    
-is_parallel()[source]
    
+
    
+is_parallel()[source]
    
 
    Indicate if estimator supports parallel estimation over chunks.
    
 
    Return true if the supports parallel estimation over chunks, where a
 chunk is one independent data set.
    
@@ -2827,16 +2932,16 @@ 
    Submodules
-
    
-symbol_array_to_binary(spikes_in_window, number_of_bins_d)[source]
    
+
    
+symbol_array_to_binary(spikes_in_window, number_of_bins_d)[source]
    
 
    Given an array of 1s and 0s, representing spikes and the absence
 thereof, read the array as a binary number to obtain a
 (base 10) integer.
    
 
    
 
 
    
-
    
-symbol_binary_to_array(symbol_binary, number_of_bins_d)[source]
    
+
    
+symbol_binary_to_array(symbol_binary, number_of_bins_d)[source]
    
 
    Given a binary representation of a symbol (cf symbol_array_to_binary),
 convert it back into its array-representation.
    
 
    
@@ -2844,8 +2949,8 @@ 
    Submodules
-
    
-class idtxl.estimators_Rudelt.RudeltAbstractNSBEstimator(settings=None)[source]
    
+
    
+class idtxl.estimators_Rudelt.RudeltAbstractNSBEstimator(settings=None)[source]
    
 
    Bases: idtxl.estimators_Rudelt.RudeltAbstractEstimator
    
 
    Abstract class for implementation of NSB estimators from Rudelt.
    
 
    Abstract class for implementation of Nemenman-Shafee-Bialek (NSB)
@@ -2893,67 +2998,67 @@ 
    Submodules
-
    
-H1(beta, mk, K, N)[source]
    
+
    
+H1(beta, mk, K, N)[source]
    
 
    Compute the first moment (expectation value) of the entropy H.
    
 
    H is the entropy one obtains with a symmetric Dirichlet prior
 with concentration parameter beta and a multinomial likelihood.
    
 
    
 
 
    
-
    
-alpha_ML(mk, K1, N)[source]
    
+
    
+alpha_ML(mk, K1, N)[source]
    
 
    Compute first guess for the beta_MAP (cf get_beta_MAP) parameter
 via the posterior of a Dirichlet process.
    
 
    
 
 
    
-
    
-d2_log_rho(beta, mk, K, N)[source]
    
+
    
+d2_log_rho(beta, mk, K, N)[source]
    
 
    Second derivate of the logarithm of the Dirichlet multinomial likelihood.
    
 
    
 
 
    
-
    
-d2_log_rho_xi(beta, mk, K, N)[source]
    
+
    
+d2_log_rho_xi(beta, mk, K, N)[source]
    
 
    Second derivative of the logarithm of the nsb (unnormalized) posterior.
    
 
    
 
 
    
-
    
-d2_xi(beta, K)[source]
    
+
    
+d2_xi(beta, K)[source]
    
 
    Second derivative of xi(beta) (cf d_xi).
    
 
    
 
 
    
-
    
-d3_xi(beta, K)[source]
    
+
    
+d3_xi(beta, K)[source]
    
 
    Third derivative of xi(beta) (cf d_xi).
    
 
    
 
 
    
-
    
-d_log_rho(beta, mk, K, N)[source]
    
+
    
+d_log_rho(beta, mk, K, N)[source]
    
 
    First derivate of the logarithm of the Dirichlet multinomial likelihood.
    
 
    
 
 
    
-
    
-d_log_rho_xi(beta, mk, K, N)[source]
    
+
    
+d_log_rho_xi(beta, mk, K, N)[source]
    
 
    First derivative of the logarithm of the nsb (unnormalized) posterior.
    
 
    
 
 
    
-
    
-d_xi(beta, K)[source]
    
+
    
+d_xi(beta, K)[source]
    
 
    First derivative of xi(beta).
    
 
    xi(beta) is the entropy of the system when no data has been observed.
 d_xi is the prior for the nsb estimator
    
 
    
 
 
    
-
    
-get_beta_MAP(mk, K, N)[source]
    
+
    
+get_beta_MAP(mk, K, N)[source]
    
 
    Get the maximum a posteriori (MAP) value for beta.
    
 
    Provides the location of the peak, around which we integrate.
    
 
    beta_MAP is the value for beta for which the posterior of the
@@ -2962,8 +3067,8 @@ 
    Submodules
-
    
-get_integration_bounds(mk, K, N)[source]
    
+
    
+get_integration_bounds(mk, K, N)[source]
    
 
    Find the integration bounds for the estimator.
    
 
    Typically it is a delta-like distribution so it is sufficient
 to integrate around this peak. (If not this function is not
@@ -2971,17 +3076,17 @@ 
    Submodules
-
    
-log_likelihood_DP_alpha(a, K1, N)[source]
    
+
    
+log_likelihood_DP_alpha(a, K1, N)[source]
    
 
    Alpha-dependent terms of the log-likelihood of a Dirichlet Process.
    
 
    
 
 
    
-
    
-nsb_entropy(mk, K, N)[source]
    
+
    
+nsb_entropy(mk, K, N)[source]
    
 
    Estimate the entropy of a system using the NSB estimator.
    
 
    
-
    Parameters:
    
+
    Parameters
    
 
      
 
    • mk – multiplicities
      • 
 
    • K – number of possible symbols/ state space of the system
      • 
@@ -2992,16 +3097,16 @@ 
      Submodules
-
      
-rho(beta, mk, K, N)[source]
      
+
      
+rho(beta, mk, K, N)[source]
      
 
      rho(beta, data) is the Dirichlet multinomial likelihood.
      
 
      rho(beta, data) together with the d_xi(beta) make up
 the posterior for the nsb estimator
      
 
    
 
 
    
-
    
-unnormalized_posterior(beta, mk, K, N)[source]
    
+
    
+unnormalized_posterior(beta, mk, K, N)[source]
    
 
    The (unnormalized) posterior in the nsb estimator.
    
 
    Product of the likelihood rho and the prior d_xi;
 the normalizing factor is given by the marginal likelihood
    
@@ -3010,8 +3115,8 @@ 
    Submodules
-
    
-class idtxl.estimators_Rudelt.RudeltBBCEstimator(settings=None)[source]
    
+
    
+class idtxl.estimators_Rudelt.RudeltBBCEstimator(settings=None)[source]
    
 
    Bases: idtxl.estimators_Rudelt.RudeltAbstractEstimator
    
 
    Bayesian bias criterion (BBC) Estimator using NSB and Plugin estimator
    
 
    Calculate the mutual information (MI) of one variable depending on its past
@@ -3047,11 +3152,11 @@ 
    Submodules
-
    
-bayesian_bias_criterion(R_nsb, R_plugin, bbc_tolerance)[source]
    
+
    
+bayesian_bias_criterion(R_nsb, R_plugin, bbc_tolerance)[source]
    
 
    Get whether the Bayesian bias criterion (bbc) is passed.
    
 
    
-
    Parameters:
    
+
    Parameters
    
 
      
 
    • R_nsb – history dependence computed with NSB estimator
      • 
 
    • R_plugin – history dependence computed with plugin estimator
      • 
@@ -3062,8 +3167,8 @@ 
      Submodules
-
      
-estimate(symbol_array, past_symbol_array, current_symbol_array, bbc_tolerance=None)[source]
      
+
      
+estimate(symbol_array, past_symbol_array, current_symbol_array, bbc_tolerance=None)[source]
      
 
      Calculate the mutual information (MI) of one variable depending on its past
 using nsb and plugin estimator and check if bias criterion is passed/
      
 
      
@@ -3093,12 +3198,12 @@ 
      Submodules
-
      
-get_bbc_term(R_nsb, R_plugin)[source]
      
+
      
+get_bbc_term(R_nsb, R_plugin)[source]
      
 
      Get the bbc tolerance-independent term of the Bayesian bias
 criterion (bbc).
      
 
      
-
      Parameters:
      
+
      Parameters
      
 
      
 
      
-
      
-class idtxl.estimators_multivariate_pid.SxPID(settings)[source]
      
+
      
+class idtxl.estimators_multivariate_pid.SxPID(settings)[source]
      
 
      Bases: idtxl.estimator.Estimator
      
 
      Estimate partial information decomposition for multiple inputs.
      
 
      Implementation of the multivariate partial information decomposition (PID)
@@ -4967,8 +5173,8 @@ 
      Submodules
-
      
-estimate(s, t)[source]
      
+
      
+estimate(s, t)[source]
      
 
      
 
      Args:
      
 
      slist of numpy arrays
      1D arrays containing realizations of a discrete random variable
      
@@ -4995,8 +5201,8 @@ 
      Submodules
-
      
-is_analytic_null_estimator()[source]
      
+
      
+is_analytic_null_estimator()[source]
      
 
      Indicate if estimator supports analytic surrogates.
      
 
      Return true if the estimator implements estimate_surrogates_analytic()
 where data is formatted as per the estimate method for this estimator.
      
@@ -5007,8 +5213,8 @@ 
      Submodules
-
      
-is_parallel()[source]
      
+
      
+is_parallel()[source]
      
 
      Indicate if estimator supports parallel estimation over chunks.
      
 
      Return true if the supports parallel estimation over chunks, where a
 chunk is one independent data set.
      
@@ -5029,8 +5235,8 @@ 
      Submoduleshttp://doi.org/10.3390/e16042161
      
 
      
-
      
-class idtxl.estimators_pid.SydneyPID(settings)[source]
      
+
      
+class idtxl.estimators_pid.SydneyPID(settings)[source]
      
 
      Bases: idtxl.estimator.Estimator
      
 
      Estimate partial information decomposition of discrete variables.
      
 
      Fast implementation of the BROJA partial information decomposition (PID)
@@ -5090,8 +5296,8 @@ 
      Submodules
-
      
-estimate(s1, s2, t)[source]
      
+
      
+estimate(s1, s2, t)[source]
      
 
      
 
      Args:
      
 
      s1numpy array
      1D array containing realizations of a discrete random variable
      
@@ -5112,8 +5318,8 @@ 
      Submodules
-
      
-is_analytic_null_estimator()[source]
      
+
      
+is_analytic_null_estimator()[source]
      
 
      Indicate if estimator supports analytic surrogates.
      
 
      Return true if the estimator implements estimate_surrogates_analytic()
 where data is formatted as per the estimate method for this estimator.
      
@@ -5124,8 +5330,8 @@ 
      Submodules
-
      
-is_parallel()[source]
      
+
      
+is_parallel()[source]
      
 
      Indicate if estimator supports parallel estimation over chunks.
      
 
      Return true if the supports parallel estimation over chunks, where a
 chunk is one independent data set.
      
@@ -5138,8 +5344,8 @@ 
      Submodules
-
      
-class idtxl.estimators_pid.TartuPID(settings)[source]
      
+
      
+class idtxl.estimators_pid.TartuPID(settings)[source]
      
 
      Bases: idtxl.estimator.Estimator
      
 
      Estimate partial information decomposition for two inputs and one output
      
 
      Implementation of the partial information decomposition (PID) estimator for
@@ -5172,8 +5378,8 @@ 
      Submodules
-
      
-estimate(s1, s2, t)[source]
      
+
      
+estimate(s1, s2, t)[source]
      
 
      
 
      Args:
      
 
      s1numpy array
      1D array containing realizations of a discrete random variable
      
@@ -5193,8 +5399,8 @@ 
      Submodules
-
      
-is_analytic_null_estimator()[source]
      
+
      
+is_analytic_null_estimator()[source]
      
 
      Indicate if estimator supports analytic surrogates.
      
 
      Return true if the estimator implements estimate_surrogates_analytic()
 where data is formatted as per the estimate method for this estimator.
      
@@ -5205,8 +5411,8 @@ 
      Submodules
-
      
-is_parallel()[source]
      
+
      
+is_parallel()[source]
      
 
      Indicate if estimator supports parallel estimation over chunks.
      
 
      Return true if the supports parallel estimation over chunks, where a
 chunk is one independent data set.
      
@@ -5223,8 +5429,8 @@ 
      Submodules
      idtxl.idtxl_exceptions module
      
 
      Provide error handling and warnings.
      
 
      
-
      
-exception idtxl.idtxl_exceptions.AlgorithmExhaustedError(message)[source]
      
+
      
+exception idtxl.idtxl_exceptions.AlgorithmExhaustedError(message)[source]
      
 
      Bases: Exception
      
 
      Exception raised to signal that the estimators can no longer be used
 for this particular target (e.g. because of memory errors in high
@@ -5236,14 +5442,14 @@ 
      Submodules
-
      
-exception idtxl.idtxl_exceptions.BROJA_2PID_Exception[source]
      
+
      
+exception idtxl.idtxl_exceptions.BROJA_2PID_Exception[source]
      
 
      Bases: Exception
      
 
      
 
 
      
-
      
-exception idtxl.idtxl_exceptions.JidtOutOfMemoryError(message)[source]
      
+
      
+exception idtxl.idtxl_exceptions.JidtOutOfMemoryError(message)[source]
      
 
      Bases: idtxl.idtxl_exceptions.AlgorithmExhaustedError
      
 
      
 
      Exception raised to signal a Java OutOfMemoryException.
      It is a child class of AlgorithmExhaustedError.
      
@@ -5254,8 +5460,8 @@ 
      Submodules
-
      
-idtxl.idtxl_exceptions.package_missing(err, message)[source]
      
+
      
+idtxl.idtxl_exceptions.package_missing(err, message)[source]
      
 
      Report a missing optional package upon import.
      
 
      
 
@@ -5266,8 +5472,8 @@ 
      Submodules
-
      
-idtxl.idtxl_io.export_brain_net_viewer(adjacency_matrix, mni_coord, file_name, **kwargs)[source]
      
+
      
+idtxl.idtxl_io.export_brain_net_viewer(adjacency_matrix, mni_coord, file_name, **kwargs)[source]
      
 
      Export network to BrainNet Viewer.
      
 
      Export networks to BrainNet Viewer (project home page:
 http://www.nitrc.org/projects/bnv/). BrainNet Viewer is a MATLAB
@@ -5308,8 +5514,8 @@ 
      Submodules
-
      
-idtxl.idtxl_io.export_networkx_graph(adjacency_matrix, weights)[source]
      
+
      
+idtxl.idtxl_io.export_networkx_graph(adjacency_matrix, weights)[source]
      
 
      Export networkx graph object for an inferred network.
      
