Right now, when calling left_orth(A) -> (Q, R) on a matrix of BLAS floats without any algorithm specifications, MatrixAlgebraKit.jl defaults to returning a non-positive R, since by default it ends up using LAPACK_HouseholderQR which uses a default value positive = false. In many cases a positive R is actually preferred (which is admittedly a very biased statement), so I was wondering: does it make sense to change the default to LAPACK_HouseholderQR(; blocksize, positive = true, pivoted = false)? Or would this be an undesirable choice for some reason?

For context, I bumped into this after QuantumKitHub/TensorKit.jl#312, where the default convention positive = true in TensorKit.jl was removed in favor of switching to the MatrixAlgebraKit.jl defaults where positive = false is chosen (see also QuantumKitHub/PEPSKit.jl#314).