QuantumKitHub · lkdvos · Feb 26, 2026 · Feb 26, 2026 · Feb 26, 2026 · Feb 26, 2026
diff --git a/ext/MatrixAlgebraKitAMDGPUExt/MatrixAlgebraKitAMDGPUExt.jl b/ext/MatrixAlgebraKitAMDGPUExt/MatrixAlgebraKitAMDGPUExt.jl
@@ -4,34 +4,28 @@ using MatrixAlgebraKit
 using MatrixAlgebraKit: @algdef, Algorithm, check_input
 using MatrixAlgebraKit: one!, zero!, uppertriangular!, lowertriangular!
 using MatrixAlgebraKit: diagview, sign_safe
-using MatrixAlgebraKit: LQViaTransposedQR, TruncationStrategy, NoTruncation, TruncationByValue, AbstractAlgorithm
+using MatrixAlgebraKit: ROCSOLVER, LQViaTransposedQR, TruncationStrategy, NoTruncation, TruncationByValue, AbstractAlgorithm
 using MatrixAlgebraKit: default_qr_algorithm, default_lq_algorithm, default_svd_algorithm, default_eigh_algorithm
-import MatrixAlgebraKit: _gpu_geqrf!, _gpu_ungqr!, _gpu_unmqr!, _gpu_gesvd!, _gpu_Xgesvdp!, _gpu_gesvdj!
+import MatrixAlgebraKit: geqrf!, ungqr!, unmqr!, _gpu_gesvd!, _gpu_Xgesvdp!, _gpu_gesvdj!
 import MatrixAlgebraKit: _gpu_heevj!, _gpu_heevd!, _gpu_heev!, _gpu_heevx!, _sylvester, svd_rank
 using AMDGPU
 using LinearAlgebra
 using LinearAlgebra: BlasFloat
 
 include("yarocsolver.jl")
 
-function MatrixAlgebraKit.default_qr_algorithm(::Type{T}; kwargs...) where {T <: StridedROCMatrix}
-    return ROCSOLVER_HouseholderQR(; kwargs...)
-end
-function MatrixAlgebraKit.default_lq_algorithm(::Type{T}; kwargs...) where {T <: StridedROCMatrix}
-    qr_alg = ROCSOLVER_HouseholderQR(; kwargs...)
-    return LQViaTransposedQR(qr_alg)
-end
+MatrixAlgebraKit.default_householder_driver(::StridedROCMatrix{<:BlasFloat}) = ROCSOLVER()
 function MatrixAlgebraKit.default_svd_algorithm(::Type{T}; kwargs...) where {T <: StridedROCMatrix}
     return ROCSOLVER_QRIteration(; kwargs...)
 end
 function MatrixAlgebraKit.default_eigh_algorithm(::Type{T}; kwargs...) where {T <: StridedROCMatrix}
     return ROCSOLVER_DivideAndConquer(; kwargs...)
 end
 
-_gpu_geqrf!(A::StridedROCMatrix) = YArocSOLVER.geqrf!(A)
-_gpu_ungqr!(A::StridedROCMatrix, τ::StridedROCVector) = YArocSOLVER.ungqr!(A, τ)
-_gpu_unmqr!(side::AbstractChar, trans::AbstractChar, A::StridedROCMatrix, τ::StridedROCVector, C::StridedROCVecOrMat) =
-    YArocSOLVER.unmqr!(side, trans, A, τ, C)
+for f in (:geqrf!, :ungqr!, :unmqr!)
+    @eval $f(::ROCSOLVER, args...) = YArocSOLVER.$f(args...)
+end
+
 _gpu_gesvd!(A::StridedROCMatrix, S::StridedROCVector, U::StridedROCMatrix, Vᴴ::StridedROCMatrix) =
     YArocSOLVER.gesvd!(A, S, U, Vᴴ)
 # not yet supported

