Add support for Dirac weights

src/weight_fitting.jl

@@ -62,13 +62,27 @@ end
 """
   project_onto_nonnegative_orthant(vector)
 
-Projects `vector` onto the nonnegative_orthant. This projection is trivial:
+Projects `vector` onto the nonnegative orthant. This projection is trivial:
 replace negative components of the vector with zeros.
 """
 function project_onto_nonnegative_orthant(vector::Vector{Float64})
   return max.(vector, 0.0)
 end
 
+"""
+  project_onto_standard_basis(vector)
+
+Projects `vector` onto the standard basis. This projection is trivial:
+replace all components of the vector with zeros, except for the largest one,
+which is replaced with one.
+"""
+function project_onto_standard_basis(vector::Vector{Float64})
+  i = argmax(vector)
+  result = zeros(size(vector))
+  result[i] = 1.0
+  return result
+end
+
 """
   projected_subgradient_descent!(x; gradient, projection, niters, rtol, learning_rate, adaptive_grad)
 
@@ -166,7 +180,9 @@ function fit_rep_period_weights!(
   args...,
 )
   # Determine the appropriate projection method
-  if weight_type == :convex
+  if weight_type == :dirac
+    projection = project_onto_standard_basis
+  elseif weight_type == :convex
     projection = project_onto_simplex
   elseif weight_type == :conical
     projection = project_onto_nonnegative_orthant

test/test-weight-fitting.jl

@@ -15,6 +15,23 @@
       TulipaClustering.project_onto_simplex(x) ≈ [0.0, 1.0]
     end
   end
+
+  @testset "Make sure that projection onto standard basis works correctly" begin
+    @test begin
+      x = [1.0, 10.0]
+      TulipaClustering.project_onto_standard_basis(x) == [0.0, 1.0]
+    end
+
+    @test begin
+      x = [10.0, 1.0]
+      TulipaClustering.project_onto_standard_basis(x) == [1.0, 0.0]
+    end
+
+    @test begin
+      x = [-2.0, 1.0]
+      TulipaClustering.project_onto_standard_basis(x) == [0.0, 1.0]
+    end
+  end
 end
 
 @testset "Subgradient descent" begin
@@ -42,6 +59,23 @@ end
     return DBInterface.execute(con, "SELECT * FROM profiles") |> DataFrame
   end
 
+  @testset "Make sure that weight fitting works correctly for Dirac weights" begin
+    @test begin
+      clustering_data = get_data()
+      split_into_periods!(clustering_data; period_duration = 24 * 7)
+      clustering_result = find_representative_periods(
+        clustering_data,
+        10;
+        drop_incomplete_last_period = false,
+        method = :k_means,
+        distance = SqEuclidean(),
+        init = :kmcen,
+      )
+      TulipaClustering.fit_rep_period_weights!(clustering_result; weight_type = :dirac, niters = 5)
+      all(sum(clustering_result.weight_matrix[1:(end - 1), :], dims = 2) .== 1.0)
+    end
+  end
+
   @testset "Make sure that weight fitting works correctly for convex weights" begin
     @test begin
       clustering_data = get_data()