From 93732e94161272d332541c1a89681151a62b41e9 Mon Sep 17 00:00:00 2001
From: Jishnu Bhattacharya <jishnub.github@gmail.com>
Date: Thu, 11 Sep 2025 20:33:47 +0530
Subject: [PATCH 1/7] Add `sym_uplo_unsafe` to skip validation

---
 src/LinearAlgebra.jl  | 18 +++++++++++
 src/bidiag.jl         |  2 +-
 src/bunchkaufman.jl   |  4 ++-
 src/special.jl        | 12 ++++----
 src/symmetric.jl      | 72 +++++++++++++++++++++----------------------
 src/symmetriceigen.jl | 12 +++++---
 6 files changed, 72 insertions(+), 48 deletions(-)

diff --git a/src/LinearAlgebra.jl b/src/LinearAlgebra.jl
index d97c308b..e9b90d23 100644
--- a/src/LinearAlgebra.jl
+++ b/src/LinearAlgebra.jl
@@ -363,6 +363,11 @@ function char_uplo(uplo::Symbol)
     end
 end
 
+"""
+    sym_uplo(uplo::Char)
+
+Return the `Symbol` corresponding to the `uplo` `Char` by checking for validity.
+"""
 function sym_uplo(uplo::Char)
     if uplo == 'U'
         return :U
@@ -372,6 +377,19 @@ function sym_uplo(uplo::Char)
         throw_uplo()
     end
 end
+"""
+    sym_uplo_unsafe(uplo::Char)
+
+Return the `Symbol` corresponding to the `uplo` `Char` without checking for validity.
+See also `sym_uplo`, which checks for validity.
+"""
+function sym_uplo_unsafe(uplo::Char)
+    if uplo == 'U'
+        return :U
+    else
+        return :L
+    end
+end
 
 @noinline throw_uplo() = throw(ArgumentError("uplo argument must be either :U (upper) or :L (lower)"))
 
diff --git a/src/bidiag.jl b/src/bidiag.jl
index cc5e6de7..c7de41b7 100644
--- a/src/bidiag.jl
+++ b/src/bidiag.jl
@@ -295,7 +295,7 @@ function show(io::IO, M::Bidiagonal)
     print(io, ", ")
     show(io, M.ev)
     print(io, ", ")
-    show(io, sym_uplo(M.uplo))
+    show(io, sym_uplo_unsafe(M.uplo))
     print(io, ")")
 end
 
diff --git a/src/bunchkaufman.jl b/src/bunchkaufman.jl
index 7efe57eb..440f723c 100644
--- a/src/bunchkaufman.jl
+++ b/src/bunchkaufman.jl
@@ -130,7 +130,9 @@ function bunchkaufman!(A::StridedMatrix{<:BlasFloat}, rook::Bool = false; check:
 end
 
 bkcopy_oftype(A, S) = eigencopy_oftype(A, S)
-bkcopy_oftype(A::Symmetric{<:Complex}, S) = Symmetric(copytrito!(similar(parent(A), S, size(A)), A.data, A.uplo), sym_uplo(A.uplo))
+function bkcopy_oftype(A::Symmetric{<:Complex}, S)
+    Symmetric(copytrito!(similar(parent(A), S, size(A)), A.data, A.uplo), sym_uplo_unsafe(A.uplo))
+end
 
 """
     bunchkaufman(A, rook::Bool=false; check = true) -> S::BunchKaufman
diff --git a/src/special.jl b/src/special.jl
index 83880ca5..4bbe885b 100644
--- a/src/special.jl
+++ b/src/special.jl
@@ -292,19 +292,19 @@ end
 
 for f in (:+, :-)
     @eval function $f(D::Diagonal{<:Number}, S::Symmetric)
-        uplo = sym_uplo(S.uplo)
+        uplo = sym_uplo_unsafe(S.uplo)
         return Symmetric(parentof_applytri($f, Symmetric(D, uplo), S), uplo)
     end
     @eval function $f(S::Symmetric, D::Diagonal{<:Number})
-        uplo = sym_uplo(S.uplo)
+        uplo = sym_uplo_unsafe(S.uplo)
         return Symmetric(parentof_applytri($f, S, Symmetric(D, uplo)), uplo)
     end
     @eval function $f(D::Diagonal{<:Real}, H::Hermitian)
-        uplo = sym_uplo(H.uplo)
+        uplo = sym_uplo_unsafe(H.uplo)
         return Hermitian(parentof_applytri($f, Hermitian(D, uplo), H), uplo)
     end
     @eval function $f(H::Hermitian, D::Diagonal{<:Real})
-        uplo = sym_uplo(H.uplo)
+        uplo = sym_uplo_unsafe(H.uplo)
         return Hermitian(parentof_applytri($f, H, Hermitian(D, uplo)), uplo)
     end
 end
@@ -608,8 +608,8 @@ end
 # tridiagonal cholesky factorization
 function cholesky(S::RealSymHermitian{<:BiTriSym}, ::NoPivot = NoPivot(); check::Bool = true)
     T = choltype(S)
-    B = Bidiagonal{T}(diag(S, 0), diag(S, S.uplo == 'U' ? 1 : -1), sym_uplo(S.uplo))
-    cholesky!(Hermitian(B, sym_uplo(S.uplo)), NoPivot(); check = check)
+    B = Bidiagonal{T}(diag(S, 0), diag(S, S.uplo == 'U' ? 1 : -1), sym_uplo_unsafe(S.uplo))
+    cholesky!(Hermitian(B, sym_uplo_unsafe(S.uplo)), NoPivot(); check = check)
 end
 
