Add optional epsilon vector and keyword arg for error

src/implementations/svd.jl

@@ -206,10 +206,36 @@ function svd_vals!(A::AbstractMatrix, S, alg::LAPACK_SVDAlgorithm)
     return S
 end
 
-function svd_trunc!(A, USVᴴ, alg::TruncatedAlgorithm)
+# nothing case here to handle GenericLinearAlgebra
+function svd_trunc!(A, USVᴴϵ::Tuple{TU, TS, TVᴴ, Tϵ}, alg::TruncatedAlgorithm) where {TU, TS, TVᴴ, Tϵ}
+    U, S, Vᴴ, ϵ = USVᴴϵ
+    U, S, Vᴴ = svd_compact!(A, (U, S, Vᴴ), alg.alg)
+    USVᴴtrunc, ind = truncate(svd_trunc!, (U, S, Vᴴ), alg.trunc)
+    if !isempty(ϵ)
+        ϵ[1] = truncation_error!(diagview(S), ind)
+    end
+    return USVᴴtrunc..., ϵ
+end
+function svd_trunc!(A, USVᴴϵ::Tuple{Nothing, Tϵ}, alg::TruncatedAlgorithm) where {Tϵ}
+    USVᴴ, ϵ = USVᴴϵ
     U, S, Vᴴ = svd_compact!(A, USVᴴ, alg.alg)
     USVᴴtrunc, ind = truncate(svd_trunc!, (U, S, Vᴴ), alg.trunc)
-    return USVᴴtrunc..., truncation_error!(diagview(S), ind)
+    if !isempty(ϵ)
+        ϵ[1] = truncation_error!(diagview(S), ind)
+    end
+    return USVᴴtrunc..., ϵ
+end
+
+function svd_trunc!(A, USVᴴ::Tuple{TU, TS, TVᴴ}, alg::TruncatedAlgorithm; compute_error::Bool = true) where {TU, TS, TVᴴ}
+    ϵ = similar(S, compute_error)
+    (U, S, Vᴴ, ϵ) = svd_trunc!(A, (USVᴴ..., ϵ), alg)
+    return compute_error ? (U, S, Vᴴ, ϵ[1]) : (U, S, Vᴴ, -one(eltype(ϵ)))
+end
+function svd_trunc!(A, USVᴴ::Nothing, alg::TruncatedAlgorithm; compute_error::Bool = true)
+    Tr = real(eltype(A))
+    ϵ = compute_error ? zeros(Tr, 1) : zeros(Tr, 0)
+    U, S, Vᴴ, ϵ = svd_trunc!(A, (USVᴴ, ϵ), alg)
+    return compute_error ? (U, S, Vᴴ, ϵ[1]::Tr) : (U, S, Vᴴ, -one(Tr))
 end
 
 # Diagonal logic
@@ -362,16 +388,18 @@ function svd_full!(A::AbstractMatrix, USVᴴ, alg::GPU_SVDAlgorithm)
     return USVᴴ
 end
 
-function svd_trunc!(A::AbstractMatrix, USVᴴ, alg::TruncatedAlgorithm{<:GPU_Randomized})
-    check_input(svd_trunc!, A, USVᴴ, alg.alg)
-    U, S, Vᴴ = USVᴴ
+function svd_trunc!(A::AbstractMatrix, USVᴴϵ::Tuple{TU, TS, TVᴴ, Tϵ}, alg::TruncatedAlgorithm{<:GPU_Randomized}) where {TU, TS, TVᴴ, Tϵ}
+    U, S, Vᴴ, ϵ = USVᴴϵ
+    check_input(svd_trunc!, A, (U, S, Vᴴ), alg.alg)
     _gpu_Xgesvdr!(A, S.diag, U, Vᴴ; alg.alg.kwargs...)
 
     # TODO: make sure that truncation is based on maxrank, otherwise this might be wrong
     (Utr, Str, Vᴴtr), _ = truncate(svd_trunc!, (U, S, Vᴴ), alg.trunc)
 
-    # normal `truncation_error!` does not work here since `S` is not the full singular value spectrum
-    ϵ = sqrt(norm(A)^2 - norm(diagview(Str))^2) # is there a more accurate way to do this?
+    if !isempty(ϵ)
+        # normal `truncation_error!` does not work here since `S` is not the full singular value spectrum
+        ϵ = sqrt(norm(A)^2 - norm(diagview(Str))^2) # is there a more accurate way to do this?
+    end
 
     do_gauge_fix = get(alg.alg.kwargs, :fixgauge, default_fixgauge())::Bool
     do_gauge_fix && gaugefix!(svd_trunc!, Utr, Vᴴtr)

test/runtests.jl

@@ -56,6 +56,23 @@ if !is_buildkite
             JET.test_package(MatrixAlgebraKit; target_defined_modules = true)
         end
     end
+
+    using GenericLinearAlgebra
+    @safetestset "QR / LQ Decomposition" begin
+        include("genericlinearalgebra/qr.jl")
+        include("genericlinearalgebra/lq.jl")
+    end
+    @safetestset "Singular Value Decomposition" begin
+        include("genericlinearalgebra/svd.jl")
+    end
+    @safetestset "Hermitian Eigenvalue Decomposition" begin
+        include("genericlinearalgebra/eigh.jl")
+    end
+
+    using GenericSchur
+    @safetestset "General Eigenvalue Decomposition" begin
+        include("genericschur/eig.jl")
+    end
 end
 
 using CUDA
@@ -110,20 +127,3 @@ if AMDGPU.functional()
         include("amd/orthnull.jl")
     end
 end
-
-using GenericLinearAlgebra
-@safetestset "QR / LQ Decomposition" begin
-    include("genericlinearalgebra/qr.jl")
-    include("genericlinearalgebra/lq.jl")
-end
-@safetestset "Singular Value Decomposition" begin
-    include("genericlinearalgebra/svd.jl")
-end
-@safetestset "Hermitian Eigenvalue Decomposition" begin
-    include("genericlinearalgebra/eigh.jl")
-end
-
-using GenericSchur
-@safetestset "General Eigenvalue Decomposition" begin
-    include("genericschur/eig.jl")
-end