Block sparse eig (#129)

Author: mtfishman

Project.toml

@@ -1,7 +1,7 @@
 name = "BlockSparseArrays"
 uuid = "2c9a651f-6452-4ace-a6ac-809f4280fbb4"
 authors = ["ITensor developers <[email protected]> and contributors"]
-version = "0.7.1"
+version = "0.7.2"
 
 [deps]
 Adapt = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"

src/BlockSparseArrays.jl

@@ -51,5 +51,6 @@ include("factorizations/qr.jl")
 include("factorizations/lq.jl")
 include("factorizations/polar.jl")
 include("factorizations/orthnull.jl")
+include("factorizations/eig.jl")
 
 end

src/abstractblocksparsearray/wrappedabstractblocksparsearray.jl

@@ -348,6 +348,15 @@ function Base.similar(
   return @interface BlockSparseArrayInterface() similar(a, elt, axes)
 end
 
+struct BlockType{T} end
+BlockType(x) = BlockType{x}()
+function Base.similar(a::AbstractBlockSparseArray, ::BlockType{T}, ax) where {T}
+  return BlockSparseArray{eltype(T),ndims(T),T}(undef, ax)
+end
+function Base.similar(a::AbstractBlockSparseArray, T::BlockType)
+  return similar(a, T, axes(a))
+end
+
 # TODO: Implement this in a more generic way using a smarter `copyto!`,
 # which is ultimately what `Array{T,N}(::AbstractArray{<:Any,N})` calls.
 # These are defined for now to avoid scalar indexing issues when there

src/blocksparsearrayinterface/blocksparsearrayinterface.jl

@@ -45,6 +45,9 @@ end
 function eachstoredblockdiagindex(a::AbstractArray)
   return eachblockstoredindex(a) ∩ blockdiagindices(a)
 end
+function eachunstoredblockdiagindex(a::AbstractArray)
+  return setdiff(blockdiagindices(a), eachblockstoredindex(a))
+end
 
 # Like `BlockArrays.eachblock` but only iterating
 # over stored blocks.

src/factorizations/eig.jl

@@ -0,0 +1,92 @@
+using BlockArrays: blocksizes
+using DiagonalArrays: diagonal
+using LinearAlgebra: LinearAlgebra, Diagonal
+using MatrixAlgebraKit:
+  MatrixAlgebraKit,
+  TruncationStrategy,
+  check_input,
+  default_eig_algorithm,
+  default_eigh_algorithm,
+  diagview,
+  eig_full!,
+  eig_trunc!,
+  eig_vals!,
+  eigh_full!,
+  eigh_trunc!,
+  eigh_vals!,
+  findtruncated
+
+for f in [:default_eig_algorithm, :default_eigh_algorithm]
+  @eval begin
+    function MatrixAlgebraKit.$f(arrayt::Type{<:AbstractBlockSparseMatrix}; kwargs...)
+      alg = $f(blocktype(arrayt); kwargs...)
+      return BlockPermutedDiagonalAlgorithm(alg)
+    end
+  end
+end
+
+function MatrixAlgebraKit.check_input(
+  ::typeof(eig_full!), A::AbstractBlockSparseMatrix, (D, V)
+)
+  @assert isa(D, AbstractBlockSparseMatrix) && isa(V, AbstractBlockSparseMatrix)
+  @assert eltype(V) === eltype(D) === complex(eltype(A))
+  @assert axes(A, 1) == axes(A, 2)
+  @assert axes(A) == axes(D) == axes(V)
+  return nothing
+end
+function MatrixAlgebraKit.check_input(
+  ::typeof(eigh_full!), A::AbstractBlockSparseMatrix, (D, V)
+)
+  @assert isa(D, AbstractBlockSparseMatrix) && isa(V, AbstractBlockSparseMatrix)
+  @assert eltype(V) === eltype(A)
+  @assert eltype(D) === real(eltype(A))
+  @assert axes(A, 1) == axes(A, 2)
+  @assert axes(A) == axes(D) == axes(V)
+  return nothing
+end
+
+for f in [:eig_full!, :eigh_full!]
+  @eval begin
+    function MatrixAlgebraKit.initialize_output(
+      ::typeof($f), A::AbstractBlockSparseMatrix, alg::BlockPermutedDiagonalAlgorithm
+    )
+      Td, Tv = fieldtypes(Base.promote_op($f, blocktype(A), typeof(alg.alg)))
+      D = similar(A, BlockType(Td))
+      V = similar(A, BlockType(Tv))
+      return (D, V)
+    end
+    function MatrixAlgebraKit.$f(
+      A::AbstractBlockSparseMatrix, (D, V), alg::BlockPermutedDiagonalAlgorithm
+    )
+      check_input($f, A, (D, V))
+      for I in eachstoredblockdiagindex(A)
+        D[I], V[I] = $f(@view(A[I]), alg.alg)
+      end
+      for I in eachunstoredblockdiagindex(A)
+        # TODO: Support setting `LinearAlgebra.I` directly, and/or
+        # using `FillArrays.Eye`.
+        V[I] = LinearAlgebra.I(size(@view(V[I]), 1))
+      end
+      return (D, V)
+    end
+  end
+end
+
+for f in [:eig_vals!, :eigh_vals!]
+  @eval begin
+    function MatrixAlgebraKit.initialize_output(
+      ::typeof($f), A::AbstractBlockSparseMatrix, alg::BlockPermutedDiagonalAlgorithm
+    )
+      T = Base.promote_op($f, blocktype(A), typeof(alg.alg))
+      return similar(A, BlockType(T), axes(A, 1))
+    end
+    function MatrixAlgebraKit.$f(
+      A::AbstractBlockSparseMatrix, D, alg::BlockPermutedDiagonalAlgorithm
+    )
+      for I in eachblockstoredindex(A)
+        D[I] = $f(@view!(A[I]), alg.alg)
+      end
+      return D
+    end
+  end
+end

