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linalg_lapack.j
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linalg_lapack.j
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libLAPACK = libBLAS
# SUBROUTINE DPOTRF( UPLO, N, A, LDA, INFO )
# * .. Scalar Arguments ..
# CHARACTER UPLO
# INTEGER INFO, LDA, N
# * .. Array Arguments ..
# DOUBLE PRECISION A( LDA, * )
macro lapack_chol(fname, eltype)
quote
function chol(A::DenseMatrix{$eltype})
info = [0]
n = size(A, 1)
R = triu(A)
ccall(dlsym(libLAPACK, $fname),
Void,
(Ptr{Uint8}, Ptr{Int32}, Ptr{$eltype}, Ptr{Int32}, Ptr{Int32}),
"U", n, R, n, info)
if info[1] == 0; return R; end
if info[1] > 0; error("Matrix not Positive Definite"); end
error("Error in CHOL")
end
end
end
@lapack_chol "dpotrf_" Float64
@lapack_chol "spotrf_" Float32
# SUBROUTINE DGETRF( M, N, A, LDA, IPIV, INFO )
# * .. Scalar Arguments ..
# INTEGER INFO, LDA, M, N
# * .. Array Arguments ..
# INTEGER IPIV( * )
# DOUBLE PRECISION A( LDA, * )
lu(A::DenseMatrix) = lu(A, false)
macro lapack_lu(fname, eltype)
quote
function lu(A::DenseMatrix{$eltype}, economy::Bool)
info = [0]
m, n = size(A)
LU = A
if !economy
LU = copy(A)
end
ipiv = Array(Int32, min(m,n))
ccall(dlsym(libLAPACK, $fname),
Void,
(Ptr{Int32}, Ptr{Int32}, Ptr{$eltype},
Ptr{Int32}, Ptr{Int32}, Ptr{Int32}),
m, n, LU, m, ipiv, info)
if info[1] > 0; error("Matrix is singular"); end
P = linspace(1, m)
for i=1:min(m,n); t = P[i]; P[i] = P[ipiv[i]]; P[ipiv[i]] = t ; end
if info[1] == 0
if economy
return (LU, P)
else
L = tril(LU, -1) + eye(m,n)
U = m <= n ? triu(LU) : triu(LU)[1:n, :]
return (L, U, P)
end
end
error("Error in LU")
end
end
end
@lapack_lu "dgetrf_" Float64
@lapack_lu "sgetrf_" Float32
# 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( * )
# 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( * )
macro lapack_qr(fname, fname2, eltype)
quote
function qr(A::DenseMatrix{$eltype})
info = [0]
m, n = size(A)
QR = copy(A)
jpvt = zeros(Int32, n)
k = min(m,n)
tau = Array($eltype, k)
# Workspace query for QR factorization
work = [0.0]
lwork = -1
ccall(dlsym(libLAPACK, $fname),
Void,
(Ptr{Int32}, Ptr{Int32}, Ptr{$eltype}, Ptr{Int32},
Ptr{Int32}, Ptr{$eltype}, Ptr{$eltype}, Ptr{Int32}, Ptr{Int32}),
m, n, QR, m, jpvt, tau, work, lwork, info)
if info[1] == 0; lwork = int32(work[1]); work = Array($eltype, lwork);
else error("Error in ", $fname); end
# Compute QR factorization
ccall(dlsym(libLAPACK, $fname),
Void,
(Ptr{Int32}, Ptr{Int32}, Ptr{$eltype}, Ptr{Int32},
Ptr{Int32}, Ptr{$eltype}, Ptr{$eltype}, Ptr{Int32}, Ptr{Int32}),
m, n, QR, m, jpvt, tau, work, lwork, info)
if info[1] > 0; error("Matrix is singular"); end
R = triu(QR)
# Workspace query to form Q
lwork2 = -1
ccall(dlsym(libLAPACK, $fname2),
Void,
(Ptr{Int32}, Ptr{Int32}, Ptr{Int32}, Ptr{$eltype},
Ptr{Int32}, Ptr{$eltype}, Ptr{$eltype}, Ptr{Int32}, Ptr{Int32}),
m, k, k, QR, m, tau, work, lwork2, info)
if info[1] == 0; lwork = int32(work[1]); work = Array($eltype, lwork);
else error("Error in ", $fname2); end
# Compute Q
ccall(dlsym(libLAPACK, $fname2),
Void,
(Ptr{Int32}, Ptr{Int32}, Ptr{Int32}, Ptr{$eltype},
Ptr{Int32}, Ptr{$eltype}, Ptr{$eltype}, Ptr{Int32}, Ptr{Int32}),
m, k, k, QR, m, tau, work, lwork, info)
if info[1] == 0; return (QR[:, 1:k], R[1:k, :], jpvt); end
error("Error in ", $fname);
