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lapack.jl
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lapack.jl
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## The LAPACK module of interfaces to LAPACK subroutines
module LAPACK
const liblapack = Base.liblapack_name
import Base.BlasFloat
import Base.BlasChar
import Base.BlasInt
import Base.blas_int
type LapackException <: Exception
info::BlasInt
end
type SingularException <: Exception
info::BlasInt
end
type LapackDimMisMatch <: Exception
name::ASCIIString
end
function chkstride1(A::StridedVecOrMat...)
for a in A
if stride(a,1) != 1 error("LAPACK: Matrix must have contiguous columns") end
end
end
function chksquare(A::Matrix...)
for a in A
m, n = size(a)
if m != n error("LAPACK: Matrix must be square") end
end
end
# (GB) general banded matrices, LU decomposition and solver
for (gbtrf, gbtrs, elty) in
((:dgbtrf_,:dgbtrs_,:Float64),
(:sgbtrf_,:sgbtrs_,:Float32),
(:zgbtrf_,:zgbtrs_,:Complex128),
(:cgbtrf_,:cgbtrs_,:Complex64))
@eval begin
# SUBROUTINE DGBTRF( M, N, KL, KU, AB, LDAB, IPIV, INFO )
# * .. Scalar Arguments ..
# INTEGER INFO, KL, KU, LDAB, M, N
# * .. Array Arguments ..
# INTEGER IPIV( * )
# DOUBLE PRECISION AB( LDAB, * )
function gbtrf!(kl::Integer, ku::Integer, m::Integer, AB::StridedMatrix{$elty})
chkstride1(AB)
info = Array(BlasInt, 1)
n = size(AB, 2)
mnmn = min(m, n)
ipiv = Array(BlasInt, mnmn)
ccall(($(string(gbtrf)),liblapack), Void,
(Ptr{BlasInt}, Ptr{BlasInt}, Ptr{BlasInt}, Ptr{BlasInt},
Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt}, Ptr{BlasInt}),
&m, &n, &kl, &ku, AB, &stride(AB,2), ipiv, info)
if info[1] != 0 throw(LapackException(info[1])) end
AB, ipiv
end
# SUBROUTINE DGBTRS( TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO)
# * .. Scalar Arguments ..
# CHARACTER TRANS
# INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS
# * .. Array Arguments ..
# INTEGER IPIV( * )
# DOUBLE PRECISION AB( LDAB, * ), B( LDB, * )
function gbtrs!(trans::BlasChar, kl::Integer, ku::Integer, m::Integer,
AB::StridedMatrix{$elty}, ipiv::Vector{BlasInt},
B::StridedVecOrMat{$elty})
chkstride1(AB, B)
info = Array(BlasInt, 1)
n = size(AB,2)
if m != n || m != size(B,1) throw(LapackDimMisMatch("gbtrs!")) end
ccall(($(string(gbtrs)),liblapack), Void,
(Ptr{Uint8}, Ptr{BlasInt}, Ptr{BlasInt}, Ptr{BlasInt}, Ptr{BlasInt},
Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt},
Ptr{BlasInt}),
&trans, &n, &kl, &ku, &size(B,2), AB, &stride(AB,2), ipiv,
B, &stride(B,2), info)
if info[1] != 0 throw(LapackException(info[1])) end
B
end
end
end
## (GE) general matrices: balancing and back-transforming
for (gebal, gebak, elty, relty) in
((:dgebal_, :dgebak_, :Float64, :Float64),
(:sgebal_, :sgebak_, :Float32, :Float32),
(:zgebal_, :zgebak_, :Complex128, :Float64),
(:cgebal_, :cgebak_, :Complex64, :Float32))
@eval begin
# SUBROUTINE DGEBAL( JOB, N, A, LDA, ILO, IHI, SCALE, INFO )
#* .. Scalar Arguments ..
# CHARACTER JOB
# INTEGER IHI, ILP, INFO, LDA, N
# .. Array Arguments ..
# DOUBLE PRECISION A( LDA, * ), SCALE( * )
function gebal!(job::BlasChar, A::StridedMatrix{$elty})
chkstride1(A)
chksquare(A)
n = size(A, 2)
info = Array(BlasInt, 1)
ihi = Array(BlasInt, 1)
ilo = Array(BlasInt, 1)
scale = Array($relty, n)
ccall(($(string(gebal)),liblapack), Void,
(Ptr{Uint8}, Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt},
Ptr{BlasInt}, Ptr{BlasInt}, Ptr{$relty}, Ptr{BlasInt}),
&job, &n, A, &stride(A,2), ilo, ihi, scale, info)
if info[1] != 0 throw(LapackException(info[1])) end
ilo[1], ihi[1], scale
end
# SUBROUTINE DGEBAK( JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV, INFO )
#* .. Scalar Arguments ..
