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.

Parameters

• network (Network) – The network the subsystem belongs to.

• state (tuple[int]) – The state of the network.

Keyword Arguments

• 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

The network the subsystem belongs to.

Type

Network

tpm

The TPM conditioned on the state of the external nodes.

Type

np.ndarray

cm

The connectivity matrix after applying the cut.

Type

np.ndarray

state

The state of the network.

Type

tuple[int]

node_indices

The indices of the nodes in the subsystem.

Type

tuple[int]

cut

The cut that has been applied to this subsystem.

Type

Cut

null_cut

The cut object representing no cut.

Type

Cut

property nodes

The nodes in this Subsystem.

Type

tuple[Node]

property proper_state

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].

Type

tuple[int]

property connectivity_matrix

Alias for cm.

Type

np.ndarray

property size

The number of nodes in the subsystem.

Type

int

property is_cut

True if this Subsystem has a cut applied to it.

Type

bool

property cut_indices

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]

Type

tuple[int]

property cut_mechanisms

The mechanisms that are cut in this system.

Type

list[tuple[int]]

property cut_node_labels

Labels for the nodes of this system that will be cut.

Type

NodeLabels

property tpm_size

The number of nodes in the TPM.

Type

int

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.

Parameters

• direction (Direction) – CAUSE or EFFECT.

• repertoire (np.ndarray) – The repertoire to expand.

Keyword Arguments

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.

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.

Keyword Arguments

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.

Parameters

• direction (Direction) – CAUSE or EFFECT.

• mechanism (tuple[int]) – The mechanism of interest.

Keyword Arguments

purviews (tuple[int]) – Optional subset of purviews of interest.

find_mice(direction, mechanism, purviews=False)

Return the MaximallyIrreducibleCause or MaximallyIrreducibleEffect for a mechanism.

Parameters

• direction (Direction) – :CAUSE or EFFECT.

• mechanism (tuple[int]) – The mechanism to be tested for irreducibility.

Keyword Arguments

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.

property 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.

Parameters

mechanism (tuple[int]) – The candidate set of nodes.

Keyword Arguments

• 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