Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3 - 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

SYNOPSIS

       SUBROUTINE DGELS( TRANS, M, N, NRHS, A, LDA, B, LDB, WORK, LWORK, INFO )

           CHARACTER     TRANS

           INTEGER       INFO, LDA, LDB, LWORK, M, N, NRHS

           DOUBLE        PRECISION A( LDA, * ), B( LDB, * ), WORK( * )

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.

ARGUMENTS

        TRANS   (input) CHARACTER*1
                = 'N': the linear system involves A;
                = 'T': the linear system involves A**T.

        M       (input) INTEGER
                The number of rows of the matrix A.  M >= 0.

        N       (input) INTEGER
                The number of columns of the matrix A.  N >= 0.

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

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

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

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

        LWORK   (input) 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    (output) 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.

 LAPACK driver routine (version 3.3.1)      April 2011                             DGELS(3lapack)