unify methods for cholesky (#21595)

base/linalg/cholesky.jl

@@ -16,10 +16,7 @@
 # supported for the four LAPACK element types. For other types, e.g. BigFloats Val{true} will
 # give an error. It is required that the input is Hermitian (including real symmetric) either
 # through the Hermitian and Symmetric views or exact symmetric or Hermitian elements which
-# is checked for and an error is thrown if the check fails. The dispatch
-# is further complicated by a limitation in the formulation of Unions. The relevant union
-# would be Union{Symmetric{T<:Real,S}, Hermitian} but, right now, it doesn't work in Julia
-# so we'll have to define methods for the two elements of the union separately.
+# is checked for and an error is thrown if the check fails.
 
 # FixMe? The dispatch below seems overly complicated. One simplification could be to
 # merge the two Cholesky types into one. It would remove the need for Val completely but
@@ -121,9 +118,7 @@ non_hermitian_error(f) = throw(ArgumentError("matrix is not symmetric/" *
 
 # chol!. Destructive methods for computing Cholesky factor of real symmetric or Hermitian
 # matrix
-chol!(A::Hermitian) =
-    _chol!(A.uplo == 'U' ? A.data : LinAlg.copytri!(A.data, 'L', true), UpperTriangular)
-chol!(A::Symmetric{<:Real,<:StridedMatrix}) =
+chol!(A::RealHermSymComplexHerm{<:Real,<:StridedMatrix}) =
     _chol!(A.uplo == 'U' ? A.data : LinAlg.copytri!(A.data, 'L', true), UpperTriangular)
 function chol!(A::StridedMatrix)
     ishermitian(A) || non_hermitian_error("chol!")
@@ -134,7 +129,7 @@ end
 
 # chol. Non-destructive methods for computing Cholesky factor of a real symmetric or
 # Hermitian matrix. Promotes elements to a type that is stable under square roots.
-function chol(A::Hermitian)
+function chol(A::RealHermSymComplexHerm)
     T = promote_type(typeof(chol(one(eltype(A)))), Float32)
     AA = similar(A, T, size(A))
     if A.uplo == 'U'
@@ -144,16 +139,6 @@ function chol(A::Hermitian)
     end
     chol!(Hermitian(AA, :U))
 end
-function chol(A::Symmetric{T,<:AbstractMatrix}) where T<:Real
-    TT = promote_type(typeof(chol(one(T))), Float32)
-    AA = similar(A, TT, size(A))
-    if A.uplo == 'U'
-        copy!(AA, A.data)
-    else
-        Base.ctranspose!(AA, A.data)
-    end
-    chol!(Hermitian(AA, :U))
-end
 
 ## for StridedMatrices, check that matrix is symmetric/Hermitian
 """
@@ -206,14 +191,7 @@ chol(x::Number, args...) = _chol!(x, nothing)
 # cholfact!. Destructive methods for computing Cholesky factorization of real symmetric
 # or Hermitian matrix
 ## No pivoting
-function cholfact!(A::Hermitian, ::Type{Val{false}})
-    if A.uplo == 'U'
-        Cholesky(_chol!(A.data, UpperTriangular).data, 'U')
-    else
-        Cholesky(_chol!(A.data, LowerTriangular).data, 'L')
-    end
-end
-function cholfact!(A::Symmetric{<:Real}, ::Type{Val{false}})
+function cholfact!(A::RealHermSymComplexHerm, ::Type{Val{false}})
     if A.uplo == 'U'
         Cholesky(_chol!(A.data, UpperTriangular).data, 'U')
     else
@@ -248,8 +226,8 @@ function cholfact!(A::StridedMatrix, uplo::Symbol, ::Type{Val{false}})
 end
 
 ### Default to no pivoting (and storing of upper factor) when not explicit
-cholfact!(A::Hermitian) = cholfact!(A, Val{false})
-cholfact!(A::Symmetric{<:Real}) = cholfact!(A, Val{false})
+cholfact!(A::RealHermSymComplexHerm) = cholfact!(A, Val{false})
+
 #### for StridedMatrices, check that matrix is symmetric/Hermitian
 function cholfact!(A::StridedMatrix, uplo::Symbol = :U)
     ishermitian(A) || non_hermitian_error("cholfact!")
@@ -288,9 +266,7 @@ end
 # cholfact. Non-destructive methods for computing Cholesky factorization of real symmetric
 # or Hermitian matrix
 ## No pivoting
-cholfact(A::Hermitian, ::Type{Val{false}}) =
-    cholfact!(copy_oftype(A, promote_type(typeof(chol(one(eltype(A)))),Float32)), Val{false})
-cholfact(A::Symmetric{<:Real,<:StridedMatrix}, ::Type{Val{false}}) =
+cholfact(A::RealHermSymComplexHerm{<:Real,<:StridedMatrix}, ::Type{Val{false}}) =
     cholfact!(copy_oftype(A, promote_type(typeof(chol(one(eltype(A)))),Float32)), Val{false})
 
 ### for StridedMatrices, check that matrix is symmetric/Hermitian
@@ -342,8 +318,8 @@ function cholfact(A::StridedMatrix, uplo::Symbol, ::Type{Val{false}})
 end
 
 ### Default to no pivoting (and storing of upper factor) when not explicit
-cholfact(A::Hermitian) = cholfact(A, Val{false})
-cholfact(A::Symmetric{<:Real,<:StridedMatrix}) = cholfact(A, Val{false})
+cholfact(A::RealHermSymComplexHerm{<:Real,<:StridedMatrix}) = cholfact(A, Val{false})
+
 #### for StridedMatrices, check that matrix is symmetric/Hermitian
 function cholfact(A::StridedMatrix, uplo::Symbol = :U)
     ishermitian(A) || non_hermitian_error("cholfact")
@@ -352,9 +328,6 @@ end
 
 
 ## With pivoting
-cholfact(A::Hermitian, ::Type{Val{true}}; tol = 0.0) =
-        cholfact!(copy_oftype(A, promote_type(typeof(chol(one(eltype(A)))),Float32)),
-            Val{true}; tol = tol)
 cholfact(A::RealHermSymComplexHerm{<:Real,<:StridedMatrix}, ::Type{Val{true}}; tol = 0.0) =
         cholfact!(copy_oftype(A, promote_type(typeof(chol(one(eltype(A)))),Float32)),
             Val{true}; tol = tol)