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WIP:Make LinAlg more type stable #8796

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WIP:Make LinAlg more type stable #8796

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7 changes: 6 additions & 1 deletion base/linalg.jl
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Expand Up @@ -33,6 +33,7 @@ export
Triangular,
Diagonal,
UniformScaling,
Token,

# Functions
axpy!,
Expand Down Expand Up @@ -189,11 +190,15 @@ macro chkuplo()
Valid choices are 'U' (upper) or 'L' (lower).""")))
end

immutable Token{T}
end

char_uplo(::Type{Token{:U}}) = 'U'
char_uplo(::Type{Token{:L}}) = 'L'
const CHARU = 'U'
const CHARL = 'L'
char_uplo(uplo::Symbol) = uplo == :U ? CHARU : (uplo == :L ? CHARL : throw(ArgumentError("uplo argument must be either :U or :L")))


include("linalg/exceptions.jl")
include("linalg/generic.jl")

Expand Down
125 changes: 68 additions & 57 deletions base/linalg/cholesky.jl
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Expand Up @@ -13,86 +13,97 @@ immutable CholeskyPivoted{T} <: Factorization{T}
info::BlasInt
end

function chol!{T<:BlasFloat}(A::StridedMatrix{T}, uplo::Symbol=:U)
C, info = LAPACK.potrf!(char_uplo(uplo), A)
return @assertposdef Triangular{eltype(C),typeof(C),uplo,false}(C) info
for (uplos, uploc) in ((:(:U), 'U'), (:(:L), 'L'))
@eval begin
function chol!{T<:BlasFloat}(A::StridedMatrix{T}, ::Type{Token{$uplos}})
C, info = LAPACK.potrf!($uploc, A)
return @assertposdef Triangular{eltype(C),typeof(C),$uplos,false}(C) info
end
end
end

function chol!{T}(A::AbstractMatrix{T}, uplo::Symbol=:U)
function chol!{T}(A::AbstractMatrix{T}, ::Type{Token{:L}})
n = chksquare(A)
@inbounds begin
if uplo == :L
for k = 1:n
for i = 1:k - 1
A[k,k] -= A[k,i]*A[k,i]'
end
A[k,k] = chol!(A[k,k], uplo)
AkkInv = inv(A[k,k]')
for j = 1:k
for i = k + 1:n
j == 1 && (A[i,k] = A[i,k]*AkkInv)
j < k && (A[i,k] -= A[i,j]*A[k,j]'*AkkInv)
end
for k = 1:n
for i = 1:k - 1
A[k,k] -= A[k,i]*A[k,i]'
end
A[k,k] = chol!(A[k,k], Token{:L})
AkkInv = inv(A[k,k]')
for j = 1:k
for i = k + 1:n
j == 1 && (A[i,k] = A[i,k]*AkkInv)
j < k && (A[i,k] -= A[i,j]*A[k,j]'*AkkInv)
end
end
elseif uplo == :U
for k = 1:n
end
end
return Triangular{T,typeof(A),:L,false}(A)
end
function chol!{T}(A::AbstractMatrix{T}, ::Type{Token{:U}})
n = chksquare(A)
@inbounds begin
for k = 1:n
for i = 1:k - 1
A[k,k] -= A[i,k]'A[i,k]
end
A[k,k] = chol!(A[k,k], Token{:U})
AkkInv = inv(A[k,k])
for j = k + 1:n
for i = 1:k - 1
A[k,k] -= A[i,k]'A[i,k]
end
A[k,k] = chol!(A[k,k], uplo)
AkkInv = inv(A[k,k])
for j = k + 1:n
for i = 1:k - 1
A[k,j] -= A[i,k]'A[i,j]
end
A[k,j] = A[k,k]'\A[k,j]
A[k,j] -= A[i,k]'A[i,j]
end
A[k,j] = A[k,k]'\A[k,j]
end
else
throw(ArgumentError("uplo must be either :U or :L but was $(uplo)"))
end
end
return Triangular(A, uplo, false)
return Triangular{T,typeof(A),:U,false}(A)
end
chol!(A::AbstractMatrix) = chol!(A, Token{:U})

