dgglse(3S)

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

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

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

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

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
     DGGLSE 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (P)
             On entry, D contains the right hand side vector for the
             constrained equation.  On exit, D is destroyed.

     X       (output) DOUBLE PRECISION array, dimension (N)
             On exit, X is the solution of the LSE problem.

     WORK    (workspace/output) DOUBLE PRECISION 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 DGEQRF, SGERQF,
             DORMQR 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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