 
      Export a weighted, directed graph object from the network of inferred
 (multivariate) interactions (e.g., multivariate TE), using the networkx
@@ -5333,8 +5539,8 @@ 
      Submodules
-
      
-idtxl.idtxl_io.export_networkx_source_graph(results, target, sign_sources=True, fdr=True)[source]
      
+
      
+idtxl.idtxl_io.export_networkx_source_graph(results, target, sign_sources=True, fdr=True)[source]
      
 
      Export graph object of source variables for a single target.
      
 
      Export graph object from the network of (multivariate) interactions (e.g.,
 multivariate TE) between single source variables and a target process using
@@ -5364,8 +5570,8 @@ 
      Submodules
-
      
-idtxl.idtxl_io.import_fieldtrip(file_name, ft_struct_name, file_version, normalise=True)[source]
      
+
      
+idtxl.idtxl_io.import_fieldtrip(file_name, ft_struct_name, file_version, normalise=True)[source]
      
 
      Convert FieldTrip-style MATLAB-file into an IDTxl Data object.
      
 
      Import a MATLAB structure with fields  “trial” (data), “label” (channel
 labels), “time” (time stamps for data samples), and “fsample” (sampling
@@ -5405,8 +5611,8 @@ 
      Submodules
-
      
-idtxl.idtxl_io.import_matarray(file_name, array_name, file_version, dim_order, normalise=True)[source]
      
+
      
+idtxl.idtxl_io.import_matarray(file_name, array_name, file_version, dim_order, normalise=True)[source]
      
 
      Read Matlab hdf5 file into IDTxl.
      
 
      reads a matlab hdf5 file (“-v7.3’ or higher, .mat) or non-hdf5 files with a
 SINGLE array inside and returns an IDTxl Data() object.
      
@@ -5444,8 +5650,8 @@ 
      Submodules
-
      
-idtxl.idtxl_io.load_json(file_path)[source]
      
+
      
+idtxl.idtxl_io.load_json(file_path)[source]
      
 
      Load dictionary saved as JSON file from disk.
      
 
      
 
      Args:
      
@@ -5463,14 +5669,14 @@ 
      Submodules
-
      
-idtxl.idtxl_io.load_pickle(name)[source]
      
+
      
+idtxl.idtxl_io.load_pickle(name)[source]
      
 
      Load objects that have been saved using Python’s pickle module.
      
 
      
 
 
      
-
      
-idtxl.idtxl_io.save_json(d, file_path)[source]
      
+
      
+idtxl.idtxl_io.save_json(d, file_path)[source]
      
 
      Save dictionary to disk as JSON file.
      
 
      Writes dictionary to disk at the specified file path.
      
 
      
@@ -5487,8 +5693,8 @@ 
      Submodules
-
      
-idtxl.idtxl_io.save_pickle(obj, name)[source]
      
+
      
+idtxl.idtxl_io.save_pickle(obj, name)[source]
      
 
      Save objects using Python’s pickle module.
      
 
      
 
      Note:
      pickle.HIGHEST_PROTOCOL is a binary format, which may be inconvenient,
@@ -5502,26 +5708,26 @@ 
      Submodules
      idtxl.idtxl_utils module
      
 
      Provide IDTxl utility functions.
      
 
      
-
      
-idtxl.idtxl_utils.argsort_descending(a)[source]
      
+
      
+idtxl.idtxl_utils.argsort_descending(a)[source]
      
 
      Sort array in descending order and return sortind indices.
      
 
      
 
 
      
-
      
-idtxl.idtxl_utils.autocorrelation(x)[source]
      
+
      
+idtxl.idtxl_utils.autocorrelation(x)[source]
      
 
      Calculate autocorrelation of a vector.
      
 
      
 
 
      
-
      
-idtxl.idtxl_utils.calculate_mi(corr)[source]
      
+
      
+idtxl.idtxl_utils.calculate_mi(corr)[source]
      
 
      Calculate mutual information from correlation coefficient.
      
 
      
 
 
      
-
      
-idtxl.idtxl_utils.combine_discrete_dimensions(a, numBins)[source]
      
+
      
+idtxl.idtxl_utils.combine_discrete_dimensions(a, numBins)[source]
      
 
      Combine multi-dimensional discrete variable into a single dimension.
      
 
      Combine all dimensions for a discrete variable down into a single
 dimensional value for each sample. This is done basically by multiplying
@@ -5547,8 +5753,8 @@ 
      Submodules
-
      
-idtxl.idtxl_utils.conflicting_entries(dict_1, dict_2)[source]
      
+
      
+idtxl.idtxl_utils.conflicting_entries(dict_1, dict_2)[source]
      
 
      Test two dictionaries for unequal entries.
      
 
      Note that only keys that are present in both dicts are compared. If one
 dictionary contains an entry not present in the other dictionary, the
@@ -5556,8 +5762,8 @@ 
      Submodules
-
      
-idtxl.idtxl_utils.discretise(a, numBins)[source]
      
+
      
+idtxl.idtxl_utils.discretise(a, numBins)[source]
      
 
      Discretise continuous data.
      
 
      Discretise continuous data into discrete values (with 0 as lowest) by
 evenly partitioning the range of the data, one dimension at a time.
@@ -5581,8 +5787,8 @@ 
      Submodules
-
      
-idtxl.idtxl_utils.discretise_max_ent(a, numBins)[source]
      
+
      
+idtxl.idtxl_utils.discretise_max_ent(a, numBins)[source]
      
 
      Discretise continuous data using maximum entropy partitioning.
      
 
      Discretise continuous data into discrete values (with 0 as lowest) by
 making a maximum entropy partitioning, one dimension at a time. Adapted
@@ -5606,20 +5812,20 @@ 
      Submodules
-
      
-idtxl.idtxl_utils.equal_dicts(dict_1, dict_2)[source]
      
+
      
+idtxl.idtxl_utils.equal_dicts(dict_1, dict_2)[source]
      
 
      Test two dictionaries for equality.
      
 
      
 
 
      
-
      
-idtxl.idtxl_utils.print_dict(d, indent=4)[source]
      
+
      
+idtxl.idtxl_utils.print_dict(d, indent=4)[source]
      
 
      Use Python’s pretty printer to print dictionaries to the console.
      
 
      
 
 
      
-
      
-idtxl.idtxl_utils.remove_column(a, j)[source]
      
+
      
+idtxl.idtxl_utils.remove_column(a, j)[source]
      
 
      Remove a column from a numpy array.
      
 
      This is faster than logical indexing (‘25 times faster’), because it does
 not make copies, see
@@ -5636,8 +5842,8 @@ 
      Submodules
-
      
-idtxl.idtxl_utils.remove_row(a, i)[source]
      
+
      
+idtxl.idtxl_utils.remove_row(a, i)[source]
      
 
      Remove a row from a numpy array.
      
 
      This is faster than logical indexing (‘25 times faster’), because it does
 not make copies, see
@@ -5654,8 +5860,8 @@ 
      Submodules
-
      
-idtxl.idtxl_utils.separate_arrays(idx_all, idx_single, a)[source]
      
+
      
+idtxl.idtxl_utils.separate_arrays(idx_all, idx_single, a)[source]
      
 
      Separate a single column from all other columns in a 2D-array.
      
 
      Return the separated single column and the remaining columns of a 2D-
 array.
      
@@ -5682,14 +5888,14 @@ 
      Submodules
-
      
-idtxl.idtxl_utils.sort_descending(a)[source]
      
+
      
+idtxl.idtxl_utils.sort_descending(a)[source]
      
 
      Sort array in descending order.
      
 
      
 
 
      
-
      
-idtxl.idtxl_utils.standardise(a, dimension=0, df=1)[source]
      
+
      
+idtxl.idtxl_utils.standardise(a, dimension=0, df=1)[source]
      
 
      Z-standardise a numpy array along a given dimension.
      
 
      Standardise array along the axis defined in dimension using the denominator
 (N - df) for the calculation of the standard deviation.
      
@@ -5712,8 +5918,8 @@ 
      Submodules
-
      
-idtxl.idtxl_utils.swap_chars(s, i_1, i_2)[source]
      
+
      
+idtxl.idtxl_utils.swap_chars(s, i_1, i_2)[source]
      
 
      Swap to characters in a string.
      
 
      
 
      Example:
      >>> print(swap_chars('heLlotHere', 2, 6))
@@ -5724,50 +5930,67 @@ 
      Submodules
+
      
+class idtxl.idtxl_utils.timeout(timeout_duration, exception_message='Timeout')[source]
      
+
      Bases: object
      
+
      Context manager for a timeout using threading module.
+args:
      
+
      
+
      timeout_duration: float, number of seconds to wait before timeout is triggered
+exception_message: string, message to put in the exception
      
+
      
+
      
+
      
+timeout_handler()[source]
      
+
      
+
+
      
+
 
 
      
 
      idtxl.network_analysis module
      
 
      Parent class for network inference and network comparison.
      
 
      
-
      
-class idtxl.network_analysis.NetworkAnalysis[source]
      
+
      
+class idtxl.network_analysis.NetworkAnalysis[source]
      
 
      Bases: object
      
 
      Provide an analysis setup for network inference or comparison.
      
 
      The class provides routines to check user input and set defaults.
      
-
      
-
      
-property current_value
      
+
      
+
      
+property current_value
      
 
      Get index of the current_value.
      
 
      
 
 
      
-
      
-resume_checkpoint(file_path)[source]
      
+
      
+resume_checkpoint(file_path)[source]
      
 
      Resume analysis from a checkpoint saved to disk.
      
 
      
 
      Args:
      
-
      file_pathstr
      path to checkpoint file (excluding extension: *.ckp)
      
+
      file_pathstr
      path to checkpoint file (excluding extension: *.ckp)
      
 
      
 
      
 
      
 
      
 
      
 
-
      
-
      
-property selected_vars_full
      
+
      
+
      
+property selected_vars_full
      
 
      List of indices of the full conditional set.
      
 
      
 
-
      
-
      
-property selected_vars_sources
      
+
      
+
      
+property selected_vars_sources
      
 
      List of indices of source samples in the conditional set.
      
 
      
 
-
      
-
      
-property selected_vars_target
      
+
      
+
      
+property selected_vars_target
      
 
      List of indices of target samples in the conditional set.
      
 
      
 
@@ -5778,8 +6001,8 @@ 
      Submodules
      idtxl.network_inference module
      
 
      Parent class for all network inference.
      
 
      
-
      
-class idtxl.network_inference.NetworkInference[source]
      
+
      
+class idtxl.network_inference.NetworkInference[source]
      
 
      Bases: idtxl.network_analysis.NetworkAnalysis
      
 
      Parent class for network inference algorithms.
      
 
      Hold variables that are relevant for network inference using for example
@@ -5805,29 +6028,29 @@ 
      Submodules
-
      
-class idtxl.network_inference.NetworkInferenceBivariate[source]
      
+
      
+class idtxl.network_inference.NetworkInferenceBivariate[source]
      
 
      Bases: idtxl.network_inference.NetworkInference
      
 
      Parent class for bivariate network inference algorithms.
      
 
      
 
 
      
-
      
-class idtxl.network_inference.NetworkInferenceMI[source]
      
+
      
+class idtxl.network_inference.NetworkInferenceMI[source]
      
 
      Bases: idtxl.network_inference.NetworkInference
      
 
      Parent class for mutual information network inference algorithms.
      
 
      
 
 
      
-
      
-class idtxl.network_inference.NetworkInferenceMultivariate[source]
      
+
      
+class idtxl.network_inference.NetworkInferenceMultivariate[source]
      
 
      Bases: idtxl.network_inference.NetworkInference
      
 
      Parent class for multivariate network inference algorithms.
      
 
      
 
 
      
-
      
-class idtxl.network_inference.NetworkInferenceTE[source]
      
+
      
+class idtxl.network_inference.NetworkInferenceTE[source]
      
 
      Bases: idtxl.network_inference.NetworkInference
      
 
      Parent class for transfer entropy network inference algorithms.
      
 
      
@@ -5837,8 +6060,8 @@ 
      Submodules
      idtxl.single_process_analysis module
      
 
      Parent class for analysis of single processes in the network.
      
 
      
-
      
-class idtxl.single_process_analysis.SingleProcessAnalysis[source]
      
+
      
+class idtxl.single_process_analysis.SingleProcessAnalysis[source]
      
 
      Bases: idtxl.network_analysis.NetworkAnalysis
      
 
      
 
@@ -5847,14 +6070,19 @@ 
      Submodules
      idtxl.network_comparison module
      
 
      Perform inference statistics on groups of data.
      
 
      
-
      
-class idtxl.network_comparison.NetworkComparison[source]
      
+
      
+class idtxl.network_comparison.NetworkComparison[source]
      
 
      Bases: idtxl.network_analysis.NetworkAnalysis
      
 
      Set up network comparison between two experimental conditions.
      
 
      The class provides methods for the comparison of networks inferred from
 data recorded under two experimental conditions A and B. Four statistical
 tests are implemented:
      
 
+++++
@@ -5889,8 +6117,8 @@ 
      Submodules
-
+
 
      Calculate the information transfer for whole links into a target.
      
 
      Calculate the information transfer for whole links as the joint
 information transfer from all variables selected for a single source
@@ -5920,8 +6148,8 @@ 
      Submodules
-
      
-compare_between(settings, network_set_a, network_set_b, data_set_a, data_set_b)[source]
      
+
      
+compare_between(settings, network_set_a, network_set_b, data_set_a, data_set_b)[source]
      
 
      Compare networks inferred under two conditions between subjects.
      
 
      Compare two sets of networks inferred from two sets of data recorded
 under different experimental conditions within multiple subjects, i.e.,
@@ -5954,8 +6182,8 @@ 
      Submodules
-
+
 
      Compare two links within the same network.
      
 
      Compare two links within the same network. Check if information
 transfer is different from information transfer in a second link.
      
@@ -6004,8 +6232,8 @@ 
      Submodules
-
      
-compare_within(settings, network_a, network_b, data_a, data_b)[source]
      
+
      
+compare_within(settings, network_a, network_b, data_a, data_b)[source]
      
 
      Compare networks inferred under two conditions within one subject.
      
