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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( * )



     #include <sunperf.h>

     void dgesvd(char jobu, char jobvt, int m, int n, double *da,
               int  lda,  double  *s, double *du, int ldu, double
               *dvt, int ldvt, int *info);

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  vec-
               tors) 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  singu-
               lar 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 orthog-
               onal 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,  dimen-
               sion (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 ille-
               gal value.
               > 0:  if DBDSQR did not converge,  INFO  specifies
               how many superdiagonals of an intermediate bidiag-
               onal form B did not  converge  to  zero.  See  the
               description of WORK above for details.

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