Clarify which args are modified in mul! (JuliaLang#25421)

base/essentials.jl

@@ -371,7 +371,7 @@ julia> sizeof(ComplexF64)
 If `T` does not have a specific size, an error is thrown.
 
 ```jldoctest
-julia> sizeof(Base.LinAlg.LU)
+julia> sizeof(AbstractArray)
 ERROR: argument is an abstract type; size is indeterminate
 Stacktrace:
 [...]

base/hashing2.jl

@@ -178,4 +178,4 @@ function hash(s::Union{String,SubString{String}}, h::UInt)
  # note: use pointer(s) here (see #6058).
  ccall(memhash, UInt, (Ptr{UInt8}, Csize_t, UInt32), pointer(s), sizeof(s), h % UInt32) + h
 end
-hash(s::AbstractString, h::UInt) = hash(String(s), h)
+hash(s::AbstractString, h::UInt) = hash(String(s), h)

base/reflection.jl

@@ -9,8 +9,8 @@ Get the name of a `Module` as a `Symbol`.
 
 # Examples
 ```jldoctest
-julia> module_name(Base.LinAlg)
-:LinAlg
+julia> module_name(Base)
+:Base
 ```
 """
 module_name(m::Module) = ccall(:jl_module_name, Ref{Symbol}, (Any,), m)
@@ -25,8 +25,8 @@ Get a module's enclosing `Module`. `Main` is its own parent.
 julia> parentmodule(Main)
 Main
 
-julia> parentmodule(Base.LinAlg.BLAS)
-Base.LinAlg
+julia> parentmodule(Base.Sys)
+Base
 ```
 """
 parentmodule(m::Module) = ccall(:jl_module_parent, Ref{Module}, (Any,), m)

stdlib/LinearAlgebra/src/LinearAlgebra.jl

@@ -240,11 +240,9 @@ function char_uplo(uplo::Symbol)
 end
 
 """
- ldiv!([Y,] A, B) -> Y
+ ldiv!(Y, A, B) -> Y
 
 Compute `A \\ B` in-place and store the result in `Y`, returning the result.
-If only two arguments are passed, then `ldiv!(A, B)` overwrites `B` with
-the result.
 
 The argument `A` should *not* be a matrix. Rather, instead of matrices it should be a
 factorization object (e.g. produced by [`factorize`](@ref) or [`cholfact`](@ref)).
@@ -256,11 +254,24 @@ control over the factorization of `A`.
 ldiv!(Y, A, B)
 
 """
- rdiv!([Y,] A, B) -> Y
+ ldiv!(A, B)
 
-Compute `A / B` in-place and store the result in `Y`, returning the result.
-If only two arguments are passed, then `rdiv!(A, B)` overwrites `A` with
-the result.
+Compute `A \\ B` in-place and overwriting `B` to store the result.
+
+The argument `A` should *not* be a matrix. Rather, instead of matrices it should be a
+factorization object (e.g. produced by [`factorize`](@ref) or [`cholfact`](@ref)).
+The reason for this is that factorization itself is both expensive and typically allocates memory
+(although it can also be done in-place via, e.g., [`lufact!`](@ref)),
+and performance-critical situations requiring `ldiv!` usually also require fine-grained
+control over the factorization of `A`.
+"""
+ldiv!(A, B)
+
+
+"""
+ rdiv!(A, B)
+
+Compute `A / B` in-place and overwriting `A` to store the result.
 
 The argument `B` should *not* be a matrix. Rather, instead of matrices it should be a
 factorization object (e.g. produced by [`factorize`](@ref) or [`cholfact`](@ref)).
@@ -269,7 +280,7 @@ The reason for this is that factorization itself is both expensive and typically
 and performance-critical situations requiring `rdiv!` usually also require fine-grained
 control over the factorization of `B`.
 """
-rdiv!(Y, A, B)
+rdiv!(A, B)
 
 copy_oftype(A::AbstractArray{T}, ::Type{T}) where {T} = copy(A)
 copy_oftype(A::AbstractArray{T,N}, ::Type{S}) where {T,N,S} = convert(AbstractArray{S,N}, A)

stdlib/LinearAlgebra/src/diagonal.jl

@@ -151,107 +151,97 @@ end
 (*)(Da::Diagonal, Db::Diagonal) = Diagonal(Da.diag .* Db.diag)
 (*)(D::Diagonal, V::AbstractVector) = D.diag .* V
 