 
      Compare two networks inferred from data recorded under two different
 experimental conditions within one subject (units of observations are
@@ -6059,25 +6287,25 @@ 
      Submodules
      idtxl.results module
      
 
      Provide results class for IDTxl network analysis.
      
 
      
-
      
-class idtxl.results.AdjacencyMatrix(n_nodes, weight_type)[source]
      
+
      
+class idtxl.results.AdjacencyMatrix(n_nodes, weight_type)[source]
      
 
      Bases: object
      
 
      Adjacency matrix representing inferred networks.
      
 
      
-
      
-add_edge(i, j, weight)[source]
      
+
      
+add_edge(i, j, weight)[source]
      
 
      Add weighted edge (i, j) to adjacency matrix.
      
 
      
 
 
      
-
      
-add_edge_list(i_list, j_list, weights)[source]
      
+
      
+add_edge_list(i_list, j_list, weights)[source]
      
 
      Add multiple weighted edges (i, j) to adjacency matrix.
      
 
      
 
 
      
-
      
-get_edge_list()[source]
      
+
      
+get_edge_list()[source]
      
 
      Return list of weighted edges.
      
 
      
 
      Returns
      
@@ -6089,27 +6317,27 @@ 
      Submodules
-
      
-n_edges()[source]
      
+
      
+n_edges()[source]
      
 
      
 
 
      
-
      
-n_nodes()[source]
      
+
      
+n_nodes()[source]
      
 
      Return number of nodes.
      
 
      
 
 
      
-
      
-print_matrix()[source]
      
+
      
+print_matrix()[source]
      
 
      Print weight and edge matrix.
      
 
      
 
 
      
 
 
      
-
      
-class idtxl.results.DotDict[source]
      
+
      
+class idtxl.results.DotDict[source]
      
 
      Bases: dict
      
 
      Dictionary with dot-notation access to values.
      
 
      Provides the same functionality as a regular dict, but also allows
@@ -6126,8 +6354,8 @@ 
      Submodules
-
      
-class idtxl.results.Results(n_nodes, n_realisations, normalised)[source]
      
+
      
+class idtxl.results.Results(n_nodes, n_realisations, normalised)[source]
      
 
      Bases: object
      
 
      Parent class for results of network analysis algorithms.
      
 
      Provide a container for results of network analysis algorithms, e.g.,
@@ -6154,8 +6382,8 @@ 
      Submodules
-
      
-combine_results(*results)[source]
      
+
      
+combine_results(*results)[source]
      
 
      Combine multiple (partial) results objects.
      
 
      Combine a list of partial network analysis results into a single
 results object (e.g., results from analysis parallelized over
@@ -6187,8 +6415,8 @@ 
      Submodules
-
      
-class idtxl.results.ResultsMultivariatePID(n_nodes, n_realisations, normalised)[source]
      
+
      
+class idtxl.results.ResultsMultivariatePID(n_nodes, n_realisations, normalised)[source]
      
 
      Bases: idtxl.results.ResultsNetworkAnalysis
      
 
      Store results of Multivariate Partial Information Decomposition (PID)
 analysis.
      
@@ -6229,8 +6457,8 @@ 
      Submodules
-
      
-get_single_target(target)[source]
      
+
      
+get_single_target(target)[source]
      
 
      Return results for a single target in the network.
      
 
      Results for single targets include for each target
      
 
      ++++++++
 
@@ -243,6 +251,15 @@ 
      The Data Class
+
      ++++++++
 
@@ -287,20 +304,20 @@ 
      The Data Class
-
      
-get_seed()[source]
      
+
      
+get_seed()[source]
      
 
      return the initial seed of the data
      
 
      
 
 
      
-
      
-get_state()[source]
      
+
      
+get_state()[source]
      
 
      return the current state of the random seed
      
 
      
 
 
      
-
      
-n_realisations(current_value=None)[source]
      
+
      
+n_realisations(current_value=None)[source]
      
 
      Number of realisations over samples and replications.
      
 
      
 
      Args:
      
@@ -316,14 +333,14 @@ 
      The Data Class
-
      
-n_realisations_repl()[source]
      
+
      
+n_realisations_repl()[source]
      
 
      Number of realisations over replications.
      
 
      
 
 
      
-
      
-n_realisations_samples(current_value=None)[source]
      
+
      
+n_realisations_samples(current_value=None)[source]
      
 
      Number of realisations over samples.
      
 
      
 
      Args:
      
@@ -338,8 +355,8 @@ 
      The Data Class
-
      
-permute_replications(current_value, idx_list)[source]
      
+
      
+permute_replications(current_value, idx_list)[source]
      
 
      Return realisations with permuted replications (time stays intact).
      
 
      Create surrogate data by permuting realisations over replications while
 keeping the temporal structure (order of samples) intact. Return
@@ -348,6 +365,15 @@ 
      The Data Class
+
      ++++++++
 
@@ -369,6 +395,15 @@ 
      The Data Class
+
      ++++++++
 
@@ -410,8 +445,8 @@ 
      The Data Class
-
      
-permute_samples(current_value, idx_list, perm_settings)[source]
      
+
      
+permute_samples(current_value, idx_list, perm_settings)[source]
      
 
      Return realisations with permuted samples (repl. stays intact).
      
 
      Create surrogate data by permuting realisations over samples (time)
 while keeping the order of replications intact. Surrogates can be
@@ -430,6 +465,13 @@ 
      The Data Class
+
      ++++++
 
@@ -447,6 +489,13 @@ 
      The Data Class
+
      ++++++
 
@@ -464,6 +513,13 @@ 
      The Data Class
+
      ++++++
 
@@ -481,6 +537,13 @@ 
      The Data Class
+
      ++++++
 
@@ -498,6 +561,13 @@ 
      The Data Class
+
      ++++++
 
@@ -586,8 +656,8 @@ 
      The Data Class
-
      
-set_data(data, dim_order)[source]
      
+
      
+set_data(data, dim_order)[source]
      
 
      Overwrite data in an existing Data object.
      
 
      
 
      Args:
      
@@ -603,8 +673,8 @@ 
      The Data Class
-
      
-slice_permute_replications(process)[source]
      
+
      
+slice_permute_replications(process)[source]
      
 
      Return data slice with permuted replications (time stays intact).
      
 
      Create surrogate data by permuting realisations over replications while
 keeping the temporal structure (order of samples) intact. Return
@@ -614,8 +684,8 @@ 
      The Data Class
-
      
-slice_permute_samples(process, perm_settings)[source]
      
+
      
+slice_permute_samples(process, perm_settings)[source]
      
 
      Return slice of data with permuted samples (repl. stays intact).
      
 
      Create surrogate data by permuting data in a slice over samples (time)
 while keeping the order of replications intact. Return slice for the
@@ -623,6 +693,13 @@ 
      The Data Class
+
      ++++++
 
@@ -640,6 +717,13 @@ 
      The Data Class
+
      ++++++
 
@@ -657,6 +741,13 @@ 
      The Data Class
+
      ++++++
 
@@ -674,6 +765,13 @@ 
      The Data Class
+
      ++++++
 
@@ -691,6 +789,13 @@ 
      The Data Class
+
      ++++++
 
@@ -788,12 +893,16 @@ 
      The Data Class
         
      
-  
      Previous topic
      
-  
      Welcome to IDTxl’s documentation!
      
-  
      Next topic
      
-  
      Algorithms for network inference
      
+  
+  
   
      
     
      This Page
      
     
     
      
     
   
 
\ No newline at end of file
diff --git a/docs/html/idtxl_estimators.html b/docs/html/idtxl_estimators.html
index 197d4534..44976117 100644
--- a/docs/html/idtxl_estimators.html
+++ b/docs/html/idtxl_estimators.html
@@ -4,16 +4,15 @@
 
   
     
-    
+    
 
-    Information theoretic estimators — IDTxl 1.4 documentation
-    
-    
-    
+    Information theoretic estimators — IDTxl 1.5 documentation
+    
+    
+    
     
     
     
-    
     
     
     
@@ -41,7 +40,7 @@ 
      Navigation
      
         
    • 
           previous |
      • 
-        
    • IDTxl 1.4 documentation »
      • 
+        
    • IDTxl 1.5 documentation »
      • 
         
    • Information theoretic estimators
      •  
       
     
        
@@ -57,8 +56,8 @@ 
      Information theoretic estimators
      Provide JIDT estimators.
      
-
      
-class idtxl.estimators_jidt.JidtDiscrete(settings)[source]
      
+
      
+class idtxl.estimators_jidt.JidtDiscrete(settings)[source]
      
 
      Abstract class for implementation of discrete JIDT-estimators.
      
 
      Abstract class for implementation of plug-in JIDT-estimators for discrete
 data. Child classes implement estimators for mutual information (MI),
@@ -90,8 +89,8 @@ 
      JIDT Estimators (CPU)
 
      
-
      
-estimate_surrogates_analytic(n_perm=200, **data)[source]
      
+
      
+estimate_surrogates_analytic(n_perm=200, **data)[source]
      
 
      Return estimate of the analytical surrogate distribution.
      
 
      This method must be implemented because this class’
 is_analytic_null_estimator() method returns true.
      
@@ -116,8 +115,8 @@ 
      JIDT Estimators (CPU)
      
-
      
-abstract get_analytic_distribution(**data)[source]
      
+
      
+abstract get_analytic_distribution(**data)[source]
      
 
      Return a JIDT AnalyticNullDistribution object.
      
 
      Required so that our estimate_surrogates_analytic method can use the
 common_estimate_surrogates_analytic() method, where data is formatted
@@ -139,8 +138,8 @@ 
      JIDT Estimators (CPU)
      
-
      
-is_analytic_null_estimator()[source]
      
+
      
+is_analytic_null_estimator()[source]
      
 
      Indicate if estimator supports analytic surrogates.
      
 
      Return true if the estimator implements estimate_surrogates_analytic()
 where data is formatted as per the estimate method for this estimator.
      
@@ -153,8 +152,8 @@ 
      JIDT Estimators (CPU)
      
-
      
-class idtxl.estimators_jidt.JidtDiscreteAIS(settings)[source]
      
+
      
+class idtxl.estimators_jidt.JidtDiscreteAIS(settings)[source]
      
 
      Calculate AIS with JIDT’s discrete-variable implementation.
      
 
      Calculate the active information storage (AIS) for one process. Call JIDT
 via jpype and use the discrete estimator. See parent class for references.
      
@@ -184,8 +183,8 @@ 
      JIDT Estimators (CPU)
 
      
-
      
-estimate(process, return_calc=False)[source]
      
+
      
+estimate(process, return_calc=False)[source]
      
 
      Estimate active information storage.
      
 
      
 
      Args:
      
@@ -217,8 +216,8 @@ 
      JIDT Estimators (CPU)
      
 
 
      
-
      
-get_analytic_distribution(process)[source]
      
+
      
+get_analytic_distribution(process)[source]
      
 
      Return a JIDT AnalyticNullDistribution object.
      
 
      Required so that our estimate_surrogates_analytic method can use the
 common_estimate_surrogates_analytic() method, where data is formatted
@@ -243,8 +242,8 @@ 
      JIDT Estimators (CPU)
      
 
 
      
-
      
-class idtxl.estimators_jidt.JidtDiscreteCMI(settings=None)[source]
      
+
      
+class idtxl.estimators_jidt.JidtDiscreteCMI(settings=None)[source]
      
 
      Calculate CMI with JIDT’s implementation for discrete variables.
      
 
      Calculate the conditional mutual information between two variables given
 the third. Call JIDT via jpype and use the discrete estimator. See parent
@@ -278,8 +277,8 @@ 
      JIDT Estimators (CPU)
 
      
 
      
-
      
-estimate(var1, var2, conditional=None, return_calc=False)[source]
      
+
      
+estimate(var1, var2, conditional=None, return_calc=False)[source]
      
 
      Estimate conditional mutual information.
      
 
      
 
      Args:
      
@@ -316,8 +315,8 @@ 
      JIDT Estimators (CPU)
      
 
 
      
-
      
-get_analytic_distribution(var1, var2, conditional=None)[source]
      
+
      
+get_analytic_distribution(var1, var2, conditional=None)[source]
      
 
      Return a JIDT AnalyticNullDistribution object.
      
 
      Required so that our estimate_surrogates_analytic method can use the
 common_estimate_surrogates_analytic() method, where data is formatted
@@ -347,8 +346,8 @@ 
      JIDT Estimators (CPU)
      
 
 
      
-
      
-class idtxl.estimators_jidt.JidtDiscreteMI(settings=None)[source]
      
+
      
+class idtxl.estimators_jidt.JidtDiscreteMI(settings=None)[source]
      
 
      Calculate MI with JIDT’s discrete-variable implementation.
      
 
      Calculate the mutual information (MI) between two variables. Call JIDT via
 jpype and use the discrete estimator. See parent class for references.
      
@@ -381,8 +380,8 @@ 
      JIDT Estimators (CPU)
 
      
 
      
-
      
-estimate(var1, var2, return_calc=False)[source]
      
+
      
+estimate(var1, var2, return_calc=False)[source]
      
 
      Estimate mutual information.
      
 
      
 
      Args:
      
@@ -416,8 +415,8 @@ 
      JIDT Estimators (CPU)
      
 
 
      
-
      
-get_analytic_distribution(var1, var2)[source]
      
+
      
+get_analytic_distribution(var1, var2)[source]
      
 
      Return a JIDT AnalyticNullDistribution object.
      
 
      Required so that our estimate_surrogates_analytic method can use the
 common_estimate_surrogates_analytic() method, where data is formatted
@@ -444,8 +443,8 @@ 
      JIDT Estimators (CPU)
      
 
 
      
-
      
-class idtxl.estimators_jidt.JidtDiscreteTE(settings)[source]
      
+
      
+class idtxl.estimators_jidt.JidtDiscreteTE(settings)[source]
      
 
      Calculate TE with JIDT’s implementation for discrete variables.
      
