CGESVD(1) LAPACK driver routine (version 3.2) CGESVD(1)NAME
CGESVD - computes the singular value decomposition (SVD) of a complex
M-by-N matrix A, optionally computing the left and/or right singular
vectors
SYNOPSIS
SUBROUTINE CGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT,
WORK, LWORK, RWORK, INFO )
CHARACTER JOBU, JOBVT
INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N
REAL RWORK( * ), S( * )
COMPLEX A( LDA, * ), U( LDU, * ), VT( LDVT, * ), WORK( * )
PURPOSE
CGESVD computes the singular value decomposition (SVD) of a complex M-
by-N matrix A, optionally computing the left and/or right singular vec‐
tors. The SVD is written
A = U * SIGMA * conjugate-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 unitary matrix, and V is an N-by-N
unitary 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**H, 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**H:
= 'A': all N rows of V**H are returned in the array VT;
= 'S': the first min(m,n) rows of V**H (the right singular
vectors) are returned in the array VT; = 'O': the first
min(m,n) rows of V**H (the right singular vectors) are over‐
written on the array A; = 'N': no rows of V**H (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) COMPLEX 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**H (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) REAL array, dimension (min(M,N))
The singular values of A, sorted so that S(i) >= S(i+1).
U (output) COMPLEX 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 unitary matrix U; if JOBU = 'S', U
contains the first min(m,n) columns of U (the left singular
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) COMPLEX array, dimension (LDVT,N)
If JOBVT = 'A', VT contains the N-by-N unitary matrix V**H; if
JOBVT = 'S', VT contains the first min(m,n) rows of V**H (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) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >=
MAX(1,2*MIN(M,N)+MAX(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.
RWORK (workspace) REAL array, dimension (5*min(M,N))
On exit, if INFO > 0, RWORK(1:MIN(M,N)-1) contains the uncon‐
verged superdiagonal 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 sin‐
gular vectors related by U and VT.
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if CBDSQR did not converge, INFO specifies how many
superdiagonals of an intermediate bidiagonal form B did not
converge to zero. See the description of RWORK above for
details.
LAPACK driver routine (version 3November 2008 CGESVD(1)