SRC/cgetsls.f(3)           Library Functions Manual           SRC/cgetsls.f(3)

NAME
       SRC/cgetsls.f

SYNOPSIS
   Functions/Subroutines
       subroutine cgetsls (trans, m, n, nrhs, a, lda, b, ldb, work, lwork,
           info)
           CGETSLS

Function/Subroutine Documentation
   subroutine cgetsls (character trans, integer m, integer n, integer nrhs,
       complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, *
       ) b, integer ldb, complex, dimension( * ) work, integer lwork, integer
       info)
       CGETSLS

       Purpose:


            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.



            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
           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.
                     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 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.

       Definition at line 160 of file cgetsls.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                SRC/cgetsls.f(3)