/* -- translated by f2c (version 20100827).
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
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
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*/
#include "f2c.h"
/* Table of constant values */
static integer c__10 = 10;
static integer c__1 = 1;
static integer c__2 = 2;
static integer c__3 = 3;
static integer c__4 = 4;
static integer c_n1 = -1;
/* > \brief <b> DSYEVR computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY mat
rices</b>
=========== DOCUMENTATION ===========
Online html documentation available at
http://www.netlib.org/lapack/explore-html/
> \htmlonly
> Download DSYEVR + dependencies
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsyevr.
f">
> [TGZ]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsyevr.
f">
> [ZIP]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsyevr.
f">
> [TXT]</a>
> \endhtmlonly
Definition:
===========
SUBROUTINE DSYEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU,
ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK,
IWORK, LIWORK, INFO )
CHARACTER JOBZ, RANGE, UPLO
INTEGER IL, INFO, IU, LDA, LDZ, LIWORK, LWORK, M, N
DOUBLE PRECISION ABSTOL, VL, VU
INTEGER ISUPPZ( * ), IWORK( * )
DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ), Z( LDZ, * )
> \par Purpose:
=============
>
> \verbatim
>
> DSYEVR computes selected eigenvalues and, optionally, eigenvectors
> of a real symmetric matrix A. Eigenvalues and eigenvectors can be
> selected by specifying either a range of values or a range of
> indices for the desired eigenvalues.
>
> DSYEVR first reduces the matrix A to tridiagonal form T with a call
> to DSYTRD. Then, whenever possible, DSYEVR calls DSTEMR to compute
> the eigenspectrum using Relatively Robust Representations. DSTEMR
> computes eigenvalues by the dqds algorithm, while orthogonal
> eigenvectors are computed from various "good" L D L^T representations
> (also known as Relatively Robust Representations). Gram-Schmidt
> orthogonalization is avoided as far as possible. More specifically,
> the various steps of the algorithm are as follows.
>
> For each unreduced block (submatrix) of T,
> (a) Compute T - sigma I = L D L^T, so that L and D
> define all the wanted eigenvalues to high relative accuracy.
> This means that small relative changes in the entries of D and L
> cause only small relative changes in the eigenvalues and
> eigenvectors. The standard (unfactored) representation of the
> tridiagonal matrix T does not have this property in general.
> (b) Compute the eigenvalues to suitable accuracy.
> If the eigenvectors are desired, the algorithm attains full
> accuracy of the computed eigenvalues only right before
> the corresponding vectors have to be computed, see steps c) and d).
> (c) For each cluster of close eigenvalues, select a new
> shift close to the cluster, find a new factorization, and refine
> the shifted eigenvalues to suitable accuracy.
> (d) For each eigenvalue with a large enough relative separation compute
> the corresponding eigenvector by forming a rank revealing twisted
> factorization. Go back to (c) for any clusters that remain.
>
> The desired accuracy of the output can be specified by the input
> parameter ABSTOL.
>
> For more details, see DSTEMR's documentation and:
> - Inderjit S. Dhillon and Beresford N. Parlett: "Multiple representations
> to compute orthogonal eigenvectors of symmetric tridiagonal matrices,"
> Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004.
> - Inderjit Dhillon and Beresford Parlett: "Orthogonal Eigenvectors and
> Relative Gaps," SIAM Journal on Matrix Analysis and Applications, Vol. 25,
> 2004. Also LAPACK Working Note 154.
> - Inderjit Dhillon: "A new O(n^2) algorithm for the symmetric
> tridiagonal eigenvalue/eigenvector problem",
> Computer Science Division Technical Report No. UCB/CSD-97-971,
> UC Berkeley, May 1997.
>
>
> Note 1 : DSYEVR calls DSTEMR when the full spectrum is requested
> on machines which conform to the ieee-754 floating point standard.
> DSYEVR calls DSTEBZ and SSTEIN on non-ieee machines and
> when partial spectrum requests are made.
>
> Normal execution of DSTEMR may create NaNs and infinities and
> hence may abort due to a floating point exception in environments
> which do not handle NaNs and infinities in the ieee standard default
> manner.
