Porting SDiagonal from Bridge.jl

Originally contributed by D. Getz (https://github.com/getzdan), M. Schauer
at https://github.com/mschauer/Bridge.jl under MIT License

Author: mschauer

src/SDiagonal.jl

@@ -0,0 +1,116 @@
+# Originally contributed by D. Getz (https://github.com/getzdan), M. Schauer
+# at https://github.com/mschauer/Bridge.jl under MIT License
+
+import Base: getindex,setindex!,==,-,+,*,/,\,transpose,ctranspose,convert, size, abs, real, imag, conj, eye, inv
+import Base.LinAlg: ishermitian, issymmetric, isposdef, factorize, diag, trace, det, logdet, expm, logm, sqrtm
+
+@generated function scalem{T, M, N}(a::SMatrix{M,N, T}, b::SVector{N, T})
+    expr = vec([:(a[$j,$i]*b[$i]) for j=1:M, i=1:N])
+    :(SMatrix{M,N,T}($(expr...)))
+end
+@generated function scalem{T, M, N}(a::SVector{M,T}, b::SMatrix{M, N, T})
+    expr = vec([:(b[$j,$i]*a[$j]) for j=1:M, i=1:N])
+    :(SMatrix{M,N,T}($(expr...)))
+end
+
+struct SDiagonal{N,T}
+    diag::SVector{N,T}
+end    
+
+function \{T,M}(D::SDiagonal, b::SVector{M,T} )
+    D.diag .* b
+end
+
+SDiagonal(A::SMatrix) = SDiagonal(diag(A))
+
+
+convert{N,T}(::Type{SDiagonal{N,T}}, D::SDiagonal{N,T}) = D
+convert{N,T}(::Type{SDiagonal{N,T}}, D::SDiagonal) = SDiagonal{N,T}(convert(SVector{N,T}, D.diag))
+
+size(D::SDiagonal) = (length(D.diag),length(D.diag))
+
+function size(D::SDiagonal,d::Integer)
+    if d<1
+        throw(ArgumentError("dimension must be ≥ 1, got $d"))
+    end
+    return d<=2 ? length(D.diag) : 1
+end
+
+function getindex{T}(D::SDiagonal{T}, i::Int, j::Int)  
+    if i == j
+        D.diag[i]
+    else
+        zero(T)
+    end
+end
+function setindex!(D::SDiagonal, v, i::Int, j::Int)
+    if i == j
+        unsafe_setindex!(D.diag, v, i)
+    elseif v != 0
+        throw(ArgumentError("cannot set an off-diagonal index ($i, $j) to a nonzero value ($v)"))
+    end
+    D
+end
+
+ishermitian{T<:Real}(D::SDiagonal{T}) = true
+ishermitian(D::SDiagonal) = all(D.diag .== real(D.diag))
+issym(D::SDiagonal) = true
+isposdef(D::SDiagonal) = all(D.diag .> 0)
+
+factorize(D::SDiagonal) = D
+
+abs(D::SDiagonal) = SDiagonal(abs(D.diag))
+real(D::SDiagonal) = SDiagonal(real(D.diag))
+imag(D::SDiagonal) = SDiagonal(imag(D.diag))
+
+==(Da::SDiagonal, Db::SDiagonal) = Da.diag == Db.diag
+-(A::SDiagonal) = SDiagonal(-A.diag)
++(Da::SDiagonal, Db::SDiagonal) = SDiagonal(Da.diag + Db.diag)
+-(Da::SDiagonal, Db::SDiagonal) = SDiagonal(Da.diag - Db.diag)
+-(A::SDiagonal, B::SMatrix) = eye(typeof(B))*A - B
+
+
+*{T<:Number}(x::T, D::SDiagonal) = SDiagonal(x * D.diag)
+*{T<:Number}(D::SDiagonal, x::T) = SDiagonal(D.diag * x)
+/{T<:Number}(D::SDiagonal, x::T) = SDiagonal(D.diag / x)
+*(Da::SDiagonal, Db::SDiagonal) = SDiagonal(Da.diag .* Db.diag)
+*(D::SDiagonal, V::SVector) = D.diag .* V
+*(V::SVector, D::SDiagonal) = D.diag .* V
+*(A::SMatrix, D::SDiagonal) = scalem(A,D.diag)
+*(D::SDiagonal, A::SMatrix) = scalem(D.diag,A)
+
+/(Da::SDiagonal, Db::SDiagonal) = SDiagonal(Da.diag ./ Db.diag )
+
+conj(D::SDiagonal) = SDiagonal(conj(D.diag))
+transpose(D::SDiagonal) = D
+ctranspose(D::SDiagonal) = conj(D)
+
+diag(D::SDiagonal) = D.diag
+trace(D::SDiagonal) = sum(D.diag)
+det(D::SDiagonal) = prod(D.diag)
+logdet{N,T<:Real}(D::SDiagonal{N,T}) = sum(log.(D.diag))
+function logdet{N,T<:Complex}(D::SDiagonal{N,T}) #Make sure branch cut is correct
+    x = sum(log.(D.diag))
+    -pi<imag(x)<pi ? x : real(x)+(mod2pi(imag(x)+pi)-pi)*im
+end
+
+
+eye{N,T}(::Type{SDiagonal{N,T}}) = SDiagonal(one(SVector{n,Int}))
+
+expm(D::SDiagonal) = SDiagonal(exp.(D.diag))
+logm(D::SDiagonal) = SDiagonal(log.(D.diag))
+sqrtm(D::SDiagonal) = SDiagonal(sqrt.(D.diag))
+
+\(D::SDiagonal, B::SMatrix) = scalem(1 ./ D.diag, B)
+/(B::SMatrix, D::SDiagonal) = scalem(1 ./ D.diag, B)
+\(Da::SDiagonal, Db::SDiagonal) = SDiagonal(Db.diag ./ Da.diag)
+
+function inv{N,T}(D::SDiagonal{N,T})
+    for i = 1:length(D.diag)
+        if D.diag[i] == zero(T)
+            throw(SingularException(i))
+        end
+    end
+    SDiagonal(one(T)./D.diag)
+end
+

src/StaticArrays.jl

@@ -19,6 +19,7 @@ export Scalar, SArray, SVector, SMatrix
 export MArray, MVector, MMatrix
 export FieldVector
 export SizedArray, SizedVector, SizedMatrix
+export SDiagonal
 
 export Size, Length
 
@@ -79,6 +80,7 @@ include("MArray.jl")
 include("MVector.jl")
 include("MMatrix.jl")
 include("SizedArray.jl")
+include("SDiagonal.jl")
 
 include("abstractarray.jl")
 include("indexing.jl")