DGESVD(l) ) DGESVD(l)NAME
DGESVD - compute the singular value decomposition (SVD) of a real M-by-
N matrix A, optionally computing the left and/or right singular vectors
SYNOPSIS
SUBROUTINE DGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT,
WORK, LWORK, INFO )
CHARACTER JOBU, JOBVT
INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N
DOUBLE PRECISION A( LDA, * ), S( * ), U( LDU, * ), VT(
LDVT, * ), WORK( * )
PURPOSE
DGESVD computes the singular value decomposition (SVD) of a real M-by-N
matrix A, optionally computing the left and/or right singular vectors.
The SVD is written
A = U * SIGMA * transpose(V)
where SIGMA is an M-by-N matrix which is zero except for its min(m,n)
diagonal elements, U is an M-by-M orthogonal matrix, and V is an N-by-N
orthogonal matrix. The diagonal elements of SIGMA are the singular
values of A; they are real and non-negative, and are returned in
descending order. The first min(m,n) columns of U and V are the left
and right singular vectors of A.
Note that the routine returns V**T, not V.
ARGUMENTS
JOBU (input) CHARACTER*1
Specifies options for computing all or part of the matrix U:
= 'A': all M columns of U are returned in array U:
= 'S': the first min(m,n) columns of U (the left singular vec‐
tors) are returned in the array U; = 'O': the first min(m,n)
columns of U (the left singular vectors) are overwritten on the
array A; = 'N': no columns of U (no left singular vectors) are
computed.
JOBVT (input) CHARACTER*1
Specifies options for computing all or part of the matrix V**T:
= 'A': all N rows of V**T are returned in the array VT;
= 'S': the first min(m,n) rows of V**T (the right singular
vectors) are returned in the array VT; = 'O': the first
min(m,n) rows of V**T (the right singular vectors) are over‐
written on the array A; = 'N': no rows of V**T (no right sin‐
gular vectors) are computed.
JOBVT and JOBU cannot both be 'O'.
M (input) INTEGER
The number of rows of the input matrix A. M >= 0.
N (input) INTEGER
The number of columns of the input matrix A. N >= 0.
A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the M-by-N matrix A. On exit, if JOBU = 'O', A is
overwritten with the first min(m,n) columns of U (the left sin‐
gular vectors, stored columnwise); if JOBVT = 'O', A is over‐
written with the first min(m,n) rows of V**T (the right singu‐
lar vectors, stored rowwise); if JOBU .ne. 'O' and JOBVT .ne.
'O', the contents of A are destroyed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
S (output) DOUBLE PRECISION array, dimension (min(M,N))
The singular values of A, sorted so that S(i) >= S(i+1).
U (output) DOUBLE PRECISION array, dimension (LDU,UCOL)
(LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'. If JOBU
= 'A', U contains the M-by-M orthogonal matrix U; if JOBU =
'S', U contains the first min(m,n) columns of U (the left sin‐
gular vectors, stored columnwise); if JOBU = 'N' or 'O', U is
not referenced.
LDU (input) INTEGER
The leading dimension of the array U. LDU >= 1; if JOBU = 'S'
or 'A', LDU >= M.
VT (output) DOUBLE PRECISION array, dimension (LDVT,N)
If JOBVT = 'A', VT contains the N-by-N orthogonal matrix V**T;
if JOBVT = 'S', VT contains the first min(m,n) rows of V**T
(the right singular vectors, stored rowwise); if JOBVT = 'N' or
'O', VT is not referenced.
LDVT (input) INTEGER
The leading dimension of the array VT. LDVT >= 1; if JOBVT =
'A', LDVT >= N; if JOBVT = 'S', LDVT >= min(M,N).
WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK; if
INFO > 0, WORK(2:MIN(M,N)) contains the unconverged superdiago‐
nal elements of an upper bidiagonal matrix B whose diagonal is
in S (not necessarily sorted). B satisfies A = U * B * VT, so
it has the same singular values as A, and singular vectors
related by U and VT.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= 1. LWORK >=
MAX(3*MIN(M,N)+MAX(M,N),5*MIN(M,N)). For good performance,
LWORK should generally be larger.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if DBDSQR did not converge, INFO specifies how many
superdiagonals of an intermediate bidiagonal form B did not
converge to zero. See the description of WORK above for
details.
LAPACK version 3.0 15 June 2000 DGESVD(l)
