DGGLSE (3lapack)

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( * )

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.

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