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dggglm.f(3)				      LAPACK				      dggglm.f(3)

NAME
       dggglm.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dggglm (N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LWORK, INFO)
	    DGGEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors
	   for GE matrices

Function/Subroutine Documentation
   subroutine dggglm (integerN, integerM, integerP, double precision, dimension( lda, * )A,
       integerLDA, double precision, dimension( ldb, * )B, integerLDB, double precision,
       dimension( * )D, double precision, dimension( * )X, double precision, dimension( * )Y,
       double precision, dimension( * )WORK, integerLWORK, integerINFO)
	DGGEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for
       GE matrices

       Purpose:

	    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 the matrices (A, B) given by

	       A = Q*(R),   B = Q*T*Z.
		     (0)

	    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.

       Parameters:
	   N

		     N is INTEGER
		     The number of rows of the matrices A and B.  N >= 0.

	   M

		     M is INTEGER
		     The number of columns of the matrix A.  0 <= M <= N.

	   P

		     P is INTEGER
		     The number of columns of the matrix B.  P >= N-M.

	   A

		     A is DOUBLE PRECISION array, dimension (LDA,M)
		     On entry, the N-by-M matrix A.
		     On exit, the upper triangular part of the array A contains
		     the M-by-M upper triangular matrix R.

	   LDA

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

	   B

		     B is DOUBLE PRECISION array, dimension (LDB,P)
		     On entry, the N-by-P matrix B.
		     On exit, if N <= P, the upper triangle of the subarray
		     B(1:N,P-N+1:P) contains the N-by-N upper triangular matrix T;
		     if N > P, the elements on and above the (N-P)th subdiagonal
		     contain the N-by-P upper trapezoidal matrix T.

	   LDB

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

	   D

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

	   X

		     X is DOUBLE PRECISION array, dimension (M)

	   Y

		     Y is DOUBLE PRECISION array, dimension (P)

		     On exit, X and Y are the solutions of the GLM problem.

	   WORK

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

	   LWORK

		     LWORK is 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

		     INFO is INTEGER
		     = 0:  successful exit.
		     < 0:  if INFO = -i, the i-th argument had an illegal value.
		     = 1:  the upper triangular factor R associated with A in the
			   generalized QR factorization of the pair (A, B) is
			   singular, so that rank(A) < M; the least squares
			   solution could not be computed.
		     = 2:  the bottom (N-M) by (N-M) part of the upper trapezoidal
			   factor T associated with B in the generalized QR
			   factorization of the pair (A, B) is singular, so that
			   rank( A B ) < N; the least squares solution could not
			   be computed.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Definition at line 185 of file dggglm.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      dggglm.f(3)
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