text: /* cgeqrf.f -- translated by f2c (version 20061008).
     You must link the resulting object file with libf2c:
  	on Microsoft Windows system, link with libf2c.lib;
  	on Linux or Unix systems, link with .../path/to/libf2c.a -lm
  	or, if you install libf2c.a in a standard place, with -lf2c -lm
  	-- in that order, at the end of the command line, as in
  		cc *.o -lf2c -lm
  	Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
  
  		http://www.netlib.org/f2c/libf2c.zip
  */
  
  #include "f2c.h"
  #include "blaswrap.h"
  
  /* Table of constant values */
  
  static integer c__1 = 1;
  static integer c_n1 = -1;
  static integer c__3 = 3;
  static integer c__2 = 2;
  
  /* Subroutine */ int cgeqrf_(integer *m, integer *n, complex *a, integer *lda, 
  	 complex *tau, complex *work, integer *lwork, integer *info)
  {
      /* System generated locals */
      integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6;
      real r__1;
  
      /* Local variables */
      integer i__, j, k, ib, nb, nt, nx, iws;
      extern doublereal sceil_(real *);
      integer nbmin, iinfo;
      extern /* Subroutine */ int cgeqr2_(integer *, integer *, complex *, 
  	    integer *, complex *, complex *, integer *), clarfb_(char *, char 
  	    *, char *, char *, integer *, integer *, integer *, complex *, 
  	    integer *, complex *, integer *, complex *, integer *, complex *, 
  	    integer *), clarft_(char *, char *
  , integer *, integer *, complex *, integer *, complex *, complex *
  , integer *), xerbla_(char *, integer *);
      extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
  	    integer *, integer *);
      integer lbwork, llwork, lwkopt;
      logical lquery;
  
  
  /*  -- LAPACK routine (version 3.1) -- */
  /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
  /*     March 2008 */
  
  /*     .. Scalar Arguments .. */
  /*     .. */
  /*     .. Array Arguments .. */
  /*     .. */
  
  /*  Purpose */
  /*  ======= */
  
  /*  CGEQRF computes a QR factorization of a real M-by-N matrix A: */
  /*  A = Q * R. */
  
  /*  This is the left-looking Level 3 BLAS version of the algorithm. */
  
  /*  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 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) COMPLEX array, dimension (min(M,N)) */
  /*          The scalar factors of the elementary reflectors (see Further */
  /*          Details). */
  
  /*  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK)) */
  /*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
  
  /*  LWORK   (input) INTEGER */
  
  /*          The dimension of the array WORK. The dimension can be divided into three parts. */
  
  /*          1) The part for the triangular factor T. If the very last T is not bigger */
  /*             than any of the rest, then this part is NB x ceiling(K/NB), otherwise, */
  /*             NB x (K-NT), where K = min(M,N) and NT is the dimension of the very last T */
  
  /*          2) The part for the very last T when T is bigger than any of the rest T. */
  /*             The size of this part is NT x NT, where NT = K - ceiling ((K-NX)/NB) x NB, */
  /*             where K = min(M,N), NX is calculated by */
  /*                   NX = MAX( 0, ILAENV( 3, 'CGEQRF', ' ', M, N, -1, -1 ) ) */
  
  /*          3) The part for dlarfb is of size max((N-M)*K, (N-M)*NB, K*NB, NB*NB) */
  
  /*          So LWORK = part1 + part2 + part3 */
  
  /*          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). */
  
  /*  ===================================================================== */
  
  /*     .. Local Scalars .. */
  /*     .. */
  /*     .. External Subroutines .. */
  /*     .. */
  /*     .. Intrinsic Functions .. */
  /*     .. */
  /*     .. External Functions .. */
  /*     .. */
  /*     .. Executable Statements .. */
      /* Parameter adjustments */
      a_dim1 = *lda;
      a_offset = 1 + a_dim1;
      a -= a_offset;
      --tau;
      --work;
  
      /* Function Body */
      *info = 0;
      nbmin = 2;
      nx = 0;
      iws = *n;
      k = min(*m,*n);
      nb = ilaenv_(&c__1, "CGEQRF", " ", m, n, &c_n1, &c_n1);
      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, "CGEQRF", " ", m, n, &c_n1, &c_n1);
  	nx = max(i__1,i__2);
      }
  
