add defaults and more tests

Author: Jutho

src/interface/lq.jl

@@ -72,6 +72,9 @@ default_lq_algorithm(A; kwargs...) = default_lq_algorithm(typeof(A); kwargs...)
 function default_lq_algorithm(T::Type; kwargs...)
     throw(MethodError(default_lq_algorithm, (T,)))
 end
+function default_lq_algorithm(::Type{T}; kwargs...) where {T <: AbstractMatrix}
+    return Native_HouseholderLQ(; kwargs...)
+end
 function default_lq_algorithm(::Type{T}; kwargs...) where {T <: YALAPACK.MaybeBlasMat}
     return LAPACK_HouseholderLQ(; kwargs...)
 end

src/interface/qr.jl

@@ -72,6 +72,9 @@ default_qr_algorithm(A; kwargs...) = default_qr_algorithm(typeof(A); kwargs...)
 function default_qr_algorithm(T::Type; kwargs...)
     throw(MethodError(default_qr_algorithm, (T,)))
 end
+function default_qr_algorithm(::Type{T}; kwargs...) where {T <: AbstractMatrix}
+    return Native_HouseholderQR(; kwargs...)
+end
 function default_qr_algorithm(::Type{T}; kwargs...) where {T <: YALAPACK.MaybeBlasMat}
     return LAPACK_HouseholderQR(; kwargs...)
 end