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WIP: Linear Algebra bikeshedding #2212

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WIP: Linear Algebra bikeshedding #2212

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df8f86e
Reinstate all the commits from #2069.
ViralBShah Feb 4, 2013
bc7dec7
Get rid of chold. Add documentation for chol.
ViralBShah Feb 6, 2013
fe13a03
Rename cholpd to cholpivot. Add docs for cholpivot.
ViralBShah Feb 6, 2013
ccf2024
Improve UMFpack interface
dmbates Feb 6, 2013
b96e9c2
Merge remote-tracking branch 'origin/vs/linalg2' into origin-vs-linalg2
dmbates Feb 6, 2013
c5b0fe0
Rename lud to lu. Update docs.
ViralBShah Feb 7, 2013
2fe3c04
Rename QRPDense to QRDensePivoted. Use qr and qrpivot instead of qrd …
ViralBShah Feb 7, 2013
b259333
Deprecate old dense matrix factorization names.
ViralBShah Feb 7, 2013
bf427cd
Replace lud with lu in suitesparse.jl
ViralBShah Feb 7, 2013
1187918
Merge branch 'master' into vs/linalg2
ViralBShah Feb 7, 2013
5ddf16b
Got the basic CHOLMOD functions associated with a dense matrix workin…
dmbates Feb 7, 2013
2ce6abc
Defined a CholmodSparse type
dmbates Feb 7, 2013
614530e
Incorporate suggestion from Jameson on keeping pointer contents alive
dmbates Feb 8, 2013
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254 changes: 124 additions & 130 deletions base/blas.jl
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6 changes: 6 additions & 0 deletions base/deprecated.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -52,6 +52,11 @@ end
@deprecate chars collect
@deprecate elements collect
@deprecate strcat string
@deprecate chold chol
@deprecate cholpd cholpivot
@deprecate lud lu
@deprecate qrd qr
@deprecate qrpd qrpivot
@deprecate iswalnum isalnum
@deprecate iswalpha isalpha
@deprecate iswascii isascii
Expand All @@ -67,6 +72,7 @@ end
@deprecate iswxdigit isxdigit
@deprecate copy_to copy!


export randi
function randi(n,x...)
warn_once("randi(n,...) is deprecated, use rand(1:n,...) instead.")
Expand Down
20 changes: 8 additions & 12 deletions base/exports.jl
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Expand Up @@ -109,7 +109,7 @@ export
LUTridiagonal,
LDLTTridiagonal,
QRDense,
QRPDense,
QRDensePivoted,
InsertionSort,
QuickSort,
MergeSort,
Expand Down Expand Up @@ -523,10 +523,9 @@ export

# linear algebra
chol,
chold,
chold!,
cholpd,
cholpd!,
chol!,
cholpivot,
cholpivot!,
cond,
cross,
ctranspose,
Expand Down Expand Up @@ -554,18 +553,15 @@ export
ldltd,
linreg,
lu,
lud,
lud!,
lu!,
norm,
normfro,
null,
pinv,
qr,
qrd!,
qrd,
qrp,
qrpd!,
qrpd,
qr!,
qrpivot,
qrpivot!,
randsym,
rank,
rref,
Expand Down
8 changes: 8 additions & 0 deletions base/lapack.jl
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Expand Up @@ -12,6 +12,14 @@ type LapackException <: Exception
info::BlasInt
end

type PosDefException <: Exception
info::BlasInt
end

type RankDeficientException <: Exception
info::BlasInt
end

type SingularException <: Exception
info::BlasInt
end
Expand Down
129 changes: 65 additions & 64 deletions base/linalg_dense.jl
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Expand Up @@ -389,13 +389,15 @@ end

\{T<:BlasFloat}(B::BunchKaufman{T}, R::StridedVecOrMat{T}) =
LAPACK.sytrs!(B.UL, B.LD, B.ipiv, copy(R))


