dgeqlf(3F)

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 )

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, dimension (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 illegal 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).