add tolerances

Author: lkdvos

test/testsuite/TestSuite.jl

@@ -30,6 +30,9 @@ testargs_summary(args...) = string(args)
 instantiate_matrix(::Type{T}, size) where {T <: Number} = randn(T, size)
 instantiate_matrix(::Type{AT}, size) where {AT <: Array} = randn(eltype(AT), size)
 
+precision(::Type{T}) where {T <: Number} = sqrt(eps(real(T)))
+precision(::Type{T}) where {T} = precision(eltype(T))
+
 function has_positive_diagonal(A)
     T = eltype(A)
     return if T <: Real
@@ -39,7 +42,8 @@ function has_positive_diagonal(A)
             all(≈(zero(real(T))), imag(diagview(A)))
     end
 end
-isleftnull(N, A; kwargs...) = isapprox(norm(N' * A), 0; kwargs...)
+isleftnull(N, A; atol::Real = 0, rtol::Real = precision(eltype(A))) =
+    isapprox(norm(A' * N), 0; atol = max(atol, norm(A) * rtol))
 
 # TODO: actually make this a test
 macro testinferred(ex)

test/testsuite/qr.jl

@@ -1,4 +1,4 @@
-function test_qr(::Type{T}, sz; kwargs...) where {T}
+function test_qr(T::Type, sz; kwargs...)
     summary_str = testargs_summary(T, sz)
     return @testset "qr $summary_str" begin
         test_qr_compact(T, sz; kwargs...)
@@ -8,9 +8,11 @@ function test_qr(::Type{T}, sz; kwargs...) where {T}
 end
 
 function test_qr_compact(
-        ::Type{T}, sz;
-        test_positive = true, test_pivoted = true, test_blocksize = true, kwargs...
-    ) where {T <: Number}
+        T::Type, sz;
+        test_positive = true, test_pivoted = true, test_blocksize = true,
+        atol::Real = 0, rtol::Real = precision(T),
+        kwargs...
+    )
     summary_str = testargs_summary(T, sz)
     return @testset "qr_compact! $summary_str" begin
         A = instantiate_matrix(T, sz)
@@ -19,21 +21,21 @@ function test_qr_compact(
         # does the elementary functionality work
         Q, R = @testinferred qr_compact(A)
         @test Q * R ≈ A
-        @test isisometric(Q)
+        @test isisometric(Q; atol, rtol)
         @test istriu(R)
         @test A == Ac
 
         # can I pass in outputs?
         Q2, R2 = @testinferred qr_compact!(deepcopy(A), (Q, R))
         @test Q2 * R2 ≈ A
-        @test isisometric(Q2)
+        @test isisometric(Q2; atol, rtol)
         @test istriu(R2)
 
         # do we support `positive = true`?
         if test_positive
             Qpos, Rpos = @testinferred qr_compact(A; positive = true)
             @test Qpos * Rpos ≈ A
-            @test isisometric(Qpos)
+            @test isisometric(Qpos; atol, rtol)
             @test istriu(Rpos)
             @test has_positive_diagonal(Rpos)
         else
@@ -44,7 +46,7 @@ function test_qr_compact(
         if test_pivoted
             Qpiv, Rpiv = @testinferred qr_compact(A; pivoted = true)
             @test Qpiv * Rpiv ≈ A
-            @test isisometric(Qpos)
+            @test isisometric(Qpos; atol, rtol)
         else
             @test_throws ArgumentError qr_compact(A; pivoted = true)
         end
@@ -53,17 +55,19 @@ function test_qr_compact(
         if test_blocksize
             Qblocked, Rblocked = @testinferred qr_compact(A; blocksize = 2)
             @test Qblocked * Rblocked ≈ A
-            @test isisometric(Qblocked)
+            @test isisometric(Qblocked; atol, rtol)
         else
             @test_throws ArgumentError qr_compact(A; blocksize = 2)
         end
     end
 end
 
