ZGGGLM (3lapack)

solve a general Gauss-Markov linear model (GLM) problem

SYNOPSIS

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

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

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

PURPOSE

  ZGGGLM 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) COMPLEX*16 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) COMPLEX*16 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) COMPLEX*16 array, dimension (N)
          On entry, D is the left hand side of the GLM equation.  On exit, D
          is destroyed.

  X       (output) COMPLEX*16 array, dimension (M)
          Y       (output) COMPLEX*16 array, dimension (P) On exit, X and Y
          are the solutions of the GLM 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,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 ZGEQRF, CGERQF,
          ZUNMQR and CUNMRQ.

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