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 gen­
       eralized 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.

               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 equa­
               tion.  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 prob­
               lem.

       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.

               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 ille­
               gal value.


Man(1) output converted with man2html