 function test_qr_full(
-        ::Type{T}, sz;
-        test_positive = true, test_pivoted = true, test_blocksize = true, kwargs...
-    ) where {T <: Number}
+        T::Type, sz;
+        test_positive = true, test_pivoted = true, test_blocksize = true,
+        atol::Real = 0, rtol::Real = precision(T),
+        kwargs...
+    )
     summary_str = testargs_summary(T, sz)
     return @testset "qr_full! $summary_str" begin
         A = instantiate_matrix(T, sz)
@@ -72,21 +76,21 @@ function test_qr_full(
         # does the elementary functionality work
         Q, R = @testinferred qr_full(A)
         @test Q * R ≈ A
-        @test isunitary(Q)
+        @test isunitary(Q; atol, rtol)
         @test istriu(R)
         @test A == Ac
 
         # can I pass in outputs?
         Q2, R2 = @testinferred qr_full!(deepcopy(A), (Q, R))
         @test Q2 * R2 ≈ A
-        @test isunitary(Q2)
+        @test isunitary(Q2; atol, rtol)
         @test istriu(R2)
 
         # do we support `positive = true`?
         if test_positive
             Qpos, Rpos = @testinferred qr_full(A; positive = true)
             @test Qpos * Rpos ≈ A
-            @test isunitary(Qpos)
+            @test isunitary(Qpos; atol, rtol)
             @test istriu(Rpos)
             @test has_positive_diagonal(Rpos)
         else
@@ -97,7 +101,7 @@ function test_qr_full(
         if test_pivoted
             Qpiv, Rpiv = @testinferred qr_full(A; pivoted = true)
             @test Qpiv * Rpiv ≈ A
-            @test isunitary(Qpos)
+            @test isunitary(Qpos; atol, rtol)
         else
             @test_throws ArgumentError qr_full(A; pivoted = true)
         end
@@ -106,47 +110,49 @@ function test_qr_full(
         if test_blocksize
             Qblocked, Rblocked = @testinferred qr_full(A; blocksize = 2)
             @test Qblocked * Rblocked ≈ A
-            @test isunitary(Qblocked)
+            @test isunitary(Qblocked; atol, rtol)
         else
             @test_throws ArgumentError qr_full(A; blocksize = 2)
         end
     end
 end
 
 function test_qr_null(
-        ::Type{T}, sz;
-        test_pivoted = true, test_blocksize = true, kwargs...
-    ) where {T <: Number}
+        T::Type, sz;
+        test_pivoted = true, test_blocksize = true,
+        atol::Real = 0, rtol::Real = precision(T),
+        kwargs...
+    )
     summary_str = testargs_summary(T, sz)
     return @testset "qr_null! $summary_str" begin
         A = instantiate_matrix(T, sz)
         Ac = deepcopy(A)
 
         # does the elementary functionality work
         N = @testinferred qr_null(A)
-        @test isleftnull(N, A)
-        @test isisometric(N)
+        @test isleftnull(N, A; atol, rtol)
+        @test isisometric(N; atol, rtol)
         @test A == Ac
 
         # can I pass in outputs?
         N2 = @testinferred qr_null!(deepcopy(A), N)
-        @test isleftnull(N2, A)
-        @test isisometric(N2)
+        @test isleftnull(N2, A; atol, rtol)
+        @test isisometric(N2; atol, rtol)
 
         # do we support `pivoted = true`?
         if test_pivoted
             Npiv = @testinferred qr_null(A; pivoted = true)
-            @test isleftnull(Npiv, A)
-            @test isisometric(Npiv)
+            @test isleftnull(Npiv, A; atol, rtol)
+            @test isisometric(Npiv; atol, rtol)
         else
             @test_throws ArgumentError qr_null(A; pivoted = true)
         end
 
         # do we support `blocksize = Int`?
         if test_blocksize
             Nblocked = @testinferred qr_null(A; blocksize = 2)
-            @test isleftnull(Nblocked, A)
-            @test isisometric(Nblocked)
+            @test isleftnull(Nblocked, A; atol, rtol)
+            @test isisometric(Nblocked; atol, rtol)
         else
             @test_throws ArgumentError qr_null(A; blocksize = 2)
         end