function cholfact!{T<:BlasFloat}(A::StridedMatrix{T}, uplo::Symbol=:U; pivot=false, tol=0.0)
uplochar = char_uplo(uplo)
if pivot
A, piv, rank, info = LAPACK.pstrf!(uplochar, A, tol)
return CholeskyPivoted{T}(A, uplochar, piv, rank, tol, info)
end
return Cholesky{T,typeof(A),uplo}(chol!(A, uplo).data)
cholfact!{T<:BlasFloat,uplo}(A::StridedMatrix{T}, ::Type{Token{uplo}}) = Cholesky{T,typeof(A),uplo}(chol!(A, Token{uplo}).data)
function cholfact!{T<:BlasFloat,uplo}(A::StridedMatrix{T}, ::Type{Token{uplo}}, ::Type{Token{:pivot}}; tol = 0.0)
uplochar = char_uplo(Token{uplo})
A, piv, rank, info = LAPACK.pstrf!(uplochar, A, tol)
return CholeskyPivoted{T}(A, uplochar, piv, rank, tol, info)
end
cholfact!(A::AbstractMatrix, uplo::Symbol=:U) = Cholesky{eltype(A),typeof(A),uplo}(chol!(A, uplo).data)
cholfact!{T<:BlasFloat}(A::StridedMatrix{T}, ::Type{Token{:pivot}}; tol = 0.0) = cholfact!(A, Token{:U}, Token{:pivot}, tol = tol)

cholfact!{UpLo}(A::AbstractMatrix, ::Type{Token{UpLo}}) = Cholesky{eltype(A),typeof(A),UpLo}(chol!(A, Token{UpLo}).data)
cholfact!(A::AbstractMatrix) = cholfact!(A, Token{:U})

function cholfact!{T<:BlasFloat,S,UpLo}(C::Cholesky{T,S,UpLo})
_, info = LAPACK.potrf!(char_uplo(UpLo), C.UL)
info[1]>0 && throw(PosDefException(info[1]))
C
end

cholfact{T<:BlasFloat}(A::StridedMatrix{T}, uplo::Symbol=:U; pivot=false, tol=0.0) = cholfact!(copy(A), uplo, pivot=pivot, tol=tol)
function cholfact{T}(A::StridedMatrix{T}, uplo::Symbol=:U; pivot=false, tol=0.0)
cholfact{T<:BlasFloat}(A::StridedMatrix{T}, args...; kwargs...) = cholfact!(copy(A), args...; kwargs...)
function cholfact{T}(A::AbstractMatrix{T}, args...; kwargs...)
S = promote_type(typeof(chol(one(T))),Float32)
S <: BlasFloat && return cholfact!(convert(AbstractMatrix{S}, A), uplo, pivot = pivot, tol = tol)
pivot && throw(ArgumentError("pivot only supported for Float32, Float64, Complex{Float32} and Complex{Float64}"))
S != T && return cholfact!(convert(AbstractMatrix{S}, A), uplo)
return cholfact!(copy(A), uplo)
# S <: BlasFloat && return cholfact!(convert(AbstractMatrix{S}, A), args...; kwargs...)
# pivot && throw(ArgumentError("pivot only supported for Float32, Float64, Complex{Float32} and Complex{Float64}"))
S != T && return cholfact!(convert(AbstractMatrix{S}, A), args..., kwargs...)
return cholfact!(copy(A), args...; kwargs...)
end
function cholfact(x::Number, uplo::Symbol=:U)
function cholfact(x::Number, ::Type{Token{:U}})
xf = fill(chol!(x), 1, 1)
Cholesky{:U, eltype(xf), typeof(xf)}(xf)
end
function cholfact(x::Number, ::Type{Token{:L}})
xf = fill(chol!(x), 1, 1)
Cholesky{:L, eltype(xf), typeof(xf)}(xf)
end

chol(A::AbstractMatrix, uplo::Symbol=:U) = chol!(copy(A), uplo)
function chol!(x::Number, uplo::Symbol=:U)
chol(A::AbstractMatrix, args...) = chol!(copy(A), args...)
function chol!(x::Number, args...)
rx = real(x)
rx == abs(x) || throw(DomainError())
rxr = sqrt(rx)
convert(promote_type(typeof(x), typeof(rxr)), rxr)
end
chol(x::Number, uplo::Symbol=:U) = chol!(x, uplo)
chol(x::Number, args...) = chol!(x, args...)