 # istriu/istril for triangular wrappers of structured matrices
diff --git a/src/symmetric.jl b/src/symmetric.jl
index 2cc74763..b448636c 100644
--- a/src/symmetric.jl
+++ b/src/symmetric.jl
@@ -198,7 +198,7 @@ for (S, H) in ((:Symmetric, :Hermitian), (:Hermitian, :Symmetric))
                 throw(ArgumentError("Cannot construct $($S); uplo doesn't match"))
             end
         end
-        $S(A::$H) = $S(A, sym_uplo(A.uplo))
+        $S(A::$H) = $S(A, sym_uplo_unsafe(A.uplo))
         function $S(A::$H, uplo::Symbol)
             if A.uplo == char_uplo(uplo)
                 if $H === Hermitian && !(eltype(A) <: Real) &&
@@ -206,7 +206,7 @@ for (S, H) in ((:Symmetric, :Hermitian), (:Hermitian, :Symmetric))
 
                     throw(ArgumentError("Cannot construct $($S)($($H))); diagonal contains complex values"))
                 end
-                return $S(A.data, sym_uplo(A.uplo))
+                return $S(A.data, sym_uplo_unsafe(A.uplo))
             else
                 throw(ArgumentError("Cannot construct $($S); uplo doesn't match"))
             end
@@ -251,7 +251,7 @@ end
 @inline function getindex(A::Symmetric, i::Int, j::Int)
     @boundscheck checkbounds(A, i, j)
     @inbounds if i == j
-        return symmetric(A.data[i, j], sym_uplo(A.uplo))::symmetric_type(eltype(A.data))
+        return symmetric(A.data[i, j], sym_uplo_unsafe(A.uplo))::symmetric_type(eltype(A.data))
     elseif (A.uplo == 'U') == (i < j)
         return A.data[i, j]
     else
@@ -261,7 +261,7 @@ end
 @inline function getindex(A::Hermitian, i::Int, j::Int)
     @boundscheck checkbounds(A, i, j)
     @inbounds if i == j
-        return hermitian(A.data[i, j], sym_uplo(A.uplo))::hermitian_type(eltype(A.data))
+        return hermitian(A.data[i, j], sym_uplo_unsafe(A.uplo))::hermitian_type(eltype(A.data))
     elseif (A.uplo == 'U') == (i < j)
         return A.data[i, j]
     else
@@ -294,14 +294,14 @@ Base._reverse(A::Hermitian, ::Colon) = Hermitian(reverse(A.data), A.uplo == 'U'
 end
 
 Base.dataids(A::HermOrSym) = Base.dataids(parent(A))
-Base.unaliascopy(A::Hermitian) = Hermitian(Base.unaliascopy(parent(A)), sym_uplo(A.uplo))
-Base.unaliascopy(A::Symmetric) = Symmetric(Base.unaliascopy(parent(A)), sym_uplo(A.uplo))
+Base.unaliascopy(A::Hermitian) = Hermitian(Base.unaliascopy(parent(A)), sym_uplo_unsafe(A.uplo))
+Base.unaliascopy(A::Symmetric) = Symmetric(Base.unaliascopy(parent(A)), sym_uplo_unsafe(A.uplo))
 
 _conjugation(::Union{Symmetric, Hermitian{<:Real}}) = transpose
 _conjugation(::Hermitian) = adjoint
 
-diag(A::Symmetric) = symmetric.(diag(parent(A)), sym_uplo(A.uplo))
-diag(A::Hermitian) = hermitian.(diag(parent(A)), sym_uplo(A.uplo))
+diag(A::Symmetric) = symmetric.(diag(parent(A)), sym_uplo_unsafe(A.uplo))
+diag(A::Hermitian) = hermitian.(diag(parent(A)), sym_uplo_unsafe(A.uplo))
 
 function applytri(f, A::HermOrSym)
     if A.uplo == 'U'
@@ -345,15 +345,15 @@ similar(A::Union{Symmetric,Hermitian}, ::Type{T}, dims::Dims{N}) where {T,N} = s
 parent(A::HermOrSym) = A.data
 Symmetric{T,S}(A::Symmetric{T,S}) where {T,S<:AbstractMatrix{T}} = A
 Symmetric{T,S}(A::Symmetric) where {T,S<:AbstractMatrix{T}} = Symmetric{T,S}(convert(S,A.data),A.uplo)
-AbstractMatrix{T}(A::Symmetric) where {T} = Symmetric(convert(AbstractMatrix{T}, A.data), sym_uplo(A.uplo))
+AbstractMatrix{T}(A::Symmetric) where {T} = Symmetric(convert(AbstractMatrix{T}, A.data), sym_uplo_unsafe(A.uplo))
 AbstractMatrix{T}(A::Symmetric{T}) where {T} = copy(A)
 Hermitian{T,S}(A::Hermitian{T,S}) where {T,S<:AbstractMatrix{T}} = A
 Hermitian{T,S}(A::Hermitian) where {T,S<:AbstractMatrix{T}} = Hermitian{T,S}(convert(S,A.data),A.uplo)
-AbstractMatrix{T}(A::Hermitian) where {T} = Hermitian(convert(AbstractMatrix{T}, A.data), sym_uplo(A.uplo))
+AbstractMatrix{T}(A::Hermitian) where {T} = Hermitian(convert(AbstractMatrix{T}, A.data), sym_uplo_unsafe(A.uplo))
 AbstractMatrix{T}(A::Hermitian{T}) where {T} = copy(A)
 
-copy(A::Symmetric) = (Symmetric(parentof_applytri(copy, A), sym_uplo(A.uplo)))
-copy(A::Hermitian) = (Hermitian(parentof_applytri(copy, A), sym_uplo(A.uplo)))
+copy(A::Symmetric) = (Symmetric(parentof_applytri(copy, A), sym_uplo_unsafe(A.uplo)))
+copy(A::Hermitian) = (Hermitian(parentof_applytri(copy, A), sym_uplo_unsafe(A.uplo)))
 
 function copyto!(dest::Symmetric, src::Symmetric)
     if axes(dest) != axes(src)
@@ -394,13 +394,13 @@ end
 end
 @inline function _symmetrize_diagonal!(B, A::Symmetric)
     for i = 1:size(A, 1)
-        B[i,i] = symmetric(A[i,i], sym_uplo(A.uplo))::symmetric_type(eltype(A.data))
+        B[i,i] = symmetric(A[i,i], sym_uplo_unsafe(A.uplo))::symmetric_type(eltype(A.data))
     end
     return B
 end
 @inline function _symmetrize_diagonal!(B, A::Hermitian)
     for i = 1:size(A, 1)
-        B[i,i] = hermitian(A[i,i], sym_uplo(A.uplo))::hermitian_type(eltype(A.data))
+        B[i,i] = hermitian(A[i,i], sym_uplo_unsafe(A.uplo))::hermitian_type(eltype(A.data))
     end
     return B
 end
@@ -472,9 +472,9 @@ transpose(A::Hermitian{<:Real}) = A
 
