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RFC: Fix type instability for \ #9196

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RFC: Fix type instability for \ #9196

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a29910e
Fix #9191 on 0.3 and partly fix it on 0.4. Type instability in \. Als…
andreasnoack Nov 28, 2014
33f36aa
Fix #9191 for 0.4. Type instability of \
andreasnoack Nov 29, 2014
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1 change: 1 addition & 0 deletions base/exports.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -16,6 +16,7 @@ export
Markdown,

# Types
€,
AbstractMatrix,
AbstractSparseArray,
AbstractSparseMatrix,
Expand Down
2 changes: 2 additions & 0 deletions base/linalg.jl
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Expand Up @@ -9,6 +9,7 @@ export
BLAS,

# Types
€,
SymTridiagonal,
Tridiagonal,
Bidiagonal,
Expand Down Expand Up @@ -193,6 +194,7 @@ 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")))

immutable €{T} end

include("linalg/exceptions.jl")
include("linalg/generic.jl")
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94 changes: 47 additions & 47 deletions base/linalg/cholesky.jl
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Expand Up @@ -13,20 +13,20 @@ 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
function chol!{T<:BlasFloat,UpLo}(A::StridedMatrix{T}, ::Type{€{UpLo}})
C, info = LAPACK.potrf!(char_uplo(UpLo), A)
return @assertposdef Triangular{eltype(C),typeof(C),UpLo,false}(C) info
end

function chol!{T}(A::AbstractMatrix{T}, uplo::Symbol=:U)
function chol!{T,UpLo}(A::AbstractMatrix{T}, ::Type{€{UpLo}})
n = chksquare(A)
@inbounds begin
if uplo == :L
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)
A[k,k] = chol!(A[k,k], €{UpLo})
AkkInv = inv(A[k,k]')
for j = 1:k
for i = k + 1:n
Expand All @@ -35,12 +35,12 @@ function chol!{T}(A::AbstractMatrix{T}, uplo::Symbol=:U)
end
end
end
elseif uplo == :U
elseif UpLo == :U
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], uplo)
A[k,k] = chol!(A[k,k], €{UpLo})
AkkInv = inv(A[k,k])
for j = k + 1:n
for i = 1:k - 1
Expand All @@ -50,49 +50,55 @@ function chol!{T}(A::AbstractMatrix{T}, uplo::Symbol=:U)
end
end
else
throw(ArgumentError("uplo must be either :U or :L but was $(uplo)"))
throw(ArgumentError("UpLo must be either :U or :L but was $(UpLo)"))
end
end
return Triangular(A, uplo, false)
return Triangular(A, €{UpLo}, €{false})
end
chol!(A::AbstractMatrix) = chol!(A, €{:U})

function cholfact!{T<:BlasFloat}(A::StridedMatrix{T}, uplo::Symbol=:U; pivot=false, tol=0.0)
uplochar = char_uplo(uplo)
function cholfact!{T<:BlasFloat,UpLo}(A::StridedMatrix{T}, ::Type{€{UpLo}}; 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)
return Cholesky{T,typeof(A),UpLo}(chol!(A, €{UpLo}).data)
end
cholfact!(A::AbstractMatrix, uplo::Symbol=:U) = Cholesky{eltype(A),typeof(A),uplo}(chol!(A, uplo).data)
cholfact!{UpLo}(A::AbstractMatrix, ::Type{€{UpLo}}) = Cholesky{eltype(A),typeof(A),UpLo}(chol!(A, €{UpLo}).data)
cholfact!(A::AbstractMatrix) = cholfact!(A, €{: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,UpLo}(A::StridedMatrix{T}, ::Type{€{UpLo}}; pivot=false, tol=0.0) = cholfact!(copy(A), €{UpLo}, pivot=pivot, tol=tol)
function cholfact{T,UpLo}(A::StridedMatrix{T}, ::Type{€{UpLo}}; pivot=false, tol=0.0)
S = promote_type(typeof(chol(one(T))),Float32)
S <: BlasFloat && return cholfact!(convert(AbstractMatrix{S}, A), uplo, pivot = pivot, tol = tol)
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 != T && return cholfact!(convert(AbstractMatrix{S}, A), €{UpLo})
return cholfact!(copy(A), €{UpLo})
end
function cholfact(x::Number, uplo::Symbol=:U)
function cholfact{UpLo}(x::Number, ::Type{€{UpLo}})
xf = fill(chol!(x), 1, 1)
Cholesky{:U, eltype(xf), typeof(xf)}(xf)
end
cholfact(A; pivot=false, tol=0.0) = cholfact(A, €{:U}; pivot = pivot, tol = tol)

