Support eigh for CUDA

kshyatt · kshyatt · commit e0c8aa5e2ecc · 2025-08-20T06:40:37.000-04:00
diff --git a/ext/MatrixAlgebraKitCUDAExt/MatrixAlgebraKitCUDAExt.jl b/ext/MatrixAlgebraKitCUDAExt/MatrixAlgebraKitCUDAExt.jl
@@ -5,8 +5,9 @@ using MatrixAlgebraKit: @algdef, Algorithm, check_input
 using MatrixAlgebraKit: one!, zero!, uppertriangular!, lowertriangular!
 using MatrixAlgebraKit: diagview, sign_safe
 using MatrixAlgebraKit: LQViaTransposedQR
-using MatrixAlgebraKit: default_qr_algorithm, default_lq_algorithm, default_svd_algorithm
+using MatrixAlgebraKit: default_qr_algorithm, default_lq_algorithm, default_svd_algorithm, default_eigh_algorithm
 import MatrixAlgebraKit: _gpu_geqrf!, _gpu_ungqr!, _gpu_unmqr!, _gpu_gesvd!, _gpu_Xgesvdp!, _gpu_Xgesvdr!, _gpu_gesvdj!
+import MatrixAlgebraKit: _gpu_heevj!, _gpu_heevd!
 using CUDA
 using LinearAlgebra
 using LinearAlgebra: BlasFloat
@@ -23,6 +24,9 @@ end
 function MatrixAlgebraKit.default_svd_algorithm(::Type{T}; kwargs...) where {T<:StridedCuMatrix}
     return CUSOLVER_QRIteration(; kwargs...)
 end
+function MatrixAlgebraKit.default_eigh_algorithm(::Type{T}; kwargs...) where {T<:StridedCuMatrix}
+    return CUSOLVER_DivideAndConquer(; kwargs...)
+end
 
 
 _gpu_geqrf!(A::StridedCuMatrix) = YACUSOLVER.geqrf!(A)
@@ -33,4 +37,7 @@ _gpu_Xgesvdp!(A::StridedCuMatrix, S::StridedCuVector, U::StridedCuMatrix, Vᴴ::
 _gpu_Xgesvdr!(A::StridedCuMatrix, S::StridedCuVector, U::StridedCuMatrix, Vᴴ::StridedCuMatrix; kwargs...) = YACUSOLVER.Xgesvdr!(A, S, U, Vᴴ; kwargs...) 
 _gpu_gesvdj!(A::StridedCuMatrix, S::StridedCuVector, U::StridedCuMatrix, Vᴴ::StridedCuMatrix; kwargs...) = YACUSOLVER.gesvdj!(A, S, U, Vᴴ; kwargs...)
 
+_gpu_heevj!(A::StridedCuMatrix, Dd::StridedCuVector, V::StridedCuMatrix; kwargs...) = YACUSOLVER.heevj!(A, Dd, V; kwargs...)
+_gpu_heevd!(A::StridedCuMatrix, Dd::StridedCuVector, V::StridedCuMatrix; kwargs...) = YACUSOLVER.heevd!(A, Dd, V; kwargs...)
+
 end
diff --git a/ext/MatrixAlgebraKitCUDAExt/yacusolver.jl b/ext/MatrixAlgebraKitCUDAExt/yacusolver.jl
@@ -1,7 +1,7 @@
 module YACUSOLVER
 
 using LinearAlgebra
-using LinearAlgebra: BlasInt, BlasFloat, checksquare, chkstride1, require_one_based_indexing
+using LinearAlgebra: BlasInt, BlasFloat, BlasReal, checksquare, chkstride1, require_one_based_indexing
 using LinearAlgebra.LAPACK: chkargsok, chklapackerror, chktrans, chkside, chkdiag, chkuplo
 
