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NAME
     sgelqf - compute an LQ factorization of a real M-by-N matrix
     A

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

     INTEGER INFO, LDA, LWORK, M, N

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



     #include <sunperf.h>

     void sgelqf(int m, int n, float *sa, int  lda,  float  *tau,
               int *info) ;

PURPOSE
     SGELQF computes an LQ factorization of a real M-by-N  matrix
     A:  A = L * Q.


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, the  ele-
               ments  on and below the diagonal of the array con-
               tain the m-by-min(m,n) lower trapezoidal matrix  L
               (L  is  lower  triangular if m <= n); the elements
               above the diagonal, 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/output) 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,M).   For optimum performance LWORK >= M*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(1:i-1) = 0 and v(i) = 1; v(i+1:n) is  stored  on  exit  in
     A(i,i+1:n), and tau in TAU(i).

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