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NAME
     zgelss - compute the minimum  norm  solution  to  a  complex
     linear least squares problem

SYNOPSIS
     SUBROUTINE ZGELSS( M, N, NRHS, A, LDA,  B,  LDB,  S,  RCOND,
               RANK, WORK, LWORK, RWORK, INFO )

     INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS, RANK

     DOUBLE PRECISION RCOND

     DOUBLE PRECISION RWORK( * ), S( * )

     COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )



     #include <sunperf.h>

     void zgelss(int m, int n, int nrhs, doublecomplex  *za,  int
               lda, doublecomplex *zb, int ldb, double *s, double
               rcond, int *rank, int *info) ;

PURPOSE
     ZGELSS computes the  minimum  norm  solution  to  a  complex
     linear least squares problem:

     Minimize 2-norm(| b - A*x |).

     using the singular value decomposition (SVD) of A. A  is  an
     M-by-N matrix which may be rank-deficient.

     Several right hand side vectors b and solution vectors x can
     be  handled in a single call; they are stored as the columns
     of the M-by-NRHS right hand side matrix B and the  N-by-NRHS
     solution matrix X.

     The effective rank of A is determined by  treating  as  zero
     those  singular  values  which are less than RCOND times the
     largest singular value.


ARGUMENTS
     M         (input) INTEGER
               The number of rows of the matrix A. M >= 0.

     N         (input) INTEGER
               The number of columns of the matrix A. N >= 0.

     NRHS      (input) INTEGER
               The number of right hand sides, i.e.,  the  number
               of columns of the matrices B and X. NRHS >= 0.

     A         (input/output) COMPLEX*16 array, dimension (LDA,N)
               On entry, the M-by-N matrix A.  On exit, the first
               min(m,n)  rows of A are overwritten with its right
               singular vectors, stored rowwise.

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

     B         (input/output)   COMPLEX*16    array,    dimension
               (LDB,NRHS)
               On entry, the M-by-NRHS right hand side matrix  B.
               On  exit,  B is overwritten by the N-by-NRHS solu-
               tion matrix X.  If m >= n and RANK = n, the  resi-
               dual  sum-of-squares  for the solution in the i-th
               column is given by the sum of squares of  elements
               n+1:m in that column.

     LDB       (input) INTEGER
               The leading dimension of  the  array  B.   LDB  >=
               max(1,M,N).

     S         (output)   DOUBLE   PRECISION   array,   dimension
               (min(M,N))
               The singular values of A in decreasing order.  The
               condition   number   of   A   in   the   2-norm  =
               S(1)/S(min(m,n)).

     RCOND     (input) DOUBLE PRECISION
               RCOND is used to determine the effective  rank  of
               A.  Singular values S(i) <= RCOND*S(1) are treated
               as zero.  If RCOND < 0, machine precision is  used
               instead.

     RANK      (output) INTEGER
               The effective rank  of  A,  i.e.,  the  number  of
               singular values which are greater than RCOND*S(1).

     WORK      (workspace/output)  COMPLEX*16  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,  and
               also:   LWORK  >=   2*min(M,N) + max(M,N,NRHS) For
               good  performance,  LWORK  should   generally   be
               larger.

     RWORK     (workspace)  DOUBLE  PRECISION  array,   dimension
               (5*min(M,N)-1)

     INFO      (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille-
               gal value.
               > 0:  the algorithm for computing the  SVD  failed
               to  converge; if INFO = i, i off-diagonal elements
               of an intermediate bidiagonal form  did  not  con-
               verge to zero.

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