 real(A::Symmetric{<:Real}) = A
 real(A::Hermitian{<:Real}) = A
-real(A::Symmetric) = Symmetric(parentof_applytri(real, A), sym_uplo(A.uplo))
-real(A::Hermitian) = Hermitian(parentof_applytri(real, A), sym_uplo(A.uplo))
-imag(A::Symmetric) = Symmetric(parentof_applytri(imag, A), sym_uplo(A.uplo))
+real(A::Symmetric) = Symmetric(parentof_applytri(real, A), sym_uplo_unsafe(A.uplo))
+real(A::Hermitian) = Hermitian(parentof_applytri(real, A), sym_uplo_unsafe(A.uplo))
+imag(A::Symmetric) = Symmetric(parentof_applytri(imag, A), sym_uplo_unsafe(A.uplo))
 
 Base.copy(A::Adjoint{<:Any,<:Symmetric}) =
     Symmetric(copy(adjoint(A.parent.data)), ifelse(A.parent.uplo == 'U', :L, :U))
@@ -484,8 +484,8 @@ Base.copy(A::Transpose{<:Any,<:Hermitian}) =
 tr(A::Symmetric{<:Number}) = tr(A.data) # to avoid AbstractMatrix fallback (incl. allocations)
 tr(A::Hermitian{<:Number}) = real(tr(A.data))
 
-Base.conj(A::Symmetric) = Symmetric(parentof_applytri(conj, A), sym_uplo(A.uplo))
-Base.conj(A::Hermitian) = Hermitian(parentof_applytri(conj, A), sym_uplo(A.uplo))
+Base.conj(A::Symmetric) = Symmetric(parentof_applytri(conj, A), sym_uplo_unsafe(A.uplo))
+Base.conj(A::Hermitian) = Hermitian(parentof_applytri(conj, A), sym_uplo_unsafe(A.uplo))
 Base.conj!(A::HermOrSym) = typeof(A)(parentof_applytri(conj!, A), A.uplo)
 
 # tril/triu
@@ -702,25 +702,25 @@ function _hermkron!(C, A, B, conj, real, Auplo, Buplo)
     end
 end
 
-(-)(A::Symmetric) = Symmetric(parentof_applytri(-, A), sym_uplo(A.uplo))
-(-)(A::Hermitian) = Hermitian(parentof_applytri(-, A), sym_uplo(A.uplo))
+(-)(A::Symmetric) = Symmetric(parentof_applytri(-, A), sym_uplo_unsafe(A.uplo))
+(-)(A::Hermitian) = Hermitian(parentof_applytri(-, A), sym_uplo_unsafe(A.uplo))
 
 ## Addition/subtraction
 for f ∈ (:+, :-), Wrapper ∈ (:Hermitian, :Symmetric)
     @eval function $f(A::$Wrapper, B::$Wrapper)
-        uplo = A.uplo == B.uplo ? sym_uplo(A.uplo) : (:U)
+        uplo = A.uplo == B.uplo ? sym_uplo_unsafe(A.uplo) : (:U)
         $Wrapper(parentof_applytri($f, A, B), uplo)
     end
 end
 
 for f in (:+, :-)
     @eval begin
-        $f(A::Hermitian, B::Symmetric{<:Real}) = $f(A, Hermitian(parent(B), sym_uplo(B.uplo)))
-        $f(A::Symmetric{<:Real}, B::Hermitian) = $f(Hermitian(parent(A), sym_uplo(A.uplo)), B)
-        $f(A::SymTridiagonal, B::Symmetric) = $f(Symmetric(A, sym_uplo(B.uplo)), B)
-        $f(A::Symmetric, B::SymTridiagonal) = $f(A, Symmetric(B, sym_uplo(A.uplo)))
-        $f(A::SymTridiagonal{<:Real}, B::Hermitian) = $f(Hermitian(A, sym_uplo(B.uplo)), B)
-        $f(A::Hermitian, B::SymTridiagonal{<:Real}) = $f(A, Hermitian(B, sym_uplo(A.uplo)))
+        $f(A::Hermitian, B::Symmetric{<:Real}) = $f(A, Hermitian(parent(B), sym_uplo_unsafe(B.uplo)))
+        $f(A::Symmetric{<:Real}, B::Hermitian) = $f(Hermitian(parent(A), sym_uplo_unsafe(A.uplo)), B)
+        $f(A::SymTridiagonal, B::Symmetric) = $f(Symmetric(A, sym_uplo_unsafe(B.uplo)), B)
+        $f(A::Symmetric, B::SymTridiagonal) = $f(A, Symmetric(B, sym_uplo_unsafe(A.uplo)))
+        $f(A::SymTridiagonal{<:Real}, B::Hermitian) = $f(Hermitian(A, sym_uplo_unsafe(B.uplo)), B)
+        $f(A::Hermitian, B::SymTridiagonal{<:Real}) = $f(A, Hermitian(B, sym_uplo_unsafe(A.uplo)))
     end
 end
 
@@ -770,12 +770,12 @@ function dot(x::AbstractVector, A::HermOrSym, y::AbstractVector)
 end
 