# CHARACTER JOB, SIDE
# INTEGER IHI, ILP, INFO, LDV, M, N
# .. Array Arguments ..
# DOUBLE PRECISION SCALE( * ), V( LDV, * )
function gebak!(job::BlasChar, side::BlasChar,
ilo::BlasInt, ihi::BlasInt, scale::Vector{$elty},
V::StridedMatrix{$elty})
chkstride1(V)
chksquare(V)
info = Array(BlasInt, 1)
ccall(($(string(gebak)),liblapack), Void,
(Ptr{Uint8}, Ptr{Uint8}, Ptr{BlasInt}, Ptr{BlasInt}, Ptr{BlasInt},
Ptr{$elty}, Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt}),
&job, &side, &size(V,1), &ilo, &ihi, scale, &n, V, &stride(V,2), info)
if info[1] != 0 throw(LapackException(info[1])) end
V
end
end
end
# (GE) general matrices, direct decompositions
# gebrd - reduction to bidiagonal form Q'*A*P=B where Q and P are orthogonal
# gelqf - unpivoted LQ decomposition
# geqlf - unpivoted QL decomposition
# geqrf - unpivoted QR decomposition
# gegp3 - pivoted QR decomposition
# gerqf - unpivoted RQ decomposition
# getrf - LU decomposition
for (gebrd, gelqf, geqlf, geqrf, geqp3, gerqf, getrf, elty, relty) in
((:dgebrd_,:dgelqf_,:dgeqlf_,:dgeqrf_,:dgeqp3_,:dgerqf_,:dgetrf_,:Float64, Float64),
(:sgebrd_,:sgelqf_,:sgeqlf_,:sgeqrf_,:sgeqp3_,:sgerqf_,:sgetrf_,:Float32, Float32),
(:zgebrd_,:zgelqf_,:zgeqlf_,:zgeqrf_,:zgeqp3_,:zgerqf_,:zgetrf_,:Complex128, Float64),
(:cgebrd_,:cgelqf_,:cgeqlf_,:cgeqrf_,:cgeqp3_,:cgerqf_,:cgetrf_,:Complex64, Float32))
@eval begin
# SUBROUTINE DGEBRD( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK,
# INFO )
# .. Scalar Arguments ..
# INTEGER INFO, LDA, LWORK, M, N
# .. Array Arguments ..
# DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAUP( * ),
# TAUQ( * ), WORK( * )
function gebrd!(A::StridedMatrix{$elty})
chkstride1(A)
m, n = size(A)
k = min(m, n)
d = Array($elty, k)
s = Array($elty, k)
tauq = Array($elty, k)
taup = Array($elty, k)
work = Array($elty, 1)
lwork = blas_int(-1)
info = Array(BlasInt, 1)
for i in 1:2
ccall(($(string(gebrd)),liblapack), Void,
(Ptr{BlasInt}, Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt},
Ptr{$elty}, Ptr{$elty}, Ptr{$elty}, Ptr{$elty},
Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt}),
&m, &n, A, &stride(A,2), d, s, tauq, taup, work, &lwork, info)
if info[1] != 0 throw(LapackException(info[1])) end
if lwork < 0
lwork = blas_int(real(work[1]))
work = Array($elty, lwork)
end
end
end
# SUBROUTINE DGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
# * .. Scalar Arguments ..
# INTEGER INFO, LDA, LWORK, M, N
# * .. Array Arguments ..
# DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
function gelqf!(A::StridedMatrix{$elty})
chkstride1(A)
info = Array(BlasInt, 1)
m = blas_int(size(A, 1))
n = blas_int(size(A, 2))
lda = blas_int(stride(A, 2))
tau = Array($elty, n)
lwork = blas_int(-1)
work = Array($elty, (1,))
for i in 1:2 # first call returns lwork as work[1]
ccall(($(string(gelqf)),liblapack), Void,
(Ptr{BlasInt}, Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt},
Ptr{$elty}, Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt}),
&m, &n, A, &lda, tau, work, &lwork, info)
if info[1] != 0 throw(LapackException(info[1])) end
if lwork < 0
lwork = blas_int(real(work[1]))
work = Array($elty, lwork)
end
end
A, tau
end
# SUBROUTINE DGEQLF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
# * .. Scalar Arguments ..
# INTEGER INFO, LDA, LWORK, M, N
# * .. Array Arguments ..
# DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
function geqlf!(A::StridedMatrix{$elty})
chkstride1(A)
info = Array(BlasInt, 1)
m = blas_int(size(A, 1))
n = blas_int(size(A, 2))
lda = blas_int(stride(A, 2))
tau = Array($elty, n)
lwork = blas_int(-1)
work = Array($elty, (1,))
for i in 1:2 # first call returns lwork as work[1]
ccall(($(string(geqlf)),liblapack), Void,
(Ptr{BlasInt}, Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt},
Ptr{$elty}, Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt}),
&m, &n, A, &lda, tau, work, &lwork, info)
if info[1] != 0 throw(LapackException(info[1])) end
if lwork < 0
lwork = blas_int(real(work[1]))
work = Array($elty, lwork)
end
end
A, tau
end
# SUBROUTINE DGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO )
# * .. Scalar Arguments ..
# INTEGER INFO, LDA, LWORK, M, N
# * .. Array Arguments ..
# INTEGER JPVT( * )
# DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
function geqp3!(A::StridedMatrix{$elty})
chkstride1(A)
m, n = size(A)
jpvt = zeros(BlasInt, n)
tau = Array($elty, n)
work = Array($elty, 1)
lwork = blas_int(-1)
info = Array(BlasInt, 1)
cmplx = iscomplex(A)
if cmplx; rwork = Array($relty, 2n); end
for i in 1:2
if cmplx
ccall(($(string(geqp3)),liblapack), Void,
(Ptr{BlasInt}, Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt},
Ptr{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ptr{BlasInt},
Ptr{$relty}, Ptr{BlasInt}),
&m, &n, A, &stride(A,2), jpvt, tau, work, &lwork, rwork, info)
else
ccall(($(string(geqp3)),liblapack), Void,
(Ptr{BlasInt}, Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt},
Ptr{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ptr{BlasInt},
Ptr{BlasInt}),
&m, &n, A, &stride(A,2), jpvt, tau, work, &lwork, info)
end
if info[1] != 0 throw(LapackException(info[1])) end
if lwork < 0
lwork = blas_int(real(work[1]))
work = Array($elty, lwork)