> \endverbatim
Arguments:
==========
> \param[in] JOBZ
> \verbatim
> JOBZ is CHARACTER*1
> = 'N': Compute eigenvalues only;
> = 'V': Compute eigenvalues and eigenvectors.
> \endverbatim
>
> \param[in] RANGE
> \verbatim
> RANGE is CHARACTER*1
> = 'A': all eigenvalues will be found.
> = 'V': all eigenvalues in the half-open interval (VL,VU]
> will be found.
> = 'I': the IL-th through IU-th eigenvalues will be found.
> For RANGE = 'V' or 'I' and IU - IL < N - 1, DSTEBZ and
> DSTEIN are called
> \endverbatim
>
> \param[in] UPLO
> \verbatim
> UPLO is CHARACTER*1
> = 'U': Upper triangle of A is stored;
> = 'L': Lower triangle of A is stored.
> \endverbatim
>
> \param[in] N
> \verbatim
> N is INTEGER
> The order of the matrix A. N >= 0.
> \endverbatim
>
> \param[in,out] A
> \verbatim
> A is DOUBLE PRECISION array, dimension (LDA, N)
> On entry, the symmetric matrix A. If UPLO = 'U', the
> leading N-by-N upper triangular part of A contains the
> upper triangular part of the matrix A. If UPLO = 'L',
> the leading N-by-N lower triangular part of A contains
> the lower triangular part of the matrix A.
> On exit, the lower triangle (if UPLO='L') or the upper
> triangle (if UPLO='U') of A, including the diagonal, is
> destroyed.
> \endverbatim
>
> \param[in] LDA
> \verbatim
> LDA is INTEGER
> The leading dimension of the array A. LDA >= max(1,N).
> \endverbatim
>
> \param[in] VL
> \verbatim
> VL is DOUBLE PRECISION
> \endverbatim
>
> \param[in] VU
> \verbatim
> VU is DOUBLE PRECISION
> If RANGE='V', the lower and upper bounds of the interval to
> be searched for eigenvalues. VL < VU.
> Not referenced if RANGE = 'A' or 'I'.
> \endverbatim
>
> \param[in] IL
> \verbatim
> IL is INTEGER
> \endverbatim
>
> \param[in] IU
> \verbatim
> IU is INTEGER
> If RANGE='I', the indices (in ascending order) of the
> smallest and largest eigenvalues to be returned.
> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
> Not referenced if RANGE = 'A' or 'V'.
> \endverbatim
>
> \param[in] ABSTOL
> \verbatim
> ABSTOL is DOUBLE PRECISION
> The absolute error tolerance for the eigenvalues.
> An approximate eigenvalue is accepted as converged
> when it is determined to lie in an interval [a,b]
> of width less than or equal to
>
> ABSTOL + EPS * max( |a|,|b| ) ,
>
> where EPS is the machine precision. If ABSTOL is less than
> or equal to zero, then EPS*|T| will be used in its place,
> where |T| is the 1-norm of the tridiagonal matrix obtained
> by reducing A to tridiagonal form.
>
> See "Computing Small Singular Values of Bidiagonal Matrices
> with Guaranteed High Relative Accuracy," by Demmel and
> Kahan, LAPACK Working Note #3.
>
> If high relative accuracy is important, set ABSTOL to
> DLAMCH( 'Safe minimum' ). Doing so will guarantee that
> eigenvalues are computed to high relative accuracy when
> possible in future releases. The current code does not
> make any guarantees about high relative accuracy, but
> future releases will. See J. Barlow and J. Demmel,
> "Computing Accurate Eigensystems of Scaled Diagonally
> Dominant Matrices", LAPACK Working Note #7, for a discussion
> of which matrices define their eigenvalues to high relative
> accuracy.
> \endverbatim
>
> \param[out] M
> \verbatim
> M is INTEGER
> The total number of eigenvalues found. 0 <= M <= N.
> If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
> \endverbatim
>
> \param[out] W
> \verbatim
> W is DOUBLE PRECISION array, dimension (N)
> The first M elements contain the selected eigenvalues in
> ascending order.