end
end
end
@lapack_qr "dgeqp3_" "dorgqr_" Float64
@lapack_qr "sgeqp3_" "sorgqr_" Float32
# SUBROUTINE DSYEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO )
# * .. Scalar Arguments ..
# CHARACTER JOBZ, UPLO
# INTEGER INFO, LDA, LWORK, N
# * .. Array Arguments ..
# DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * )
macro lapack_eig(fname, eltype)
quote
function eig(A::DenseMatrix{$eltype})
if !issymmetric(A); error("Matrix must be symmetric"); end
jobz = "V"
uplo = "U"
n = size(A, 1)
EV = copy(A)
W = Array($eltype, n)
info = [0]
# Workspace query
work = [0.0]
lwork = -1
ccall(dlsym(libLAPACK, $fname),
Void,
(Ptr{Uint8}, Ptr{Uint8}, Ptr{Int32}, Ptr{$eltype}, Ptr{Int32},
Ptr{$eltype}, Ptr{$eltype}, Ptr{Int32}, Ptr{Int32}),
jobz, uplo, n, EV, n, W, work, lwork, info)
if info[1] == 0; lwork = int32(work[1]); work = Array($eltype, lwork);
else error("Error in ", $fname); end
# Compute eigenvalues, eigenvectors
ccall(dlsym(libLAPACK, $fname),
Void,
(Ptr{Uint8}, Ptr{Uint8}, Ptr{Int32}, Ptr{$eltype}, Ptr{Int32},
Ptr{$eltype}, Ptr{$eltype}, Ptr{Int32}, Ptr{Int32}),
jobz, uplo, n, EV, n, W, work, lwork, info)
if info[1] == 0; return (diagm(W), EV); end
error("Error in EIG");
end
end
end
@lapack_eig "dsyev_" Float64
@lapack_eig "ssyev_" Float32
# 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( * )
macro lapack_svd(fname, eltype)
quote
function svd(A::DenseMatrix{$eltype})
jobu = "A"
jobvt = "A"
m, n = size(A)
k = min(m,n)
X = copy(A)
S = Array($eltype, k)
U = Array($eltype, m, m)
VT = Array($eltype, n, n)
info = [0]
# Workspace query
work = [0.0]
lwork = -1
ccall(dlsym(libLAPACK, $fname),
Void,
(Ptr{Uint8}, Ptr{Uint8}, Ptr{Int32}, Ptr{Int32}, Ptr{$eltype}, Ptr{Int32},
Ptr{$eltype}, Ptr{$eltype}, Ptr{Int32}, Ptr{$eltype}, Ptr{Int32},
Ptr{$eltype}, Ptr{Int32}, Ptr{Int32}),
jobu, jobvt, m, n, X, m, S, U, m, VT, n, work, lwork, info)
if info[1] == 0; lwork = int32(work[1]); work = Array($eltype, lwork);
else error("Error in ", $fname); end
# Compute SVD
ccall(dlsym(libLAPACK, $fname),
Void,
(Ptr{Uint8}, Ptr{Uint8}, Ptr{Int32}, Ptr{Int32}, Ptr{$eltype}, Ptr{Int32},
Ptr{$eltype}, Ptr{$eltype}, Ptr{Int32}, Ptr{$eltype}, Ptr{Int32},
Ptr{$eltype}, Ptr{Int32}, Ptr{Int32}),
jobu, jobvt, m, n, X, m, S, U, m, VT, n, work, lwork, info)
SIGMA = zeros($eltype, m, n)
for i=1:k; SIGMA[i,i] = S[i]; end
if info[1] == 0; return (U,SIGMA,VT); end
error("Error in SVD");
