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sgesdd.f(3) LAPACK sgesdd.f(3)

NAME

sgesdd.f -

SYNOPSIS

Functions/Subroutines


subroutine sgesdd (JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, IWORK, INFO)
SGESDD

Function/Subroutine Documentation

subroutine sgesdd (characterJOBZ, integerM, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( * )S, real, dimension( ldu, * )U, integerLDU, real, dimension( ldvt, * )VT, integerLDVT, real, dimension( * )WORK, integerLWORK, integer, dimension( * )IWORK, integerINFO)

SGESDD

Purpose:


SGESDD 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 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 REAL 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


LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).

S


S is REAL array, dimension (min(M,N))
The singular values of A, sorted so that S(i) >= S(i+1).

U


U is 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 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


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 REAL 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 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 REAL 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),6*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 i-th argument had an illegal value.
> 0: SBDSDC 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 sgesdd.f.

Author

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Tue Sep 25 2012 Version 3.4.2