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sgeqlf

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

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

          INTEGER        INFO, LDA, LWORK, M, N

          REAL           A( LDA, * ), TAU( * ), WORK( LWORK )

 PURPOSE
      SGEQLF 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) REAL 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 super-
              diagonal 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) REAL array, dimension (min(M,N))
              The scalar factors of the elementary reflectors (see
              Further Details).

      WORK    (workspace) REAL 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).