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NAME
     cgesvd - compute the singular value decomposition (SVD) of a
     complex  M-by-N  matrix  A,  optionally  computing  the left
     and/or right singular vectors

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

     CHARACTER JOBU, JOBVT

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

     REAL RWORK( * ), S( * )

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



     #include <sunperf.h>

     void cgesvd(char jobu, char jobvt, int  m,  int  n,  complex
               *ca, int lda, float *s, complex *cu, int ldu, com-
               plex *cvt, int ldvt, int *info);

PURPOSE
     CGESVD computes the singular value decomposition (SVD) of  a
     complex  M-by-N  matrix  A,  optionally  computing  the left
     and/or right singular vectors. 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 V**H, 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**H:
               = 'A':  all N rows of V**H  are  returned  in  the
               array VT;
               = 'S':  the first min(m,n) rows of V**H (the right
               singular  vectors) are returned in the array VT; =
               'O':  the first min(m,n) rows of V**H  (the  right
               singular  vectors) are overwritten on the array A;
               = 'N':  no rows of V**H (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) COMPLEX 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**H (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) 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)
               (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU  =
               'S'.  If JOBU = 'A', U contains the M-by-M unitary
               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) COMPLEX array, dimension (LDVT,N)
               If JOBVT = 'A', VT  contains  the  N-by-N  unitary
               matrix V**H; if JOBVT = 'S', VT contains the first
               min(m,n) rows of V**H (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)   COMPLEX   array,    dimension
               (LWORK)
               On exit, if INFO = 0, WORK(1) returns the  optimal
               LWORK.

     LWORK     (input) INTEGER
               The dimension of  the  array  WORK.  LWORK  >=  1.
               LWORK  >=   2*MIN(M,N)+MAX(M,N).  For good perfor-
               mance, LWORK should generally be larger.

     RWORK     (workspace) REAL array, dimension
               (max(3*min(M,N),5*min(M,N)-4)) On exit, if INFO  >
               0,  RWORK(1:MIN(M,N)-1)  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 vec-
               tors related by U and VT.

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

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