/*  -- translated by f2c (version 20240504).
   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"

/* Table of constant values */

static integer c__1 = 1;

/* > \brief \b DGEHD2 reduces a general square matrix to upper Hessenberg form using an unblocked algorithm. 
  

    =========== DOCUMENTATION ===========   

   Online html documentation available at   
              http://www.netlib.org/lapack/explore-html/   

   > \htmlonly   
   > Download DGEHD2 + dependencies   
   > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgehd2.
f">   
   > [TGZ]</a>   
   > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgehd2.
f">   
   > [ZIP]</a>   
   > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgehd2.
f">   
   > [TXT]</a>   
   > \endhtmlonly   

    Definition:   
    ===========   

         SUBROUTINE DGEHD2( N, ILO, IHI, A, LDA, TAU, WORK, INFO )   

         INTEGER            IHI, ILO, INFO, LDA, N   
         DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )   


   > \par Purpose:   
    =============   
   >   
   > \verbatim   
   >   
   > DGEHD2 reduces a real general matrix A to upper Hessenberg form H by   
   > an orthogonal similarity transformation:  Q**T * A * Q = H .   
   > \endverbatim   

    Arguments:   
    ==========   

   > \param[in] N   
   > \verbatim   
   >          N is INTEGER   
   >          The order of the matrix A.  N >= 0.   
   > \endverbatim   
   >   
   > \param[in] ILO   
   > \verbatim   
   >          ILO is INTEGER   
   > \endverbatim   
   >   
   > \param[in] IHI   
   > \verbatim   
   >          IHI is INTEGER   
   >   
   >          It is assumed that A is already upper triangular in rows   
   >          and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally   
   >          set by a previous call to DGEBAL; otherwise they should be   
   >          set to 1 and N respectively. See Further Details.   
   >          1 <= ILO <= IHI <= max(1,N).   
   > \endverbatim   
   >   
   > \param[in,out] A   
   > \verbatim   
   >          A is DOUBLE PRECISION array, dimension (LDA,N)   
   >          On entry, the n by n general matrix to be reduced.   
   >          On exit, the upper triangle and the first subdiagonal of A   
   >          are overwritten with the upper Hessenberg matrix H, and the   
   >          elements below the first subdiagonal, with the array TAU,   
   >          represent the orthogonal matrix Q as a product of elementary   
   >          reflectors. See Further Details.   
   > \endverbatim   
   >   
   > \param[in] LDA   
   > \verbatim   
   >          LDA is INTEGER   
   >          The leading dimension of the array A.  LDA >= max(1,N).   
   > \endverbatim   
   >   
   > \param[out] TAU   
   > \verbatim   
   >          TAU is DOUBLE PRECISION array, dimension (N-1)   
   >          The scalar factors of the elementary reflectors (see Further   
   >          Details).   
   > \endverbatim   
   >   
   > \param[out] WORK   
   > \verbatim   
   >          WORK is DOUBLE PRECISION array, dimension (N)   
   > \endverbatim   
   >   
   > \param[out] INFO   
   > \verbatim   
   >          INFO is INTEGER   
   >          = 0:  successful exit.   
   >          < 0:  if INFO = -i, the i-th argument had an illegal value.   
   > \endverbatim   

    Authors:   
    ========   

   > \author Univ. of Tennessee   
   > \author Univ. of California Berkeley   
   > \author Univ. of Colorado Denver   
   > \author NAG Ltd.   

