proper diagonal in copytri! (fix #30055) (#30066)

* proper diagonal in copytri! (fix #30055)

* added sprandn methods with Type

* additional parameter in copytri! for diagonal

* @inline copytri! to enforce constant propagation

Author: KlausC

stdlib/LinearAlgebra/src/matmul.jl

@@ -327,14 +327,16 @@ function mul!(C::AbstractMatrix, adjA::Adjoint{<:Any,<:AbstractVecOrMat}, transB
 end
 # Supporting functions for matrix multiplication
 
-function copytri!(A::AbstractMatrix, uplo::AbstractChar, conjugate::Bool=false)
+# copy transposed(adjoint) of upper(lower) side-digonals. Optionally include diagonal.
+@inline function copytri!(A::AbstractMatrix, uplo::AbstractChar, conjugate::Bool=false, diag::Bool=false)
     n = checksquare(A)
+    off = diag ? 0 : 1
     if uplo == 'U'
-        for i = 1:(n-1), j = (i+1):n
+        for i = 1:n, j = (i+off):n
             A[j,i] = conjugate ? adjoint(A[i,j]) : transpose(A[i,j])
         end
     elseif uplo == 'L'
-        for i = 1:(n-1), j = (i+1):n
+        for i = 1:n, j = (i+off):n
             A[i,j] = conjugate ? adjoint(A[j,i]) : transpose(A[j,i])
         end
     else

stdlib/LinearAlgebra/src/symmetric.jl

@@ -237,14 +237,14 @@ similar(A::Union{Symmetric,Hermitian}, ::Type{T}, dims::Dims{N}) where {T,N} = s
 function Matrix(A::Symmetric)
     B = copytri!(convert(Matrix, copy(A.data)), A.uplo)
     for i = 1:size(A, 1)
-        B[i,i] = symmetric(B[i,i], sym_uplo(A.uplo))::symmetric_type(eltype(A.data))
+        B[i,i] = symmetric(A[i,i], sym_uplo(A.uplo))::symmetric_type(eltype(A.data))
     end
     return B
 end
 function Matrix(A::Hermitian)
     B = copytri!(convert(Matrix, copy(A.data)), A.uplo, true)
     for i = 1:size(A, 1)
-        B[i,i] = hermitian(B[i,i], sym_uplo(A.uplo))::hermitian_type(eltype(A.data))
+        B[i,i] = hermitian(A[i,i], sym_uplo(A.uplo))::hermitian_type(eltype(A.data))
     end
     return B
 end

stdlib/LinearAlgebra/src/triangular.jl

@@ -346,14 +346,14 @@ Base.copy(A::Transpose{<:Any,<:UpperTriangular}) = transpose!(copy(A.parent))
 Base.copy(A::Transpose{<:Any,<:UnitLowerTriangular}) = transpose!(copy(A.parent))
 Base.copy(A::Transpose{<:Any,<:UnitUpperTriangular}) = transpose!(copy(A.parent))
 
-transpose!(A::LowerTriangular) = UpperTriangular(copytri!(A.data, 'L'))
-transpose!(A::UnitLowerTriangular) = UnitUpperTriangular(copytri!(A.data, 'L'))
-transpose!(A::UpperTriangular) = LowerTriangular(copytri!(A.data, 'U'))
-transpose!(A::UnitUpperTriangular) = UnitLowerTriangular(copytri!(A.data, 'U'))
-adjoint!(A::LowerTriangular) = UpperTriangular(copytri!(A.data, 'L' , true))
-adjoint!(A::UnitLowerTriangular) = UnitUpperTriangular(copytri!(A.data, 'L' , true))
-adjoint!(A::UpperTriangular) = LowerTriangular(copytri!(A.data, 'U' , true))
-adjoint!(A::UnitUpperTriangular) = UnitLowerTriangular(copytri!(A.data, 'U' , true))
+transpose!(A::LowerTriangular) = UpperTriangular(copytri!(A.data, 'L', false, true))
+transpose!(A::UnitLowerTriangular) = UnitUpperTriangular(copytri!(A.data, 'L', false, true))
+transpose!(A::UpperTriangular) = LowerTriangular(copytri!(A.data, 'U', false, true))
+transpose!(A::UnitUpperTriangular) = UnitLowerTriangular(copytri!(A.data, 'U', false, true))
+adjoint!(A::LowerTriangular) = UpperTriangular(copytri!(A.data, 'L' , true, true))
+adjoint!(A::UnitLowerTriangular) = UnitUpperTriangular(copytri!(A.data, 'L' , true, true))
+adjoint!(A::UpperTriangular) = LowerTriangular(copytri!(A.data, 'U' , true, true))
+adjoint!(A::UnitUpperTriangular) = UnitLowerTriangular(copytri!(A.data, 'U' , true, true))
 
 diag(A::LowerTriangular) = diag(A.data)
 diag(A::UnitLowerTriangular) = fill(one(eltype(A)), size(A,1))

stdlib/LinearAlgebra/test/matmul.jl

@@ -301,6 +301,27 @@ end
 
 @test_throws ArgumentError LinearAlgebra.copytri!(Matrix{Float64}(undef,10,10),'Z')
 
+@testset "Issue 30055" begin
+    B = [1+im 2+im 3+im; 4+im 5+im 6+im; 7+im 9+im im]
+    A = UpperTriangular(B)
+    @test copy(transpose(A)) == transpose(A)
+    @test copy(A') == A'
+    A = LowerTriangular(B)
+    @test copy(transpose(A)) == transpose(A)
+    @test copy(A') == A'
+    B = Matrix{Matrix{Complex{Int}}}(undef, 2, 2)
+    B[1,1] = [1+im 2+im; 3+im 4+im]
+    B[2,1] = [1+2im 1+3im;1+3im 1+4im]
+    B[1,2] = [7+im 8+2im; 9+3im 4im]
+    B[2,2] = [9+im 8+im; 7+im 6+im]
+    A = UpperTriangular(B)
+    @test copy(transpose(A)) == transpose(A)
+    @test copy(A') == A'
+    A = LowerTriangular(B)
+    @test copy(transpose(A)) == transpose(A)
+    @test copy(A') == A'
+end
+
 @testset "gemv! and gemm_wrapper for $elty" for elty in [Float32,Float64,ComplexF64,ComplexF32]
     A10x10, x10, x11 = Array{elty}.(undef, ((10,10), 10, 11))
     @test_throws DimensionMismatch LinearAlgebra.gemv!(x10,'N',A10x10,x11)