Add Metropolis-Hastings algorithm for Potts modelling

src/GardenOptim.jl

@@ -1,5 +1,50 @@
 module GardenOptim
 
-greet() = print("Hello World!")
+using Logging
+
+export update!
+
+function swap!(grid::Array{Int, 2}, i::Int, j::Int)
+    t = grid[i]
+    grid[i] = grid[j]
+    grid[j] = t
+    grid
+end
+
+function neighbours(grid::Array{Int, 2}, idx)
+    m = size(grid, 1)
+    j, i = divrem(idx - 1, m)
+    i += 1
+    j += 1
+    neighbourindices = [(i, j-1), (i, j+1), (i-1, j), (i+1, j)]
+    [grid[k, l] for (k, l) in neighbourindices if 0 < k <= m && 0 < l <= m]
+end
+
+function deltacost(grid::Array{Int, 2}, costs::Array{Float64, 2}, i::Int, j::Int)
+    cost = 0
+    for k in neighbours(grid, i)
+        cost += costs[k, grid[j]] - costs[k, grid[i]]
+    end
+    for k in neighbours(grid, j)
+        cost += costs[k, grid[i]] - costs[k, grid[j]]
+    end
+    cost
+end
+
+function update!(grid::Array{Int, 2}, costs::Array{Float64, 2}, beta::Float64 = 10.0)
+    N = length(grid)
+    i, j = 0, 0
+    while i == j
+        i, j = rand(1:N, 2)
+    end
+    d = deltacost(grid, costs, i, j)
+    @debug "cost difference $d"
+    if rand() < exp(- beta * d)
+        @debug "swapping indices $i and $j"
+        return swap!(grid, i, j)
+    end
+    grid
+end
+
 
 end # module