Add graph references
This commit is contained in:
Abdelrahman Said
+759
@@ -0,0 +1,759 @@
|
||||
/* -- 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__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_ */
|
||||
|
||||
Reference in New Issue
Block a user