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View Code? Open in Web Editor NEWEstimating the transfer operator (Perron Frobenius operator) and invariant measures from time series.
License: Other
Estimating the transfer operator (Perron Frobenius operator) and invariant measures from time series.
License: Other
The extra binning steps needed for the transfer operator estimation, which is now being done in StateSpaceReconstruction.rectangularbinning
should be moved to PerronFrobenius.transferoperator
.
It would be useful to be able to directly estimate an invariant measure for an embedding E
and a bin size ϵ
. We could use an abstract InvariantMeasure
type, with subtypes RectangularInvariantMeasure
for rectangular partitions and TriangulationInvariantMeasure
for triangulation partitions.
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We need a way of converting densities of triangulated partitions to rectangular partitions. The easiest way to do this is as follows.
to
is the transfer operator and typeof(to) <: AbstractTriangulationTransferOperator
, then we can compute the invariant measure by finding the left eigenvector of to
, i.e. invdist = left_eigenvector(to)
.StateSpaceReconstruction.assign_bin_labels
. Together with the bin index information, store the value of the measure of the point.@JuliaRegistrator register
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It would be nice not to have to provide an embedding for the invariantizing procedure.
(on the v1.0 branch)
If using MMatrix
for the SimplexApprox
transfer operator estimator, an order of magnitude speed-up can be achieved for dimension <= 4. Try that.
The tag name "v.0.1.3" is not of the appropriate SemVer form (vX.Y.Z).
cc: @kahaaga
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