text: /* dorgrq.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 dorgrq_(integer *m, integer *n, integer *k, doublereal *
  	a, integer *lda, doublereal *tau, doublereal *work, integer *lwork, 
  	integer *info)
  {
      /* System generated locals */
      integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
  
      /* Local variables */
      integer i__, j, l, ib, nb, ii, kk, nx, iws, nbmin, iinfo;
      extern /* Subroutine */ int dorgr2_(integer *, integer *, integer *, 
  	    doublereal *, integer *, doublereal *, doublereal *, integer *), 
  	    dlarfb_(char *, char *, char *, char *, integer *, integer *, 
  	    integer *, doublereal *, integer *, doublereal *, integer *, 
  	    doublereal *, integer *, doublereal *, integer *), dlarft_(char *, char *, integer *, integer *, 
  	    doublereal *, integer *, doublereal *, doublereal *, integer *), xerbla_(char *, integer *);
      extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
  	    integer *, integer *);
      integer ldwork, lwkopt;
      logical lquery;
  
  
  /*  -- LAPACK routine (version 3.2) -- */
  /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
  /*     November 2006 */
  
  /*     .. Scalar Arguments .. */
  /*     .. */
  /*     .. Array Arguments .. */
  /*     .. */
  
  /*  Purpose */
  /*  ======= */
  
  /*  DORGRQ generates an M-by-N real matrix Q with orthonormal rows, */
  /*  which is defined as the last M rows of a product of K elementary */
  /*  reflectors of order N */
  
  /*        Q  =  H(1) H(2) . . . H(k) */
  
  /*  as returned by DGERQF. */
  
  /*  Arguments */
  /*  ========= */
  
  /*  M       (input) INTEGER */
  /*          The number of rows of the matrix Q. M >= 0. */
  
  /*  N       (input) INTEGER */
  /*          The number of columns of the matrix Q. N >= M. */
  
  /*  K       (input) INTEGER */
  /*          The number of elementary reflectors whose product defines the */
  /*          matrix Q. M >= K >= 0. */
  
  /*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
  /*          On entry, the (m-k+i)-th row must contain the vector which */
  /*          defines the elementary reflector H(i), for i = 1,2,...,k, as */
  /*          returned by DGERQF in the last k rows of its array argument */
  /*          A. */
  /*          On exit, the M-by-N matrix Q. */
  
  /*  LDA     (input) INTEGER */
  /*          The first dimension of the array A. LDA >= max(1,M). */
  
  /*  TAU     (input) DOUBLE PRECISION array, dimension (K) */
  /*          TAU(i) must contain the scalar factor of the elementary */
  /*          reflector H(i), as returned by DGERQF. */
  
  /*  WORK    (workspace/output) DOUBLE PRECISION 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. LWORK >= max(1,M). */
  /*          For optimum performance LWORK >= M*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 has an illegal value */
  
  /*  ===================================================================== */
  
  /*     .. Parameters .. */
  /*     .. */
  /*     .. Local Scalars .. */
  /*     .. */
  /*     .. External Subroutines .. */
  /*     .. */
  /*     .. Intrinsic Functions .. */
  /*     .. */
  /*     .. External Functions .. */
  /*     .. */
  /*     .. Executable Statements .. */
  
  /*     Test the input arguments */
  
      /* Parameter adjustments */
      a_dim1 = *lda;
      a_offset = 1 + a_dim1;
      a -= a_offset;
      --tau;
      --work;
  
      /* Function Body */
      *info = 0;
      lquery = *lwork == -1;
      if (*m < 0) {
  	*info = -1;
      } else if (*n < *m) {
  	*info = -2;
      } else if (*k < 0 || *k > *m) {
  	*info = -3;
      } else if (*lda < max(1,*m)) {
  	*info = -5;
      }
  
      if (*info == 0) {
  	if (*m <= 0) {
  	    lwkopt = 1;
  	} else {
  	    nb = ilaenv_(&c__1, "DORGRQ", " ", m, n, k, &c_n1);
  	    lwkopt = *m * nb;
  	}
  	work[1] = (doublereal) lwkopt;
  
  	if (*lwork < max(1,*m) && ! lquery) {
  	    *info = -8;
  	}
      }
  
      if (*info != 0) {
  	i__1 = -(*info);
  	xerbla_("DORGRQ", &i__1);
  	return 0;
      } else if (lquery) {
  	return 0;
      }
  
