CGGLSE(1) LAPACK driver routine (version 3.2) CGGLSE(1)NAME
CGGLSE - solves the linear equality-constrained least squares (LSE)
problem
SYNOPSIS
SUBROUTINE CGGLSE( M, N, P, A, LDA, B, LDB, C, D, X, WORK, LWORK, INFO
)
INTEGER INFO, LDA, LDB, LWORK, M, N, P
COMPLEX A( LDA, * ), B( LDB, * ), C( * ), D( * ), WORK( * ),
X( * )
PURPOSE
CGGLSE solves the linear equality-constrained least squares (LSE) prob‐
lem:
minimize || c - A*x ||_2 subject to B*x = d
where A is an M-by-N matrix, B is a P-by-N matrix, c is a given M-vec‐
tor, and d is a given P-vector. 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) COMPLEX array, dimension (LDA,N)
On entry, the M-by-N matrix A. On exit, the elements on and
above the diagonal of the array contain the min(M,N)-by-N upper
trapezoidal matrix T.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
B (input/output) COMPLEX array, dimension (LDB,N)
On entry, the P-by-N matrix B. On exit, the upper triangle of
the subarray B(1:P,N-P+1:N) contains the P-by-P upper triangu‐
lar matrix R.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,P).
C (input/output) COMPLEX 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 ele‐
ments N-P+1 to M of vector C.
D (input/output) COMPLEX array, dimension (P)
On entry, D contains the right hand side vector for the con‐
strained equation. On exit, D is destroyed.
X (output) COMPLEX array, dimension (N)
On exit, X is the solution of the LSE problem.
WORK (workspace/output) COMPLEX 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 CGEQRF,
CGERQF, CUNMQR 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 i-th 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 com‐
puted. = 2: the (N-P) by (N-P) 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.
LAPACK driver routine (version 3November 2008 CGGLSE(1)