src/factorizations/svd.jl

@@ -1,4 +1,5 @@
-using MatrixAlgebraKit: MatrixAlgebraKit, default_svd_algorithm, svd_compact!, svd_full!
+using MatrixAlgebraKit:
+  MatrixAlgebraKit, check_input, default_svd_algorithm, svd_compact!, svd_full!
 
 """
     BlockPermutedDiagonalAlgorithm(A::MatrixAlgebraKit.AbstractAlgorithm)
@@ -152,45 +153,40 @@ function MatrixAlgebraKit.initialize_output(
 end
 
 function MatrixAlgebraKit.check_input(
-  ::typeof(svd_compact!), A::AbstractBlockSparseMatrix, USVᴴ
+  ::typeof(svd_compact!), A::AbstractBlockSparseMatrix, (U, S, Vᴴ)
 )
-  U, S, Vt = USVᴴ
   @assert isa(U, AbstractBlockSparseMatrix) &&
     isa(S, AbstractBlockSparseMatrix) &&
-    isa(Vt, AbstractBlockSparseMatrix)
-  @assert eltype(A) == eltype(U) == eltype(Vt)
+    isa(Vᴴ, AbstractBlockSparseMatrix)
+  @assert eltype(A) == eltype(U) == eltype(Vᴴ)
   @assert real(eltype(A)) == eltype(S)
-  @assert axes(A, 1) == axes(U, 1) && axes(A, 2) == axes(Vt, 2)
+  @assert axes(A, 1) == axes(U, 1) && axes(A, 2) == axes(Vᴴ, 2)
   @assert axes(S, 1) == axes(S, 2)
-
   return nothing
 end
 
 function MatrixAlgebraKit.check_input(
-  ::typeof(svd_full!), A::AbstractBlockSparseMatrix, USVᴴ
+  ::typeof(svd_full!), A::AbstractBlockSparseMatrix, (U, S, Vᴴ)
 )
-  U, S, Vt = USVᴴ
   @assert isa(U, AbstractBlockSparseMatrix) &&
     isa(S, AbstractBlockSparseMatrix) &&
-    isa(Vt, AbstractBlockSparseMatrix)
-  @assert eltype(A) == eltype(U) == eltype(Vt)
+    isa(Vᴴ, AbstractBlockSparseMatrix)
+  @assert eltype(A) == eltype(U) == eltype(Vᴴ)
   @assert real(eltype(A)) == eltype(S)
-  @assert axes(A, 1) == axes(U, 1) && axes(A, 2) == axes(Vt, 1) == axes(Vt, 2)
+  @assert axes(A, 1) == axes(U, 1) && axes(A, 2) == axes(Vᴴ, 1) == axes(Vᴴ, 2)
   @assert axes(S, 2) == axes(A, 2)
-
   return nothing
 end
 
