Fix ==/sum/issymmetric for (Sym)Tridiagonal with non-number elt…

…ype (#43066)

stdlib/LinearAlgebra/src/tridiag.jl

@@ -125,17 +125,13 @@ AbstractMatrix{T}(S::SymTridiagonal) where {T} =
 function Matrix{T}(M::SymTridiagonal) where T
     n = size(M, 1)
     Mf = zeros(T, n, n)
-    if n == 0
-        return Mf
-    end
-    @inbounds begin
-        @simd for i = 1:n-1
-            Mf[i,i] = M.dv[i]
-            Mf[i+1,i] = M.ev[i]
-            Mf[i,i+1] = M.ev[i]
-        end
-        Mf[n,n] = M.dv[n]
+    n == 0 && return Mf
+    @inbounds for i = 1:n-1
+        Mf[i,i] = symmetric(M.dv[i], :U)
+        Mf[i+1,i] = transpose(M.ev[i])
+        Mf[i,i+1] = M.ev[i]
     end
+    Mf[n,n] = symmetric(M.dv[n], :U)
     return Mf
 end
 Matrix(M::SymTridiagonal{T}) where {T} = Matrix{T}(M)
@@ -612,8 +608,8 @@ transpose(S::Tridiagonal{<:Number}) = Tridiagonal(S.du, S.d, S.dl)
 Base.copy(aS::Adjoint{<:Any,<:Tridiagonal}) = (S = aS.parent; Tridiagonal(map(x -> copy.(adjoint.(x)), (S.du, S.d, S.dl))...))
 Base.copy(tS::Transpose{<:Any,<:Tridiagonal}) = (S = tS.parent; Tridiagonal(map(x -> copy.(transpose.(x)), (S.du, S.d, S.dl))...))
 
-ishermitian(S::Tridiagonal) = isreal(S.d) && S.du == adjoint.(S.dl)
-issymmetric(S::Tridiagonal) = S.du == S.dl
+ishermitian(S::Tridiagonal) = all(ishermitian, S.d) && all(Iterators.map((x, y) -> x == y', S.du, S.dl))
+issymmetric(S::Tridiagonal) = all(issymmetric, S.d) && all(Iterators.map((x, y) -> x == transpose(y), S.du, S.dl))
 
 \(A::Adjoint{<:Any,<:Tridiagonal}, B::Adjoint{<:Any,<:StridedVecOrMat}) = copy(A) \ B
 
@@ -744,8 +740,12 @@ end
 \(B::Number, A::Tridiagonal) = Tridiagonal(B\A.dl, B\A.d, B\A.du)
 
 ==(A::Tridiagonal, B::Tridiagonal) = (A.dl==B.dl) && (A.d==B.d) && (A.du==B.du)
-==(A::Tridiagonal, B::SymTridiagonal) = (A.dl==A.du==B.ev) && (A.d==B.dv)
-==(A::SymTridiagonal, B::Tridiagonal) = (B.dl==B.du==A.ev) && (B.d==A.dv)
+function ==(A::Tridiagonal, B::SymTridiagonal)
+    iseq = all(Iterators.map((x, y) -> x == transpose(y), A.du, A.dl))
+    iseq = iseq && A.du == _evview(B)
+    iseq && all(Iterators.map((x, y) -> x == symmetric(y, :U), A.d, B.dv))
+end
+==(A::SymTridiagonal, B::Tridiagonal) = B == A
 
 det(A::Tridiagonal) = det_usmani(A.dl, A.d, A.du)
 
@@ -760,7 +760,10 @@ function SymTridiagonal{T}(M::Tridiagonal) where T
 end
 
 Base._sum(A::Tridiagonal, ::Colon) = sum(A.d) + sum(A.dl) + sum(A.du)
-Base._sum(A::SymTridiagonal, ::Colon) = sum(A.dv) + 2sum(A.ev)
+function Base._sum(A::SymTridiagonal, ::Colon)
+    se = sum(_evview(A))
+    symmetric(sum(A.dv), :U) + se + transpose(se)
+end
 
 function Base._sum(A::Tridiagonal, dims::Integer)
     res = Base.reducedim_initarray(A, dims, zero(eltype(A)))
@@ -807,24 +810,24 @@ function Base._sum(A::SymTridiagonal, dims::Integer)
     end
     @inbounds begin
         if dims == 1
-            res[1] = A.ev[1] + A.dv[1]
+            res[1] = transpose(A.ev[1]) + symmetric(A.dv[1], :U)
             for i = 2:n-1
-                res[i] = A.ev[i] + A.dv[i] + A.ev[i-1]
+                res[i] = transpose(A.ev[i]) + symmetric(A.dv[i], :U) + A.ev[i-1]
             end
-            res[n] = A.dv[n] + A.ev[n-1]
+            res[n] = symmetric(A.dv[n], :U) + A.ev[n-1]
         elseif dims == 2
-            res[1] = A.dv[1] + A.ev[1]
+            res[1] = symmetric(A.dv[1], :U) + A.ev[1]
             for i = 2:n-1
-                res[i] = A.ev[i-1] + A.dv[i] + A.ev[i]
+                res[i] = transpose(A.ev[i-1]) + symmetric(A.dv[i], :U) + A.ev[i]
             end
-            res[n] = A.ev[n-1] + A.dv[n]
+            res[n] = transpose(A.ev[n-1]) + symmetric(A.dv[n], :U)
         elseif dims >= 3
             for i = 1:n-1
                 res[i,i+1] = A.ev[i]
-                res[i,i]   = A.dv[i]
-                res[i+1,i] = A.ev[i]
+                res[i,i]   = symmetric(A.dv[i], :U)
+                res[i+1,i] = transpose(A.ev[i])
             end
-            res[n,n] = A.dv[n]
+            res[n,n] = symmetric(A.dv[n], :U)
         end
     end
     res