diff --git a/ext/MatrixAlgebraKitCUDAExt/MatrixAlgebraKitCUDAExt.jl b/ext/MatrixAlgebraKitCUDAExt/MatrixAlgebraKitCUDAExt.jl
@@ -4,9 +4,9 @@ using MatrixAlgebraKit
 using MatrixAlgebraKit: @algdef, Algorithm, check_input
 using MatrixAlgebraKit: one!, zero!, uppertriangular!, lowertriangular!
 using MatrixAlgebraKit: diagview, sign_safe
-using MatrixAlgebraKit: LQViaTransposedQR, TruncationByValue, AbstractAlgorithm
+using MatrixAlgebraKit: CUSOLVER, LQViaTransposedQR, TruncationByValue, AbstractAlgorithm
 using MatrixAlgebraKit: default_qr_algorithm, default_lq_algorithm, default_svd_algorithm, default_eig_algorithm, default_eigh_algorithm
-import MatrixAlgebraKit: _gpu_geqrf!, _gpu_ungqr!, _gpu_unmqr!, _gpu_gesvd!, _gpu_Xgesvdp!, _gpu_Xgesvdr!, _gpu_gesvdj!, _gpu_geev!
+import MatrixAlgebraKit: geqrf!, ungqr!, unmqr!, _gpu_gesvd!, _gpu_Xgesvdp!, _gpu_Xgesvdr!, _gpu_gesvdj!, _gpu_geev!
 import MatrixAlgebraKit: _gpu_heevj!, _gpu_heevd!, _sylvester, svd_rank
 using CUDA, CUDA.CUBLAS
 using CUDA: i32
@@ -15,13 +15,7 @@ using LinearAlgebra: BlasFloat
 
 include("yacusolver.jl")
 
-function MatrixAlgebraKit.default_qr_algorithm(::Type{T}; kwargs...) where {TT <: BlasFloat, T <: StridedCuMatrix{TT}}
-    return CUSOLVER_HouseholderQR(; kwargs...)
-end
-function MatrixAlgebraKit.default_lq_algorithm(::Type{T}; kwargs...) where {TT <: BlasFloat, T <: StridedCuMatrix{TT}}
-    qr_alg = CUSOLVER_HouseholderQR(; kwargs...)
-    return LQViaTransposedQR(qr_alg)
-end
+MatrixAlgebraKit.default_householder_driver(::StridedCuMatrix{<:BlasFloat}) = CUSOLVER()
 function MatrixAlgebraKit.default_svd_algorithm(::Type{T}; kwargs...) where {TT <: BlasFloat, T <: StridedCuMatrix{TT}}
     return CUSOLVER_QRIteration(; kwargs...)
 end
@@ -33,31 +27,25 @@ function MatrixAlgebraKit.default_eigh_algorithm(::Type{T}; kwargs...) where {TT
 end
 
 # include for block sector support
-function MatrixAlgebraKit.default_qr_algorithm(::Type{Base.ReshapedArray{T, 2, SubArray{T, 1, A, Tuple{UnitRange{Int}}, true}, Tuple{}}}; kwargs...) where {T <: BlasFloat, A <: CuVecOrMat{T}}
-    return CUSOLVER_HouseholderQR(; kwargs...)
-end
-function MatrixAlgebraKit.default_lq_algorithm(::Type{Base.ReshapedArray{T, 2, SubArray{T, 1, A, Tuple{UnitRange{Int}}, true}, Tuple{}}}; kwargs...) where {T <: BlasFloat, A <: CuVecOrMat{T}}
-    qr_alg = CUSOLVER_HouseholderQR(; kwargs...)
-    return LQViaTransposedQR(qr_alg)
-end
-function MatrixAlgebraKit.default_svd_algorithm(::Type{Base.ReshapedArray{T, 2, SubArray{T, 1, A, Tuple{UnitRange{Int}}, true}, Tuple{}}}; kwargs...) where {T <: BlasFloat, A <: CuVecOrMat{T}}
+const BlockView{T, A} = Base.ReshapedArray{T, 2, SubArray{T, 1, A, Tuple{UnitRange{Int}}, true}}
+
+MatrixAlgebraKit.default_householder_driver(::BlockView{T, A}) where {T <: BlasFloat, A <: CuVecOrMat{T}} = CUSOLVER()
+function MatrixAlgebraKit.default_svd_algorithm(::Type{BlockView{T, A}}; kwargs...) where {T <: BlasFloat, A <: CuVecOrMat{T}}
     return CUSOLVER_Jacobi(; kwargs...)
 end
-function MatrixAlgebraKit.default_eig_algorithm(::Type{Base.ReshapedArray{T, 2, SubArray{T, 1, A, Tuple{UnitRange{Int}}, true}, Tuple{}}}; kwargs...) where {T <: BlasFloat, A <: CuVecOrMat{T}}
+function MatrixAlgebraKit.default_eig_algorithm(::Type{BlockView{T, A}}; kwargs...) where {T <: BlasFloat, A <: CuVecOrMat{T}}
     return CUSOLVER_Simple(; kwargs...)
 end
-function MatrixAlgebraKit.default_eigh_algorithm(::Type{Base.ReshapedArray{T, 2, SubArray{T, 1, A, Tuple{UnitRange{Int}}, true}, Tuple{}}}; kwargs...) where {T <: BlasFloat, A <: CuVecOrMat{T}}
+function MatrixAlgebraKit.default_eigh_algorithm(::Type{BlockView{T, A}}; kwargs...) where {T <: BlasFloat, A <: CuVecOrMat{T}}
     return CUSOLVER_DivideAndConquer(; kwargs...)
 end
 
