Bugfix in matrix multiplication involving adj/trans

src/fillalgebra.jl

@@ -212,15 +212,21 @@ for (T, f) in ((:Adjoint, :adjoint), (:Transpose, :transpose))
     end
 end
 
-function mul!(C::AbstractMatrix, A::AbstractFillMatrix, B::AbstractFillMatrix, alpha::Number, beta::Number)
+# unnecessary indirection, added for ambiguity resolution
+function _mulfill!(C::AbstractMatrix, A::AbstractFillMatrix, B::AbstractFillMatrix, alpha, beta)
     check_matmul_sizes(C, A, B)
     ABα = getindex_value(A) * getindex_value(B) * alpha * size(B,1)
     if iszero(beta)
         C .= ABα
     else
         C .= ABα .+ C .* beta
     end
-    C
+    return C
+end
+
+function mul!(C::AbstractMatrix, A::AbstractFillMatrix, B::AbstractFillMatrix, alpha::Number, beta::Number)
+    _mulfill!(C, A, B, alpha, beta)
+    return C
 end
 
 function copyfirstcol!(C)
@@ -229,50 +235,72 @@ function copyfirstcol!(C)
     end
     return C
 end
-function copyfirstcol!(C::Union{Adjoint, Transpose})
-    # in this case, we copy the first row of the parent to others
-    Cp = parent(C)
-    for colind in axes(Cp, 2)
-        Cp[2:end, colind] .= Cp[1, colind]
+
+_firstcol(C::AbstractMatrix) = first(eachcol(C))
+
+function copyfirstrow!(C)
+    # C[begin+1:end, ind] .= permutedims(_firstrow(C))
+    # we loop here as the aliasing check isn't smart enough to
+    # detect that the two sides don't alias, and ends up materializing the RHS
+    for (ind, v) in pairs(_firstrow(C))
+        C[begin+1:end, ind] .= Ref(v)
     end
     return C
 end
+_firstrow(C::AbstractMatrix) = first(eachrow(C))
 
-_firstcol(C::AbstractMatrix) = view(C, :, 1)
-_firstcol(C::Union{Adjoint, Transpose}) = view(parent(C), 1, :)
-
-function _mulfill!(C, A, B::AbstractFillMatrix, alpha, beta)
+function _mulfill!(C::AbstractMatrix, A::AbstractMatrix, B::AbstractFillMatrix, alpha, beta)
+    check_matmul_sizes(C, A, B)
+    iszero(size(B,2)) && return C # no columns in B and C, empty matrix
+    if iszero(beta)
+        # the mat-vec product sums along the rows of A
+        mul!(_firstcol(C), A, _firstcol(B), alpha, beta)
+        copyfirstcol!(C)
+    else
+        # the mat-vec product sums along the rows of A, which produces the first column of ABα
+        # allocate a temporary column vector to store the result
+        v = A * (_firstcol(B) * alpha)
+        C .= v .+ C .* beta
+    end
+    return C
+end
+function _mulfill!(C::AbstractMatrix, A::AbstractFillMatrix, B::AbstractMatrix, alpha, beta)
     check_matmul_sizes(C, A, B)
-    if iszero(size(B,2))
-        return rmul!(C, beta)
+    iszero(size(A,1)) && return C # no rows in A and C, empty matrix
+    Aval = getindex_value(A)
+    if iszero(beta)
+        Crow = _firstrow(C)
+        # sum along the columns of B
+        Crow .= Ref(Aval) .* sum.(eachcol(B)) .* alpha
+        copyfirstrow!(C)
+    else
+        # sum along the columns of B, and allocate the result.
+        # This is the first row of ABα
+        ABα_row = Ref(Aval) .* sum.(eachcol(B)) .* alpha
+        C .= permutedims(ABα_row) .+ C .* beta
     end
-    mul!(_firstcol(C), A, view(B, :, 1), alpha, beta)
-    copyfirstcol!(C)
-    C
+    return C
 end
 
 function mul!(C::StridedMatrix, A::StridedMatrix, B::AbstractFillMatrix, alpha::Number, beta::Number)
     _mulfill!(C, A, B, alpha, beta)
+    return C
 end
-
-for T in (:Adjoint, :Transpose)
-    @eval function mul!(C::StridedMatrix, A::$T{<:Any, <:StridedMatrix}, B::AbstractFillMatrix, alpha::Number, beta::Number)
-        _mulfill!(C, A, B, alpha, beta)
-    end
-end
-
 function mul!(C::StridedMatrix, A::AbstractFillMatrix, B::StridedMatrix, alpha::Number, beta::Number)
-    check_matmul_sizes(C, A, B)
-    for (colC, colB) in zip(eachcol(C), eachcol(B))
-        mul!(colC, A, colB, alpha, beta)
-    end
-    C
+    _mulfill!(C, A, B, alpha, beta)
+    return C
 end
 
-for (T, f) in ((:Adjoint, :adjoint), (:Transpose, :transpose))
-    @eval function mul!(C::StridedMatrix, A::AbstractFillMatrix, B::$T{<:Any, <:StridedMatrix}, alpha::Number, beta::Number)
-        _mulfill!($f(C), $f(B), $f(A), alpha, beta)
-        C
+for T in (:Adjoint, :Transpose)
+    @eval begin
+        function mul!(C::StridedMatrix, A::$T{<:Any, <:StridedMatrix}, B::AbstractFillMatrix, alpha::Number, beta::Number)
+            _mulfill!(C, A, B, alpha, beta)
+            return C
+        end
+        function mul!(C::StridedMatrix, A::AbstractFillMatrix, B::$T{<:Any, <:StridedMatrix}, alpha::Number, beta::Number)
+            _mulfill!(C, A, B, alpha, beta)
+            return C
+        end
     end
 end
 

test/runtests.jl

@@ -1716,6 +1716,16 @@ end
         @test transpose(A)*fillmat ≈ transpose(A)*Array(fillmat)
         @test adjoint(A)*fillvec ≈ adjoint(A)*Array(fillvec)
         @test adjoint(A)*fillmat ≈ adjoint(A)*Array(fillmat)
+
+        # inplace C = F * B' * alpha + C * beta
+        F = Fill(fv, m, k)
+        A = Array(F)
+        B = rand(T, n, k)
+        C = rand(T, m, n)
+        @testset for f in (adjoint, transpose)
+            @test mul!(copy(C), F, f(B)) ≈ mul!(copy(C), A, f(B))
+            @test mul!(copy(C), F, f(B), 1.0, 2.0) ≈ mul!(copy(C), A, f(B), 1.0, 2.0)
+        end
     end
 
     @testset "non-commutative" begin