SRC/sgesdd.f(3)

NAME
SRC/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 (character jobz, integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real, dimension( ldu, * ) u, integer ldu, real, dimension( ldvt, * ) vt, integer ldvt, real, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer info)

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.
    !>
    !>

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 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.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

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

Definition at line 211 of file sgesdd.f.

Author

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