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references/igraph-1.0.1/vendor/lapack/dlaqr2.c
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/* -- 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;
static integer c_n1 = -1;
static doublereal c_b12 = 0.;
static doublereal c_b13 = 1.;
static logical c_true = TRUE_;
/* > \brief \b DLAQR2 performs the orthogonal similarity transformation of a Hessenberg matrix to detect and d
eflate fully converged eigenvalues from a trailing principal submatrix (aggressive early deflation).
=========== DOCUMENTATION ===========
Online html documentation available at
http://www.netlib.org/lapack/explore-html/
> \htmlonly
> Download DLAQR2 + dependencies
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqr2.
f">
> [TGZ]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqr2.
f">
> [ZIP]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqr2.
f">
> [TXT]</a>
> \endhtmlonly
Definition:
===========
SUBROUTINE DLAQR2( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ,
IHIZ, Z, LDZ, NS, ND, SR, SI, V, LDV, NH, T,
LDT, NV, WV, LDWV, WORK, LWORK )
INTEGER IHIZ, ILOZ, KBOT, KTOP, LDH, LDT, LDV, LDWV,
$ LDZ, LWORK, N, ND, NH, NS, NV, NW
LOGICAL WANTT, WANTZ
DOUBLE PRECISION H( LDH, * ), SI( * ), SR( * ), T( LDT, * ),
$ V( LDV, * ), WORK( * ), WV( LDWV, * ),
$ Z( LDZ, * )
> \par Purpose:
=============
>
> \verbatim
>
> DLAQR2 is identical to DLAQR3 except that it avoids
> recursion by calling DLAHQR instead of DLAQR4.
>
> Aggressive early deflation:
>
> This subroutine accepts as input an upper Hessenberg matrix
> H and performs an orthogonal similarity transformation
> designed to detect and deflate fully converged eigenvalues from
> a trailing principal submatrix. On output H has been over-
> written by a new Hessenberg matrix that is a perturbation of
> an orthogonal similarity transformation of H. It is to be
> hoped that the final version of H has many zero subdiagonal
> entries.
> \endverbatim
Arguments:
==========
> \param[in] WANTT
> \verbatim
> WANTT is LOGICAL
> If .TRUE., then the Hessenberg matrix H is fully updated
> so that the quasi-triangular Schur factor may be
> computed (in cooperation with the calling subroutine).
> If .FALSE., then only enough of H is updated to preserve
> the eigenvalues.
> \endverbatim
>
> \param[in] WANTZ
> \verbatim
> WANTZ is LOGICAL
> If .TRUE., then the orthogonal matrix Z is updated so
> so that the orthogonal Schur factor may be computed
> (in cooperation with the calling subroutine).
> If .FALSE., then Z is not referenced.
> \endverbatim
>
> \param[in] N
> \verbatim
> N is INTEGER
> The order of the matrix H and (if WANTZ is .TRUE.) the
> order of the orthogonal matrix Z.
> \endverbatim
>
> \param[in] KTOP
> \verbatim
> KTOP is INTEGER
> It is assumed that either KTOP = 1 or H(KTOP,KTOP-1)=0.
> KBOT and KTOP together determine an isolated block
> along the diagonal of the Hessenberg matrix.
> \endverbatim
>
> \param[in] KBOT
> \verbatim
> KBOT is INTEGER
> It is assumed without a check that either
> KBOT = N or H(KBOT+1,KBOT)=0. KBOT and KTOP together
> determine an isolated block along the diagonal of the
> Hessenberg matrix.
> \endverbatim
>
> \param[in] NW
> \verbatim
> NW is INTEGER
> Deflation window size. 1 .LE. NW .LE. (KBOT-KTOP+1).
> \endverbatim
>
> \param[in,out] H
> \verbatim
> H is DOUBLE PRECISION array, dimension (LDH,N)
> On input the initial N-by-N section of H stores the
> Hessenberg matrix undergoing aggressive early deflation.
> On output H has been transformed by an orthogonal
> similarity transformation, perturbed, and the returned
> to Hessenberg form that (it is to be hoped) has some
> zero subdiagonal entries.
> \endverbatim
>
> \param[in] LDH
> \verbatim
> LDH is integer
> Leading dimension of H just as declared in the calling
> subroutine. N .LE. LDH
> \endverbatim
>
> \param[in] ILOZ
> \verbatim
> ILOZ is INTEGER
> \endverbatim
>
> \param[in] IHIZ
> \verbatim
> IHIZ is INTEGER
> Specify the rows of Z to which transformations must be
> applied if WANTZ is .TRUE.. 1 .LE. ILOZ .LE. IHIZ .LE. N.
