Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  computes the singular value decomposition (SVD) of a complex M-by-N matrix A,
       optionally computing the left and/or right singular vectors, by  using  divide-and-conquer
       method

SYNOPSIS

       SUBROUTINE CGESDD( JOBZ,  M,  N,  A,  LDA, S, U, LDU, VT, LDVT, WORK, LWORK, RWORK, IWORK,
                          INFO )

           CHARACTER      JOBZ

           INTEGER        INFO, LDA, LDU, LDVT, LWORK, M, N

           INTEGER        IWORK( * )

           REAL           RWORK( * ), S( * )

           COMPLEX        A( LDA, * ), U( LDU, * ), VT( LDVT, * ), WORK( * )

PURPOSE

       CGESDD computes the singular value decomposition (SVD)  of  a  complex  M-by-N  matrix  A,
       optionally  computing  the left and/or right singular vectors, by using divide-and-conquer
       method. The SVD is written
             A = U * SIGMA * conjugate-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 unitary matrix, and
        V is an N-by-N unitary 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**H, 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.

ARGUMENTS

        JOBZ    (input) 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**H 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**H are returned in the arrays U
                and VT;
                = 'O':  If M >= N, the first N columns of U are overwritten
                in the array A and all rows of V**H are returned in
                the array VT;
                otherwise, all columns of U are returned in the
                array U and the first M rows of V**H are overwritten
                in the array A;
                = 'N':  no columns of U or rows of V**H are computed.

        M       (input) INTEGER
                The number of rows of the input matrix A.  M >= 0.

        N       (input) INTEGER
                The number of columns of the input matrix A.  N >= 0.

        A       (input/output) COMPLEX 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**H (the right singular vectors, stored
                rowwise) otherwise.
                if JOBZ .ne. 'O', the contents of A are destroyed.

        LDA     (input) INTEGER
                The leading dimension of the array A.  LDA >= max(1,M).

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

        U       (output) COMPLEX 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
                unitary 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     (input) INTEGER
                The leading dimension of the array U.  LDU >= 1; if
                JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M.

        VT      (output) COMPLEX array, dimension (LDVT,N)
                If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the
                N-by-N unitary matrix V**H;
                if JOBZ = 'S', VT contains the first min(M,N) rows of
                V**H (the right singular vectors, stored rowwise);
                if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced.

        LDVT    (input) 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    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
                On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

        LWORK   (input) INTEGER
                The dimension of the array WORK. LWORK >= 1.
                if JOBZ = 'N', LWORK >= 2*min(M,N)+max(M,N).
                if JOBZ = 'O',
                LWORK >= 2*min(M,N)*min(M,N)+2*min(M,N)+max(M,N).
                if JOBZ = 'S' or 'A',
                LWORK >= min(M,N)*min(M,N)+2*min(M,N)+max(M,N).
                For good performance, LWORK should generally be larger.
                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.

        RWORK   (workspace) REAL array, dimension (MAX(1,LRWORK))
                If JOBZ = 'N', LRWORK >= 5*min(M,N).
                Otherwise,
                LRWORK >= min(M,N)*max(5*min(M,N)+7,2*max(M,N)+2*min(M,N)+1)

        IWORK   (workspace) INTEGER array, dimension (8*min(M,N))

        INFO    (output) INTEGER
                = 0:  successful exit.
                < 0:  if INFO = -i, the i-th argument had an illegal value.
                > 0:  The updating process of SBDSDC did not converge.

FURTHER DETAILS

        Based on contributions by
           Ming Gu and Huan Ren, Computer Science Division, University of
           California at Berkeley, USA

 LAPACK driver routine (version 3.2.2)      April 2011                            CGESDD(3lapack)