end
end
end
@lapack_svd "dgesvd_" Float64
@lapack_svd "sgesvd_" Float32
# 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, * )
# 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
# SUBROUTINE DTRTRS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, INFO )
# * .. Scalar Arguments ..
# CHARACTER DIAG, TRANS, UPLO
# INTEGER INFO, LDA, LDB, N, NRHS
# * .. Array Arguments ..
# DOUBLE PRECISION A( LDA, * ), B( LDB, * )
macro lapack_backslash(fname_lu, fname_chol, fname_lsq, fname_tri, eltype)
quote
function \(A::DenseMatrix{$eltype}, B::DenseVecOrMat{$eltype})
info = [0]
m = size(A, 1)
n = size(A, 2)
if isa(B, Vector); nrhs = 1; else nrhs = size(B, 2); end
Acopy = copy(A)
X = copy(B)
if m == n # Square
case = :general
if isuppertriangular(A); case = :upper_triangular; end
if islowertriangular(A); case = :lower_triangular; end
if case == :general # General
ipiv = Array(Int32, n)
# Check for SPD matrix
if issymmetric(Acopy) && all([ Acopy[i,i] > 0 | i=1:n ])
case = :spd
end
if case == :spd
uplo = "U"
ccall(dlsym(libLAPACK, $fname_chol),
Void,
(Ptr{Uint8}, Ptr{Int32}, Ptr{Int32}, Ptr{$eltype}, Ptr{Int32},
Ptr{$eltype}, Ptr{Int32}, Ptr{Int32}),
uplo, n, nrhs, Acopy, n, X, n, info)
if info[1] != 0
Acopy = copy(A)
case = :general
end
end
if case == :general
info[1] = 0
ccall(dlsym(libLAPACK, $fname_lu),
Void,
(Ptr{Int32}, Ptr{Int32}, Ptr{$eltype}, Ptr{Int32}, Ptr{Int32},
Ptr{$eltype}, Ptr{Int32}, Ptr{Int32}),
n, nrhs, Acopy, n, ipiv, X, n, info)
end
else # Triangular
uplo = "U"
if case == :lower_triangular; uplo = "L"; end
ccall(dlsym(libLAPACK, $fname_tri),
Void,
(Ptr{Uint8}, Ptr{Uint8}, Ptr{Uint8}, Ptr{Int32}, Ptr{Int32},
Ptr{$eltype}, Ptr{Int32}, Ptr{$eltype}, Ptr{Int32}, Ptr{Int32}),
uplo, "N", "N", n, nrhs, Acopy, n, X, n, info)
end
else # Rectangular
# Workspace query
lwork = -1
work = [0.0]
ccall(dlsym(libLAPACK, $fname_lsq),
Void,
(Ptr{Uint8}, Ptr{Int32}, Ptr{Int32}, Ptr{Int32}, Ptr{$eltype}, Ptr{Int32},
Ptr{$eltype}, Ptr{Int32}, Ptr{$eltype}, Ptr{Int32}, Ptr{Int32}),
"N", m, n, nrhs, Acopy, m, X, max(m,n), work, lwork, info)
if info[1] == 0; lwork = int32(work[1]); work = Array($eltype, lwork);
else error("Error in ", $fname_lsq); end
ccall(dlsym(libLAPACK, $fname_lsq),
Void,
(Ptr{Uint8}, Ptr{Int32}, Ptr{Int32}, Ptr{Int32}, Ptr{$eltype}, Ptr{Int32},
Ptr{$eltype}, Ptr{Int32}, Ptr{$eltype}, Ptr{Int32}, Ptr{Int32}),
"N", m, n, nrhs, Acopy, m, X, max(m,n), work, lwork, info)
end # if m == n...
if info[1] == 0; return X; end
error("Error in solving A*X = B")
end # function...
end # quote...
end # macro...
@lapack_backslash "dgesv_" "dposv_" "dgels_" "dtrtrs_" Float64
@lapack_backslash "sgesv_" "sposv_" "sgels_" "strtrs_" Float32
## BIDIAG ##
bidiag(A) = bidiag(A, max(1,div(min(size(A)),2)), 2)
function bidiag(A::Array{Float64,2}, nb, nargout)
(m,n) = size(A)
s=min(m,n)
w=max(m,n)
D=zeros(s)
E=zeros(s-1)
tauq=zeros(s); taup=zeros(s)
A0 = A = copy(A)
k = 1-nb
for k=1:nb:s-nb
Dblk = zeros(nb)
Eblk = zeros(nb)
tauqblk = zeros(nb)
taupblk = zeros(nb)
X = zeros(m-k+1, nb)