> \endverbatim
>
> \param[out] Z
> \verbatim
> Z is DOUBLE PRECISION array, dimension (LDZ, max(1,M))
> If JOBZ = 'V', then if INFO = 0, the first M columns of Z
> contain the orthonormal eigenvectors of the matrix A
> corresponding to the selected eigenvalues, with the i-th
> column of Z holding the eigenvector associated with W(i).
> If JOBZ = 'N', then Z is not referenced.
> Note: the user must ensure that at least max(1,M) columns are
> supplied in the array Z; if RANGE = 'V', the exact value of M
> is not known in advance and an upper bound must be used.
> Supplying N columns is always safe.
> \endverbatim
>
> \param[in] LDZ
> \verbatim
> LDZ is INTEGER
> The leading dimension of the array Z. LDZ >= 1, and if
> JOBZ = 'V', LDZ >= max(1,N).
> \endverbatim
>
> \param[out] ISUPPZ
> \verbatim
> ISUPPZ is INTEGER array, dimension ( 2*max(1,M) )
> The support of the eigenvectors in Z, i.e., the indices
> indicating the nonzero elements in Z. The i-th eigenvector
> is nonzero only in elements ISUPPZ( 2*i-1 ) through
> ISUPPZ( 2*i ).
> Implemented only for RANGE = 'A' or 'I' and IU - IL = N - 1
> \endverbatim
>
> \param[out] WORK
> \verbatim
> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
> \endverbatim
>
> \param[in] LWORK
> \verbatim
> LWORK is INTEGER
> The dimension of the array WORK. LWORK >= max(1,26*N).
> For optimal efficiency, LWORK >= (NB+6)*N,
> where NB is the max of the blocksize for DSYTRD and DORMTR
> returned by ILAENV.
>
> 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.
> \endverbatim
>
> \param[out] IWORK
> \verbatim
> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
> On exit, if INFO = 0, IWORK(1) returns the optimal LWORK.
> \endverbatim
>
> \param[in] LIWORK
> \verbatim
> LIWORK is INTEGER
> The dimension of the array IWORK. LIWORK >= max(1,10*N).
>
> If LIWORK = -1, then a workspace query is assumed; the
> routine only calculates the optimal size of the IWORK array,
> returns this value as the first entry of the IWORK array, and
> no error message related to LIWORK is issued by XERBLA.
> \endverbatim
>
> \param[out] INFO
> \verbatim
> INFO is INTEGER
> = 0: successful exit
> < 0: if INFO = -i, the i-th argument had an illegal value
> > 0: Internal error
> \endverbatim
Authors:
========
> \author Univ. of Tennessee
> \author Univ. of California Berkeley
> \author Univ. of Colorado Denver
> \author NAG Ltd.
> \date September 2012
> \ingroup doubleSYeigen
> \par Contributors:
==================
>
> Inderjit Dhillon, IBM Almaden, USA \n
> Osni Marques, LBNL/NERSC, USA \n
> Ken Stanley, Computer Science Division, University of
> California at Berkeley, USA \n
> Jason Riedy, Computer Science Division, University of
> California at Berkeley, USA \n
>
=====================================================================
Subroutine */ int igraphdsyevr_(char *jobz, char *range, char *uplo, integer *n,
doublereal *a, integer *lda, doublereal *vl, doublereal *vu, integer *
il, integer *iu, doublereal *abstol, integer *m, doublereal *w,
doublereal *z__, integer *ldz, integer *isuppz, doublereal *work,
integer *lwork, integer *iwork, integer *liwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, z_dim1, z_offset, i__1, i__2;
doublereal d__1, d__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__, j, nb, jj;
