rewrite diag(::StructuredMatrix[, k=0])

 - diag(A::StructuredMatrix[, k=0]) now return a new vector,
   such that it does not alias the wrapped vector. This now
   behaves the same for eg Matrix, where we get a new vector.
   It is also consistent with getindex (diag is essentially a
   special case of getindex).

 - diag(A::StructuredMatrix{T,VectorType}[, k=0]) always return
   a vector of type VectorType, i.e. the same type which the
   diagonals are stored as. This is problematic for wrapped
   UnitRanges but that is already pretty broken for this case.

Author: fredrikekre

base/linalg/bidiag.jl

@@ -270,15 +270,13 @@ function triu!(M::Bidiagonal, k::Integer=0)
     return M
 end
 
-function diag(M::Bidiagonal{T}, n::Integer=0) where T
+function diag(M::Bidiagonal, n::Integer=0)
     if n == 0
-        return M.dv
-    elseif n == 1
-        return M.uplo == 'U' ? M.ev : zeros(T, size(M,1)-1)
-    elseif n == -1
-        return M.uplo == 'L' ? M.ev : zeros(T, size(M,1)-1)
+        return copy!(similar(M.dv, length(M.dv)), M.dv)
+    elseif (n == 1 && M.uplo == 'U') ||  (n == -1 && M.uplo == 'L')
+        return copy!(similar(M.ev, length(M.ev)), M.ev)
     elseif -size(M,1) <= n <= size(M,1)
-        return zeros(T, size(M,1)-abs(n))
+        return fill!(similar(M.dv, size(M,1)-abs(n)), 0)
     else
         throw(ArgumentError(string("requested diagonal, $n, must be at least $(-size(M, 1)) ",
             "and at most $(size(M, 2)) for an $(size(M, 1))-by-$(size(M, 2)) matrix")))

base/linalg/diagonal.jl

@@ -322,7 +322,16 @@ transpose(D::Diagonal) = Diagonal(transpose.(D.diag))
 adjoint(D::Diagonal{<:Number}) = conj(D)
 adjoint(D::Diagonal) = Diagonal(adjoint.(D.diag))
 
-diag(D::Diagonal) = D.diag
+function diag(D::Diagonal, k::Integer=0)
+    if k == 0
+        return copy!(similar(D.diag, length(D.diag)), D.diag)
+    elseif -size(D,1) <= k <= size(D,1)
+        return fill!(similar(D.diag, size(D,1)-abs(k)), 0)
+    else
+        throw(ArgumentError(string("requested diagonal, $k, must be at least $(-size(D, 1)) ",
+            "and at most $(size(D, 2)) for an $(size(D, 1))-by-$(size(D, 2)) matrix")))
+    end
+end
 trace(D::Diagonal) = sum(D.diag)
 det(D::Diagonal) = prod(D.diag)
 logdet(D::Diagonal{<:Real}) = sum(log, D.diag)

base/linalg/tridiag.jl

@@ -130,14 +130,14 @@ broadcast(::typeof(ceil), ::Type{T}, M::SymTridiagonal) where {T<:Integer} = Sym
 transpose(M::SymTridiagonal) = M #Identity operation
 adjoint(M::SymTridiagonal) = conj(M)
 
-function diag(M::SymTridiagonal{T}, n::Integer=0) where T
+function diag(M::SymTridiagonal, n::Integer=0)
     absn = abs(n)
     if absn == 0
-        return M.dv
+        return copy!(similar(M.dv, length(M.dv)), M.dv)
     elseif absn==1
-        return M.ev
+        return copy!(similar(M.ev, length(M.ev)), M.ev)
     elseif absn <= size(M,1)
-        return zeros(T,size(M,1)-absn)
+        return fill!(similar(M.dv, size(M,1)-absn), 0)
     else
         throw(ArgumentError(string("requested diagonal, $n, must be at least $(-size(M, 1)) ",
             "and at most $(size(M, 2)) for an $(size(M, 1))-by-$(size(M, 2)) matrix")))
@@ -536,13 +536,13 @@ adjoint(M::Tridiagonal) = conj(transpose(M))
 
