
CGESDD(l) ) CGESDD(l)
NAME
CGESDD  compute the singular value decomposition (SVD) of a complex MbyN matrix A,
optionally computing the left and/or right singular vectors, by using divideandconquer
method
SYNOPSIS
SUBROUTINE CGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, RWORK, IWORK,
INFO )
CHARACTER JOBZ
INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N
INTEGER IWORK( * )
REAL RWORK( * ), S( * )
COMPLEX A( LDA, * ), U( LDU, * ), VT( LDVT, * ), WORK( * )
PURPOSE
CGESDD computes the singular value decomposition (SVD) of a complex MbyN matrix A,
optionally computing the left and/or right singular vectors, by using divideandconquer
method. The SVD is written
A = U * SIGMA * conjugatetranspose(V)
where SIGMA is an MbyN matrix which is zero except for its min(m,n) diagonal elements, U
is an MbyM unitary matrix, and V is an NbyN unitary matrix. The diagonal elements of
SIGMA are the singular values of A; they are real and nonnegative, 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 VT = V**H, not V.
The divide and conquer algorithm makes very mild assumptions about floating point arith
metic. It will work on machines with a guard digit in add/subtract, or on those binary
machines without guard digits which subtract like the Cray XMP, Cray YMP, Cray C90, or
Cray2. It could conceivably fail on hexadecimal or decimal machines without guard digits,
but we know of none.
ARGUMENTS
JOBZ (input) CHARACTER*1
Specifies options for computing all or part of the matrix U:
= 'A': all M columns of U and all N rows of V**H are returned in the arrays U and
VT; = 'S': the first min(M,N) columns of U and the first min(M,N) rows of V**H
are returned in the arrays U and VT; = 'O': If M >= N, the first N columns of U
are overwritten on the array A and all rows of V**H are returned in the array VT;
otherwise, all columns of U are returned in the array U and the first M rows of
V**H are overwritten in the array VT; = 'N': no columns of U or rows of V**H are
computed.
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 MbyN matrix A. On exit, if JOBZ = 'O', A is overwritten with the
first N columns of U (the left singular vectors, stored columnwise) if M >= N; A
is overwritten with the first M rows of V**H (the right singular vectors, stored
rowwise) otherwise. if JOBZ .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)
UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N; UCOL = min(M,N) if JOBZ = 'S'. If
JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the MbyM unitary matrix U; if
JOBZ = 'S', U contains the first min(M,N) columns of U (the left singular vectors,
stored columnwise); if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced.
LDU (input) INTEGER
The leading dimension of the array U. LDU >= 1; if JOBZ = 'S' or 'A' or JOBZ =
'O' and M < N, LDU >= M.
VT (output) COMPLEX array, dimension (LDVT,N)
If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the NbyN unitary matrix
V**H; if JOBZ = 'S', VT contains the first min(M,N) rows of V**H (the right singu
lar vectors, stored rowwise); if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not
referenced.
LDVT (input) INTEGER
The leading dimension of the array VT. LDVT >= 1; if JOBZ = 'A' or JOBZ = 'O' and
M >= N, LDVT >= N; if JOBZ = 'S', LDVT >= min(M,N).
WORK (workspace/output) COMPLEX array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= 1. if JOBZ = 'N', LWORK >=
2*min(M,N)+max(M,N). if JOBZ = 'O', LWORK >=
2*min(M,N)*min(M,N)+2*min(M,N)+max(M,N). if JOBZ = 'S' or 'A', LWORK >=
min(M,N)*min(M,N)+2*min(M,N)+max(M,N). For good performance, LWORK should gener
ally be larger. If LWORK < 0 but other input arguments are legal, WORK(1) returns
the optimal LWORK.
RWORK (workspace) REAL array, dimension (LRWORK)
If JOBZ = 'N', LRWORK >= 7*min(M,N). Otherwise, LRWORK >= 5*min(M,N)*min(M,N) +
5*min(M,N)
IWORK (workspace) INTEGER array, dimension (8*min(M,N))
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = i, the ith argument had an illegal value.
> 0: The updating process of SBDSDC did not converge.
FURTHER DETAILS
Based on contributions by
Ming Gu and Huan Ren, Computer Science Division, University of
California at Berkeley, USA
LAPACK version 3.0 15 June 2000 CGESDD(l) 