> \endverbatim
>
> \param[in,out] Z
> \verbatim
> Z is DOUBLE PRECISION array, dimension (LDZ,N)
> IF WANTZ is .TRUE., then on output, the orthogonal
> similarity transformation mentioned above has been
> accumulated into Z(ILOZ:IHIZ,ILO:IHI) from the right.
> If WANTZ is .FALSE., then Z is unreferenced.
> \endverbatim
>
> \param[in] LDZ
> \verbatim
> LDZ is integer
> The leading dimension of Z just as declared in the
> calling subroutine. 1 .LE. LDZ.
> \endverbatim
>
> \param[out] NS
> \verbatim
> NS is integer
> The number of unconverged (ie approximate) eigenvalues
> returned in SR and SI that may be used as shifts by the
> calling subroutine.
> \endverbatim
>
> \param[out] ND
> \verbatim
> ND is integer
> The number of converged eigenvalues uncovered by this
> subroutine.
> \endverbatim
>
> \param[out] SR
> \verbatim
> SR is DOUBLE PRECISION array, dimension (KBOT)
> \endverbatim
>
> \param[out] SI
> \verbatim
> SI is DOUBLE PRECISION array, dimension (KBOT)
> On output, the real and imaginary parts of approximate
> eigenvalues that may be used for shifts are stored in
> SR(KBOT-ND-NS+1) through SR(KBOT-ND) and
> SI(KBOT-ND-NS+1) through SI(KBOT-ND), respectively.
> The real and imaginary parts of converged eigenvalues
> are stored in SR(KBOT-ND+1) through SR(KBOT) and
> SI(KBOT-ND+1) through SI(KBOT), respectively.
> \endverbatim
>
> \param[out] V
> \verbatim
> V is DOUBLE PRECISION array, dimension (LDV,NW)
> An NW-by-NW work array.
> \endverbatim
>
> \param[in] LDV
> \verbatim
> LDV is integer scalar
> The leading dimension of V just as declared in the
> calling subroutine. NW .LE. LDV
> \endverbatim
>
> \param[in] NH
> \verbatim
> NH is integer scalar
> The number of columns of T. NH.GE.NW.
> \endverbatim
>
> \param[out] T
> \verbatim
> T is DOUBLE PRECISION array, dimension (LDT,NW)
> \endverbatim
>
> \param[in] LDT
> \verbatim
> LDT is integer
> The leading dimension of T just as declared in the
> calling subroutine. NW .LE. LDT
> \endverbatim
>
> \param[in] NV
> \verbatim
> NV is integer
> The number of rows of work array WV available for
> workspace. NV.GE.NW.
> \endverbatim
>
> \param[out] WV
> \verbatim
> WV is DOUBLE PRECISION array, dimension (LDWV,NW)
> \endverbatim
>
> \param[in] LDWV
> \verbatim
> LDWV is integer
> The leading dimension of W just as declared in the
> calling subroutine. NW .LE. LDV
> \endverbatim
>
> \param[out] WORK
> \verbatim
> WORK is DOUBLE PRECISION array, dimension (LWORK)
> On exit, WORK(1) is set to an estimate of the optimal value
> of LWORK for the given values of N, NW, KTOP and KBOT.
> \endverbatim
>
> \param[in] LWORK
> \verbatim
> LWORK is integer
> The dimension of the work array WORK. LWORK = 2*NW
> suffices, but greater efficiency may result from larger
> values of LWORK.
>
> If LWORK = -1, then a workspace query is assumed; DLAQR2
> only estimates the optimal workspace size for the given
> values of N, NW, KTOP and KBOT. The estimate is returned
> in WORK(1). No error message related to LWORK is issued
> by XERBLA. Neither H nor Z are accessed.
> \endverbatim
Authors:
========
> \author Univ. of Tennessee
> \author Univ. of California Berkeley
> \author Univ. of Colorado Denver
> \author NAG Ltd.
