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

NAME

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

SYNOPSIS

       SUBROUTINE DGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, INFO )

           CHARACTER      JOBU, JOBVT

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

           DOUBLE         PRECISION A( LDA, * ), S( * ), U( LDU, * ), VT( LDVT, * ), WORK( * )

PURPOSE

       DGESVD computes the singular  value  decomposition  (SVD)  of  a  real  M-by-N  matrix  A,
       optionally computing the left and/or right singular vectors. 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 V**T, not V.

ARGUMENTS

        JOBU    (input) CHARACTER*1
                Specifies options for computing all or part of the matrix U:
                = 'A':  all M columns of U are returned in array U:
                = 'S':  the first min(m,n) columns of U (the left singular
                vectors) are returned in the array U;
                = 'O':  the first min(m,n) columns of U (the left singular
                vectors) are overwritten on the array A;
                = 'N':  no columns of U (no left singular vectors) are
                computed.

        JOBVT   (input) CHARACTER*1
                Specifies options for computing all or part of the matrix
                V**T:
                = 'A':  all N rows of V**T are returned in the array VT;
                = 'S':  the first min(m,n) rows of V**T (the right singular
                vectors) are returned in the array VT;
                = 'O':  the first min(m,n) rows of V**T (the right singular
                vectors) are overwritten on the array A;
                = 'N':  no rows of V**T (no right singular vectors) are
                computed.
                JOBVT and JOBU cannot both be 'O'.

        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) DOUBLE PRECISION array, dimension (LDA,N)
                On entry, the M-by-N matrix A.
                On exit,
                if JOBU = 'O',  A is overwritten with the first min(m,n)
                columns of U (the left singular vectors,
                stored columnwise);
                if JOBVT = 'O', A is overwritten with the first min(m,n)
                rows of V**T (the right singular vectors,
                stored rowwise);
                if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents of A
                are destroyed.

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

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

        U       (output) DOUBLE PRECISION array, dimension (LDU,UCOL)
                (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'.
                If JOBU = 'A', U contains the M-by-M orthogonal matrix U;
                if JOBU = 'S', U contains the first min(m,n) columns of U
                (the left singular vectors, stored columnwise);
                if JOBU = 'N' or 'O', U is not referenced.

        LDU     (input) INTEGER
                The leading dimension of the array U.  LDU >= 1; if
                JOBU = 'S' or 'A', LDU >= M.

        VT      (output) DOUBLE PRECISION array, dimension (LDVT,N)
                If JOBVT = 'A', VT contains the N-by-N orthogonal matrix
                V**T;
                if JOBVT = 'S', VT contains the first min(m,n) rows of
                V**T (the right singular vectors, stored rowwise);
                if JOBVT = 'N' or 'O', VT is not referenced.

        LDVT    (input) INTEGER
                The leading dimension of the array VT.  LDVT >= 1; if
                JOBVT = 'A', LDVT >= N; if JOBVT = 'S', LDVT >= min(M,N).

        WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
                On exit, if INFO = 0, WORK(1) returns the optimal LWORK;
                if INFO > 0, WORK(2:MIN(M,N)) contains the unconverged
                superdiagonal elements of an upper bidiagonal matrix B
                whose diagonal is in S (not necessarily sorted). B
                satisfies A = U * B * VT, so it has the same singular values
                as A, and singular vectors related by U and VT.

        LWORK   (input) INTEGER
                The dimension of the array WORK.
                LWORK >= MAX(1,5*MIN(M,N)) for the paths (see comments inside code):
                - PATH 1  (M much larger than N, JOBU='N')
                - PATH 1t (N much larger than M, JOBVT='N')
                LWORK >= MAX(1,3*MIN(M,N)+MAX(M,N),5*MIN(M,N)) for the other paths
                For good performance, LWORK should generally be larger.
                If LWORK = -1, then a workspace query is assumed; the routine
                only calculates the optimal size of the WORK array, returns
                this value as the first entry of the WORK array, and no error
                message related to LWORK is issued by XERBLA.

        INFO    (output) INTEGER
                = 0:  successful exit.
                < 0:  if INFO = -i, the i-th argument had an illegal value.
                > 0:  if DBDSQR did not converge, INFO specifies how many
                superdiagonals of an intermediate bidiagonal form B
                did not converge to zero. See the description of WORK
                above for details.

 LAPACK driver routine (version 3.3.1)      April 2011                            DGESVD(3lapack)