NormalState#

class graph_tool.dynamics.NormalState(g, w=0, sigma=1, s=None)[source]#

Bases: DiscreteStateBase

Multivariate Normal distribution.

Parameters:

gGraph: Graph represening the conditional dependencies.
wEdgePropertyMap or float (optional, default: 0): Inverse covariance (i.e. coupling strength) between nodes.
sigmaVertexPropertyMap or float (optional, default: 1): Node standard deviation.
sVertexPropertyMap (optional, default: None): Initial global state. If not provided, a random state will be chosen.

Notes

This implements a zero-mean multivariate Normal distribution.

If a node \(i\) is updated at time \(t\), the transition to state \(s_i(t+1)\) is given by

\[P(s_i(t+1)|\boldsymbol s(t), \boldsymbol A, \boldsymbol w, \boldsymbol \sigma) = \frac{\exp\left[-\frac{\left(s_i(t+1)+\sigma_i^2\sum_jA_{ij}w_{ij}s_j(t)\right)^2} {2\sigma_i^2}\right]} {\sqrt{2\pi}\sigma_i}\]

which will lead, asymptotically with \(t\to\infty\), to a zero-mean multivariate Normal distribution:

\[P(\boldsymbol s | \boldsymbol W) = \frac{\mathrm{e}^{-\frac{1}{2} {\boldsymbol x}^{\top}\boldsymbol W \boldsymbol x}} {\sqrt{(2\pi)^N |\boldsymbol W^{-1}|}},\]

where \(W_{ij}=w_{ij}\) for \(i\neq j\) and \(W_{ii}=1/\sigma_i^2\).

References

[normal]

https://en.wikipedia.org/wiki/Multivariate_normal_distribution

Examples

>>> g = gt.GraphView(gt.collection.data["polblogs"].copy(), directed=False)
>>> gt.remove_parallel_edges(g)
>>> g = gt.extract_largest_component(g, prune=True)
>>> state = gt.NormalState(g, sigma=0.001, w=-100)
>>> ret = state.iterate_sync(niter=1000)
>>> gt.graph_draw(g, g.vp.pos, vertex_fill_color=state.s,
...               output="polblogs-normal.svg")
<...>

../_images/polblogs-normal.svg — Sample of a multivariate Normal on a political blog network.#

Methods

`copy`()	Return a copy of the state.
`get_active`()	Returns list of "active" nodes, for states where this concept is used.
`get_state`()	Returns the internal `VertexPropertyMap` with the current state.
`iterate_async`([niter])	Updates nodes asynchronously (i.e. single vertex chosen randomly), niter number of times.
`iterate_sync`([niter])	Updates nodes synchronously (i.e. a full "sweep" of all nodes in parallel), niter number of times.
`reset_active`()	Resets list of "active" nodes, for states where this concept is used.
`set_active`(active)	Sets the list of "active" nodes, for states where this concept is used.

copy()#: Return a copy of the state.

get_active()#: Returns list of “active” nodes, for states where this concept is used.

get_state()#: Returns the internal VertexPropertyMap with the current state.

iterate_async(niter=1)#: Updates nodes asynchronously (i.e. single vertex chosen randomly), niter number of times. This function returns the number of nodes that changed state.

iterate_sync(niter=1)#: Updates nodes synchronously (i.e. a full “sweep” of all nodes in parallel), niter number of times. This function returns the number of nodes that changed state.

Parallel implementation.

If enabled during compilation, this algorithm will run in parallel using OpenMP. See the parallel algorithms section for information about how to control several aspects of parallelization.

reset_active()#: Resets list of “active” nodes, for states where this concept is used.

set_active(active)#: Sets the list of “active” nodes, for states where this concept is used.

NormalState

Contents

NormalState#