+for f in (:geqrf!, :ungqr!, :unmqr!)
+    @eval $f(::CUSOLVER, args...) = YACUSOLVER.$f(args...)
+end
+
 _gpu_geev!(A::StridedCuMatrix, D::StridedCuVector, V::StridedCuMatrix) =
     YACUSOLVER.Xgeev!(A, D, V)
-_gpu_geqrf!(A::StridedCuMatrix) =
-    YACUSOLVER.geqrf!(A)
-_gpu_ungqr!(A::StridedCuMatrix, τ::StridedCuVector) =
-    YACUSOLVER.ungqr!(A, τ)
-_gpu_unmqr!(side::AbstractChar, trans::AbstractChar, A::StridedCuMatrix, τ::StridedCuVector, C::StridedCuVecOrMat) =
-    YACUSOLVER.unmqr!(side, trans, A, τ, C)
 _gpu_gesvd!(A::StridedCuMatrix, S::StridedCuVector, U::StridedCuMatrix, Vᴴ::StridedCuMatrix) =
     YACUSOLVER.gesvd!(A, S, U, Vᴴ)
 _gpu_Xgesvdp!(A::StridedCuMatrix, S::StridedCuVector, U::StridedCuMatrix, Vᴴ::StridedCuMatrix; kwargs...) =

diff --git a/ext/MatrixAlgebraKitGenericLinearAlgebraExt.jl b/ext/MatrixAlgebraKitGenericLinearAlgebraExt.jl
@@ -1,8 +1,7 @@
 module MatrixAlgebraKitGenericLinearAlgebraExt
 
 using MatrixAlgebraKit
-using MatrixAlgebraKit: sign_safe, check_input, diagview, gaugefix!, one!, default_fixgauge
-using MatrixAlgebraKit: left_orth_alg
+using MatrixAlgebraKit: sign_safe, check_input, diagview, gaugefix!, one!, zero!, default_fixgauge
 using GenericLinearAlgebra: svd!, svdvals!, eigen!, eigvals!, Hermitian, qr!
 using LinearAlgebra: I, Diagonal, lmul!
 
@@ -57,81 +56,65 @@ function MatrixAlgebraKit.eigh_vals!(A::AbstractMatrix, D, ::GLA_QRIteration)
     return eigvals!(Hermitian(A); sortby = real)
 end
 
-function MatrixAlgebraKit.default_qr_algorithm(::Type{T}; kwargs...) where {T <: StridedMatrix{<:Union{Float16, ComplexF16, BigFloat, Complex{BigFloat}}}}
-    return GLA_HouseholderQR(; kwargs...)
-end
-
-function MatrixAlgebraKit.qr_full!(A::AbstractMatrix, QR, alg::GLA_HouseholderQR)
-    check_input(qr_full!, A, QR, alg)
-    Q, R = QR
-    return _gla_householder_qr!(A, Q, R; alg.kwargs...)
-end
-
-function MatrixAlgebraKit.qr_compact!(A::AbstractMatrix, QR, alg::GLA_HouseholderQR)
-    check_input(qr_compact!, A, QR, alg)
-    Q, R = QR
-    return _gla_householder_qr!(A, Q, R; alg.kwargs...)
-end
-
-function MatrixAlgebraKit.qr_null!(A::AbstractMatrix, N, alg::GLA_HouseholderQR)
-    check_input(qr_null!, A, N, alg)
-    return _gla_householder_qr_null!(A, N; alg.kwargs...)
-end
-
-function _gla_householder_qr!(A::AbstractMatrix, Q, R; positive = true, blocksize = 1, pivoted = false)
-    pivoted && throw(ArgumentError("Only pivoted = false implemented for GLA_HouseholderQR."))
-    (blocksize == 1) || throw(ArgumentError("Only blocksize = 1 implemented for GLA_HouseholderQR."))
+function MatrixAlgebraKit.householder_qr!(
+        driver::MatrixAlgebraKit.GLA, A::AbstractMatrix, Q::AbstractMatrix, R::AbstractMatrix;
+        positive::Bool = true, pivoted::Bool = false, blocksize::Int = 1
+    )
+    blocksize == 1 ||
+        throw(ArgumentError(lazy"$driver does not provide a blocked QR decomposition"))
+    pivoted &&
+        throw(ArgumentError(lazy"$driver does not provide a pivoted QR decomposition"))
 