 
      Calculate the transfer entropy between two time series processes.
 Call JIDT via jpype and use the discrete estimator. Transfer entropy is
@@ -490,8 +489,8 @@ 
      JIDT Estimators (CPU)
 
      
 
      
-
      
-estimate(source, target, return_calc=False)[source]
      
+
      
+estimate(source, target, return_calc=False)[source]
      
 
      Estimate transfer entropy from a source to a target variable.
      
 
      
 
      Args:
      
@@ -525,8 +524,8 @@ 
      JIDT Estimators (CPU)
      
 
 
      
-
      
-get_analytic_distribution(source, target)[source]
      
+
      
+get_analytic_distribution(source, target)[source]
      
 
      Return a JIDT AnalyticNullDistribution object.
      
 
      Required so that our estimate_surrogates_analytic method can use the
 common_estimate_surrogates_analytic() method, where data is formatted
@@ -553,8 +552,8 @@ 
      JIDT Estimators (CPU)
      
 
 
      
-
      
-class idtxl.estimators_jidt.JidtEstimator(settings=None)[source]
      
+
      
+class idtxl.estimators_jidt.JidtEstimator(settings=None)[source]
      
 
      Abstract class for implementation of JIDT estimators.
      
 
      Abstract class for implementation of JIDT estimators, child classes
 implement estimators for mutual information (MI), conditional mutual
@@ -590,8 +589,8 @@ 
      JIDT Estimators (CPU)
 
      
 
      
-
      
-is_parallel()[source]
      
+
      
+is_parallel()[source]
      
 
      Indicate if estimator supports parallel estimation over chunks.
      
 
      Return true if the supports parallel estimation over chunks, where a
 chunk is one independent data set.
      
@@ -604,8 +603,8 @@ 
      JIDT Estimators (CPU)
      
 
 
      
-
      
-class idtxl.estimators_jidt.JidtGaussian(CalcClass, settings)[source]
      
+
      
+class idtxl.estimators_jidt.JidtGaussian(CalcClass, settings)[source]
      
 
      Abstract class for implementation of JIDT Gaussian-estimators.
      
 
      Abstract class for implementation of JIDT Gaussian-estimators, child
 classes implement estimators for mutual information (MI), conditional
@@ -631,10 +630,10 @@ 
      JIDT Estimators (CPU)
 
      
 
      
-
      
-estimate_surrogates_analytic(n_perm=200, **data)[source]
      
-
      Estimate the surrogate distribution analytically.
      
-
      This method must be implemented because this class’
+
      
+estimate_surrogates_analytic(n_perm=200, **data)[source]
      
+
      Estimate the surrogate distribution analytically.
+This method must be implemented because this class’
 is_analytic_null_estimator() method returns true
      
 
      
 
      Args:
      
@@ -657,8 +656,8 @@ 
      JIDT Estimators (CPU)
      
 
 
      
-
      
-get_analytic_distribution(**data)[source]
      
+
      
+get_analytic_distribution(**data)[source]
      
 
      Return a JIDT AnalyticNullDistribution object.
      
 
      Required so that our estimate_surrogates_analytic method can use the
 common_estimate_surrogates_analytic() method, where data is formatted
@@ -680,8 +679,8 @@ 
      JIDT Estimators (CPU)
      
 
 
      
-
      
-is_analytic_null_estimator()[source]
      
+
      
+is_analytic_null_estimator()[source]
      
 
      Indicate if estimator supports analytic surrogates.
      
 
      Return true if the estimator implements estimate_surrogates_analytic()
 where data is formatted as per the estimate method for this estimator.
      
@@ -694,8 +693,8 @@ 
      JIDT Estimators (CPU)
      
 
 
      
-
      
-class idtxl.estimators_jidt.JidtGaussianAIS(settings)[source]
      
+
      
+class idtxl.estimators_jidt.JidtGaussianAIS(settings)[source]
      
 
      Calculate active information storage with JIDT’s Gaussian implementation.
      
 
      Calculate active information storage (AIS) for some process using JIDT’s
 implementation of the Gaussian estimator. AIS is defined as the
@@ -729,8 +728,8 @@ 
      JIDT Estimators (CPU)
 
      
 
      
-
      
-estimate(process)[source]
      
+
      
+estimate(process)[source]
      
 
      Estimate active information storage.
      
 
      
 
      Args:
      
@@ -752,8 +751,8 @@ 
      JIDT Estimators (CPU)
      
 
 
      
-
      
-class idtxl.estimators_jidt.JidtGaussianCMI(settings=None)[source]
      
+
      
+class idtxl.estimators_jidt.JidtGaussianCMI(settings=None)[source]
      
 
      Calculate conditional mutual infor with JIDT’s Gaussian implementation.
      
 
      Computes the differential conditional mutual information of two
 multivariate sets of observations, conditioned on another, assuming that
@@ -784,8 +783,8 @@ 
      JIDT Estimators (CPU)
 
      
 
      
-
      
-estimate(var1, var2, conditional=None)[source]
      
+
      
+estimate(var1, var2, conditional=None)[source]
      
 
      Estimate conditional mutual information.
      
 
      
 
      Args:
      
@@ -810,8 +809,8 @@ 
      JIDT Estimators (CPU)
      
 
 
      
-
      
-get_analytic_distribution(var1, var2, conditional=None)[source]
      
+
      
+get_analytic_distribution(var1, var2, conditional=None)[source]
      
 
      Return a JIDT AnalyticNullDistribution object.
      
 
      Required so that our estimate_surrogates_analytic method can use the
 common_estimate_surrogates_analytic() method, where data is formatted
@@ -840,8 +839,8 @@ 
      JIDT Estimators (CPU)
      
 
 
      
-
      
-class idtxl.estimators_jidt.JidtGaussianMI(settings=None)[source]
      
+
      
+class idtxl.estimators_jidt.JidtGaussianMI(settings=None)[source]
      
 
      Calculate mutual information with JIDT’s Gaussian implementation.
      
 
      Calculate the mutual information between two variables. Call JIDT via jpype
 and use the Gaussian estimator. See parent class for references.
      
@@ -868,8 +867,8 @@ 
      JIDT Estimators (CPU)
 
      
 
      
-
      
-estimate(var1, var2)[source]
      
+
      
+estimate(var1, var2)[source]
      
 
      Estimate mutual information.
      
 
      
 
      Args:
      
@@ -893,8 +892,8 @@ 
      JIDT Estimators (CPU)
      
 
 
      
-
      
-class idtxl.estimators_jidt.JidtGaussianTE(settings)[source]
      
+
      
+class idtxl.estimators_jidt.JidtGaussianTE(settings)[source]
      
 
      Calculate transfer entropy with JIDT’s Gaussian implementation.
      
 
      Calculate transfer entropy between a source and a target variable using
 JIDT’s implementation of the Gaussian estimator. Transfer entropy is
@@ -937,8 +936,8 @@ 
      JIDT Estimators (CPU)
 
      
 
      
-
      
-estimate(source, target)[source]
      
+
      
+estimate(source, target)[source]
      
 
      Estimate transfer entropy from a source to a target variable.
      
 
      
 
      Args:
      
@@ -962,8 +961,8 @@ 
      JIDT Estimators (CPU)
      
 
 
      
-
      
-class idtxl.estimators_jidt.JidtKraskov(CalcClass, settings=None)[source]
      
+
      
+class idtxl.estimators_jidt.JidtKraskov(CalcClass, settings=None)[source]
      
 
      Abstract class for implementation of JIDT Kraskov-estimators.
      
 
      Abstract class for implementation of JIDT Kraskov-estimators, child classes
 implement estimators for mutual information (MI), conditional mutual
@@ -1003,8 +1002,8 @@ 
      JIDT Estimators (CPU)
 
      
 
      
-
      
-is_analytic_null_estimator()[source]
      
+
      
+is_analytic_null_estimator()[source]
      
 
      Indicate if estimator supports analytic surrogates.
      
 
      Return true if the estimator implements estimate_surrogates_analytic()
 where data is formatted as per the estimate method for this estimator.
      
@@ -1017,8 +1016,8 @@ 
      JIDT Estimators (CPU)
      
 
 
      
-
      
-class idtxl.estimators_jidt.JidtKraskovAIS(settings)[source]
      
+
      
+class idtxl.estimators_jidt.JidtKraskovAIS(settings)[source]
      
 
      Calculate active information storage with JIDT’s Kraskov implementation.
      
 
      Calculate active information storage (AIS) for some process using JIDT’s
 implementation of the Kraskov type 1 estimator. AIS is defined as the
@@ -1064,8 +1063,8 @@ 
      JIDT Estimators (CPU)
 
      
 
      
-
      
-estimate(process)[source]
      
+
      
+estimate(process)[source]
      
 
      Estimate active information storage.
      
 
      
 
      Args:
      
@@ -1087,8 +1086,8 @@ 
      JIDT Estimators (CPU)
      
 
 
      
-
      
-class idtxl.estimators_jidt.JidtKraskovCMI(settings=None)[source]
      
+
      
+class idtxl.estimators_jidt.JidtKraskovCMI(settings=None)[source]
      
 
      Calculate conditional mutual inform with JIDT’s Kraskov implementation.
      
 
      Calculate the conditional mutual information (CMI) between three variables.
 Call JIDT via jpype and use the Kraskov 1 estimator. If no conditional is
@@ -1129,8 +1128,8 @@ 
      JIDT Estimators (CPU)
 
      
 
      
-
      
-estimate(var1, var2, conditional=None)[source]
      
+
      
+estimate(var1, var2, conditional=None)[source]
      
 
      Estimate conditional mutual information.
      
 
      
 
      Args:
      
@@ -1157,8 +1156,8 @@ 
      JIDT Estimators (CPU)
      
 
 
      
-
      
-class idtxl.estimators_jidt.JidtKraskovMI(settings=None)[source]
      
+
      
+class idtxl.estimators_jidt.JidtKraskovMI(settings=None)[source]
      
 
      Calculate mutual information with JIDT’s Kraskov implementation.
      
 
      Calculate the mutual information between two variables. Call JIDT via jpype
 and use the Kraskov 1 estimator. See parent class for references.
      
@@ -1197,8 +1196,8 @@ 
      JIDT Estimators (CPU)
 
      
 
      
-
      
-estimate(var1, var2)[source]
      
+
      
+estimate(var1, var2)[source]
      
 
      Estimate mutual information.
      
 
      
 
      Args:
      
@@ -1222,8 +1221,8 @@ 
      JIDT Estimators (CPU)
      
 
 
      
-
      
-class idtxl.estimators_jidt.JidtKraskovTE(settings)[source]
      
+
      
+class idtxl.estimators_jidt.JidtKraskovTE(settings)[source]
      
 
      Calculate transfer entropy with JIDT’s Kraskov implementation.
      
 
      Calculate transfer entropy between a source and a target variable using
 JIDT’s implementation of the Kraskov type 1 estimator. Transfer entropy is
@@ -1268,8 +1267,8 @@ 
      JIDT Estimators (CPU)
 
      
 
      
-
      
-estimate(source, target)[source]
      
+
      
+estimate(source, target)[source]
      
 
      Estimate transfer entropy from a source to a target variable.
      
 
      
 
      Args:
      
@@ -1293,8 +1292,8 @@ 
      JIDT Estimators (CPU)
      
 
 
      
-
      
-idtxl.estimators_jidt.common_estimate_surrogates_analytic(estimator, n_perm=200, **data)[source]
      
+
      
+idtxl.estimators_jidt.common_estimate_surrogates_analytic(estimator, n_perm=200, **data)[source]
      
 
      Estimate the surrogate distribution analytically for JidtEstimator.
      
 
      Estimate the surrogate distribution analytically for a JidtEstimator
 which is_analytic_null_estimator(), by sampling estimates at random
@@ -1320,12 +1319,52 @@ 
      JIDT Estimators (CPU)
 
      
 
+
+
      
+
      Python Estimators (CPU)
      
+
      
+
      
+class idtxl.estimators_python.PythonKraskovCMI(settings)[source]
      
+
      Estimate conditional mutual information using Kraskov’s first estimator.
      
+
      
+
      
+estimate(var1: numpy.ndarray, var2: numpy.ndarray, conditional=None)[source]
      
+
      Estimate conditional mutual information between var1 and var2, given
+conditional.
      
+
      
+
+
      
+
      
+is_analytic_null_estimator()[source]
      
+
      Indicate if estimator supports analytic surrogates.
      
+
      Return true if the estimator implements estimate_surrogates_analytic()
+where data is formatted as per the estimate method for this estimator.
      
+
      
+
      Returns:
      bool
      
+
      
+
      
+
      
+
+
      
+
      
+is_parallel()[source]
      
+
      Indicate if estimator supports parallel estimation over chunks.
      
+
      Return true if the supports parallel estimation over chunks, where a
+chunk is one independent data set.
      
+
      
+
      Returns:
      bool
      
+
      
+
      
+
      
+
+
      
+
 
      
 
      
 
      OpenCL Estimators (GPU)
      
 
      
-
      
-class idtxl.estimators_opencl.OpenCLKraskov(settings=None)[source]
      
+
      
+class idtxl.estimators_opencl.OpenCLKraskov(settings=None)[source]
      
 
      Abstract class for implementation of OpenCL estimators.
      
 
      Abstract class for implementation of OpenCL estimators, child classes
 implement estimators for mutual information (MI) and conditional mutual
@@ -1377,8 +1416,8 @@ 
      OpenCL Estimators (GPU)
 
      
 
      
-
      
-is_analytic_null_estimator()[source]
      
+
      
+is_analytic_null_estimator()[source]
      
 
      Indicate if estimator supports analytic surrogates.
      
 
      Return true if the estimator implements estimate_surrogates_analytic()
 where data is formatted as per the estimate method for this estimator.
      
@@ -1389,8 +1428,8 @@ 
      OpenCL Estimators (GPU)
      
 
 
      
-
      
-is_parallel()[source]
      
+
      
+is_parallel()[source]
      
 
      Indicate if estimator supports parallel estimation over chunks.
      
 
      Return true if the supports parallel estimation over chunks, where a
 chunk is one independent data set.
      
@@ -1403,8 +1442,8 @@ 
      OpenCL Estimators (GPU)
      
 
 
      
-
      
-class idtxl.estimators_opencl.OpenCLKraskovCMI(settings=None)[source]
      
+
      
+class idtxl.estimators_opencl.OpenCLKraskovCMI(settings=None)[source]
      
 
      Calculate conditional mutual inform with OpenCL Kraskov implementation.
      