 using CUDA
@@ -612,42 +612,92 @@ end
 #     return X, info
 # end
 
-# for (jname, bname, fname, elty, relty) in
-#     ((:syevd!, :cusolverDnSsyevd_bufferSize, :cusolverDnSsyevd, :Float32, :Float32),
-#      (:syevd!, :cusolverDnDsyevd_bufferSize, :cusolverDnDsyevd, :Float64, :Float64),
-#      (:heevd!, :cusolverDnCheevd_bufferSize, :cusolverDnCheevd, :ComplexF32, :Float32),
-#      (:heevd!, :cusolverDnZheevd_bufferSize, :cusolverDnZheevd, :ComplexF64, :Float64))
-#     @eval begin
-#         function $jname(jobz::Char,
-#                         uplo::Char,
-#                         A::StridedCuMatrix{$elty})
-#             chkuplo(uplo)
-#             n = checksquare(A)
-#             lda = max(1, stride(A, 2))
-#             W = CuArray{$relty}(undef, n)
-#             dh = dense_handle()
+for (bname, fname, elty, relty) in ((:(CUSOLVER.cusolverDnSsyevj_bufferSize), :(CUSOLVER.cusolverDnSsyevj), :Float32, :Float32),
+                                    (:(CUSOLVER.cusolverDnDsyevj_bufferSize), :(CUSOLVER.cusolverDnDsyevj), :Float64, :Float64),
+                                    (:(CUSOLVER.cusolverDnCheevj_bufferSize), :(CUSOLVER.cusolverDnCheevj), :ComplexF32, :Float32),
+                                    (:(CUSOLVER.cusolverDnZheevj_bufferSize), :(CUSOLVER.cusolverDnZheevj), :ComplexF64, :Float64))
+    @eval begin
+        function heevj!(A::StridedCuMatrix{$elty},
+                        W::StridedCuVector{$relty},
+                        V::StridedCuMatrix{$elty};
+                        uplo::Char='U',
+                        tol::$relty=eps($relty),
+                        max_sweeps::Int=100
+                       )
+            chkuplo(uplo)
+            n   = checksquare(A)
+            lda = max(1, stride(A, 2))
+            dh  = CUSOLVER.dense_handle()
+            length(W) == n || throw(DimensionMismatch("size mismatch between A and W"))
+            if length(V) == 0
+                jobz = 'N'
+            else
+                size(V) == (n, n) || throw(DimensionMismatch("size mismatch between A and V"))
+                jobz = 'V'
+            end
+            params    = Ref{CUSOLVER.syevjInfo_t}(C_NULL)
+            CUSOLVER.cusolverDnCreateSyevjInfo(params)
+            CUSOLVER.cusolverDnXsyevjSetTolerance(params[], tol)
+            CUSOLVER.cusolverDnXsyevjSetMaxSweeps(params[], max_sweeps)
+            function bufferSize()
+                out = Ref{Cint}(0)
+                $bname(dh, jobz, uplo, n, A, lda, W, out, params[])
+                return out[] * sizeof($elty)
+            end
+            CUDA.with_workspace(dh.workspace_gpu, bufferSize) do buffer
+                $fname(dh, jobz, uplo, n, A, lda, W, buffer,
+                       sizeof(buffer) ÷ sizeof($elty), dh.info, params[])
+            end
 
-#             function bufferSize()
-#                 out = Ref{Cint}(0)
-#                 $bname(dh, jobz, uplo, n, A, lda, W, out)
-#                 return out[] * sizeof($elty)
-#             end
+            info = @allowscalar dh.info[1]
+            chkargsok(BlasInt(info))
 
-#             with_workspace(dh.workspace_gpu, bufferSize) do buffer
-#                 return $fname(dh, jobz, uplo, n, A, lda, W,
-#                               buffer, sizeof(buffer) ÷ sizeof($elty), dh.info)
-#             end
+            if jobz == 'V' && V !== A
+                copy!(V, A)
+            end
+            return W, V
+        end
+    end
+end
 
-#             info = @allowscalar dh.info[1]
-#             chkargsok(BlasInt(info))
+function heevd!(A::StridedCuMatrix{T},
+                W::StridedCuVector{Tr},
+                V::StridedCuMatrix{T};
+                uplo::Char='U') where {T<:BlasFloat, Tr<:BlasReal}
+    chkuplo(uplo)
+    n   = checksquare(A)
+    lda = max(1, stride(A, 2))
+    dh  = CUSOLVER.dense_handle()
+    length(W) == n || throw(DimensionMismatch("size mismatch between A and W"))
+    if length(V) == 0
+        jobz = 'N'
+    else
+        size(V) == (n, n) || throw(DimensionMismatch("size mismatch between A and V"))
+        jobz = 'V'
+    end
 
