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

/* Subroutine */ int sgeqrf_(integer *m, integer *n, real *a, integer *lda, 
	real *tau, real *work, integer *lwork, integer *info)
{
/*  -- LAPACK routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       June 30, 1999   


    Purpose   
    =======   

    SGEQRF computes a QR factorization of a real M-by-N matrix A:   
    A = Q * R.   

    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 elements on and above the diagonal of the array   
            contain the min(M,N)-by-N upper trapezoidal matrix R (R is   
            upper triangular if m >= n); the elements below the diagonal,   
            with the array TAU, represent the orthogonal matrix Q as a   
            product of min(m,n) 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,N).   
            For optimum performance LWORK >= N*NB, where NB is   
            the optimal blocksize.   

            If LWORK = -1, then a workspace query is assumed; the routine   
            only calculates the optimal size of the WORK array, returns   
            this value as the first entry of the WORK array, and no error   
            message related to LWORK is issued by XERBLA.   

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

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


       Test the input arguments   

       Parameter adjustments */
    /* Table of constant values */
    static integer c__1 = 1;
    static integer c_n1 = -1;
    static integer c__3 = 3;
    static integer c__2 = 2;
    
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
    /* Local variables */
    static integer i__, k, nbmin, iinfo;
    extern /* Subroutine */ int sgeqr2_(integer *, integer *, real *, integer 
	    *, real *, real *, integer *);
    static integer ib, nb, nx;
    extern /* Subroutine */ int slarfb_(char *, char *, char *, char *, 
	    integer *, integer *, integer *, real *, integer *, real *, 
	    integer *, real *, integer *, real *, integer *), xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    extern /* Subroutine */ int slarft_(char *, char *, integer *, integer *, 
	    real *, integer *, real *, real *, integer *);
    static integer ldwork, lwkopt;
    static logical lquery;
    static integer iws;
#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;
    nb = ilaenv_(&c__1, "SGEQRF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)
	    1);
    lwkopt = *n * nb;
    work[1] = (real) lwkopt;
    lquery = *lwork == -1;
    if (*m < 0) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*lda < max(1,*m)) {
	*info = -4;
    } else if (*lwork < max(1,*n) && ! lquery) {
	*info = -7;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SGEQRF", &i__1);
	return 0;
    } else if (lquery) {
	return 0;
    }

/*     Quick return if possible */

    k = min(*m,*n);
    if (k == 0) {
	work[1] = 1.f;
	return 0;
    }

    nbmin = 2;
    nx = 0;
    iws = *n;
    if (nb > 1 && nb < k) {

/*        Determine when to cross over from blocked to unblocked code.   

   Computing MAX */
	i__1 = 0, i__2 = ilaenv_(&c__3, "SGEQRF", " ", m, n, &c_n1, &c_n1, (
		ftnlen)6, (ftnlen)1);
	nx = max(i__1,i__2);
	if (nx < k) {

/*           Determine if workspace is large enough for blocked code. */

	    ldwork = *n;
	    iws = ldwork * nb;
	    if (*lwork < iws) {

/*              Not enough workspace to use optimal NB:  reduce NB and   
                determine the minimum value of NB. */

		nb = *lwork / ldwork;
/* Computing MAX */
		i__1 = 2, i__2 = ilaenv_(&c__2, "SGEQRF", " ", m, n, &c_n1, &
			c_n1, (ftnlen)6, (ftnlen)1);
		nbmin = max(i__1,i__2);
	    }
	}
    }

    if (nb >= nbmin && nb < k && nx < k) {

/*        Use blocked code initially */

	i__1 = k - nx;
	i__2 = nb;
	for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/* Computing MIN */
	    i__3 = k - i__ + 1;
	    ib = min(i__3,nb);

/*           Compute the QR factorization of the current block   
             A(i:m,i:i+ib-1) */

	    i__3 = *m - i__ + 1;
	    sgeqr2_(&i__3, &ib, &a_ref(i__, i__), lda, &tau[i__], &work[1], &
		    iinfo);
	    if (i__ + ib <= *n) {

/*              Form the triangular factor of the block reflector   
                H = H(i) H(i+1) . . . H(i+ib-1) */

		i__3 = *m - i__ + 1;
		slarft_("Forward", "Columnwise", &i__3, &ib, &a_ref(i__, i__),
			 lda, &tau[i__], &work[1], &ldwork);

/*              Apply H' to A(i:m,i+ib:n) from the left */

		i__3 = *m - i__ + 1;
		i__4 = *n - i__ - ib + 1;
		slarfb_("Left", "Transpose", "Forward", "Columnwise", &i__3, &
			i__4, &ib, &a_ref(i__, i__), lda, &work[1], &ldwork, &
			a_ref(i__, i__ + ib), lda, &work[ib + 1], &ldwork);
	    }
/* L10: */
	}
    } else {
	i__ = 1;
    }

/*     Use unblocked code to factor the last or only block. */

    if (i__ <= k) {
	i__2 = *m - i__ + 1;
	i__1 = *n - i__ + 1;
	sgeqr2_(&i__2, &i__1, &a_ref(i__, i__), lda, &tau[i__], &work[1], &
		iinfo);
    }

    work[1] = (real) iws;
    return 0;

/*     End of SGEQRF */

} /* sgeqrf_ */

#undef a_ref