-(*)(A::AbstractTriangular, D::Diagonal) = mul!(copy(A), D)
-(*)(D::Diagonal, B::AbstractTriangular) = mul!(D, copy(B))
+(*)(A::AbstractTriangular, D::Diagonal) = mul1!(copy(A), D)
+(*)(D::Diagonal, B::AbstractTriangular) = mul2!(D, copy(B))
 
 (*)(A::AbstractMatrix, D::Diagonal) =
  scale!(similar(A, promote_op(*, eltype(A), eltype(D.diag)), size(A)), A, D.diag)
 (*)(D::Diagonal, A::AbstractMatrix) =
  scale!(similar(A, promote_op(*, eltype(A), eltype(D.diag)), size(A)), D.diag, A)
 
-mul!(A::Union{LowerTriangular,UpperTriangular}, D::Diagonal) = typeof(A)(mul!(A.data, D))
-function mul!(A::UnitLowerTriangular, D::Diagonal)
- mul!(A.data, D)
+
+mul1!(A::Union{LowerTriangular,UpperTriangular}, D::Diagonal) = typeof(A)(mul1!(A.data, D))
+function mul1!(A::UnitLowerTriangular, D::Diagonal)
+ mul1!(A.data, D)
  for i = 1:size(A, 1)
  A.data[i,i] = D.diag[i]
  end
  LowerTriangular(A.data)
 end
-function mul!(A::UnitUpperTriangular, D::Diagonal)
- mul!(A.data, D)
+function mul1!(A::UnitUpperTriangular, D::Diagonal)
+ mul1!(A.data, D)
  for i = 1:size(A, 1)
  A.data[i,i] = D.diag[i]
  end
  UpperTriangular(A.data)
 end
-function mul!(D::Diagonal, B::UnitLowerTriangular)
- mul!(D, B.data)
+
+function mul2!(D::Diagonal, B::UnitLowerTriangular)
+ mul2!(D, B.data)
  for i = 1:size(B, 1)
  B.data[i,i] = D.diag[i]
  end
  LowerTriangular(B.data)
 end
-function mul!(D::Diagonal, B::UnitUpperTriangular)
- mul!(D, B.data)
+function mul2!(D::Diagonal, B::UnitUpperTriangular)
+ mul2!(D, B.data)
  for i = 1:size(B, 1)
  B.data[i,i] = D.diag[i]
  end
  UpperTriangular(B.data)
 end
 
 *(D::Adjoint{<:Any,<:Diagonal}, B::Diagonal) = Diagonal(adjoint.(D.parent.diag) .* B.diag)
-*(A::Adjoint{<:Any,<:AbstractTriangular}, D::Diagonal) = mul!(copy(A), D)
+*(A::Adjoint{<:Any,<:AbstractTriangular}, D::Diagonal) = mul1!(copy(A), D)
 function *(adjA::Adjoint{<:Any,<:AbstractMatrix}, D::Diagonal)
  A = adjA.parent
  Ac = similar(A, promote_op(*, eltype(A), eltype(D.diag)), (size(A, 2), size(A, 1)))
  adjoint!(Ac, A)
- mul!(Ac, D)
+ mul1!(Ac, D)
 end
 
 *(D::Transpose{<:Any,<:Diagonal}, B::Diagonal) = Diagonal(transpose.(D.parent.diag) .* B.diag)
-*(A::Transpose{<:Any,<:AbstractTriangular}, D::Diagonal) = mul!(copy(A), D)
+*(A::Transpose{<:Any,<:AbstractTriangular}, D::Diagonal) = mul1!(copy(A), D)
 function *(transA::Transpose{<:Any,<:AbstractMatrix}, D::Diagonal)
  A = transA.parent
  At = similar(A, promote_op(*, eltype(A), eltype(D.diag)), (size(A, 2), size(A, 1)))
  transpose!(At, A)
- mul!(At, D)
+ mul1!(At, D)
 end
 
