Add PiecewiseLinearTransiogram

src/GeoStatsFunctions.jl

@@ -96,6 +96,7 @@ export
   # theoretical transiogram
   Transiogram,
   ExponentialTransiogram,
+  PiecewiseLinearTransiogram,
 
   # fitting algorithms
   WeightedLeastSquares,

src/theoretical/transiogram.jl

@@ -25,3 +25,4 @@ Base.range(t::Transiogram) = maximum(ranges(t))
 # ----------------
 
 include("transiogram/exponential.jl")
+include("transiogram/piecewiselinear.jl")

src/theoretical/transiogram/piecewiselinear.jl

@@ -0,0 +1,47 @@
+# ------------------------------------------------------------------
+# Licensed under the MIT License. See LICENSE in the project root.
+# ------------------------------------------------------------------
+
+"""
+    PiecewiseLinear(abscissas, ordinates)
+
+A piecewise-linear transiogram model from `abscissas` and matrix `ordinates`.
+
+## References
+
+* Li, W. & Zhang, C. 2005. [Application of Transiograms to Markov Chain
+  Simulation and Spatial Uncertainty Assessment of Land-Cover Classes]
+  (https://www.tandfonline.com/doi/abs/10.2747/1548-1603.42.4.297)
+
+* Li, W. & Zhang, C. 2010. [Linear interpolation and joint model fitting
+  of experimental transiograms for Markov chain simulation of categorical
+  spatial variables](https://www.tandfonline.com/doi/abs/10.1080/13658810903127991)
+"""
+struct PiecewiseLinearTransiogram{ℒ<:Len,M} <: Transiogram
+  abscissas::Vector{ℒ}
+  ordinates::Vector{M}
+end
+
+function PiecewiseLinearTransiogram(abscissas::AbstractVector, ordinates::AbstractMatrix)
+  n = length(abscissas)
+  m = size(ordinates, 1)
+  ordinates′ = map(1:n) do k
+    SMatrix{m, m}([ordinates[i, j][k] for i in 1:m, j in 1:m])
+  end
+  PiecewiseLinearTransiogram(abscissas, ordinates′)
+end
+
+function (t::PiecewiseLinearTransiogram)(h)
+  hs = t.abscissas
+  if h < first(hs) # left extrapolation
+    ((first(hs) - h) * I + h * first(t.ordinates)) / first(hs)
+  elseif h > last(hs) # right extrapolation
+    T = last(t.ordinates)
+    m = size(T, 1)
+    p = normalize(SVector{m}(T[j, j] for j in 1:m), 1)
+    SMatrix{m, m}(p[j] for i in 1:m, j in 1:m)
+  else # middle interpolation
+    k = findfirst(≥(h), hs)
+    ((hs[k + 1] - h) * t.ordinates[k] + (h - hs[k]) * t.ordinates[k + 1]) / (hs[k + 1] - hs[k])
+  end
+end