zggglm.f - Man Page

subroutine zggglm (n, m, p, a, lda, b, ldb, d, x, y, work, lwork, info)
ZGGGLM

ZGGGLM  

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 the matrices (A, B) given by

    A = Q*(R),   B = Q*T*Z.
          (0)

 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.

Parameters

N

          N is INTEGER
          The number of rows of the matrices A and B.  N >= 0.

M

          M is INTEGER
          The number of columns of the matrix A.  0 <= M <= N.

P

          P is INTEGER
          The number of columns of the matrix B.  P >= N-M.

A

          A is COMPLEX*16 array, dimension (LDA,M)
          On entry, the N-by-M matrix A.
          On exit, the upper triangular part of the array A contains
          the M-by-M upper triangular matrix R.

LDA

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

B

          B is COMPLEX*16 array, dimension (LDB,P)
          On entry, the N-by-P matrix B.
          On exit, if N <= P, the upper triangle of the subarray
          B(1:N,P-N+1:P) contains the N-by-N upper triangular matrix T;
          if N > P, the elements on and above the (N-P)th subdiagonal
          contain the N-by-P upper trapezoidal matrix T.

LDB

          LDB is INTEGER
          The leading dimension of the array B. LDB >= max(1,N).

D

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

X

          X is COMPLEX*16 array, dimension (M)

Y

          Y is COMPLEX*16 array, dimension (P)

          On exit, X and Y are the solutions of the GLM problem.

WORK

          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is 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, ZGERQF, ZUNMQR and ZUNMRQ.

          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

          INFO is INTEGER
          = 0:  successful exit.
          < 0:  if INFO = -i, the i-th argument had an illegal value.
          = 1:  the upper triangular factor R associated with A in the
                generalized QR factorization of the pair (A, B) is
                singular, so that rank(A) < M; the least squares
                solution could not be computed.
          = 2:  the bottom (N-M) by (N-M) part of the upper trapezoidal
                factor T associated with B in the generalized QR
                factorization of the pair (A, B) is singular, so that
                rank( A B ) < N; the least squares solution could not
                be computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 183 of file zggglm.f.