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Add: julia-0.6.2

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mollusk
2018-02-10 10:27:19 -07:00
parent 94220957d7
commit 019f8e3064
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julia-0.6.2/share/julia/base/linalg/special.jl Normal file
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# This file is a part of Julia. License is MIT: https://julialang.org/license
# Methods operating on different special matrix types
# Interconversion between special matrix types
convert(::Type{Bidiagonal}, A::Diagonal{T}) where {T} =
Bidiagonal(A.diag, zeros(T, size(A.diag,1)-1), true)
convert(::Type{SymTridiagonal}, A::Diagonal{T}) where {T} =
SymTridiagonal(A.diag, zeros(T, size(A.diag,1)-1))
convert(::Type{Tridiagonal}, A::Diagonal{T}) where {T} =
Tridiagonal(zeros(T, size(A.diag,1)-1), A.diag, zeros(T, size(A.diag,1)-1))
function convert(::Type{Diagonal}, A::Union{Bidiagonal, SymTridiagonal})
if !iszero(A.ev)
throw(ArgumentError("matrix cannot be represented as Diagonal"))
end
Diagonal(A.dv)
end
function convert(::Type{SymTridiagonal}, A::Bidiagonal)
if !iszero(A.ev)
throw(ArgumentError("matrix cannot be represented as SymTridiagonal"))
end
SymTridiagonal(A.dv, A.ev)
end
convert(::Type{Tridiagonal}, A::Bidiagonal{T}) where {T} =
Tridiagonal(A.isupper ? zeros(T, size(A.dv,1)-1) : A.ev, A.dv,
A.isupper ? A.ev:zeros(T, size(A.dv,1)-1))
function convert(::Type{Bidiagonal}, A::SymTridiagonal)
if !iszero(A.ev)
throw(ArgumentError("matrix cannot be represented as Bidiagonal"))
end
Bidiagonal(A.dv, A.ev, true)
end
function convert(::Type{Diagonal}, A::Tridiagonal)
if !(iszero(A.dl) && iszero(A.du))
throw(ArgumentError("matrix cannot be represented as Diagonal"))
end
Diagonal(A.d)
end
function convert(::Type{Bidiagonal}, A::Tridiagonal)
if iszero(A.dl)
return Bidiagonal(A.d, A.du, true)
elseif iszero(A.du)
return Bidiagonal(A.d, A.dl, false)
else
throw(ArgumentError("matrix cannot be represented as Bidiagonal"))
end
end
function convert(::Type{SymTridiagonal}, A::Tridiagonal)
if A.dl != A.du
throw(ArgumentError("matrix cannot be represented as SymTridiagonal"))
end
SymTridiagonal(A.d, A.dl)
end
function convert(::Type{Tridiagonal}, A::SymTridiagonal)
Tridiagonal(copy(A.ev), A.dv, A.ev)
end
function convert(::Type{Diagonal}, A::AbstractTriangular)
if full(A) != diagm(diag(A))
throw(ArgumentError("matrix cannot be represented as Diagonal"))
end
Diagonal(diag(A))
end
function convert(::Type{Bidiagonal}, A::AbstractTriangular)
fA = full(A)
if fA == diagm(diag(A)) + diagm(diag(fA, 1), 1)
return Bidiagonal(diag(A), diag(fA,1), true)
elseif fA == diagm(diag(A)) + diagm(diag(fA, -1), -1)
return Bidiagonal(diag(A), diag(fA,-1), false)
else
throw(ArgumentError("matrix cannot be represented as Bidiagonal"))
end
end
convert(::Type{SymTridiagonal}, A::AbstractTriangular) =
convert(SymTridiagonal, convert(Tridiagonal, A))
function convert(::Type{Tridiagonal}, A::AbstractTriangular)
fA = full(A)
if fA == diagm(diag(A)) + diagm(diag(fA, 1), 1) + diagm(diag(fA, -1), -1)
return Tridiagonal(diag(fA, -1), diag(A), diag(fA,1))
else
throw(ArgumentError("matrix cannot be represented as Tridiagonal"))
end
end
# Constructs two method definitions taking into account (assumed) commutativity
# e.g. @commutative f{S,T}(x::S, y::T) = x+y is the same is defining
# f{S,T}(x::S, y::T) = x+y
# f{S,T}(y::T, x::S) = f(x, y)
macro commutative(myexpr)
@assert myexpr.head===:(=) || myexpr.head===:function # Make sure it is a function definition
y = copy(myexpr.args[1].args[2:end])
reverse!(y)
reversed_call = Expr(:(=), Expr(:call,myexpr.args[1].args[1],y...), myexpr.args[1])
esc(Expr(:block, myexpr, reversed_call))
end
for op in (:+, :-)
SpecialMatrices = [:Diagonal, :Bidiagonal, :Tridiagonal, :Matrix]
for (idx, matrixtype1) in enumerate(SpecialMatrices) # matrixtype1 is the sparser matrix type
for matrixtype2 in SpecialMatrices[idx+1:end] # matrixtype2 is the denser matrix type
@eval begin # TODO quite a few of these conversions are NOT defined
($op)(A::($matrixtype1), B::($matrixtype2)) = ($op)(convert(($matrixtype2), A), B)
($op)(A::($matrixtype2), B::($matrixtype1)) = ($op)(A, convert(($matrixtype2), B))
end
end
end
for matrixtype1 in (:SymTridiagonal,) # matrixtype1 is the sparser matrix type
for matrixtype2 in (:Tridiagonal, :Matrix) # matrixtype2 is the denser matrix type
@eval begin
($op)(A::($matrixtype1), B::($matrixtype2)) = ($op)(convert(($matrixtype2), A), B)
($op)(A::($matrixtype2), B::($matrixtype1)) = ($op)(A, convert(($matrixtype2), B))
end
end
end
for matrixtype1 in (:Diagonal, :Bidiagonal) # matrixtype1 is the sparser matrix type
for matrixtype2 in (:SymTridiagonal,) # matrixtype2 is the denser matrix type
@eval begin
($op)(A::($matrixtype1), B::($matrixtype2)) = ($op)(convert(($matrixtype2), A), B)
($op)(A::($matrixtype2), B::($matrixtype1)) = ($op)(A, convert(($matrixtype2), B))
end
end
end
for matrixtype1 in (:Diagonal,)
for (matrixtype2,matrixtype3) in ((:UpperTriangular,:UpperTriangular),
(:UnitUpperTriangular,:UpperTriangular),
(:LowerTriangular,:LowerTriangular),
(:UnitLowerTriangular,:LowerTriangular))
@eval begin
($op)(A::($matrixtype1), B::($matrixtype2)) = ($op)(($matrixtype3)(A), B)
($op)(A::($matrixtype2), B::($matrixtype1)) = ($op)(A, ($matrixtype3)(B))
end
end
end
for matrixtype in (:SymTridiagonal,:Tridiagonal,:Bidiagonal,:Matrix)
@eval begin
($op)(A::AbstractTriangular, B::($matrixtype)) = ($op)(full(A), B)
($op)(A::($matrixtype), B::AbstractTriangular) = ($op)(A, full(B))
end
end
end
A_mul_Bc!(A::AbstractTriangular, B::QRCompactWYQ) = A_mul_Bc!(full!(A),B)
A_mul_Bc!(A::AbstractTriangular, B::QRPackedQ) = A_mul_Bc!(full!(A),B)
A_mul_Bc(A::AbstractTriangular, B::Union{QRCompactWYQ,QRPackedQ}) = A_mul_Bc(full(A), B)