Review of codebase and docs - Probabilities and Encodings- Datseris (#…

…213) * update probabilities table * CountOccurrences works with `Any` input * better terminology header * simpler headers in probabilities * Add encodings page * simplify SymbolicPermutation docstring * reference complexity measures * correct dosctring to reference isrand * more organized tests for symbolic permutat * full rewrite of `SymbolicPermutation` and proper `encode` for Ordinal. * type optimization in making the embedding * remove entropy! * simplifi probabilities! even more * move fasthist to encoding folder * complete unification of symbolic perm methods * docstring for weighted fversion * add docstring to amplkitude aware * delete ALL other files * fix all symbolic permutation tests * fix all permutation tests (and one file only) * clarify source code of encode Gaussian * better docstring for GaussEncod * simplify docstring of Dispersion * more tests for naivekernel * Zhu -> Correa * shorter docstring for spatial permutation * port spatial permutation example to Examples * re-write SpatialSymb to have encoding as field. All tests pass. * better display of exampels in decode * better doc for ordinal encoding * Some typos/nitpickery * Probabilities can't compute. Computations are done with probabilities as *input* * Don't duplicate `SpatialDispersion` * Clarify docstrings a bit * Typo * Cross-reference spatial estimators Co-authored-by: Kristian Haaga <[email protected]>
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diff --git a/docs/Project.toml b/docs/Project.toml
@@ -2,7 +2,6 @@
 CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0"
 ChaosTools = "608a59af-f2a3-5ad4-90b4-758bdf3122a7"
 CoordinateTransformations = "150eb455-5306-5404-9cee-2592286d6298"
-DelayEmbeddings = "5732040d-69e3-5649-938a-b6b4f237613f"
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
 DocumenterTools = "35a29f4d-8980-5a13-9543-d66fff28ecb8"

diff --git a/docs/make.jl b/docs/make.jl
@@ -2,10 +2,10 @@ cd(@__DIR__)
 using Pkg
 CI = get(ENV, "CI", nothing) == "true" || get(ENV, "GITHUB_TOKEN", nothing) !== nothing
 using Entropies
-using DelayEmbeddings
 using Documenter
 using DocumenterTools: Themes
 using CairoMakie
+using Entropies.DelayEmbeddings
 import Entropies.Wavelets
 
 # %% JuliaDynamics theme
@@ -35,6 +35,7 @@ ENV["JULIA_DEBUG"] = "Documenter"
 ENTROPIES_PAGES = [
     "index.md",
     "probabilities.md",
+    "encodings.md",
     "entropies.md",
     "complexity.md",
     "multiscale.md",

diff --git a/docs/src/devdocs.md b/docs/src/devdocs.md
@@ -11,7 +11,7 @@ Good practices in developing a code base apply in every Pull Request. The [Good
 5. If suitable, the estimator may be able to operate based on [`Encoding`]s. If so, it is preferred to implement an `Encoding` subtype and extend the methods [`encode`](@ref) and [`decode`](@ref). This will allow your probabilities estimator to be used with a larger span of entropy and complexity methods without additional effort.
 6. Implement dispatch for [`probabilities_and_outcomes`](@ref) and your probabilities estimator type.
 7. Implement dispatch for [`outcome_space`](@ref) and your probabilities estimator type.
-8. Add your probabilities estimator type to the list in the docstring of [`ProbabilitiyEstimator`](@ref), and if you also made an encoding, add it to the [`Encoding`](@ref) docstring.
+8. Add your probabilities estimator type to the table list in the documentation page of probabilities. If you made an encoding, also add it to corresponding table in the encodings section.
 
 ### Optional steps
 You may extend any of the following functions if there are potential performance benefits in doing so:

diff --git a/docs/src/encodings.md b/docs/src/encodings.md
@@ -0,0 +1,20 @@
+# Encodings
+
+## Encoding API
+
+Some probability estimators first "encode" input data into an intermediate representation indexed by the positive integers. This intermediate representation is called an "encoding" and its API is defined by the following:
+
+```@docs
+Encoding
+encode
+decode
+```
+
+## Available encodings
+
+```@docs
+OrdinalPatternEncoding
+GaussianCDFEncoding
+RectangularBinEncoding
+```
+
diff --git a/docs/src/examples.md b/docs/src/examples.md
@@ -233,7 +233,7 @@ fig
 
 ### Kaniadakis entropy
 
-Here, we show how [`Kaniadakis`](@ref) entropy changes as function of the parameter `a` for 
+Here, we show how [`Kaniadakis`](@ref) entropy changes as function of the parameter `a` for
 a range of two-element probability distributions given by
 `Probabilities([p, 1 - p] for p in 1:0.0:0.01:1.0)`.
 
