sgesdd.f man page

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 >= min(M,N)*(6+4*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:

November 2013

Contributors:

Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA

Definition at line 216 of file sgesdd.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

sgesdd(3) is an alias of sgesdd.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK