relax truncation error tolerances

Author: lkdvos

test/eig.jl

@@ -42,25 +42,26 @@ end
         D₀ = sort!(eig_vals(A); by = abs, rev = true)
         rmin = findfirst(i -> abs(D₀[end - i]) != abs(D₀[end - i - 1]), 1:(m - 2))
         r = length(D₀) - rmin
+        atol = sqrt(eps(real(T)))
 
         D1, V1, ϵ1 = @constinferred eig_trunc(A; alg, trunc = truncrank(r))
         @test length(D1.diag) == r
         @test A * V1 ≈ V1 * D1
-        @test ϵ1 ≈ norm(view(D₀, (r + 1):m))
+        @test ϵ1 ≈ norm(view(D₀, (r + 1):m)) atol = atol
 
         s = 1 + sqrt(eps(real(T)))
         trunc = trunctol(; atol = s * abs(D₀[r + 1]))
         D2, V2, ϵ2 = @constinferred eig_trunc(A; alg, trunc)
         @test length(diagview(D2)) == r
         @test A * V2 ≈ V2 * D2
-        @test ϵ2 ≈ norm(view(D₀, (r + 1):m))
+        @test ϵ2 ≈ norm(view(D₀, (r + 1):m)) atol = atol
 
         s = 1 - sqrt(eps(real(T)))
         trunc = truncerror(; atol = s * norm(@view(D₀[r:end]), 1), p = 1)
         D3, V3, ϵ3 = @constinferred eig_trunc(A; alg, trunc)
         @test length(diagview(D3)) == r
         @test A * V3 ≈ V3 * D3
-        @test ϵ3 ≈ norm(view(D₀, (r + 1):m))
+        @test ϵ3 ≈ norm(view(D₀, (r + 1):m)) atol = atol
 
         # trunctol keeps order, truncrank might not
         # test for same subspace
@@ -74,26 +75,28 @@ end
 @testset "eig_trunc! specify truncation algorithm T = $T" for T in BLASFloats
     rng = StableRNG(123)
     m = 4
+    atol = sqrt(eps(real(T)))
     V = randn(rng, T, m, m)
     D = Diagonal(real(T)[0.9, 0.3, 0.1, 0.01])
     A = V * D * inv(V)
     alg = TruncatedAlgorithm(LAPACK_Simple(), truncrank(2))
     D2, V2, ϵ2 = @constinferred eig_trunc(A; alg)
     @test diagview(D2) ≈ diagview(D)[1:2] rtol = sqrt(eps(real(T)))
-    @test ϵ2 ≈ norm(diagview(D)[3:4])
+    @test ϵ2 ≈ norm(diagview(D)[3:4]) atol = atol
     @test_throws ArgumentError eig_trunc(A; alg, trunc = (; maxrank = 2))
 
     alg = TruncatedAlgorithm(LAPACK_Simple(), truncerror(; atol = 0.2, p = 1))
     D3, V3, ϵ3 = @constinferred eig_trunc(A; alg)
     @test diagview(D3) ≈ diagview(D)[1:2] rtol = sqrt(eps(real(T)))
-    @test ϵ3 ≈ norm(diagview(D)[3:4])
+    @test ϵ3 ≈ norm(diagview(D)[3:4]) atol = atol
 end
 
 @testset "eig for Diagonal{$T}" for T in BLASFloats
     rng = StableRNG(123)
     m = 54
     Ad = randn(rng, T, m)
     A = Diagonal(Ad)
+    atol = sqrt(eps(real(T)))
 
     D, V = @constinferred eig_full(A)
     @test D isa Diagonal{T} && size(D) == size(A)
@@ -108,5 +111,5 @@ end
     alg = TruncatedAlgorithm(DiagonalAlgorithm(), truncrank(2))
     D2, V2, ϵ2 = @constinferred eig_trunc(A2; alg)
     @test diagview(D2) ≈ diagview(A2)[1:2]
-    @test ϵ2 ≈ norm(diagview(A2)[3:4])
+    @test ϵ2 ≈ norm(diagview(A2)[3:4]) atol = atol
 end

test/eigh.jl

@@ -49,27 +49,28 @@ end
         D₀ = reverse(eigh_vals(A))
         r = m - 2
         s = 1 + sqrt(eps(real(T)))
+        atol = sqrt(eps(real(T)))
 
