zgglse()

subroutine zgglse	(	integer	m,
		integer	n,
		integer	p,
		complex*16, dimension( lda, * )	a,
		integer	lda,
		complex*16, dimension( ldb, * )	b,
		integer	ldb,
		complex*16, dimension( * )	c,
		complex*16, dimension( * )	d,
		complex*16, dimension( * )	x,
		complex*16, dimension( * )	work,
		integer	lwork,
		integer	info )

ZGGLSE solves overdetermined or underdetermined systems for OTHER matrices

Download ZGGLSE + dependencies [TGZ] [ZIP] [TXT]

Purpose:

!>
!> ZGGLSE solves the linear equality-constrained least squares (LSE)
!> problem:
!>
!>         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-vector, 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.
!>
!> Callers of this subroutine should note that the singularity/rank-deficiency checks
!> implemented in this subroutine are rudimentary. The ZTRTRS subroutine called by this
!> subroutine only signals a failure due to singularity if the problem is exactly singular.
!>
!> It is conceivable for one (or more) of the factors involved in the generalized RQ
!> factorization of the pair (B, A) to be subnormally close to singularity without this
!> subroutine signalling an error. The solutions computed for such almost-rank-deficient
!> problems may be less accurate due to a loss of numerical precision.
!> 
!> 

Parameters

[in]	M	!> M is INTEGER !> The number of rows of the matrix A. M >= 0. !>
[in]	N	!> N is INTEGER !> The number of columns of the matrices A and B. N >= 0. !>
[in]	P	!> P is INTEGER !> The number of rows of the matrix B. 0 <= P <= N <= M+P. !>
[in,out]	A	!> A is COMPLEX*16 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. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,M). !>
[in,out]	B	!> B is COMPLEX*16 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 triangular matrix R. !>
[in]	LDB	!> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,P). !>
[in,out]	C	!> C is COMPLEX*16 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 N-P+1 to M of !> vector C. !>
[in,out]	D	!> D is COMPLEX*16 array, dimension (P) !> On entry, D contains the right hand side vector for the !> constrained equation. !> On exit, D is destroyed. !>
[out]	X	!> X is COMPLEX*16 array, dimension (N) !> On exit, X is the solution of the LSE problem. !>
[out]	WORK	!> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !>
[in]	LWORK	!> LWORK is 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 !> 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. !>
[out]	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 B in the !> generalized RQ factorization of the pair (B, A) is exactly !> singular, so that rank(B) < P; the least squares !> solution could not be computed. !> = 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 exactly singular, so that !> rank( (A) ) < N; the least squares solution could not !> ( (B) ) !> be computed. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.