sgesvd(3F)

NAME
     SGESVD - 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 SGESVD( 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

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

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

     U       (output) REAL 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) REAL 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) REAL 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)-4).  For good performance,
             LWORK should generally be larger.

     INFO    (output) INTEGER
             = 0:  successful exit.
             < 0:  if INFO = -i, the i-th argument had an illegal value.
             > 0:  if SBDSQR 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.