end
end
A, tau, jpvt
end
## Several variants of geqrf! could be defined.
## geqrfp! - positive elements on diagonal of R
## geqrt! - compact WY representation of Q (blocked algorithm)
## geqrt3! - recursive algorithm producing compact WY representation of Q
# SUBROUTINE DGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
# * .. Scalar Arguments ..
# INTEGER INFO, LDA, LWORK, M, N
# * .. Array Arguments ..
# DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
function geqrf!(A::StridedMatrix{$elty})
chkstride1(A)
m, n = size(A)
tau = Array($elty, n)
work = Array($elty, 1)
lwork = blas_int(-1)
info = Array(BlasInt, 1)
for i in 1:2 # first call returns lwork as work[1]
ccall(($(string(geqrf)),liblapack), Void,
(Ptr{BlasInt}, Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt},
Ptr{$elty}, Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt}),
&m, &n, A, &stride(A,2), tau, work, &lwork, info)
if info[1] != 0 throw(LapackException(info[1])) end
if lwork < 0
lwork = blas_int(real(work[1]))
work = Array($elty, lwork)
end
end
A, tau
end
# SUBROUTINE DGERQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
# * .. Scalar Arguments ..
# INTEGER INFO, LDA, LWORK, M, N
# * .. Array Arguments ..
# DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
function gerqf!(A::StridedMatrix{$elty})
chkstride1(A)
info = Array(BlasInt, 1)
m, n = size(A)
tau = Array($elty, n)
lwork = blas_int(-1)
work = Array($elty, 1)
for i in 1:2 # first call returns lwork as work[1]
ccall(($(string(gerqf)),liblapack), Void,
(Ptr{BlasInt}, Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt},
Ptr{$elty}, Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt}),
&m, &n, A, &stride(A,2), tau, work, &lwork, info)
if info[1] != 0 throw(LapackException(info[1])) end
if lwork < 0
lwork = blas_int(real(work[1]))
work = Array($elty, lwork)
end
end
A, tau
end
# SUBROUTINE DGETRF( M, N, A, LDA, IPIV, INFO )
# * .. Scalar Arguments ..
# INTEGER INFO, LDA, M, N
# * .. Array Arguments ..
# INTEGER IPIV( * )
# DOUBLE PRECISION A( LDA, * )
function getrf!(A::StridedMatrix{$elty})
chkstride1(A)
info = Array(BlasInt, 1)
m, n = size(A)
lda = stride(A, 2)
ipiv = Array(BlasInt, min(m,n))
ccall(($(string(getrf)),liblapack), Void,
(Ptr{BlasInt}, Ptr{BlasInt}, Ptr{$elty},
Ptr{BlasInt}, Ptr{BlasInt}, Ptr{BlasInt}),
&m, &n, A, &lda, ipiv, info)
if info[1] < 0 throw(LapackException(info[1])) end
A, ipiv, info[1]
end
end
end
## (GE) general matrices, solvers with factorization, solver and inverse
for (gels, gesv, getrs, getri, elty) in
((:dgels_,:dgesv_,:dgetrs_,:dgetri_,:Float64),
(:sgels_,:sgesv_,:sgetrs_,:sgetri_,:Float32),
(:zgels_,:zgesv_,:zgetrs_,:zgetri_,:Complex128),
(:cgels_,:cgesv_,:cgetrs_,:cgetri_,:Complex64))
@eval begin
# SUBROUTINE DGELS( TRANS, M, N, NRHS, A, LDA, B, LDB, WORK, LWORK,INFO)
# * .. Scalar Arguments ..
# CHARACTER TRANS
# INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
function gels!(trans::BlasChar, A::StridedMatrix{$elty}, B::StridedVecOrMat{$elty})
chkstride1(A, B)
btrn = trans == 'T'
m, n = size(A)
if size(B,1) != (btrn ? n : m) throw(LapackDimMisMatch("gels!")) end
info = Array(BlasInt, 1)
work = Array($elty, 1)
lwork = blas_int(-1)
for i in 1:2
ccall(($(string(gels)),liblapack), Void,
(Ptr{Uint8}, Ptr{BlasInt}, Ptr{BlasInt}, Ptr{BlasInt},
Ptr{$elty}, Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt},
Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt}),
&(btrn?'T':'N'), &m, &n, &size(B,2), A, &stride(A,2),
B, &stride(B,2), work, &lwork, info)
if info[1] != 0 throw(LapackException(info[1])) end
if lwork < 0
lwork = blas_int(real(work[1]))
work = Array($elty, lwork)
end
end
k = min(m, n)
F = m < n ? tril(A[1:k, 1:k]) : triu(A[1:k, 1:k])
F, isa(B, Vector) ? B[1:k] : B[1:k,:], [sum(B[(k+1):size(B,1), i].^2) for i=1:size(B,2)]
end
# SUBROUTINE DGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO )
# * .. Scalar Arguments ..
# INTEGER INFO, LDA, LDB, N, NRHS
# * ..
# * .. Array Arguments ..
# INTEGER IPIV( * )
# DOUBLE PRECISION A( LDA, * ), B( LDB, * )
function gesv!(A::StridedMatrix{$elty}, B::StridedVecOrMat{$elty})
chkstride1(A, B)
chksquare(A)
n = size(A,1)
if size(B,1) != n throw(LapackDimMisMatch("gesv!")) end
ipiv = Array(BlasInt, n)
info = Array(BlasInt, 1)
ccall(($(string(gesv)),liblapack), Void,
(Ptr{BlasInt}, Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt},
Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt}),
&n, &size(B,2), A, &stride(A,2), ipiv, B, &stride(B,2), info)
if info[1] < 0 throw(LapackException(info[1])) end
B, A, ipiv, info[1]
end
# SUBROUTINE DGETRS( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
#* .. Scalar Arguments ..