  /*     Get NT, the size of the very last T, which is the left-over from in-between K-NX and K to K, eg.: */
  
  /*            NB=3     2NB=6       K=10 */
  /*            |        |           | */
  /*      1--2--3--4--5--6--7--8--9--10 */
  /*                  |     \________/ */
  /*               K-NX=5      NT=4 */
  
  /*     So here 4 x 4 is the last T stored in the workspace */
  
      r__1 = (real) (k - nx) / (real) nb;
      nt = k - sceil_(&r__1) * nb;
  
  /*     optimal workspace = space for dlarfb + space for normal T's + space for the last T */
  
  /* Computing MAX */
  /* Computing MAX */
      i__3 = (*n - *m) * k, i__4 = (*n - *m) * nb;
  /* Computing MAX */
      i__5 = k * nb, i__6 = nb * nb;
      i__1 = max(i__3,i__4), i__2 = max(i__5,i__6);
      llwork = max(i__1,i__2);
      r__1 = (real) llwork / (real) nb;
      llwork = sceil_(&r__1);
      if (nt > nb) {
  	lbwork = k - nt;
  
  /*         Optimal workspace for dlarfb = MAX(1,N)*NT */
  
  	lwkopt = (lbwork + llwork) * nb;
  	i__1 = lwkopt + nt * nt;
  	work[1].r = (real) i__1, work[1].i = 0.f;
      } else {
  	r__1 = (real) k / (real) nb;
  	lbwork = sceil_(&r__1) * nb;
  	lwkopt = (lbwork + llwork - nb) * nb;
  	work[1].r = (real) lwkopt, work[1].i = 0.f;
      }
  
  /*     Test the input arguments */
  
      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_("CGEQRF", &i__1);
  	return 0;
      } else if (lquery) {
  	return 0;
      }
  
  /*     Quick return if possible */
  
      if (k == 0) {
  	work[1].r = 1.f, work[1].i = 0.f;
  	return 0;
      }
  
      if (nb > 1 && nb < k) {
  	if (nx < k) {
  
  /*           Determine if workspace is large enough for blocked code. */
  
  	    if (nt <= nb) {
  		iws = (lbwork + llwork - nb) * nb;
  	    } else {
  		iws = (lbwork + llwork) * nb + nt * nt;
  	    }
  	    if (*lwork < iws) {
  
  /*              Not enough workspace to use optimal NB:  reduce NB and */
  /*              determine the minimum value of NB. */
  
  		if (nt <= nb) {
  		    nb = *lwork / (llwork + (lbwork - nb));
  		} else {
  		    nb = (*lwork - nt * nt) / (lbwork + llwork);
  		}
  /* Computing MAX */
  		i__1 = 2, i__2 = ilaenv_(&c__2, "CGEQRF", " ", m, n, &c_n1, &
  			c_n1);
  		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);
  
  /*           Update the current column using old T's */
  
  	    i__3 = i__ - nb;
  	    i__4 = nb;
  	    for (j = 1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) {
  
  /*              Apply H' to A(J:M,I:I+IB-1) from the left */
  
  		i__5 = *m - j + 1;
  		clarfb_("Left", "Transpose", "Forward", "Columnwise", &i__5, &
  			ib, &nb, &a[j + j * a_dim1], lda, &work[j], &lbwork, &
  			a[j + i__ * a_dim1], lda, &work[lbwork * nb + nt * nt 
  			+ 1], &ib);
  /* L20: */
  	    }
  
  /*           Compute the QR factorization of the current block */
  /*           A(I:M,I:I+IB-1) */
  
  	    i__4 = *m - i__ + 1;
  	    cgeqr2_(&i__4, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[
  		    lbwork * nb + nt * nt + 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__4 = *m - i__ + 1;
  		clarft_("Forward", "Columnwise", &i__4, &ib, &a[i__ + i__ * 
  			a_dim1], lda, &tau[i__], &work[i__], &lbwork);
  
  	    }
  /* L10: */
  	}
      } else {
  	i__ = 1;
      }
  
  /*     Use unblocked code to factor the last or only block. */
  
      if (i__ <= k) {
  	if (i__ != 1) {
  	    i__2 = i__ - nb;
  	    i__1 = nb;
  	    for (j = 1; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) {
  
