Add SVD support for BlockDiagonal

Author: lkdvos

src/blocksvd.jl

@@ -3,10 +3,16 @@ SVD on blockmatrices:
 Interpret the matrix as a linear map acting on vector spaces with a direct sum structure, which is reflected in the structure of U and V.
 In the generic case, the SVD does not preserve this structure, and can mix up the blocks, so S becomes a single block.
 (Implementation-wise, also most efficiently done by first mapping to a `BlockedArray`)
+In the case of `BlockDiagonal` however, the structure is preserved and carried over to the structure of `S`.
 =#
 
 LinearAlgebra.eigencopy_oftype(A::AbstractBlockMatrix, S) = BlockedArray(Array{S}(A), blocksizes(A, 1), blocksizes(A, 2))
 
+function LinearAlgebra.eigencopy_oftype(A::BlockDiagonal, S)
+    diag = map(Base.Fix2(LinearAlgebra.eigencopy_oftype, S), A.blocks.diag)
+    return BlockDiagonal(diag)
+end
+
 function LinearAlgebra.svd!(A::BlockedMatrix; full::Bool=false, alg::LinearAlgebra.Algorithm=default_svd_alg(A))
     USV = svd!(parent(A); full, alg)
 
@@ -19,3 +25,11 @@ function LinearAlgebra.svd!(A::BlockedMatrix; full::Bool=false, alg::LinearAlgeb
     vt = BlockedArray(USV.Vt, bsz2, bsz3)
     return SVD(u, s, vt)
 end
+
+function LinearAlgebra.svd!(A::BlockDiagonal; full::Bool=false, alg::LinearAlgebra.Algorithm=default_svd_alg(A))
+    USVs = map(a -> svd!(a; full, alg), A.blocks.diag)
+    Us = map(Base.Fix2(getproperty, :U), USVs)
+    Ss = map(Base.Fix2(getproperty, :S), USVs)
+    Vts = map(Base.Fix2(getproperty, :Vt), USVs)
+    return SVD(BlockDiagonal(Us), mortar(Ss), BlockDiagonal(Vts))
+end

test/test_blocksvd.jl

@@ -1,6 +1,7 @@
 module TestBlockSVD
 
 using BlockArrays, Test, LinearAlgebra, Random
+using BlockArrays: BlockDiagonal
 
 Random.seed!(0)
 
@@ -70,4 +71,37 @@ end
     @test U_blocked * Diagonal(S_blocked) * Vt_blocked ≈ y
 end
 
+@testset "BlockDiagonal SVD ($T)" for T in eltypes
+    blocksz = (2, 3, 1)
+    y = BlockDiagonal([rand(T, d, d) for d in blocksz])
+    x = Array(y)
+    
+    USV = svd(x)
+    U, S, Vt = USV.U, USV.S, USV.Vt
+    
+    # https://github.com/JuliaArrays/BlockArrays.jl/issues/425
+    # USV_blocked = @inferred svd(y)
+    USV_block = svd(y)
+    U_block, S_block, Vt_block = USV_block.U, USV_block.S, USV_block.Vt
+
+    # test types
+    @test U_block isa BlockDiagonal
+    @test eltype(U_block) == float(T)
+    @test S_block isa BlockVector
+    @test eltype(S_block) == real(float(T))
+    @test Vt_block isa BlockDiagonal
+    @test eltype(Vt_block) == float(T)
+
+    # test structure
+    @test blocksizes(U_block, 1) == blocksizes(y, 1)
+    @test length(blocksizes(U_block, 2)) == length(blocksz)
+    @test blocksizes(Vt_block, 2) == blocksizes(y, 2)
+    @test length(blocksizes(Vt_block, 1)) == length(blocksz)
+
+    # test correctness: SVD is not unique, so cannot compare to dense
+    @test U_block * BlockDiagonal(Diagonal.(S_block.blocks)) * Vt_block ≈ y
+    @test U_block' * U_block ≈ LinearAlgebra.I
+    @test Vt_block * Vt_block' ≈ LinearAlgebra.I
+end
+
 end # module