> \date September 2012
> \ingroup doubleOTHERauxiliary
> \par Contributors:
==================
>
> Karen Braman and Ralph Byers, Department of Mathematics,
> University of Kansas, USA
>
=====================================================================
Subroutine */ int igraphdlaqr2_(logical *wantt, logical *wantz, integer *n,
integer *ktop, integer *kbot, integer *nw, doublereal *h__, integer *
ldh, integer *iloz, integer *ihiz, doublereal *z__, integer *ldz,
integer *ns, integer *nd, doublereal *sr, doublereal *si, doublereal *
v, integer *ldv, integer *nh, doublereal *t, integer *ldt, integer *
nv, doublereal *wv, integer *ldwv, doublereal *work, integer *lwork)
{
/* System generated locals */
integer h_dim1, h_offset, t_dim1, t_offset, v_dim1, v_offset, wv_dim1,
wv_offset, z_dim1, z_offset, i__1, i__2, i__3, i__4;
doublereal d__1, d__2, d__3, d__4, d__5, d__6;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__, j, k;
doublereal s, aa, bb, cc, dd, cs, sn;
integer jw;
doublereal evi, evk, foo;
integer kln;
doublereal tau, ulp;
integer lwk1, lwk2;
doublereal beta;
integer kend, kcol, info, ifst, ilst, ltop, krow;
extern /* Subroutine */ int igraphdlarf_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
doublereal *), igraphdgemm_(char *, char *, integer *, integer *
, integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *);
logical bulge;
extern /* Subroutine */ int igraphdcopy_(integer *, doublereal *, integer *,
doublereal *, integer *);
integer infqr, kwtop;
extern /* Subroutine */ int igraphdlanv2_(doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *), igraphdlabad_(
doublereal *, doublereal *);
extern doublereal igraphdlamch_(char *);
extern /* Subroutine */ int igraphdgehrd_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
integer *), igraphdlarfg_(integer *, doublereal *, doublereal *,
integer *, doublereal *), igraphdlahqr_(logical *, logical *, integer *,
integer *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *, integer *, doublereal *, integer *,
integer *), igraphdlacpy_(char *, integer *, integer *, doublereal *,
integer *, doublereal *, integer *);
doublereal safmin;
extern /* Subroutine */ int igraphdlaset_(char *, integer *, integer *,
doublereal *, doublereal *, doublereal *, integer *);
doublereal safmax;
extern /* Subroutine */ int igraphdtrexc_(char *, integer *, doublereal *,
integer *, doublereal *, integer *, integer *, integer *,
doublereal *, integer *), igraphdormhr_(char *, char *, integer
*, integer *, integer *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *, doublereal *, integer *,
integer *);
logical sorted;
doublereal smlnum;
integer lwkopt;
/* -- LAPACK auxiliary 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
================================================================
==== Estimate optimal workspace. ====
Parameter adjustments */
h_dim1 = *ldh;
h_offset = 1 + h_dim1;
h__ -= h_offset;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--sr;
--si;
v_dim1 = *ldv;
v_offset = 1 + v_dim1;
v -= v_offset;
t_dim1 = *ldt;
t_offset = 1 + t_dim1;
t -= t_offset;
wv_dim1 = *ldwv;
wv_offset = 1 + wv_dim1;
wv -= wv_offset;
--work;
/* Function Body
Computing MIN */
i__1 = *nw, i__2 = *kbot - *ktop + 1;
jw = min(i__1,i__2);
if (jw <= 2) {
lwkopt = 1;
} else {
/* ==== Workspace query call to DGEHRD ==== */
i__1 = jw - 1;
igraphdgehrd_(&jw, &c__1, &i__1, &t[t_offset], ldt, &work[1], &work[1], &
c_n1, &info);
lwk1 = (integer) work[1];
/* ==== Workspace query call to DORMHR ==== */
i__1 = jw - 1;
igraphdormhr_("R", "N", &jw, &jw, &c__1, &i__1, &t[t_offset], ldt, &work[1],
&v[v_offset], ldv, &work[1], &c_n1, &info);
lwk2 = (integer) work[1];
/* ==== Optimal workspace ==== */
lwkopt = jw + max(lwk1,lwk2);
}
/* ==== Quick return in case of workspace query. ==== */
if (*lwork == -1) {
work[1] = (doublereal) lwkopt;
return 0;
}
/* ==== Nothing to do ...
