Getting started¶
This page provides a walkthrough of how to use PyPhi in an interactive Python session.
Tip
An illustrated tutorial on how Φ is calculated is available as a supplement to the formal PyPhi paper.
To explore the following examples, install IPython by running pip install ipython
on the
command line. Then run it with the command ipython
.
Lines of code beginning with >>>
and ...
can be pasted directly into
IPython.
Basic Usage¶
Let’s make a simple 3-node network and compute its \(\Phi\).
To make a network, we need a TPM and (optionally) a connectivity matrix. The
TPM can be in more than one form; see the documentation for Network
. Here
we’ll use the 2-dimensional state-by-node form.
>>> import pyphi
>>> import numpy as np
>>> tpm = np.array([
... [0, 0, 0],
... [0, 0, 1],
... [1, 0, 1],
... [1, 0, 0],
... [1, 1, 0],
... [1, 1, 1],
... [1, 1, 1],
... [1, 1, 0]
... ])
The connectivity matrix is a square matrix such that the \((i,j)^{\textrm{th}}\) entry is 1 if there is a connection from node \(i\) to node \(j\), and 0 otherwise.
>>> cm = np.array([
... [0, 0, 1],
... [1, 0, 1],
... [1, 1, 0]
... ])
We’ll also make labels for the network nodes so that PyPhi’s output is easier to read.
>>> labels = ('A', 'B', 'C')
Now we construct the network itself with the arguments we just created:
>>> network = pyphi.Network(tpm, cm=cm, node_labels=labels)
The next step is to define a subsystem for which we want to evaluate \(\Phi\). To make a subsystem, we need the network that it belongs to, the state of that network, and the indices of the subset of nodes which should be included.
The state should be an \(n\)-tuple, where \(n\) is the number of nodes in the network, and where the \(i^{\textrm{th}}\) element is the state of the \(i^{\textrm{th}}\) node in the network.
>>> state = (1, 0, 0)
In this case, we want the \(\Phi\) of the entire network, so we simply include every node in the network in our subsystem:
>>> node_indices = (0, 1, 2)
>>> subsystem = pyphi.Subsystem(network, state, node_indices)
Tip
If you do not explicitly provide node indices to a Subsystem
the system
will, by default, cover the entire network. For example, the following is
equivalent to the above definition of subsystem
:
>>> subsystem = pyphi.Subsystem(network, state)
Tip
Node labels can be used instead of indices when constructing a Subsystem
:
>>> pyphi.Subsystem(network, state, ('B', 'C'))
Subsystem(B, C)
Now we use the phi()
function to compute the \(\Phi\) of our
subsystem:
>>> pyphi.compute.phi(subsystem)
2.3125
If we want to take a deeper look at the integrated-information-theoretic
properties of our network, we can access all the intermediate quantities and
structures that are calculated in the course of arriving at a final \(\Phi\)
value by using sia()
. This returns a nested object,
SystemIrreducibilityAnalysis
, that contains data about the subsystem’s
cause-effect structure, cause and effect repertoires, etc.
>>> sia = pyphi.compute.sia(subsystem)
For instance, we can see that this network has 4 concepts:
>>> len(sia.ces)
4
See the documentation for SystemIrreducibilityAnalysis
and Concept
for more
information on these objects.
Tip
The network and subsystem discussed here are returned by the
pyphi.examples.basic_network()
and
pyphi.examples.basic_subsystem()
functions.