function convert{Tnew,Told,S,UpLo}(::Type{Cholesky{Tnew}},C::Cholesky{Told,S,UpLo})
Cnew = convert(AbstractMatrix{Tnew}, C.UL)
Expand All @@ -113,14 +124,14 @@ size(C::Union(Cholesky, CholeskyPivoted)) = size(C.UL)
size(C::Union(Cholesky, CholeskyPivoted), d::Integer) = size(C.UL,d)

function getindex{T,S,UpLo}(C::Cholesky{T,S,UpLo}, d::Symbol)
d == :U && return Triangular(UpLo == d ? C.UL : C.UL',:U)
d == :L && return Triangular(UpLo == d ? C.UL : C.UL',:L)
d == :UL && return Triangular(C.UL, UpLo)
d == :U && return Triangular(UpLo == d ? C.UL : C.UL', Token{:U})
d == :L && return Triangular(UpLo == d ? C.UL : C.UL', Token{:L})
d == :UL && return Triangular(C.UL, Token{UpLo})
throw(KeyError(d))
end
function getindex{T<:BlasFloat}(C::CholeskyPivoted{T}, d::Symbol)
d == :U && return Triangular(symbol(C.uplo) == d ? C.UL : C.UL', :U)
d == :L && return Triangular(symbol(C.uplo) == d ? C.UL : C.UL', :L)
d == :U && return Triangular(symbol(C.uplo) == d ? C.UL : C.UL', Token{:U})
d == :L && return Triangular(symbol(C.uplo) == d ? C.UL : C.UL', Token{:L})
d == :p && return C.piv
if d == :P
n = size(C, 1)
Expand All @@ -137,8 +148,8 @@ show{T,S<:AbstractMatrix,UpLo}(io::IO, C::Cholesky{T,S,UpLo}) = (println("$(type

A_ldiv_B!{T<:BlasFloat,S<:AbstractMatrix}(C::Cholesky{T,S,:U}, B::StridedVecOrMat{T}) = LAPACK.potrs!('U', C.UL, B)
A_ldiv_B!{T<:BlasFloat,S<:AbstractMatrix}(C::Cholesky{T,S,:L}, B::StridedVecOrMat{T}) = LAPACK.potrs!('L', C.UL, B)
A_ldiv_B!{T,S<:AbstractMatrix}(C::Cholesky{T,S,:L}, B::StridedVecOrMat) = Ac_ldiv_B!(Triangular(C.UL, :L, false), A_ldiv_B!(Triangular(C.UL, :L, false), B))
A_ldiv_B!{T,S<:AbstractMatrix}(C::Cholesky{T,S,:U}, B::StridedVecOrMat) = A_ldiv_B!(Triangular(C.UL, :U, false), Ac_ldiv_B!(Triangular(C.UL, :U, false), B))
A_ldiv_B!{T,S<:AbstractMatrix}(C::Cholesky{T,S,:L}, B::StridedVecOrMat) = Ac_ldiv_B!(Triangular(C.UL, Token{:L}), A_ldiv_B!(Triangular(C.UL, Token{:L}), B))
A_ldiv_B!{T,S<:AbstractMatrix}(C::Cholesky{T,S,:U}, B::StridedVecOrMat) = A_ldiv_B!(Triangular(C.UL, Token{:U}), Ac_ldiv_B!(Triangular(C.UL, Token{:U}), B))

function A_ldiv_B!{T<:BlasFloat}(C::CholeskyPivoted{T}, B::StridedVector{T})
chkfullrank(C)
Expand All @@ -156,8 +167,8 @@ function A_ldiv_B!{T<:BlasFloat}(C::CholeskyPivoted{T}, B::StridedMatrix{T})
end
B
end
A_ldiv_B!(C::CholeskyPivoted, B::StridedVector) = C.uplo=='L' ? Ac_ldiv_B!(Triangular(C.UL, symbol(C.uplo), false), A_ldiv_B!(Triangular(C.UL, symbol(C.uplo), false), B[C.piv]))[invperm(C.piv)] : A_ldiv_B!(Triangular(C.UL, symbol(C.uplo), false), Ac_ldiv_B!(Triangular(C.UL, symbol(C.uplo), false), B[C.piv]))[invperm(C.piv)]
A_ldiv_B!(C::CholeskyPivoted, B::StridedMatrix) = C.uplo=='L' ? Ac_ldiv_B!(Triangular(C.UL, symbol(C.uplo), false), A_ldiv_B!(Triangular(C.UL, symbol(C.uplo), false), B[C.piv,:]))[invperm(C.piv),:] : A_ldiv_B!(Triangular(C.UL, symbol(C.uplo), false), Ac_ldiv_B!(Triangular(C.UL, symbol(C.uplo), false), B[C.piv,:]))[invperm(C.piv),:]
A_ldiv_B!(C::CholeskyPivoted, B::StridedVector) = C.uplo == 'L' ? Ac_ldiv_B!(Triangular(C.UL, Token{symbol(C.uplo)}), A_ldiv_B!(Triangular(C.UL, Token{symbol(C.uplo)}), B[C.piv]))[invperm(C.piv)] : A_ldiv_B!(Triangular(C.UL, Token{symbol(C.uplo)}), Ac_ldiv_B!(Triangular(C.UL, Token{symbol(C.uplo)}), B[C.piv]))[invperm(C.piv)]
A_ldiv_B!(C::CholeskyPivoted, B::StridedMatrix) = C.uplo=='L' ? Ac_ldiv_B!(Triangular(C.UL, Token{symbol(C.uplo)}), A_ldiv_B!(Triangular(C.UL, Token{symbol(C.uplo)}), B[C.piv,:]))[invperm(C.piv),:] : A_ldiv_B!(Triangular(C.UL, Token{symbol(C.uplo)}), Ac_ldiv_B!(Triangular(C.UL, Token{symbol(C.uplo)}), B[C.piv,:]))[invperm(C.piv),:]