# Dense Cholesky factorization

type CholeskyDense{T<:BlasFloat} <: Factorization{T}
LR::Matrix{T}
UL::BlasChar
function CholeskyDense(A::Matrix{T}, UL::BlasChar)
function CholeskyDense{T<:BlasFloat}(A::Matrix{T}, UL::BlasChar)
A, info = LAPACK.potrf!(UL, A)
if info != 0 error("Matrix A not positive-definite") end
if info != 0; throw(LAPACK.PosDefException(info)); end
if UL == 'U'
new(triu!(A), UL)
elseif UL == 'L'
Expand All @@ -407,7 +409,7 @@ type CholeskyDense{T<:BlasFloat} <: Factorization{T}
end

size(C::CholeskyDense) = size(C.LR)
size(C::CholeskyDense,d::Integer) = size(C.LR,d)
size(C::CholeskyDense, d::Integer) = size(C.LR, d)

factors(C::CholeskyDense) = C.LR

Expand All @@ -417,28 +419,27 @@ factors(C::CholeskyDense) = C.LR
function det{T}(C::CholeskyDense{T})
ff = C.LR
dd = one(T)
for i in 1:size(ff,1) dd *= abs2(ff[i,i]) end
for i in 1:size(ff,1); dd *= abs2(ff[i,i]); end
dd
end

function inv(C::CholeskyDense)
Ci, info = LAPACK.potri!(C.UL, copy(C.LR))
if info != 0 error("Matrix singular") end
if info != 0; throw(LAPACK.SingularException(info)); end
symmetrize!(Ci, C.UL)
end

## Should these functions check that the matrix is Hermitian?
chold!{T<:BlasFloat}(A::Matrix{T}, UL::BlasChar) = CholeskyDense{T}(A, UL)
chold!{T<:BlasFloat}(A::Matrix{T}) = chold!(A, 'U')
chold{T<:BlasFloat}(A::Matrix{T}, UL::BlasChar) = chold!(copy(A), UL)
chold{T<:Number}(A::Matrix{T}, UL::BlasChar) = chold(float64(A), UL)
chold{T<:Number}(A::Matrix{T}) = chold(A, 'U')

## Matlab (and R) compatible
chol(A::Matrix, UL::BlasChar) = factors(chold(A, UL))
chol(A::Matrix) = chol(A, 'U')
chol!{T<:BlasFloat}(A::Matrix{T}, UL::BlasChar) = CholeskyDense{T}(A, UL)
chol!{T<:BlasFloat}(A::Matrix{T}) = chol!(A, 'U')
chol{T<:BlasFloat}(A::Matrix{T}, UL::BlasChar) = chol!(copy(A), UL)
chol{T<:Number}(A::Matrix{T}, UL::BlasChar) = chol(float64(A), UL)
chol{T<:Number}(A::Matrix{T}) = chol(A, 'U')

chol(x::Number) = imag(x) == 0 && real(x) > 0 ? sqrt(x) : error("Argument not positive-definite")

# Pivoted Cholesky factorization

type CholeskyDensePivoted{T<:BlasFloat} <: Factorization{T}
LR::Matrix{T}
UL::BlasChar
Expand All @@ -447,6 +448,7 @@ type CholeskyDensePivoted{T<:BlasFloat} <: Factorization{T}
tol::Real
function CholeskyDensePivoted(A::Matrix{T}, UL::BlasChar, tol::Real)
A, piv, rank, info = LAPACK.pstrf!(UL, A, tol)
if info != 0; throw(LAPACK.RankDeficientException(info)); end
if UL == 'U'
new(triu!(A), UL, piv, rank, tol)
elseif UL == 'L'
Expand All @@ -463,11 +465,12 @@ size(C::CholeskyDensePivoted,d::Integer) = size(C.LR,d)
factors(C::CholeskyDensePivoted) = C.LR, C.piv

function \{T<:BlasFloat}(C::CholeskyDensePivoted{T}, B::StridedVector{T})
if C.rank < size(C.LR, 1) error("Matrix is not positive-definite") end
if C.rank < size(C.LR, 1); throw(LAPACK.RankDeficientException(info)); end
LAPACK.potrs!(C.UL, C.LR, copy(B)[C.piv])[invperm(C.piv)]
end

function \{T<:BlasFloat}(C::CholeskyDensePivoted{T}, B::StridedMatrix{T})
if C.rank < size(C.LR, 1) error("Matrix is not positive-definite") end
if C.rank < size(C.LR, 1); throw(LAPACK.RankDeficientException(info)); end
LAPACK.potrs!(C.UL, C.LR, copy(B)[C.piv,:])[invperm(C.piv),:]
end

