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NAME
     dgels - solve overdetermined or underdetermined real  linear
     systems  involving  an  M-by-N  matrix  A, or its transpose,
     using a QR or LQ factorization of A

SYNOPSIS
     SUBROUTINE DGELS( TRANS, M, N, NRHS, A, LDA, B,  LDB,  WORK,
               LWORK, INFO )

     CHARACTER TRANS

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

     DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( LWORK )



     #include <sunperf.h>

     void dgels(char trans, int m, int n, int nrhs,  double  *da,
               int lda, double *db, int ldb, int *info) ;

PURPOSE
     DGELS solves overdetermined or underdetermined  real  linear
     systems  involving  an  M-by-N  matrix  A, or its transpose,
     using a QR or LQ factorization of A.  It is assumed  that  A
     has full rank.

     The following options are provided:

     1. If TRANS = 'N' and m >= n:  find the least squares  solu-
     tion  of  an  overdetermined  system,  i.e., solve the least
     squares problem
                     minimize || B - A*X ||.

     2. If TRANS = 'N' and m < n:  find the minimum norm solution
     of an underdetermined system A * X = B.

     3. If TRANS = 'T' and m >= n:  find the minimum  norm  solu-
     tion of an undetermined system A**T * X = B.

     4. If TRANS = 'T' and m < n:  find the least  squares  solu-
     tion  of  an  overdetermined  system,  i.e., solve the least
     squares problem
                     minimize || B - A**T * X ||.

     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.


ARGUMENTS
     TRANS     (input) CHARACTER
               = 'N': the linear system involves A;
               = 'T': the linear system involves A**T.

     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) DOUBLE PRECISION  array,  dimension
               (LDA,N)
               On entry, the M-by-N matrix A.  On exit, if  M  >=
               N,  A is overwritten by details of its QR factori-
               zation as returned by DGEQRF; if  M  <   N,  A  is
               overwritten  by details of its LQ factorization as
               returned by DGELQF.

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

     B         (input/output) DOUBLE PRECISION  array,  dimension
               (LDB,NRHS)
               On entry, the matrix B of right hand side vectors,
               stored  columnwise; B is M-by-NRHS if TRANS = 'N',
               or N-by-NRHS if  TRANS  =  'T'.   On  exit,  B  is
               overwritten   by   the  solution  vectors,  stored
               columnwise:  if TRANS = 'N' and m >= n, rows 1  to
               n of B contain the least squares solution vectors;
               the residual sum of squares for  the  solution  in
               each column is given by the sum of squares of ele-
               ments N+1 to M in that column; if TRANS = 'N'  and
               m  <  n, rows 1 to N of B contain the minimum norm
               solution vectors; if TRANS = 'T' and m >= n,  rows
               1 to M of B contain the minimum norm solution vec-
               tors; if TRANS = 'T' and m < n, rows 1 to M  of  B
               contain  the  least  squares solution vectors; the
               residual sum of squares for the solution  in  each
               column  is given by the sum of squares of elements
               M+1 to N in that column.

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

     WORK      (workspace/output)   DOUBLE    PRECISION    array,
               dimension (LWORK)
               On exit, if INFO = 0, WORK(1) returns the  optimal
               LWORK.

     LWORK     (input) INTEGER
               The  dimension  of  the  array  WORK.   LWORK   >=
               min(M,N)  +  MAX(1,M,N,NRHS).  For optimal perfor-
               mance, LWORK >= min(M,N) +  MAX(1,M,N,NRHS)  *  NB
               where NB is the optimum block size.

     INFO      (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille-
               gal value

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