SRC/dgesdd.f(3)            Library Functions Manual            SRC/dgesdd.f(3)

NAME
       SRC/dgesdd.f

SYNOPSIS
   Functions/Subroutines
       subroutine dgesdd (jobz, m, n, a, lda, s, u, ldu, vt, ldvt, work,
           lwork, iwork, info)
           DGESDD

Function/Subroutine Documentation
   subroutine dgesdd (character jobz, integer m, integer n, double precision,
       dimension( lda, * ) a, integer lda, double precision, dimension( * ) s,
       double precision, dimension( ldu, * ) u, integer ldu, double precision,
       dimension( ldvt, * ) vt, integer ldvt, double precision, dimension( * )
       work, integer lwork, integer, dimension( * ) iwork, integer info)
       DGESDD

       Purpose:


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

           U

                     U is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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:  DBDSDC 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 dgesdd.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                 SRC/dgesdd.f(3)