gameanalysis.fixedpoint module¶
Module for finding fixed points of functions on a simplex
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gameanalysis.fixedpoint.fixed_point(func, init, **kwargs)[source]¶ Compute an approximate fixed point of a function
- Parameters
func (ndarray -> ndarray) – A continuous function mapping from the d-simplex to itself.
init (ndarray) – An initial guess for the fixed point. Since many may exist, the choice of starting point will affect the solution.
kwargs (options) – Additional options to pass on to labeled_subsimplex. See other options for details.
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gameanalysis.fixedpoint.labeled_subsimplex(label_func, init, disc)[source]¶ Find approximate center of a fully labeled subsimplex
This runs once at the discretization provided. It is recommended that this be run several times with successively finer discretization and warm started with the past result.
- Parameters
label_func (ndarray -> int) – A proper lableing function. A labeling function takes an element of the d-simplex and returns a label in [0, d). It is proper if the label always coresponds to a dimension in support.
init (ndarray) – An initial guess for where the fully labeled element might be. This will be projected onto the simplex if it is not already.
disc (int) – The discretization to use. Fixed points will be approximated by the reciprocal this much.
- Returns
ret – A discretized simplex with 1 coarser resolution (i.e. ret.sum() + 1 == init.sum()) that is fully labeled.
- Return type
ndarray
Notes
This is an implementation of the sandwhich method from 5 and 6