 function MatrixAlgebraKit.svd_compact!(
-  A::AbstractBlockSparseMatrix, USVᴴ, alg::BlockPermutedDiagonalAlgorithm
+  A::AbstractBlockSparseMatrix, (U, S, Vᴴ), alg::BlockPermutedDiagonalAlgorithm
 )
-  MatrixAlgebraKit.check_input(svd_compact!, A, USVᴴ)
-  U, S, Vt = USVᴴ
+  check_input(svd_compact!, A, (U, S, Vᴴ))
 
   # do decomposition on each block
   for bI in eachblockstoredindex(A)
     brow, bcol = Tuple(bI)
-    usvᴴ = (@view!(U[brow, bcol]), @view!(S[bcol, bcol]), @view!(Vt[bcol, bcol]))
+    usvᴴ = (@view!(U[brow, bcol]), @view!(S[bcol, bcol]), @view!(Vᴴ[bcol, bcol]))
     usvᴴ′ = svd_compact!(@view!(A[bI]), usvᴴ, alg.alg)
     @assert usvᴴ === usvᴴ′ "svd_compact! might not be in-place"
   end
@@ -203,25 +199,24 @@ function MatrixAlgebraKit.svd_compact!(
   emptycols = setdiff(1:blocksize(A, 2), bcolIs)
   # needs copyto! instead because size(::LinearAlgebra.I) doesn't work
   # U[Block(row, col)] = LinearAlgebra.I
-  # Vt[Block(col, col)] = LinearAlgebra.I
+  # Vᴴ[Block(col, col)] = LinearAlgebra.I
   for (row, col) in zip(emptyrows, emptycols)
     copyto!(@view!(U[Block(row, col)]), LinearAlgebra.I)
-    copyto!(@view!(Vt[Block(col, col)]), LinearAlgebra.I)
+    copyto!(@view!(Vᴴ[Block(col, col)]), LinearAlgebra.I)
   end
 
-  return USVᴴ
+  return (U, S, Vᴴ)
 end
 
 function MatrixAlgebraKit.svd_full!(
-  A::AbstractBlockSparseMatrix, USVᴴ, alg::BlockPermutedDiagonalAlgorithm
+  A::AbstractBlockSparseMatrix, (U, S, Vᴴ), alg::BlockPermutedDiagonalAlgorithm
 )
-  MatrixAlgebraKit.check_input(svd_full!, A, USVᴴ)
-  U, S, Vt = USVᴴ
+  check_input(svd_full!, A, (U, S, Vᴴ))
 
   # do decomposition on each block
   for bI in eachblockstoredindex(A)
     brow, bcol = Tuple(bI)
-    usvᴴ = (@view!(U[brow, bcol]), @view!(S[bcol, bcol]), @view!(Vt[bcol, bcol]))
+    usvᴴ = (@view!(U[brow, bcol]), @view!(S[bcol, bcol]), @view!(Vᴴ[bcol, bcol]))
     usvᴴ′ = svd_full!(@view!(A[bI]), usvᴴ, alg.alg)
     @assert usvᴴ === usvᴴ′ "svd_full! might not be in-place"
   end
@@ -237,17 +232,17 @@ function MatrixAlgebraKit.svd_full!(
   # Vt[Block(col, col)] = LinearAlgebra.I
   for (row, col) in zip(emptyrows, emptycols)
     copyto!(@view!(U[Block(row, col)]), LinearAlgebra.I)
-    copyto!(@view!(Vt[Block(col, col)]), LinearAlgebra.I)
+    copyto!(@view!(Vᴴ[Block(col, col)]), LinearAlgebra.I)
   end
 
