Add convert for banded matrix types

Author: jishnub

src/bidiag.jl

@@ -118,6 +118,13 @@ Bidiagonal(A::Bidiagonal) = A
 Bidiagonal{T}(A::Bidiagonal{T}) where {T} = A
 Bidiagonal{T}(A::Bidiagonal) where {T} = Bidiagonal{T}(A.dv, A.ev, A.uplo)
 
+function convert(::Type{T}, A::AbstractMatrix) where T<:Bidiagonal
+    checksquare(A)
+    isbanded(A, -1, 1) || throw(InexactError(:convert, T, A))
+    iszero(diagview(A, 1)) ? T(A, :L) :
+        iszero(diagview(A, -1)) ? T(A, :U) : throw(InexactError(:convert, T, A))
+end
+
 _offdiagind(uplo) = uplo == 'U' ? 1 : -1
 
 @inline function Base.isassigned(A::Bidiagonal, i::Int, j::Int)

src/tridiag.jl

@@ -109,16 +109,18 @@ julia> SymTridiagonal(B)
 """
 function SymTridiagonal(A::AbstractMatrix)
     checksquare(A)
-    du = diag(A, 1)
-    d  = diag(A)
-    dl = diag(A, -1)
-    if all(((x, y),) -> x == transpose(y), zip(du, dl)) && all(issymmetric, d)
+    if _checksymmetric(A)
+        du = diag(A, 1)
+        d  = diag(A)
         SymTridiagonal(d, du)
     else
         throw(ArgumentError("matrix is not symmetric; cannot convert to SymTridiagonal"))
     end
 end
 
+_checksymmetric(d, du, dl) = all(((x, y),) -> x == transpose(y), zip(du, dl)) && all(issymmetric, d)
+_checksymmetric(A::AbstractMatrix) = _checksymmetric(diagview(A), diagview(A, 1), diagview(A, -1))
+
 SymTridiagonal{T,V}(S::SymTridiagonal{T,V}) where {T,V<:AbstractVector{T}} = S
 SymTridiagonal{T,V}(S::SymTridiagonal) where {T,V<:AbstractVector{T}} =
     SymTridiagonal(convert(V, S.dv)::V, convert(V, S.ev)::V)
@@ -128,6 +130,11 @@ SymTridiagonal{T}(S::SymTridiagonal) where {T} =
                     convert(AbstractVector{T}, S.ev)::AbstractVector{T})
 SymTridiagonal(S::SymTridiagonal) = S
 
+function convert(::Type{T}, A::AbstractMatrix) where T<:SymTridiagonal
+    checksquare(A)
+    _checksymmetric(A) && isbanded(A, -1, 1) ? T(A) : throw(InexactError(:convert, T, A))
+end
+
 AbstractMatrix{T}(S::SymTridiagonal) where {T} = SymTridiagonal{T}(S)
 AbstractMatrix{T}(S::SymTridiagonal{T}) where {T} = copy(S)
 
@@ -605,6 +612,11 @@ function Tridiagonal{T,V}(A::Tridiagonal) where {T,V<:AbstractVector{T}}
     end
 end
 
+function convert(::Type{T}, A::AbstractMatrix) where T<:Tridiagonal
+    checksquare(A)
+    isbanded(A, -1, 1) ? T(A) : throw(InexactError(:convert, T, A))
+end
+
 size(M::Tridiagonal) = (n = length(M.d); (n, n))
 axes(M::Tridiagonal) = (ax = axes(M.d,1); (ax, ax))