stdlib/LinearAlgebra/test/tridiag.jl

@@ -695,4 +695,35 @@ end
     end
 end
 
+isdefined(Main, :SizedArrays) || @eval Main include(joinpath($(BASE_TEST_PATH), "testhelpers", "SizedArrays.jl"))
+using .Main.SizedArrays
+@testset "non-number eltype" begin
+    @testset "sum for SymTridiagonal" begin
+        dv = [SizedArray{(2,2)}(rand(1:2048,2,2)) for i in 1:10]
+        ev = [SizedArray{(2,2)}(rand(1:2048,2,2)) for i in 1:10]
+        S = SymTridiagonal(dv, ev)
+        Sdense = Matrix(S)
+        @test Sdense == collect(S)
+        @test sum(S) == sum(Sdense)
+        @test sum(S, dims = 1) == sum(Sdense, dims = 1)
+        @test sum(S, dims = 2) == sum(Sdense, dims = 2)
+    end
+    @testset "issymmetric/ishermitian for Tridiagonal" begin
+        @test !issymmetric(Tridiagonal([[1 2;3 4]], [[1 2;2 3], [1 2;2 3]], [[1 2;3 4]]))
+        @test !issymmetric(Tridiagonal([[1 3;2 4]], [[1 2;3 4], [1 2;3 4]], [[1 2;3 4]]))
+        @test issymmetric(Tridiagonal([[1 3;2 4]], [[1 2;2 3], [1 2;2 3]], [[1 2;3 4]]))
+
+        @test ishermitian(Tridiagonal([[1 3;2 4].+im], [[1 2;2 3].+0im, [1 2;2 3].+0im], [[1 2;3 4].-im]))
+        @test !ishermitian(Tridiagonal([[1 3;2 4].+im], [[1 2;2 3].+0im, [1 2;2 3].+0im], [[1 2;3 4].+im]))
+        @test !ishermitian(Tridiagonal([[1 3;2 4].+im], [[1 2;2 3].+im, [1 2;2 3].+0im], [[1 2;3 4].-im]))
+    end
+    @testset "== between Tridiagonal and SymTridiagonal" begin
+        dv = [SizedArray{(2,2)}([1 2;3 4]) for i in 1:4]
+        ev = [SizedArray{(2,2)}([3 4;1 2]) for i in 1:4]
+        S = SymTridiagonal(dv, ev)
+        Sdense = Matrix(S)
+        @test S == Tridiagonal(diag(Sdense, -1), diag(Sdense),  diag(Sdense, 1)) == S
+        @test S !== Tridiagonal(diag(Sdense, 1), diag(Sdense),  diag(Sdense, 1)) !== S
+    end
+end
 end # module TestTridiagonal

test/testhelpers/SizedArrays.jl

@@ -0,0 +1,40 @@
+# This file is a part of Julia. License is MIT: https://julialang.org/license
+
+# SizedArrays
+
+# This test file defines an array wrapper with statical size. It can be used to
+# test the action of LinearAlgebra with non-number eltype.
+
+module SizedArrays
+
+import Base: +, *, ==
+
+export SizedArray
+
+struct SizedArray{SZ,T,N,A<:AbstractArray} <: AbstractArray{T,N}
+    data::A
+    function SizedArray{SZ}(data::AbstractArray{T,N}) where {SZ,T,N}
+        SZ == size(data) || throw(ArgumentError("size mismatch!"))
+        new{SZ,T,N,typeof(data)}(data)
+    end
+    function SizedArray{SZ,T,N,A}(data::AbstractArray{T,N}) where {SZ,T,N,A}
+        SZ == size(data) || throw(ArgumentError("size mismatch!"))
+        new{SZ,T,N,A}(A(data))
+    end
+end
+Base.convert(::Type{SizedArray{SZ,T,N,A}}, data::AbstractArray) where {SZ,T,N,A} = SizedArray{SZ,T,N,A}(data)
+
+# Minimal AbstractArray interface
+Base.size(a::SizedArray) = size(typeof(a))
+Base.size(::Type{<:SizedArray{SZ}}) where {SZ} = SZ
+Base.getindex(A::SizedArray, i...) = getindex(A.data, i...)
+Base.zero(::Type{T}) where T <: SizedArray = SizedArray{size(T)}(zeros(eltype(T), size(T)))
++(S1::SizedArray{SZ}, S2::SizedArray{SZ}) where {SZ} = SizedArray{SZ}(S1.data + S2.data)
+==(S1::SizedArray{SZ}, S2::SizedArray{SZ}) where {SZ} = S1.data == S2.data
+function *(S1::SizedArray, S2::SizedArray)
+    0 < ndims(S1) < 3 && 0 < ndims(S2) < 3 && size(S1, 2) == size(S2, 1) || throw(ArgumentError("size mismatch!"))
+    data = S1.data * S2.data
+    SZ = ndims(data) == 1 ? (size(S1, 1), ) : (size(S1, 1), size(S2, 2))
+    SizedArray{SZ}(data)
+end
+end