# CHARACTER TRANS
# INTEGER INFO, LDA, LDB, N, NRHS
# .. Array Arguments ..
# INTEGER IPIV( * )
# DOUBLE PRECISION A( LDA, * ), B( LDB, * )
function getrs!(trans::BlasChar, A::StridedMatrix{$elty}, ipiv::Vector{BlasInt}, B::StridedVecOrMat{$elty})
chkstride1(A, B)
m, n = size(A)
if m != n || size(B, 1) != m error("getrs!: dimension mismatch") end
nrhs = size(B, 2)
info = Array(BlasInt, 1)
ccall(($(string(getrs)),liblapack), Void,
(Ptr{Uint8}, Ptr{BlasInt}, Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt},
Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt}),
&trans, &n, &size(B,2), A, &stride(A,2), ipiv, B, &stride(B,2), info)
if info[1] != 0 throw(LapackException(info[1])) end
B
end
# SUBROUTINE DGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO )
#* .. Scalar Arguments ..
# INTEGER INFO, LDA, LWORK, N
#* .. Array Arguments ..
# INTEGER IPIV( * )
# DOUBLE PRECISION A( LDA, * ), WORK( * )
function getri!(A::StridedMatrix{$elty}, ipiv::Vector{BlasInt})
chkstride1(A)
m, n = size(A)
if m != n || n != length(ipiv) error("getri!: dimension mismatch") end
lda = stride(A, 2)
info = Array(BlasInt, 1)
lwork = -1
work = Array($elty, 1)
for i in 1:2
ccall(($(string(getri)),liblapack), Void,
(Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt},
Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt}),
&n, A, &lda, ipiv, work, &lwork, info)
if info[1] != 0 error("getri!: error $(info[1])") end
if lwork < 0
lwork = blas_int(real(work[1]))
work = Array($elty, lwork)
end
end
A
end
end
end
for (gelsd, elty) in ((:dgelsd_, Float64),
(:sgelsd_, Float32))
@eval begin
# SUBROUTINE DGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,
# $ WORK, LWORK, IWORK, INFO )
# * .. Scalar Arguments ..
# INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS, RANK
# DOUBLE PRECISION RCOND
# * ..
# * .. Array Arguments ..
# INTEGER IWORK( * )
# DOUBLE PRECISION A( LDA, * ), B( LDB, * ), S( * ), WORK( * )
function gelsd!(A::StridedMatrix{$elty}, B::StridedVecOrMat{$elty}, rcond)
LAPACK.chkstride1(A, B)
m, n = size(A)
if size(B, 1) != m; throw(LAPACK.LapackDimMisMatch("gelsd!")); end
if size(B, 1) < n
newB = Array($elty, n, size(B, 2))
newB[1:size(B, 1), :] = B
else
newB = B
end
s = Array($elty, min(m, n))
rnk = Array(BlasInt, 1)
info = Array(BlasInt, 1)
work = Array($elty, 1)
lwork = blas_int(-1)
iwork = Array(BlasInt, 1)
for i in 1:2
ccall(($(string(gelsd)),liblapack), Void,
(Ptr{BlasInt}, Ptr{BlasInt}, Ptr{BlasInt},
Ptr{$elty}, Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt},
Ptr{$elty}, Ptr{$elty}, Ptr{BlasInt}, Ptr{$elty},
Ptr{BlasInt}, Ptr{BlasInt}, Ptr{BlasInt}),
&m, &n, &size(B,2), A, &max(1,stride(A,2)),
newB, &max(1,stride(B,2),n), s, &rcond, rnk, work, &lwork, iwork, info)
if info[1] != 0 throw(LapackException(info[1])) end
if lwork < 0
lwork = blas_int(real(work[1]))
work = Array($elty, lwork)
iwork = Array(BlasInt, iwork[1])
end
end
isa(B, Vector) ? newB[1:n] : newB[1:n,:], rnk[1]
end
gelsd!(A::StridedMatrix{$elty}, B::StridedVecOrMat{$elty}) = gelsd!(A, B, -1.)