 # Scaling with Number
-*(A::Symmetric, x::Number) = Symmetric(parentof_applytri(y -> y * x, A), sym_uplo(A.uplo))
-*(x::Number, A::Symmetric) = Symmetric(parentof_applytri(y -> x * y, A), sym_uplo(A.uplo))
-*(A::Hermitian, x::Real) = Hermitian(parentof_applytri(y -> y * x, A), sym_uplo(A.uplo))
-*(x::Real, A::Hermitian) = Hermitian(parentof_applytri(y -> x * y, A), sym_uplo(A.uplo))
-/(A::Symmetric, x::Number) = Symmetric(parentof_applytri(y -> y/x, A), sym_uplo(A.uplo))
-/(A::Hermitian, x::Real) = Hermitian(parentof_applytri(y -> y/x, A), sym_uplo(A.uplo))
+*(A::Symmetric, x::Number) = Symmetric(parentof_applytri(y -> y * x, A), sym_uplo_unsafe(A.uplo))
+*(x::Number, A::Symmetric) = Symmetric(parentof_applytri(y -> x * y, A), sym_uplo_unsafe(A.uplo))
+*(A::Hermitian, x::Real) = Hermitian(parentof_applytri(y -> y * x, A), sym_uplo_unsafe(A.uplo))
+*(x::Real, A::Hermitian) = Hermitian(parentof_applytri(y -> x * y, A), sym_uplo_unsafe(A.uplo))
+/(A::Symmetric, x::Number) = Symmetric(parentof_applytri(y -> y/x, A), sym_uplo_unsafe(A.uplo))
+/(A::Hermitian, x::Real) = Hermitian(parentof_applytri(y -> y/x, A), sym_uplo_unsafe(A.uplo))
 
 factorize(A::HermOrSym) = _factorize(A)
 function _factorize(A::HermOrSym{T}; check::Bool=true) where T
@@ -821,8 +821,8 @@ function _inv(A::HermOrSym)
     B
 end
 # StridedMatrix restriction seems necessary due to inv! call in _inv above
-inv(A::Hermitian{<:Any,<:StridedMatrix}) = Hermitian(_inv(A), sym_uplo(A.uplo))
-inv(A::Symmetric{<:Any,<:StridedMatrix}) = Symmetric(_inv(A), sym_uplo(A.uplo))
+inv(A::Hermitian{<:Any,<:StridedMatrix}) = Hermitian(_inv(A), sym_uplo_unsafe(A.uplo))
+inv(A::Symmetric{<:Any,<:StridedMatrix}) = Symmetric(_inv(A), sym_uplo_unsafe(A.uplo))
 
 function svd(A::RealHermSymComplexHerm; full::Bool=false)
     vals, vecs = eigen(A)
diff --git a/src/symmetriceigen.jl b/src/symmetriceigen.jl
index f6640bc1..2edb6a51 100644
--- a/src/symmetriceigen.jl
+++ b/src/symmetriceigen.jl
@@ -2,8 +2,12 @@
 
 # preserve HermOrSym wrapper
 # Call `copytrito!` instead of `copy_similar` to only copy the matching triangular half
-eigencopy_oftype(A::Hermitian, ::Type{S}) where S = Hermitian(copytrito!(similar(parent(A), S, size(A)), A.data, A.uplo), sym_uplo(A.uplo))
-eigencopy_oftype(A::Symmetric, ::Type{S}) where S = Symmetric(copytrito!(similar(parent(A), S, size(A)), A.data, A.uplo), sym_uplo(A.uplo))
+function eigencopy_oftype(A::Hermitian, ::Type{S}) where S
+    Hermitian(copytrito!(similar(parent(A), S, size(A)), A.data, A.uplo), sym_uplo_unsafe(A.uplo))
+end
+function eigencopy_oftype(A::Symmetric, ::Type{S}) where S
+    Symmetric(copytrito!(similar(parent(A), S, size(A)), A.data, A.uplo), sym_uplo_unsafe(A.uplo))
+end
 eigencopy_oftype(A::Symmetric{<:Complex}, ::Type{S}) where S = copyto!(similar(parent(A), S), A)
 
 """
@@ -314,8 +318,8 @@ end
 
 # Perform U' \ A / U in-place, where U::Union{UpperTriangular,Diagonal}
 UtiAUi!(A, U) = _UtiAUi!(A, U)
-UtiAUi!(A::Symmetric, U) = Symmetric(_UtiAUi!(copytri!(parent(A), A.uplo), U), sym_uplo(A.uplo))
-UtiAUi!(A::Hermitian, U) = Hermitian(_UtiAUi!(copytri!(parent(A), A.uplo, true), U), sym_uplo(A.uplo))
+UtiAUi!(A::Symmetric, U) = Symmetric(_UtiAUi!(copytri!(parent(A), A.uplo), U), sym_uplo_unsafe(A.uplo))
+UtiAUi!(A::Hermitian, U) = Hermitian(_UtiAUi!(copytri!(parent(A), A.uplo, true), U), sym_uplo_unsafe(A.uplo))
 _UtiAUi!(A, U) = rdiv!(ldiv!(U', A), U)
 
 function eigvals(A::HermOrSym{TA}, B::HermOrSym{TB}; kws...) where {TA,TB}

From 91f5fd74a2eac19bcadc689c45844b3d693ac3d4 Mon Sep 17 00:00:00 2001
From: Jishnu Bhattacharya <jishnub.github@gmail.com>
Date: Thu, 11 Sep 2025 20:40:10 +0530
Subject: [PATCH 2/7] Update docstrings

---
 src/LinearAlgebra.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/LinearAlgebra.jl b/src/LinearAlgebra.jl
index e9b90d23..a0d163a4 100644
--- a/src/LinearAlgebra.jl
+++ b/src/LinearAlgebra.jl
@@ -366,7 +366,7 @@ end
 """
     sym_uplo(uplo::Char)
 
-Return the `Symbol` corresponding to the `uplo` `Char` by checking for validity.
+Return the `Symbol` corresponding the `uplo` by checking for validity.
 """
 function sym_uplo(uplo::Char)
     if uplo == 'U'
@@ -380,7 +380,7 @@ end
 """
     sym_uplo_unsafe(uplo::Char)
 
-Return the `Symbol` corresponding to the `uplo` `Char` without checking for validity.
+Return the `Symbol` corresponding to `uplo` without checking for validity.
 See also `sym_uplo`, which checks for validity.
 """
 function sym_uplo_unsafe(uplo::Char)

From 7b44cdd5ca3e79f0b3af439ff73c769f3407379a Mon Sep 17 00:00:00 2001
From: Jishnu Bhattacharya <jishnub.github@gmail.com>
Date: Mon, 15 Sep 2025 16:40:26 +0530
Subject: [PATCH 3/7] Make the method a one-liner

