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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(
               * )



     #include <sunperf.h>

     void sggglm(int n, int m, int p, float *sa, int  lda,  float
               *sb,  int ldb, float *d, float *sx, float *sy, int
               *info) ;

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 des-
               troyed.

     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 des-
               troyed.

     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.

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

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