@@ -370,11 +370,41 @@ end
 You see that while the direct entropy values of the chaotic and noisy signals change massively with `N` but they are almost the same for the normalized version.
 For the regular signals, the entropy decreases nevertheless because the noise contribution of the Fourier computation becomes less significant.
 
+## Spatiotemporal permutation entropy
+
+Usage of a [``SpatialSymbolicPermutation`](@ref) estimator is straightforward.
+Here we get the spatial permutation entropy of a 2D array (e.g., an image):
+
+```@example MAIN
+using Entropies
+x = rand(50, 50) # some image
+stencil = [1 1; 0 1] # or one of the other ways of specifying stencils
+est = SpatialSymbolicPermutation(stencil, x)
+h = entropy(est, x)
+```
+
+To apply this to timeseries of spatial data, simply loop over the call, e.g.:
+
+```@example MAIN
+data = [rand(50, 50) for i in 1:10] # e.g., evolution of a 2D field of a PDE
+est = SpatialSymbolicPermutation(stencil, first(data))
+h_vs_t = map(d -> entropy(est, d), data)
+```
+
+Computing any other generalized spatiotemporal permutation entropy is trivial, e.g. with [`Renyi`](@ref):
+
+```@example MAIN
+x = reshape(repeat(1:5, 500) .+ 0.1*rand(500*5), 50, 50)
+est = SpatialSymbolicPermutation(stencil, x)
+entropy(Renyi(q = 2), est, x)
+```
+
+
 ## Spatial discrete entropy: Fabio
 
 Let's see how the normalized permutation and dispersion entropies increase for an image that gets progressively more noise added to it.
 
-```@example
+```@example MAIN
 using Entropies
 using Distributions
 using CairoMakie
@@ -386,11 +416,11 @@ rot = warp(img, recenter(RotMatrix(-3pi/2), center(img));)
 original = Float32.(rot)
 noise_levels = collect(0.0:0.25:1.0) .* std(original) * 5 # % of 1 standard deviation
 
-noisy_imgs = [i == 1 ? original : original .+ rand(Uniform(0, nL), size(original)) 
+noisy_imgs = [i == 1 ? original : original .+ rand(Uniform(0, nL), size(original))
     for (i, nL) in enumerate(noise_levels)]
 
 # a 2x2 stencil (i.e. dispersion/permutation patterns of length 4)
-stencil = ((2, 2), (1, 1)) 
+stencil = ((2, 2), (1, 1))
 
 est_disp = SpatialDispersion(stencil, original; c = 5, periodic = false)
 est_perm = SpatialSymbolicPermutation(stencil, original; periodic = false)
@@ -399,8 +429,8 @@ hs_perm = [entropy_normalized(est_perm, img) for img in noisy_imgs]
 
 # Plot the results
 fig = Figure(size = (800, 1000))
-ax = Axis(fig[1, 1:length(noise_levels)], 
-    xlabel = "Noise level", 
+ax = Axis(fig[1, 1:length(noise_levels)],
+    xlabel = "Noise level",
     ylabel = "Normalized entropy")
 scatterlines!(ax, noise_levels, hs_disp, label = "Dispersion")
 scatterlines!(ax, noise_levels, hs_perm, label = "Permutation")

diff --git a/docs/src/index.md b/docs/src/index.md
@@ -8,23 +8,22 @@ Entropies
     You are reading the development version of the documentation of Entropies.jl,
     that will become version 2.0.
 
-## API & terminology
+## Terminology
 
 !!! note
     The documentation here follows (loosely) chapter 5 of
     [Nonlinear Dynamics](https://link.springer.com/book/10.1007/978-3-030-91032-7),
     Datseris & Parlitz, Springer 2022.
 
 In the literature, the term "entropy" is used (and abused) in multiple contexts.
-The API and documentation of Entropies.jl aim to clarify some aspects of its usage, and
-to provide a simple way to obtain probabilities, entropies, or other complexity measures.
+The API and documentation of Entropies.jl aim to clarify some aspects of its usage, and to provide a simple way to obtain probabilities, entropies, or other complexity measures.
 