 
      Calculate the conditional mutual information (CMI) between three variables
 using OpenCL GPU-code. If no conditional is given (is None), the function
@@ -1436,8 +1475,8 @@ 
      OpenCL Estimators (GPU)
 
      
 
      
-
      
-estimate(var1, var2, conditional=None, n_chunks=1)[source]
      
+
      
+estimate(var1, var2, conditional=None, n_chunks=1)[source]
      
 
      Estimate conditional mutual information.
      
 
      If conditional is None, the mutual information between var1 and var2 is
 calculated.
      
@@ -1472,8 +1511,8 @@ 
      OpenCL Estimators (GPU)
      
 
 
      
-
      
-class idtxl.estimators_opencl.OpenCLKraskovMI(settings=None)[source]
      
+
      
+class idtxl.estimators_opencl.OpenCLKraskovMI(settings=None)[source]
      
 
      Calculate mutual information with OpenCL Kraskov implementation.
      
 
      Calculate the mutual information (MI) between two variables using OpenCL
 GPU-code. See parent class for references.
      
@@ -1505,8 +1544,8 @@ 
      OpenCL Estimators (GPU)
 
      
 
      
-
      
-estimate(var1, var2, n_chunks=1)[source]
      
+
      
+estimate(var1, var2, n_chunks=1)[source]
      
 
      Estimate mutual information.
      
 
      
 
      Args:
      
@@ -1536,6 +1575,65 @@ 
      OpenCL Estimators (GPU)
      
 
+
      
+
      
+
      MPI Estimators (CPU)
      
+
      
+
      
+class idtxl.estimators_mpi.MPIEstimator(est, settings)[source]
      
+
      MPI Wrapper for arbitrary Estimator implementations
      
+
      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
      
+
      Call using mpiexec:
+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>
      
+
      Call using slurm:
+srun -n $SLURM_NTASKS –mpi=pmi2 python -m mpi4py.futures <python script>
      
+
      
+
      
+estimate(*, n_chunks=1, **data)[source]
      
+
      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
      
+
      
+
      
+
      Returns:
      numpy array: Estimates of information-theoretic quantities as np.double values
      
+
      
+
      
+
      
+
+
      
+
      
+estimate_surrogates_analytic(**data)[source]
      
+
      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.
      
+
      
+
+
      
+
      
+is_analytic_null_estimator()[source]
      
+
      Test if the base Estimator is an analytic null estimator.
      
+
      
+
+
      
+
      
+is_parallel()[source]
      
+
      Indicate if estimator supports parallel estimation over chunks.
      
+
      Return true if the supports parallel estimation over chunks, where a
+chunk is one independent data set.
      
+
      
+
      Returns:
      bool
      
+
      
+
      
+
      
+
+
      
+
 
      
 
      
 
      PID Estimators
      
@@ -1545,8 +1643,8 @@ 
      PID Estimatorshttp://doi.org/10.3390/e16042161
      
 
      
-
      
-class idtxl.estimators_pid.SydneyPID(settings)[source]
      
+
      
+class idtxl.estimators_pid.SydneyPID(settings)[source]
      
 
      Estimate partial information decomposition of discrete variables.
      
 
      Fast implementation of the BROJA partial information decomposition (PID)
 estimator for discrete data (Bertschinger, 2014). The estimator does not
@@ -1605,8 +1703,8 @@ 
      PID Estimators
-
      
-estimate(s1, s2, t)[source]
      
+
      
+estimate(s1, s2, t)[source]
      
 
      
 
      Args:
      
 
      s1numpy array
      1D array containing realizations of a discrete random variable
      
@@ -1627,8 +1725,8 @@ 
      PID Estimators
-
      
-is_analytic_null_estimator()[source]
      
+
      
+is_analytic_null_estimator()[source]
      
 
      Indicate if estimator supports analytic surrogates.
      
 
      Return true if the estimator implements estimate_surrogates_analytic()
 where data is formatted as per the estimate method for this estimator.
      
@@ -1639,8 +1737,8 @@ 
      PID Estimators
-
      
-is_parallel()[source]
      
+
      
+is_parallel()[source]
      
 
      Indicate if estimator supports parallel estimation over chunks.
      
 
      Return true if the supports parallel estimation over chunks, where a
 chunk is one independent data set.
      
@@ -1653,8 +1751,8 @@ 
      PID Estimators
-
      
-class idtxl.estimators_pid.TartuPID(settings)[source]
      
+
      
+class idtxl.estimators_pid.TartuPID(settings)[source]
      
 
      Estimate partial information decomposition for two inputs and one output
      
 
      Implementation of the partial information decomposition (PID) estimator for
 discrete data. The estimator finds shared information, unique information
@@ -1686,8 +1784,8 @@ 
      PID Estimators
-
      
-estimate(s1, s2, t)[source]
      
+
      
+estimate(s1, s2, t)[source]
      
 
      
 
      Args:
      
 
      s1numpy array
      1D array containing realizations of a discrete random variable
      
@@ -1707,8 +1805,8 @@ 
      PID Estimators
-
      
-is_analytic_null_estimator()[source]
      
+
      
+is_analytic_null_estimator()[source]
      
 
      Indicate if estimator supports analytic surrogates.
      
 
      Return true if the estimator implements estimate_surrogates_analytic()
 where data is formatted as per the estimate method for this estimator.
      
@@ -1719,8 +1817,8 @@ 
      PID Estimators
-
      
-is_parallel()[source]
      
+
      
+is_parallel()[source]
      
 
      Indicate if estimator supports parallel estimation over chunks.
      
 
      Return true if the supports parallel estimation over chunks, where a
 chunk is one independent data set.
      
@@ -1742,22 +1840,30 @@ 
      PID Estimators
         
      
-  
      Table of Contents
      
-  
     
        
@@ -57,26 +56,26 @@ 
      Helper functions
      
 
      Provide IDTxl utility functions.
      
 
      
-
      
-idtxl.idtxl_utils.argsort_descending(a)[source]
      
+
      
+idtxl.idtxl_utils.argsort_descending(a)[source]
      
 
      Sort array in descending order and return sortind indices.
      
 
      
 
 
      
-
      
-idtxl.idtxl_utils.autocorrelation(x)[source]
      
+
      
+idtxl.idtxl_utils.autocorrelation(x)[source]
      
 
      Calculate autocorrelation of a vector.
      
 
      
 
 
      
-
      
-idtxl.idtxl_utils.calculate_mi(corr)[source]
      
+
      
+idtxl.idtxl_utils.calculate_mi(corr)[source]
      
 
      Calculate mutual information from correlation coefficient.
      
 
      
 
 
      
-
      
-idtxl.idtxl_utils.combine_discrete_dimensions(a, numBins)[source]
      
+
      
+idtxl.idtxl_utils.combine_discrete_dimensions(a, numBins)[source]
      
 
      Combine multi-dimensional discrete variable into a single dimension.
      
 
      Combine all dimensions for a discrete variable down into a single
 dimensional value for each sample. This is done basically by multiplying
@@ -102,8 +101,8 @@ 
      utils module
-
      
-idtxl.idtxl_utils.conflicting_entries(dict_1, dict_2)[source]
      
+
      
+idtxl.idtxl_utils.conflicting_entries(dict_1, dict_2)[source]
      
 
      Test two dictionaries for unequal entries.
      
 
      Note that only keys that are present in both dicts are compared. If one
 dictionary contains an entry not present in the other dictionary, the
@@ -111,8 +110,8 @@ 
      utils module
-
      
-idtxl.idtxl_utils.discretise(a, numBins)[source]
      
+
      
+idtxl.idtxl_utils.discretise(a, numBins)[source]
      
 
      Discretise continuous data.
      
 
      Discretise continuous data into discrete values (with 0 as lowest) by
 evenly partitioning the range of the data, one dimension at a time.
@@ -136,8 +135,8 @@ 
      utils module
-
      
-idtxl.idtxl_utils.discretise_max_ent(a, numBins)[source]
      
+
      
+idtxl.idtxl_utils.discretise_max_ent(a, numBins)[source]
      
 
      Discretise continuous data using maximum entropy partitioning.
      
 
      Discretise continuous data into discrete values (with 0 as lowest) by
 making a maximum entropy partitioning, one dimension at a time. Adapted
@@ -161,20 +160,20 @@ 
      utils module
-
      
-idtxl.idtxl_utils.equal_dicts(dict_1, dict_2)[source]
      
+
      
+idtxl.idtxl_utils.equal_dicts(dict_1, dict_2)[source]
      
 
      Test two dictionaries for equality.
      
 
      
 
 
      
-
      
-idtxl.idtxl_utils.print_dict(d, indent=4)[source]
      
+
      
+idtxl.idtxl_utils.print_dict(d, indent=4)[source]
      
 
      Use Python’s pretty printer to print dictionaries to the console.
      
 
      
 
 
      
-
      
-idtxl.idtxl_utils.remove_column(a, j)[source]
      
+
      
+idtxl.idtxl_utils.remove_column(a, j)[source]
      
 
      Remove a column from a numpy array.
      
 
      This is faster than logical indexing (‘25 times faster’), because it does
 not make copies, see
@@ -191,8 +190,8 @@ 
      utils module
-
      
-idtxl.idtxl_utils.remove_row(a, i)[source]
      
+
      
+idtxl.idtxl_utils.remove_row(a, i)[source]
      
 
      Remove a row from a numpy array.
      
 
      This is faster than logical indexing (‘25 times faster’), because it does
 not make copies, see
@@ -209,8 +208,8 @@ 
      utils module
-
      
-idtxl.idtxl_utils.separate_arrays(idx_all, idx_single, a)[source]
      
+
      
+idtxl.idtxl_utils.separate_arrays(idx_all, idx_single, a)[source]
      
 
      Separate a single column from all other columns in a 2D-array.
      
 
      Return the separated single column and the remaining columns of a 2D-
 array.
      
@@ -237,14 +236,14 @@ 
      utils module
-
      
-idtxl.idtxl_utils.sort_descending(a)[source]
      
+
      
+idtxl.idtxl_utils.sort_descending(a)[source]
      
 
      Sort array in descending order.
      
 
      
 
 
      
-
      
-idtxl.idtxl_utils.standardise(a, dimension=0, df=1)[source]
      
+
      
+idtxl.idtxl_utils.standardise(a, dimension=0, df=1)[source]
      
 
      Z-standardise a numpy array along a given dimension.
      
 
      Standardise array along the axis defined in dimension using the denominator
 (N - df) for the calculation of the standard deviation.
      
@@ -267,8 +266,8 @@ 
      utils module
-
      
-idtxl.idtxl_utils.swap_chars(s, i_1, i_2)[source]
      
+
      
+idtxl.idtxl_utils.swap_chars(s, i_1, i_2)[source]
      
 
      Swap to characters in a string.
      
 
      
 
      Example:
      >>> print(swap_chars('heLlotHere', 2, 6))
@@ -279,13 +278,24 @@ 
      utils module
+
      
+class idtxl.idtxl_utils.timeout(timeout_duration, exception_message='Timeout')[source]
      
+
      Context manager for a timeout using threading module.
+args:
      
+
      
+
      timeout_duration: float, number of seconds to wait before timeout is triggered
+exception_message: string, message to put in the exception
      
+
      
+
      
+
 
      
 
      
 
      stats module
      
 
      Provide statistics functions.
      
 
      
-
      
-idtxl.stats.ais_fdr(settings=None, *results)[source]
      
+
      
+idtxl.stats.ais_fdr(settings=None, *results)[source]
      
 
      Perform FDR-correction on results of network AIS estimation.
      
 
      Perform correction of the false discovery rate (FDR) after estimation of
 active information storage (AIS) for all processes in the network. FDR
@@ -325,8 +335,8 @@ 
      stats module
-
      
-idtxl.stats.check_n_perm(n_perm, alpha)[source]
      
+
      
+idtxl.stats.check_n_perm(n_perm, alpha)[source]
      
 
      Check if no. permutations is big enough to obtain the requested alpha.
      
 
      
 
      Note:
      The no. permutations must be big enough to theoretically allow for the
@@ -338,8 +348,8 @@ 
      stats module
-
      
-idtxl.stats.max_statistic(analysis_setup, data, candidate_set, te_max_candidate, conditional)[source]
      
+
      
+idtxl.stats.max_statistic(analysis_setup, data, candidate_set, te_max_candidate, conditional)[source]
      
 
      Perform maximum statistics for one candidate source.
      
 
      Test if a transfer entropy value is significantly bigger than the maximum
 values obtained from surrogates of all remanining candidates.
      
@@ -387,8 +397,8 @@ 
      stats module
-
      
-idtxl.stats.max_statistic_sequential(analysis_setup, data)[source]
      
+
      
+idtxl.stats.max_statistic_sequential(analysis_setup, data)[source]
      
 
      Perform sequential maximum statistics for a set of candidate sources.
      
 
      Test multivariate/bivariate MI/TE values against surrogates. Test highest
 TE/MI value against distribution of highest surrogate values, second
@@ -417,7 +427,7 @@ 
      stats module
 
    • n_perm_max_seq : int [optional] - number of permutations
-(default=’n_perm_min_stat’|500)
      • 
+(default=’n_perm_min_stat’|500)
      
 
    • alpha_max_seq : float [optional] - critical alpha level
 (default=0.05)
      • 
 
    • permute_in_time : bool [optional] - generate surrogates by
@@ -443,8 +453,8 @@ 
      stats module
-
      
-idtxl.stats.max_statistic_sequential_bivariate(analysis_setup, data)[source]
      
+
      
+idtxl.stats.max_statistic_sequential_bivariate(analysis_setup, data)[source]
      
 
      Perform sequential maximum statistics for a set of candidate sources.
      