function det{T,S,UpLo}(C::Cholesky{T,S,UpLo})
dd = one(T)
Expand Down
16 changes: 8 additions & 8 deletions base/linalg/dense.jl
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Expand Up @@ -303,15 +303,15 @@ function sqrtm{T<:Real}(A::StridedMatrix{T})
issym(A) && return sqrtm(Symmetric(A))
n = chksquare(A)
SchurF = schurfact(complex(A))
R = full(sqrtm(Triangular(SchurF[:T], :U, false)))
R = full(sqrtm(Triangular(SchurF[:T], Token{:U})))
retmat = SchurF[:vectors]*R*SchurF[:vectors]'
all(imag(retmat) .== 0) ? real(retmat) : retmat
end
function sqrtm{T<:Complex}(A::StridedMatrix{T})
ishermitian(A) && return sqrtm(Hermitian(A))
n = chksquare(A)
SchurF = schurfact(A)
R = full(sqrtm(Triangular(SchurF[:T], :U, false)))
R = full(sqrtm(Triangular(SchurF[:T], Token{:U})))
SchurF[:vectors]*R*SchurF[:vectors]'
end
sqrtm(a::Number) = (b = sqrt(complex(a)); imag(b) == 0 ? real(b) : b)
Expand All @@ -321,9 +321,9 @@ function inv{S}(A::StridedMatrix{S})
T = typeof(one(S)/one(S))
Ac = convert(AbstractMatrix{T}, A)
if istriu(Ac)
Ai = inv(Triangular(A, :U, false))
Ai = inv(Triangular(A, Token{:U}))
elseif istril(Ac)
Ai = inv(Triangular(A, :L, false))
Ai = inv(Triangular(A, Token{:L}))
else
Ai = inv(lufact(Ac))
end
Expand Down Expand Up @@ -373,7 +373,7 @@ function factorize{T}(A::Matrix{T})
if utri1
return Bidiagonal(diag(A), diag(A, -1), false)
end
return Triangular(A, :L)
return Triangular(A, Token{:L})
end
if utri
return Bidiagonal(diag(A), diag(A, 1), true)
Expand All @@ -388,7 +388,7 @@ function factorize{T}(A::Matrix{T})
end
end
if utri
return Triangular(A, :U)
return Triangular(A, Token{:U})
end
if herm
try
Expand All @@ -409,9 +409,9 @@ function (\)(A::StridedMatrix, B::StridedVecOrMat)
m, n = size(A)
if m == n
if istril(A)
return istriu(A) ? \(Diagonal(A),B) : \(Triangular(A, :L),B)
return istriu(A) ? \(Diagonal(A),B) : \(Triangular(A, Token{:L}),B)
end
istriu(A) && return \(Triangular(A, :U),B)
istriu(A) && return \(Triangular(A, Token{:U}),B)
return \(lufact(A),B)
end
return qrfact(A,pivot=eltype(A)<:BlasFloat)\B
Expand Down
2 changes: 1 addition & 1 deletion base/linalg/factorization.jl
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Expand Up @@ -289,7 +289,7 @@ function A_ldiv_B!{T<:BlasFloat}(A::Union(QRCompactWY{T},QRPivoted{T}), B::Strid
# if cond(r[1:rnk, 1:rnk])*rcond < 1 break end
end
C, τ = LAPACK.tzrzf!(A.factors[1:rnk,:])
A_ldiv_B!(Triangular(C[1:rnk,1:rnk],:U),sub(Ac_mul_B!(getq(A),sub(B, 1:mA, 1:nrhs)),1:rnk,1:nrhs))
A_ldiv_B!(Triangular(C[1:rnk,1:rnk], Token{:U}), sub(Ac_mul_B!(getq(A), sub(B, 1:mA, 1:nrhs)), 1:rnk, 1:nrhs))
B[rnk+1:end,:] = zero(T)
LAPACK.ormrz!('L', iseltype(B, Complex) ? 'C' : 'T', C, τ, sub(B,1:nA,1:nrhs))
return isa(A,QRPivoted) ? B[invperm(A[:p]::Vector{BlasInt}),:] : B[1:nA,:], rnk
Expand Down
2 changes: 1 addition & 1 deletion base/linalg/generic.jl
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Expand Up @@ -424,7 +424,7 @@ function elementaryRightTrapezoid!(A::AbstractMatrix, row::Integer)
end