 ### Probabilities
 
 Entropies and other complexity measures are typically computed based on _probability distributions_.
-These are obtained from [Input data for Entropies.jl](@ref) in a plethora of different ways.
-The central API function that returns a probability distribution (in fact, just a vector of probabilities) is [`probabilities`](@ref), which takes in a subtype of [`ProbabilitiesEstimator`](@ref) to specify how the probabilities are computed.
-All estimators available in Entropies.jl can be found in the [estimators page](@ref probabilities_estimators).
+These can be obtained from input data in a plethora of different ways.
+The central API function that returns a probability distribution (or more precisely a probability mass function) is [`probabilities`](@ref), which takes in a subtype of [`ProbabilitiesEstimator`](@ref) to specify how the probabilities are computed.
+All available estimators can be found in the [estimators page](@ref probabilities_estimators).
 
 ### Entropies
 
@@ -40,24 +39,28 @@ Thus, any of the implemented [probabilities estimators](@ref probabilities_estim
 
     These names are commonplace, and so in Entropies.jl we provide convenience functions like [`entropy_wavelet`](@ref). However, it should be noted that these functions really aren't anything more than 2-lines-of-code wrappers that call [`entropy`](@ref) with the appropriate [`ProbabilitiesEstimator`](@ref).
 
-    In addition to `ProbabilitiesEstimators`, we also provide [`EntropyEstimator`](@ref)s, 
-    which compute entropies via alternate means, without explicitly computing some 
+    In addition to `ProbabilitiesEstimators`, we also provide [`EntropyEstimator`](@ref)s,
+    which compute entropies via alternate means, without explicitly computing some
     probability distribution. Differential/continuous entropy, for example, is computed
-    using a dedicated [`EntropyEstimator`](@ref). For example, the [`Kraskov`](@ref) 
-    estimator computes Shannon differential entropy via a nearest neighbor algorithm, while 
-    the [`Zhu`](@ref) estimator computes Shannon differential entropy using order statistics.
+    using a dedicated [`EntropyEstimator`](@ref). For example, the [`Kraskov`](@ref)
+    estimator computes Shannon differential entropy via a nearest neighbor algorithm, while
+    the [`Correa`](@ref) estimator computes Shannon differential entropy using order statistics.
 
 ### Other complexity measures
 
-Other complexity measures, which strictly speaking don't compute entropies, and may or may
-not explicitly compute probability distributions, are found in
-[Complexity.jl](https://github.com/JuliaDynamics/Complexity.jl) package. This includes
-measures like sample entropy and approximate entropy.
+Other complexity measures, which strictly speaking don't compute entropies, and may or may not explicitly compute probability distributions, are found in
+[Complexity measures](@ref) page.
+This includes measures like sample entropy and approximate entropy.
 
 ## [Input data for Entropies.jl](@id input_data)
 
-The input data type typically depend on the probability estimator chosen. In general though, the standard DynamicalSystems.jl approach is taken and as such we have three types of input data:
+The input data type typically depend on the probability estimator chosen.
+In general though, the standard DynamicalSystems.jl approach is taken and as such we have three types of input data:
 
 - _Timeseries_, which are `AbstractVector{<:Real}`, used in e.g. with [`WaveletOverlap`](@ref).
 - _Multi-dimensional timeseries, or datasets, or state space sets_, which are [`Dataset`](@ref), used e.g. with [`NaiveKernel`](@ref).
 - _Spatial data_, which are higher dimensional standard `Array`s, used e.g. with  [`SpatialSymbolicPermutation`](@ref).
+
+```@docs
+Dataset
+```
diff --git a/docs/src/probabilities.md b/docs/src/probabilities.md
@@ -1,4 +1,4 @@
-# [Probabilities](@id probabilities_estimators)
+# Probabilities
 
 ## Probabilities API
 
@@ -8,67 +8,77 @@ The probabilities API is defined by
 - [`probabilities`](@ref)
 - [`probabilities_and_outcomes`](@ref)
 
+and related functions that you will find in the following documentation blocks:
+
+### Probabilitities
+
 ```@docs
 ProbabilitiesEstimator
 probabilities
 probabilities!
 Probabilities
+```
+
+### Outcomes
+
+```@docs
 probabilities_and_outcomes
 outcomes
 outcome_space
 total_outcomes
 missing_outcomes
 ```
 
