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

NAME
  DGGGLM - solve a generalized linear regression model (GLM) problem

SYNOPSIS

  SUBROUTINE DGGGLM( N,	M, P, A, LDA, B, LDB, D, X, Y, WORK, LWORK, INFO )

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

      DOUBLE	     PRECISION A( LDA, * ), B( LDB, * ), D( * ), WORK( * ),
		     X(	* ), Y(	* )

PURPOSE
  DGGGLM solves	a generalized linear regression	model (GLM) problem:

	  minimize y'*y	    subject to	  d = A*x + B*y
	    x,y

  using	a generalized QR factorization of A and	B, where A is an N-by-M
  matrix, B is a given N-by-P matrix, and d is a given N vector.  It is	also
  assumed that M <= N <= M+P and

	     rank(A) = M    and	   rank([ A B ]) = N.

  Under	these assumptions, the constrained equation is always consistent, and
  there	is a unique solution x and a minimal 2-norm solution y.

  In particular, if matrix B is	square nonsingular, then the problem GLM is
  equivalent to	the following weighted linear least squares problem
	       minimize	|| inv(B)*(b-A*x) ||
		  x
  where	||.|| is vector	2-norm,	and inv(B) denotes the inverse of matrix B.

ARGUMENTS

  N	  (input) INTEGER
	  The number of	rows of	the matrices A and B.  N >= 0.

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

  P	  (input) INTEGER
	  The number of	columns	of the matrix B.  P >= 0.  Assume that M <= N
	  <= M+P.

  A	  (input/output) DOUBLE	PRECISION array, dimension (LDA,M)
	  On entry, the	N-by-M matrix A.  On exit, A is	destroyed.

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

  B	  (input/output) DOUBLE	PRECISION array, dimension (LDB,P)
	  On entry, the	N-by-P matrix B.  On exit, B is	destroyed.

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

  D	  (input) DOUBLE PRECISION array, dimension (N)
	  On entry, D is the left hand side of the GLM equation.  On exit, D
	  is destroyed.

  X	  (output) DOUBLE PRECISION array, dimension (M)
	  Y	  (output) DOUBLE PRECISION array, dimension (P) On exit, X
	  and Y	are the	solutions of the GLM problem.

  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 >= M+P+max(N,M,P).  For
	  optimum performance, LWORK >=	M+P+max(N,M,P)*max(NB1,NB2), where
	  NB1 is the optimal blocksize for the QR factorization	of an N-by-M
	  matrix A.  NB2 is the	optimal	blocksize for the RQ factorization of
	  an N-by-P matrix B.

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