---
 src/LinearAlgebra.jl | 8 +-------
 1 file changed, 1 insertion(+), 7 deletions(-)

diff --git a/src/LinearAlgebra.jl b/src/LinearAlgebra.jl
index a0d163a4..a3b06624 100644
--- a/src/LinearAlgebra.jl
+++ b/src/LinearAlgebra.jl
@@ -383,13 +383,7 @@ end
 Return the `Symbol` corresponding to `uplo` without checking for validity.
 See also `sym_uplo`, which checks for validity.
 """
-function sym_uplo_unsafe(uplo::Char)
-    if uplo == 'U'
-        return :U
-    else
-        return :L
-    end
-end
+sym_uplo_unsafe(uplo::Char) = uplo == 'U' ? (:U) : (:L)
 
 @noinline throw_uplo() = throw(ArgumentError("uplo argument must be either :U (upper) or :L (lower)"))
 

From 34c26b78b99a0dc49ea31ae70ec6c35b3c5c8cf7 Mon Sep 17 00:00:00 2001
From: Jishnu Bhattacharya <jishnub.github@gmail.com>
Date: Mon, 15 Sep 2025 19:04:49 +0530
Subject: [PATCH 4/7] Tests for `sym_uplo`

---
 test/symmetric.jl | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/test/symmetric.jl b/test/symmetric.jl
index 707b392d..c6ab1144 100644
--- a/test/symmetric.jl
+++ b/test/symmetric.jl
@@ -1343,4 +1343,10 @@ end
     @test_throws msg LinearAlgebra.fillband!(Symmetric(A), 2, 0, 1)
 end
 
+@testset "sym_uplo" begin
+    @test LinearAlgebra.sym_uplo('U') == :U
+    @test LinearAlgebra.sym_uplo('L') == :L
+    @test_throws ArgumentError LinearAlgebra.sym_uplo('N')
+end
+
 end # module TestSymmetric

From 14ce3f18f0430eeaa0904ead602ad33b76ee9c3d Mon Sep 17 00:00:00 2001
From: Jishnu Bhattacharya <jishnub.github@gmail.com>
Date: Mon, 15 Sep 2025 19:06:14 +0530
Subject: [PATCH 5/7] Add a comment

---
 src/LinearAlgebra.jl | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/src/LinearAlgebra.jl b/src/LinearAlgebra.jl
index a3b06624..096926de 100644
--- a/src/LinearAlgebra.jl
+++ b/src/LinearAlgebra.jl
@@ -369,6 +369,8 @@ end
 Return the `Symbol` corresponding the `uplo` by checking for validity.
 """
 function sym_uplo(uplo::Char)
+    # This method is called by other packages, and isn't used within LinearAlgebra
+    # It's retained here for backward compatibility.
     if uplo == 'U'
         return :U
     elseif uplo == 'L'

From ef5ab42b3519db4b4466c5fb2ad20ead6ddd9b39 Mon Sep 17 00:00:00 2001
From: Jishnu Bhattacharya <jishnub.github@gmail.com>
Date: Wed, 17 Sep 2025 19:40:59 +0530
Subject: [PATCH 6/7] Rename to `_sym_uplo`

---
 src/LinearAlgebra.jl  |  4 ++--
 src/bidiag.jl         |  2 +-
 src/bunchkaufman.jl   |  2 +-
 src/special.jl        | 12 ++++++------
 src/symmetriceigen.jl |  8 ++++----
 5 files changed, 14 insertions(+), 14 deletions(-)

diff --git a/src/LinearAlgebra.jl b/src/LinearAlgebra.jl
index 096926de..4d4eb029 100644
--- a/src/LinearAlgebra.jl
+++ b/src/LinearAlgebra.jl
@@ -380,12 +380,12 @@ function sym_uplo(uplo::Char)
     end
 end
 """
-    sym_uplo_unsafe(uplo::Char)
+    _sym_uplo(uplo::Char)
 
 Return the `Symbol` corresponding to `uplo` without checking for validity.
 See also `sym_uplo`, which checks for validity.
 """
-sym_uplo_unsafe(uplo::Char) = uplo == 'U' ? (:U) : (:L)
+_sym_uplo(uplo::Char) = uplo == 'U' ? (:U) : (:L)
 
 @noinline throw_uplo() = throw(ArgumentError("uplo argument must be either :U (upper) or :L (lower)"))
 
diff --git a/src/bidiag.jl b/src/bidiag.jl
index c7de41b7..f74f759a 100644
--- a/src/bidiag.jl
+++ b/src/bidiag.jl
@@ -295,7 +295,7 @@ function show(io::IO, M::Bidiagonal)
     print(io, ", ")
     show(io, M.ev)
     print(io, ", ")
-    show(io, sym_uplo_unsafe(M.uplo))
+    show(io, _sym_uplo(M.uplo))
     print(io, ")")
 end
 
diff --git a/src/bunchkaufman.jl b/src/bunchkaufman.jl
index 440f723c..69811fde 100644
--- a/src/bunchkaufman.jl
+++ b/src/bunchkaufman.jl
@@ -131,7 +131,7 @@ end
 
 bkcopy_oftype(A, S) = eigencopy_oftype(A, S)
 function bkcopy_oftype(A::Symmetric{<:Complex}, S)
-    Symmetric(copytrito!(similar(parent(A), S, size(A)), A.data, A.uplo), sym_uplo_unsafe(A.uplo))
+    Symmetric(copytrito!(similar(parent(A), S, size(A)), A.data, A.uplo), _sym_uplo(A.uplo))
 end
 
 """
diff --git a/src/special.jl b/src/special.jl
index 4bbe885b..9dff10a4 100644
--- a/src/special.jl
+++ b/src/special.jl
@@ -292,19 +292,19 @@ end
 
