@TimHoly thanks. I was able to use the described approach to add in
functionality for arbitrary eltype, so everything in my original request is
satisfied. This is good since I realized earlier that I also will need a
Complex eltype later down the road.
Best,
G
On Friday, March 13, 2015 at 9:59:58 AM UTC+1, Tim Holy wrote:
>
> Note that
>
> BlockMatrix{S,TA<:AbstractMatrix{S},TB<:AbstractMatrix{S},TC<:
> AbstractMatrix{S},TD<:AbstractMatrix{S}}
>
> is a syntax that (1) has come to be called "triangular dispatch" and (2)
> is
> not actually supported by julia yet, although neither does it throw an
> error.
> It just won't always do what you think it will do.
>
> There are more indirect strategies to achieve this; see one here:
>
> http://docs.julialang.org/en/release-0.3/manual/faq/#how-should-i-declare-abstract-container-type-fields
>
> (the part about the inner constructor).
>
> --Tim
>
> On Thursday, March 12, 2015 07:20:45 PM Greg Plowman wrote:
> > I don't really understand how this works, but this might point someone
> in
> > the right direction.
> > It seems Julia can't fully infer types, in particular the element type
> S.
> > So we get further if we give a hint:
> >
> > type BlockMatrix{S,TA<:AbstractMatrix{S},TB<:AbstractMatrix{S},TC<:
> > AbstractMatrix{S},TD<:AbstractMatrix{S}} <: AbstractMatrix{S}
> > A::TA
> > B::TB
> > C::TC
> > D::TD
> > end
> >
> > typealias Block{S} BlockMatrix{S,AbstractMatrix{S},AbstractMatrix{S},
> > AbstractMatrix{S},AbstractMatrix{S}}
> >
> > # not really sure what size() should be, but need to define for output
> > Base.size(x::BlockMatrix) = (size(x.A,1) + size(x.C,1), size(x.A,2) +
> size(x
> > .B,2))
> >
> > N = Block{Float64}(A,A,A,B)
> >
> >
> > julia> N.A
> > 4x4 Array{Float64,2}:
> > 0.805914 0.473687 0.721984 0.464178
> > 0.306 0.728015 0.148804 0.776728
> > 0.439048 0.566558 0.72709 0.524761
> > 0.255731 0.16528 0.331941 0.167353
> > julia> N.B
> > 4x4 Array{Float64,2}:
> > 0.805914 0.473687 0.721984 0.464178
> > 0.306 0.728015 0.148804 0.776728
> > 0.439048 0.566558 0.72709 0.524761
> > 0.255731 0.16528 0.331941 0.167353
> > julia> N.C
> > 4x4 Array{Float64,2}:
> > 0.805914 0.473687 0.721984 0.464178
> > 0.306 0.728015 0.148804 0.776728
> > 0.439048 0.566558 0.72709 0.524761
> > 0.255731 0.16528 0.331941 0.167353
> > julia> N.D
> > 4x4 Diagonal{Float64}:
> > 1.0 0.0 0.0 0.0
> > 0.0 2.0 0.0 0.0
> > 0.0 0.0 3.0 0.0
> > 0.0 0.0 0.0 4.0
> >
> > On Friday, March 13, 2015 at 8:49:41 AM UTC+11, Gabriel Mitchell wrote:
> > > @ggggg Sorry, I guess I didn't state my intent that clearly. While
> your
> > > example does enforce the Matrix/eltype constraint that is only part of
> > > what
> > > I am after. Having a type parameter for each block is a main thing
> that I
> > > am interested in. The reason is that I can write methods that dispatch
> on
> > > those types. An example of such a method with an explicit 4-ary
> structure
> > > would be
> > >
> > > #generic fallback
> > > det(A::Matrix,B::Matrix,C::Matrix,D::Matrix) = det([A B; C D])
> > >
> > > #specialized method, should actually, check for A invertible, but you
> get
> > > the idea
> > > det(A::Diagonal,B::Diagonal,C::Diagonal,D::Diagonal) =
> > > det(A)*det(D-C*inv(A)*B)
> > >
> > > #etc...
> > >
> > > In my applications there are at least a dozen situations where certain
> > > block structure allow for significantly more efficient implementations
> > > than
> > > the generic fallback. One would like to make the calls to these
> methods
> > > (det,inv,trace, and so on) with the normal 1-ary argument, that matrix
> M
> > > itself. This would be possible if the type information of the blocks
> could
> > > be read out of the type of M. I hope this clear up my motivation for
> the
> > > above question.
> > >
> > > On Thursday, March 12, 2015 at 8:49:05 PM UTC+1, ggggg wrote:
> > >> BlockMatrix only needs one type parameter to fully specify the type,
> so
> > >> you should probably only use one type parameter. Like so:
> > >>
> > >> *type BlockMatrix{S} <: AbstractMatrix{S}*
> > >>
> > >>> * A::AbstractMatrix{S}*
> > >>>
> > >>> * B::AbstractMatrix{S}*
> > >>>
> > >>> * C::AbstractMatrix{S}*
> > >>>
> > >>> * D::AbstractMatrix{S}*
> > >>>
> > >>> *end*
> > >>
> > >> I'm sure someone else can explain in more detail why yours didn't
> work.
>
>