 
      Test multivariate/bivariate MI/TE values against surrogates. Test highest
 TE/MI value against distribution of highest surrogate values, second
@@ -473,7 +483,7 @@ 
      stats module
 
    • n_perm_max_seq : int [optional] - number of permutations
-(default=’n_perm_min_stat’|500)
      • 
+(default=’n_perm_min_stat’|500)
      • 
 
    • alpha_max_seq : float [optional] - critical alpha level
 (default=0.05)
      • 
 
    • permute_in_time : bool [optional] - generate surrogates by
@@ -499,8 +509,8 @@ 
      stats module
-
      
-idtxl.stats.mi_against_surrogates(analysis_setup, data)[source]
      
+
      
+idtxl.stats.mi_against_surrogates(analysis_setup, data)[source]
      
 
      Test estimated mutual information for significance against surrogate data.
      
 
      Shuffle realisations of the current value (point to be predicted) and re-
 calculate mutual information (MI) for shuffled data. The actual estimated
@@ -542,8 +552,8 @@ 
      stats module
-
      
-idtxl.stats.min_statistic(analysis_setup, data, candidate_set, te_min_candidate, conditional=None)[source]
      
+
      
+idtxl.stats.min_statistic(analysis_setup, data, candidate_set, te_min_candidate, conditional=None)[source]
      
 
      Perform minimum statistics for one candidate source.
      
 
      Test if a transfer entropy value is significantly bigger than the minimum
 values obtained from surrogates of all remanining candidates.
      
@@ -592,8 +602,8 @@ 
      stats module
-
      
-idtxl.stats.network_fdr(settings=None, *results)[source]
      
+
      
+idtxl.stats.network_fdr(settings=None, *results)[source]
      
 
      Perform FDR-correction on results of network inference.
      
 
      Perform correction of the false discovery rate (FDR) after network
 analysis. FDR correction can either be applied at the target level
@@ -637,8 +647,8 @@ 
      stats module
-
      
-idtxl.stats.omnibus_test(analysis_setup, data)[source]
      
+
      
+idtxl.stats.omnibus_test(analysis_setup, data)[source]
      
 
      Perform an omnibus test on identified conditional variables.
      
 
      Test the joint information transfer from all identified sources to the
 current value conditional on candidates in the target’s past. To test for
@@ -682,8 +692,8 @@ 
      stats module
-
      
-idtxl.stats.syn_shd_against_surrogates(analysis_setup, data)[source]
      
+
      
+idtxl.stats.syn_shd_against_surrogates(analysis_setup, data)[source]
      
 
      Test the shared/synergistic information in the PID estimate.
      
 
      Shuffle realisations of the target and re-calculate PID, in particular the
 synergistic and shared information from shuffled data. The original
@@ -722,8 +732,8 @@ 
      stats module
-
      
-idtxl.stats.unq_against_surrogates(analysis_setup, data)[source]
      
+
      
+idtxl.stats.unq_against_surrogates(analysis_setup, data)[source]
      
 
      Test the unique information in the PID estimate against surrogate data.
      
 
      Shuffle realisations of both sources individually and re-calculate PID,
 in particular the unique information from shuffled data. The original
@@ -771,8 +781,9 @@ 
      stats module
         
      
-  
      Table of Contents
      
-  
     
        
@@ -54,13 +53,18 @@ 
      Navigation
      
   
      
 
      Network comparison
      
 
      
-
      
-class idtxl.network_comparison.NetworkComparison[source]
      
+
      
+class idtxl.network_comparison.NetworkComparison[source]
      
 
      Set up network comparison between two experimental conditions.
      
 
      The class provides methods for the comparison of networks inferred from
 data recorded under two experimental conditions A and B. Four statistical
 tests are implemented:
      
 
      • 




 
 
      units of observation/
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      repl. ind.
      		
 
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      repl. ind.
      		
 
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+++++
@@ -95,8 +99,8 @@ 
      Network comparison
-
      
-calculate_link_te(data, target, sources='all')[source]
      
+
      
+calculate_link_te(data, target, sources='all')[source]
      
 
      Calculate the information transfer for whole links into a target.
      
 
      Calculate the information transfer for whole links as the joint
 information transfer from all variables selected for a single source
@@ -126,8 +130,8 @@ 
      Network comparison
-
      
-compare_between(settings, network_set_a, network_set_b, data_set_a, data_set_b)[source]
      
+
      
+compare_between(settings, network_set_a, network_set_b, data_set_a, data_set_b)[source]
      
 
      Compare networks inferred under two conditions between subjects.
      
 
      Compare two sets of networks inferred from two sets of data recorded
 under different experimental conditions within multiple subjects, i.e.,
@@ -160,8 +164,8 @@ 
      Network comparison
-
      
-compare_links_within(settings, link_a, link_b, network, data)[source]
      
+
      
+compare_links_within(settings, link_a, link_b, network, data)[source]
      
 
      Compare two links within the same network.
      
 
      Compare two links within the same network. Check if information
 transfer is different from information transfer in a second link.
      
@@ -210,8 +214,8 @@ 
      Network comparison
-
      
-compare_within(settings, network_a, network_b, data_a, data_b)[source]
      
+
      
+compare_within(settings, network_a, network_b, data_a, data_b)[source]
      
 
      Compare networks inferred under two conditions within one subject.
      
 
      Compare two networks inferred from data recorded under two different
 experimental conditions within one subject (units of observations are
@@ -269,12 +273,16 @@ 
      Network comparison
         
      
-  
      Previous topic
      
-  
      Algorithms for the analysis of node dynamics
      
-  
      Next topic
      
-  
      The Results Class
      
+  
+  
      
+    
      Next topic
      
+    
      The Results Class
      
+  
      
   
      
     
      This Page
      
     
     
      
     
   
 
\ No newline at end of file
diff --git a/docs/html/idtxl_network_inference.html b/docs/html/idtxl_network_inference.html
index db32e782..eb5cd0a9 100644
--- a/docs/html/idtxl_network_inference.html
+++ b/docs/html/idtxl_network_inference.html
@@ -4,16 +4,15 @@
 
   
     
-    
+    
 
-    Algorithms for network inference — IDTxl 1.4 documentation
-    
-    
-    
+    Algorithms for network inference — IDTxl 1.5 documentation
+    
+    
+    
     
     
     
-    
     
     
     
@@ -41,7 +40,7 @@ 
      Navigation
      
         
    • 
           previous |
      • 
-        
    • IDTxl 1.4 documentation »
      • 
+        
    • IDTxl 1.5 documentation »
      • 
         
    • Algorithms for network inference
      •  
       
     
        
@@ -56,8 +55,8 @@ 
      Algorithms for network inference
 
      Multivariate Transfer Entropy (mTE)
      
 
      
-
      
-class idtxl.multivariate_te.MultivariateTE[source]
      
+
      
+class idtxl.multivariate_te.MultivariateTE[source]
      
 
      Perform network inference using multivariate transfer entropy.
      
 
      Perform network inference using multivariate transfer entropy (TE). To
 perform network inference call analyse_network() on the whole network or a
@@ -80,9 +79,8 @@ 
      Multivariate Transfer Entropy (mTE)http://doi.org/10.1103/PhysRevE.83.051112
      
 
-
      Attributes:
      
-
      
-
      
+
      
+
      Attributes:
      
 
      source_setlist
      indices of source processes tested for their influence on the
 target
      
 
      
@@ -110,10 +108,11 @@ 
      Multivariate Transfer Entropy (mTE)bool
      statistical significance of the over-all TE
      
 
      
 
      
-
      
+
      
+
      
 
      
-
      
-analyse_network(settings, data, targets='all', sources='all')[source]
      
+
      
+analyse_network(settings, data, targets='all', sources='all')[source]
      
 
      Find multivariate transfer entropy between all nodes in the network.
      
 
      Estimate multivariate transfer entropy (TE) between all nodes in the
 network or between selected sources and targets.
      
@@ -175,8 +174,8 @@ 
      Multivariate Transfer Entropy (mTE)
-
      
-analyse_single_target(settings, data, target, sources='all')[source]
      
+
      
+analyse_single_target(settings, data, target, sources='all')[source]
      
 
      Find multivariate transfer entropy between sources and a target.
      
 
      Find multivariate transfer entropy (TE) between all source processes
 and the target process. Uses multivariate, non-uniform embedding found
@@ -289,8 +288,8 @@ 
      Multivariate Transfer Entropy (mTE)
 
      Bivariate Transfer Entropy (bTE)
      
 
      
-
      
-class idtxl.bivariate_te.BivariateTE[source]
      
+
      
+class idtxl.bivariate_te.BivariateTE[source]
      
 
      Perform network inference using bivariate transfer entropy.
      
 
      Perform network inference using bivariate transfer entropy (TE). To
 perform network inference call analyse_network() on the whole network or a
@@ -345,8 +344,8 @@ 
      Bivariate Transfer Entropy (bTE)
-
      
-analyse_network(settings, data, targets='all', sources='all')[source]
      
+
      
+analyse_network(settings, data, targets='all', sources='all')[source]
      
 
      Find bivariate transfer entropy between all nodes in the network.
      
 
      Estimate bivariate transfer entropy (TE) between all nodes in the
 network or between selected sources and targets.
      
@@ -407,8 +406,8 @@ 
      Bivariate Transfer Entropy (bTE)
-
      
-analyse_single_target(settings, data, target, sources='all')[source]
      
+
      
+analyse_single_target(settings, data, target, sources='all')[source]
      
 
      Find bivariate transfer entropy between sources and a target.
      
 
      Find bivariate transfer entropy (TE) between all potential source
 processes and the target process. Uses bivariate, non-uniform embedding
@@ -525,8 +524,8 @@ 
      Bivariate Transfer Entropy (bTE)
 
      Multivariate Mutual Information (mMI)
      
 
      
-
      
-class idtxl.multivariate_mi.MultivariateMI[source]
      
+
      
+class idtxl.multivariate_mi.MultivariateMI[source]
      
 
      Perform network inference using multivariate mutual information.
      
 
      Perform network inference using multivariate mutual information (MI). To
 perform network inference call analyse_network() on the whole network or a
@@ -573,8 +572,8 @@ 
      Multivariate Mutual Information (mMI)
-
      
-analyse_network(settings, data, targets='all', sources='all')[source]
      
+
      
+analyse_network(settings, data, targets='all', sources='all')[source]
      
 
      Find multivariate mutual information between nodes in the network.
      
 
      Estimate multivariate mutual information (MI) between all nodes in the
 network or between selected sources and targets.
      
@@ -642,8 +641,8 @@ 
      Multivariate Mutual Information (mMI)
-
      
-analyse_single_target(settings, data, target, sources='all')[source]
      
+
      
+analyse_single_target(settings, data, target, sources='all')[source]
      
 
      Find multivariate mutual information between sources and a target.
      
 
      Find multivariate mutual information (MI) between all source processes
 and the target process. Uses multivariate, non-uniform embedding found
@@ -758,8 +757,8 @@ 
      Multivariate Mutual Information (mMI)
 
      Bivariate Mutual Information (bMI)
      
 
      
-
      
-class idtxl.bivariate_mi.BivariateMI[source]
      
+
      
+class idtxl.bivariate_mi.BivariateMI[source]
      
 
      Perform network inference using bivariate mutual information.
      
 
      Perform network inference using bivariate mutual information (MI). To
 perform network inference call analyse_network() on the whole network or a
@@ -808,8 +807,8 @@ 
      Bivariate Mutual Information (bMI)
-
      
-analyse_network(settings, data, targets='all', sources='all')[source]
      
+
      
+analyse_network(settings, data, targets='all', sources='all')[source]
      
 
      Find bivariate mutual information between all nodes in the network.
      
 
      Estimate bivariate mutual information (MI) between all nodes in the
 network or between selected sources and targets.
      
@@ -873,8 +872,8 @@ 
      Bivariate Mutual Information (bMI)
-
      
-analyse_single_target(settings, data, target, sources='all')[source]
      
+
      
+analyse_single_target(settings, data, target, sources='all')[source]
      
 
      Find bivariate mutual information between sources and a target.
      
 
      Find bivariate mutual information (MI) between all potential source
 processes and the target process. Uses bivariate, non-uniform embedding
@@ -998,8 +997,9 @@ 
      Bivariate Mutual Information (bMI)
         
      
-  
      Table of Contents
      
-  
     
        
@@ -56,8 +55,8 @@ 
      Postprocessing of inferred networks
 
      Significant subgraph mining
      
 
      
-
      
-class idtxl.postprocessing.SignificantSubgraphMining(resultsA, resultsB, alpha, design, graph_type='directed', data_format='adjacency')[source]
      
+
      
+class idtxl.postprocessing.SignificantSubgraphMining(resultsA, resultsB, alpha, design, graph_type='directed', data_format='adjacency')[source]
      
 
      Implementation of significant subgraph mining as described in
      
 
      Sugiyama M, Lopez FL, Kasenburg N, Borgwardt KM.  Significant
 subgraph mining with multiple testing correction.
@@ -151,8 +150,8 @@ 
      Significant subgraph mining
-
      
-count_discordants(indices, where='original')[source]
      
+
      
+count_discordants(indices, where='original')[source]
      
 
      Counts the discordant pairs for a given subgraph represented as a
 list of indices.
      
 
      
@@ -176,8 +175,8 @@ 
      Significant subgraph mining
-
      
-count_discordants_wylight(indices, k)[source]
      
+
      
+count_discordants_wylight(indices, k)[source]
      
 
      Counts discordant pairs for subgraph given by list if indices
 in k-th permuted data set.
      
 
      
@@ -199,8 +198,8 @@ 
      Significant subgraph mining
-
      
-count_subgraph(indices, where='original')[source]
      
+
      
+count_subgraph(indices, where='original')[source]
      
 
      Counts the number of occurrences of a subgraph represented by a list of
 indices
      
 
      
@@ -222,8 +221,8 @@ 
      Significant subgraph mining
-
      
-count_subgraph_wylight(indices, k)[source]
      
+
      
+count_subgraph_wylight(indices, k)[source]
      
 
      Counts subgraph occurrences in k-th permuted data set
      
 
      
 
      Args:
      
@@ -243,8 +242,8 @@ 
      Significant subgraph mining
-
      
-decode(indices)[source]
      
+
      
+decode(indices)[source]
      
 
      Converts a given list of indices (representing a subgraph) into
 a list of corresponding target-source-lag triplets using the mapping
 described in the coding list.
      
