`subsystem`¶

Represents a candidate system for \(\varphi\) and \(\Phi\) evaluation.

class pyphi.subsystem.Subsystem(network, state, nodes=None, cut=None, mice_cache=None, repertoire_cache=None, single_node_repertoire_cache=None, _external_indices=None)¶

A set of nodes in a network.

Keyword Arguments:
Parameters:	network (Network) – The network the subsystem belongs to. state (tuple[int]) – The state of the network.
	nodes (tuple[int] or tuple[str]) – The nodes of the network which are in this subsystem. Nodes can be specified either as indices or as labels if the `Network` was passed `node_labels`. If this is `None` then the full network will be used. cut (Cut) – The unidirectional `Cut` to apply to this subsystem.

network¶: Network – The network the subsystem belongs to.

tpm¶: np.ndarray – The TPM conditioned on the state of the external nodes.

cm¶: np.ndarray – The connectivity matrix after applying the cut.

state¶: tuple[int] – The state of the network.

node_indices¶: tuple[int] – The indices of the nodes in the subsystem.

cut¶: Cut – The cut that has been applied to this subsystem.

null_cut¶: Cut – The cut object representing no cut.

nodes¶: tuple[Node] – The nodes in this Subsystem.

proper_state¶

tuple[int] – The state of the subsystem.

proper_state[i] gives the state of the \(i^{\textrm{th}}\) node in the subsystem. Note that this is not the state of nodes[i].

connectivity_matrix¶: np.ndarray – Alias for cm.

size¶: int – The number of nodes in the subsystem.

is_cut¶: bool – True if this Subsystem has a cut applied to it.

cut_indices¶

tuple[int] – The nodes of this subsystem to cut for \(\Phi\) computations.

This was added to support MacroSubsystem, which cuts indices other than node_indices.

Yields:	tuple[int]

cut_mechanisms¶: list[tuple[int]] – The mechanisms that are cut in this system.

cut_node_labels¶: NodeLabels – Labels for the nodes of this system that will be cut.

tpm_size¶: int – The number of nodes in the TPM.

cache_info()¶: Report repertoire cache statistics.

clear_caches()¶: Clear the mice and repertoire caches.

__bool__()¶: Return False if the Subsystem has no nodes, True otherwise.

__eq__(other)¶

Return whether this Subsystem is equal to the other object.

Two Subsystems are equal if their sets of nodes, networks, and cuts are equal.

__lt__(other)¶: Return whether this subsystem has fewer nodes than the other.

__gt__(other)¶: Return whether this subsystem has more nodes than the other.

__len__()¶: Return the number of nodes in this Subsystem.

to_json()¶: Return a JSON-serializable representation.

apply_cut(cut)¶

Return a cut version of this Subsystem.

Parameters:	cut (Cut) – The cut to apply to this `Subsystem`.
Returns:	The cut subsystem.
Return type:	Subsystem

indices2nodes(indices)¶

Return Node for these indices.

Parameters:	indices (tuple[int]) – The indices in question.
Returns:	The `Node` objects corresponding to these indices.
Return type:	tuple[Node]
Raises:	`ValueError` – If requested indices are not in the subsystem.

cause_repertoire(mechanism, purview)¶

Return the cause repertoire of a mechanism over a purview.

Parameters:	mechanism (tuple[int]) – The mechanism for which to calculate the cause repertoire. purview (tuple[int]) – The purview over which to calculate the cause repertoire.
Returns:	The cause repertoire of the mechanism over the purview.
Return type:	np.ndarray

Note

The returned repertoire is a distribution over purview node states, not the states of the whole network.

effect_repertoire(mechanism, purview)¶

Return the effect repertoire of a mechanism over a purview.

Parameters:	mechanism (tuple[int]) – The mechanism for which to calculate the effect repertoire. purview (tuple[int]) – The purview over which to calculate the effect repertoire.
Returns:	The effect repertoire of the mechanism over the purview.
Return type:	np.ndarray

Note

The returned repertoire is a distribution over purview node states, not the states of the whole network.

repertoire(direction, mechanism, purview)¶

Return the cause or effect repertoire based on a direction.

Parameters:	direction (Direction) – `CAUSE` or `EFFECT`. mechanism (tuple[int]) – The mechanism for which to calculate the repertoire. purview (tuple[int]) – The purview over which to calculate the repertoire.
Returns:	The cause or effect repertoire of the mechanism over the purview.
Return type:	np.ndarray
Raises:	`ValueError` – If `direction` is invalid.

unconstrained_repertoire(direction, purview)¶: Return the unconstrained cause/effect repertoire over a purview.

unconstrained_cause_repertoire(purview)¶

Return the unconstrained cause repertoire for a purview.

This is just the cause repertoire in the absence of any mechanism.

unconstrained_effect_repertoire(purview)¶

Return the unconstrained effect repertoire for a purview.

This is just the effect repertoire in the absence of any mechanism.

partitioned_repertoire(direction, partition)¶: Compute the repertoire of a partitioned mechanism and purview.

expand_repertoire(direction, repertoire, new_purview=None)¶

Distribute an effect repertoire over a larger purview.