Y = zeros(n-k+1, nb)
ccall(dlsym(libLAPACK, :dlabrd_), Void,
(Ptr{Int32}, Ptr{Int32}, Ptr{Int32}, Ptr{Float64}, Ptr{Int32},
Ptr{Float64}, Ptr{Float64}, Ptr{Float64}, Ptr{Float64},
Ptr{Float64},
Ptr{Int32}, Ptr{Float64}, Ptr{Int32}),
m-k+1, n-k+1, nb, A, m-k+1, Dblk, Eblk, tauqblk, taupblk,
X, m-k+1, Y, n-k+1)
b = k+nb-1 # end of block
# accumulate reduced leading portion
A0[k:b, k:end] = A[1:nb, :]
A0[k:end, k:b] = A[:, 1:nb]
D[k:b] = Dblk
E[k:b] = Eblk
tauq[k:b] = tauqblk
taup[k:b] = taupblk
# Update the trailing submatrix A[k+nb:m,k+nb:n],
# using an update of the form A := A - V*Y' - X*U'
l = nb+1
A = A[l:end,l:end]-A[l:end,1:nb]*Y[l:end,:]'-X[l:end,:]*A[1:nb,l:end]
A0[k+nb:m, k+nb:n] = A
end
k = k+nb
tauqblk = zeros(s-k+1)
taupblk = zeros(s-k+1)
ccall(dlsym(libLAPACK,:dgebd2_), Void,
(Ptr{Int32}, Ptr{Int32}, Ptr{Float64}, Ptr{Int32},
Ptr{Float64}, Ptr{Float64}, Ptr{Float64}, Ptr{Float64},
Ptr{Float64}, Ptr{Int32}),
m-k+1, n-k+1, A, m-k+1, zeros(s-k+1), zeros(s-k),
tauqblk, taupblk, zeros(w-k+1), 0)
A0[k:m,k:n] = A
tauq[k:end] = tauqblk
taup[k:end] = taupblk
for j=k:s-1
l = j-k+1
D[j] = A[l,l]
if m >= n
E[j] = A[l,l+1]
else
E[j] = A[l+1,l]
end
end
D[s] = A[s-k+1,s-k+1]
if nargout == 2
return (D, E)
end
if m >= n
Q = copy(A0)
ccall(dlsym(libLAPACK,:dorgbr_), Void,
(Ptr{Uint8}, Ptr{Int32}, Ptr{Int32}, Ptr{Int32},
Ptr{Float64}, Ptr{Int32}, Ptr{Float64}, Ptr{Float64},
Ptr{Int32}, Ptr{Int32}),
"Q", m, n, n, Q, m, tauq, zeros(s), s, 0)
PT = A0
ccall(dlsym(libLAPACK,:dorgbr_), Void,
(Ptr{Uint8}, Ptr{Int32}, Ptr{Int32}, Ptr{Int32},
Ptr{Float64}, Ptr{Int32}, Ptr{Float64}, Ptr{Float64},
Ptr{Int32}, Ptr{Int32}),
"P", n, n, n, PT, m, taup, zeros(s), s, 0)
PT = PT[1:n,:]
else
Q = copy(A0)
ccall(dlsym(libLAPACK,:dorgbr_), Void,
(Ptr{Uint8}, Ptr{Int32}, Ptr{Int32}, Ptr{Int32},
Ptr{Float64}, Ptr{Int32}, Ptr{Float64}, Ptr{Float64},
Ptr{Int32}, Ptr{Int32}),
"Q", m, m, n, Q, m, tauq, zeros(s), s, 0)
Q = Q[:,1:m]
PT = A0
ccall(dlsym(libLAPACK,:dorgbr_), Void,
(Ptr{Uint8}, Ptr{Int32}, Ptr{Int32}, Ptr{Int32},
Ptr{Float64}, Ptr{Int32}, Ptr{Float64}, Ptr{Float64},
Ptr{Int32}, Ptr{Int32}),
"P", m, n, m, PT, m, taup, zeros(s), s, 0)
end
return (Q, D, E, PT)
end
blksvd(A) = blksvd(A, 1)
function blksvd(A::Array{Float64,2}, nargout)
(m, n) = size(A)
nb = 3
(Q, D, E, PT) = bidiag(A, nb, 4)
if m >= n
ccall(dlsym(libLAPACK,:dbdsqr_), Void,
(Ptr{Uint8}, Ptr{Int32}, Ptr{Int32}, Ptr{Int32}, Ptr{Int32},
Ptr{Float64}, Ptr{Float64}, Ptr{Float64}, Ptr{Int32},
Ptr{Float64}, Ptr{Int32}, Ptr{Float64}, Ptr{Int32},
Ptr{Float64}, Ptr{Int32}),
"U",
n, n, m, 0, D, E, PT, n, Q, m, zeros(1,1), 1, zeros(4*n,1), 0)
else
ccall(dlsym(libLAPACK,:dbdsqr_), Void,
(Ptr{Uint8}, Ptr{Int32}, Ptr{Int32}, Ptr{Int32}, Ptr{Int32},
Ptr{Float64}, Ptr{Float64}, Ptr{Float64}, Ptr{Int32},
Ptr{Float64}, Ptr{Int32}, Ptr{Float64}, Ptr{Int32},
Ptr{Float64}, Ptr{Int32}),
"L",
m, n, m, 0, D, E, PT, m, Q, m, zeros(1,1), 1, zeros(4*m,1), 0)
end
S = D
if nargout == 1
return S
end
U = Q
VT = PT
V = VT'
S = diagm(S)
return (U, S, V)
end