cgetsls3

!>
!> CGETSLS 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.
!> 

TRANS

!>          TRANS is CHARACTER*1
!>          = 'N': the linear system involves A;
!>          = 'C': the linear system involves A**H.
!> 

M

!>          M is INTEGER
!>          The number of rows of the matrix A.  M >= 0.
!> 

N

!>          N is INTEGER
!>          The number of columns of the matrix A.  N >= 0.
!> 

NRHS

!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of
!>          columns of the matrices B and X. NRHS >=0.
!> 

A

!>          A is COMPLEX 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 CGEQR or CGELQ.
!> 

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,M).
!> 

B

!>          B is COMPLEX 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.
!> 

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B. LDB >= MAX(1,M,N).
!> 

WORK

!>          (workspace) COMPLEX 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.
!> 

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).
!> 

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.
!> 

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