 for f in (:+, :-)
     @eval function $f(D::Diagonal{<:Number}, S::Symmetric)
-        uplo = sym_uplo_unsafe(S.uplo)
+        uplo = _sym_uplo(S.uplo)
         return Symmetric(parentof_applytri($f, Symmetric(D, uplo), S), uplo)
     end
     @eval function $f(S::Symmetric, D::Diagonal{<:Number})
-        uplo = sym_uplo_unsafe(S.uplo)
+        uplo = _sym_uplo(S.uplo)
         return Symmetric(parentof_applytri($f, S, Symmetric(D, uplo)), uplo)
     end
     @eval function $f(D::Diagonal{<:Real}, H::Hermitian)
-        uplo = sym_uplo_unsafe(H.uplo)
+        uplo = _sym_uplo(H.uplo)
         return Hermitian(parentof_applytri($f, Hermitian(D, uplo), H), uplo)
     end
     @eval function $f(H::Hermitian, D::Diagonal{<:Real})
-        uplo = sym_uplo_unsafe(H.uplo)
+        uplo = _sym_uplo(H.uplo)
         return Hermitian(parentof_applytri($f, H, Hermitian(D, uplo)), uplo)
     end
 end
@@ -608,8 +608,8 @@ end
 # tridiagonal cholesky factorization
 function cholesky(S::RealSymHermitian{<:BiTriSym}, ::NoPivot = NoPivot(); check::Bool = true)
     T = choltype(S)
-    B = Bidiagonal{T}(diag(S, 0), diag(S, S.uplo == 'U' ? 1 : -1), sym_uplo_unsafe(S.uplo))
-    cholesky!(Hermitian(B, sym_uplo_unsafe(S.uplo)), NoPivot(); check = check)
+    B = Bidiagonal{T}(diag(S, 0), diag(S, S.uplo == 'U' ? 1 : -1), _sym_uplo(S.uplo))
+    cholesky!(Hermitian(B, _sym_uplo(S.uplo)), NoPivot(); check = check)
 end
 
 # istriu/istril for triangular wrappers of structured matrices
diff --git a/src/symmetriceigen.jl b/src/symmetriceigen.jl
index 2edb6a51..a8a54037 100644
--- a/src/symmetriceigen.jl
+++ b/src/symmetriceigen.jl
@@ -3,10 +3,10 @@
 # preserve HermOrSym wrapper
 # Call `copytrito!` instead of `copy_similar` to only copy the matching triangular half
 function eigencopy_oftype(A::Hermitian, ::Type{S}) where S
-    Hermitian(copytrito!(similar(parent(A), S, size(A)), A.data, A.uplo), sym_uplo_unsafe(A.uplo))
+    Hermitian(copytrito!(similar(parent(A), S, size(A)), A.data, A.uplo), _sym_uplo(A.uplo))
 end
 function eigencopy_oftype(A::Symmetric, ::Type{S}) where S
-    Symmetric(copytrito!(similar(parent(A), S, size(A)), A.data, A.uplo), sym_uplo_unsafe(A.uplo))
+    Symmetric(copytrito!(similar(parent(A), S, size(A)), A.data, A.uplo), _sym_uplo(A.uplo))
 end
 eigencopy_oftype(A::Symmetric{<:Complex}, ::Type{S}) where S = copyto!(similar(parent(A), S), A)
 
@@ -318,8 +318,8 @@ end
 
 # Perform U' \ A / U in-place, where U::Union{UpperTriangular,Diagonal}
 UtiAUi!(A, U) = _UtiAUi!(A, U)
-UtiAUi!(A::Symmetric, U) = Symmetric(_UtiAUi!(copytri!(parent(A), A.uplo), U), sym_uplo_unsafe(A.uplo))
-UtiAUi!(A::Hermitian, U) = Hermitian(_UtiAUi!(copytri!(parent(A), A.uplo, true), U), sym_uplo_unsafe(A.uplo))
+UtiAUi!(A::Symmetric, U) = Symmetric(_UtiAUi!(copytri!(parent(A), A.uplo), U), _sym_uplo(A.uplo))
+UtiAUi!(A::Hermitian, U) = Hermitian(_UtiAUi!(copytri!(parent(A), A.uplo, true), U), _sym_uplo(A.uplo))
 _UtiAUi!(A, U) = rdiv!(ldiv!(U', A), U)
 
 function eigvals(A::HermOrSym{TA}, B::HermOrSym{TB}; kws...) where {TA,TB}

From eb5a514836466b8371dea2bba3215ce094f7a8df Mon Sep 17 00:00:00 2001
From: Jishnu Bhattacharya <jishnub.github@gmail.com>
Date: Wed, 17 Sep 2025 19:42:38 +0530
Subject: [PATCH 7/7] Replace in symmetric.jl

---
 src/symmetric.jl | 72 ++++++++++++++++++++++++------------------------
 1 file changed, 36 insertions(+), 36 deletions(-)

diff --git a/src/symmetric.jl b/src/symmetric.jl
index b448636c..f7885a6b 100644
--- a/src/symmetric.jl
+++ b/src/symmetric.jl
@@ -198,7 +198,7 @@ for (S, H) in ((:Symmetric, :Hermitian), (:Hermitian, :Symmetric))
                 throw(ArgumentError("Cannot construct $($S); uplo doesn't match"))
             end
         end
-        $S(A::$H) = $S(A, sym_uplo_unsafe(A.uplo))
+        $S(A::$H) = $S(A, _sym_uplo(A.uplo))
         function $S(A::$H, uplo::Symbol)
             if A.uplo == char_uplo(uplo)
                 if $H === Hermitian && !(eltype(A) <: Real) &&
@@ -206,7 +206,7 @@ for (S, H) in ((:Symmetric, :Hermitian), (:Hermitian, :Symmetric))
 
                     throw(ArgumentError("Cannot construct $($S)($($H))); diagonal contains complex values"))
                 end
-                return $S(A.data, sym_uplo_unsafe(A.uplo))
+                return $S(A.data, _sym_uplo(A.uplo))
             else
                 throw(ArgumentError("Cannot construct $($S); uplo doesn't match"))
             end
@@ -251,7 +251,7 @@ end
 @inline function getindex(A::Symmetric, i::Int, j::Int)
     @boundscheck checkbounds(A, i, j)
     @inbounds if i == j
-        return symmetric(A.data[i, j], sym_uplo_unsafe(A.uplo))::symmetric_type(eltype(A.data))
+        return symmetric(A.data[i, j], _sym_uplo(A.uplo))::symmetric_type(eltype(A.data))
     elseif (A.uplo == 'U') == (i < j)
         return A.data[i, j]
     else
@@ -261,7 +261,7 @@ end
 @inline function getindex(A::Hermitian, i::Int, j::Int)
     @boundscheck checkbounds(A, i, j)
     @inbounds if i == j
-        return hermitian(A.data[i, j], sym_uplo_unsafe(A.uplo))::hermitian_type(eltype(A.data))
+        return hermitian(A.data[i, j], _sym_uplo(A.uplo))::hermitian_type(eltype(A.data))
     elseif (A.uplo == 'U') == (i < j)
         return A.data[i, j]
     else
@@ -294,14 +294,14 @@ Base._reverse(A::Hermitian, ::Colon) = Hermitian(reverse(A.data), A.uplo == 'U'
 end
 
