DGELS(l)	     LAPACK driver routine (version 1.1)	     DGELS(l)

NAME
  DGELS	- solve	overdetermined or underdetermined real linear systems involv-
  ing 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 )

PURPOSE
  DGELS	solves overdetermined or underdetermined real linear systems involv-
  ing 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	solution 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 solution	of
     an	undetermined system A**T * X = B.

  4. If	TRANS =	'T' and	m < n:	find the least squares solution	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 factorization as returned by
	  DGEQRF; if M <  N, A is overwritten by details of its	LQ factoriza-
	  tion 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 column-
	  wise;	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 column-
	  wise:	 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 elements
	  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	vectors; 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) 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	performance, 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 illegal value