juliadynamics / perronfrobenius.jl

Estimating the transfer operator (Perron Frobenius operator) and invariant measures from time series.

JuliaDynamics

This repository serves the following purposes:

• Contains the source code for the JuliaDynamics website in the src and build folders.
• Hosts the website via GitHub-pages and Jekyll.
• Contains tutorials for all packages of JuliaDynamics in the tutorials folder.
• Contains video resources for all packages of JuliaDynamics in the videos folder.

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The website was modeled after the website of QuantumOptics.jl and most code that builds the site was re-used from the repository of QuantumOptics.jl (with permission).

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To build locally do follow the instructions from here: https://jekyllrb.com/docs/

(install Jekyll and then do bundle exec jekyll serve which serves by default to http://localhost:4000)

perronfrobenius.jl's Issues

Register v1

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Move functionality from StateSpaceReconstruction.jl to PerronFrobenius.jl

The extra binning steps needed for the transfer operator estimation, which is now being done in StateSpaceReconstruction.rectangularbinning should be moved to PerronFrobenius.transferoperator.

RectangularInvariantMeasure type and constructor

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.

Error tagging new release

The tag name "v.0.1.3" is not of the appropriate SemVer form (vX.Y.Z).
cc: @kahaaga

`invariantize` for any set of points

It would be nice not to have to provide an embedding for the invariantizing procedure.

Given AbstractTriangulationTransferOperator, compute density over rectangular grid

We need a way of converting densities of triangulated partitions to rectangular partitions. The easiest way to do this is as follows.

1. If 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).
2. We then represent each simplex by a cloud of points, each point having measure equal to the measure of the simplex (this is valid because the computed measures are for each simplex volume of the partition).
3. For each point, assign an integer tuple label using StateSpaceReconstruction.assign_bin_labels. Together with the bin index information, store the value of the measure of the point.
4. After we've checked which bins are visited by which points, go over the bins one by one, taking the measure of that bin as the normalised measure of all the points lying inside the bin.

Register v1.0.1

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Speedup: use `MMatrix` for determinant computations

(on the v1.0 branch)
If using MMatrixfor the SimplexApprox transfer operator estimator, an order of magnitude speed-up can be achieved for dimension <= 4. Try that.

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