zgetsls()

subroutine zgetsls	(	character	trans,
		integer	m,
		integer	n,
		integer	nrhs,
		complex*16, dimension( lda, * )	a,
		integer	lda,
		complex*16, dimension( ldb, * )	b,
		integer	ldb,
		complex*16, dimension( * )	work,
		integer	lwork,
		integer	info )

ZGETSLS

Purpose:

!>
!> ZGETSLS solves overdetermined or underdetermined complex linear systems
!> involving an M-by-N matrix A, using a tall skinny QR or short wide LQ
!> factorization of A.
!>
!> It is assumed that A has full rank, and only a rudimentary protection
!> against rank-deficient matrices is provided. This subroutine only detects
!> exact rank-deficiency, where a diagonal element of the triangular factor
!> of A is exactly zero.
!>
!> It is conceivable for one (or more) of the diagonal elements of the triangular
!> factor of A to be subnormally tiny numbers without this subroutine signalling
!> an error. The solutions computed for such almost-rank-deficient matrices may
!> be less accurate due to a loss of numerical precision.
!>
!>
!> The following options are provided:
!>
!> 1. If TRANS = 'N' and m >= n:  find the least squares solution of
!>    an overdetermined system, i.e., solve the least squares problem
!>                 minimize || B - A*X ||.
!>
!> 2. If TRANS = 'N' and m < n:  find the minimum norm solution of
!>    an underdetermined system A * X = B.
!>
!> 3. If TRANS = 'C' and m >= n:  find the minimum norm solution of
!>    an undetermined system A**T * X = B.
!>
!> 4. If TRANS = 'C' and m < n:  find the least squares solution of
!>    an overdetermined system, i.e., solve the least squares problem
!>                 minimize || B - A**T * X ||.
!>
!> Several right hand side vectors b and solution vectors x can be
!> handled in a single call; they are stored as the columns of the
!> M-by-NRHS right hand side matrix B and the N-by-NRHS solution
!> matrix X.
!> 

Parameters

[in]	TRANS	!> TRANS is CHARACTER*1 !> = 'N': the linear system involves A; !> = 'C': the linear system involves A**H. !>
[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 matrix A. N >= 0. !>
[in]	NRHS	!> NRHS is INTEGER !> The number of right hand sides, i.e., the number of !> columns of the matrices B and X. NRHS >=0. !>
[in,out]	A	!> A is COMPLEX*16 array, dimension (LDA,N) !> On entry, the M-by-N matrix A. !> On exit, !> A is overwritten by details of its QR or LQ !> factorization as returned by ZGEQR or ZGELQ. !>
[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,NRHS) !> On entry, the matrix B of right hand side vectors, stored !> columnwise; B is M-by-NRHS if TRANS = 'N', or N-by-NRHS !> if TRANS = 'C'. !> On exit, if INFO = 0, B is overwritten by the solution !> vectors, stored columnwise: !> if TRANS = 'N' and m >= n, rows 1 to n of B contain the least !> squares solution vectors. !> if TRANS = 'N' and m < n, rows 1 to N of B contain the !> minimum norm solution vectors; !> if TRANS = 'C' and m >= n, rows 1 to M of B contain the !> minimum norm solution vectors; !> if TRANS = 'C' and m < n, rows 1 to M of B contain the !> least squares solution vectors. !>
[in]	LDB	!> LDB is INTEGER !> The leading dimension of the array B. LDB >= MAX(1,M,N). !>
[out]	WORK	!> (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) contains optimal (or either minimal !> or optimal, if query was assumed) LWORK. !> See LWORK for details. !>
[in]	LWORK	!> LWORK is INTEGER !> The dimension of the array WORK. LWORK >= 1. !> If LWORK = -1 or -2, then a workspace query is assumed. !> If LWORK = -1, the routine calculates optimal size of WORK for the !> optimal performance and returns this value in WORK(1). !> If LWORK = -2, the routine calculates minimal size of WORK and !> returns this value in WORK(1). !>
[out]	INFO	!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: if INFO = i, the i-th diagonal element of the !> triangular factor of A is exactly zero, so that A does not have !> full rank; the least squares solution could not be !> computed. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.