NAME

       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 (characterJOBZ, integerM, integerN, double precision, dimension( lda, * )A,
       integerLDA, double precision, dimension( * )S, double precision, dimension( ldu, * )U,
       integerLDU, double precision, dimension( ldvt, * )VT, integerLDVT, double precision,
       dimension( * )WORK, integerLWORK, integer, dimension( * )IWORK, integerINFO)
       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.

            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 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 JOBZ = 'N',
                       LWORK >= 3*min(M,N) + max(max(M,N),7*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:  DBDSDC 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 dgesdd.f.

Author

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