... for an empty active block ... ==== */
*ns = 0;
*nd = 0;
work[1] = 1.;
if (*ktop > *kbot) {
return 0;
}
/* ... nor for an empty deflation window. ==== */
if (*nw < 1) {
return 0;
}
/* ==== Machine constants ==== */
safmin = igraphdlamch_("SAFE MINIMUM");
safmax = 1. / safmin;
igraphdlabad_(&safmin, &safmax);
ulp = igraphdlamch_("PRECISION");
smlnum = safmin * ((doublereal) (*n) / ulp);
/* ==== Setup deflation window ====
Computing MIN */
i__1 = *nw, i__2 = *kbot - *ktop + 1;
jw = min(i__1,i__2);
kwtop = *kbot - jw + 1;
if (kwtop == *ktop) {
s = 0.;
} else {
s = h__[kwtop + (kwtop - 1) * h_dim1];
}
if (*kbot == kwtop) {
/* ==== 1-by-1 deflation window: not much to do ==== */
sr[kwtop] = h__[kwtop + kwtop * h_dim1];
si[kwtop] = 0.;
*ns = 1;
*nd = 0;
/* Computing MAX */
d__2 = smlnum, d__3 = ulp * (d__1 = h__[kwtop + kwtop * h_dim1], abs(
d__1));
if (abs(s) <= max(d__2,d__3)) {
*ns = 0;
*nd = 1;
if (kwtop > *ktop) {
h__[kwtop + (kwtop - 1) * h_dim1] = 0.;
}
}
work[1] = 1.;
return 0;
}
/* ==== Convert to spike-triangular form. (In case of a
. rare QR failure, this routine continues to do
. aggressive early deflation using that part of
. the deflation window that converged using INFQR
. here and there to keep track.) ==== */
igraphdlacpy_("U", &jw, &jw, &h__[kwtop + kwtop * h_dim1], ldh, &t[t_offset],
ldt);
i__1 = jw - 1;
i__2 = *ldh + 1;
i__3 = *ldt + 1;
igraphdcopy_(&i__1, &h__[kwtop + 1 + kwtop * h_dim1], &i__2, &t[t_dim1 + 2], &
i__3);
igraphdlaset_("A", &jw, &jw, &c_b12, &c_b13, &v[v_offset], ldv);
igraphdlahqr_(&c_true, &c_true, &jw, &c__1, &jw, &t[t_offset], ldt, &sr[kwtop],
&si[kwtop], &c__1, &jw, &v[v_offset], ldv, &infqr);
/* ==== DTREXC needs a clean margin near the diagonal ==== */
i__1 = jw - 3;
for (j = 1; j <= i__1; ++j) {
t[j + 2 + j * t_dim1] = 0.;
t[j + 3 + j * t_dim1] = 0.;
/* L10: */
}
if (jw > 2) {
t[jw + (jw - 2) * t_dim1] = 0.;
}
/* ==== Deflation detection loop ==== */
*ns = jw;
ilst = infqr + 1;
L20:
if (ilst <= *ns) {
if (*ns == 1) {
bulge = FALSE_;
} else {
bulge = t[*ns + (*ns - 1) * t_dim1] != 0.;
}
/* ==== Small spike tip test for deflation ==== */
if (! bulge) {
/* ==== Real eigenvalue ==== */
foo = (d__1 = t[*ns + *ns * t_dim1], abs(d__1));
if (foo == 0.) {
foo = abs(s);
}
/* Computing MAX */
d__2 = smlnum, d__3 = ulp * foo;
if ((d__1 = s * v[*ns * v_dim1 + 1], abs(d__1)) <= max(d__2,d__3))
{
/* ==== Deflatable ==== */
--(*ns);
} else {
/* ==== Undeflatable. Move it up out of the way.
. (DTREXC can not fail in this case.) ==== */
ifst = *ns;
igraphdtrexc_("V", &jw, &t[t_offset], ldt, &v[v_offset], ldv, &ifst,
&ilst, &work[1], &info);
++ilst;
}
} else {
/* ==== Complex conjugate pair ==== */
foo = (d__3 = t[*ns + *ns * t_dim1], abs(d__3)) + sqrt((d__1 = t[*
ns + (*ns - 1) * t_dim1], abs(d__1))) * sqrt((d__2 = t[*
ns - 1 + *ns * t_dim1], abs(d__2)));
if (foo == 0.) {
foo = abs(s);
}
/* Computing MAX */
d__3 = (d__1 = s * v[*ns * v_dim1 + 1], abs(d__1)), d__4 = (d__2 =
s * v[(*ns - 1) * v_dim1 + 1], abs(d__2));
/* Computing MAX */
d__5 = smlnum, d__6 = ulp * foo;
if (max(d__3,d__4) <= max(d__5,d__6)) {
/* ==== Deflatable ==== */
*ns += -2;
} else {
/* ==== Undeflatable. Move them up out of the way.