function det(A::AbstractMatrix)
(istriu(A) || istril(A)) && return det(Triangular(A, :U, false))
(istriu(A) || istril(A)) && return det(Triangular(A, Token{:U}))
return det(lufact(A))
end
det(x::Number) = x
Expand Down
4 changes: 2 additions & 2 deletions base/linalg/lu.jl
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Expand Up @@ -112,8 +112,8 @@ function getindex{T,S<:StridedMatrix}(A::LU{T,S}, d::Symbol)
end

A_ldiv_B!{T<:BlasFloat, S<:StridedMatrix}(A::LU{T, S}, B::StridedVecOrMat{T}) = @assertnonsingular LAPACK.getrs!('N', A.factors, A.ipiv, B) A.info
A_ldiv_B!{T,S<:StridedMatrix}(A::LU{T,S}, b::StridedVector) = A_ldiv_B!(Triangular(A.factors, :U, false), A_ldiv_B!(Triangular(A.factors, :L, true), b[ipiv2perm(A.ipiv, length(b))]))
A_ldiv_B!{T,S<:StridedMatrix}(A::LU{T,S}, B::StridedMatrix) = A_ldiv_B!(Triangular(A.factors, :U, false), A_ldiv_B!(Triangular(A.factors, :L, true), B[ipiv2perm(A.ipiv, size(B, 1)),:]))
A_ldiv_B!{T,S<:StridedMatrix}(A::LU{T,S}, b::StridedVector) = A_ldiv_B!(Triangular(A.factors, Token{:U}), A_ldiv_B!(Triangular(A.factors, Token{:L}, Token{true}), b[ipiv2perm(A.ipiv, length(b))]))
A_ldiv_B!{T,S<:StridedMatrix}(A::LU{T,S}, B::StridedMatrix) = A_ldiv_B!(Triangular(A.factors, Token{:U}), A_ldiv_B!(Triangular(A.factors, Token{:L}, Token{true}), B[ipiv2perm(A.ipiv, size(B, 1)),:]))
At_ldiv_B{T<:BlasFloat,S<:StridedMatrix}(A::LU{T,S}, B::StridedVecOrMat{T}) = @assertnonsingular LAPACK.getrs!('T', A.factors, A.ipiv, copy(B)) A.info
Ac_ldiv_B{T<:BlasComplex,S<:StridedMatrix}(A::LU{T,S}, B::StridedVecOrMat{T}) = @assertnonsingular LAPACK.getrs!('C', A.factors, A.ipiv, copy(B)) A.info
At_ldiv_Bt{T<:BlasFloat,S<:StridedMatrix}(A::LU{T,S}, B::StridedVecOrMat{T}) = @assertnonsingular LAPACK.getrs!('T', A.factors, A.ipiv, transpose(B)) A.info
Expand Down
4 changes: 2 additions & 2 deletions base/linalg/special.jl
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Expand Up @@ -4,8 +4,8 @@
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{Triangular}, A::Diagonal) = Triangular(full(A), :L)
convert(::Type{Triangular}, A::Bidiagonal) = Triangular(full(A), A.isupper ? :U : :L)
convert(::Type{Triangular}, A::Diagonal) = Triangular(full(A), Token{:L})
convert(::Type{Triangular}, A::Bidiagonal) = Triangular(full(A), Token{A.isupper ? :U : :L})
convert(::Type{Matrix}, D::Diagonal) = diagm(D.diag)

function convert(::Type{Diagonal}, A::Union(Bidiagonal, SymTridiagonal))
Expand Down
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