Add EmpiricalTransiogram (#28)

* Refactor accumulate

* Update comments

* Add CarleEstimator

* Add :carle option to estimalgo

* Add EmpiricalTransiogram

* More refactoring

* More refactoring

* More refactoring

* Refactor ExponentialTransiogram

* Fix CarleEstimator

* Refactor varioplot

* Refactor transioplot

* Fix missing condition in accumulate

* Update 'accumulate'

* More refactoring

* Rename AccumAlgorithm -> AccumAlgo

* Rename VariogramFitAlgo -> FitAlgo

---------

Co-authored-by: Elias Carvalho <eliascarvdev@gmail.com>

Project.toml

@@ -21,6 +21,7 @@ Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 Setfield = "efcf1570-3423-57d1-acb7-fd33fddbac46"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
+TableTransforms = "0d432bfd-3ee1-4ac1-886a-39f05cc69a3e"
 Tables = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
 Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
 
@@ -49,6 +50,7 @@ Random = "1.9"
 Setfield = "1.0"
 StaticArrays = "1.9"
 Statistics = "1.9"
+TableTransforms = "1.33"
 Tables = "1.6"
 Unitful = "1.11"
 julia = "1.9"

ext/transioplot.jl

@@ -2,16 +2,81 @@
 # Licensed under the MIT License. See LICENSE in the project root.
 # ------------------------------------------------------------------
 
+# ----------
+# EMPIRICAL
+# ----------
+
+function transioplot(
+  t::EmpiricalTransiogram;
+  # common transiogram options
+  color=:slategray,
+  size=1.5,
+  maxlag=nothing,
+  levels=nothing,
+
+  # empirical transiogram options
+  pointsize=12,
+  showtext=true,
+  textsize=12,
+  showhist=true,
+  histcolor=:slategray
+)
+  # number of labels
+  L = Base.size(t.ordinates, 1)
+
+  # retrieve labels
+  l = isnothing(levels) ? (1:L) : levels
+
+  fig = Makie.Figure()
+  for i in 1:L, j in 1:L
+    lᵢ, lⱼ = l[i], l[j]
+    ax = Makie.Axis(fig[i, j])
+
+    # retrieve coordinates and counts
+    x = t.abscissas
+    y = t.ordinates[i, j]
+    n = t.counts
+
+    # discard empty bins
+    x = x[n .> 0]
+    y = y[n .> 0]
+    n = n[n .> 0]
+
+    # visualize frequencies as bars
+    if showhist
+      f = n * (maximum(y) / maximum(n)) / 10
+      Makie.barplot!(ax, x, f, color=histcolor, alpha=0.3, gap=0.0)
+    end
+
+    # visualize transiogram
+    Makie.scatterlines!(ax, x, y, color=color, markersize=pointsize, linewidth=size, label="$lᵢ → $lⱼ")
+
+    # visualize text counts
+    if showtext
+      text = string.(n)
+      Makie.text!(ax, x, y, text=text, fontsize=textsize)
+    end
+
+    Makie.axislegend(position=i == j ? :rt : :rb)
+  end
+  fig
+end
+
+# ------------
+# THEORETICAL
+# ------------
+
 function transioplot(
   t::Transiogram;
   # common transiogram options
   color=:slategray,
   size=1.5,
-  maxlag=nothing
+  maxlag=nothing,
+  levels=nothing
 )
   # effective ranges and labels
   r = GeoStatsFunctions.ranges(t)
-  l = GeoStatsFunctions.levels(t)
+  l = isnothing(levels) ? (1:length(r)) : levels
 
   # number of labels
   L = length(l)

ext/varioplot.jl

@@ -35,10 +35,9 @@ function Makie.plot!(plot::VarioPlot{<:Tuple{EmpiricalVariogram}})
   γ = plot[:γ]
 
   # get the data
-  xyn = Makie.@lift values($γ)
-  x = Makie.@lift $xyn[1]
-  y = Makie.@lift $xyn[2]
-  n = Makie.@lift $xyn[3]
+  x = Makie.@lift $γ.abscissas
+  y = Makie.@lift $γ.ordinates
+  n = Makie.@lift $γ.counts
 
   # discard empty bins
   x = Makie.@lift $x[$n .> 0]
@@ -78,43 +77,44 @@ function Makie.plot!(plot::VarioPlot{<:Tuple{EmpiricalVarioplane}})
   θs = Makie.@lift $v.θs
 