  /*                Apply H' to A(J:M,I:K) from the left */
  
  		i__4 = *m - j + 1;
  		i__3 = k - i__ + 1;
  		i__5 = k - i__ + 1;
  		clarfb_("Left", "Transpose", "Forward", "Columnwise", &i__4, &
  			i__3, &nb, &a[j + j * a_dim1], lda, &work[j], &lbwork, 
  			 &a[j + i__ * a_dim1], lda, &work[lbwork * nb + nt * 
  			nt + 1], &i__5);
  /* L30: */
  	    }
  	    i__1 = *m - i__ + 1;
  	    i__2 = k - i__ + 1;
  	    cgeqr2_(&i__1, &i__2, &a[i__ + i__ * a_dim1], lda, &tau[i__], &
  		    work[lbwork * nb + nt * nt + 1], &iinfo);
  	} else {
  
  /*        Use unblocked code to factor the last or only block. */
  
  	    i__1 = *m - i__ + 1;
  	    i__2 = *n - i__ + 1;
  	    cgeqr2_(&i__1, &i__2, &a[i__ + i__ * a_dim1], lda, &tau[i__], &
  		    work[1], &iinfo);
  	}
      }
  
  /*     Apply update to the column M+1:N when N > M */
  
      if (*m < *n && i__ != 1) {
  
  /*         Form the last triangular factor of the block reflector */
  /*         H = H(i) H(i+1) . . . H(i+ib-1) */
  
  	if (nt <= nb) {
  	    i__1 = *m - i__ + 1;
  	    i__2 = k - i__ + 1;
  	    clarft_("Forward", "Columnwise", &i__1, &i__2, &a[i__ + i__ * 
  		    a_dim1], lda, &tau[i__], &work[i__], &lbwork);
  	} else {
  	    i__1 = *m - i__ + 1;
  	    i__2 = k - i__ + 1;
  	    clarft_("Forward", "Columnwise", &i__1, &i__2, &a[i__ + i__ * 
  		    a_dim1], lda, &tau[i__], &work[lbwork * nb + 1], &nt);
  	}
  
  /*         Apply H' to A(1:M,M+1:N) from the left */
  
  	i__1 = k - nx;
  	i__2 = nb;
  	for (j = 1; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
  /* Computing MIN */
  	    i__4 = k - j + 1;
  	    ib = min(i__4,nb);
  	    i__4 = *m - j + 1;
  	    i__3 = *n - *m;
  	    i__5 = *n - *m;
  	    clarfb_("Left", "Transpose", "Forward", "Columnwise", &i__4, &
  		    i__3, &ib, &a[j + j * a_dim1], lda, &work[j], &lbwork, &a[
  		    j + (*m + 1) * a_dim1], lda, &work[lbwork * nb + nt * nt 
  		    + 1], &i__5);
  /* L40: */
  	}
  	if (nt <= nb) {
  	    i__2 = *m - j + 1;
  	    i__1 = *n - *m;
  	    i__4 = k - j + 1;
  	    i__3 = *n - *m;
  	    clarfb_("Left", "Transpose", "Forward", "Columnwise", &i__2, &
  		    i__1, &i__4, &a[j + j * a_dim1], lda, &work[j], &lbwork, &
  		    a[j + (*m + 1) * a_dim1], lda, &work[lbwork * nb + nt * 
  		    nt + 1], &i__3);
  	} else {
  	    i__2 = *m - j + 1;
  	    i__1 = *n - *m;
  	    i__4 = k - j + 1;
  	    i__3 = *n - *m;
  	    clarfb_("Left", "Transpose", "Forward", "Columnwise", &i__2, &
  		    i__1, &i__4, &a[j + j * a_dim1], lda, &work[lbwork * nb + 
  		    1], &nt, &a[j + (*m + 1) * a_dim1], lda, &work[lbwork * 
  		    nb + nt * nt + 1], &i__3);
  	}
      }
      work[1].r = (real) iws, work[1].i = 0.f;
      return 0;
  
  /*     End of CGEQRF */
  
  } /* cgeqrf_ */
  