-#             if jobz == 'N'
-#                 return W
-#             elseif jobz == 'V'
-#                 return W, A
-#             end
-#         end
-#     end
-# end
+    params = CUSOLVER.CuSolverParameters()
+    function bufferSize()
+        out_cpu = Ref{Csize_t}(0)
+        out_gpu = Ref{Csize_t}(0)
+        CUSOLVER.cusolverDnXsyevd_bufferSize(dh, params, jobz, uplo, n, T, A, lda, Tr, W, T, out_gpu, out_cpu)
+        return out_gpu[], out_cpu[]
+    end
+
+    CUSOLVER.with_workspaces(dh.workspace_gpu, dh.workspace_cpu,
+                             bufferSize()...) do buffer_gpu, buffer_cpu
+        return CUSOLVER.cusolverDnXsyevd(dh, params, jobz, uplo, n, T, A, lda, Tr, W,
+                                         T, buffer_gpu, sizeof(buffer_gpu), buffer_cpu,
+                                         sizeof(buffer_cpu), dh.info)
+    end
+
+    info = @allowscalar dh.info[1]
+    chkargsok(BlasInt(info))
+
+    if jobz == 'V' && V !== A
+        copy!(V, A)
+    end
+    return W, V
+end
 
 end
diff --git a/src/MatrixAlgebraKit.jl b/src/MatrixAlgebraKit.jl
@@ -33,7 +33,7 @@ export LAPACK_HouseholderQR, LAPACK_HouseholderLQ,
        LAPACK_QRIteration, LAPACK_Bisection, LAPACK_MultipleRelativelyRobustRepresentations,
        LAPACK_DivideAndConquer, LAPACK_Jacobi,
        LQViaTransposedQR,
-       CUSOLVER_HouseholderQR, CUSOLVER_QRIteration, CUSOLVER_SVDPolar, CUSOLVER_Jacobi, CUSOLVER_Randomized,
+       CUSOLVER_HouseholderQR, CUSOLVER_QRIteration, CUSOLVER_SVDPolar, CUSOLVER_Jacobi, CUSOLVER_Randomized, CUSOLVER_DivideAndConquer,
        ROCSOLVER_HouseholderQR, ROCSOLVER_QRIteration, ROCSOLVER_Jacobi
 export truncrank, trunctol, truncabove, TruncationKeepSorted, TruncationKeepFiltered
 
diff --git a/src/implementations/eigh.jl b/src/implementations/eigh.jl
@@ -61,11 +61,7 @@ function eigh_full!(A::AbstractMatrix, DV, alg::LAPACK_EighAlgorithm)
         YALAPACK.heevx!(A, Dd, V; alg.kwargs...)
     end
     # TODO: make this controllable using a `gaugefix` keyword argument
-    for j in 1:size(V, 2)
-        v = view(V, :, j)
-        s = conj(sign(argmax(abs, v)))
-        v .*= s
-    end
+    V = gaugefix!(V)
     return D, V
 end
 