. Fortunately, DTREXC does the right thing with
. ILST in case of a rare exchange failure. ==== */
ifst = *ns;
igraphdtrexc_("V", &jw, &t[t_offset], ldt, &v[v_offset], ldv, &ifst,
&ilst, &work[1], &info);
ilst += 2;
}
}
/* ==== End deflation detection loop ==== */
goto L20;
}
/* ==== Return to Hessenberg form ==== */
if (*ns == 0) {
s = 0.;
}
if (*ns < jw) {
/* ==== sorting diagonal blocks of T improves accuracy for
. graded matrices. Bubble sort deals well with
. exchange failures. ==== */
sorted = FALSE_;
i__ = *ns + 1;
L30:
if (sorted) {
goto L50;
}
sorted = TRUE_;
kend = i__ - 1;
i__ = infqr + 1;
if (i__ == *ns) {
k = i__ + 1;
} else if (t[i__ + 1 + i__ * t_dim1] == 0.) {
k = i__ + 1;
} else {
k = i__ + 2;
}
L40:
if (k <= kend) {
if (k == i__ + 1) {
evi = (d__1 = t[i__ + i__ * t_dim1], abs(d__1));
} else {
evi = (d__3 = t[i__ + i__ * t_dim1], abs(d__3)) + sqrt((d__1 =
t[i__ + 1 + i__ * t_dim1], abs(d__1))) * sqrt((d__2 =
t[i__ + (i__ + 1) * t_dim1], abs(d__2)));
}
if (k == kend) {
evk = (d__1 = t[k + k * t_dim1], abs(d__1));
} else if (t[k + 1 + k * t_dim1] == 0.) {
evk = (d__1 = t[k + k * t_dim1], abs(d__1));
} else {
evk = (d__3 = t[k + k * t_dim1], abs(d__3)) + sqrt((d__1 = t[
k + 1 + k * t_dim1], abs(d__1))) * sqrt((d__2 = t[k +
(k + 1) * t_dim1], abs(d__2)));
}
if (evi >= evk) {
i__ = k;
} else {
sorted = FALSE_;
ifst = i__;
ilst = k;
igraphdtrexc_("V", &jw, &t[t_offset], ldt, &v[v_offset], ldv, &ifst,
&ilst, &work[1], &info);
if (info == 0) {
i__ = ilst;
} else {
i__ = k;
}
}
if (i__ == kend) {
k = i__ + 1;
} else if (t[i__ + 1 + i__ * t_dim1] == 0.) {
k = i__ + 1;
} else {
k = i__ + 2;
}
goto L40;
}
goto L30;
L50:
;
}
/* ==== Restore shift/eigenvalue array from T ==== */
i__ = jw;
L60:
if (i__ >= infqr + 1) {
if (i__ == infqr + 1) {
sr[kwtop + i__ - 1] = t[i__ + i__ * t_dim1];
si[kwtop + i__ - 1] = 0.;
--i__;
} else if (t[i__ + (i__ - 1) * t_dim1] == 0.) {
sr[kwtop + i__ - 1] = t[i__ + i__ * t_dim1];
si[kwtop + i__ - 1] = 0.;
--i__;
} else {
aa = t[i__ - 1 + (i__ - 1) * t_dim1];
cc = t[i__ + (i__ - 1) * t_dim1];
bb = t[i__ - 1 + i__ * t_dim1];
dd = t[i__ + i__ * t_dim1];
igraphdlanv2_(&aa, &bb, &cc, &dd, &sr[kwtop + i__ - 2], &si[kwtop + i__
- 2], &sr[kwtop + i__ - 1], &si[kwtop + i__ - 1], &cs, &
sn);
i__ += -2;
}
goto L60;
}
if (*ns < jw || s == 0.) {
if (*ns > 1 && s != 0.) {
/* ==== Reflect spike back into lower triangle ==== */
igraphdcopy_(ns, &v[v_offset], ldv, &work[1], &c__1);
beta = work[1];
igraphdlarfg_(ns, &beta, &work[2], &c__1, &tau);
work[1] = 1.;
i__1 = jw - 2;
i__2 = jw - 2;
igraphdlaset_("L", &i__1, &i__2, &c_b12, &c_b12, &t[t_dim1 + 3], ldt);
igraphdlarf_("L", ns, &jw, &work[1], &c__1, &tau, &t[t_offset], ldt, &
work[jw + 1]);
