/* -- translated by f2c (version 20100827).
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*/
#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/
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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_ */