Left vector multiply

Author: JeffFessler

src/wrappedmap.jl

@@ -1,3 +1,5 @@
+import LinearAlgebra: AdjointAbsVec, TransposeAbsVec
+
 struct WrappedMap{T, A<:MapOrMatrix} <: LinearMap{T}
     lmap::A
     _issymmetric::Bool
@@ -71,3 +73,8 @@ Base.:(-)(A₁::AbstractMatrix, A₂::LinearMap) = -(WrappedMap(A₁), A₂)
 
 Base.:(*)(A₁::LinearMap, A₂::AbstractMatrix) = *(A₁, WrappedMap(A₂))
 Base.:(*)(A₁::AbstractMatrix, A₂::LinearMap) = *(WrappedMap(A₁), A₂)
+
+# An AdjointAbsVec isa AbstractMatrix but we handle it like a vector (Issue#99)
+# which is an exception to the left multiplication rule that makes a WrappedMap
+Base.:(*)(y::AdjointAbsVec, A::LinearMap) = adjoint(*(A', y'))
+Base.:(*)(y::TransposeAbsVec, A::LinearMap) = transpose(transpose(A) * transpose(y))

test/wrappedmap.jl

@@ -15,3 +15,33 @@ using Test, LinearMaps, LinearAlgebra
     @test @inferred isposdef(MA)
     @test @inferred isposdef(MB)
 end
+
+# y'*L is an exception to the left multiplication rule that makes a WrappedMap
+@testset "left mul vec" begin
+    T = ComplexF32
+    A = rand(T, 4, 5)
+    x = rand(T, 5)
+    y = rand(T, 4)
+    L = LinearMap{T}(A)
+    @test y'A ≈ y'L
+    @test (y' * A) * x ≈ y' * (L * x) # associative
+    @test transpose(y) * A ≈ transpose(y) * L
+
+    LL = L * [L' L'] # stress test with CompositeMap & BlockMap
+    AA = A * [A' A']
+    x = rand(T, 8)
+    @test y'AA ≈ y'LL
+    @test (y' * AA) * x ≈ y' * (LL * x) # associative
+    @test transpose(y)*AA ≈ transpose(y)*LL
+
+    # mul! versions
+    b1 = y'*L
+    b2 = similar(b1)
+    mul!(b2, y', A)
+    @test b1 ≈ b2
+
+    b1 = transpose(y)*L
+    b2 = similar(b1)
+    mul!(b2, transpose(y), A)
+    @test b1 ≈ b2
+end