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

/* Subroutine */ int zgeqlf_(integer *m, integer *n, doublecomplex *a, 
	integer *lda, doublecomplex *tau, doublecomplex *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   
    =======   

    ZGEQLF computes a QL factorization of a complex 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) COMPLEX*16 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   
            unitary 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) COMPLEX*16 array, dimension (min(M,N))   
            The scalar factors of the elementary reflectors (see Further   
            Details).   

    WORK    (workspace/output) COMPLEX*16 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(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 complex scalar, and v is a complex 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).   

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


       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 zgeql2_(integer *, integer *, doublecomplex *,
	     integer *, doublecomplex *, doublecomplex *, integer *);
    static integer ib, nb, ki, kk, mu, nu, nx;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *, 
	    integer *, integer *, integer *, doublecomplex *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, 
	    doublecomplex *, integer *);
    static integer ldwork;
    extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
	    integer *);
    static integer lwkopt;
    static logical lquery;
    static integer iws;
#define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1
#define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)]


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

    /* Function Body */
    *info = 0;
    nb = ilaenv_(&c__1, "ZGEQLF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)
	    1);
    lwkopt = *n * nb;
    work[1].r = (doublereal) lwkopt, work[1].i = 0.;
    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_("ZGEQLF", &i__1);
	return 0;
    } else if (lquery) {
	return 0;
    }

/*     Quick return if possible */

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

    nbmin = 2;
    nx = 1;
    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, "ZGEQLF", " ", 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, "ZGEQLF", " ", 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.   
          The last kk columns are handled by the block method. */

	ki = (k - nx - 1) / nb * nb;
/* Computing MIN */
	i__1 = k, i__2 = ki + nb;
	kk = min(i__1,i__2);

	i__1 = k - kk + 1;
	i__2 = -nb;
	for (i__ = k - kk + ki + 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 QL factorization of the current block   
             A(1:m-k+i+ib-1,n-k+i:n-k+i+ib-1) */

	    i__3 = *m - k + i__ + ib - 1;
	    zgeql2_(&i__3, &ib, &a_ref(1, *n - k + i__), lda, &tau[i__], &
		    work[1], &iinfo);
	    if (*n - k + i__ > 1) {

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

		i__3 = *m - k + i__ + ib - 1;
		zlarft_("Backward", "Columnwise", &i__3, &ib, &a_ref(1, *n - 
			k + i__), lda, &tau[i__], &work[1], &ldwork);

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

		i__3 = *m - k + i__ + ib - 1;
		i__4 = *n - k + i__ - 1;
		zlarfb_("Left", "Conjugate transpose", "Backward", "Columnwi"
			"se", &i__3, &i__4, &ib, &a_ref(1, *n - k + i__), lda, 
			&work[1], &ldwork, &a[a_offset], lda, &work[ib + 1], &
			ldwork);
	    }
/* L10: */
	}
	mu = *m - k + i__ + nb - 1;
	nu = *n - k + i__ + nb - 1;
    } else {
	mu = *m;
	nu = *n;
    }

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

    if (mu > 0 && nu > 0) {
	zgeql2_(&mu, &nu, &a[a_offset], lda, &tau[1], &work[1], &iinfo);
    }

    work[1].r = (doublereal) iws, work[1].i = 0.;
    return 0;

/*     End of ZGEQLF */

} /* zgeqlf_ */

#undef a_ref
#undef a_subscr