-## Overview
+## [Overview of probabilities estimators](@id probabilities_estimators)
 
-Any of the following estimators can be used with [`probabilities`](@ref).
+Any of the following estimators can be used with [`probabilities`](@ref)
+(in the column "input data"  it is assumed that the `eltype` of the input is `<: Real`).
 
 | Estimator                                   | Principle                   | Input data          |
-| ------------------------------------------- | --------------------------- | ------------------- |
-| [`CountOccurrences`](@ref)                  | Frequencies                 | `Vector`, `Dataset` |
+|:--------------------------------------------|:----------------------------|:--------------------|
+| [`CountOccurrences`](@ref)                  | Count of unique elements    | `Any` |
 | [`ValueHistogram`](@ref)                    | Binning (histogram)         | `Vector`, `Dataset` |
 | [`TransferOperator`](@ref)                  | Binning (transfer operator) | `Vector`, `Dataset` |
 | [`NaiveKernel`](@ref)                       | Kernel density estimation   | `Dataset`           |
-| [`SymbolicPermutation`](@ref)               | Ordinal patterns            | `Vector`            |
-| [`SymbolicWeightedPermutation`](@ref)       | Ordinal patterns            | `Vector`            |
-| [`SymbolicAmplitudeAwarePermutation`](@ref) | Ordinal patterns            | `Vector`            |
+| [`SymbolicPermutation`](@ref)               | Ordinal patterns            | `Vector`, `Dataset` |
+| [`SymbolicWeightedPermutation`](@ref)       | Ordinal patterns            | `Vector`, `Dataset` |
+| [`SymbolicAmplitudeAwarePermutation`](@ref) | Ordinal patterns            | `Vector`, `Dataset` |
+| [`SpatialSymbolicPermutation`](@ref)        | Ordinal patterns in space   | `Array` |
 | [`Dispersion`](@ref)                        | Dispersion patterns         | `Vector`            |
+| [`SpatialDispersion`](@ref)                 | Dispersion patterns in space  | `Array` |
 | [`Diversity`](@ref)                         | Cosine similarity           | `Vector`            |
 | [`WaveletOverlap`](@ref)                    | Wavelet transform           | `Vector`            |
-| [`PowerSpectrum`](@ref)                     | Fourier spectra             | `Vector`, `Dataset` |
+| [`PowerSpectrum`](@ref)                     | Fourier transform           | `Vector` |
 
-## Count occurrences (counting)
+## Count occurrences
 
 ```@docs
 CountOccurrences
 ```
 
-## Visitation frequency (histograms)
+## Histograms
 
 ```@docs
 ValueHistogram
 RectangularBinning
 FixedRectangularBinning
 ```
 
-## Permutation (symbolic)
+## Symbolic permutations
 
 ```@docs
 SymbolicPermutation
 SymbolicWeightedPermutation
 SymbolicAmplitudeAwarePermutation
-SpatialSymbolicPermutation
 ```
 
-## Dispersion (symbolic)
+## Dispersion patterns
 
 ```@docs
 Dispersion
-SpatialDispersion
 ```
 
-## Transfer operator (binning)
+## Transfer operator
 
 ```@docs
 TransferOperator
@@ -100,3 +110,10 @@ PowerSpectrum
 ```@docs
 Diversity
 ```
+
+## Spatial estimators
+
+```@docs
+SpatialSymbolicPermutation
+SpatialDispersion
+```
diff --git a/src/Entropies.jl b/src/Entropies.jl
@@ -24,10 +24,10 @@ include("complexity.jl")
 include("multiscale.jl")
 
 # Library implementations (files include other files)
+include("encoding/all_encodings.jl") # other structs depend on these
 include("probabilities_estimators/probabilities_estimators.jl")
 include("entropies/entropies.jl")
-include("encoding/all_encodings.jl")
-include("complexity/complexity_measures.jl") # relies on encodings, so include after
+include("complexity/complexity_measures.jl")
 include("deprecations.jl")
 
 

diff --git a/src/encoding/all_encodings.jl b/src/encoding/all_encodings.jl
@@ -1,2 +1,4 @@
+include("fasthist.jl")
+include("rectangular_binning.jl")
 include("gaussian_cdf.jl")
 include("ordinal_pattern.jl")