dsvd doesn't work for FixedUnits

[b-r-hamilton]

The following code block

using Unitful, UnitfulLinearAlgebra, LinearAlgebra
permil = Unitful.FixedUnits(u"permille")
urange = fill(permil, 2)
udomain = fill(permil, 3)
A = UnitfulMatrix(randn(length(urange),length(udomain)),urange,udomain)
Pr = UnitfulMatrix(I(length(urange)),urange.^-1,urange)
Pd = UnitfulMatrix(I(length(udomain)),udomain.^-1,udomain)
U,Λ,V = dsvd(A,Pr,Pd)

throws the following error

ERROR: DimensionMismatch: Dimension index [, ] and Unitful.Units[, ] do not match

This seems to trace back to the fact that when the following is called https://github.com/ggebbie/UnitfulLinearAlgebra.jl/blob/de6592342d2aaf7c2eaae4d59125cc2b04a8f690/src/dsvd.jl#L61 F.Qy and F.U′ have different unitranges/domains, so the ldiv can't be called. E.g.

julia> svd = dsvd(A,Pr,Pd)
julia> svd.Qy.dims
Units Unitful.FixedUnits{(), NoDims, nothing}[, ],
Units Sampled{Unitful.FixedUnits{(‰,), NoDims, nothing}} Unitful.FixedUnits{(‰,), NoDims, nothing}[‰, ‰] Unordered Irregular Points

julia> svd.U′.dims
Units Categorical{Unitful.Units} Unitful.Units[, ] Unordered,
Units Categorical{Unitful.Units} Unitful.Units[, ] Unordered

It seems to me like the Categorical Units versus the Sampled Units is the problem, and I'm not sure how to fix this. Would there be a way to expand on the test of equivalent dimensions that ldiv calls to make it broader? Like if the vector version of the units is equivalent, it's okay to ldiv?

[ggebbie]

converting the unitrange of Uprime is one solution. dsvd.jl is updated in PR #100 to do this for all cases, which may not be necessary and may slow things down.

There is a similar issue with Vprime in DSVD solved with same approach in PR #100 .

A wider solution could be: 1) keep Uprime and Vprime not UnitfulMatrixs (just Matrix{Quantity} instead), 2) make sure ldiv works properly between a UnitfulMatrix and Matrix{Quantity} (including updating the exact criteria for multiplication, including automatically converting the unitranges of inexact matrices).

[b-r-hamilton]

The code snippet I commented here now runs with the new UnitfulLinearAlgebra. It took a little work to get BLUEs.jl/runtests.jl to work with it, but that's also running with new ULA.