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LAPACK version 3.0
dggglm(3)

PURPOSE
  DGGGLM - solve a general Gauss-Markov linear model (GLM) problem

SYNTAX
  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( * )

DESCRIPTION
  DGGGLM solves a general Gauss-Markov linear model (GLM) problem:
	  minimize || y ||_2   subject to   d = A*x + B*y
	      x

  where A is an N-by-M matrix, B is an N-by-P matrix, and d is a given N-
  vector. It is 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, which is
  obtained using a generalized QR factorization of A and B.

  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)*(d-A*x) ||_2
		   x

  where inv(B) denotes the inverse of 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.  0 <= M <= N.

  P	  (input) INTEGER
	  The number of columns of the matrix B.  P >= N-M.

  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/output) 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/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 >= max(1,N+M+P).  For
	  optimum performance, LWORK >= M+min(N,P)+max(N,P)*NB, where NB is
	  an upper bound for the optimal blocksizes for DGEQRF, SGERQF,
	  DORMQR and SORMRQ.

	  If LWORK = -1, then a workspace query is assumed; the routine only
	  calculates the optimal size of the WORK array, returns this value
	  as the first entry of the WORK array, and no error message related
	  to LWORK is issued by XERBLA.

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