 *(D::Diagonal, B::Adjoint{<:Any,<:Diagonal}) = Diagonal(D.diag .* adjoint.(B.parent.diag))
-*(D::Diagonal, B::Adjoint{<:Any,<:AbstractTriangular}) = mul!(D, collect(B))
-*(D::Diagonal, adjQ::Adjoint{<:Any,<:Union{QRCompactWYQ,QRPackedQ}}) = (Q = adjQ.parent; mul!(Array(D), adjoint(Q)))
+*(D::Diagonal, B::Adjoint{<:Any,<:AbstractTriangular}) = mul2!(D, collect(B))
+*(D::Diagonal, adjQ::Adjoint{<:Any,<:Union{QRCompactWYQ,QRPackedQ}}) = (Q = adjQ.parent; mul1!(Array(D), adjoint(Q)))
 function *(D::Diagonal, adjA::Adjoint{<:Any,<:AbstractMatrix})
  A = adjA.parent
  Ac = similar(A, promote_op(*, eltype(A), eltype(D.diag)), (size(A, 2), size(A, 1)))
  adjoint!(Ac, A)
- mul!(D, Ac)
+ mul2!(D, Ac)
 end
 
 *(D::Diagonal, B::Transpose{<:Any,<:Diagonal}) = Diagonal(D.diag .* transpose.(B.parent.diag))
-*(D::Diagonal, B::Transpose{<:Any,<:AbstractTriangular}) = mul!(D, copy(B))
+*(D::Diagonal, B::Transpose{<:Any,<:AbstractTriangular}) = mul2!(D, copy(B))
 function *(D::Diagonal, transA::Transpose{<:Any,<:AbstractMatrix})
  A = transA.parent
  At = similar(A, promote_op(*, eltype(A), eltype(D.diag)), (size(A, 2), size(A, 1)))
  transpose!(At, A)
- mul!(D, At)
+ mul2!(D, At)
 end
 
 *(D::Adjoint{<:Any,<:Diagonal}, B::Adjoint{<:Any,<:Diagonal}) =
  Diagonal(adjoint.(D.parent.diag) .* adjoint.(B.parent.diag))
 *(D::Transpose{<:Any,<:Diagonal}, B::Transpose{<:Any,<:Diagonal}) =
  Diagonal(transpose.(D.parent.diag) .* transpose.(B.parent.diag))
 
-mul!(A::Diagonal, B::Diagonal) = throw(MethodError(mul!, (A, B)))
-mul!(A::QRPackedQ, D::Diagonal) = throw(MethodError(mul!, (A, D)))
-mul!(A::QRPackedQ, B::Adjoint{<:Any,<:Diagonal}) = throw(MethodError(mul!, (A, B)))
-mul!(A::QRPackedQ, B::Transpose{<:Any,<:Diagonal}) = throw(MethodError(mul!, (A, B)))
-mul!(A::Adjoint{<:Any,<:QRPackedQ}, B::Diagonal) = throw(MethodError(mul!, (A, B)))
-mul!(A::Adjoint{<:Any,<:QRPackedQ}, B::Adjoint{<:Any,<:Diagonal}) = throw(MethodError(mul!, (A, B)))
-mul!(A::Adjoint{<:Any,<:QRPackedQ}, B::Transpose{<:Any,<:Diagonal}) = throw(MethodError(mul!, (A, B)))
-mul!(A::Diagonal, B::Adjoint{<:Any,<:Diagonal}) = throw(MethodError(mul!, (A, B)))
-mul!(A::Diagonal, B::Transpose{<:Any,<:Diagonal}) = throw(MethodError(mul!, (A, B)))
-mul!(A::Adjoint{<:Any,<:Diagonal}, B::Adjoint{<:Any,<:Diagonal}) = throw(MethodError(mul!, (A, B)))
-mul!(A::Adjoint{<:Any,<:Diagonal}, B::Transpose{<:Any,<:Diagonal}) = throw(MethodError(mul!, (A, B)))
-mul!(A::Transpose{<:Any,<:Diagonal}, B::Adjoint{<:Any,<:Diagonal}) = throw(MethodError(mul!, (A, B)))
-mul!(A::Transpose{<:Any,<:Diagonal}, B::Transpose{<:Any,<:Diagonal}) = throw(MethodError(mul!, (A, B)))
-mul!(A::Transpose{<:Any,<:Diagonal}, B::Diagonal) = throw(MethodError(mul!, (A, B)))
-mul!(A::Adjoint{<:Any,<:Diagonal}, B::Diagonal) = throw(MethodError(mul!, (A, B)))
-mul!(A::Diagonal, B::AbstractMatrix) = scale!(A.diag, B)
-mul!(adjA::Adjoint{<:Any,<:Diagonal}, B::AbstractMatrix) = (A = adjA.parent; scale!(conj(A.diag),B))
-mul!(transA::Transpose{<:Any,<:Diagonal}, B::AbstractMatrix) = (A = transA.parent; scale!(A.diag,B))
-mul!(A::AbstractMatrix, B::Diagonal) = scale!(A,B.diag)
-mul!(A::AbstractMatrix, adjB::Adjoint{<:Any,<:Diagonal}) = (B = adjB.parent; scale!(A,conj(B.diag)))
-mul!(A::AbstractMatrix, transB::Transpose{<:Any,<:Diagonal}) = (B = transB.parent; scale!(A,B.diag))
+mul1!(A::Diagonal,B::Diagonal) = Diagonal(A.diag .*= B.diag)
+mul2!(A::Diagonal,B::Diagonal) = Diagonal(B.diag .= A.diag .* B.diag)
+
+mul2!(A::Diagonal, B::AbstractMatrix) = scale!(A.diag, B)
+mul2!(adjA::Adjoint{<:Any,<:Diagonal}, B::AbstractMatrix) = (A = adjA.parent; scale!(conj(A.diag),B))
+mul2!(transA::Transpose{<:Any,<:Diagonal}, B::AbstractMatrix) = (A = transA.parent; scale!(A.diag,B))
+mul1!(A::AbstractMatrix, B::Diagonal) = scale!(A,B.diag)
+mul1!(A::AbstractMatrix, adjB::Adjoint{<:Any,<:Diagonal}) = (B = adjB.parent; scale!(A,conj(B.diag)))
+mul1!(A::AbstractMatrix, transB::Transpose{<:Any,<:Diagonal}) = (B = transB.parent; scale!(A,B.diag))
 
