general edits

Author: dkarrasch

src/LinearMaps.jl

@@ -243,6 +243,7 @@ include("composition.jl") # composition of linear maps
 include("functionmap.jl") # using a function as linear map
 include("blockmap.jl") # block linear maps
 include("kronecker.jl") # Kronecker product of linear maps
+include("fillmap.jl") # linear maps representing constantly filled matrices
 include("conversion.jl") # conversion of linear maps to matrices
 include("show.jl") # show methods for LinearMap objects
 
@@ -283,6 +284,8 @@ LinearMap(f, M::Int; kwargs...) = LinearMap{Float64}(f, M; kwargs...)
 LinearMap(f, M::Int, N::Int; kwargs...) = LinearMap{Float64}(f, M, N; kwargs...)
 LinearMap(f, fc, M::Int; kwargs...) = LinearMap{Float64}(f, fc, M; kwargs...)
 LinearMap(f, fc, M::Int, N::Int; kwargs...) = LinearMap{Float64}(f, fc, M, N; kwargs...)
+LinearMap(λ::Number, M::Int, N::Int) = LinearMap(λ, (M, N))
+LinearMap(λ::Number, dims::Dims{2}) = FillMap(λ, dims)
 
 LinearMap{T}(A::MapOrMatrix; kwargs...) where {T} = WrappedMap{T}(A; kwargs...)
 LinearMap{T}(f, args...; kwargs...) where {T} = FunctionMap{T}(f, args...; kwargs...)

src/fillmap.jl

@@ -1,18 +1,28 @@
 struct FillMap{T} <: LinearMaps.LinearMap{T}
     λ::T
     size::Dims{2}
+    function FillMap(λ::T, dims) where {T}
+        all(d -> d >= 0, dims) || throw(ArgumentError("dims of FillMap must be non-negative"))
+        promote_type(T, typeof(λ)) == T || throw(InexactError())
+        return new{T}(λ, dims)
+    end
 end
 
 # properties
 Base.size(A::FillMap) = A.size
 MulStyle(A::FillMap) = FiveArg()
 LinearAlgebra.issymmetric(A::FillMap) = A.size[1] == A.size[2]
 LinearAlgebra.ishermitian(A::FillMap) = isreal(A) && A.size[1] == A.size[2]
-LinearAlgebra.isposdef(A::FillMap) = false
+LinearAlgebra.isposdef(A::FillMap) = (size(A, 1) == size(A, 2) == 1 && isposdef(A.λ))
 Base.:(==)(A::FillMap, B::FillMap) = A.λ == B.λ && A.size == B.size
 
-LinearAlgebra.adjoint(A::FillMap) = FillMap(adjoint(A.λ), revert(A.size))
-LinearAlgebra.transpose(A::FillMap) = FillMap(transpose(A.λ), revert(A.size))
+LinearAlgebra.adjoint(A::FillMap) = FillMap(adjoint(A.λ), reverse(A.size))
+LinearAlgebra.transpose(A::FillMap) = FillMap(transpose(A.λ), reverse(A.size))
+
+function Base.:(*)(A::FillMap, x::AbstractVector)
+    T = typeof(oneunit(eltype(A)) * (zero(eltype(x)) + zero(eltype(x))))
+    return fill(iszero(A.λ) ? zero(T) : A.λ*sum(x), A.size[1])
+end
 
 function _unsafe_mul!(y::AbstractVecOrMat, A::FillMap, x::AbstractVector)
     return fill!(y, iszero(A.λ) ? zero(eltype(y)) : A.λ*sum(x))
@@ -31,13 +41,16 @@ function _unsafe_mul!(y::AbstractVecOrMat, A::FillMap, x::AbstractVector, α::Nu
         else
             y .= y .* β .+ temp
         end
+    end
     return y
 end
 
 Base.:(+)(A::FillMap, B::FillMap) = A.size == B.size ? FillMap(A.λ + B.λ, A.size) : throw(DimensionMismatch())
 Base.:(-)(A::FillMap) = FillMap(-A.λ, A.size)
 Base.:(*)(λ::Number, A::FillMap) = FillMap(λ * A.λ, size(A))
 Base.:(*)(A::FillMap, λ::Number) = FillMap(A.λ * λ, size(A))
+Base.:(*)(λ::RealOrComplex, A::FillMap) = FillMap(λ * A.λ, size(A))
+Base.:(*)(A::FillMap, λ::RealOrComplex) = FillMap(A.λ * λ, size(A))
 
 function Base.:(*)(A::FillMap, B::FillMap)
     mA, nA = size(A)