 function diag(M::Tridiagonal{T}, n::Integer=0) where T
     if n == 0
-        return M.d
+        return copy!(similar(M.d, length(M.d)), M.d)
     elseif n == -1
-        return M.dl
+        return copy!(similar(M.dl, length(M.dl)), M.dl)
     elseif n == 1
-        return M.du
+        return copy!(similar(M.du, length(M.du)), M.du)
     elseif abs(n) <= size(M,1)
-        return zeros(T,size(M,1)-abs(n))
+        return fill!(similar(M.d, size(M,1)-abs(n)), 0)
     else
         throw(ArgumentError(string("requested diagonal, $n, must be at least $(-size(M, 1)) ",
             "and at most $(size(M, 2)) for an $(size(M, 1))-by-$(size(M, 2)) matrix")))

test/linalg/bidiag.jl

@@ -216,10 +216,18 @@ srand(1)
             end
         end
 
-        @testset "Diagonals" begin
-            @test diag(T,2) == zeros(elty, n-2)
+        @testset "diag" begin
+            @test (@inferred diag(T))::typeof(dv) == dv
+            @test (@inferred diag(T, uplo == :U ? 1 : -1))::typeof(dv) == ev
+            @test (@inferred diag(T,2))::typeof(dv) == zeros(elty, n-2)
             @test_throws ArgumentError diag(T, -n - 1)
-            @test_throws ArgumentError diag(T, n + 1)
+            @test_throws ArgumentError diag(T,  n + 1)
+            # test diag with another wrapped vector type
+            gdv, gev = GenericArray(dv), GenericArray(ev)
+            G = Bidiagonal(gdv, gev, uplo)
+            @test (@inferred diag(G))::typeof(gdv) == gdv
+            @test (@inferred diag(G, uplo == :U ? 1 : -1))::typeof(gdv) == gev
+            @test (@inferred diag(G,2))::typeof(gdv) == GenericArray(zeros(elty, n-2))
         end
 
         @testset "Eigensystems" begin

test/linalg/diagonal.jl

@@ -39,7 +39,6 @@ srand(1)
         @test Array(imag(D)) == imag(DM)
 
         @test parent(D) == dd
-        @test diag(D) == dd
         @test D[1,1] == dd[1]
         @test D[1,2] == 0
 
@@ -51,6 +50,18 @@ srand(1)
         end
     end
 
+    @testset "diag" begin
+        @test_throws ArgumentError diag(D,  n+1)
+        @test_throws ArgumentError diag(D, -n-1)
+        @test (@inferred diag(D))::typeof(dd) == dd
+        @test (@inferred diag(D, 0))::typeof(dd) == dd
+        @test (@inferred diag(D, 1))::typeof(dd) == zeros(elty, n-1)
+        DG = Diagonal(GenericArray(dd))
+        @test (@inferred diag(DG))::typeof(GenericArray(dd)) == GenericArray(dd)
+        @test (@inferred diag(DG, 1))::typeof(GenericArray(dd)) == GenericArray(zeros(elty, n-1))
+    end
+
+
     @testset "Simple unary functions" begin
         for op in (-,)
             @test op(D)==op(DM)

test/linalg/tridiag.jl

@@ -153,14 +153,17 @@ guardsrand(123) do
                     @test_throws ArgumentError A[2, 3] = 1 # test assignment on the superdiagonal
                 end
             end
-            @testset "Diagonal extraction" begin
-                @test diag(A, 1) === (mat_type == Tridiagonal ? du : dl)
-                @test diag(A, -1) === dl
-                @test diag(A, 0) === d
-                @test diag(A) === d
-                @test diag(A, n - 1) == zeros(elty, 1)
+            @testset "diag" begin
+                @test (@inferred diag(A))::typeof(d) == d
+                @test (@inferred diag(A, 0))::typeof(d) == d
+                @test (@inferred diag(A, 1))::typeof(d) == (mat_type == Tridiagonal ? du : dl)
+                @test (@inferred diag(A, -1))::typeof(d) == dl
+                @test (@inferred diag(A, n-1))::typeof(d) == zeros(elty, 1)
                 @test_throws ArgumentError diag(A, -n - 1)
                 @test_throws ArgumentError diag(A, n + 1)
+                GA = mat_type == Tridiagonal ? mat_type(GenericArray.((dl, d, du))...) : mat_type(GenericArray.((d, dl))...)
+                @test (@inferred diag(GA))::typeof(GenericArray(d)) == GenericArray(d)
+                @test (@inferred diag(GA, -1))::typeof(GenericArray(d)) == GenericArray(dl)
             end
             @testset "Idempotent tests" begin
                 for func in (conj, transpose, adjoint)