   > \date September 2012   

   > \ingroup doubleGEcomputational   

   > \par Further Details:   
    =====================   
   >   
   > \verbatim   
   >   
   >  The matrix Q is represented as a product of (ihi-ilo) elementary   
   >  reflectors   
   >   
   >     Q = H(ilo) H(ilo+1) . . . H(ihi-1).   
   >   
   >  Each H(i) has the form   
   >   
   >     H(i) = I - tau * v * v**T   
   >   
   >  where tau is a real scalar, and v is a real vector with   
   >  v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on   
   >  exit in A(i+2:ihi,i), and tau in TAU(i).   
   >   
   >  The contents of A are illustrated by the following example, with   
   >  n = 7, ilo = 2 and ihi = 6:   
   >   
   >  on entry,                        on exit,   
   >   
   >  ( a   a   a   a   a   a   a )    (  a   a   h   h   h   h   a )   
   >  (     a   a   a   a   a   a )    (      a   h   h   h   h   a )   
   >  (     a   a   a   a   a   a )    (      h   h   h   h   h   h )   
   >  (     a   a   a   a   a   a )    (      v2  h   h   h   h   h )   
   >  (     a   a   a   a   a   a )    (      v2  v3  h   h   h   h )   
   >  (     a   a   a   a   a   a )    (      v2  v3  v4  h   h   h )   
   >  (                         a )    (                          a )   
   >   
   >  where a denotes an element of the original matrix A, h denotes a   
   >  modified element of the upper Hessenberg matrix H, and vi denotes an   
   >  element of the vector defining H(i).   
   > \endverbatim   
   >   
    =====================================================================   
   Subroutine */ int igraphdgehd2_(integer *n, integer *ilo, integer *ihi, 
	doublereal *a, integer *lda, doublereal *tau, doublereal *work, 
	integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3;

    /* Local variables */
    integer i__;
    doublereal aii;
    extern /* Subroutine */ int igraphdlarf_(char *, integer *, integer *, 
	    doublereal *, integer *, doublereal *, doublereal *, integer *, 
	    doublereal *), igraphdlarfg_(integer *, doublereal *, 
	    doublereal *, integer *, doublereal *), igraphxerbla_(char *, integer *,
	     ftnlen);


/*  -- LAPACK computational routine (version 3.4.2) --   
    -- LAPACK is a software package provided by Univ. of Tennessee,    --   
    -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--   
       September 2012   


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


       Test the input parameters   

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

    /* Function Body */
    *info = 0;
    if (*n < 0) {
	*info = -1;
    } else if (*ilo < 1 || *ilo > max(1,*n)) {
	*info = -2;
    } else if (*ihi < min(*ilo,*n) || *ihi > *n) {
	*info = -3;
    } else if (*lda < max(1,*n)) {
	*info = -5;
    }
    if (*info != 0) {
	i__1 = -(*info);
	igraphxerbla_("DGEHD2", &i__1, (ftnlen)6);
	return 0;
    }

    i__1 = *ihi - 1;
    for (i__ = *ilo; i__ <= i__1; ++i__) {

/*        Compute elementary reflector H(i) to annihilate A(i+2:ihi,i) */

	i__2 = *ihi - i__;
/* Computing MIN */
	i__3 = i__ + 2;
	igraphdlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3,*n) + i__ * 
		a_dim1], &c__1, &tau[i__]);
	aii = a[i__ + 1 + i__ * a_dim1];
	a[i__ + 1 + i__ * a_dim1] = 1.;

/*        Apply H(i) to A(1:ihi,i+1:ihi) from the right */

	i__2 = *ihi - i__;
	igraphdlarf_("Right", ihi, &i__2, &a[i__ + 1 + i__ * a_dim1], &c__1, &tau[
		i__], &a[(i__ + 1) * a_dim1 + 1], lda, &work[1]);

/*        Apply H(i) to A(i+1:ihi,i+1:n) from the left */

	i__2 = *ihi - i__;
	i__3 = *n - i__;
	igraphdlarf_("Left", &i__2, &i__3, &a[i__ + 1 + i__ * a_dim1], &c__1, &tau[
		i__], &a[i__ + 1 + (i__ + 1) * a_dim1], lda, &work[1]);

	a[i__ + 1 + i__ * a_dim1] = aii;
/* L10: */
    }

    return 0;

/*     End of DGEHD2 */

} /* igraphdgehd2_ */

