add tests

Author: dkarrasch

test/linalg.jl

@@ -147,6 +147,42 @@ end
     end
 end
 
+@testset "destination array density in solves" begin
+    O = diagm(-1 => fill(-1, 9), 0 => fill(2, 10), 1 => fill(-1, 9))
+    wrappers = (a -> Bidiagonal(a, :U),
+                a -> Bidiagonal(a, :L),
+                a -> SymTridiagonal(2diag(a), -diag(a, 1)),
+                a -> Tridiagonal(-diag(a, -1), 2diag(a), -diag(a, 1)),
+                LowerTriangular,
+                UnitLowerTriangular,
+                UpperTriangular,
+                UnitUpperTriangular,
+                UpperHessenberg)
+    for T in wrappers
+        A = T(O)
+        bs = sprandn(10, 0.3)
+        bd = Array(bs)
+        x = A \ bs
+        @test x ≈ A \ bd
+        @test !issparse(x)
+        Bs = sprandn(10, 3, 0.2)
+        Bd = Matrix(Bs)
+        X = A \ Bs
+        @test X ≈ A \ Bd
+        @test !issparse(X)
+        Cs = copy(Bs')
+        Cd = Matrix(Cs)
+        Y = Cs / A
+        @test Y ≈ Cd / A
+        @test !issparse(Y)
+    end
+    b, B = ones(Int, 10), ones(Int, 10, 10)
+    for T in (UnitLowerTriangular, UnitUpperTriangular)
+        A = T(O)
+        @test eltype(A \ b) == eltype(A \ B) == eltype(B / A) == Int
+    end
+end
+
 @testset "multiplication of special sparse with dense matrix" begin
     # this results in a call of the most generic multiplication code in LinearAlgebra.jl
     A = randn(2, 2)
@@ -228,6 +264,7 @@ begin
         AW = tr(wr(A))
         MAW = tr(wr(MA))
         @test AW \ B ≈ MAW \ B
+        @test !issparse(AW \ B)
         # and for SparseMatrixCSCView - a view of all rows and unit range of cols
         vAW = tr(wr(view([zero(A)+I A], :, (n+1):2n)))
         @test vAW \ B ≈ AW \ B