doublereal eps, vll, vuu, tmp1;
integer indd, inde;
doublereal anrm;
integer imax;
doublereal rmin, rmax;
integer inddd, indee;
extern /* Subroutine */ int igraphdscal_(integer *, doublereal *, doublereal *,
integer *);
doublereal sigma;
extern logical igraphlsame_(char *, char *);
integer iinfo;
char order[1];
integer indwk;
extern /* Subroutine */ int igraphdcopy_(integer *, doublereal *, integer *,
doublereal *, integer *), igraphdswap_(integer *, doublereal *, integer
*, doublereal *, integer *);
integer lwmin;
logical lower, wantz;
extern doublereal igraphdlamch_(char *);
logical alleig, indeig;
integer iscale, ieeeok, indibl, indifl;
logical valeig;
doublereal safmin;
extern integer igraphilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int igraphxerbla_(char *, integer *, ftnlen);
doublereal abstll, bignum;
integer indtau, indisp;
extern /* Subroutine */ int igraphdstein_(integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *, integer *, doublereal *,
integer *, doublereal *, integer *, integer *, integer *),
igraphdsterf_(integer *, doublereal *, doublereal *, integer *);
integer indiwo, indwkn;
extern doublereal igraphdlansy_(char *, char *, integer *, doublereal *,
integer *, doublereal *);
extern /* Subroutine */ int igraphdstebz_(char *, char *, integer *, doublereal
*, doublereal *, integer *, integer *, doublereal *, doublereal *,
doublereal *, integer *, integer *, doublereal *, integer *,
integer *, doublereal *, integer *, integer *),
igraphdstemr_(char *, char *, integer *, doublereal *, doublereal *,
doublereal *, doublereal *, integer *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, integer *,
logical *, doublereal *, integer *, integer *, integer *, integer
*);
integer liwmin;
logical tryrac;
extern /* Subroutine */ int igraphdormtr_(char *, char *, char *, integer *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *, integer *);
integer llwrkn, llwork, nsplit;
doublereal smlnum;
extern /* Subroutine */ int igraphdsytrd_(char *, integer *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, doublereal *,
integer *, integer *);
integer lwkopt;
logical lquery;
/* -- LAPACK driver 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;
--w;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--isuppz;
--work;
--iwork;
/* Function Body */
ieeeok = igraphilaenv_(&c__10, "DSYEVR", "N", &c__1, &c__2, &c__3, &c__4, (
ftnlen)6, (ftnlen)1);
lower = igraphlsame_(uplo, "L");
wantz = igraphlsame_(jobz, "V");
alleig = igraphlsame_(range, "A");
valeig = igraphlsame_(range, "V");
indeig = igraphlsame_(range, "I");
lquery = *lwork == -1 || *liwork == -1;
/* Computing MAX */
i__1 = 1, i__2 = *n * 26;
lwmin = max(i__1,i__2);
/* Computing MAX */
i__1 = 1, i__2 = *n * 10;
liwmin = max(i__1,i__2);
*info = 0;
if (! (wantz || igraphlsame_(jobz, "N"))) {
*info = -1;
} else if (! (alleig || valeig || indeig)) {
*info = -2;
} else if (! (lower || igraphlsame_(uplo, "U"))) {
*info = -3;
} else if (*n < 0) {
*info = -4;
} else if (*lda < max(1,*n)) {
*info = -6;
} else {
if (valeig) {
if (*n > 0 && *vu <= *vl) {
*info = -8;
}
} else if (indeig) {
if (*il < 1 || *il > max(1,*n)) {
*info = -9;
} else if (*iu < min(*n,*il) || *iu > *n) {
*info = -10;
}
}
}
if (*info == 0) {