@@ -88,3 +84,45 @@ function eigh_trunc!(A::AbstractMatrix, DV, alg::TruncatedAlgorithm)
     D, V = eigh_full!(A, DV, alg.alg)
     return truncate!(eigh_trunc!, (D, V), alg.trunc)
 end
+
+_gpu_heevj!(A::AbstractMatrix, Dd::AbstractVector, V::AbstractMatrix; kwargs...) = throw(MethodError(_gpu_heevj!, (A, Dd, V)))
+_gpu_heevd!(A::AbstractMatrix, Dd::AbstractVector, V::AbstractMatrix; kwargs...) = throw(MethodError(_gpu_heevd!, (A, Dd, V)))
+_gpu_heev!(A::AbstractMatrix, Dd::AbstractVector, V::AbstractMatrix; kwargs...) = throw(MethodError(_gpu_heev!, (A, Dd, V)))
+_gpu_heevx!(A::AbstractMatrix, Dd::AbstractVector, V::AbstractMatrix; kwargs...) = throw(MethodError(_gpu_heevx!, (A, Dd, V)))
+
+function eigh_full!(A::AbstractMatrix, DV, alg::GPU_EighAlgorithm)
+    check_input(eigh_full!, A, DV, alg)
+    D, V = DV
+    Dd = D.diag
+    if alg isa GPU_Jacobi 
+        _gpu_heevj!(A, Dd, V; alg.kwargs...)
+    elseif alg isa GPU_DivideAndConquer
+        _gpu_heevd!(A, Dd, V; alg.kwargs...)
+    elseif alg isa GPU_QRIteration # alg isa GPU_QRIteration == GPU_Simple
+        _gpu_heev!(A, Dd, V; alg.kwargs...)
+    elseif alg isa GPU_Bisection # alg isa GPU_Bisection == GPU_Expert
+        _gpu_heevx!(A, Dd, V; alg.kwargs...)
+    else
+        throw(ArgumentError("Unsupported eigh algorithm"))
+    end
+    # TODO: make this controllable using a `gaugefix` keyword argument
+    V = gaugefix!(V)
+    return D, V
+end
+
+function eigh_vals!(A::AbstractMatrix, D, alg::GPU_EighAlgorithm)
+    check_input(eigh_vals!, A, D, alg)
+    V = similar(A, (size(A, 1), 0))
+    if alg isa GPU_Jacobi 
+        _gpu_heevj!(A, D, V; alg.kwargs...)
+    elseif alg isa GPU_DivideAndConquer
+        _gpu_heevd!(A, D, V; alg.kwargs...)
+    elseif alg isa GPU_QRIteration
+        _gpu_heev!(A, D, V; alg.kwargs...)
+    elseif alg isa GPU_Bisection
+        _gpu_heevx!(A, D, V; alg.kwargs...)
+    else
+        throw(ArgumentError("Unsupported eigh algorithm"))
+    end
+    return D
+end
diff --git a/src/implementations/svd.jl b/src/implementations/svd.jl
@@ -215,9 +215,7 @@ const ROCSOLVER_SVDAlgorithm = Union{ROCSOLVER_QRIteration,
                                      ROCSOLVER_Jacobi}
 const GPU_SVDAlgorithm = Union{CUSOLVER_SVDAlgorithm, ROCSOLVER_SVDAlgorithm}
 
-const GPU_QRIteration = Union{CUSOLVER_QRIteration, ROCSOLVER_QRIteration}
 const GPU_SVDPolar = Union{CUSOLVER_SVDPolar}
-const GPU_Jacobi = Union{CUSOLVER_Jacobi, ROCSOLVER_Jacobi}
 const GPU_Randomized = Union{CUSOLVER_Randomized}
 
 function check_input(::typeof(svd_trunc!), A::AbstractMatrix, USVᴴ, alg::CUSOLVER_Randomized)
diff --git a/src/interface/decompositions.jl b/src/interface/decompositions.jl
@@ -164,6 +164,15 @@ a general matrix using the randomized SVD algorithm.
 """
 @algdef CUSOLVER_Randomized
 
