Preliminary support for matrix multiplication.

- New methods for * for combinations of OffsetArray and AbstractArray
  Unfortunately this introduces method ambiguities with Base.
- As an alternative, tried defining a new promote_rule, but somehow it doesn't get invoked.

New convenience constructors
- Wrap any (non-offset) array as an OffsetArray with standard indices
- Remove layer of indirection when constructing with explicit offsets

Cosmetic edits to constructor section for improved readability

src/OffsetArrays.jl

@@ -1,6 +1,8 @@
 module OffsetArrays
 
 using Base: Indices, tail, @propagate_inbounds
+import Base: (*), convert, promote_rule
+
 @static if !isdefined(Base, :IdentityUnitRange)
     const IdentityUnitRange = Base.Slice
 else
@@ -45,10 +47,12 @@ OffsetArray(A::AbstractArray{T,N}, offsets::Vararg{Int,N}) where {T,N} =
     OffsetArray(A, offsets)
 OffsetArray(A::AbstractArray{T,0}) where {T} = OffsetArray(A, ())
 
+# Create an uninitialized OffsetArray with given element type
 const ArrayInitializer = Union{UndefInitializer, Missing, Nothing}
 OffsetArray{T,N}(init::ArrayInitializer, inds::Indices{N}) where {T,N} =
     OffsetArray(Array{T,N}(init, map(indexlength, inds)), map(indexoffset, inds))
 OffsetArray{T}(init::ArrayInitializer, inds::Indices{N}) where {T,N} = OffsetArray{T,N}(init, inds)
+# Same thing, but taking multiple args for offsets/indices
 OffsetArray{T,N}(init::ArrayInitializer, inds::Vararg{AbstractUnitRange,N}) where {T,N} = OffsetArray{T,N}(init, inds)
 OffsetArray{T}(init::ArrayInitializer, inds::Vararg{AbstractUnitRange,N}) where {T,N} = OffsetArray{T,N}(init, inds)
 
@@ -403,6 +407,28 @@ end
 no_offset_view(A::OffsetArray) = no_offset_view(parent(A))
 
 
+# Quick hack for matrix multiplication.
+# Ideally, one would instead improve LinearAlgebra's support of custom indexing.
+function (*)(A::OffsetMatrix, B::OffsetMatrix)
+    matmult_check_axes(A, B)
+    C = OffsetArray(parent(A) * parent(B), (axes(A,1), axes(B,2)))
+end
+
+function (*)(A::OffsetMatrix, B::OffsetVector)
+    matmult_check_axes(A, B)
+    C = OffsetArray(parent(A) * parent(B), axes(A,1))
+end
+matmult_check_axes(A, B) = axes(A, 2) == axes(B, 1) || error("axes(A,2) must equal axes(B,1)")
+
+(*)(A::OffsetMatrix, B::AbstractMatrix) = A * OffsetArray(B)
+(*)(A::OffsetMatrix, B::AbstractVector) = A * OffsetArray(B)
+(*)(A::AbstractMatrix, B::OffsetArray) = OffsetArray(A) * B
+(*)(A::AbstractVector, B::OffsetArray) = OffsetArray(A) * B
+
+# An alternative to the above four methods would be to use promote_rule, but it doesn't get invoked
+# promote_rule(::Type{A1}, ::Type{A2}) where A1<:AbstractArray{<:Any,N}  where A2<:OffsetArray{<:Any,N,A3} where {N,A3} = OffsetArray{eltype(promote_type(A1, A3)), N, promote_type(A1, A3)}
+
+
 ####
 # work around for segfault in searchsorted*
 #  https://github.com/JuliaLang/julia/issues/33977