utils
¶
Functions used by more than one PyPhi module or class, or that might be of external use.

pyphi.utils.
state_of
(nodes, network_state)¶ Return the statetuple of the given nodes.

pyphi.utils.
condition_tpm
(tpm, fixed_nodes, state)¶ Return a TPM conditioned on the given fixed node indices, whose states are fixed according to the given statetuple.
The dimensions of the new TPM that correspond to the fixed nodes are collapsed onto their state, making those dimensions singletons suitable for broadcasting. The number of dimensions of the conditioned TPM will be the same as the unconditioned TPM.

pyphi.utils.
apply_cut
(cut, connectivity_matrix)¶ Return a modified connectivity matrix where the connections from one set of nodes to the other are destroyed.

pyphi.utils.
fully_connected
(connectivity_matrix, nodes1, nodes2)¶ Test connectivity of one set of nodes to another.
Parameters:  connectivity_matrix (
np.ndarrray
) – The connectivity matrix  nodes1 (tuple(int) – The nodes whose outputs to
nodes2
will be tested.  nodes2 (tuple(int) – The nodes whose inputs from
nodes1
will be tested.
Returns:  Returns True if all elements in
nodes1
output to some element in
nodes2
AND all elements innodes2
have an input from some element innodes1
. Otherwise return False. Return True if either set of nodes is empty.
Return type: bool
 connectivity_matrix (

pyphi.utils.
apply_boundary_conditions_to_cm
(external_indices, connectivity_matrix)¶ Return a connectivity matrix with all connections to or from external nodes removed.

pyphi.utils.
get_inputs_from_cm
(index, connectivity_matrix)¶ Return a tuple of node indices that have connections to the node with the given index.

pyphi.utils.
get_outputs_from_cm
(index, connectivity_matrix)¶ Return a tuple of node indices that the node with the given index has connections to.

pyphi.utils.
np_hash
(a)¶ Return a hash of a NumPy array.

pyphi.utils.
phi_eq
(x, y)¶ Compare two phi values up to
constants.PRECISION
.

pyphi.utils.
combs
(a, r)¶ NumPy implementation of itertools.combinations.
Return successive \(r\)length combinations of elements in the array
a
.Parameters:  a (np.ndarray) – The array from which to get combinations.
 r (int) – The length of the combinations.
Returns: combinations – An array of combinations.
Return type: np.ndarray

pyphi.utils.
comb_indices
(n, k)¶ ND version of itertools.combinations.
Parameters:  a (np.ndarray) – The array from which to get combinations.
 k (int) – The desired length of the combinations.
Returns: combination_indices –
 Indices that give the
\(k\)combinations of \(n\) elements.
Return type: np.ndarray
Example
>>> n, k = 3, 2 >>> data = np.arange(6).reshape(2, 3) >>> data[:, comb_indices(n, k)] array([[[0, 1], [0, 2], [1, 2]], [[3, 4], [3, 5], [4, 5]]])

pyphi.utils.
powerset
(iterable)¶ Return the power set of an iterable (see itertools recipes).
Parameters: iterable (Iterable) – The iterable from which to generate the power set. Returns: chain – An chained iterator over the power set. Return type: Iterable
Example
>>> ps = powerset(np.arange(2)) >>> print(list(ps)) [(), (0,), (1,), (0, 1)]

pyphi.utils.
uniform_distribution
(number_of_nodes)¶ Return the uniform distribution for a set of binary nodes, indexed by state (so there is one dimension per node, the size of which is the number of possible states for that node).
Parameters: nodes (np.ndarray) – A set of indices of binary nodes. Returns: distribution –  The uniform distribution over the set of
 nodes.
Return type: np.ndarray

pyphi.utils.
marginalize_out
(index, tpm, perturb_value=0.5)¶ Marginalize out a node from a TPM.
Parameters:  index (list) – The index of the node to be marginalized out.
 tpm (np.ndarray) – The TPM to marginalize the node out of.
Returns: tpm –
 A TPM with the same number of dimensions, with
the node marginalized out.
Return type: np.ndarray

pyphi.utils.
max_entropy_distribution
(node_indices, number_of_nodes, perturb_vector=None)¶ Return the maximum entropy distribution over a set of nodes.
This is different from the network’s uniform distribution because nodes outside
node_indices
are fixed and treated as if they have only 1 state.Parameters:  node_indices (tuple(int) – The set of node indices over which to take the distribution.
 number_of_nodes (int) – The total number of nodes in the network.
Returns: distribution –
 The maximum entropy distribution over
the set of nodes.
Return type: np.ndarray

pyphi.utils.
hamming_emd
(d1, d2)¶ Return the Earth Mover’s Distance between two distributions (indexed by state, one dimension per node).
Singleton dimensions are sqeezed out.