 Base.dataids(A::HermOrSym) = Base.dataids(parent(A))
-Base.unaliascopy(A::Hermitian) = Hermitian(Base.unaliascopy(parent(A)), sym_uplo_unsafe(A.uplo))
-Base.unaliascopy(A::Symmetric) = Symmetric(Base.unaliascopy(parent(A)), sym_uplo_unsafe(A.uplo))
+Base.unaliascopy(A::Hermitian) = Hermitian(Base.unaliascopy(parent(A)), _sym_uplo(A.uplo))
+Base.unaliascopy(A::Symmetric) = Symmetric(Base.unaliascopy(parent(A)), _sym_uplo(A.uplo))
 
 _conjugation(::Union{Symmetric, Hermitian{<:Real}}) = transpose
 _conjugation(::Hermitian) = adjoint
 
-diag(A::Symmetric) = symmetric.(diag(parent(A)), sym_uplo_unsafe(A.uplo))
-diag(A::Hermitian) = hermitian.(diag(parent(A)), sym_uplo_unsafe(A.uplo))
+diag(A::Symmetric) = symmetric.(diag(parent(A)), _sym_uplo(A.uplo))
+diag(A::Hermitian) = hermitian.(diag(parent(A)), _sym_uplo(A.uplo))
 
 function applytri(f, A::HermOrSym)
     if A.uplo == 'U'
@@ -345,15 +345,15 @@ similar(A::Union{Symmetric,Hermitian}, ::Type{T}, dims::Dims{N}) where {T,N} = s
 parent(A::HermOrSym) = A.data
 Symmetric{T,S}(A::Symmetric{T,S}) where {T,S<:AbstractMatrix{T}} = A
 Symmetric{T,S}(A::Symmetric) where {T,S<:AbstractMatrix{T}} = Symmetric{T,S}(convert(S,A.data),A.uplo)
-AbstractMatrix{T}(A::Symmetric) where {T} = Symmetric(convert(AbstractMatrix{T}, A.data), sym_uplo_unsafe(A.uplo))
+AbstractMatrix{T}(A::Symmetric) where {T} = Symmetric(convert(AbstractMatrix{T}, A.data), _sym_uplo(A.uplo))
 AbstractMatrix{T}(A::Symmetric{T}) where {T} = copy(A)
 Hermitian{T,S}(A::Hermitian{T,S}) where {T,S<:AbstractMatrix{T}} = A
 Hermitian{T,S}(A::Hermitian) where {T,S<:AbstractMatrix{T}} = Hermitian{T,S}(convert(S,A.data),A.uplo)
-AbstractMatrix{T}(A::Hermitian) where {T} = Hermitian(convert(AbstractMatrix{T}, A.data), sym_uplo_unsafe(A.uplo))
+AbstractMatrix{T}(A::Hermitian) where {T} = Hermitian(convert(AbstractMatrix{T}, A.data), _sym_uplo(A.uplo))
 AbstractMatrix{T}(A::Hermitian{T}) where {T} = copy(A)
 
-copy(A::Symmetric) = (Symmetric(parentof_applytri(copy, A), sym_uplo_unsafe(A.uplo)))
-copy(A::Hermitian) = (Hermitian(parentof_applytri(copy, A), sym_uplo_unsafe(A.uplo)))
+copy(A::Symmetric) = (Symmetric(parentof_applytri(copy, A), _sym_uplo(A.uplo)))
+copy(A::Hermitian) = (Hermitian(parentof_applytri(copy, A), _sym_uplo(A.uplo)))
 
 function copyto!(dest::Symmetric, src::Symmetric)
     if axes(dest) != axes(src)
@@ -394,13 +394,13 @@ end
 end
 @inline function _symmetrize_diagonal!(B, A::Symmetric)
     for i = 1:size(A, 1)
-        B[i,i] = symmetric(A[i,i], sym_uplo_unsafe(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
 @inline function _symmetrize_diagonal!(B, A::Hermitian)
     for i = 1:size(A, 1)
-        B[i,i] = hermitian(A[i,i], sym_uplo_unsafe(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
@@ -472,9 +472,9 @@ transpose(A::Hermitian{<:Real}) = A
 
 real(A::Symmetric{<:Real}) = A
 real(A::Hermitian{<:Real}) = A
-real(A::Symmetric) = Symmetric(parentof_applytri(real, A), sym_uplo_unsafe(A.uplo))
-real(A::Hermitian) = Hermitian(parentof_applytri(real, A), sym_uplo_unsafe(A.uplo))
-imag(A::Symmetric) = Symmetric(parentof_applytri(imag, A), sym_uplo_unsafe(A.uplo))
+real(A::Symmetric) = Symmetric(parentof_applytri(real, A), _sym_uplo(A.uplo))
+real(A::Hermitian) = Hermitian(parentof_applytri(real, A), _sym_uplo(A.uplo))
+imag(A::Symmetric) = Symmetric(parentof_applytri(imag, A), _sym_uplo(A.uplo))
 
 Base.copy(A::Adjoint{<:Any,<:Symmetric}) =
     Symmetric(copy(adjoint(A.parent.data)), ifelse(A.parent.uplo == 'U', :L, :U))
@@ -484,8 +484,8 @@ Base.copy(A::Transpose{<:Any,<:Hermitian}) =
 tr(A::Symmetric{<:Number}) = tr(A.data) # to avoid AbstractMatrix fallback (incl. allocations)
 tr(A::Hermitian{<:Number}) = real(tr(A.data))
 