Keyword Arguments:
Parameters:	direction (Direction) – `CAUSE` or `EFFECT`. repertoire (np.ndarray) – The repertoire to expand.
	new_purview (tuple[int]) – The new purview to expand the repertoire over. If `None` (the default), the new purview is the entire network.
Returns:	A distribution over the new purview, where probability is spread out over the new nodes.
Return type:	np.ndarray
Raises:	`ValueError` – If the expanded purview doesn’t contain the original purview.

expand_cause_repertoire(repertoire, new_purview=None)¶: Alias for expand_repertoire() with direction set to CAUSE.

expand_effect_repertoire(repertoire, new_purview=None)¶: Alias for expand_repertoire() with direction set to EFFECT.

cause_info(mechanism, purview)¶: Return the cause information for a mechanism over a purview.

effect_info(mechanism, purview)¶: Return the effect information for a mechanism over a purview.

cause_effect_info(mechanism, purview)¶

Return the cause-effect information for a mechanism over a purview.

This is the minimum of the cause and effect information.

evaluate_partition(direction, mechanism, purview, partition, repertoire=None)¶

Return the \(\varphi\) of a mechanism over a purview for the given partition.

Keyword Arguments:
Parameters:	direction (Direction) – `CAUSE` or `EFFECT`. mechanism (tuple[int]) – The nodes in the mechanism. purview (tuple[int]) – The nodes in the purview. partition (Bipartition) – The partition to evaluate.
	repertoire (np.array) – The unpartitioned repertoire. If not supplied, it will be computed.
Returns:	The distance between the unpartitioned and partitioned repertoires, and the partitioned repertoire.
Return type:	tuple[int, np.ndarray]

find_mip(direction, mechanism, purview)¶

Return the minimum information partition for a mechanism over a purview.

Parameters:	direction (Direction) – `CAUSE` or `EFFECT`. mechanism (tuple[int]) – The nodes in the mechanism. purview (tuple[int]) – The nodes in the purview.
Returns:	The irreducibility analysis for the mininum-information partition in one temporal direction.
Return type:	RepertoireIrreducibilityAnalysis

cause_mip(mechanism, purview)¶

Return the irreducibility analysis for the cause MIP.

Alias for find_mip() with direction set to CAUSE.

effect_mip(mechanism, purview)¶

Return the irreducibility analysis for the effect MIP.

Alias for find_mip() with direction set to EFFECT.

phi_cause_mip(mechanism, purview)¶

Return the \(\varphi\) of the cause MIP.

This is the distance between the unpartitioned cause repertoire and the MIP cause repertoire.

phi_effect_mip(mechanism, purview)¶

Return the \(\varphi\) of the effect MIP.

This is the distance between the unpartitioned effect repertoire and the MIP cause repertoire.

phi(mechanism, purview)¶: Return the \(\varphi\) of a mechanism over a purview.

potential_purviews(direction, mechanism, purviews=False)¶

Return all purviews that could belong to the MaximallyIrreducibleCause/MaximallyIrreducibleEffect.

Filters out trivially-reducible purviews.

Keyword Arguments:
Parameters:	direction (Direction) – `CAUSE` or `EFFECT`. mechanism (tuple[int]) – The mechanism of interest.
	purviews (tuple[int]) – Optional subset of purviews of interest.

find_mice(direction, mechanism, purviews=False)¶

Return the MaximallyIrreducibleCause or MaximallyIrreducibleEffect for a mechanism.

Keyword Arguments:
Parameters:	direction (Direction) – :`CAUSE` or `EFFECT`. mechanism (tuple[int]) – The mechanism to be tested for irreducibility.
	purviews (tuple[int]) – Optionally restrict the possible purviews to a subset of the subsystem. This may be useful for _e.g._ finding only concepts that are “about” a certain subset of nodes.
Returns:	The `MaximallyIrreducibleCause` or `MaximallyIrreducibleEffect`.
Return type:	MaximallyIrreducibleCauseOrEffect

mic(mechanism, purviews=False)¶

Return the mechanism’s maximally-irreducible cause (MaximallyIrreducibleCause).

Alias for find_mice() with direction set to CAUSE.

mie(mechanism, purviews=False)¶

Return the mechanism’s maximally-irreducible effect (MaximallyIrreducibleEffect).

Alias for find_mice() with direction set to EFFECT.

phi_max(mechanism)¶

Return the \(\varphi^{\textrm{max}}\) of a mechanism.

This is the maximum of \(\varphi\) taken over all possible purviews.

null_concept¶

Return the null concept of this subsystem.

The null concept is a point in concept space identified with the unconstrained cause and effect repertoire of this subsystem.

concept(mechanism, purviews=False, cause_purviews=False, effect_purviews=False)¶

Return the concept specified by a mechanism within this subsytem.

Keyword Arguments:
Parameters:	mechanism (tuple[int]) – The candidate set of nodes.
	purviews (tuple[tuple[int]]) – Restrict the possible purviews to those in this list. cause_purviews (tuple[tuple[int]]) – Restrict the possible cause purviews to those in this list. Takes precedence over `purviews`. effect_purviews (tuple[tuple[int]]) – Restrict the possible effect purviews to those in this list. Takes precedence over `purviews`.
Returns:	The pair of maximally irreducible cause/effect repertoires that constitute the concept specified by the given mechanism.
Return type:	Concept

subsystem¶

`subsystem`¶