SYNOPSIS
 SUBROUTINE SGGGLM(
 N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LWORK, INFO )
 INTEGER INFO, LDA, LDB, LWORK, M, N, P
 REAL A( LDA, * ), B( LDB, * ), D( * ), WORK( * ), X( * ), Y( * )
PURPOSE
SGGGLM 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 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)*(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) REAL array, dimension (LDA,M)
 On entry, the NbyM matrix A. On exit, the upper triangular part of the array A contains the MbyM upper triangular matrix R.
 LDA (input) INTEGER
 The leading dimension of the array A. LDA >= max(1,N).
 B (input/output) REAL array, dimension (LDB,P)
 On entry, the NbyP matrix B. On exit, if N <= P, the upper triangle of the subarray B(1:N,PN+1:P) contains the NbyN upper triangular matrix T; if N > P, the elements on and above the (NP)th subdiagonal contain the NbyP upper trapezoidal matrix T.
 LDB (input) INTEGER
 The leading dimension of the array B. LDB >= max(1,N).
 D (input/output) REAL array, dimension (N)
 On entry, D is the left hand side of the GLM equation. On exit, D is destroyed.
 X (output) REAL array, dimension (M)
 Y (output) REAL array, dimension (P) On exit, X and Y are the solutions of the GLM problem.
 WORK (workspace/output) REAL array, dimension (MAX(1,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 SGEQRF, SGERQF, SORMQR and SORMRQ. 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.
= 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 (NM) by (NM) 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.