end
end
for (gelsd, elty, relty) in ((:zgelsd_, Complex128, Float64),
(:cgelsd_, Complex64, Float32))
@eval begin
# SUBROUTINE ZGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,
# $ WORK, LWORK, RWORK, IWORK, INFO )
# * .. Scalar Arguments ..
# INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS, RANK
# DOUBLE PRECISION RCOND
# * ..
# * .. Array Arguments ..
# INTEGER IWORK( * )
# DOUBLE PRECISION RWORK( * ), S( * )
# COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
function gelsd!(A::StridedMatrix{$elty}, B::StridedVecOrMat{$elty}, rcond)
LAPACK.chkstride1(A, B)
m, n = size(A)
if size(B,1) != m; throw(LAPACK.LapackDimMisMatch("gelsd!")); end
if size(B, 1) < n
newB = Array($elty, n, size(B, 2))
newB[1:size(B, 1), :] = B
else
newB = B
end
s = Array($elty, min(m, n))
rnk = Array(BlasInt, 1)
info = Array(BlasInt, 1)
work = Array($elty, 1)
lwork = blas_int(-1)
rwork = Array($relty, 1)
iwork = Array(BlasInt, 1)
for i in 1:2
ccall(($(string(gelsd)),liblapack), Void,
(Ptr{BlasInt}, Ptr{BlasInt}, Ptr{BlasInt}, Ptr{$elty},
Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt}, Ptr{$relty},
Ptr{$relty}, Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt},
Ptr{$relty}, Ptr{BlasInt}, Ptr{BlasInt}),
&m, &n, &size(B,2), A, &max(1,stride(A,2)),
newB, &max(1,stride(B,2),n), s, &rcond, rnk, work, &lwork, rwork, iwork, info)
if info[1] != 0 throw(LapackException(info[1])) end
if lwork < 0
lwork = blas_int(real(work[1]))
work = Array($elty, lwork)
rwork = Array($relty, blas_int(rwork[1]))
iwork = Array(BlasInt, iwork[1])
end
end
isa(B, Vector) ? newB[1:n] : newB[1:n,:], rnk[1]
end
gelsd!(A::StridedMatrix{$elty}, B::StridedVecOrMat{$elty}) = gelsd!(A, B, -1.)
end
end
# (GE) general matrices eigenvalue-eigenvector and singular value decompositions
for (geev, gesvd, gesdd, elty, relty) in
((:dgeev_,:dgesvd_,:dgesdd_,:Float64, Float64),
(:sgeev_,:sgesvd_,:sgesdd_,:Float32, Float32),
(:zgeev_,:zgesvd_,:zgesdd_,:Complex128, Float64),
(:cgeev_,:cgesvd_,:cgesdd_,:Complex64, Float32))
@eval begin
# SUBROUTINE DGEEV( JOBVL, JOBVR, N, A, LDA, WR, WI, VL, LDVL, VR,
# $ LDVR, WORK, LWORK, INFO )
# * .. Scalar Arguments ..
# CHARACTER JOBVL, JOBVR
# INTEGER INFO, LDA, LDVL, LDVR, LWORK, N
# * .. Array Arguments ..
# DOUBLE PRECISION A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ),
# $ WI( * ), WORK( * ), WR( * )
function geev!(jobvl::BlasChar, jobvr::BlasChar, A::StridedMatrix{$elty})
chkstride1(A)
chksquare(A)
m, n = size(A)
lvecs = jobvl == 'V'
rvecs = jobvr == 'V'
VL = Array($elty, (n, lvecs ? n : 0))
VR = Array($elty, (n, rvecs ? n : 0))
cmplx = iscomplex(A)
if cmplx
W = Array($elty, n)
rwork = Array($relty, 2n)
else
WR = Array($elty, n)
WI = Array($elty, n)
end
work = Array($elty, 1)
lwork = blas_int(-1)
info = Array(BlasInt, 1)
for i = 1:2
if cmplx
ccall(($(string(geev)),liblapack), Void,
(Ptr{Uint8}, Ptr{Uint8}, Ptr{BlasInt}, Ptr{$elty},
Ptr{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ptr{BlasInt},
Ptr{$elty}, Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt},
Ptr{$relty}, Ptr{BlasInt}),
&jobvl, &jobvr, &n, A, &stride(A,2), W, VL, &n, VR, &n,
work, &lwork, rwork, info)
else
ccall(($(string(geev)),liblapack), Void,
(Ptr{Uint8}, Ptr{Uint8}, Ptr{BlasInt}, Ptr{$elty},
Ptr{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ptr{$elty},
Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt}, Ptr{$elty},
Ptr{BlasInt}, Ptr{BlasInt}),
&jobvl, &jobvr, &n, A, &stride(A,2), WR, WI, VL, &n,
VR, &n, work, &lwork, info)
end
if info[1] != 0 throw(LapackException(info[1])) end
if lwork < 0
lwork = blas_int(real(work[1]))
work = Array($elty, lwork)
end
end
cmplx ? (VL, W, VR) : (VL, WR, WI, VR)
end
# SUBROUTINE DGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK,
# LWORK, IWORK, INFO )
#* .. Scalar Arguments ..
# CHARACTER JOBZ
# INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N
#* ..
#* .. Array Arguments ..