@@ -257,14 +256,14 @@ 
      Significant subgraph mining
-
      
-decode_adjacency(indices)[source]
      
+
      
+decode_adjacency(indices)[source]
      
 
      Decodes list of indices as adjacency matrix
      
 
      
 
 
      
-
      
-determine_tarone_factor()[source]
      
+
      
+determine_tarone_factor()[source]
      
 
      Determines Tarone’s correction factor in case there are at least two
 testable subgraphs.
      
 
      
@@ -277,8 +276,8 @@ 
      Significant subgraph mining
-
      
-encode()[source]
      
+
      
+encode()[source]
      
 
      Encodes all subject networks as lists of indices. The ith entry
 describes the occurrence of the ith target-source-lag triplet
 in the coding list (self.coding_list).
      
@@ -294,14 +293,14 @@ 
      Significant subgraph mining
-
      
-encode_adjacency()[source]
      
+
      
+encode_adjacency()[source]
      
 
      Encodes all input adjacency matrices as lists of indices
      
 
      
 
 
      
-
      
-enumerate_frequent_graphs(freq)[source]
      
+
      
+enumerate_frequent_graphs(freq)[source]
      
 
      Adds all subgraphs occuring at least freq times to self.frequent_graphs
 The process is carried out recursively using the extend() method.
 Individual links of the union network are successively extended to
@@ -320,8 +319,8 @@ 
      Significant subgraph mining
-
      
-enumerate_significant_subgraphs(method='Hommel', wy_algorithm='simple_depth_first', verbose=True, num_perm=10000, max_depth=inf)[source]
      
+
      
+enumerate_significant_subgraphs(method='Hommel', wy_algorithm='simple_depth_first', verbose=True, num_perm=10000, max_depth=inf)[source]
      
 
      This is the main function carrying out significant subgraph mining
 according to the multiple comparisons correction method (and algorithm
 in the case of Westfall-Young) of choice. It calls the relevant
@@ -357,8 +356,8 @@ 
      Significant subgraph mining
-
      
-extend(to_be_extended, freq)[source]
      
+
      
+extend(to_be_extended, freq)[source]
      
 
      Recursively extends the input subgraph checking at each recursion
 step if the current subgraph occurs frequently enough to reach
 significance at level alpha. If this is not the case, it is not
@@ -388,8 +387,8 @@ 
      Significant subgraph mining
-
      
-extend_mcnemar(to_be_extended, freq)[source]
      
+
      
+extend_mcnemar(to_be_extended, freq)[source]
      
 
      Same as extend() method but using McNemar’s test for within subject
 designs
      
 
      
@@ -411,8 +410,8 @@ 
      Significant subgraph mining
-
      
-extend_wy(to_be_extended)[source]
      
+
      
+extend_wy(to_be_extended)[source]
      
 
      Determines the smallest observed p-value in permuted version of the
 data set by recursively extending the input subgraph. At each
 recursion step the function checks if the current subgraph occurs
@@ -434,8 +433,8 @@ 
      Significant subgraph mining
-
      
-extend_wy_light(to_be_extended)[source]
      
+
      
+extend_wy_light(to_be_extended)[source]
      
 
      Westfall-Young light extension method. Evaluates all permutations
 at the same time for each subgraph. The goal is to determine the
 Westfall-Young corrected level, i.e. the alpha quantile of the
@@ -455,8 +454,8 @@ 
      Significant subgraph mining
-
      
-extend_wy_light_mcnemar(to_be_extended)[source]
      
+
      
+extend_wy_light_mcnemar(to_be_extended)[source]
      
 
      Westfall-Young light extension method for the within-subjects case
 using McNemars test. Recursively, evaluates subgraphs and updates
 the current estimate of the Westfall-Young corrected level
@@ -473,8 +472,8 @@ 
      Significant subgraph mining
-
      
-extend_wy_mcnemar(to_be_extended)[source]
      
+
      
+extend_wy_mcnemar(to_be_extended)[source]
      
 
      Same as extend_wy but using McNemars test
      
 
      
 
      Args:
      list of indices of coding list. Each such list represent
@@ -486,8 +485,8 @@ 
      Significant subgraph mining
-
      
-generate_coding_list()[source]
      
+
      
+generate_coding_list()[source]
      
 
      If data_format = “idtxl”: Creates list of all target-source-lag
 triplets occuring at least once
 in the data set. This list is used to encode subject networks as
@@ -514,8 +513,8 @@ 
      Significant subgraph mining
-
      
-generate_min_p_table(design)[source]
      
+
      
+generate_min_p_table(design)[source]
      
 
      Computes list of minimum p_values depending on the total number of
 occurrences and given the group sample sizes.
      
 
      
@@ -528,8 +527,8 @@ 
      Significant subgraph mining
-
      
-generate_p_table(design)[source]
      
+
      
+generate_p_table(design)[source]
      
 
      Computes table of p-values depending on the total number of
 occurrences, the occurrences in Group A, and given the group
 sample sizes.
      
@@ -549,8 +548,8 @@ 
      Significant subgraph mining
-
      
-westfall_young(num_perm=10000, verbose=True)[source]
      
+
      
+westfall_young(num_perm=10000, verbose=True)[source]
      
 
      Determines significant subgraphs using the Westfall-Young Permutation
 procedure for multiple comparisons correction. This algorithm computes
 the permutation distribution of the smallest observed p-value
@@ -569,8 +568,8 @@ 
      Significant subgraph mining
-
      
-westfall_young_light(num_perm=10000, verbose=True)[source]
      
+
      
+westfall_young_light(num_perm=10000, verbose=True)[source]
      
 
      Determines significant subgraphs using the Westfall-Young light
 algorithm described in
      
 
      Llinares-Lopez F, Sugiyama M, Papaxanthos L, Borgwardt K.  Fast and
@@ -602,20 +601,26 @@ 
      Significant subgraph mining
         
      
-  
      Table of Contents
      
-  
     
        
@@ -56,8 +55,8 @@ 
      Algorithms for the analysis of node dynamics
 
      Active Information Storage (AIS)
      
 
      
-
      
-class idtxl.active_information_storage.ActiveInformationStorage[source]
      
+
      
+class idtxl.active_information_storage.ActiveInformationStorage[source]
      
 
      Estimate active information storage in individual processes.
      
 
      Estimate active information storage (AIS) in individual processes of the
 network. To perform AIS estimation call analyse_network() on the whole
@@ -99,8 +98,8 @@ 
      Active Information Storage (AIS)
-
      
-analyse_network(settings, data, processes='all')[source]
      
+
      
+analyse_network(settings, data, processes='all')[source]
      
 
      Estimate active information storage for multiple network processes.
      
 
      Estimate active information storage for all or a subset of processes in
 the network.
      
@@ -158,8 +157,8 @@ 
      Active Information Storage (AIS)
-
      
-analyse_single_process(settings, data, process)[source]
      
+
      
+analyse_single_process(settings, data, process)[source]
      
 
      Estimate active information storage for a single process.
      
 
      Estimate active information storage for one process in the network.
 Uses non-uniform embedding found through information maximisation. This
@@ -235,8 +234,8 @@ 
      Active Information Storage (AIS)
 
      Multivariate Partial Information Decomposition (PID)
      
 
      
-
      
-class idtxl.multivariate_pid.MultivariatePID[source]
      
+
      
+class idtxl.multivariate_pid.MultivariatePID[source]
      
 
      Perform partial information decomposition for individual processes.
      
 
      Perform partial information decomposition (PID) for multiple source
 processes (up to 4 sources) and a target process in the network.
@@ -267,8 +266,8 @@ 
      Multivariate Partial Information Decomposition (PID)
 
      
 
      
-
      
-analyse_network(settings, data, targets, sources)[source]
      
+
      
+analyse_network(settings, data, targets, sources)[source]
      
 
      Estimate partial information decomposition for network nodes.
      
 
      Estimate, for multiple nodes (target processes), the partial
 information decomposition (PID) for multiple source processes
@@ -332,8 +331,8 @@ 
      Multivariate Partial Information Decomposition (PID)
      
 
 
      
-
      
-analyse_single_target(settings, data, target, sources)[source]
      
+
      
+analyse_single_target(settings, data, target, sources)[source]
      
 
      Estimate partial information decomposition for a network node.
      
 
      Estimate partial information decomposition (PID) for multiple source
 processes (up to 4 sources) and a target process in the network.
      
@@ -398,8 +397,8 @@ 
      Multivariate Partial Information Decomposition (PID)
 
      Bivariate Partial Information Decomposition (PID)
      
 
      
-
      
-class idtxl.bivariate_pid.BivariatePID[source]
      
+
      
+class idtxl.bivariate_pid.BivariatePID[source]
      
 
      Perform partial information decomposition for individual processes.
      
 
      Perform partial information decomposition (PID) for two source processes
 and one target process in the network. Estimate unique, shared, and
@@ -430,8 +429,8 @@ 
      Bivariate Partial Information Decomposition (PID)
 
      
 
      
-
      
-analyse_network(settings, data, targets, sources)[source]
      
+
      
+analyse_network(settings, data, targets, sources)[source]
      
 
      Estimate partial information decomposition for network nodes.
      
 
      Estimate partial information decomposition (PID) for multiple nodes in
 the network.
      
@@ -494,8 +493,8 @@ 
      Bivariate Partial Information Decomposition (PID)
      
 
 
      
-
      
-analyse_single_target(settings, data, target, sources)[source]
      
+
      
+analyse_single_target(settings, data, target, sources)[source]
      
 
      Estimate partial information decomposition for a network node.
      
 
      Estimate partial information decomposition (PID) for a target node in
 the network.
      
@@ -565,8 +564,8 @@ 
      History-dependence estimator for neural spiking data
 
      Embedding optimization
      
 
      
-
      
-class idtxl.embedding_optimization_ais_Rudelt.OptimizationRudelt(settings=None)[source]
      
+
      
+class idtxl.embedding_optimization_ais_Rudelt.OptimizationRudelt(settings=None)[source]
      
 
      Optimization of embedding parameters of spike times using the history dependence estimators
      
 
      References:
      
 
      
@@ -754,21 +753,21 @@ 
      Embedding optimization
 
      
 
      
-
      
-analyse_auto_MI(spike_times)[source]
      
+
      
+analyse_auto_MI(spike_times)[source]
      
 
      Get the auto MI for the spike times.  If it is available from file, load
 it, else compute it.
      
 
      
 
 
      
-
      
-check_inputs()[source]
      
+
      
+check_inputs()[source]
      
 
      Check input settings for completeness
      
 
      
 
 
      
-
      
-compute_CIs(data, target_R='R_max', symbol_block_length=None)[source]
      
+
      
+compute_CIs(data, target_R='R_max', symbol_block_length=None)[source]
      
 
      Compute bootstrap replications of the history dependence estimate
 which can be used to obtain confidence intervals.
      
 
      
@@ -796,56 +795,56 @@ 
      Embedding optimization
      
 
 
      
-
      
-get_auto_MI(spike_times, bin_size, number_of_delays)[source]
      
+
      
+get_auto_MI(spike_times, bin_size, number_of_delays)[source]
      
 
      Compute the auto mutual information in the neuron’s activity, a
 measure closely related to history dependence.
      
 
      
 
 
      
-
      
-get_bootstrap_history_dependence(data, embedding, number_of_bootstraps, symbol_block_length=None)[source]
      
+
      
+get_bootstrap_history_dependence(data, embedding, number_of_bootstraps, symbol_block_length=None)[source]
      
 
      For a given embedding, return bootstrap replications for R.
      
 
      
 
 
      
-
      
-get_embeddings(embedding_past_range_set, embedding_number_of_bins_set, embedding_scaling_exponent_set)[source]
      
+
      
+get_embeddings(embedding_past_range_set, embedding_number_of_bins_set, embedding_scaling_exponent_set)[source]
      
 
      Get all combinations of parameters T, d, k, based on the
 sets of selected parameters.
      
 
      
 
 
      
-
      
-get_embeddings_that_maximise_R(bbc_tolerance=None, dependent_var='T', get_as_list=False)[source]
      
+
      
+get_embeddings_that_maximise_R(bbc_tolerance=None, dependent_var='T', get_as_list=False)[source]
      
 
      For each T (or d), get the embedding for which R is maximised.
      
 
      For the bbc estimator, here the bbc_tolerance is applied, ie
 get the unbiased embeddings that maximise R.
      
 
      
 
 
      
-
      
-get_history_dependence(data, process)[source]
      
+
      
+get_history_dependence(data, process)[source]
      
 
      Estimate the history dependence for each embedding to all given processes.
      
 
      
 
 
      
-
      
-get_information_timescale_tau_R()[source]
      
+
      
+get_information_timescale_tau_R()[source]
      
 
      Get the information timescale tau_R, a characteristic
 timescale of history dependence similar to an autocorrelation
 time.
      
 
      
 
 
      
-
      
-get_past_range(number_of_bins_d, first_bin_size, scaling_k)[source]
      
+
      
+get_past_range(number_of_bins_d, first_bin_size, scaling_k)[source]
      
 
      Get the past range T of the embedding, based on the parameters d, tau_1 and k.
      
 
      
 
 
      
-
      
-get_set_of_scalings(past_range_T, number_of_bins_d, number_of_scalings, min_first_bin_size, min_step_for_scaling)[source]
      
+
      
+get_set_of_scalings(past_range_T, number_of_bins_d, number_of_scalings, min_first_bin_size, min_step_for_scaling)[source]
      
 
      Get scaling exponents such that the uniform embedding as well as
 the embedding for which the first bin has a length of
 min_first_bin_size (in seconds), as well as linearly spaced
@@ -854,8 +853,8 @@ 
      Embedding optimization
      
 
 
      
-
      
-get_temporal_depth_T_D(get_R_thresh=False)[source]
      
+
      
+get_temporal_depth_T_D(get_R_thresh=False)[source]
      
 
      Get the temporal depth T_D, the past range for the
 ‘optimal’ embedding parameters.
      
 
      Given the maximal history dependence R at each past range T,
@@ -866,8 +865,8 @@ 
      Embedding optimization
      
 
 
      
-
      
-optimize(data, processes='all')[source]
      
+
      
+optimize(data, processes='all')[source]
      
 
      Optimize the embedding parameters of spike time data using the Rudelt history dependence estimator.
      