-Base.conj(A::Symmetric) = Symmetric(parentof_applytri(conj, A), sym_uplo_unsafe(A.uplo))
-Base.conj(A::Hermitian) = Hermitian(parentof_applytri(conj, A), sym_uplo_unsafe(A.uplo))
+Base.conj(A::Symmetric) = Symmetric(parentof_applytri(conj, A), _sym_uplo(A.uplo))
+Base.conj(A::Hermitian) = Hermitian(parentof_applytri(conj, A), _sym_uplo(A.uplo))
 Base.conj!(A::HermOrSym) = typeof(A)(parentof_applytri(conj!, A), A.uplo)
 
 # tril/triu
@@ -702,25 +702,25 @@ function _hermkron!(C, A, B, conj, real, Auplo, Buplo)
     end
 end
 
-(-)(A::Symmetric) = Symmetric(parentof_applytri(-, A), sym_uplo_unsafe(A.uplo))
-(-)(A::Hermitian) = Hermitian(parentof_applytri(-, A), sym_uplo_unsafe(A.uplo))
+(-)(A::Symmetric) = Symmetric(parentof_applytri(-, A), _sym_uplo(A.uplo))
+(-)(A::Hermitian) = Hermitian(parentof_applytri(-, A), _sym_uplo(A.uplo))
 
 ## Addition/subtraction
 for f ∈ (:+, :-), Wrapper ∈ (:Hermitian, :Symmetric)
     @eval function $f(A::$Wrapper, B::$Wrapper)
-        uplo = A.uplo == B.uplo ? sym_uplo_unsafe(A.uplo) : (:U)
+        uplo = A.uplo == B.uplo ? _sym_uplo(A.uplo) : (:U)
         $Wrapper(parentof_applytri($f, A, B), uplo)
     end
 end
 
 for f in (:+, :-)
     @eval begin
-        $f(A::Hermitian, B::Symmetric{<:Real}) = $f(A, Hermitian(parent(B), sym_uplo_unsafe(B.uplo)))
-        $f(A::Symmetric{<:Real}, B::Hermitian) = $f(Hermitian(parent(A), sym_uplo_unsafe(A.uplo)), B)
-        $f(A::SymTridiagonal, B::Symmetric) = $f(Symmetric(A, sym_uplo_unsafe(B.uplo)), B)
-        $f(A::Symmetric, B::SymTridiagonal) = $f(A, Symmetric(B, sym_uplo_unsafe(A.uplo)))
-        $f(A::SymTridiagonal{<:Real}, B::Hermitian) = $f(Hermitian(A, sym_uplo_unsafe(B.uplo)), B)
-        $f(A::Hermitian, B::SymTridiagonal{<:Real}) = $f(A, Hermitian(B, sym_uplo_unsafe(A.uplo)))
+        $f(A::Hermitian, B::Symmetric{<:Real}) = $f(A, Hermitian(parent(B), _sym_uplo(B.uplo)))
+        $f(A::Symmetric{<:Real}, B::Hermitian) = $f(Hermitian(parent(A), _sym_uplo(A.uplo)), B)
+        $f(A::SymTridiagonal, B::Symmetric) = $f(Symmetric(A, _sym_uplo(B.uplo)), B)
+        $f(A::Symmetric, B::SymTridiagonal) = $f(A, Symmetric(B, _sym_uplo(A.uplo)))
+        $f(A::SymTridiagonal{<:Real}, B::Hermitian) = $f(Hermitian(A, _sym_uplo(B.uplo)), B)
+        $f(A::Hermitian, B::SymTridiagonal{<:Real}) = $f(A, Hermitian(B, _sym_uplo(A.uplo)))
     end
 end
 
@@ -770,12 +770,12 @@ function dot(x::AbstractVector, A::HermOrSym, y::AbstractVector)
 end
 
 # Scaling with Number
-*(A::Symmetric, x::Number) = Symmetric(parentof_applytri(y -> y * x, A), sym_uplo_unsafe(A.uplo))
-*(x::Number, A::Symmetric) = Symmetric(parentof_applytri(y -> x * y, A), sym_uplo_unsafe(A.uplo))
-*(A::Hermitian, x::Real) = Hermitian(parentof_applytri(y -> y * x, A), sym_uplo_unsafe(A.uplo))
-*(x::Real, A::Hermitian) = Hermitian(parentof_applytri(y -> x * y, A), sym_uplo_unsafe(A.uplo))
-/(A::Symmetric, x::Number) = Symmetric(parentof_applytri(y -> y/x, A), sym_uplo_unsafe(A.uplo))
-/(A::Hermitian, x::Real) = Hermitian(parentof_applytri(y -> y/x, A), sym_uplo_unsafe(A.uplo))
+*(A::Symmetric, x::Number) = Symmetric(parentof_applytri(y -> y * x, A), _sym_uplo(A.uplo))
+*(x::Number, A::Symmetric) = Symmetric(parentof_applytri(y -> x * y, A), _sym_uplo(A.uplo))
+*(A::Hermitian, x::Real) = Hermitian(parentof_applytri(y -> y * x, A), _sym_uplo(A.uplo))
+*(x::Real, A::Hermitian) = Hermitian(parentof_applytri(y -> x * y, A), _sym_uplo(A.uplo))
+/(A::Symmetric, x::Number) = Symmetric(parentof_applytri(y -> y/x, A), _sym_uplo(A.uplo))
+/(A::Hermitian, x::Real) = Hermitian(parentof_applytri(y -> y/x, A), _sym_uplo(A.uplo))
 
 factorize(A::HermOrSym) = _factorize(A)
 function _factorize(A::HermOrSym{T}; check::Bool=true) where T
@@ -821,8 +821,8 @@ function _inv(A::HermOrSym)
     B
 end
 # StridedMatrix restriction seems necessary due to inv! call in _inv above
-inv(A::Hermitian{<:Any,<:StridedMatrix}) = Hermitian(_inv(A), sym_uplo_unsafe(A.uplo))
-inv(A::Symmetric{<:Any,<:StridedMatrix}) = Symmetric(_inv(A), sym_uplo_unsafe(A.uplo))
+inv(A::Hermitian{<:Any,<:StridedMatrix}) = Hermitian(_inv(A), _sym_uplo(A.uplo))
+inv(A::Symmetric{<:Any,<:StridedMatrix}) = Symmetric(_inv(A), _sym_uplo(A.uplo))
 
 function svd(A::RealHermSymComplexHerm; full::Bool=false)
     vals, vecs = eigen(A)