DGESDD(3S)DGESDD(3S)NAMEDGESDD - compute the singular value decomposition (SVD) of a real M-by-N
matrix A, optionally computing the left and right singular vectors
SYNOPSIS
SUBROUTINE DGESDD( 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( * )
DOUBLE PRECISION A( LDA, * ), S( * ), U( LDU, * ), VT( LDVT,
* ), WORK( * )
IMPLEMENTATION
These routines are part of the SCSL Scientific Library and can be loaded
using either the -lscs or the -lscs_mp option. The -lscs_mp option
directs the linker to use the multi-processor version of the library.
When linking to SCSL with -lscs or -lscs_mp, the default integer size is
4 bytes (32 bits). Another version of SCSL is available in which integers
are 8 bytes (64 bits). This version allows the user access to larger
memory sizes and helps when porting legacy Cray codes. It can be loaded
by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
only one of the two versions; 4-byte integer and 8-byte integer library
calls cannot be mixed.
PURPOSEDGESDD computes the singular value decomposition (SVD) of a real M-by-N
matrix A, optionally computing the left and right singular vectors. If
singular vectors are desired, it uses a divide-and-conquer algorithm.
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 VT = V**T, not V.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. 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 X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could
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DGESDD(3S)DGESDD(3S)
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) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the M-by-N 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) 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)
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 M-by-M 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) DOUBLE PRECISION array, dimension (LDVT,N)
If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the N-by-N
orthogonal matrix V**T; if JOBZ = 'S', VT contains the first
min(M,N) rows of V**T (the right singular vectors, stored
rowwise); if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not
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DGESDD(3S)DGESDD(3S)
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) DOUBLE PRECISION 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
performance, LWORK should generally be larger. If LWORK < 0 but
other input arguments 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 i-th argument had an illegal value.
> 0: DBDSDC 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
SEE ALSOINTRO_LAPACK(3S), INTRO_SCSL(3S)
This man page is available only online.
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