Getting started

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)


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)


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)

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)

See the documentation for SystemIrreducibilityAnalysis and Concept for more information on these objects.


The network and subsystem discussed here are returned by the pyphi.examples.basic_network() and pyphi.examples.basic_subsystem() functions.