#include "blaswrap.h"
#include "f2c.h"

/* Subroutine */ int sgerq2_(integer *m, integer *n, real *a, integer *lda, 
	real *tau, real *work, integer *info)
{
/*  -- LAPACK routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       February 29, 1992   


    Purpose   
    =======   

    SGERQ2 computes an RQ factorization of a real m by n matrix A:   
    A = R * 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, if m <= n, the upper triangle of the subarray   
            A(1:m,n-m+1:n) contains the m by m upper triangular matrix R;   
            if m >= n, the elements on and above the (m-n)-th subdiagonal   
            contain the m by n upper trapezoidal matrix R; 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 (M)   

    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(1) H(2) . . . H(k), 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(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in   
    A(m-k+i,1:n-k+i-1), and tau in TAU(i).   

    =====================================================================   


       Test the input arguments   

       Parameter adjustments */
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2;
    /* Local variables */
    static integer i__, k;
    extern /* Subroutine */ int slarf_(char *, integer *, integer *, real *, 
	    integer *, real *, real *, integer *, real *), xerbla_(
	    char *, integer *), slarfg_(integer *, real *, real *, 
	    integer *, real *);
    static real aii;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]

    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    --tau;
    --work;

    /* Function Body */
    *info = 0;
    if (*m < 0) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*lda < max(1,*m)) {
	*info = -4;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SGERQ2", &i__1);
	return 0;
    }

    k = min(*m,*n);

    for (i__ = k; i__ >= 1; --i__) {

/*        Generate elementary reflector H(i) to annihilate   
          A(m-k+i,1:n-k+i-1) */

	i__1 = *n - k + i__;
	slarfg_(&i__1, &a_ref(*m - k + i__, *n - k + i__), &a_ref(*m - k + 
		i__, 1), lda, &tau[i__]);

/*        Apply H(i) to A(1:m-k+i-1,1:n-k+i) from the right */

	aii = a_ref(*m - k + i__, *n - k + i__);
	a_ref(*m - k + i__, *n - k + i__) = 1.f;
	i__1 = *m - k + i__ - 1;
	i__2 = *n - k + i__;
	slarf_("Right", &i__1, &i__2, &a_ref(*m - k + i__, 1), lda, &tau[i__],
		 &a[a_offset], lda, &work[1]);
	a_ref(*m - k + i__, *n - k + i__) = aii;
/* L10: */
    }
    return 0;

/*     End of SGERQ2 */

} /* sgerq2_ */

#undef a_ref



.