 
      References:
      
 
      
@@ -907,8 +906,8 @@ 
      Embedding optimization
      
 
 
      
-
      
-optimize_single_run(data, process)[source]
      
+
      
+optimize_single_run(data, process)[source]
      
 
      optimizes a single realisation of spike time data given the process number
      
 
      
 
      Args:
      
@@ -963,8 +962,8 @@ 
      Embedding optimization
      
 
 
      
-
      
-remove_subresults_single_process()[source]
      
+
      
+remove_subresults_single_process()[source]
      
 
      delete results from self from single process
      
 
      
 
@@ -975,8 +974,8 @@ 
      Embedding optimizationEstimators
      
 
      Provide HDE estimators.
      
 
      
-
      
-class idtxl.estimators_Rudelt.RudeltAbstractEstimator(settings=None)[source]
      
+
      
+class idtxl.estimators_Rudelt.RudeltAbstractEstimator(settings=None)[source]
      
 
      Abstract class for implementation of nsb and plugin estimators from Rudelt.
      
 
      Abstract class for implementation of nsb and plugin estimators, child classes
 implement estimators for mutual information (MI) .
      
@@ -1019,16 +1018,16 @@ 
      Estimators
-
      
-get_median_number_of_spikes_per_bin(raw_symbols)[source]
      
+
      
+get_median_number_of_spikes_per_bin(raw_symbols)[source]
      
 
      Given raw symbols (in which the number of spikes per bin are counted,
 ie not necessarily binary quantity), get the median number of spikes
 for each bin, among all symbols obtained by the embedding.
      
 
      
 
 
      
-
      
-get_multiplicities(symbol_counts, alphabet_size)[source]
      
+
      
+get_multiplicities(symbol_counts, alphabet_size)[source]
      
 
      Get the multiplicities of some given symbol counts.
      
 
      To estimate the entropy of a system, it is only important how
 often a symbol/ event occurs (the probability that it occurs), not
@@ -1038,28 +1037,28 @@ 
      Estimators
-
      
-get_past_range(number_of_bins_d, first_bin_size, scaling_k)[source]
      
+
      
+get_past_range(number_of_bins_d, first_bin_size, scaling_k)[source]
      
 
      Get the past range T of the embedding, based on the parameters d, tau_1 and k.
      
 
      
 
 
      
-
      
-get_raw_symbols(spike_times, embedding, first_bin_size)[source]
      
+
      
+get_raw_symbols(spike_times, embedding, first_bin_size)[source]
      
 
      Get the raw symbols (in which the number of spikes per bin are counted,
 ie not necessarily binary quantity), as obtained by applying the
 embedding.
      
 
      
 
 
      
-
      
-get_symbol_counts(symbol_array)[source]
      
+
      
+get_symbol_counts(symbol_array)[source]
      
 
      Count how often symbols occur
      
 
      
 
 
      
-
      
-get_window_delimiters(number_of_bins_d, scaling_k, first_bin_size)[source]
      
+
      
+get_window_delimiters(number_of_bins_d, scaling_k, first_bin_size)[source]
      
 
      Get delimiters of the window, used to describe the embedding. The
 window includes both the past embedding and the response.
      
 
      The delimiters are times, relative to the first bin, that separate
@@ -1067,8 +1066,8 @@ 
      Estimators
-
      
-is_analytic_null_estimator()[source]
      
+
      
+is_analytic_null_estimator()[source]
      
 
      Indicate if estimator supports analytic surrogates.
      
 
      Return true if the estimator implements estimate_surrogates_analytic()
 where data is formatted as per the estimate method for this estimator.
      
@@ -1079,8 +1078,8 @@ 
      Estimators
-
      
-is_parallel()[source]
      
+
      
+is_parallel()[source]
      
 
      Indicate if estimator supports parallel estimation over chunks.
      
 
      Return true if the supports parallel estimation over chunks, where a
 chunk is one independent data set.
      
@@ -1091,16 +1090,16 @@ 
      Estimators
-
      
-symbol_array_to_binary(spikes_in_window, number_of_bins_d)[source]
      
+
      
+symbol_array_to_binary(spikes_in_window, number_of_bins_d)[source]
      
 
      Given an array of 1s and 0s, representing spikes and the absence
 thereof, read the array as a binary number to obtain a
 (base 10) integer.
      
 
      
 
 
      
-
      
-symbol_binary_to_array(symbol_binary, number_of_bins_d)[source]
      
+
      
+symbol_binary_to_array(symbol_binary, number_of_bins_d)[source]
      
 
      Given a binary representation of a symbol (cf symbol_array_to_binary),
 convert it back into its array-representation.
      
 
      
@@ -1108,8 +1107,8 @@ 
      Estimators
-
      
-class idtxl.estimators_Rudelt.RudeltAbstractNSBEstimator(settings=None)[source]
      
+
      
+class idtxl.estimators_Rudelt.RudeltAbstractNSBEstimator(settings=None)[source]
      
 
      Abstract class for implementation of NSB estimators from Rudelt.
      
 
      Abstract class for implementation of Nemenman-Shafee-Bialek (NSB)
 estimators, child classes implement nsb estimators for mutual information
@@ -1156,67 +1155,67 @@ 
      Estimators
-
      
-H1(beta, mk, K, N)[source]
      
+
      
+H1(beta, mk, K, N)[source]
      
 
      Compute the first moment (expectation value) of the entropy H.
      
 
      H is the entropy one obtains with a symmetric Dirichlet prior
 with concentration parameter beta and a multinomial likelihood.
      
 
      
 
 
      
-
      
-alpha_ML(mk, K1, N)[source]
      
+
      
+alpha_ML(mk, K1, N)[source]
      
 
      Compute first guess for the beta_MAP (cf get_beta_MAP) parameter
 via the posterior of a Dirichlet process.
      
 
      
 
 
      
-
      
-d2_log_rho(beta, mk, K, N)[source]
      
+
      
+d2_log_rho(beta, mk, K, N)[source]
      
 
      Second derivate of the logarithm of the Dirichlet multinomial likelihood.
      
 
      
 
 
      
-
      
-d2_log_rho_xi(beta, mk, K, N)[source]
      
+
      
+d2_log_rho_xi(beta, mk, K, N)[source]
      
 
      Second derivative of the logarithm of the nsb (unnormalized) posterior.
      
 
      
 
 
      
-
      
-d2_xi(beta, K)[source]
      
+
      
+d2_xi(beta, K)[source]
      
 
      Second derivative of xi(beta) (cf d_xi).
      
 
      
 
 
      
-
      
-d3_xi(beta, K)[source]
      
+
      
+d3_xi(beta, K)[source]
      
 
      Third derivative of xi(beta) (cf d_xi).
      
 
      
 
 
      
-
      
-d_log_rho(beta, mk, K, N)[source]
      
+
      
+d_log_rho(beta, mk, K, N)[source]
      
 
      First derivate of the logarithm of the Dirichlet multinomial likelihood.
      
 
      
 
 
      
-
      
-d_log_rho_xi(beta, mk, K, N)[source]
      
+
      
+d_log_rho_xi(beta, mk, K, N)[source]
      
 
      First derivative of the logarithm of the nsb (unnormalized) posterior.
      
 
      
 
 
      
-
      
-d_xi(beta, K)[source]
      
+
      
+d_xi(beta, K)[source]
      
 
      First derivative of xi(beta).
      
 
      xi(beta) is the entropy of the system when no data has been observed.
 d_xi is the prior for the nsb estimator
      
 
      
 
 
      
-
      
-get_beta_MAP(mk, K, N)[source]
      
+
      
+get_beta_MAP(mk, K, N)[source]
      
 
      Get the maximum a posteriori (MAP) value for beta.
      
 
      Provides the location of the peak, around which we integrate.
      
 
      beta_MAP is the value for beta for which the posterior of the
@@ -1225,8 +1224,8 @@ 
      Estimators
-
      
-get_integration_bounds(mk, K, N)[source]
      
+
      
+get_integration_bounds(mk, K, N)[source]
      
 
      Find the integration bounds for the estimator.
      
 
      Typically it is a delta-like distribution so it is sufficient
 to integrate around this peak. (If not this function is not
@@ -1234,17 +1233,17 @@ 
      Estimators
-
      
-log_likelihood_DP_alpha(a, K1, N)[source]
      
+
      
+log_likelihood_DP_alpha(a, K1, N)[source]
      
 
      Alpha-dependent terms of the log-likelihood of a Dirichlet Process.
      
 
      
 
 
      
-
      
-nsb_entropy(mk, K, N)[source]
      
+
      
+nsb_entropy(mk, K, N)[source]
      
 
      Estimate the entropy of a system using the NSB estimator.
      
 
      
-
      Parameters:
      
+
      Parameters
      
 
        
 
      • mk – multiplicities
        • 
 
      • K – number of possible symbols/ state space of the system
        • 
@@ -1255,16 +1254,16 @@ 
        Estimators
-
        
-rho(beta, mk, K, N)[source]
        
+
        
+rho(beta, mk, K, N)[source]
        
 
        rho(beta, data) is the Dirichlet multinomial likelihood.
        
 
        rho(beta, data) together with the d_xi(beta) make up
 the posterior for the nsb estimator
        
 
      
 
 
      
-
      
-unnormalized_posterior(beta, mk, K, N)[source]
      
+
      
+unnormalized_posterior(beta, mk, K, N)[source]
      
 
      The (unnormalized) posterior in the nsb estimator.
      
 
      Product of the likelihood rho and the prior d_xi;
 the normalizing factor is given by the marginal likelihood
      
@@ -1273,8 +1272,8 @@ 
      Estimators
-
      
-class idtxl.estimators_Rudelt.RudeltBBCEstimator(settings=None)[source]
      
+
      
+class idtxl.estimators_Rudelt.RudeltBBCEstimator(settings=None)[source]
      
 
      Bayesian bias criterion (BBC) Estimator using NSB and Plugin estimator
      
 
      Calculate the mutual information (MI) of one variable depending on its past
 using nsb and plugin estimator and check if bias criterion is passed.
@@ -1309,11 +1308,11 @@ 
      Estimators
-
      
-bayesian_bias_criterion(R_nsb, R_plugin, bbc_tolerance)[source]
      
+
      
+bayesian_bias_criterion(R_nsb, R_plugin, bbc_tolerance)[source]
      
 
      Get whether the Bayesian bias criterion (bbc) is passed.
      
 
      
-
      Parameters:
      
+
      Parameters
      
 
      
+     
+       
+       
+     
+       
+       
      




 
 
      units of observation/
 comparison type
      		   
        idtxl.estimators_jidt
        
         
+       idtxl.estimators_mpi
+       
      
      
      
        
           
@@ -112,6 +116,11 @@ 
      Python Module Index
      
              		   
        idtxl.estimators_pid
        
         
+       idtxl.estimators_python
+       
      
      
      
        
           
@@ -195,7 +204,7 @@ 
      Python Module Index
      
   
      Quick search
      
     
      
     
      
-      
+      
       
     
      
     
      
@@ -214,13 +223,13 @@ 
      Navigation
      
         
    • 
           modules |
      • 
-        
    • IDTxl 1.4 documentation »
      • 
+        
    • IDTxl 1.5 documentation »
      • 
         
    • Python Module Index
      •  
       
     
     
   
 
\ No newline at end of file
diff --git a/docs/html/search.html b/docs/html/search.html
index b9f91326..eed72933 100644
--- a/docs/html/search.html
+++ b/docs/html/search.html
@@ -5,16 +5,16 @@
   
     
     
-    Search — IDTxl 1.4 documentation
-    
-    
+    Search — IDTxl 1.5 documentation
+    
+    
     
-    
+    
     
     
     
-    
     
+    
     
     
   
@@ -37,7 +37,7 @@ 
      Navigation
      
         
    • 
           modules |
      • 
-        
    • IDTxl 1.4 documentation »
      • 
+        
    • IDTxl 1.5 documentation »
      • 
         
    • Search
      •  
       
       
@@ -48,26 +48,35 @@ 
      Navigation
      
           
      
             
   
      Search
      
-  
      
-  
+  
+  
+  
+  
   
      
     Searching for multiple words only shows matches that contain
     all words.
   
      
+  
+  
   
      
-    
+    
     
     
   
      
   
+  
+  
   
      
   
   
      
+  
 
             
      
           
      
@@ -88,13 +97,13 @@ 
      Navigation
      
         
    • 
           modules |
      • 
-        
    • IDTxl 1.4 documentation »
      • 
+        
    • IDTxl 1.5 documentation »
      • 
         
    • Search
      •  
       
     
      
     
   
 
\ No newline at end of file
diff --git a/docs/html/searchindex.js b/docs/html/searchindex.js
index 16c81a04..1f0c8fac 100644
--- a/docs/html/searchindex.js
+++ b/docs/html/searchindex.js
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\ No newline at end of file
diff --git a/docs/idtxl.rst b/docs/idtxl.rst
index 6dc6d645..c7d1de0f 100644
--- a/docs/idtxl.rst
+++ b/docs/idtxl.rst
@@ -101,6 +101,25 @@ idtxl.estimators_opencl module
     :undoc-members:
     :show-inheritance:
 
+
+idtxl.estimators_mpi module
+------------------------------
+
+.. automodule:: idtxl.estimators_mpi
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+
+idtxl.estimators_python module
+------------------------------
+
+.. automodule:: idtxl.estimators_python
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
+
 idtxl.estimators_multivariate_pid module
 ----------------------------------------
 
diff --git a/docs/idtxl_estimators.rst b/docs/idtxl_estimators.rst
index 95e8f492..a30caeb0 100644
--- a/docs/idtxl_estimators.rst
+++ b/docs/idtxl_estimators.rst
@@ -7,12 +7,24 @@ JIDT Estimators (CPU)
     :members:
     :noindex:
 
+Python Estimators (CPU)
+-----------------------
+.. automodule:: idtxl.estimators_python
+    :members:
+    :noindex:
+
 OpenCL Estimators (GPU)
 -----------------------
 .. automodule:: idtxl.estimators_opencl
     :members:
     :noindex:
 
+MPI Estimators (CPU)
+-------------------------
+.. automodule:: idtxl.estimators_mpi
+    :members:
+    :noindex:
+
 PID Estimators
 --------------
 .. automodule:: idtxl.estimators_pid