More correctness tests for symmetric coloring (#74)

* Add tests for symmetric coloring

* Typo

Author: gdalle

src/graph.jl

@@ -24,6 +24,9 @@ vertices(g::Graph) = 1:length(g)
 neighbors(g::Graph, v::Integer) = view(g.rowval, g.colptr[v]:(g.colptr[v + 1] - 1))
 degree(g::Graph, v::Integer) = length(g.colptr[v]:(g.colptr[v + 1] - 1))
 
+maximum_degree(g::Graph) = maximum(Base.Fix1(degree, g), vertices(g))
+minimum_degree(g::Graph) = minimum(Base.Fix1(degree, g), vertices(g))
+
 ## Bipartite graph
 
 """

test/reference/what_table_41_42.csv

@@ -0,0 +1,7 @@
+row,modified,group,name,V,E,Δ,δ,δbar,KD2,KS1,KS2
+1,false,,mrng1,257000,505048,4,2,3,12,8,10
+2,false,,mrng2,1017253,2015714,4,2,3,12,9,10
+3,false,DIMACS10,598a,110971,741934,26,5,13,38,27,32
+4,false,DIMACS10,144,144649,1074393,26,4,14,41,28,35
+5,false,DIMACS10,m14b,214765,1679018,40,4,15,42,29,34
+6,false,DIMACS10,auto,448695,3314611,37,4,14,42,29,36

test/runtests.jl

@@ -47,6 +47,9 @@ include("utils.jl")
         @testset "Random instances" begin
             include("random.jl")
         end
+        @testset "Instances with known colorings" begin
+            include("theory.jl")
+        end
     end
     @testset verbose = true "Performance" begin
         if VERSION >= v"1.10"

test/suitesparse.jl

@@ -1,4 +1,3 @@
-using ADTypes: column_coloring, row_coloring, symmetric_coloring
 using CSV
 using DataFrames
 using LinearAlgebra
@@ -79,3 +78,24 @@ what_table_31_32 = CSV.read(
 end;
 
 ## Star coloring
+
+what_table_41_42 = CSV.read(
+    joinpath(@__DIR__, "reference", "what_table_41_42.csv"), DataFrame
+)
+
+@testset "Star coloring (survey paper)" begin
+    @testset "$(row[:name])" for row in eachrow(what_table_41_42)
+        ismissing(row[:group]) && continue
+        @info "Testing star coloring for $(row[:name]) against survey paper"
+        original_mat = matrixdepot("$(row[:group])/$(row[:name])")
+        mat = dropzeros(sparse(original_mat))
+        ag = adjacency_graph(mat)
+        bg = bipartite_graph(mat)
+        @test length(ag) == row[:V]
+        @test nnz(ag) ÷ 2 == row[:E]
+        @test maximum_degree(ag) == row[:Δ]
+        @test minimum_degree(ag) == row[:δ]
+        color_N, _ = star_coloring(ag, NaturalOrder())
+        @test row[:KS1] <= length(unique(color_N)) <= row[:KS2]  # TODO: find better
+    end
+end;

test/theory.jl

@@ -0,0 +1,43 @@
+using SparseArrays
+using SparseMatrixColorings
+using Test
+
+## Banded
+
+#=
+Per the recovery paper "Efficient computation of sparse Hessians using Coloring and Automatic Differentiation", for a symmetric banded matrix with ρ non-diagonal bands:
+- acyclic coloring uses ⌊ρ/2⌋+1 colors
+- star coloring uses 2⌊ρ/2⌋+1 colors
+=#
+
+problem = ColoringProblem(; structure=:symmetric, partition=:column)
+
+function banded_matrix(n::Integer, ρ::Integer)
+    return spdiagm([k => ones(Bool, n - abs(k)) for k in (-(ρ ÷ 2)):(ρ ÷ 2)]...)
+end
+
+@testset "Star coloring" begin
+    algo = GreedyColoringAlgorithm(; decompression=:direct)
+    for n in [5, 10, 20] .* 1000
+        S = banded_matrix(n, 10)
+        direct_result = coloring(S, problem, algo)
+        @test length(column_groups(direct_result)) == 11
+
+        S = banded_matrix(n, 20)
+        direct_result = coloring(S, problem, algo)
+        @test length(column_groups(direct_result)) == 21
+    end
+end
+
+@testset "Acyclic coloring" begin
+    algo = GreedyColoringAlgorithm(; decompression=:substitution)
+    for n in [5, 10, 20] .* 1000
+        S = banded_matrix(n, 10)
+        substitution_result = coloring(S, problem, algo)
+        @test length(column_groups(substitution_result)) == 6
+
+        S = banded_matrix(n, 20)
+        substitution_result = coloring(S, problem, algo)
+        @test length(column_groups(substitution_result)) == 11
+    end
+end