NAME

       dgels.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dgels (TRANS, M, N, NRHS, A, LDA, B, LDB, WORK, LWORK, INFO)
            DGELS solves overdetermined or underdetermined systems for GE matrices

Function/Subroutine Documentation

   subroutine dgels (characterTRANS, integerM, integerN, integerNRHS, double precision,
       dimension( lda, * )A, integerLDA, double precision, dimension( ldb, * )B, integerLDB,
       double precision, dimension( * )WORK, integerLWORK, integerINFO)
        DGELS solves overdetermined or underdetermined systems for GE matrices

       Purpose:

            DGELS solves overdetermined or underdetermined real linear systems
            involving an M-by-N matrix A, or its transpose, using a QR or 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 = 'T' and m >= n:  find the minimum norm solution of
               an undetermined system A**T * X = B.

            4. If TRANS = 'T' 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;
                     = 'T': the linear system involves A**T.

           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 DOUBLE PRECISION array, dimension (LDA,N)
                     On entry, the M-by-N matrix A.
                     On exit,
                       if M >= N, A is overwritten by details of its QR
                                  factorization as returned by DGEQRF;
                       if M <  N, A is overwritten by details of its LQ
                                  factorization as returned by DGELQF.

           LDA

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

           B

                     B is DOUBLE PRECISION 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 = 'T'.
                     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; the residual sum of squares for the
                     solution in each column is given by the sum of squares of
                     elements N+1 to M in that column;
                     if TRANS = 'N' and m < n, rows 1 to N of B contain the
                     minimum norm solution vectors;
                     if TRANS = 'T' and m >= n, rows 1 to M of B contain the
                     minimum norm solution vectors;
                     if TRANS = 'T' and m < n, rows 1 to M of B contain the
                     least squares solution vectors; the residual sum of squares
                     for the solution in each column is given by the sum of
                     squares of elements M+1 to N in that column.

           LDB

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

           WORK

                     WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK

                     LWORK is INTEGER
                     The dimension of the array WORK.
                     LWORK >= max( 1, MN + max( MN, NRHS ) ).
                     For optimal performance,
                     LWORK >= max( 1, MN + max( MN, NRHS )*NB ).
                     where MN = min(M,N) and NB is the optimum block size.

                     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

                     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.

       Date:
           November 2011

       Definition at line 183 of file dgels.f.

Author

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