ZGGLSE (3lapack)

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

SYNOPSIS

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

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

      COMPLEX*16     A( LDA, * ), B( LDB, * ), C( * ), D( * ), WORK( * ), X(
                     * )

PURPOSE

  ZGGLSE 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) COMPLEX*16 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) COMPLEX*16 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) COMPLEX*16 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) COMPLEX*16 array, dimension (P)
          On entry, D contains the right hand side vector for the constrained
          equation.  On exit, D is destroyed.

  X       (output) COMPLEX*16 array, dimension (N)
          On exit, X is the solution of the LSE problem.

  WORK    (workspace/output) COMPLEX*16 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 ZGEQRF, CGERQF, ZUNMQR
          and CUNMRQ.

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