Interim progress for polar/orthnull

Author: kshyatt

Project.toml

@@ -47,5 +47,5 @@ Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 test = ["Aqua", "JET", "SafeTestsets", "Test", "TestExtras","ChainRulesCore", "ChainRulesTestUtils", "StableRNGs", "Zygote", "CUDA", "AMDGPU"]
 
 [sources]
-CUDA = {url = "https://github.com/JuliaGPU/CUDA.jl", rev = "master"}
+CUDA = {path = "/home/kshyatt/.julia/dev/CUDA"}
 AMDGPU = {url = "https://github.com/JuliaGPU/AMDGPU.jl", rev = "master"}

test/cuda/orthnull.jl

@@ -66,7 +66,7 @@ end
         @test isisometry(V)
         @test LinearAlgebra.norm(A' * N) ≈ 0 atol = MatrixAlgebraKit.defaulttol(T)
         @test isisometry(N)
-        @test V * V' + N * N' ≈ I
+        @test V * V' + N * N' ≈ I atol = 100 * MatrixAlgebraKit.defaulttol(T)
 
         M = LinearMap(A)
         VM, CM = @constinferred left_orth(M; kind=:svd)
@@ -96,7 +96,7 @@ end
             @test isisometry(V)
             @test LinearAlgebra.norm(A' * N) ≈ 0 atol = MatrixAlgebraKit.defaulttol(T)
             @test isisometry(N)
-            @test V * V' + N * N' ≈ I
+            @test V * V' + N * N' ≈ I atol = MatrixAlgebraKit.defaulttol(T)
         end
 
         Ac = similar(A)
@@ -109,7 +109,7 @@ end
         @test isisometry(V2)
         @test LinearAlgebra.norm(A' * N2) ≈ 0 atol = MatrixAlgebraKit.defaulttol(T)
         @test isisometry(N2)
-        @test V2 * V2' + N2 * N2' ≈ I
+        @test V2 * V2' + N2 * N2' ≈ I atol = MatrixAlgebraKit.defaulttol(T)
 
         atol = eps(real(T))
         #V2, C2 = @constinferred left_orth!(copy!(Ac, A), (V, C); trunc=(; atol=atol))
@@ -150,7 +150,7 @@ end
                 @test N2 === N
                 @test LinearAlgebra.norm(A' * N2) ≈ 0 atol = MatrixAlgebraKit.defaulttol(T)
                 @test isisometry(N2)
-                @test V2 * V2' + N2 * N2' ≈ I
+                @test V2 * V2' + N2 * N2' ≈ I atol = MatrixAlgebraKit.defaulttol(T)
             end
 
             # with kind and tol kwargs
@@ -165,7 +165,7 @@ end
                 #@test V2 * C2 ≈ A
                 #@test V2' * V2 ≈ I
                 @test LinearAlgebra.norm(A' * N2) ≈ 0 atol = MatrixAlgebraKit.defaulttol(T)
-                @test N2' * N2 ≈ I
+                @test isisometry(N2)
                 #@test V2 * V2' + N2 * N2' ≈ I
 
                 #V2, C2 = @constinferred left_orth!(copy!(Ac, A), (V, C); kind=kind,
@@ -210,7 +210,7 @@ end
         @test isisometry(Vᴴ; side=:right)
         @test LinearAlgebra.norm(A * adjoint(Nᴴ)) ≈ 0 atol = MatrixAlgebraKit.defaulttol(T)
         @test isisometry(Nᴴ; side=:right)
-        @test Vᴴ' * Vᴴ + Nᴴ' * Nᴴ ≈ I
+        @test Vᴴ' * Vᴴ + Nᴴ' * Nᴴ ≈ I atol = MatrixAlgebraKit.defaulttol(T)
 
         M = LinearMap(A)
         CM, VMᴴ = @constinferred right_orth(M; kind=:svd)
@@ -259,15 +259,14 @@ end
             C2, Vᴴ2 = @constinferred right_orth!(copy!(Ac, A), (C, Vᴴ); kind=kind)
             @test C2 === C
             @test Vᴴ2 === Vᴴ
-            A2 = C2 * Vᴴ2
-            @test A2 ≈ A
+            @test C2 * Vᴴ2 ≈ A
             @test isisometry(Vᴴ2; side=:right)
             if kind != :polar
                 Nᴴ2 = @constinferred right_null!(copy!(Ac, A), Nᴴ; kind=kind)
                 @test Nᴴ2 === Nᴴ
                 @test LinearAlgebra.norm(A * adjoint(Nᴴ2)) ≈ 0 atol = MatrixAlgebraKit.defaulttol(T)
                 @test isisometry(Nᴴ2; side=:right)
-                @test Vᴴ2' * Vᴴ2 + Nᴴ2' * Nᴴ2 ≈ I
+                @test Vᴴ2' * Vᴴ2 + Nᴴ2' * Nᴴ2 ≈ I atol = 100 * MatrixAlgebraKit.defaulttol(T)
             end
 
             if kind == :svd