dgesvd(3S)

NAME
     DGESVD - compute 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( * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

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 (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 >= 1.  LWORK >=
             MAX(3*MIN(M,N)+MAX(M,N),5*MIN(M,N)).  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.

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

     This man page is available only online.