Make conversion from Bidiagonal to (Upper|Lower)Triangular preserve B…

…idiagional storage structure. Add equivalent methods for conversion from Bidiagonal to Unit(Upper|Lower)Triangular. Group methods and revise error messages. Test.

base/linalg/special.jl

@@ -6,14 +6,45 @@
 convert{T}(::Type{Bidiagonal}, A::Diagonal{T})=Bidiagonal(A.diag, zeros(T, size(A.diag,1)-1), true)
 convert{T}(::Type{SymTridiagonal}, A::Diagonal{T})=SymTridiagonal(A.diag, zeros(T, size(A.diag,1)-1))
 convert{T}(::Type{Tridiagonal}, A::Diagonal{T})=Tridiagonal(zeros(T, size(A.diag,1)-1), A.diag, zeros(T, size(A.diag,1)-1))
-convert(::Type{LowerTriangular}, A::Bidiagonal) = !A.isupper ? LowerTriangular(full(A)) : throw(ArgumentError("Bidiagonal matrix must have lower off diagonal to be converted to LowerTriangular"))
-convert(::Type{UpperTriangular}, A::Bidiagonal) = A.isupper ? UpperTriangular(full(A)) : throw(ArgumentError("Bidiagonal matrix must have upper off diagonal to be converted to UpperTriangular"))
+
+# methods for conversion from Bidiagonal to [Unit](Upper|Lower)Triangular
+function convert(::Type{LowerTriangular}, A::Bidiagonal)
+    if A.isupper
+        throw(ArgumentError("upper Bidiagonal matrices cannot be converted to LowerTriangular"))
+    end
+    LowerTriangular(A)
+end
+function convert(::Type{UpperTriangular}, A::Bidiagonal)
+    if !A.isupper
+        throw(ArgumentError("lower Bidiagonal matrices cannot be converted to UpperTriangular"))
+    end
+    UpperTriangular(A)
+end
+function convert(::Type{UnitLowerTriangular}, A::Bidiagonal)
+    if A.isupper
+        throw(ArgumentError("upper Bidiagonal matrices cannot be converted to UnitLowerTriangular"))
+    elseif !all(A.ev .== one(eltype(A)))
+        throw(ArgumentError(string("Bidiagonal matrices with non-one entries on the ",
+            "diagonal cannot be converted to UnitLowerTriangular")))
+    end
+    UnitLowerTriangular(A)
+end
+function convert(::Type{UnitUpperTriangular}, A::Bidiagonal)
+    if !A.isupper
+        throw(ArgumentError("lower Bidiagonal matrices cannot be converted to UnitUpperTriangular"))
+    elseif !all(A.ev .== one(eltype(A)))
+        throw(ArgumentError(string("Bidiagonal matrices with non-one entries on the ",
+            "diagonal cannot be converted to UnitUpperTriangular")))
+    end
+    UnitUpperTriangular(A)
+end
 
 function convert(::Type{UnitUpperTriangular}, A::Diagonal)
     if !all(A.diag .== one(eltype(A)))
         throw(ArgumentError("matrix cannot be represented as UnitUpperTriangular"))
     end
     UnitUpperTriangular(full(A))
+    UnitUpperTriangular(A)
 end
 
 function convert(::Type{UnitLowerTriangular}, A::Diagonal)

test/linalg/special.jl

@@ -128,3 +128,28 @@ for typ in [UpperTriangular,LowerTriangular,Base.LinAlg.UnitUpperTriangular,Base
     @test Base.LinAlg.A_mul_Bc(atri,qrb[:Q]) ≈ full(atri) * qrb[:Q]'
     @test Base.LinAlg.A_mul_Bc!(copy(atri),qrb[:Q]) ≈ full(atri) * qrb[:Q]'
 end
+
+# Test conversion from Bidiagonal to <:AbstractTriangular
+let
+    lowerbidiagmat = Bidiagonal(rand(3), rand(2), false)
+    upperbidiagmat = Bidiagonal(rand(3), rand(2), true)
+    unitlowerbidiagmat = Bidiagonal(ones(3), rand(2), false)
+    unitupperbidiagmat = Bidiagonal(ones(3), rand(2), true)
+    # test that conversion from upper(lower) bidiagonal to lower(upper) [unit]triangular throws
+    @test_throws ArgumentError convert(UpperTriangular, unitlowerbidiagmat)
+    @test_throws ArgumentError convert(LowerTriangular, unitupperbidiagmat)
+    @test_throws ArgumentError convert(UnitUpperTriangular, unitlowerbidiagmat)
+    @test_throws ArgumentError convert(UnitLowerTriangular, unitupperbidiagmat)
+    # test that conversion from non-unit bidiag to unit triangular throws
+    @test_throws ArgumentError convert(UnitUpperTriangular, upperbidiagmat)
+    @test_throws ArgumentError convert(UnitLowerTriangular, lowerbidiagmat)
+    # test that conversion from bidiagonal to triangular preserves bidiagonal storage structure
+    @test typeof(convert(UpperTriangular, upperbidiagmat)) ==
+        UpperTriangular{eltype(upperbidiagmat),Bidiagonal{eltype(upperbidiagmat)}}
+    @test typeof(convert(LowerTriangular, lowerbidiagmat)) ==
+        LowerTriangular{eltype(lowerbidiagmat),Bidiagonal{eltype(lowerbidiagmat)}}
+    @test typeof(convert(Base.LinAlg.UnitUpperTriangular, unitupperbidiagmat)) ==
+        Base.LinAlg.UnitUpperTriangular{eltype(unitupperbidiagmat),Bidiagonal{eltype(unitupperbidiagmat)}}
+    @test typeof(convert(Base.LinAlg.UnitLowerTriangular, unitlowerbidiagmat)) ==
+        Base.LinAlg.UnitLowerTriangular{eltype(unitlowerbidiagmat),Bidiagonal{eltype(unitlowerbidiagmat)}}
+end