     m, n = size(A)
-    k = min(m, n)
+    minmn = min(m, n)
+    computeR = length(R) > 0
+
+    # compute QR
     Q̃, R̃ = qr!(A)
     lmul!(Q̃, MatrixAlgebraKit.one!(Q))
 
     if positive
-        @inbounds for j in 1:k
+        @inbounds for j in 1:minmn
             s = sign_safe(R̃[j, j])
             @simd for i in 1:m
                 Q[i, j] *= s
             end
         end
     end
 
-    computeR = length(R) > 0
     if computeR
         if positive
             @inbounds for j in n:-1:1
-                @simd for i in 1:min(k, j)
+                @simd for i in 1:min(minmn, j)
                     R[i, j] = R̃[i, j] * conj(sign_safe(R̃[i, i]))
                 end
-                @simd for i in (min(k, j) + 1):size(R, 1)
+                @simd for i in (min(minmn, j) + 1):size(R, 1)
                     R[i, j] = zero(eltype(R))
                 end
             end
         else
-            R[1:k, :] .= R̃
-            MatrixAlgebraKit.zero!(@view(R[(k + 1):end, :]))
+            R[1:minmn, :] .= R̃
+            MatrixAlgebraKit.zero!(@view(R[(minmn + 1):end, :]))
         end
     end
     return Q, R
 end
 
-function _gla_householder_qr_null!(
-        A::AbstractMatrix, N::AbstractMatrix;
-        positive = true, blocksize = 1, pivoted = false
+function MatrixAlgebraKit.householder_qr_null!(
+        driver::MatrixAlgebraKit.GLA, A::AbstractMatrix, N::AbstractMatrix;
+        positive::Bool = true, pivoted::Bool = false, blocksize::Int = 1
     )
-    pivoted && throw(ArgumentError("Only pivoted = false implemented for GLA_HouseholderQR."))
-    (blocksize == 1) || throw(ArgumentError("Only blocksize = 1 implemented for GLA_HouseholderQR."))
+    blocksize == 1 ||
+        throw(ArgumentError(lazy"$driver does not provide a blocked QR decomposition"))
+    pivoted &&
+        throw(ArgumentError(lazy"$driver does not provide a pivoted QR decomposition"))
+
     m, n = size(A)
     minmn = min(m, n)
-    fill!(N, zero(eltype(N)))
+    zero!(N)
     one!(view(N, (minmn + 1):m, 1:(m - minmn)))
     Q̃, = qr!(A)
-    lmul!(Q̃, N)
-    return N
-end
-
-function MatrixAlgebraKit.default_lq_algorithm(::Type{T}; kwargs...) where {T <: StridedMatrix{<:Union{Float16, ComplexF16, BigFloat, Complex{BigFloat}}}}
-    return MatrixAlgebraKit.LQViaTransposedQR(GLA_HouseholderQR(; kwargs...))
+    return lmul!(Q̃, N)
 end
 
 MatrixAlgebraKit.left_orth_alg(alg::GLA_HouseholderQR) = MatrixAlgebraKit.LeftOrthViaQR(alg)

diff --git a/src/algorithms.jl b/src/algorithms.jl
@@ -88,7 +88,7 @@ Finally, the same behavior is obtained when the keyword arguments are
 passed as the third positional argument in the form of a `NamedTuple`. 
 """ select_algorithm
 
-function select_algorithm(f::F, A, alg::Alg = nothing; kwargs...) where {F, Alg}
+Base.@assume_effects :foldable function select_algorithm(f::F, A, alg::Alg = nothing; kwargs...) where {F, Alg}
     if isnothing(alg)
         return default_algorithm(f, A; kwargs...)
     elseif alg isa Symbol
@@ -143,6 +143,59 @@ If this is not possible, for example when the output size is not known a priori
 this function may return `nothing`.
 """ initialize_output
 
