
SGESDD(l) ) SGESDD(l)
NAME
SGESDD  compute the singular value decomposition (SVD) of a real MbyN matrix A, option
ally computing the left and right singular vectors
SYNOPSIS
SUBROUTINE SGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, IWORK, INFO )
CHARACTER JOBZ
INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N
INTEGER IWORK( * )
REAL A( LDA, * ), S( * ), U( LDU, * ), VT( LDVT, * ), WORK( * )
PURPOSE
SGESDD computes the singular value decomposition (SVD) of a real MbyN matrix A, option
ally computing the left and right singular vectors. If singular vectors are desired, it
uses a divideandconquer algorithm.
The SVD is written
A = U * SIGMA * transpose(V)
where SIGMA is an MbyN matrix which is zero except for its min(m,n) diagonal elements, U
is an MbyM orthogonal matrix, and V is an NbyN orthogonal matrix. The diagonal ele
ments 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**T, 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**T 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**T
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**T are returned in the array VT;
otherwise, all columns of U are returned in the array U and the first M rows of
V**T are overwritten in the array VT; = 'N': no columns of U or rows of V**T 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) REAL 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**T (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) REAL 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 orthogonal 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) REAL array, dimension (LDVT,N)
If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the NbyN orthogonal matrix
V**T; if JOBZ = 'S', VT contains the first min(M,N) rows of V**T (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) REAL 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 >= 3*min(M,N) +
max(max(M,N),6*min(M,N)). If JOBZ = 'O', LWORK >= 3*min(M,N)*min(M,N) +
max(max(M,N),5*min(M,N)*min(M,N)+4*min(M,N)). If JOBZ = 'S' or 'A' LWORK >=
3*min(M,N)*min(M,N) + max(max(M,N),4*min(M,N)*min(M,N)+4*min(M,N)). For good per
formance, LWORK should generally be larger. If LWORK < 0 but other input argu
ments are legal, WORK(1) returns the optimal LWORK.
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: SBDSDC did not converge, updating process failed.
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 SGESDD(l) 