# INTEGER IWORK( * )
# DOUBLE PRECISION A( LDA, * ), S( * ), U( LDU, * ),
# VT( LDVT, * ), WORK( * )
function gesdd!(job::BlasChar, A::StridedMatrix{$elty})
chkstride1(A)
m, n = size(A)
minmn = min(m, n)
if job == 'A'
U = Array($elty, (m, m))
VT = Array($elty, (n, n))
elseif job == 'S'
U = Array($elty, (m, minmn))
VT = Array($elty, (minmn, n))
elseif job == 'O'
U = Array($elty, (m, m >= n ? 0 : m))
VT = Array($elty, (n, m >= n ? n : 0))
else
U = Array($elty, (m, 0))
VT = Array($elty, (n, 0))
end
work = Array($elty, 1)
lwork = blas_int(-1)
S = Array($relty, minmn)
cmplx = iscomplex(A)
if cmplx
rwork = Array($relty, job == 'N' ? 7*minmn : 5*minmn*minmn + 5*minmn)
end
iwork = Array(BlasInt, 8*minmn)
info = Array(BlasInt, 1)
for i = 1:2
if cmplx
ccall(($(string(gesdd)),liblapack), Void,
(Ptr{Uint8}, Ptr{BlasInt}, Ptr{BlasInt}, Ptr{$elty},
Ptr{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ptr{BlasInt},
Ptr{$elty}, Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt},
Ptr{$relty}, Ptr{BlasInt}, Ptr{BlasInt}),
&job, &m, &n, A, &stride(A,2), S, U, &max(1,stride(U,2)), VT, &max(1,stride(VT,2)),
work, &lwork, rwork, iwork, info)
else
ccall(($(string(gesdd)),liblapack), Void,
(Ptr{Uint8}, Ptr{BlasInt}, Ptr{BlasInt}, Ptr{$elty},
Ptr{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ptr{BlasInt},
Ptr{$elty}, Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt},
Ptr{BlasInt}, Ptr{BlasInt}),
&job, &m, &n, A, &stride(A,2), S, U, &max(1,stride(U,2)), VT, &max(1,stride(VT,2)),
work, &lwork, iwork, info)
end
if info[1] != 0 throw(LapackException(info[1])) end
if lwork < 0
lwork = blas_int(real(work[1]))
work = Array($elty, lwork)
end
end
if job == 'O'
if m >= n return (A, S, VT)
else return (U, S, A)
end
end
return (U, S, VT)
end
# SUBROUTINE DGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, INFO )
# * .. Scalar Arguments ..
# CHARACTER JOBU, JOBVT
# INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N
# * .. Array Arguments ..
# DOUBLE PRECISION A( LDA, * ), S( * ), U( LDU, * ),
# $ VT( LDVT, * ), WORK( * )
function gesvd!(jobu::BlasChar, jobvt::BlasChar, A::StridedMatrix{$elty})
chkstride1(A)
m, n = size(A)
minmn = min(m, n)
S = Array($relty, minmn)
U = Array($elty, jobu == 'A'? (m, m):(jobu == 'S'? (m, minmn) : (m, 0)))
VT = Array($elty, jobvt == 'A'? (n, n):(jobvt == 'S'? (minmn, n) : (n, 0)))
work = Array($elty, 1)
cmplx = iscomplex(A)
if cmplx; rwork = Array($relty, 5minmn); end
lwork = blas_int(-1)
info = Array(BlasInt, 1)
for i in 1:2
if cmplx
ccall(($(string(gesvd)),liblapack), Void,
(Ptr{Uint8}, Ptr{Uint8}, Ptr{BlasInt}, Ptr{BlasInt},
Ptr{$elty}, Ptr{BlasInt}, Ptr{$elty}, Ptr{$elty},
Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt}, Ptr{$elty},
Ptr{BlasInt}, Ptr{$relty}, Ptr{BlasInt}),
&jobu, &jobvt, &m, &n, A, &stride(A,2), S, U, &max(1,stride(U,2)), VT, &max(1,stride(VT,2)),
work, &lwork, rwork, info)
else
ccall(($(string(gesvd)),liblapack), Void,
(Ptr{Uint8}, Ptr{Uint8}, Ptr{BlasInt}, Ptr{BlasInt},
Ptr{$elty}, Ptr{BlasInt}, Ptr{$elty}, Ptr{$elty},
Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt}, Ptr{$elty},
Ptr{BlasInt}, Ptr{BlasInt}),
&jobu, &jobvt, &m, &n, A, &stride(A,2), S, U, &max(1,stride(U,2)), VT, &max(1,stride(VT,2)),
work, &lwork, info)
end
if info[1] != 0 throw(LapackException(info[1])) end
if lwork < 0
lwork = blas_int(real(work[1]))
work = Array($elty, lwork)
end
end
if jobu == 'O' return A, S, VT end
if jobvt == 'O' return U, S, A end
U, S, VT
end
end
end
# (GT) General tridiagonal, decomposition, solver and direct solver
for (gtsv, gttrf, gttrs, elty) in
((:dgtsv_,:dgttrf_,:dgttrs_,:Float64),
(:sgtsv_,:sgttrf_,:sgttrs_,:Float32),
(:zgtsv_,:zgttrf_,:zgttrs_,:Complex128),
(:cgtsv_,:cgttrf_,:cgttrs_,:Complex64))
@eval begin
# SUBROUTINE DGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
# .. Scalar Arguments ..
# INTEGER INFO, LDB, N, NRHS
# .. Array Arguments ..
# DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * )
function gtsv!(dl::Vector{$elty}, d::Vector{$elty}, du::Vector{$elty},
B::StridedVecOrMat{$elty})
chkstride1(B)
n = length(d)
if length(dl) != n - 1 || length(du) != n - 1
throw(LapackDimMisMatch("gtsv!"))
end
if n != size(B,1) throw(LapackDimMisMatch("gtsv!")) end
info = Array(BlasInt, 1)
ccall(($(string(gtsv)),liblapack), Void,
(Ptr{BlasInt}, Ptr{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ptr{$elty},
Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt}),
&n, &size(B,2), dl, d, du, B, &stride(B,2), info)
if info[1] != 0 throw(LapackException(info[1])) end
B
end
# SUBROUTINE DGTTRF( N, DL, D, DU, DU2, IPIV, INFO )
# .. Scalar Arguments ..
# INTEGER INFO, N
# .. Array Arguments ..
# INTEGER IPIV( * )
# DOUBLE PRECISION D( * ), DL( * ), DU( * ), DU2( * )
function gttrf!(dl::Vector{$elty}, d::Vector{$elty}, du::Vector{$elty})
n = length(d)
if length(dl) != (n-1) || length(du) != (n-1)
throw(LapackDimMisMatch("gttrf!"))