  /*     Quick return if possible */
  
      if (*m <= 0) {
  	return 0;
      }
  
      nbmin = 2;
      nx = 0;
      iws = *m;
      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, "DORGRQ", " ", m, n, k, &c_n1);
  	nx = max(i__1,i__2);
  	if (nx < *k) {
  
  /*           Determine if workspace is large enough for blocked code. */
  
  	    ldwork = *m;
  	    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, "DORGRQ", " ", m, n, k, &c_n1);
  		nbmin = max(i__1,i__2);
  	    }
  	}
      }
  
      if (nb >= nbmin && nb < *k && nx < *k) {
  
  /*        Use blocked code after the first block. */
  /*        The last kk rows are handled by the block method. */
  
  /* Computing MIN */
  	i__1 = *k, i__2 = (*k - nx + nb - 1) / nb * nb;
  	kk = min(i__1,i__2);
  
  /*        Set A(1:m-kk,n-kk+1:n) to zero. */
  
  	i__1 = *n;
  	for (j = *n - kk + 1; j <= i__1; ++j) {
  	    i__2 = *m - kk;
  	    for (i__ = 1; i__ <= i__2; ++i__) {
  		a[i__ + j * a_dim1] = 0.;
  /* L10: */
  	    }
  /* L20: */
  	}
      } else {
  	kk = 0;
      }
  
  /*     Use unblocked code for the first or only block. */
  
      i__1 = *m - kk;
      i__2 = *n - kk;
      i__3 = *k - kk;
      dorgr2_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], &work[1], &iinfo)
  	    ;
  
      if (kk > 0) {
  
  /*        Use blocked code */
  
  	i__1 = *k;
  	i__2 = nb;
  	for (i__ = *k - kk + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += 
  		i__2) {
  /* Computing MIN */
  	    i__3 = nb, i__4 = *k - i__ + 1;
  	    ib = min(i__3,i__4);
  	    ii = *m - *k + i__;
  	    if (ii > 1) {
  
  /*              Form the triangular factor of the block reflector */
  /*              H = H(i+ib-1) . . . H(i+1) H(i) */
  
  		i__3 = *n - *k + i__ + ib - 1;
  		dlarft_("Backward", "Rowwise", &i__3, &ib, &a[ii + a_dim1], 
  			lda, &tau[i__], &work[1], &ldwork);
  
  /*              Apply H' to A(1:m-k+i-1,1:n-k+i+ib-1) from the right */
  
  		i__3 = ii - 1;
  		i__4 = *n - *k + i__ + ib - 1;
  		dlarfb_("Right", "Transpose", "Backward", "Rowwise", &i__3, &
  			i__4, &ib, &a[ii + a_dim1], lda, &work[1], &ldwork, &
  			a[a_offset], lda, &work[ib + 1], &ldwork);
  	    }
  
  /*           Apply H' to columns 1:n-k+i+ib-1 of current block */
  
  	    i__3 = *n - *k + i__ + ib - 1;
  	    dorgr2_(&ib, &i__3, &ib, &a[ii + a_dim1], lda, &tau[i__], &work[1]
  , &iinfo);
  
  /*           Set columns n-k+i+ib:n of current block to zero */
  
  	    i__3 = *n;
  	    for (l = *n - *k + i__ + ib; l <= i__3; ++l) {
  		i__4 = ii + ib - 1;
  		for (j = ii; j <= i__4; ++j) {
  		    a[j + l * a_dim1] = 0.;
  /* L30: */
  		}
  /* L40: */
  	    }
  /* L50: */
  	}
      }
  
      work[1] = (doublereal) iws;
      return 0;
  
  /*     End of DORGRQ */
  
  } /* dorgrq_ */
  