Expand All @@ -490,18 +493,20 @@ function inv(C::CholeskyDensePivoted)
end

## Should these functions check that the matrix is Hermitian?
cholpd!{T<:BlasFloat}(A::Matrix{T}, UL::BlasChar, tol::Real) = CholeskyDensePivoted{T}(A, UL, tol)
cholpd!{T<:BlasFloat}(A::Matrix{T}, UL::BlasChar) = cholpd!(A, UL, -1.)
cholpd!{T<:BlasFloat}(A::Matrix{T}, tol::Real) = cholpd!(A, 'U', tol)
cholpd!{T<:BlasFloat}(A::Matrix{T}) = cholpd!(A, 'U', -1.)
cholpd{T<:Number}(A::Matrix{T}, UL::BlasChar, tol::Real) = cholpd(float64(A), UL, tol)
cholpd{T<:Number}(A::Matrix{T}, UL::BlasChar) = cholpd(float64(A), UL, -1.)
cholpd{T<:Number}(A::Matrix{T}, tol::Real) = cholpd(float64(A), true, tol)
cholpd{T<:Number}(A::Matrix{T}) = cholpd(float64(A), 'U', -1.)
cholpd{T<:BlasFloat}(A::Matrix{T}, UL::BlasChar, tol::Real) = cholpd!(copy(A), UL, tol)
cholpd{T<:BlasFloat}(A::Matrix{T}, UL::BlasChar) = cholpd!(copy(A), UL, -1.)
cholpd{T<:BlasFloat}(A::Matrix{T}, tol::Real) = cholpd!(copy(A), 'U', tol)
cholpd{T<:BlasFloat}(A::Matrix{T}) = cholpd!(copy(A), 'U', -1.)
cholpivot!{T<:BlasFloat}(A::Matrix{T}, UL::BlasChar, tol::Real) = CholeskyDensePivoted{T}(A, UL, tol)
cholpivot!{T<:BlasFloat}(A::Matrix{T}, UL::BlasChar) = cholpivot!(A, UL, -1.)
cholpivot!{T<:BlasFloat}(A::Matrix{T}, tol::Real) = cholpivot!(A, 'U', tol)
cholpivot!{T<:BlasFloat}(A::Matrix{T}) = cholpivot!(A, 'U', -1.)
cholpivot{T<:Number}(A::Matrix{T}, UL::BlasChar, tol::Real) = cholpivot(float64(A), UL, tol)
cholpivot{T<:Number}(A::Matrix{T}, UL::BlasChar) = cholpivot(float64(A), UL, -1.)
cholpivot{T<:Number}(A::Matrix{T}, tol::Real) = cholpivot(float64(A), true, tol)
cholpivot{T<:Number}(A::Matrix{T}) = cholpivot(float64(A), 'U', -1.)
cholpivot{T<:BlasFloat}(A::Matrix{T}, UL::BlasChar, tol::Real) = cholpivot!(copy(A), UL, tol)
cholpivot{T<:BlasFloat}(A::Matrix{T}, UL::BlasChar) = cholpivot!(copy(A), UL, -1.)
cholpivot{T<:BlasFloat}(A::Matrix{T}, tol::Real) = cholpivot!(copy(A), 'U', tol)
cholpivot{T<:BlasFloat}(A::Matrix{T}) = cholpivot!(copy(A), 'U', -1.)