chol(A::AbstractMatrix, uplo::Symbol=:U) = chol!(copy(A), uplo)
function chol!(x::Number, uplo::Symbol=:U)
chol{UpLo}(A::AbstractMatrix, ::Type{€{UpLo}}) = chol!(copy(A), €{UpLo})
chol(A::AbstractMatrix) = chol!(copy(A), €{:U})
function chol!(x::Number)
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, ::Type) = chol!(x)
chol(x::Number) = chol!(x)
chol(x::Number, ::Type) = chol!(x, €{:U})

function convert{Tnew,Told,S,UpLo}(::Type{Cholesky{Tnew}},C::Cholesky{Told,S,UpLo})
Cnew = convert(AbstractMatrix{Tnew}, C.UL)
Expand All @@ -106,39 +112,33 @@ convert{T}(::Type{Factorization{T}}, C::Cholesky) = convert(Cholesky{T}, C)
convert{T}(::Type{CholeskyPivoted{T}},C::CholeskyPivoted) = CholeskyPivoted(convert(AbstractMatrix{T},C.UL),C.uplo,C.piv,C.rank,C.tol,C.info)
convert{T}(::Type{Factorization{T}}, C::CholeskyPivoted) = convert(CholeskyPivoted{T}, C)

full{T,S}(C::Cholesky{T,S,:U}) = C[:U]'C[:U]
full{T,S}(C::Cholesky{T,S,:L}) = C[:L]*C[:L]'
full{T,S}(C::Cholesky{T,S,:U}) = C[€{:U}]'C[€{:U}]
full{T,S}(C::Cholesky{T,S,:L}) = C[€{:L}]*C[€{:L}]'

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)
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 == :p && return C.piv
if d == :P
n = size(C, 1)
P = zeros(T, n, n)
for i=1:n
P[C.piv[i],i] = one(T)
end
return P
getindex{T,S,UpLo}(C::Cholesky{T,S,UpLo}, ::Type{€{:U}}) = Triangular(UpLo == :U ? C.UL : C.UL', €{:U})
getindex{T,S,UpLo}(C::Cholesky{T,S,UpLo}, ::Type{€{:L}}) = Triangular(UpLo == :L ? C.UL : C.UL', €{:L})
getindex{T,S,UpLo}(C::Cholesky{T,S,UpLo}, ::Type{€{:UL}}) = Triangular(C.UL, €{UpLo})
getindex{T<:BlasFloat}(C::CholeskyPivoted{T}, ::Type{€{:U}}) = Triangular(C.uplo == 'U' ? C.UL : C.UL', €{:U})
getindex{T<:BlasFloat}(C::CholeskyPivoted{T}, ::Type{€{:L}}) = Triangular(C.uplo == 'L' ? C.UL : C.UL', €{:L})
getindex{T<:BlasFloat}(C::CholeskyPivoted{T}, ::Type{€{:p}}) = C.piv
function getindex{T<:BlasFloat}(C::CholeskyPivoted{T}, ::Type{€{:P}})
n = size(C, 1)
P = zeros(T, n, n)
for i = 1:n
P[C.piv[i],i] = one(T)
end
throw(KeyError(d))
return P
end

show{T,S<:AbstractMatrix,UpLo}(io::IO, C::Cholesky{T,S,UpLo}) = (println("$(typeof(C)) with factor:");show(io,C[UpLo]))

