sgglse(3F)

NAME
     SGGLSE - solve the linear equality-constrained least squares (LSE)
     problem

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

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

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

PURPOSE
     SGGLSE solves the linear equality-constrained least squares (LSE)
     problem:

             minimize || c - A*x ||_2   subject to   B*x = d

     where A is an M-by-N matrix, B is a P-by-N matrix, c is a given M-vector,
     and d is a given P-vector. It is assumed that
     P <= N <= M+P, and

              rank(B) = P and  rank( ( A ) ) = N.
                                   ( ( B ) )

     These conditions ensure that the LSE problem has a unique solution, which
     is obtained using a GRQ factorization of the matrices B and A.


ARGUMENTS
     M       (input) INTEGER
             The number of rows of the matrix A.  M >= 0.

     N       (input) INTEGER
             The number of columns of the matrices A and B. N >= 0.

     P       (input) INTEGER
             The number of rows of the matrix B. 0 <= P <= N <= M+P.

     A       (input/output) REAL array, dimension (LDA,N)
             On entry, the M-by-N matrix A.  On exit, A is destroyed.

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

     B       (input/output) REAL array, dimension (LDB,N)
             On entry, the P-by-N matrix B.  On exit, B is destroyed.

     LDB     (input) INTEGER
             The leading dimension of the array B. LDB >= max(1,P).
     C       (input/output) REAL array, dimension (M)
             On entry, C contains the right hand side vector for the least
             squares part of the LSE problem.  On exit, the residual sum of
             squares for the solution is given by the sum of squares of
             elements N-P+1 to M of vector C.

     D       (input/output) REAL array, dimension (P)
             On entry, D contains the right hand side vector for the
             constrained equation.  On exit, D is destroyed.

     X       (output) REAL array, dimension (N)
             On exit, X is the solution of the LSE 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,M+N+P).  For
             optimum performance LWORK >= P+min(M,N)+max(M,N)*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.