Make BlockDiagonal block storage generic

Before this commit, `BlockDiagonal` uses a `Vector{V}` to store the
blocks. The issue is that for trimmable binaries it is advantageous to
use stronger typing, such as `SizedVector` from `StaticArrays`.
To support such cases, we make the vector type generic, and make the
required modifications in the rest of the package.

Author: RomeoV

ext/ChainRulesCoreExt.jl

@@ -58,7 +58,7 @@ function ChainRulesCore.rrule(
     ::typeof(*),
     bm::BlockDiagonal{T,V},
     v::StridedVector{T},
-) where {T<:Union{Real,Complex},V<:Matrix{T}}
+) where {T<:Union{Real,Complex},V<:AbstractVector{<:Matrix{T}}}
 
     y = bm * v
 

src/blockdiagonal.jl

@@ -5,16 +5,16 @@
 
 A matrix with matrices on the diagonal, and zeros off the diagonal.
 """
-struct BlockDiagonal{T,V<:AbstractMatrix{T}} <: AbstractMatrix{T}
-    blocks::Vector{V}
+struct BlockDiagonal{T,BV<:AbstractVector{<:AbstractMatrix{T}}} <: AbstractMatrix{T}
+    blocks::BV
 
-    function BlockDiagonal{T,V}(blocks::Vector{V}) where {T,V<:AbstractMatrix{T}}
-        return new{T,V}(blocks)
+    function BlockDiagonal{T,BV}(blocks::AbstractVector{V}) where {T,V<:AbstractMatrix{T},BV<:AbstractVector{V}}
+        return new{T,typeof(blocks)}(blocks)
     end
 end
 
-function BlockDiagonal(blocks::Vector{V}) where {T,V<:AbstractMatrix{T}}
-    return BlockDiagonal{T,V}(blocks)
+function BlockDiagonal(blocks::AbstractVector{V}) where {T,V<:AbstractMatrix{T}}
+    return BlockDiagonal{T,typeof(blocks)}(blocks)
 end
 
 BlockDiagonal(B::BlockDiagonal) = B
@@ -86,7 +86,7 @@ function getblock(B::BlockDiagonal{T}, p::Integer, q::Integer) where {T}
     return p == q ? blocks(B)[p] : Zeros{T}(blocksize(B, p, q))
 end
 
-function setblock!(B::BlockDiagonal{T,V}, v::V, p::Integer) where {T,V}
+function setblock!(B::BlockDiagonal{T,V}, v::W, p::Integer) where {T,W,V<:AbstractVector{W}}
     if blocksize(B, p) != size(v)
         throw(
             DimensionMismatch(
@@ -97,7 +97,7 @@ function setblock!(B::BlockDiagonal{T,V}, v::V, p::Integer) where {T,V}
     return blocks(B)[p] = v
 end
 
-function setblock!(B::BlockDiagonal{T,V}, v::V, p::Int, q::Int) where {T,V}
+function setblock!(B::BlockDiagonal{T,V}, v::W, p::Int, q::Int) where {T,W,V<:AbstractVector{W}}
     p == q ||
         throw(ArgumentError("Cannot set off-diagonal block ($p, $q) to non-zero value."))
     return setblock!(B, v, p)
@@ -155,7 +155,7 @@ end
 end
 
 function Base.convert(::Type{BlockDiagonal{T,M}}, b::BlockDiagonal) where {T,M}
-    new_blocks = convert.(M, blocks(b))
+    new_blocks = convert(M, blocks(b))
     return BlockDiagonal(new_blocks)::BlockDiagonal{T,M}
 end
 

test/blockdiagonal.jl

@@ -175,7 +175,7 @@ using Test
         b = BlockDiagonal([special])
 
         convert_first = BlockDiagonal([convert(Matrix, special)])
-        convert_last = convert(BlockDiagonal{Float64,Matrix{Float64}}, b)
+        convert_last = convert(BlockDiagonal{Float64,Vector{Matrix{Float64}}}, b)
 
         @test convert_first == convert_last
     end

test/linalg.jl

@@ -160,7 +160,7 @@ end
         @test C.UL ≈ C.U
         @test C.uplo === 'U'
         @test C.info == 0
-        @test typeof(C) == Cholesky{Float64,BlockDiagonal{Float64,Matrix{Float64}}}
+        @test typeof(C) == Cholesky{Float64,BlockDiagonal{Float64,Vector{Matrix{Float64}}}}
         @test PDMat(cholesky(BD)) == PDMat(cholesky(Matrix(BD)))
 
         M = BlockDiagonal(map(Matrix, blocks(C.L)))
@@ -171,7 +171,7 @@ end
         @test C.UL ≈ C.L
         @test C.uplo === 'L'
         @test C.info == 0
-        @test typeof(C) == Cholesky{Float64,BlockDiagonal{Float64,Matrix{Float64}}}
+        @test typeof(C) == Cholesky{Float64,BlockDiagonal{Float64,Vector{Matrix{Float64}}}}
 
         # we didn't think we needed to support this, but #109
         d = Diagonal(rand(5))