if (*ldz < 1 || wantz && *ldz < *n) {
*info = -15;
} else if (*lwork < lwmin && ! lquery) {
*info = -18;
} else if (*liwork < liwmin && ! lquery) {
*info = -20;
}
}
if (*info == 0) {
nb = igraphilaenv_(&c__1, "DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6,
(ftnlen)1);
/* Computing MAX */
i__1 = nb, i__2 = igraphilaenv_(&c__1, "DORMTR", uplo, n, &c_n1, &c_n1, &
c_n1, (ftnlen)6, (ftnlen)1);
nb = max(i__1,i__2);
/* Computing MAX */
i__1 = (nb + 1) * *n;
lwkopt = max(i__1,lwmin);
work[1] = (doublereal) lwkopt;
iwork[1] = liwmin;
}
if (*info != 0) {
i__1 = -(*info);
igraphxerbla_("DSYEVR", &i__1, (ftnlen)6);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
*m = 0;
if (*n == 0) {
work[1] = 1.;
return 0;
}
if (*n == 1) {
work[1] = 7.;
if (alleig || indeig) {
*m = 1;
w[1] = a[a_dim1 + 1];
} else {
if (*vl < a[a_dim1 + 1] && *vu >= a[a_dim1 + 1]) {
*m = 1;
w[1] = a[a_dim1 + 1];
}
}
if (wantz) {
z__[z_dim1 + 1] = 1.;
isuppz[1] = 1;
isuppz[2] = 1;
}
return 0;
}
/* Get machine constants. */
safmin = igraphdlamch_("Safe minimum");
eps = igraphdlamch_("Precision");
smlnum = safmin / eps;
bignum = 1. / smlnum;
rmin = sqrt(smlnum);
/* Computing MIN */
d__1 = sqrt(bignum), d__2 = 1. / sqrt(sqrt(safmin));
rmax = min(d__1,d__2);
/* Scale matrix to allowable range, if necessary. */
iscale = 0;
abstll = *abstol;
if (valeig) {
vll = *vl;
vuu = *vu;
}
anrm = igraphdlansy_("M", uplo, n, &a[a_offset], lda, &work[1]);
if (anrm > 0. && anrm < rmin) {
iscale = 1;
sigma = rmin / anrm;
} else if (anrm > rmax) {
iscale = 1;
sigma = rmax / anrm;
}
if (iscale == 1) {
if (lower) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n - j + 1;
igraphdscal_(&i__2, &sigma, &a[j + j * a_dim1], &c__1);
/* L10: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
igraphdscal_(&j, &sigma, &a[j * a_dim1 + 1], &c__1);
/* L20: */
}
}
if (*abstol > 0.) {
abstll = *abstol * sigma;
}
if (valeig) {
vll = *vl * sigma;
vuu = *vu * sigma;
}
}
/* Initialize indices into workspaces. Note: The IWORK indices are
used only if DSTERF or DSTEMR fail.
WORK(INDTAU:INDTAU+N-1) stores the scalar factors of the
elementary reflectors used in DSYTRD. */
indtau = 1;
/* WORK(INDD:INDD+N-1) stores the tridiagonal's diagonal entries. */
indd = indtau + *n;
/* WORK(INDE:INDE+N-1) stores the off-diagonal entries of the
tridiagonal matrix from DSYTRD. */
inde = indd + *n;
/* WORK(INDDD:INDDD+N-1) is a copy of the diagonal entries over
-written by DSTEMR (the DSTERF path copies the diagonal to W). */
inddd = inde + *n;
/* WORK(INDEE:INDEE+N-1) is a copy of the off-diagonal entries over
-written while computing the eigenvalues in DSTERF and DSTEMR. */
indee = inddd + *n;
/* INDWK is the starting offset of the left-over workspace, and
LLWORK is the remaining workspace size. */
indwk = indee + *n;
llwork = *lwork - indwk + 1;
/* IWORK(INDIBL:INDIBL+M-1) corresponds to IBLOCK in DSTEBZ and
stores the block indices of each of the M<=N eigenvalues. */
indibl = 1;
/* IWORK(INDISP:INDISP+NSPLIT-1) corresponds to ISPLIT in DSTEBZ and
stores the starting and finishing indices of each block. */
indisp = indibl + *n;
/* IWORK(INDIFL:INDIFL+N-1) stores the indices of eigenvectors
that corresponding to eigenvectors that fail to converge in
DSTEIN. This information is discarded; if any fail, the driver