         D1, V1, ϵ1 = @constinferred eigh_trunc(A; alg, trunc = truncrank(r))
         @test length(diagview(D1)) == r
         @test isisometric(V1)
         @test A * V1 ≈ V1 * D1
         @test LinearAlgebra.opnorm(A - V1 * D1 * V1') ≈ D₀[r + 1]
-        @test ϵ1 ≈ norm(view(D₀, (r + 1):m))
+        @test ϵ1 ≈ norm(view(D₀, (r + 1):m)) atol = atol
 
         trunc = trunctol(; atol = s * D₀[r + 1])
         D2, V2, ϵ2 = @constinferred eigh_trunc(A; alg, trunc)
         @test length(diagview(D2)) == r
         @test isisometric(V2)
         @test A * V2 ≈ V2 * D2
-        @test ϵ2 ≈ norm(view(D₀, (r + 1):m))
+        @test ϵ2 ≈ norm(view(D₀, (r + 1):m)) atol = atol
 
         s = 1 - sqrt(eps(real(T)))
         trunc = truncerror(; atol = s * norm(@view(D₀[r:end]), 1), p = 1)
         D3, V3, ϵ3 = @constinferred eigh_trunc(A; alg, trunc)
         @test length(diagview(D3)) == r
         @test A * V3 ≈ V3 * D3
-        @test ϵ3 ≈ norm(view(D₀, (r + 1):m))
+        @test ϵ3 ≈ norm(view(D₀, (r + 1):m)) atol = atol
 
         # test for same subspace
         @test V1 * (V1' * V2) ≈ V2
@@ -82,6 +83,7 @@ end
 @testset "eigh_trunc! specify truncation algorithm T = $T" for T in BLASFloats
     rng = StableRNG(123)
     m = 4
+    atol = sqrt(eps(real(T)))
     V = qr_compact(randn(rng, T, m, m))[1]
     D = Diagonal(real(T)[0.9, 0.3, 0.1, 0.01])
     A = V * D * V'
@@ -90,12 +92,12 @@ end
     D2, V2, ϵ2 = @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))
-    @test ϵ2 ≈ norm(diagview(D)[3:4])
+    @test ϵ2 ≈ norm(diagview(D)[3:4]) atol = atol
 
     alg = TruncatedAlgorithm(LAPACK_QRIteration(), truncerror(; atol = 0.2))
     D3, V3, ϵ3 = @constinferred eigh_trunc(A; alg)
     @test diagview(D3) ≈ diagview(D)[1:2] rtol = sqrt(eps(real(T)))
-    @test ϵ3 ≈ norm(diagview(D)[3:4])
+    @test ϵ3 ≈ norm(diagview(D)[3:4]) atol = atol
 end
 
 @testset "eigh for Diagonal{$T}" for T in BLASFloats
@@ -104,6 +106,7 @@ end
     Ad = randn(rng, T, m)
     Ad .+= conj.(Ad)
     A = Diagonal(Ad)
+    atol = sqrt(eps(real(T)))
 
     D, V = @constinferred eigh_full(A)
     @test D isa Diagonal{real(T)} && size(D) == size(A)
@@ -118,5 +121,5 @@ end
     alg = TruncatedAlgorithm(DiagonalAlgorithm(), truncrank(2))
     D2, V2, ϵ2 = @constinferred eigh_trunc(A2; alg)
     @test diagview(D2) ≈ diagview(A2)[1:2]
-    @test ϵ2 ≈ norm(diagview(A2)[3:4])
+    @test ϵ2 ≈ norm(diagview(A2)[3:4]) atol = atol
 end

test/svd.jl

@@ -97,6 +97,7 @@ end
 @testset "svd_trunc! for T = $T" for T in BLASFloats
     rng = StableRNG(123)
     m = 54
+    atol = sqrt(eps(real(T)))
     if LinearAlgebra.LAPACK.version() < v"3.12.0"
         algs = (LAPACK_DivideAndConquer(), LAPACK_QRIteration(), LAPACK_Bisection())
     else
@@ -117,7 +118,7 @@ end
             @test length(S1.diag) == r
             @test LinearAlgebra.opnorm(A - U1 * S1 * V1ᴴ) ≈ S₀[r + 1]
             # Test truncation error
-            @test ϵ1 ≈ norm(view(S₀, (r + 1):minmn))
+            @test ϵ1 ≈ norm(view(S₀, (r + 1):minmn)) atol = atol
 
             s = 1 + sqrt(eps(real(T)))
             trunc = trunctol(; atol = s * S₀[r + 1])
@@ -187,6 +188,7 @@ end
 
 @testset "svd for Diagonal{$T}" for T in BLASFloats
     rng = StableRNG(123)
+    atol = sqrt(eps(real(T)))
     for m in (54, 0)
         Ad = randn(T, m)
         A = Diagonal(Ad)
@@ -216,6 +218,6 @@ end
         alg = TruncatedAlgorithm(DiagonalAlgorithm(), truncrank(2))
         U3, S3, Vᴴ3, ϵ3 = @constinferred svd_trunc(A; alg)
         @test diagview(S3) ≈ S2[1:min(m, 2)]
-        @test ϵ3 ≈ norm(S2[(min(m, 2) + 1):m])
+        @test ϵ3 ≈ norm(S2[(min(m, 2) + 1):m]) atol = atol
     end
 end