SYNOPSIS
 SUBROUTINE SGGLSE(
 M, N, P, A, LDA, B, LDB, C, D, X, WORK, LWORK, INFO )
 INTEGER INFO, LDA, LDB, LWORK, M, N, P
 REAL A( LDA, * ), B( LDB, * ), C( * ), D( * ), WORK( * ), X( * )
PURPOSE
SGGLSE solves the linear equalityconstrained least squares (LSE) problem:minimize  c  A*x _2 subject to B*x = d
where A is an MbyN matrix, B is a PbyN matrix, c is a given Mvector, and d is a given Pvector. 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 generalized RQ factorization of the matrices (B, A) given by
B = (0 R)*Q, A = Z*T*Q.
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) REAL array, dimension (LDA,N)
 On entry, the MbyN matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)byN upper trapezoidal matrix T.
 LDA (input) INTEGER
 The leading dimension of the array A. LDA >= max(1,M).
 B (input/output) REAL array, dimension (LDB,N)
 On entry, the PbyN matrix B. On exit, the upper triangle of the subarray B(1:P,NP+1:N) contains the PbyP upper triangular matrix R.
 LDB (input) INTEGER
 The leading dimension of the array B. LDB >= max(1,P).
 C (input/output) REAL 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 NP+1 to M of vector C.
 D (input/output) REAL array, dimension (P)
 On entry, D contains the right hand side vector for the constrained equation. On exit, D is destroyed.
 X (output) REAL array, dimension (N)
 On exit, X is the solution of the LSE 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,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 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 B in the generalized RQ factorization of the pair (B, A) is singular, so that rank(B) < P; the least squares solution could not be computed. = 2: the (NP) by (NP) part of the upper trapezoidal factor T associated with A in the generalized RQ factorization of the pair (B, A) is singular, so that rank( (A) ) < N; the least squares solution could not ( (B) ) be computed.