igraphdlarf_("R", ns, ns, &work[1], &c__1, &tau, &t[t_offset], ldt, &
work[jw + 1]);
igraphdlarf_("R", &jw, ns, &work[1], &c__1, &tau, &v[v_offset], ldv, &
work[jw + 1]);
i__1 = *lwork - jw;
igraphdgehrd_(&jw, &c__1, ns, &t[t_offset], ldt, &work[1], &work[jw + 1]
, &i__1, &info);
}
/* ==== Copy updated reduced window into place ==== */
if (kwtop > 1) {
h__[kwtop + (kwtop - 1) * h_dim1] = s * v[v_dim1 + 1];
}
igraphdlacpy_("U", &jw, &jw, &t[t_offset], ldt, &h__[kwtop + kwtop * h_dim1]
, ldh);
i__1 = jw - 1;
i__2 = *ldt + 1;
i__3 = *ldh + 1;
igraphdcopy_(&i__1, &t[t_dim1 + 2], &i__2, &h__[kwtop + 1 + kwtop * h_dim1],
&i__3);
/* ==== Accumulate orthogonal matrix in order update
. H and Z, if requested. ==== */
if (*ns > 1 && s != 0.) {
i__1 = *lwork - jw;
igraphdormhr_("R", "N", &jw, ns, &c__1, ns, &t[t_offset], ldt, &work[1],
&v[v_offset], ldv, &work[jw + 1], &i__1, &info);
}
/* ==== Update vertical slab in H ==== */
if (*wantt) {
ltop = 1;
} else {
ltop = *ktop;
}
i__1 = kwtop - 1;
i__2 = *nv;
for (krow = ltop; i__2 < 0 ? krow >= i__1 : krow <= i__1; krow +=
i__2) {
/* Computing MIN */
i__3 = *nv, i__4 = kwtop - krow;
kln = min(i__3,i__4);
igraphdgemm_("N", "N", &kln, &jw, &jw, &c_b13, &h__[krow + kwtop *
h_dim1], ldh, &v[v_offset], ldv, &c_b12, &wv[wv_offset],
ldwv);
igraphdlacpy_("A", &kln, &jw, &wv[wv_offset], ldwv, &h__[krow + kwtop *
h_dim1], ldh);
/* L70: */
}
/* ==== Update horizontal slab in H ==== */
if (*wantt) {
i__2 = *n;
i__1 = *nh;
for (kcol = *kbot + 1; i__1 < 0 ? kcol >= i__2 : kcol <= i__2;
kcol += i__1) {
/* Computing MIN */
i__3 = *nh, i__4 = *n - kcol + 1;
kln = min(i__3,i__4);
igraphdgemm_("C", "N", &jw, &kln, &jw, &c_b13, &v[v_offset], ldv, &
h__[kwtop + kcol * h_dim1], ldh, &c_b12, &t[t_offset],
ldt);
igraphdlacpy_("A", &jw, &kln, &t[t_offset], ldt, &h__[kwtop + kcol *
h_dim1], ldh);
/* L80: */
}
}
/* ==== Update vertical slab in Z ==== */
if (*wantz) {
i__1 = *ihiz;
i__2 = *nv;
for (krow = *iloz; i__2 < 0 ? krow >= i__1 : krow <= i__1; krow +=
i__2) {
/* Computing MIN */
i__3 = *nv, i__4 = *ihiz - krow + 1;
kln = min(i__3,i__4);
igraphdgemm_("N", "N", &kln, &jw, &jw, &c_b13, &z__[krow + kwtop *
z_dim1], ldz, &v[v_offset], ldv, &c_b12, &wv[
wv_offset], ldwv);
igraphdlacpy_("A", &kln, &jw, &wv[wv_offset], ldwv, &z__[krow +
kwtop * z_dim1], ldz);
/* L90: */
}
}
}
/* ==== Return the number of deflations ... ==== */
*nd = jw - *ns;
/* ==== ... and the number of shifts. (Subtracting
. INFQR from the spike length takes care
. of the case of a rare QR failure while
. calculating eigenvalues of the deflation
. window.) ==== */
*ns -= infqr;
/* ==== Return optimal workspace. ==== */
work[1] = (doublereal) lwkopt;
/* ==== End of DLAQR2 ==== */
return 0;
} /* igraphdlaqr2_ */