sggglm(3F)

NAME
     SGGGLM - solve a general Gauss-Markov linear model (GLM) problem

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

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

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

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

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

     WORK    (workspace/output) REAL 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 SGEQRF, SGERQF,
             SORMQR and SORMRQ.

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