 # Get ambiguous method if try to unify AbstractVector/AbstractMatrix here using AbstractVecOrMat
 mul!(out::AbstractVector, A::Diagonal, in::AbstractVector) = out .= A.diag .* in
@@ -287,6 +277,7 @@ mul!(C::AbstractMatrix, A::Transpose{<:Any,<:Diagonal}, B::Transpose{<:Any,<:Rea
 
 
 (/)(Da::Diagonal, Db::Diagonal) = Diagonal(Da.diag ./ Db.diag)
+
 function ldiv!(D::Diagonal{T}, v::AbstractVector{T}) where {T}
  if length(v) != length(D.diag)
  throw(DimensionMismatch("diagonal matrix is $(length(D.diag)) by $(length(D.diag)) but right hand side has $(length(v)) rows"))
@@ -316,6 +307,7 @@ function ldiv!(D::Diagonal{T}, V::AbstractMatrix{T}) where {T}
  V
 end
 
+
 ldiv!(adjD::Adjoint{<:Any,<:Diagonal{T}}, B::AbstractVecOrMat{T}) where {T} =
  (D = adjD.parent; ldiv!(conj(D), B))
 ldiv!(transD::Transpose{<:Any,<:Diagonal{T}}, B::AbstractVecOrMat{T}) where {T} =
@@ -339,6 +331,7 @@ function rdiv!(A::AbstractMatrix{T}, D::Diagonal{T}) where {T}
  A
 end
 
+
 rdiv!(A::AbstractMatrix{T}, adjD::Adjoint{<:Any,<:Diagonal{T}}) where {T} =
  (D = adjD.parent; rdiv!(A, conj(D)))
 rdiv!(A::AbstractMatrix{T}, transD::Transpose{<:Any,<:Diagonal{T}}) where {T} =

stdlib/LinearAlgebra/src/givens.jl

@@ -7,14 +7,14 @@ transpose(R::AbstractRotation) = error("transpose not implemented for $(typeof(R
 
 function *(R::AbstractRotation{T}, A::AbstractVecOrMat{S}) where {T,S}
  TS = typeof(zero(T)*zero(S) + zero(T)*zero(S))
- mul!(convert(AbstractRotation{TS}, R), TS == S ? copy(A) : convert(AbstractArray{TS}, A))
+ mul2!(convert(AbstractRotation{TS}, R), TS == S ? copy(A) : convert(AbstractArray{TS}, A))
 end
 *(A::AbstractVector, adjR::Adjoint{<:Any,<:AbstractRotation}) = _absvecormat_mul_adjrot(A, adjR)
 *(A::AbstractMatrix, adjR::Adjoint{<:Any,<:AbstractRotation}) = _absvecormat_mul_adjrot(A, adjR)
 function _absvecormat_mul_adjrot(A::AbstractVecOrMat{T}, adjR::Adjoint{<:Any,<:AbstractRotation{S}}) where {T,S}
  R = adjR.parent
  TS = typeof(zero(T)*zero(S) + zero(T)*zero(S))
- mul!(TS == T ? copy(A) : convert(AbstractArray{TS}, A), adjoint(convert(AbstractRotation{TS}, R)))
+ mul1!(TS == T ? copy(A) : convert(AbstractArray{TS}, A), adjoint(convert(AbstractRotation{TS}, R)))
 end
 """
  LinearAlgebra.Givens(i1,i2,c,s) -> G
@@ -325,10 +325,7 @@ function getindex(G::Givens, i::Integer, j::Integer)
  end
 end
 
-
-mul!(G1::Givens, G2::Givens) = error("Operation not supported. Consider *")
-
-function mul!(G::Givens, A::AbstractVecOrMat)
+function mul2!(G::Givens, A::AbstractVecOrMat)
  m, n = size(A, 1), size(A, 2)
  if G.i2 > m
  throw(DimensionMismatch("column indices for rotation are outside the matrix"))
@@ -340,7 +337,7 @@ function mul!(G::Givens, A::AbstractVecOrMat)
  end
  return A
 end
-function mul!(A::AbstractMatrix, adjG::Adjoint{<:Any,<:Givens})
+function mul1!(A::AbstractMatrix, adjG::Adjoint{<:Any,<:Givens})
  G = adjG.parent
  m, n = size(A, 1), size(A, 2)
  if G.i2 > n
@@ -353,20 +350,21 @@ function mul!(A::AbstractMatrix, adjG::Adjoint{<:Any,<:Givens})
  end
  return A
 end
-function mul!(G::Givens, R::Rotation)
+
+function mul2!(G::Givens, R::Rotation)
  push!(R.rotations, G)
  return R
 end
-function mul!(R::Rotation, A::AbstractMatrix)
+function mul2!(R::Rotation, A::AbstractMatrix)
  @inbounds for i = 1:length(R.rotations)
- mul!(R.rotations[i], A)
+ mul2!(R.rotations[i], A)
  end
  return A
 end
-function mul!(A::AbstractMatrix, adjR::Adjoint{<:Any,<:Rotation})
+function mul1!(A::AbstractMatrix, adjR::Adjoint{<:Any,<:Rotation})
  R = adjR.parent
  @inbounds for i = 1:length(R.rotations)
- mul!(A, adjoint(R.rotations[i]))
+ mul1!(A, adjoint(R.rotations[i]))
  end
  return A
 end
@@ -388,14 +386,3 @@ end
 # dismabiguation methods: *(Diag/AbsTri, Adj of AbstractRotation)
 *(A::Diagonal, B::Adjoint{<:Any,<:AbstractRotation}) = A * copy(B)
 *(A::AbstractTriangular, B::Adjoint{<:Any,<:AbstractRotation}) = A * copy(B)
-# moar disambiguation
-mul!(A::QRPackedQ, B::Adjoint{<:Any,<:Givens}) = throw(MethodError(mul!, (A, B)))
-mul!(A::QRPackedQ, B::Adjoint{<:Any,<:Rotation}) = throw(MethodError(mul!, (A, B)))
-mul!(A::Adjoint{<:Any,<:QRPackedQ}, B::Adjoint{<:Any,<:Givens}) = throw(MethodError(mul!, (A, B)))
-mul!(A::Adjoint{<:Any,<:QRPackedQ}, B::Adjoint{<:Any,<:Rotation}) = throw(MethodError(mul!, (A, B)))
-mul!(A::Diagonal, B::Adjoint{<:Any,<:Givens}) = throw(MethodError(mul!, (A, B)))
-mul!(A::Diagonal, B::Adjoint{<:Any,<:Rotation}) = throw(MethodError(mul!, (A, B)))
-mul!(A::Adjoint{<:Any,<:Diagonal}, B::Adjoint{<:Any,<:Givens}) = throw(MethodError(mul!, (A, B)))
-mul!(A::Adjoint{<:Any,<:Diagonal}, B::Adjoint{<:Any,<:Rotation}) = throw(MethodError(mul!, (A, B)))
-mul!(A::Transpose{<:Any,<:Diagonal}, B::Adjoint{<:Any,<:Rotation}) = throw(MethodError(mul!, (A, B)))
-mul!(A::Transpose{<:Any,<:Diagonal}, B::Adjoint{<:Any,<:Givens}) = throw(MethodError(mul!, (A, B)))