+"""
+    CUSOLVER_DivideAndConquer()
+
+Algorithm type to denote the CUSOLVER driver for computing the eigenvalue decomposition of a
+Hermitian matrix, or the singular value decomposition of a general matrix using the
+Divide and Conquer algorithm.
+"""
+@algdef CUSOLVER_DivideAndConquer
+
 # =========================
 # ROCSOLVER ALGORITHMS
 # =========================
@@ -192,3 +201,32 @@ Algorithm type to denote the ROCSOLVER driver for computing the singular value d
 a general matrix using the Jacobi algorithm.
 """
 @algdef ROCSOLVER_Jacobi
+
+"""
+    ROCSOLVER_Bisection()
+
+Algorithm type to denote the ROCSOLVER driver for computing the eigenvalue decomposition of a
+Hermitian matrix, or the singular value decomposition of a general matrix using the
+Bisection algorithm.
+"""
+@algdef ROCSOLVER_Bisection
+
+"""
+    ROCSOLVER_DivideAndConquer()
+
+Algorithm type to denote the ROCSOLVER driver for computing the eigenvalue decomposition of a
+Hermitian matrix, or the singular value decomposition of a general matrix using the
+Divide and Conquer algorithm.
+"""
+@algdef ROCSOLVER_DivideAndConquer
+
+
+const GPU_QRIteration = Union{CUSOLVER_QRIteration, ROCSOLVER_QRIteration}
+const GPU_Jacobi = Union{CUSOLVER_Jacobi, ROCSOLVER_Jacobi}
+const GPU_DivideAndConquer = Union{CUSOLVER_DivideAndConquer, ROCSOLVER_DivideAndConquer}
+const GPU_Bisection = Union{ROCSOLVER_Bisection}
+const GPU_EighAlgorithm = Union{GPU_QRIteration,
+                                GPU_Jacobi,
+                                GPU_DivideAndConquer,
+                                GPU_Bisection}
+
diff --git a/test/cuda/eigh.jl b/test/cuda/eigh.jl
@@ -0,0 +1,78 @@
+using MatrixAlgebraKit
+using Test
+using TestExtras
+using StableRNGs
+using LinearAlgebra: LinearAlgebra, Diagonal, I
+using MatrixAlgebraKit: TruncatedAlgorithm, diagview
+using CUDA
+
+@testset "eigh_full! for T = $T" for T in (Float32, Float64, ComplexF32, ComplexF64)
+    rng = StableRNG(123)
+    m = 54
+    for alg in (CUSOLVER_DivideAndConquer(),
+                CUSOLVER_Jacobi(),
+                )
+        A = CuArray(randn(rng, T, m, m))
+        A = (A + A') / 2
+
+        D, V = @constinferred eigh_full(A; alg)
+        @test A * V ≈ V * D
+        @test isunitary(V)
+        @test all(isreal, D)
+
+        D2, V2 = eigh_full!(copy(A), (D, V), alg)
+        @test D2 === D
+        @test V2 === V
+
+        D3 = @constinferred eigh_vals(A, alg)
+        @test parent(D) ≈ D3
+    end
+end
+
+#=@testset "eigh_trunc! for T = $T" for T in (Float32, Float64, ComplexF32, ComplexF64)
+    rng = StableRNG(123)
+    m = 54
+    for alg in (CUSOLVER_QRIteration(),
+                CUSOLVER_DivideAndConquer(),
+                )
+        A = CuArray(randn(rng, T, m, m))
+        A = A * A'
+        A = (A + A') / 2
+        Ac = similar(A)
+        D₀ = reverse(eigh_vals(A))
+        r = m - 2
+        s = 1 + sqrt(eps(real(T)))
+
+        D1, V1 = @constinferred eigh_trunc(A; alg, trunc=truncrank(r))
+        @test length(diagview(D1)) == r
+        @test isisometry(V1)
+        @test A * V1 ≈ V1 * D1
+        @test LinearAlgebra.opnorm(A - V1 * D1 * V1') ≈ D₀[r + 1]
+
+        trunc = trunctol(s * D₀[r + 1])
+        D2, V2 = @constinferred eigh_trunc(A; alg, trunc)
+        @test length(diagview(D2)) == r
+        @test isisometry(V2)
+        @test A * V2 ≈ V2 * D2
+
+        # test for same subspace
+        @test V1 * (V1' * V2) ≈ V2
+        @test V2 * (V2' * V1) ≈ V1
+    end
+end
+
+@testset "eigh_trunc! specify truncation algorithm T = $T" for T in
+                                                               (Float32, Float64,
+                                                                ComplexF32,
+                                                                ComplexF64)
+    rng = StableRNG(123)
+    m = 4
+    V = qr_compact(CuArray(randn(rng, T, m, m)))[1]
+    D = Diagonal([0.9, 0.3, 0.1, 0.01])
+    A = V * D * V'
+    A = (A + A') / 2
+    alg = TruncatedAlgorithm(CUSOLVER_QRIteration(), truncrank(2))
+    D2, V2 = @constinferred eigh_trunc(A; alg)
+    @test diagview(D2) ≈ diagview(D)[1:2] rtol = sqrt(eps(real(T)))
+    @test_throws ArgumentError eigh_trunc(A; alg, trunc=(; maxrank=2))
+end=#
diff --git a/test/runtests.jl b/test/runtests.jl
@@ -63,6 +63,9 @@ if CUDA.functional()
     @safetestset "CUDA SVD" begin
         include("cuda/svd.jl")
     end
+    @safetestset "CUDA Hermitian Eigenvalue Decomposition" begin
+        include("cuda/eigh.jl")
+    end
 end
 
 using AMDGPU 