returns INFO > 0. */
indifl = indisp + *n;
/* INDIWO is the offset of the remaining integer workspace. */
indiwo = indifl + *n;
/* Call DSYTRD to reduce symmetric matrix to tridiagonal form. */
igraphdsytrd_(uplo, n, &a[a_offset], lda, &work[indd], &work[inde], &work[
indtau], &work[indwk], &llwork, &iinfo);
/* If all eigenvalues are desired
then call DSTERF or DSTEMR and DORMTR. */
if ((alleig || indeig && *il == 1 && *iu == *n) && ieeeok == 1) {
if (! wantz) {
igraphdcopy_(n, &work[indd], &c__1, &w[1], &c__1);
i__1 = *n - 1;
igraphdcopy_(&i__1, &work[inde], &c__1, &work[indee], &c__1);
igraphdsterf_(n, &w[1], &work[indee], info);
} else {
i__1 = *n - 1;
igraphdcopy_(&i__1, &work[inde], &c__1, &work[indee], &c__1);
igraphdcopy_(n, &work[indd], &c__1, &work[inddd], &c__1);
if (*abstol <= *n * 2. * eps) {
tryrac = TRUE_;
} else {
tryrac = FALSE_;
}
igraphdstemr_(jobz, "A", n, &work[inddd], &work[indee], vl, vu, il, iu,
m, &w[1], &z__[z_offset], ldz, n, &isuppz[1], &tryrac, &
work[indwk], lwork, &iwork[1], liwork, info);
/* Apply orthogonal matrix used in reduction to tridiagonal
form to eigenvectors returned by DSTEIN. */
if (wantz && *info == 0) {
indwkn = inde;
llwrkn = *lwork - indwkn + 1;
igraphdormtr_("L", uplo, "N", n, m, &a[a_offset], lda, &work[indtau]
, &z__[z_offset], ldz, &work[indwkn], &llwrkn, &iinfo);
}
}
if (*info == 0) {
/* Everything worked. Skip DSTEBZ/DSTEIN. IWORK(:) are
undefined. */
*m = *n;
goto L30;
}
*info = 0;
}
/* Otherwise, call DSTEBZ and, if eigenvectors are desired, DSTEIN.
Also call DSTEBZ and DSTEIN if DSTEMR fails. */
if (wantz) {
*(unsigned char *)order = 'B';
} else {
*(unsigned char *)order = 'E';
}
igraphdstebz_(range, order, n, &vll, &vuu, il, iu, &abstll, &work[indd], &work[
inde], m, &nsplit, &w[1], &iwork[indibl], &iwork[indisp], &work[
indwk], &iwork[indiwo], info);
if (wantz) {
igraphdstein_(n, &work[indd], &work[inde], m, &w[1], &iwork[indibl], &iwork[
indisp], &z__[z_offset], ldz, &work[indwk], &iwork[indiwo], &
iwork[indifl], info);
/* Apply orthogonal matrix used in reduction to tridiagonal
form to eigenvectors returned by DSTEIN. */
indwkn = inde;
llwrkn = *lwork - indwkn + 1;
igraphdormtr_("L", uplo, "N", n, m, &a[a_offset], lda, &work[indtau], &z__[
z_offset], ldz, &work[indwkn], &llwrkn, &iinfo);
}
/* If matrix was scaled, then rescale eigenvalues appropriately.
Jump here if DSTEMR/DSTEIN succeeded. */
L30:
if (iscale == 1) {
if (*info == 0) {
imax = *m;
} else {
imax = *info - 1;
}
d__1 = 1. / sigma;
igraphdscal_(&imax, &d__1, &w[1], &c__1);
}
/* If eigenvalues are not in order, then sort them, along with
eigenvectors. Note: We do not sort the IFAIL portion of IWORK.
It may not be initialized (if DSTEMR/DSTEIN succeeded), and we do
not return this detailed information to the user. */
if (wantz) {
i__1 = *m - 1;
for (j = 1; j <= i__1; ++j) {
i__ = 0;
tmp1 = w[j];
i__2 = *m;
for (jj = j + 1; jj <= i__2; ++jj) {
if (w[jj] < tmp1) {
i__ = jj;
tmp1 = w[jj];
}
/* L40: */
}
if (i__ != 0) {
w[i__] = w[j];
w[j] = tmp1;
igraphdswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[j * z_dim1 + 1],
&c__1);
}
/* L50: */
}
}
/* Set WORK(1) to optimal workspace size. */
work[1] = (doublereal) lwkopt;
iwork[1] = liwmin;
return 0;
/* End of DSYEVR */
} /* igraphdsyevr_ */