# LU Factorization

type LUDense{T} <: Factorization{T}
lu::Matrix{T}
Expand Down Expand Up @@ -531,17 +536,13 @@ function factors{T}(lu::LUDense{T})
L, U, P
end

function lud!{T<:BlasFloat}(A::Matrix{T})
function lu!{T<:BlasFloat}(A::Matrix{T})
lu, ipiv, info = LAPACK.getrf!(A)
LUDense{T}(lu, ipiv, info)
end

lud{T<:BlasFloat}(A::Matrix{T}) = lud!(copy(A))
lud{T<:Number}(A::Matrix{T}) = lud(float64(A))

## Matlab-compatible
lu{T<:Number}(A::Matrix{T}) = factors(lud(A))
lu(x::Number) = (one(x), x, [1])
lu{T<:BlasFloat}(A::Matrix{T}) = lu!(copy(A))
lu{T<:Number}(A::Matrix{T}) = lu(float64(A))

function det{T}(lu::LUDense{T})
m, n = size(lu)
Expand Down Expand Up @@ -572,17 +573,16 @@ end
size(A::QRDense) = size(A.hh)
size(A::QRDense,n) = size(A.hh,n)

qrd!{T<:BlasFloat}(A::StridedMatrix{T}) = QRDense{T}(LAPACK.geqrf!(A)...)
qrd{T<:BlasFloat}(A::StridedMatrix{T}) = qrd!(copy(A))
qrd{T<:Real}(A::StridedMatrix{T}) = qrd(float64(A))
qr!{T<:BlasFloat}(A::StridedMatrix{T}) = QRDense{T}(LAPACK.geqrf!(A)...)
qr{T<:BlasFloat}(A::StridedMatrix{T}) = qr!(copy(A))
qr{T<:Real}(A::StridedMatrix{T}) = qr(float64(A))

function factors{T<:BlasFloat}(qrd::QRDense{T})
aa = copy(qrd.hh)
function factors{T<:BlasFloat}(qr::QRDense{T})
aa = copy(qr.hh)
R = triu(aa[1:min(size(aa)),:]) # must be *before* call to orgqr!
LAPACK.orgqr!(aa, qrd.tau, size(aa,2)), R
LAPACK.orgqr!(aa, qr.tau, size(aa,2)), R
end

qr{T<:Number}(x::StridedMatrix{T}) = factors(qrd(x))
qr(x::Number) = (one(x), x)

## Multiplication by Q from the QR decomposition
Expand All @@ -601,41 +601,42 @@ function (\){T<:BlasFloat}(A::QRDense{T}, B::StridedVecOrMat{T})
return ans
end

type QRPDense{T} <: Factorization{T}
## Pivoted QR decomposition

type QRDensePivoted{T} <: Factorization{T}
hh::Matrix{T}
tau::Vector{T}
jpvt::Vector{BlasInt}
function QRPDense(hh::Matrix{T}, tau::Vector{T}, jpvt::Vector{BlasInt})
function QRDensePivoted(hh::Matrix{T}, tau::Vector{T}, jpvt::Vector{BlasInt})
m, n = size(hh)
if length(tau) != min(m,n) || length(jpvt) != n
error("QRPDense: mismatched dimensions")
error("QRDensePivoted: mismatched dimensions")
end
new(hh,tau,jpvt)
end
end
size(x::QRPDense) = size(x.hh)
size(x::QRPDense,d) = size(x.hh,d)
size(x::QRDensePivoted) = size(x.hh)
size(x::QRDensePivoted,d) = size(x.hh,d)
## Multiplication by Q from the QR decomposition
(*){T<:BlasFloat}(A::QRPDense{T}, B::StridedVecOrMat{T}) =
(*){T<:BlasFloat}(A::QRDensePivoted{T}, B::StridedVecOrMat{T}) =
LAPACK.ormqr!('L', 'N', A.hh, size(A,2), A.tau, copy(B))
## Multiplication by Q' from the QR decomposition
Ac_mul_B{T<:BlasFloat}(A::QRPDense{T}, B::StridedVecOrMat{T}) =
Ac_mul_B{T<:BlasFloat}(A::QRDensePivoted{T}, B::StridedVecOrMat{T}) =
LAPACK.ormqr!('L', iscomplex(A.tau)?'C':'T', A.hh, size(A,2), A.tau, copy(B))

