sggglm(3S)

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( * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

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.

             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.

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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