Backports to release-1.13 (#717)

- [x] #715

Author: dkarrasch

src/linalg.jl

@@ -1387,7 +1387,7 @@ function _dot(x::AbstractVector, A::AbstractSparseMatrixCSC, y::AbstractVector,
     @inbounds for col in axes(A,2)
         ycol = y[col]
         xcol = x[col]
-        if _isnotzero(ycol) && _isnotzero(xcol)
+        if _isnotzero(ycol) || _isnotzero(xcol)
             for k in rangefun(A, col)
                 i = rvals[k]
                 Aij = nzvals[k]

test/linalg.jl

@@ -967,18 +967,20 @@ end
 end
 
 @testset "generalized dot product" begin
-    for i = 1:5
-        A = sprand(ComplexF64, 10, 15, 0.4)
-        Av = view(A, :, :)
-        x = sprand(ComplexF64, 10, 0.5)
-        y = sprand(ComplexF64, 15, 0.5)
+    A = sprand(ComplexF64, 10, 15, 1.0)
+    A15 = sprand(ComplexF64, 15, 15, 1.0)
+    Av = view(A, :, :)
+    vx = sprand(ComplexF64, 10, 0.5)
+    vy = sprand(ComplexF64, 15, 0.5)
+    vy2 = sprand(ComplexF64, 15, 0.5)
+    for (x, y, y2) in ((vx, vy, vy2), (Vector(vx), Vector(vy), Vector(vy2)))
         @test dot(x, A, y) ≈ dot(Vector(x), A, Vector(y)) ≈ (Vector(x)' * Matrix(A)) * Vector(y)
         @test dot(x, A, y) ≈ dot(x, Av, y)
         @test dot(x, collect(A), y) ≈ dot(x, A, y)
         @test dot(y, collect(A)', x) ≈ dot(y, A', x)
         @test dot(y, transpose(collect(A)), x) ≈ dot(y, transpose(A), x)
-        @test dot(y, Hermitian(collect(A)' * collect(A)), y) ≈ dot(y, Hermitian(A' * A), y)
-        @test dot(y, Symmetric(collect(A)' * collect(A)), y) ≈ dot(y, Symmetric(A' * A), y)
+        @test dot(y, Hermitian(collect(A15)), y2) ≈ dot(y, Hermitian(A15), y2)
+        @test dot(y, Symmetric(collect(A15)), y2) ≈ dot(y, Symmetric(A15), y2)
         B = BitMatrix(rand(Bool, 10, 15))
         @test dot(x, A, y) ≈ dot(x, Matrix(A), y)
         @test_throws DimensionMismatch dot([x, x], A, y)
@@ -990,8 +992,8 @@ end
         B = sprandn(T, 10, 10, 0.2)
         x = sprandn(T, 10, 0.4)
         xd = Vector(x)
-        S = trans(B'B, uplo)
-        Sd = trans(Matrix(B'B), uplo)
+        S = trans(B, uplo)
+        Sd = trans(Matrix(B), uplo)
         @test dot(x, S, x) ≈ dot(x, Sd, x) ≈ dot(xd, S, xd) ≈ dot(xd, Sd, xd)
     end
 end