   # also handle extra rows/cols
   for i in (length(emptyrows) + 1):length(emptycols)
-    copyto!(@view!(Vt[Block(emptycols[i], emptycols[i])]), LinearAlgebra.I)
+    copyto!(@view!(Vᴴ[Block(emptycols[i], emptycols[i])]), LinearAlgebra.I)
   end
   bn = blocksize(A, 2)
   for (i, k) in enumerate((length(emptycols) + 1):length(emptyrows))
     copyto!(@view!(U[Block(emptyrows[k], bn + i)]), LinearAlgebra.I)
   end
 
-  return USVᴴ
+  return (U, S, Vᴴ)
 end

src/factorizations/truncation.jl

@@ -1,4 +1,4 @@
-using MatrixAlgebraKit: TruncationStrategy, diagview, svd_trunc!
+using MatrixAlgebraKit: TruncationStrategy, diagview, eig_trunc!, eigh_trunc!, svd_trunc!
 
 function MatrixAlgebraKit.diagview(A::BlockSparseMatrix{T,Diagonal{T,Vector{T}}}) where {T}
   D = BlockSparseVector{T}(undef, axes(A, 1))
@@ -21,18 +21,29 @@ struct BlockPermutedDiagonalTruncationStrategy{T<:TruncationStrategy} <: Truncat
   strategy::T
 end
 
-const TBlockUSVᴴ = Tuple{
-  <:AbstractBlockSparseMatrix,<:AbstractBlockSparseMatrix,<:AbstractBlockSparseMatrix
-}
-
 function MatrixAlgebraKit.truncate!(
-  ::typeof(svd_trunc!), (U, S, Vᴴ)::TBlockUSVᴴ, strategy::TruncationStrategy
+  ::typeof(svd_trunc!),
+  (U, S, Vᴴ)::NTuple{3,AbstractBlockSparseMatrix},
+  strategy::TruncationStrategy,
 )
   # TODO assert blockdiagonal
   return MatrixAlgebraKit.truncate!(
     svd_trunc!, (U, S, Vᴴ), BlockPermutedDiagonalTruncationStrategy(strategy)
   )
 end
+for f in [:eig_trunc!, :eigh_trunc!]
+  @eval begin
+    function MatrixAlgebraKit.truncate!(
+      ::typeof($f),
+      (D, V)::NTuple{2,AbstractBlockSparseMatrix},
+      strategy::TruncationStrategy,
+    )
+      return MatrixAlgebraKit.truncate!(
+        $f, (D, V), BlockPermutedDiagonalTruncationStrategy(strategy)
+      )
+    end
+  end
+end
 
 # cannot use regular slicing here: I want to slice without altering blockstructure
 # solution: use boolean indexing and slice the mask, effectively cheaply inverting the map
@@ -47,9 +58,21 @@ end
 
 function MatrixAlgebraKit.truncate!(
   ::typeof(svd_trunc!),
-  (U, S, Vᴴ)::TBlockUSVᴴ,
+  (U, S, Vᴴ)::NTuple{3,AbstractBlockSparseMatrix},
   strategy::BlockPermutedDiagonalTruncationStrategy,
 )
   I = MatrixAlgebraKit.findtruncated(diagview(S), strategy)
   return (U[:, I], S[I, I], Vᴴ[I, :])
 end
+for f in [:eig_trunc!, :eigh_trunc!]
+  @eval begin
+    function MatrixAlgebraKit.truncate!(
+      ::typeof($f),
+      (D, V)::NTuple{2,AbstractBlockSparseMatrix},
+      strategy::BlockPermutedDiagonalTruncationStrategy,
+    )
+      I = MatrixAlgebraKit.findtruncated(diagview(D), strategy)
+      return (D[I, I], V[:, I])
+    end
+  end
+end

test/Project.toml

@@ -12,6 +12,7 @@ MatrixAlgebraKit = "6c742aac-3347-4629-af66-fc926824e5e4"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
 SparseArraysBase = "0d5efcca-f356-4864-8770-e1ed8d78f208"
+StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
 Suppressor = "fd094767-a336-5f1f-9728-57cf17d0bbfb"
 TensorAlgebra = "68bd88dc-f39d-4e12-b2ca-f046b68fcc6a"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"