end
du2 = Array($elty, n-2)
ipiv = Array(BlasInt, n)
info = Array(BlasInt, 1)
ccall(($(string(gttrf)),liblapack), Void,
(Ptr{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ptr{$elty}, Ptr{$elty},
Ptr{BlasInt}, Ptr{BlasInt}),
&n, dl, d, du, du2, ipiv, info)
if info[1] != 0 throw(LapackException(info[1])) end
dl, d, du, du2, ipiv
end
# SUBROUTINE DGTTRS( TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB, INFO )
# .. Scalar Arguments ..
# CHARACTER TRANS
# INTEGER INFO, LDB, N, NRHS
# .. Array Arguments ..
# INTEGER IPIV( * )
# DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
function gttrs!(trans::BlasChar, dl::Vector{$elty}, d::Vector{$elty},
du::Vector{$elty}, du2::Vector{$elty}, ipiv::Vector{BlasInt},
B::StridedVecOrMat{$elty})
chkstride1(B)
n = length(d)
if length(dl) != n - 1 || length(du) != n - 1 throw(LapackDimMisMatch("gttrs!")) end
if n != size(B,1) throw(LapackDimMisMatch("gttrs!")) end
info = Array(BlasInt, 1)
ccall(($(string(gttrs)),liblapack), Void,
(Ptr{Uint8}, Ptr{BlasInt}, Ptr{BlasInt},
Ptr{$elty}, Ptr{$elty}, Ptr{$elty}, Ptr{$elty},
Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt}),
&trans, &n, &size(B,2), dl, d, du, du2, ipiv, B, &stride(B,2), info)
if info[1] != 0 throw(LapackException(info[1])) end
B
end
end
end
## (OR) orthogonal (or UN, unitary) matrices, extractors and multiplication
for (orglq, orgqr, ormlq, ormqr, elty) in
((:dorglq_,:dorgqr_,:dormlq_,:dormqr_,:Float64),
(:sorglq_,:sorgqr_,:sormlq_,:sormqr_,:Float32),
(:zunglq_,:zungqr_,:zunmlq_,:zunmqr_,:Complex128),
(:cunglq_,:cungqr_,:cunmlq_,:cunmqr_,:Complex64))
@eval begin
# SUBROUTINE DORGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
# * .. Scalar Arguments ..
# INTEGER INFO, K, LDA, LWORK, M, N
# * .. Array Arguments ..
# DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
function orglq!(A::StridedMatrix{$elty}, tau::Vector{$elty}, k::Integer)
chkstride1(A)
work = Array($elty, 1)
lwork = blas_int(-1)
info = Array(BlasInt, 1)
for i in 1:2
ccall(($(string(orglq)),liblapack), Void,
(Ptr{BlasInt}, Ptr{BlasInt}, Ptr{BlasInt}, Ptr{$elty},
Ptr{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt}),
&size(A,1), &size(A,2), &k, A, &stride(A,2), tau, work, &lwork, info)
if info[1] != 0 throw(LapackException(info[1])) end
if lwork < 0
lwork = blas_int(real(work[1]))
work = Array($elty, lwork)
end
end
A
end
# SUBROUTINE DORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
# * .. Scalar Arguments ..
# INTEGER INFO, K, LDA, LWORK, M, N
# * .. Array Arguments ..
# DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
function orgqr!(A::StridedMatrix{$elty}, tau::Vector{$elty}, k::Integer)
chkstride1(A)
work = Array($elty, 1)
lwork = blas_int(-1)
info = Array(BlasInt, 1)
for i in 1:2
ccall(($(string(orgqr)),liblapack), Void,
(Ptr{BlasInt}, Ptr{BlasInt}, Ptr{BlasInt}, Ptr{$elty},
Ptr{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt}),
&size(A,1), &size(A,2), &k, A, &stride(A,2), tau, work, &lwork, info)
if info[1] != 0 throw(LapackException(info[1])) end
if lwork < 0
lwork = blas_int(real(work[1]))
work = Array($elty, lwork)
end
end
A
end
# SUBROUTINE DORMLQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
# WORK, LWORK, INFO )
# .. Scalar Arguments ..
# CHARACTER SIDE, TRANS
# INTEGER INFO, K, LDA, LDC, LWORK, M, N
# .. Array Arguments ..
# DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
function ormlq!(side::BlasChar, trans::BlasChar, A::StridedMatrix{$elty},
k::Integer, tau::Vector{$elty}, C::StridedVecOrMat{$elty})
chkstride1(A, C)
m = size(C, 1)
n = size(C, 2) # m, n = size(C) won't work if C is a Vector
work = Array($elty, 1)
lwork = blas_int(-1)
info = Array(BlasInt, 1)
for i in 1:2
ccall(($(string(ormlq)),liblapack), Void,
(Ptr{Uint8}, Ptr{Uint8}, Ptr{BlasInt}, Ptr{BlasInt}, Ptr{BlasInt},
Ptr{$elty}, Ptr{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ptr{BlasInt},
Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt}),
&side, &trans, &m, &n, &k, A, &stride(A,2), tau,
C, &stride(C,2), work, &lwork, info)
if info[1] != 0 throw(LapackException(info[1])) end
if lwork < 0
lwork = blas_int(real(work[1]))
work = Array($elty, lwork)