   # polar radius
-  rs = Makie.@lift ustrip.(values($γs[1])[1])
-
-  # variogram values for all variograms
-  Z = Makie.@lift let
-    zs = map($γs) do γ
-      zs = ustrip.(values(γ)[2])
-
-      # handle NaN values (i.e. empty bins)
-      isnan(zs[1]) && (zs[1] = 0)
-      for i in 2:length(zs)
-        isnan(zs[i]) && (zs[i] = zs[i - 1])
+  rs = Makie.@lift ustrip.($γs[1].abscissas)
+
+  # variogram ordinates for all variograms
+  H = Makie.@lift let
+    hs = map($γs) do γ
+      # retrieve ordinates without units
+      ys = ustrip.(γ.ordinates)
+
+      # handle NaN ordinates (i.e. empty bins)
+      isnan(ys[1]) && (ys[1] = 0)
+      for i in 2:length(ys)
+        isnan(ys[i]) && (ys[i] = ys[i - 1])
       end
 
-      zs
+      ys
     end
-    reduce(hcat, zs)
+    reduce(hcat, hs)
   end
 
   # exploit symmetry
   θs = Makie.@lift range(0, 2π, length=2 * length($θs))
-  Z = Makie.@lift [$Z $Z]
+  H = Makie.@lift [$H $H]
 
   # hide hole at center
   rs = Makie.@lift [0; $rs]
-  Z = Makie.@lift [$Z[1:1, :]; $Z]
+  H = Makie.@lift [$H[1:1, :]; $H]
 
   # transpose for plotting
-  Z = Makie.@lift transpose($Z)
+  H = Makie.@lift transpose($H)
 
-  Makie.surface!(plot, θs, rs, Z, colormap=plot[:colormap], shading=Makie.NoShading)
+  Makie.surface!(plot, θs, rs, H, colormap=plot[:colormap], shading=Makie.NoShading)
 
   # show model range
   if showrange[]
     ls = Makie.@lift [ustrip(range(GeoStatsFunctions.fit($rangemodel, γ))) for γ in $γs]
     ls = Makie.@lift [$ls; $ls]
-    zs = Makie.@lift fill(maximum($Z) + 1, length($ls))
-    Makie.lines!(plot, θs, ls, zs, color=plot[:rangecolor])
+    hs = Makie.@lift fill(maximum($H) + 1, length($ls))
+    Makie.lines!(plot, θs, ls, hs, color=plot[:rangecolor])
   end
 end
 

src/GeoStatsFunctions.jl

@@ -15,6 +15,7 @@ using InteractiveUtils: subtypes
 using NearestNeighbors: MinkowskiMetric
 using OhMyThreads: tmapreduce
 using DataScienceTraits
+using TableTransforms
 using CategoricalArrays
 using StaticArrays
 using LinearAlgebra
@@ -26,7 +27,6 @@ using Printf
 
 import Base: merge, +, *
 import Meshes: isisotropic
-import CategoricalArrays: levels
 
 # temporary fix for ⋅ with missing values
 # https://github.com/JuliaLang/julia/issues/40743
@@ -36,10 +36,10 @@ import LinearAlgebra: ⋅
 # utilities
 include("utils.jl")
 
-# empirical estimates
+# empirical functions
 include("empirical.jl")
 
-# theoretical models
+# theoretical functions
 include("theoretical.jl")
 
 # misc operations
@@ -49,15 +49,16 @@ include("plotting.jl")
 include("precompile.jl")
 
 export
-  # empirical variograms
+  # empirical functions
   EmpiricalVariogram,
-  EmpiricalVarioplane,
+  EmpiricalTransiogram,
+
+  # convenience functions
   DirectionalVariogram,
   PlanarVariogram,
-  distance,
-  estimator,
+  EmpiricalVarioplane,
 
-  # theoretical function
+  # theoretical functions
   GeoStatsFunction,
   isisotropic,
   metricball,
@@ -96,7 +97,6 @@ export
   ExponentialTransiogram,
 
   # fitting algorithms
-  VariogramFitAlgo,
   WeightedLeastSquares,
 
   # plotting

src/empirical.jl

@@ -15,5 +15,14 @@ include("empirical/estimalgo.jl")
 # END-USER TYPES AND FUNCTIONS
 # -----------------------------
 
+"""
+    EmpiricalFunction
+
+An empirical function estimated from data.
+"""
+abstract type EmpiricalFunction end
+
 include("empirical/variogram.jl")
+include("empirical/transiogram.jl")
+
 include("empirical/varioplane.jl")