qrpd!{T<:BlasFloat}(A::StridedMatrix{T}) = QRPDense{T}(LAPACK.geqp3!(A)...)
qrpd{T<:BlasFloat}(A::StridedMatrix{T}) = qrpd!(copy(A))
qrpd{T<:Real}(x::StridedMatrix{T}) = qrpd(float64(x))
qrpivot!{T<:BlasFloat}(A::StridedMatrix{T}) = QRDensePivoted{T}(LAPACK.geqp3!(A)...)
qrpivot{T<:BlasFloat}(A::StridedMatrix{T}) = qrpivot!(copy(A))
qrpivot{T<:Real}(x::StridedMatrix{T}) = qrpivot(float64(x))

function factors{T<:BlasFloat}(x::QRPDense{T})
function factors{T<:BlasFloat}(x::QRDensePivoted{T})
aa = copy(x.hh)
R = triu(aa[1:min(size(aa)),:])
LAPACK.orgqr!(aa, x.tau, size(aa,2)), R, x.jpvt
end

qrp{T<:BlasFloat}(x::StridedMatrix{T}) = factors(qrpd(x))
qrp{T<:Real}(x::StridedMatrix{T}) = qrp(float64(x))
qrpivot{T<:Real}(x::StridedMatrix{T}) = qrpivot(float64(x))

function (\){T<:BlasFloat}(A::QRPDense{T}, B::StridedVecOrMat{T})
function (\){T<:BlasFloat}(A::QRDensePivoted{T}, B::StridedVecOrMat{T})
n = length(A.tau)
x, info = LAPACK.trtrs!('U','N','N',A.hh[1:n,:],(A'*B)[1:n,:])
if info > 0; throw(LAPACK.SingularException(info)); end
Expand Down Expand Up @@ -675,7 +676,7 @@ function det(A::Matrix)
m, n = size(A)
if m != n; error("det only defined for square matrices"); end
if istriu(A) | istril(A); return prod(diag(A)); end
return det(lud(A))
return det(lu(A))
end
det(x::Number) = x

Expand Down Expand Up @@ -889,7 +890,7 @@ function cond(A::StridedMatrix, p)
elseif p == 1 || p == Inf
m, n = size(A)
if m != n; error("Use 2-norm for non-square matrices"); end
cnd = 1 / LAPACK.gecon!(p == 1 ? '1' : 'I', lud(A).lu, norm(A, p))
cnd = 1 / LAPACK.gecon!(p == 1 ? '1' : 'I', lu(A).lu, norm(A, p))
else
error("Norm type must be 1, 2 or Inf")
end
Expand Down Expand Up @@ -1185,16 +1186,16 @@ end

#show(io, lu::LUTridiagonal) = print(io, "LU decomposition of ", summary(lu.lu))

lud!{T}(A::Tridiagonal{T}) = LUTridiagonal{T}(LAPACK.gttrf!(A.dl,A.d,A.du)...)
lud{T}(A::Tridiagonal{T}) = LUTridiagonal{T}(LAPACK.gttrf!(copy(A.dl),copy(A.d),copy(A.du))...)
lu(A::Tridiagonal) = factors(lud(A))
lu!{T}(A::Tridiagonal{T}) = LUTridiagonal{T}(LAPACK.gttrf!(A.dl,A.d,A.du)...)
lu{T}(A::Tridiagonal{T}) = LUTridiagonal{T}(LAPACK.gttrf!(copy(A.dl),copy(A.d),copy(A.du))...)
lu(A::Tridiagonal) = factors(lu(A))

function det{T}(lu::LUTridiagonal{T})
n = length(lu.d)
prod(lu.d) * (bool(sum(lu.ipiv .!= 1:n) % 2) ? -one(T) : one(T))
end

det(A::Tridiagonal) = det(lud(A))
det(A::Tridiagonal) = det(lu(A))

(\){T<:BlasFloat}(lu::LUTridiagonal{T}, B::StridedVecOrMat{T}) =
LAPACK.gttrs!('N', lu.dl, lu.d, lu.du, lu.du2, lu.ipiv, copy(B))
Expand Down
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