end
end
C
end
# SUBROUTINE DORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
# WORK, INFO )
# .. Scalar Arguments ..
# CHARACTER SIDE, TRANS
# INTEGER INFO, K, LDA, LDC, M, N
# .. Array Arguments ..
# DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
function ormqr!(side::BlasChar, trans::BlasChar, A::StridedMatrix{$elty},
k::Integer, tau::Vector{$elty}, C::StridedVecOrMat{$elty})
chkstride1(A, C)
m = size(C, 1)
n = size(C, 2) # m, n = size(C) won't work if C is a Vector
work = Array($elty, 1)
lwork = blas_int(-1)
info = Array(BlasInt, 1)
for i in 1:2
ccall(($(string(ormqr)),liblapack), Void,
(Ptr{Uint8}, Ptr{Uint8}, Ptr{BlasInt}, Ptr{BlasInt}, Ptr{BlasInt},
Ptr{$elty}, Ptr{BlasInt}, Ptr{$elty}, Ptr{$elty}, Ptr{BlasInt},
Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt}),
&side, &trans, &m, &n, &k, A, &stride(A,2), tau,
C, &stride(C,2), work, &lwork, info)
if info[1] != 0 throw(LapackException(info[1])) end
if lwork < 0
lwork = blas_int(real(work[1]))
work = Array($elty, lwork)
end
end
C
end
end
end
# (PO) positive-definite symmetric matrices,
# Cholesky decomposition, solvers (direct and factored) and inverse.
for (posv, potrf, potri, potrs, pstrf, elty, rtyp) in
((:dposv_,:dpotrf_,:dpotri_,:dpotrs_,:dpstrf_,:Float64,:Float64),
(:sposv_,:spotrf_,:spotri_,:spotrs_,:spstrf_,:Float32,:Float32),
(:zposv_,:zpotrf_,:zpotri_,:zpotrs_,:zpstrf_,:Complex128,:Float64),
(:cposv_,:cpotrf_,:cpotri_,:cpotrs_,:cpstrf_,:Complex64,:Float32))
@eval begin
## Caller should check if returned info[1] is zero,
## positive values indicate indefiniteness
# SUBROUTINE DPOSV( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
#* .. Scalar Arguments ..
# CHARACTER UPLO
# INTEGER INFO, LDA, LDB, N, NRHS
# .. Array Arguments ..
# DOUBLE PRECISION A( LDA, * ), B( LDB, * )
function posv!(uplo::BlasChar, A::StridedMatrix{$elty}, B::StridedVecOrMat{$elty})
chkstride1(A, B)
chksquare(A)
n = size(A,1)
if size(B,1) != n throw(LapackDimMisMatch("posv!")) end
info = Array(BlasInt, 1)
ccall(($(string(posv)),liblapack), Void,
(Ptr{Uint8}, Ptr{BlasInt}, Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt},
Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt}),
&uplo, &n, &size(B,2), A, &stride(A,2), B, &stride(B,2), info)
if info[1] < 0 throw(LapackException(info[1])) end
A, B, info[1]
end
## Caller should check if returned info[1] is zero,
## positive values indicate indefiniteness
# SUBROUTINE DPOTRF( UPLO, N, A, LDA, INFO )
# * .. Scalar Arguments ..
# CHARACTER UPLO
# INTEGER INFO, LDA, N
# * .. Array Arguments ..
# DOUBLE PRECISION A( LDA, * )
function potrf!(uplo::BlasChar, A::StridedMatrix{$elty})
chkstride1(A)
chksquare(A)
info = Array(BlasInt, 1)
ccall(($(string(potrf)),liblapack), Void,
(Ptr{Uint8}, Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt}),
&uplo, &size(A,1), A, &stride(A,2), info)
if info[1] < 0 throw(LapackException(info[1])) end
A, info[1]
end
## Caller should check if returned info[1] is zero,
## positive values indicate singularity
# SUBROUTINE DPOTRI( UPLO, N, A, LDA, INFO )
# .. Scalar Arguments ..
# CHARACTER UPLO
# INTEGER INFO, LDA, N
# .. Array Arguments ..
# DOUBLE PRECISION A( LDA, * )
function potri!(uplo::BlasChar, A::StridedMatrix{$elty})
chkstride1(A)
info = Array(BlasInt, 1)
ccall(($(string(potri)),liblapack), Void,
(Ptr{Uint8}, Ptr{BlasInt}, Ptr{$elty}, Ptr{BlasInt}, Ptr{BlasInt}),
&uplo, &size(A,1), A, &stride(A,2), info)
if info[1] < 0 throw(LapackException(info[1])) end
A, info[1]
end
# SUBROUTINE DPOTRS( UPLO, N, NRHS, A, LDA, B, LDB, INFO )
# .. Scalar Arguments ..
# CHARACTER UPLO
# INTEGER INFO, LDA, LDB, N, NRHS
# .. Array Arguments ..
# DOUBLE PRECISION A( LDA, * ), B( LDB, * )
function potrs!(uplo::BlasChar, A::StridedMatrix{$elty}, B::StridedVecOrMat{$elty})
chkstride1(A, B)
chksquare(A)
n = size(A,2)
if size(B,1) != n error("potrs!: dimension mismatch") end
info = Array(BlasInt, 1)