
dgesdd.f(3) LAPACK dgesdd.f(3)
NAME
dgesdd.f 
SYNOPSIS
Functions/Subroutines
subroutine dgesdd (JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, IWORK, INFO)
DGESDD
Function/Subroutine Documentation
subroutine dgesdd (characterJOBZ, integerM, integerN, double precision, dimension( lda, * )A,
integerLDA, double precision, dimension( * )S, double precision, dimension( ldu, * )U,
integerLDU, double precision, dimension( ldvt, * )VT, integerLDVT, double precision,
dimension( * )WORK, integerLWORK, integer, dimension( * )IWORK, integerINFO)
DGESDD
Purpose:
DGESDD computes the singular value decomposition (SVD) of a real
MbyN matrix A, optionally 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 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**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 XMP, Cray YMP, Cray C90, or
Cray2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Parameters:
JOBZ
JOBZ is 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 A;
= 'N': no columns of U or rows of V**T are computed.
M
M is INTEGER
The number of rows of the input matrix A. M >= 0.
N
N is INTEGER
The number of columns of the input matrix A. N >= 0.
A
A is DOUBLE PRECISION 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
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
S
S is DOUBLE PRECISION array, dimension (min(M,N))
The singular values of A, sorted so that S(i) >= S(i+1).
U
U is 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 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
LDU is INTEGER
The leading dimension of the array U. LDU >= 1; if
JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M.
VT
VT is DOUBLE PRECISION 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 singular vectors, stored rowwise);
if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced.
LDVT
LDVT is 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
WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK;
LWORK
LWORK is INTEGER
The dimension of the array WORK. LWORK >= 1.
If JOBZ = 'N',
LWORK >= 3*min(M,N) + max(max(M,N),7*min(M,N)).
If JOBZ = 'O',
LWORK >= 3*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) +
max(max(M,N),4*min(M,N)*min(M,N)+3*min(M,N)+max(M,N)).
For good performance, LWORK should generally be larger.
If LWORK = 1 but other input arguments are legal, WORK(1)
returns the optimal LWORK.
IWORK
IWORK is INTEGER array, dimension (8*min(M,N))
INFO
INFO is INTEGER
= 0: successful exit.
< 0: if INFO = i, the ith argument had an illegal value.
> 0: DBDSDC did not converge, updating process failed.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
September 2012
Contributors:
Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley,
USA
Definition at line 217 of file dgesdd.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 dgesdd.f(3) 
