Make cholmod preserve user-specified permutation

NEWS.md

@@ -111,6 +111,8 @@ Standard library changes
 
 #### SparseArrays
 
+* `cholesky()` now fully preserves the user-specified permutation. ([#40560])
+
 
 #### Dates
 

stdlib/SuiteSparse/src/cholmod.jl

@@ -1374,9 +1374,9 @@ end
 ## Factorization methods
 
 ## Compute that symbolic factorization only
-function fact_(A::Sparse{<:VTypes};
+function symbolic(A::Sparse{<:VTypes};
     perm::Union{Nothing,AbstractVector{SuiteSparse_long}}=nothing,
-    postorder::Bool=true, userperm_only::Bool=true)
+    postorder::Bool=isnothing(perm)||isempty(perm), userperm_only::Bool=true)
 
     sA = unsafe_load(pointer(A))
     sA.stype == 0 && throw(ArgumentError("sparse matrix is not symmetric/Hermitian"))
@@ -1438,7 +1438,7 @@ function cholesky(A::Sparse; shift::Real=0.0, check::Bool = true,
     cm.print = 0
 
     # Compute the symbolic factorization
-    F = fact_(A; perm = perm)
+    F = symbolic(A; perm = perm)
 
     # Compute the numerical factorization
     cholesky!(F, A; shift = shift, check = check)
@@ -1607,7 +1607,7 @@ function ldlt(A::Sparse; shift::Real=0.0, check::Bool = true,
     cm.supernodal = 0
 
     # Compute the symbolic factorization
-    F = fact_(A; perm = perm)
+    F = symbolic(A; perm = perm)
 
     # Compute the numerical factorization
     ldlt!(F, A; shift = shift, check = check)

stdlib/SuiteSparse/test/cholmod.jl

@@ -909,3 +909,20 @@ end
     @test C * C' == Sparse(spzeros(3, 3))
     @test C' * C == Sparse(spzeros(0, 0))
 end
+
+@testset "permutation handling" begin
+    @testset "default permutation" begin
+        # Assemble arrow matrix
+        A = sparse(5I,3,3)
+        A[:,1] .= 1; A[1,:] .= A[:,1]
+
+        # Ensure cholesky eliminates the fill-in
+        @test cholesky(A).p[1] != 1
+    end
+
+    @testset "user-specified permutation" begin
+        n = 100
+        A = sprand(n,n,5/n) |> t -> t't + I
+        @test cholesky(A, perm=1:n).p == 1:n
+    end
+end