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 (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)

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 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 217 of file sgesdd.f.

Author

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