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, €{: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))

function A_ldiv_B!{T<:BlasFloat}(C::CholeskyPivoted{T}, B::StridedVector{T})
chkfullrank(C)
Expand All @@ -156,8 +156,8 @@ 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, €{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),:]

function det{T,S,UpLo}(C::Cholesky{T,S,UpLo})
dd = one(T)
Expand Down
34 changes: 17 additions & 17 deletions base/linalg/dense.jl
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Expand Up @@ -307,16 +307,16 @@ 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)))
retmat = SchurF[:vectors]*R*SchurF[:vectors]'
R = full(sqrtm(Triangular(SchurF[€{:T}], €{:U}, €{false})))
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)))
SchurF[:vectors]*R*SchurF[:vectors]'
R = full(sqrtm(Triangular(SchurF[€{:T}], €{:U}, €{false})))
SchurF[€{:vectors}]*R*SchurF[€{:vectors}]'
end
sqrtm(a::Number) = (b = sqrt(complex(a)); imag(b) == 0 ? real(b) : b)
sqrtm(a::Complex) = sqrt(a)
Expand All @@ -325,9 +325,9 @@ 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, €{:U}, €{false}))
elseif istril(Ac)
Ai = inv(Triangular(A, :L, false))
Ai = inv(Triangular(A, €{:L}, €{false}))
else
Ai = inv(lufact(Ac))
end
Expand Down Expand Up @@ -377,7 +377,7 @@ function factorize{T}(A::Matrix{T})
if utri1
return Bidiagonal(diag(A), diag(A, -1), false)
end
return Triangular(A, :L)
return Triangular(A, €{:L})
end
if utri
return Bidiagonal(diag(A), diag(A, 1), true)
Expand All @@ -392,7 +392,7 @@ function factorize{T}(A::Matrix{T})
end
end
if utri
return Triangular(A, :U)
return Triangular(A, €{:U})
end
if herm
try
Expand All @@ -413,9 +413,9 @@ 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, €{:L}),B)
end
istriu(A) && return \(Triangular(A, :U),B)
istriu(A) && return \(Triangular(A, €{:U}),B)
return \(lufact(A),B)
end
return qrfact(A,pivot=eltype(A)<:BlasFloat)\B
Expand All @@ -440,12 +440,12 @@ function pinv{T}(A::StridedMatrix{T}, tol::Real)
end
end
SVD = svdfact(A, thin=true)
S = eltype(SVD[:S])
Sinv = zeros(S, length(SVD[:S]))
index = SVD[:S] .> tol*maximum(SVD[:S])
Sinv[index] = one(S) ./ SVD[:S][index]
S = eltype(SVD[€{:S}])
Sinv = zeros(S, length(SVD[€{:S}]))
index = SVD[€{:S}] .> tol*maximum(SVD[€{:S}])
Sinv[index] = one(S) ./ SVD[€{:S}][index]
Sinv[find(!isfinite(Sinv))] = zero(S)
return SVD[:Vt]'scale(Sinv, SVD[:U]')
return SVD[€{:Vt}]'scale(Sinv, SVD[€{:U}]')
end
function pinv{T}(A::StridedMatrix{T})
tol = eps(real(float(one(T))))*maximum(size(A))
Expand All @@ -459,8 +459,8 @@ function null{T}(A::StridedMatrix{T})
m, n = size(A)
(m == 0 || n == 0) && return eye(T, n)
SVD = svdfact(A, thin=false)
indstart = sum(SVD[:S] .> max(m,n)*maximum(SVD[:S])*eps(eltype(SVD[:S]))) + 1
return SVD[:V][:,indstart:end]
indstart = sum(SVD[€{:S}] .> max(m,n)*maximum(SVD[€{:S}])*eps(eltype(SVD[€{:S}]))) + 1
return SVD[€{:V}][:,indstart:end]
end
null(a::StridedVector) = null(reshape(a, length(a), 1))

Expand Down
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