sgesdd3

!>
!> 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.
!>
!> 

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 LWORK = -1, a workspace query is assumed.  The optimal
!>          size for the WORK array is calculated and stored in WORK(1),
!>          and no other work except argument checking is performed.
!>
!>          Let mx = max(M,N) and mn = min(M,N).
!>          If JOBZ = 'N', LWORK >= 3*mn + max( mx, 7*mn ).
!>          If JOBZ = 'O', LWORK >= 3*mn + max( mx, 5*mn*mn + 4*mn ).
!>          If JOBZ = 'S', LWORK >= 4*mn*mn + 7*mn.
!>          If JOBZ = 'A', LWORK >= 4*mn*mn + 6*mn + mx.
!>          These are not tight minimums in all cases; see comments inside code.
!>          For good performance, LWORK should generally be larger;
!>          a query is recommended.
!> 

IWORK

!>          IWORK is INTEGER array, dimension (8*min(M,N))
!> 

INFO

!>          INFO is INTEGER
!>          <  0:  if INFO = -i, the i-th argument had an illegal value.
!>          = -4:  if A had a NAN entry.
!>          >  0:  SBDSDC did not converge, updating process failed.
!>          =  0:  successful exit.
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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