+
+# Drivers
+# -------
+"""
+    abstract type Driver
+
+Supertype used for customizing various implementations of the same algorithm.
+"""
+abstract type Driver end
+
+"""
+    DefaultDriver <: Driver
+
+Select a default driver at runtime, based on the input matrix.
+"""
+struct DefaultDriver <: Driver end
+
+"""
+    LAPACK <: Driver
+
+Driver to select LAPACK as the implementation strategy.
+"""
+struct LAPACK <: Driver end
+
+"""
+    CUSOLVER <: Driver
+
+Driver to select CUSOLVER as the implementation strategy.
+"""
+struct CUSOLVER <: Driver end
+
+"""
+    ROCSOLVER <: Driver
+
+Driver to select ROCSOLVER as the implementation strategy.
+"""
+struct ROCSOLVER <: Driver end
+
+"""
+    GLA <: Driver
+
+Driver to select GenericLinearAlgebra.jl as the implementation strategy.
+"""
+struct GLA <: Driver end
+
+"""
+    Native <: Driver
+
+Driver to select a native implementation in MatrixAlgebraKit as the implementation strategy.
+"""
+struct Native <: Driver end
+
+
 # Truncation strategy
 # -------------------
 """

diff --git a/src/common/householder.jl b/src/common/householder.jl
@@ -1,32 +1,32 @@
 const IndexRange{T <: Integer} = Base.AbstractRange{T}
 
 # Elementary Householder reflection
-struct Householder{T, V <: AbstractVector, R <: IndexRange}
+struct HouseholderReflection{T, V <: AbstractVector, R <: IndexRange}
     β::T
     v::V
     r::R
 end
-Base.adjoint(H::Householder) = Householder(conj(H.β), H.v, H.r)
+Base.adjoint(H::HouseholderReflection) = HouseholderReflection(conj(H.β), H.v, H.r)
 
 function householder(x::AbstractVector, r::IndexRange = axes(x, 1), k = first(r))
     i = findfirst(==(k), r)
     i == nothing && error("k = $k should be in the range r = $r")
     β, v, ν = _householder!(x[r], i)
-    return Householder(β, v, r), ν
+    return HouseholderReflection(β, v, r), ν
 end
 # Householder reflector h that zeros the elements A[r,col] (except for A[k,col]) upon lmul!(h,A)
 function householder(A::AbstractMatrix, r::IndexRange, col::Int, k = first(r))
     i = findfirst(==(k), r)
     i == nothing && error("k = $k should be in the range r = $r")
     β, v, ν = _householder!(A[r, col], i)
-    return Householder(β, v, r), ν
+    return HouseholderReflection(β, v, r), ν
 end
 # Householder reflector that zeros the elements A[row,r] (except for A[row,k]) upon rmul!(A,h')
 function householder(A::AbstractMatrix, row::Int, r::IndexRange, k = first(r))
     i = findfirst(==(k), r)
     i == nothing && error("k = $k should be in the range r = $r")
     β, v, ν = _householder!(conj!(A[row, r]), i)
-    return Householder(β, v, r), ν
+    return HouseholderReflection(β, v, r), ν
 end
 
 # generate Householder vector based on vector v, such that applying the reflection
@@ -66,7 +66,7 @@ function _householder!(v::AbstractVector{T}, i::Int = 1) where {T}
     return β, v, ν
 end
 
-function LinearAlgebra.lmul!(H::Householder, x::AbstractVector)
+function LinearAlgebra.lmul!(H::HouseholderReflection, x::AbstractVector)
     v = H.v
     r = H.r
     β = H.β
@@ -87,7 +87,7 @@ function LinearAlgebra.lmul!(H::Householder, x::AbstractVector)
     end
     return x
 end
-function LinearAlgebra.lmul!(H::Householder, A::AbstractMatrix; cols = axes(A, 2))
+function LinearAlgebra.lmul!(H::HouseholderReflection, A::AbstractMatrix; cols = axes(A, 2))
     v = H.v
     r = H.r
     β = H.β
@@ -110,7 +110,7 @@ function LinearAlgebra.lmul!(H::Householder, A::AbstractMatrix; cols = axes(A, 2
     end
     return A
 end
-function LinearAlgebra.rmul!(A::AbstractMatrix, H::Householder; rows = axes(A, 1))
+function LinearAlgebra.rmul!(A::AbstractMatrix, H::HouseholderReflection; rows = axes(A, 1))
     v = H.v
     r = H.r
     β = H.β