pyphi.utils.
bipartition
(a)¶ Return a list of bipartitions for a sequence.
Parameters: a (Iterable) – The iterable to partition. Returns: bipartition –  A list of tuples containing each
 of the two partitions.
Return type: ``list(tuple(tuple Example
>>> from pyphi.utils import bipartition >>> bipartition((1,2,3)) [((), (1, 2, 3)), ((1,), (2, 3)), ((2,), (1, 3)), ((1, 2), (3,))]

pyphi.utils.
directed_bipartition
(a)¶ Return a list of directed bipartitions for a sequence.
Parameters: a (Iterable) – The iterable to partition. Returns: bipartition –  A list of tuples containing each
 of the two partitions.
Return type: ``list(tuple(tuple Example
>>> from pyphi.utils import directed_bipartition >>> directed_bipartition((1, 2, 3)) [((), (1, 2, 3)), ((1,), (2, 3)), ((2,), (1, 3)), ((1, 2), (3,)), ((3,), (1, 2)), ((1, 3), (2,)), ((2, 3), (1,)), ((1, 2, 3), ())]

pyphi.utils.
directed_bipartition_of_one
(a)¶ Return a list of directed bipartitions for a sequence where each bipartitions includes a set of size 1.
Parameters: a (Iterable) – The iterable to partition. Returns: bipartition –  A list of tuples containing each
 of the two partitions.
Return type: ``list(tuple(tuple Example
>>> from pyphi.utils import directed_bipartition_of_one >>> directed_bipartition_of_one((1,2,3)) [((1,), (2, 3)), ((2,), (1, 3)), ((1, 2), (3,)), ((3,), (1, 2)), ((1, 3), (2,)), ((2, 3), (1,))]

pyphi.utils.
directed_bipartition_indices
(N)¶ Return indices for directed bipartitions of a sequence.
The directed bipartion
Parameters: N (int) – The length of the sequence. Returns: bipartition_indices –  A list of tuples containing the indices
 for each of the two partitions.
Return type: list
Example
>>> from pyphi.utils import directed_bipartition_indices >>> N = 3 >>> directed_bipartition_indices(N) [((), (0, 1, 2)), ((0,), (1, 2)), ((1,), (0, 2)), ((0, 1), (2,)), ((2,), (0, 1)), ((0, 2), (1,)), ((1, 2), (0,)), ((0, 1, 2), ())]

pyphi.utils.
bipartition_indices
(N)¶ Return indices for bipartitions of a sequence.
Parameters: N (int) – The length of the sequence. Returns: bipartition_indices –  A list of tuples containing the indices
 for each of the two partitions.
Return type: list
Example
>>> from pyphi.utils import bipartition_indices >>> N = 3 >>> bipartition_indices(N) [((), (0, 1, 2)), ((0,), (1, 2)), ((1,), (0, 2)), ((0, 1), (2,))]

pyphi.utils.
submatrix
(cm, nodes1, nodes2)¶ Return the submatrix of connections from
nodes1
tonodes2
.Parameters:  cm (np.ndarray) – The matrix
 nodes1 (tuple(int) – Source nodes
 nodes2 (tuple(int) – Sink nodes

pyphi.utils.
relevant_connections
(n, _from, to)¶ Construct a connectivity matrix.
Returns an \(N \times N\) connectivity matrix with the \(i,j^{\textrm{th}}\) entry set to
1
if \(i\) is in_from
and \(j\) is into
.Parameters:  n (int) – The dimensions of the matrix
 _from (tuple(int) – Nodes with outgoing connections to
to
 to (tuple(int) – Nodes with incoming connections from
_from

pyphi.utils.
block_cm
(cm)¶ Return whether
cm
can be arranged as a block connectivity matrix.If so, the corresponding mechanism/purview is trivially reducible. Technically, only square matrices are “block diagonal”, but the notion of connectivity carries over.
We test for block connectivity by trying to grow a block of nodes such that:
 ‘source’ nodes only input to nodes in the block
 ‘sink’ nodes only receive inputs from source nodes in the block
For example, the following connectivity matrix represents connections from
nodes1 = A, B, C
tonodes2 = D, E, F, G
(without loss of generality—note thatnodes1
andnodes2
may share elements):D E F G A [1, 1, 0, 0] B [1, 1, 0, 0] C [0, 0, 1, 1]
Since nodes \(AB\) only connect to nodes \(DE\), and node \(C\) only connects to nodes \(FG\), the subgraph is reducible; the cut
AB C  X  DE FG
does not change the structure of the graph.

pyphi.utils.
block_reducible
(cm, nodes1, nodes2)¶ Return whether connections from
nodes1
tonodes2
are reducible.Parameters:  cm (np.ndarray) – The network’s connectivity matrix.
 nodes1 (tuple(int) – Source nodes
 nodes2 (tuple(int) – Sink nodes

pyphi.utils.
strongly_connected
(cm, nodes=None)¶ Return whether the connectivity matrix is strongly connected.
Parameters: cm (np.ndarray) – A square connectivity matrix. Keyword Arguments: nodes (tuple(int) – An optional subset of node indices to test strong connectivity over.

pyphi.utils.
print_repertoire
(r)¶ Print a vertical, humanreadable cause/effect repertoire.

pyphi.utils.
print_repertoire_horiz
(r)¶ Print a horizontal, humanreadable cause/effect repertoire.