stdlib/LinearAlgebra/src/hessenberg.jl

@@ -73,7 +73,7 @@ function getindex(A::HessenbergQ, i::Integer, j::Integer)
  x[i] = 1
  y = zeros(eltype(A), size(A, 2))
  y[j] = 1
- return dot(x, mul!(A, y))
+ return dot(x, mul2!(A, y))
 end
 
 ## reconstruct the original matrix
@@ -84,31 +84,30 @@ AbstractArray(F::Hessenberg) = AbstractMatrix(F)
 Matrix(F::Hessenberg) = Array(AbstractArray(F))
 Array(F::Hessenberg) = Matrix(F)
 
-mul!(Q::HessenbergQ{T}, X::StridedVecOrMat{T}) where {T<:BlasFloat} =
+mul2!(Q::HessenbergQ{T}, X::StridedVecOrMat{T}) where {T<:BlasFloat} =
  LAPACK.ormhr!('L', 'N', 1, size(Q.factors, 1), Q.factors, Q.τ, X)
-mul!(X::StridedMatrix{T}, Q::HessenbergQ{T}) where {T<:BlasFloat} =
+mul1!(X::StridedMatrix{T}, Q::HessenbergQ{T}) where {T<:BlasFloat} =
  LAPACK.ormhr!('R', 'N', 1, size(Q.factors, 1), Q.factors, Q.τ, X)
-mul!(adjQ::Adjoint{<:Any,<:HessenbergQ{T}}, X::StridedVecOrMat{T}) where {T<:BlasFloat} =
+mul2!(adjQ::Adjoint{<:Any,<:HessenbergQ{T}}, X::StridedVecOrMat{T}) where {T<:BlasFloat} =
  (Q = adjQ.parent; LAPACK.ormhr!('L', ifelse(T<:Real, 'T', 'C'), 1, size(Q.factors, 1), Q.factors, Q.τ, X))
-mul!(X::StridedMatrix{T}, adjQ::Adjoint{<:Any,<:HessenbergQ{T}}) where {T<:BlasFloat} =
+mul1!(X::StridedMatrix{T}, adjQ::Adjoint{<:Any,<:HessenbergQ{T}}) where {T<:BlasFloat} =
  (Q = adjQ.parent; LAPACK.ormhr!('R', ifelse(T<:Real, 'T', 'C'), 1, size(Q.factors, 1), Q.factors, Q.τ, X))
 
-
 function (*)(Q::HessenbergQ{T}, X::StridedVecOrMat{S}) where {T,S}
  TT = typeof(zero(T)*zero(S) + zero(T)*zero(S))
- return mul!(Q, copy_oftype(X, TT))
+ return mul2!(Q, copy_oftype(X, TT))
 end
 function (*)(X::StridedVecOrMat{S}, Q::HessenbergQ{T}) where {T,S}
  TT = typeof(zero(T)*zero(S) + zero(T)*zero(S))
- return mul!(copy_oftype(X, TT), Q)
+ return mul1!(copy_oftype(X, TT), Q)
 end
 function *(adjQ::Adjoint{<:Any,<:HessenbergQ{T}}, X::StridedVecOrMat{S}) where {T,S}
  Q = adjQ.parent
  TT = typeof(zero(T)*zero(S) + zero(T)*zero(S))
- return mul!(adjoint(Q), copy_oftype(X, TT))
+ return mul2!(adjoint(Q), copy_oftype(X, TT))
 end
 function *(X::StridedVecOrMat{S}, adjQ::Adjoint{<:Any,<:HessenbergQ{T}}) where {T,S}
  Q = adjQ.parent
  TT = typeof(zero(T)*zero(S) + zero(T)*zero(S))
- return mul!(copy_oftype(X, TT), adjoint(Q))
+ return mul1!(copy_oftype(X, TT), adjoint(Q))
 end