Final bugfixes for v0.1.0 (#34)

Fixes missing branch when setting k for complete graph special cases. Also sorts the input tuple S (closes #33).

Author: Luis-Varona

src/core.jl

@@ -21,6 +21,7 @@ end
 function s_bandwidth(L::AbstractMatrix{<:Integer}, S::Tuple{Vararg{Integer}})
     _assert_matrix_is_undirected_laplacian(L)
 
+    S = _sort_tuple(S)
     spec = laplacian_s_spectra(L, S)
 
     if !spec.s_diagonalizable
@@ -39,12 +40,12 @@ function s_bandwidth(L::AbstractMatrix{<:Integer}, S::Tuple{Vararg{Integer}})
 
     # Using results from Johnston and Plosker (2025, pp. 319–323)
     if classify_laplacian(L) isa CompleteGraphLaplacian
-        if S == (-1, 0, 1)
-            if 2 < n <= 20 && n % 4 != 0 # Proven subcase of Conjecture 2 applies
-                k = 2
-            end
-        elseif n % 4 == 2 # And, of course, `S = (-1, 1)`; here Theorem 1 applies
+        if S == (-1, 0, 1) && 2 < n <= 20 && n % 4 != 0 # Subcase of Conjecture 2
+            k = 2
+        elseif S == (-1, 1) && n % 4 == 2 # Theorem 1
             k = n - 1
+        else # Back to the general case
+            k = 1
         end
     else
         k = 1
@@ -91,6 +92,7 @@ function has_s_bandwidth_at_most_k(
 )
     _assert_matrix_is_undirected_laplacian(L)
 
+    S = _sort_tuple(S)
     spec = laplacian_s_spectra(L, S)
     L_copy = copy(spec.matrix)
 
@@ -107,11 +109,9 @@ function has_s_bandwidth_at_most_k(
 
     # Using results from Johnston and Plosker (2025, pp. 319–323)
     if classify_laplacian(L_copy) isa CompleteGraphLaplacian
-        if S == (-1, 0, 1)
-            if k == 1 && 2 < n <= 20 && n % 4 != 0 # Proven subcase of Conjecture 2 applies
-                return SBandRecognitionResult(L_copy, S, nothing, k, false)
-            end
-        elseif n % 4 == 2 # And, of course, `S = (-1, 1)`; here Theorem 1 applies
+        if S == (-1, 0, 1) && k == 1 && 2 < n <= 20 && n % 4 != 0 # Subcase of Conjecture 2
+            return SBandRecognitionResult(L_copy, S, nothing, k, false)
+        elseif S == (-1, 1) && n % 4 == 2 # Theorem 1
             if k < n - 1
                 res = SBandRecognitionResult(L_copy, S, nothing, k, false)
             else
@@ -177,6 +177,7 @@ end
 function is_s_diagonalizable(L::AbstractMatrix{<:Integer}, S::Tuple{Vararg{Integer}})
     _assert_matrix_is_undirected_laplacian(L)
 
+    S = _sort_tuple(S)
     spec = laplacian_s_spectra(L, S)
     L_copy = copy(spec.matrix)
 

src/eigenvector_generation.jl

@@ -26,6 +26,8 @@ function pot_kernel_s_eigvecs(n::Integer, S::Tuple{Vararg{Integer}})
         throw(DomainError(n, "Laplacian order must be non-negative"))
     end
 
+    S = _sort_tuple(S)
+
     if S == (-1, 0, 1)
         gen = _pot_kernel_01neg_eigvecs(n)
     elseif S == (-1, 1)
@@ -59,6 +61,8 @@ function pot_nonkernel_s_eigvecs(n::Integer, S::Tuple{Vararg{Integer}})
         throw(DomainError(n, "Laplacian order must be non-negative"))
     end
 
+    S = _sort_tuple(S)
+
     if S == (-1, 0, 1)
         gen = _pot_nonkernel_01neg_eigvecs(n)
     elseif S == (-1, 1)

src/laplacian_s_spectra.jl

@@ -12,6 +12,8 @@
 function laplacian_s_spectra(L::AbstractMatrix{<:Integer}, S::Tuple{Vararg{Integer}})
     _assert_matrix_is_undirected_laplacian(L)
 
+    S = _sort_tuple(S)
+
     if S == (-1, 0, 1)
         spec = _laplacian_01neg_spectra(L)
     elseif S == (-1, 1)
@@ -409,6 +411,7 @@ function _classified_laplacian_s_spectra(
     CL::ArbitraryGraphLaplacian, S::Tuple{Vararg{Integer}}
 )
     L = CL.matrix
+    S = _sort_tuple(S)
     res = check_spectrum_integrality(L)
 
     if !res.spectrum_integral

src/utils.jl

@@ -4,6 +4,30 @@
 # http://opensource.org/licenses/MIT>. This file may not be copied, modified, or
 # distributed except according to those terms.
 
+"""
+    _sort_tuple(S::T) where {T<:Tuple{Vararg{Integer}}} -> T
+
+Return a sorted version of the input tuple.
+
+# Arguments
+- `S::T<:Tuple{Vararg{Integer}}`: the tuple to sort.
+
+# Returns
+- `::T`: a sorted version of `S`.
+
+# Examples
+```jldoctest
+julia> S = (-1, 1, 0)
+(-1, 1, 0)
+
+julia> SDiagonalizability._sort_tuple(S)
+(-1, 0, 1)
+```
+"""
+function _sort_tuple(S::Tuple{Vararg{Integer}})
+    return Tuple(sort(collect(S)))
+end
+
 """
     _extract_independent_cols(A) -> Matrix{Int}