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NAME
     dgeqlf - compute a QL factorization of a real M-by-N  matrix
     A

SYNOPSIS
     SUBROUTINE DGEQLF( M, N, A, LDA, TAU, WORK, LWORK, INFO )

     INTEGER INFO, LDA, LWORK, M, N

     DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( LWORK )



     #include <sunperf.h>

     void dgeqlf(int m, int n, double *da, int lda, double  *tau,
               int *info) ;

PURPOSE
     DGEQLF computes a QL factorization of a real  M-by-N  matrix
     A:  A = Q * L.


ARGUMENTS
     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.

     A         (input/output) DOUBLE PRECISION  array,  dimension
               (LDA,N)
               On entry, the M-by-N matrix A.  On exit, if  m  >=
               n,   the  lower  triangle  of  the  subarray  A(m-
               n+1:m,1:n) contains the  N-by-N  lower  triangular
               matrix L; if m <= n, the elements on and below the
               (n-m)-th superdiagonal contain  the  M-by-N  lower
               trapezoidal matrix L; the remaining elements, with
               the array TAU, represent the orthogonal  matrix  Q
               as a product of elementary reflectors (see Further
               Details).  LDA      (input)  INTEGER  The  leading
               dimension of the array A.  LDA >= max(1,M).

     TAU       (output)   DOUBLE   PRECISION   array,   dimension
               (min(M,N))
               The scalar factors of  the  elementary  reflectors
               (see Further Details).

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

     LWORK     (input) INTEGER
               The  dimension  of  the  array  WORK.   LWORK   >=
               max(1,N).   For optimum performance LWORK >= N*NB,
               where NB is the optimal blocksize.

     INFO      (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille-
               gal value

FURTHER DETAILS
     The matrix Q is  represented  as  a  product  of  elementary
     reflectors

        Q = H(k) . . . H(2) H(1), where k = min(m,n).

     Each H(i) has the form

        H(i) = I - tau * v * v'

     where tau is a real scalar, and v is a real vector with
     v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on
     exit in A(1:m-k+i-1,n-k+i), and tau in TAU(i).

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