

ZGGGLM(l) ) ZGGGLM(l) NAME ZGGGLM  solve a general GaussMarkov 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 GaussMarkov linear model (GLM) problem: minimize  y _2 subject to d = A*x + B*y x where A is an NbyM matrix, B is an NbyP matrix, and d is a given Nvector. 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 2norm 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)*(dA*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 >= NM. A (input/output) COMPLEX*16 array, dimension (LDA,M) On entry, the NbyM 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 NbyP 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 solu tions 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 block sizes for ZGEQRF, CGERQF, ZUNMQR and CUNMRQ. 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 ith argument had an illegal value. LAPACK version 3.0 15 June 2000 ZGGGLM(l)